/*
NOTE: This is generated code. Look in Misc/lapack_lite for information on
remaking this file.
*/
#include "Numeric/f2c.h"
#ifdef HAVE_CONFIG
#include "config.h"
#else
extern doublereal dlamch_(char *);
#define EPSILON dlamch_("Epsilon")
#define SAFEMINIMUM dlamch_("Safe minimum")
#define PRECISION dlamch_("Precision")
#define BASE dlamch_("Base")
#endif
extern doublereal dlapy2_(doublereal *x, doublereal *y);
/* Table of constant values */
static integer c__1 = 1;
static doublecomplex c_b59 = {0.,0.};
static doublecomplex c_b60 = {1.,0.};
static integer c_n1 = -1;
static integer c__3 = 3;
static integer c__2 = 2;
static integer c__0 = 0;
static integer c__8 = 8;
static integer c__4 = 4;
static integer c__65 = 65;
static integer c__6 = 6;
static integer c__9 = 9;
static doublereal c_b324 = 0.;
static doublereal c_b1015 = 1.;
static integer c__15 = 15;
static logical c_false = FALSE_;
static doublereal c_b1294 = -1.;
static doublereal c_b2210 = .5;
/* Subroutine */ int zdrot_(integer *n, doublecomplex *cx, integer *incx,
doublecomplex *cy, integer *incy, doublereal *c__, doublereal *s)
{
/* System generated locals */
integer i__1, i__2, i__3, i__4;
doublecomplex z__1, z__2, z__3;
/* Local variables */
static integer i__, ix, iy;
static doublecomplex ctemp;
/*
applies a plane rotation, where the cos and sin (c and s) are real
and the vectors cx and cy are complex.
jack dongarra, linpack, 3/11/78.
=====================================================================
*/
/* Parameter adjustments */
--cy;
--cx;
/* Function Body */
if (*n <= 0) {
return 0;
}
if ((*incx == 1 && *incy == 1)) {
goto L20;
}
/*
code for unequal increments or equal increments not equal
to 1
*/
ix = 1;
iy = 1;
if (*incx < 0) {
ix = (-(*n) + 1) * *incx + 1;
}
if (*incy < 0) {
iy = (-(*n) + 1) * *incy + 1;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = ix;
z__2.r = *c__ * cx[i__2].r, z__2.i = *c__ * cx[i__2].i;
i__3 = iy;
z__3.r = *s * cy[i__3].r, z__3.i = *s * cy[i__3].i;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
ctemp.r = z__1.r, ctemp.i = z__1.i;
i__2 = iy;
i__3 = iy;
z__2.r = *c__ * cy[i__3].r, z__2.i = *c__ * cy[i__3].i;
i__4 = ix;
z__3.r = *s * cx[i__4].r, z__3.i = *s * cx[i__4].i;
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
cy[i__2].r = z__1.r, cy[i__2].i = z__1.i;
i__2 = ix;
cx[i__2].r = ctemp.r, cx[i__2].i = ctemp.i;
ix += *incx;
iy += *incy;
/* L10: */
}
return 0;
/* code for both increments equal to 1 */
L20:
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
z__2.r = *c__ * cx[i__2].r, z__2.i = *c__ * cx[i__2].i;
i__3 = i__;
z__3.r = *s * cy[i__3].r, z__3.i = *s * cy[i__3].i;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
ctemp.r = z__1.r, ctemp.i = z__1.i;
i__2 = i__;
i__3 = i__;
z__2.r = *c__ * cy[i__3].r, z__2.i = *c__ * cy[i__3].i;
i__4 = i__;
z__3.r = *s * cx[i__4].r, z__3.i = *s * cx[i__4].i;
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
cy[i__2].r = z__1.r, cy[i__2].i = z__1.i;
i__2 = i__;
cx[i__2].r = ctemp.r, cx[i__2].i = ctemp.i;
/* L30: */
}
return 0;
} /* zdrot_ */
/* Subroutine */ int zgebak_(char *job, char *side, integer *n, integer *ilo,
integer *ihi, doublereal *scale, integer *m, doublecomplex *v,
integer *ldv, integer *info)
{
/* System generated locals */
integer v_dim1, v_offset, i__1;
/* Local variables */
static integer i__, k;
static doublereal s;
static integer ii;
extern logical lsame_(char *, char *);
static logical leftv;
extern /* Subroutine */ int zswap_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *), xerbla_(char *, integer *),
zdscal_(integer *, doublereal *, doublecomplex *, integer *);
static logical rightv;
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZGEBAK forms the right or left eigenvectors of a complex general
matrix by backward transformation on the computed eigenvectors of the
balanced matrix output by ZGEBAL.
Arguments
=========
JOB (input) CHARACTER*1
Specifies the type of backward transformation required:
= 'N', do nothing, return immediately;
= 'P', do backward transformation for permutation only;
= 'S', do backward transformation for scaling only;
= 'B', do backward transformations for both permutation and
scaling.
JOB must be the same as the argument JOB supplied to ZGEBAL.
SIDE (input) CHARACTER*1
= 'R': V contains right eigenvectors;
= 'L': V contains left eigenvectors.
N (input) INTEGER
The number of rows of the matrix V. N >= 0.
ILO (input) INTEGER
IHI (input) INTEGER
The integers ILO and IHI determined by ZGEBAL.
1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
SCALE (input) DOUBLE PRECISION array, dimension (N)
Details of the permutation and scaling factors, as returned
by ZGEBAL.
M (input) INTEGER
The number of columns of the matrix V. M >= 0.
V (input/output) COMPLEX*16 array, dimension (LDV,M)
On entry, the matrix of right or left eigenvectors to be
transformed, as returned by ZHSEIN or ZTREVC.
On exit, V is overwritten by the transformed eigenvectors.
LDV (input) INTEGER
The leading dimension of the array V. LDV >= max(1,N).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
=====================================================================
Decode and Test the input parameters
*/
/* Parameter adjustments */
--scale;
v_dim1 = *ldv;
v_offset = 1 + v_dim1 * 1;
v -= v_offset;
/* Function Body */
rightv = lsame_(side, "R");
leftv = lsame_(side, "L");
*info = 0;
if ((((! lsame_(job, "N") && ! lsame_(job, "P")) && ! lsame_(job, "S"))
&& ! lsame_(job, "B"))) {
*info = -1;
} else if ((! rightv && ! leftv)) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*ilo < 1 || *ilo > max(1,*n)) {
*info = -4;
} else if (*ihi < min(*ilo,*n) || *ihi > *n) {
*info = -5;
} else if (*m < 0) {
*info = -7;
} else if (*ldv < max(1,*n)) {
*info = -9;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGEBAK", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
if (*m == 0) {
return 0;
}
if (lsame_(job, "N")) {
return 0;
}
if (*ilo == *ihi) {
goto L30;
}
/* Backward balance */
if (lsame_(job, "S") || lsame_(job, "B")) {
if (rightv) {
i__1 = *ihi;
for (i__ = *ilo; i__ <= i__1; ++i__) {
s = scale[i__];
zdscal_(m, &s, &v[i__ + v_dim1], ldv);
/* L10: */
}
}
if (leftv) {
i__1 = *ihi;
for (i__ = *ilo; i__ <= i__1; ++i__) {
s = 1. / scale[i__];
zdscal_(m, &s, &v[i__ + v_dim1], ldv);
/* L20: */
}
}
}
/*
Backward permutation
For I = ILO-1 step -1 until 1,
IHI+1 step 1 until N do --
*/
L30:
if (lsame_(job, "P") || lsame_(job, "B")) {
if (rightv) {
i__1 = *n;
for (ii = 1; ii <= i__1; ++ii) {
i__ = ii;
if ((i__ >= *ilo && i__ <= *ihi)) {
goto L40;
}
if (i__ < *ilo) {
i__ = *ilo - ii;
}
k = (integer) scale[i__];
if (k == i__) {
goto L40;
}
zswap_(m, &v[i__ + v_dim1], ldv, &v[k + v_dim1], ldv);
L40:
;
}
}
if (leftv) {
i__1 = *n;
for (ii = 1; ii <= i__1; ++ii) {
i__ = ii;
if ((i__ >= *ilo && i__ <= *ihi)) {
goto L50;
}
if (i__ < *ilo) {
i__ = *ilo - ii;
}
k = (integer) scale[i__];
if (k == i__) {
goto L50;
}
zswap_(m, &v[i__ + v_dim1], ldv, &v[k + v_dim1], ldv);
L50:
;
}
}
}
return 0;
/* End of ZGEBAK */
} /* zgebak_ */
/* Subroutine */ int zgebal_(char *job, integer *n, doublecomplex *a, integer
*lda, integer *ilo, integer *ihi, doublereal *scale, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
doublereal d__1, d__2;
/* Builtin functions */
double d_imag(doublecomplex *), z_abs(doublecomplex *);
/* Local variables */
static doublereal c__, f, g;
static integer i__, j, k, l, m;
static doublereal r__, s, ca, ra;
static integer ica, ira, iexc;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int zswap_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
static doublereal sfmin1, sfmin2, sfmax1, sfmax2;
extern /* Subroutine */ int xerbla_(char *, integer *), zdscal_(
integer *, doublereal *, doublecomplex *, integer *);
extern integer izamax_(integer *, doublecomplex *, integer *);
static logical noconv;
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZGEBAL balances a general complex matrix A. This involves, first,
permuting A by a similarity transformation to isolate eigenvalues
in the first 1 to ILO-1 and last IHI+1 to N elements on the
diagonal; and second, applying a diagonal similarity transformation
to rows and columns ILO to IHI to make the rows and columns as
close in norm as possible. Both steps are optional.
Balancing may reduce the 1-norm of the matrix, and improve the
accuracy of the computed eigenvalues and/or eigenvectors.
Arguments
=========
JOB (input) CHARACTER*1
Specifies the operations to be performed on A:
= 'N': none: simply set ILO = 1, IHI = N, SCALE(I) = 1.0
for i = 1,...,N;
= 'P': permute only;
= 'S': scale only;
= 'B': both permute and scale.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the input matrix A.
On exit, A is overwritten by the balanced matrix.
If JOB = 'N', A is not referenced.
See Further Details.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
ILO (output) INTEGER
IHI (output) INTEGER
ILO and IHI are set to integers such that on exit
A(i,j) = 0 if i > j and j = 1,...,ILO-1 or I = IHI+1,...,N.
If JOB = 'N' or 'S', ILO = 1 and IHI = N.
SCALE (output) DOUBLE PRECISION array, dimension (N)
Details of the permutations and scaling factors applied to
A. If P(j) is the index of the row and column interchanged
with row and column j and D(j) is the scaling factor
applied to row and column j, then
SCALE(j) = P(j) for j = 1,...,ILO-1
= D(j) for j = ILO,...,IHI
= P(j) for j = IHI+1,...,N.
The order in which the interchanges are made is N to IHI+1,
then 1 to ILO-1.
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
Further Details
===============
The permutations consist of row and column interchanges which put
the matrix in the form
( T1 X Y )
P A P = ( 0 B Z )
( 0 0 T2 )
where T1 and T2 are upper triangular matrices whose eigenvalues lie
along the diagonal. The column indices ILO and IHI mark the starting
and ending columns of the submatrix B. Balancing consists of applying
a diagonal similarity transformation inv(D) * B * D to make the
1-norms of each row of B and its corresponding column nearly equal.
The output matrix is
( T1 X*D Y )
( 0 inv(D)*B*D inv(D)*Z ).
( 0 0 T2 )
Information about the permutations P and the diagonal matrix D is
returned in the vector SCALE.
This subroutine is based on the EISPACK routine CBAL.
Modified by Tzu-Yi Chen, Computer Science Division, University of
California at Berkeley, USA
=====================================================================
Test the input parameters
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--scale;
/* Function Body */
*info = 0;
if ((((! lsame_(job, "N") && ! lsame_(job, "P")) && ! lsame_(job, "S"))
&& ! lsame_(job, "B"))) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*n)) {
*info = -4;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGEBAL", &i__1);
return 0;
}
k = 1;
l = *n;
if (*n == 0) {
goto L210;
}
if (lsame_(job, "N")) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
scale[i__] = 1.;
/* L10: */
}
goto L210;
}
if (lsame_(job, "S")) {
goto L120;
}
/* Permutation to isolate eigenvalues if possible */
goto L50;
/* Row and column exchange. */
L20:
scale[m] = (doublereal) j;
if (j == m) {
goto L30;
}
zswap_(&l, &a[j * a_dim1 + 1], &c__1, &a[m * a_dim1 + 1], &c__1);
i__1 = *n - k + 1;
zswap_(&i__1, &a[j + k * a_dim1], lda, &a[m + k * a_dim1], lda);
L30:
switch (iexc) {
case 1: goto L40;
case 2: goto L80;
}
/* Search for rows isolating an eigenvalue and push them down. */
L40:
if (l == 1) {
goto L210;
}
--l;
L50:
for (j = l; j >= 1; --j) {
i__1 = l;
for (i__ = 1; i__ <= i__1; ++i__) {
if (i__ == j) {
goto L60;
}
i__2 = j + i__ * a_dim1;
if (a[i__2].r != 0. || d_imag(&a[j + i__ * a_dim1]) != 0.) {
goto L70;
}
L60:
;
}
m = l;
iexc = 1;
goto L20;
L70:
;
}
goto L90;
/* Search for columns isolating an eigenvalue and push them left. */
L80:
++k;
L90:
i__1 = l;
for (j = k; j <= i__1; ++j) {
i__2 = l;
for (i__ = k; i__ <= i__2; ++i__) {
if (i__ == j) {
goto L100;
}
i__3 = i__ + j * a_dim1;
if (a[i__3].r != 0. || d_imag(&a[i__ + j * a_dim1]) != 0.) {
goto L110;
}
L100:
;
}
m = k;
iexc = 2;
goto L20;
L110:
;
}
L120:
i__1 = l;
for (i__ = k; i__ <= i__1; ++i__) {
scale[i__] = 1.;
/* L130: */
}
if (lsame_(job, "P")) {
goto L210;
}
/*
Balance the submatrix in rows K to L.
Iterative loop for norm reduction
*/
sfmin1 = SAFEMINIMUM / PRECISION;
sfmax1 = 1. / sfmin1;
sfmin2 = sfmin1 * 8.;
sfmax2 = 1. / sfmin2;
L140:
noconv = FALSE_;
i__1 = l;
for (i__ = k; i__ <= i__1; ++i__) {
c__ = 0.;
r__ = 0.;
i__2 = l;
for (j = k; j <= i__2; ++j) {
if (j == i__) {
goto L150;
}
i__3 = j + i__ * a_dim1;
c__ += (d__1 = a[i__3].r, abs(d__1)) + (d__2 = d_imag(&a[j + i__ *
a_dim1]), abs(d__2));
i__3 = i__ + j * a_dim1;
r__ += (d__1 = a[i__3].r, abs(d__1)) + (d__2 = d_imag(&a[i__ + j *
a_dim1]), abs(d__2));
L150:
;
}
ica = izamax_(&l, &a[i__ * a_dim1 + 1], &c__1);
ca = z_abs(&a[ica + i__ * a_dim1]);
i__2 = *n - k + 1;
ira = izamax_(&i__2, &a[i__ + k * a_dim1], lda);
ra = z_abs(&a[i__ + (ira + k - 1) * a_dim1]);
/* Guard against zero C or R due to underflow. */
if (c__ == 0. || r__ == 0.) {
goto L200;
}
g = r__ / 8.;
f = 1.;
s = c__ + r__;
L160:
/* Computing MAX */
d__1 = max(f,c__);
/* Computing MIN */
d__2 = min(r__,g);
if (c__ >= g || max(d__1,ca) >= sfmax2 || min(d__2,ra) <= sfmin2) {
goto L170;
}
f *= 8.;
c__ *= 8.;
ca *= 8.;
r__ /= 8.;
g /= 8.;
ra /= 8.;
goto L160;
L170:
g = c__ / 8.;
L180:
/* Computing MIN */
d__1 = min(f,c__), d__1 = min(d__1,g);
if (g < r__ || max(r__,ra) >= sfmax2 || min(d__1,ca) <= sfmin2) {
goto L190;
}
f /= 8.;
c__ /= 8.;
g /= 8.;
ca /= 8.;
r__ *= 8.;
ra *= 8.;
goto L180;
/* Now balance. */
L190:
if (c__ + r__ >= s * .95) {
goto L200;
}
if ((f < 1. && scale[i__] < 1.)) {
if (f * scale[i__] <= sfmin1) {
goto L200;
}
}
if ((f > 1. && scale[i__] > 1.)) {
if (scale[i__] >= sfmax1 / f) {
goto L200;
}
}
g = 1. / f;
scale[i__] *= f;
noconv = TRUE_;
i__2 = *n - k + 1;
zdscal_(&i__2, &g, &a[i__ + k * a_dim1], lda);
zdscal_(&l, &f, &a[i__ * a_dim1 + 1], &c__1);
L200:
;
}
if (noconv) {
goto L140;
}
L210:
*ilo = k;
*ihi = l;
return 0;
/* End of ZGEBAL */
} /* zgebal_ */
/* Subroutine */ int zgebd2_(integer *m, integer *n, doublecomplex *a,
integer *lda, doublereal *d__, doublereal *e, doublecomplex *tauq,
doublecomplex *taup, doublecomplex *work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
doublecomplex z__1;
/* Builtin functions */
void d_cnjg(doublecomplex *, doublecomplex *);
/* Local variables */
static integer i__;
static doublecomplex alpha;
extern /* Subroutine */ int zlarf_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, doublecomplex *), xerbla_(char *, integer *), zlarfg_(integer *, doublecomplex *, doublecomplex *,
integer *, doublecomplex *), zlacgv_(integer *, doublecomplex *,
integer *);
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZGEBD2 reduces a complex general m by n matrix A to upper or lower
real bidiagonal form B by a unitary transformation: Q' * A * P = B.
If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
Arguments
=========
M (input) INTEGER
The number of rows in the matrix A. M >= 0.
N (input) INTEGER
The number of columns in the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the m by n general matrix to be reduced.
On exit,
if m >= n, the diagonal and the first superdiagonal are
overwritten with the upper bidiagonal matrix B; the
elements below the diagonal, with the array TAUQ, represent
the unitary matrix Q as a product of elementary
reflectors, and the elements above the first superdiagonal,
with the array TAUP, represent the unitary matrix P as
a product of elementary reflectors;
if m < n, the diagonal and the first subdiagonal are
overwritten with the lower bidiagonal matrix B; the
elements below the first subdiagonal, with the array TAUQ,
represent the unitary matrix Q as a product of
elementary reflectors, and the elements above the diagonal,
with the array TAUP, represent the unitary matrix P as
a product of elementary reflectors.
See Further Details.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
D (output) DOUBLE PRECISION array, dimension (min(M,N))
The diagonal elements of the bidiagonal matrix B:
D(i) = A(i,i).
E (output) DOUBLE PRECISION array, dimension (min(M,N)-1)
The off-diagonal elements of the bidiagonal matrix B:
if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1;
if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1.
TAUQ (output) COMPLEX*16 array dimension (min(M,N))
The scalar factors of the elementary reflectors which
represent the unitary matrix Q. See Further Details.
TAUP (output) COMPLEX*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors which
represent the unitary matrix P. See Further Details.
WORK (workspace) COMPLEX*16 array, dimension (max(M,N))
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
Further Details
===============
The matrices Q and P are represented as products of elementary
reflectors:
If m >= n,
Q = H(1) H(2) . . . H(n) and P = G(1) G(2) . . . G(n-1)
Each H(i) and G(i) has the form:
H(i) = I - tauq * v * v' and G(i) = I - taup * u * u'
where tauq and taup are complex scalars, and v and u are complex
vectors; v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in
A(i+1:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in
A(i,i+2:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
If m < n,
Q = H(1) H(2) . . . H(m-1) and P = G(1) G(2) . . . G(m)
Each H(i) and G(i) has the form:
H(i) = I - tauq * v * v' and G(i) = I - taup * u * u'
where tauq and taup are complex scalars, v and u are complex vectors;
v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i);
u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n);
tauq is stored in TAUQ(i) and taup in TAUP(i).
The contents of A on exit are illustrated by the following examples:
m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n):
( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 )
( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 )
( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 )
( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 )
( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 )
( v1 v2 v3 v4 v5 )
where d and e denote diagonal and off-diagonal elements of B, vi
denotes an element of the vector defining H(i), and ui an element of
the vector defining G(i).
=====================================================================
Test the input parameters
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--d__;
--e;
--tauq;
--taup;
--work;
/* Function Body */
*info = 0;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*m)) {
*info = -4;
}
if (*info < 0) {
i__1 = -(*info);
xerbla_("ZGEBD2", &i__1);
return 0;
}
if (*m >= *n) {
/* Reduce to upper bidiagonal form */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Generate elementary reflector H(i) to annihilate A(i+1:m,i) */
i__2 = i__ + i__ * a_dim1;
alpha.r = a[i__2].r, alpha.i = a[i__2].i;
i__2 = *m - i__ + 1;
/* Computing MIN */
i__3 = i__ + 1;
zlarfg_(&i__2, &alpha, &a[min(i__3,*m) + i__ * a_dim1], &c__1, &
tauq[i__]);
i__2 = i__;
d__[i__2] = alpha.r;
i__2 = i__ + i__ * a_dim1;
a[i__2].r = 1., a[i__2].i = 0.;
/* Apply H(i)' to A(i:m,i+1:n) from the left */
i__2 = *m - i__ + 1;
i__3 = *n - i__;
d_cnjg(&z__1, &tauq[i__]);
zlarf_("Left", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, &z__1,
&a[i__ + (i__ + 1) * a_dim1], lda, &work[1]);
i__2 = i__ + i__ * a_dim1;
i__3 = i__;
a[i__2].r = d__[i__3], a[i__2].i = 0.;
if (i__ < *n) {
/*
Generate elementary reflector G(i) to annihilate
A(i,i+2:n)
*/
i__2 = *n - i__;
zlacgv_(&i__2, &a[i__ + (i__ + 1) * a_dim1], lda);
i__2 = i__ + (i__ + 1) * a_dim1;
alpha.r = a[i__2].r, alpha.i = a[i__2].i;
i__2 = *n - i__;
/* Computing MIN */
i__3 = i__ + 2;
zlarfg_(&i__2, &alpha, &a[i__ + min(i__3,*n) * a_dim1], lda, &
taup[i__]);
i__2 = i__;
e[i__2] = alpha.r;
i__2 = i__ + (i__ + 1) * a_dim1;
a[i__2].r = 1., a[i__2].i = 0.;
/* Apply G(i) to A(i+1:m,i+1:n) from the right */
i__2 = *m - i__;
i__3 = *n - i__;
zlarf_("Right", &i__2, &i__3, &a[i__ + (i__ + 1) * a_dim1],
lda, &taup[i__], &a[i__ + 1 + (i__ + 1) * a_dim1],
lda, &work[1]);
i__2 = *n - i__;
zlacgv_(&i__2, &a[i__ + (i__ + 1) * a_dim1], lda);
i__2 = i__ + (i__ + 1) * a_dim1;
i__3 = i__;
a[i__2].r = e[i__3], a[i__2].i = 0.;
} else {
i__2 = i__;
taup[i__2].r = 0., taup[i__2].i = 0.;
}
/* L10: */
}
} else {
/* Reduce to lower bidiagonal form */
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Generate elementary reflector G(i) to annihilate A(i,i+1:n) */
i__2 = *n - i__ + 1;
zlacgv_(&i__2, &a[i__ + i__ * a_dim1], lda);
i__2 = i__ + i__ * a_dim1;
alpha.r = a[i__2].r, alpha.i = a[i__2].i;
i__2 = *n - i__ + 1;
/* Computing MIN */
i__3 = i__ + 1;
zlarfg_(&i__2, &alpha, &a[i__ + min(i__3,*n) * a_dim1], lda, &
taup[i__]);
i__2 = i__;
d__[i__2] = alpha.r;
i__2 = i__ + i__ * a_dim1;
a[i__2].r = 1., a[i__2].i = 0.;
/* Apply G(i) to A(i+1:m,i:n) from the right */
i__2 = *m - i__;
i__3 = *n - i__ + 1;
/* Computing MIN */
i__4 = i__ + 1;
zlarf_("Right", &i__2, &i__3, &a[i__ + i__ * a_dim1], lda, &taup[
i__], &a[min(i__4,*m) + i__ * a_dim1], lda, &work[1]);
i__2 = *n - i__ + 1;
zlacgv_(&i__2, &a[i__ + i__ * a_dim1], lda);
i__2 = i__ + i__ * a_dim1;
i__3 = i__;
a[i__2].r = d__[i__3], a[i__2].i = 0.;
if (i__ < *m) {
/*
Generate elementary reflector H(i) to annihilate
A(i+2:m,i)
*/
i__2 = i__ + 1 + i__ * a_dim1;
alpha.r = a[i__2].r, alpha.i = a[i__2].i;
i__2 = *m - i__;
/* Computing MIN */
i__3 = i__ + 2;
zlarfg_(&i__2, &alpha, &a[min(i__3,*m) + i__ * a_dim1], &c__1,
&tauq[i__]);
i__2 = i__;
e[i__2] = alpha.r;
i__2 = i__ + 1 + i__ * a_dim1;
a[i__2].r = 1., a[i__2].i = 0.;
/* Apply H(i)' to A(i+1:m,i+1:n) from the left */
i__2 = *m - i__;
i__3 = *n - i__;
d_cnjg(&z__1, &tauq[i__]);
zlarf_("Left", &i__2, &i__3, &a[i__ + 1 + i__ * a_dim1], &
c__1, &z__1, &a[i__ + 1 + (i__ + 1) * a_dim1], lda, &
work[1]);
i__2 = i__ + 1 + i__ * a_dim1;
i__3 = i__;
a[i__2].r = e[i__3], a[i__2].i = 0.;
} else {
i__2 = i__;
tauq[i__2].r = 0., tauq[i__2].i = 0.;
}
/* L20: */
}
}
return 0;
/* End of ZGEBD2 */
} /* zgebd2_ */
/* Subroutine */ int zgebrd_(integer *m, integer *n, doublecomplex *a,
integer *lda, doublereal *d__, doublereal *e, doublecomplex *tauq,
doublecomplex *taup, doublecomplex *work, integer *lwork, integer *
info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
doublereal d__1;
doublecomplex z__1;
/* Local variables */
static integer i__, j, nb, nx;
static doublereal ws;
static integer nbmin, iinfo, minmn;
extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *,
integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *), zgebd2_(integer *, integer *,
doublecomplex *, integer *, doublereal *, doublereal *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *),
xerbla_(char *, integer *), zlabrd_(integer *, integer *,
integer *, doublecomplex *, integer *, doublereal *, doublereal *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
static integer ldwrkx, ldwrky, lwkopt;
static logical lquery;
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZGEBRD reduces a general complex M-by-N matrix A to upper or lower
bidiagonal form B by a unitary transformation: Q**H * A * P = B.
If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
Arguments
=========
M (input) INTEGER
The number of rows in the matrix A. M >= 0.
N (input) INTEGER
The number of columns in the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the M-by-N general matrix to be reduced.
On exit,
if m >= n, the diagonal and the first superdiagonal are
overwritten with the upper bidiagonal matrix B; the
elements below the diagonal, with the array TAUQ, represent
the unitary matrix Q as a product of elementary
reflectors, and the elements above the first superdiagonal,
with the array TAUP, represent the unitary matrix P as
a product of elementary reflectors;
if m < n, the diagonal and the first subdiagonal are
overwritten with the lower bidiagonal matrix B; the
elements below the first subdiagonal, with the array TAUQ,
represent the unitary matrix Q as a product of
elementary reflectors, and the elements above the diagonal,
with the array TAUP, represent the unitary matrix P as
a product of elementary reflectors.
See Further Details.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
D (output) DOUBLE PRECISION array, dimension (min(M,N))
The diagonal elements of the bidiagonal matrix B:
D(i) = A(i,i).
E (output) DOUBLE PRECISION array, dimension (min(M,N)-1)
The off-diagonal elements of the bidiagonal matrix B:
if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1;
if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1.
TAUQ (output) COMPLEX*16 array dimension (min(M,N))
The scalar factors of the elementary reflectors which
represent the unitary matrix Q. See Further Details.
TAUP (output) COMPLEX*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors which
represent the unitary matrix P. See Further Details.
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The length of the array WORK. LWORK >= max(1,M,N).
For optimum performance LWORK >= (M+N)*NB, where NB
is the optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
Further Details
===============
The matrices Q and P are represented as products of elementary
reflectors:
If m >= n,
Q = H(1) H(2) . . . H(n) and P = G(1) G(2) . . . G(n-1)
Each H(i) and G(i) has the form:
H(i) = I - tauq * v * v' and G(i) = I - taup * u * u'
where tauq and taup are complex scalars, and v and u are complex
vectors; v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in
A(i+1:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in
A(i,i+2:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
If m < n,
Q = H(1) H(2) . . . H(m-1) and P = G(1) G(2) . . . G(m)
Each H(i) and G(i) has the form:
H(i) = I - tauq * v * v' and G(i) = I - taup * u * u'
where tauq and taup are complex scalars, and v and u are complex
vectors; v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in
A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in
A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
The contents of A on exit are illustrated by the following examples:
m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n):
( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 )
( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 )
( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 )
( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 )
( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 )
( v1 v2 v3 v4 v5 )
where d and e denote diagonal and off-diagonal elements of B, vi
denotes an element of the vector defining H(i), and ui an element of
the vector defining G(i).
=====================================================================
Test the input parameters
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--d__;
--e;
--tauq;
--taup;
--work;
/* Function Body */
*info = 0;
/* Computing MAX */
i__1 = 1, i__2 = ilaenv_(&c__1, "ZGEBRD", " ", m, n, &c_n1, &c_n1, (
ftnlen)6, (ftnlen)1);
nb = max(i__1,i__2);
lwkopt = (*m + *n) * nb;
d__1 = (doublereal) lwkopt;
work[1].r = d__1, work[1].i = 0.;
lquery = *lwork == -1;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*m)) {
*info = -4;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__1 = max(1,*m);
if ((*lwork < max(i__1,*n) && ! lquery)) {
*info = -10;
}
}
if (*info < 0) {
i__1 = -(*info);
xerbla_("ZGEBRD", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
minmn = min(*m,*n);
if (minmn == 0) {
work[1].r = 1., work[1].i = 0.;
return 0;
}
ws = (doublereal) max(*m,*n);
ldwrkx = *m;
ldwrky = *n;
if ((nb > 1 && nb < minmn)) {
/*
Set the crossover point NX.
Computing MAX
*/
i__1 = nb, i__2 = ilaenv_(&c__3, "ZGEBRD", " ", m, n, &c_n1, &c_n1, (
ftnlen)6, (ftnlen)1);
nx = max(i__1,i__2);
/* Determine when to switch from blocked to unblocked code. */
if (nx < minmn) {
ws = (doublereal) ((*m + *n) * nb);
if ((doublereal) (*lwork) < ws) {
/*
Not enough work space for the optimal NB, consider using
a smaller block size.
*/
nbmin = ilaenv_(&c__2, "ZGEBRD", " ", m, n, &c_n1, &c_n1, (
ftnlen)6, (ftnlen)1);
if (*lwork >= (*m + *n) * nbmin) {
nb = *lwork / (*m + *n);
} else {
nb = 1;
nx = minmn;
}
}
}
} else {
nx = minmn;
}
i__1 = minmn - nx;
i__2 = nb;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/*
Reduce rows and columns i:i+ib-1 to bidiagonal form and return
the matrices X and Y which are needed to update the unreduced
part of the matrix
*/
i__3 = *m - i__ + 1;
i__4 = *n - i__ + 1;
zlabrd_(&i__3, &i__4, &nb, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[
i__], &tauq[i__], &taup[i__], &work[1], &ldwrkx, &work[ldwrkx
* nb + 1], &ldwrky);
/*
Update the trailing submatrix A(i+ib:m,i+ib:n), using
an update of the form A := A - V*Y' - X*U'
*/
i__3 = *m - i__ - nb + 1;
i__4 = *n - i__ - nb + 1;
z__1.r = -1., z__1.i = -0.;
zgemm_("No transpose", "Conjugate transpose", &i__3, &i__4, &nb, &
z__1, &a[i__ + nb + i__ * a_dim1], lda, &work[ldwrkx * nb +
nb + 1], &ldwrky, &c_b60, &a[i__ + nb + (i__ + nb) * a_dim1],
lda);
i__3 = *m - i__ - nb + 1;
i__4 = *n - i__ - nb + 1;
z__1.r = -1., z__1.i = -0.;
zgemm_("No transpose", "No transpose", &i__3, &i__4, &nb, &z__1, &
work[nb + 1], &ldwrkx, &a[i__ + (i__ + nb) * a_dim1], lda, &
c_b60, &a[i__ + nb + (i__ + nb) * a_dim1], lda);
/* Copy diagonal and off-diagonal elements of B back into A */
if (*m >= *n) {
i__3 = i__ + nb - 1;
for (j = i__; j <= i__3; ++j) {
i__4 = j + j * a_dim1;
i__5 = j;
a[i__4].r = d__[i__5], a[i__4].i = 0.;
i__4 = j + (j + 1) * a_dim1;
i__5 = j;
a[i__4].r = e[i__5], a[i__4].i = 0.;
/* L10: */
}
} else {
i__3 = i__ + nb - 1;
for (j = i__; j <= i__3; ++j) {
i__4 = j + j * a_dim1;
i__5 = j;
a[i__4].r = d__[i__5], a[i__4].i = 0.;
i__4 = j + 1 + j * a_dim1;
i__5 = j;
a[i__4].r = e[i__5], a[i__4].i = 0.;
/* L20: */
}
}
/* L30: */
}
/* Use unblocked code to reduce the remainder of the matrix */
i__2 = *m - i__ + 1;
i__1 = *n - i__ + 1;
zgebd2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[i__], &
tauq[i__], &taup[i__], &work[1], &iinfo);
work[1].r = ws, work[1].i = 0.;
return 0;
/* End of ZGEBRD */
} /* zgebrd_ */
/* Subroutine */ int zgeev_(char *jobvl, char *jobvr, integer *n,
doublecomplex *a, integer *lda, doublecomplex *w, doublecomplex *vl,
integer *ldvl, doublecomplex *vr, integer *ldvr, doublecomplex *work,
integer *lwork, doublereal *rwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1,
i__2, i__3, i__4;
doublereal d__1, d__2;
doublecomplex z__1, z__2;
/* Builtin functions */
double sqrt(doublereal), d_imag(doublecomplex *);
void d_cnjg(doublecomplex *, doublecomplex *);
/* Local variables */
static integer i__, k, ihi;
static doublereal scl;
static integer ilo;
static doublereal dum[1], eps;
static doublecomplex tmp;
static integer ibal;
static char side[1];
static integer maxb;
static doublereal anrm;
static integer ierr, itau, iwrk, nout;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
doublecomplex *, integer *), dlabad_(doublereal *, doublereal *);
extern doublereal dznrm2_(integer *, doublecomplex *, integer *);
static logical scalea;
static doublereal cscale;
extern /* Subroutine */ int zgebak_(char *, char *, integer *, integer *,
integer *, doublereal *, integer *, doublecomplex *, integer *,
integer *), zgebal_(char *, integer *,
doublecomplex *, integer *, integer *, integer *, doublereal *,
integer *);
extern integer idamax_(integer *, doublereal *, integer *);
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
static logical select[1];
extern /* Subroutine */ int zdscal_(integer *, doublereal *,
doublecomplex *, integer *);
static doublereal bignum;
extern doublereal zlange_(char *, integer *, integer *, doublecomplex *,
integer *, doublereal *);
extern /* Subroutine */ int zgehrd_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, integer *), zlascl_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublecomplex *,
integer *, integer *), zlacpy_(char *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *);
static integer minwrk, maxwrk;
static logical wantvl;
static doublereal smlnum;
static integer hswork, irwork;
extern /* Subroutine */ int zhseqr_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *), ztrevc_(char *, char *, logical *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, integer *, integer *, doublecomplex *,
doublereal *, integer *);
static logical lquery, wantvr;
extern /* Subroutine */ int zunghr_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, integer *);
/*
-- LAPACK driver routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZGEEV computes for an N-by-N complex nonsymmetric matrix A, the
eigenvalues and, optionally, the left and/or right eigenvectors.
The right eigenvector v(j) of A satisfies
A * v(j) = lambda(j) * v(j)
where lambda(j) is its eigenvalue.
The left eigenvector u(j) of A satisfies
u(j)**H * A = lambda(j) * u(j)**H
where u(j)**H denotes the conjugate transpose of u(j).
The computed eigenvectors are normalized to have Euclidean norm
equal to 1 and largest component real.
Arguments
=========
JOBVL (input) CHARACTER*1
= 'N': left eigenvectors of A are not computed;
= 'V': left eigenvectors of are computed.
JOBVR (input) CHARACTER*1
= 'N': right eigenvectors of A are not computed;
= 'V': right eigenvectors of A are computed.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the N-by-N matrix A.
On exit, A has been overwritten.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
W (output) COMPLEX*16 array, dimension (N)
W contains the computed eigenvalues.
VL (output) COMPLEX*16 array, dimension (LDVL,N)
If JOBVL = 'V', the left eigenvectors u(j) are stored one
after another in the columns of VL, in the same order
as their eigenvalues.
If JOBVL = 'N', VL is not referenced.
u(j) = VL(:,j), the j-th column of VL.
LDVL (input) INTEGER
The leading dimension of the array VL. LDVL >= 1; if
JOBVL = 'V', LDVL >= N.
VR (output) COMPLEX*16 array, dimension (LDVR,N)
If JOBVR = 'V', the right eigenvectors v(j) are stored one
after another in the columns of VR, in the same order
as their eigenvalues.
If JOBVR = 'N', VR is not referenced.
v(j) = VR(:,j), the j-th column of VR.
LDVR (input) INTEGER
The leading dimension of the array VR. LDVR >= 1; if
JOBVR = 'V', LDVR >= N.
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,2*N).
For good performance, LWORK must generally be larger.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
RWORK (workspace) DOUBLE PRECISION array, dimension (2*N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = i, the QR algorithm failed to compute all the
eigenvalues, and no eigenvectors have been computed;
elements and i+1:N of W contain eigenvalues which have
converged.
=====================================================================
Test the input arguments
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--w;
vl_dim1 = *ldvl;
vl_offset = 1 + vl_dim1 * 1;
vl -= vl_offset;
vr_dim1 = *ldvr;
vr_offset = 1 + vr_dim1 * 1;
vr -= vr_offset;
--work;
--rwork;
/* Function Body */
*info = 0;
lquery = *lwork == -1;
wantvl = lsame_(jobvl, "V");
wantvr = lsame_(jobvr, "V");
if ((! wantvl && ! lsame_(jobvl, "N"))) {
*info = -1;
} else if ((! wantvr && ! lsame_(jobvr, "N"))) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if (*ldvl < 1 || (wantvl && *ldvl < *n)) {
*info = -8;
} else if (*ldvr < 1 || (wantvr && *ldvr < *n)) {
*info = -10;
}
/*
Compute workspace
(Note: Comments in the code beginning "Workspace:" describe the
minimal amount of workspace needed at that point in the code,
as well as the preferred amount for good performance.
CWorkspace refers to complex workspace, and RWorkspace to real
workspace. NB refers to the optimal block size for the
immediately following subroutine, as returned by ILAENV.
HSWORK refers to the workspace preferred by ZHSEQR, as
calculated below. HSWORK is computed assuming ILO=1 and IHI=N,
the worst case.)
*/
minwrk = 1;
if ((*info == 0 && (*lwork >= 1 || lquery))) {
maxwrk = *n + *n * ilaenv_(&c__1, "ZGEHRD", " ", n, &c__1, n, &c__0, (
ftnlen)6, (ftnlen)1);
if ((! wantvl && ! wantvr)) {
/* Computing MAX */
i__1 = 1, i__2 = (*n) << (1);
minwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = ilaenv_(&c__8, "ZHSEQR", "EN", n, &c__1, n, &c_n1, (ftnlen)
6, (ftnlen)2);
maxb = max(i__1,2);
/*
Computing MIN
Computing MAX
*/
i__3 = 2, i__4 = ilaenv_(&c__4, "ZHSEQR", "EN", n, &c__1, n, &
c_n1, (ftnlen)6, (ftnlen)2);
i__1 = min(maxb,*n), i__2 = max(i__3,i__4);
k = min(i__1,i__2);
/* Computing MAX */
i__1 = k * (k + 2), i__2 = (*n) << (1);
hswork = max(i__1,i__2);
maxwrk = max(maxwrk,hswork);
} else {
/* Computing MAX */
i__1 = 1, i__2 = (*n) << (1);
minwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + (*n - 1) * ilaenv_(&c__1, "ZUNGHR",
" ", n, &c__1, n, &c_n1, (ftnlen)6, (ftnlen)1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = ilaenv_(&c__8, "ZHSEQR", "SV", n, &c__1, n, &c_n1, (ftnlen)
6, (ftnlen)2);
maxb = max(i__1,2);
/*
Computing MIN
Computing MAX
*/
i__3 = 2, i__4 = ilaenv_(&c__4, "ZHSEQR", "SV", n, &c__1, n, &
c_n1, (ftnlen)6, (ftnlen)2);
i__1 = min(maxb,*n), i__2 = max(i__3,i__4);
k = min(i__1,i__2);
/* Computing MAX */
i__1 = k * (k + 2), i__2 = (*n) << (1);
hswork = max(i__1,i__2);
/* Computing MAX */
i__1 = max(maxwrk,hswork), i__2 = (*n) << (1);
maxwrk = max(i__1,i__2);
}
work[1].r = (doublereal) maxwrk, work[1].i = 0.;
}
if ((*lwork < minwrk && ! lquery)) {
*info = -12;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGEEV ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Get machine constants */
eps = PRECISION;
smlnum = SAFEMINIMUM;
bignum = 1. / smlnum;
dlabad_(&smlnum, &bignum);
smlnum = sqrt(smlnum) / eps;
bignum = 1. / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
anrm = zlange_("M", n, n, &a[a_offset], lda, dum);
scalea = FALSE_;
if ((anrm > 0. && anrm < smlnum)) {
scalea = TRUE_;
cscale = smlnum;
} else if (anrm > bignum) {
scalea = TRUE_;
cscale = bignum;
}
if (scalea) {
zlascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, &
ierr);
}
/*
Balance the matrix
(CWorkspace: none)
(RWorkspace: need N)
*/
ibal = 1;
zgebal_("B", n, &a[a_offset], lda, &ilo, &ihi, &rwork[ibal], &ierr);
/*
Reduce to upper Hessenberg form
(CWorkspace: need 2*N, prefer N+N*NB)
(RWorkspace: none)
*/
itau = 1;
iwrk = itau + *n;
i__1 = *lwork - iwrk + 1;
zgehrd_(n, &ilo, &ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1,
&ierr);
if (wantvl) {
/*
Want left eigenvectors
Copy Householder vectors to VL
*/
*(unsigned char *)side = 'L';
zlacpy_("L", n, n, &a[a_offset], lda, &vl[vl_offset], ldvl)
;
/*
Generate unitary matrix in VL
(CWorkspace: need 2*N-1, prefer N+(N-1)*NB)
(RWorkspace: none)
*/
i__1 = *lwork - iwrk + 1;
zunghr_(n, &ilo, &ihi, &vl[vl_offset], ldvl, &work[itau], &work[iwrk],
&i__1, &ierr);
/*
Perform QR iteration, accumulating Schur vectors in VL
(CWorkspace: need 1, prefer HSWORK (see comments) )
(RWorkspace: none)
*/
iwrk = itau;
i__1 = *lwork - iwrk + 1;
zhseqr_("S", "V", n, &ilo, &ihi, &a[a_offset], lda, &w[1], &vl[
vl_offset], ldvl, &work[iwrk], &i__1, info);
if (wantvr) {
/*
Want left and right eigenvectors
Copy Schur vectors to VR
*/
*(unsigned char *)side = 'B';
zlacpy_("F", n, n, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr);
}
} else if (wantvr) {
/*
Want right eigenvectors
Copy Householder vectors to VR
*/
*(unsigned char *)side = 'R';
zlacpy_("L", n, n, &a[a_offset], lda, &vr[vr_offset], ldvr)
;
/*
Generate unitary matrix in VR
(CWorkspace: need 2*N-1, prefer N+(N-1)*NB)
(RWorkspace: none)
*/
i__1 = *lwork - iwrk + 1;
zunghr_(n, &ilo, &ihi, &vr[vr_offset], ldvr, &work[itau], &work[iwrk],
&i__1, &ierr);
/*
Perform QR iteration, accumulating Schur vectors in VR
(CWorkspace: need 1, prefer HSWORK (see comments) )
(RWorkspace: none)
*/
iwrk = itau;
i__1 = *lwork - iwrk + 1;
zhseqr_("S", "V", n, &ilo, &ihi, &a[a_offset], lda, &w[1], &vr[
vr_offset], ldvr, &work[iwrk], &i__1, info);
} else {
/*
Compute eigenvalues only
(CWorkspace: need 1, prefer HSWORK (see comments) )
(RWorkspace: none)
*/
iwrk = itau;
i__1 = *lwork - iwrk + 1;
zhseqr_("E", "N", n, &ilo, &ihi, &a[a_offset], lda, &w[1], &vr[
vr_offset], ldvr, &work[iwrk], &i__1, info);
}
/* If INFO > 0 from ZHSEQR, then quit */
if (*info > 0) {
goto L50;
}
if (wantvl || wantvr) {
/*
Compute left and/or right eigenvectors
(CWorkspace: need 2*N)
(RWorkspace: need 2*N)
*/
irwork = ibal + *n;
ztrevc_(side, "B", select, n, &a[a_offset], lda, &vl[vl_offset], ldvl,
&vr[vr_offset], ldvr, n, &nout, &work[iwrk], &rwork[irwork],
&ierr);
}
if (wantvl) {
/*
Undo balancing of left eigenvectors
(CWorkspace: none)
(RWorkspace: need N)
*/
zgebak_("B", "L", n, &ilo, &ihi, &rwork[ibal], n, &vl[vl_offset],
ldvl, &ierr);
/* Normalize left eigenvectors and make largest component real */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
scl = 1. / dznrm2_(n, &vl[i__ * vl_dim1 + 1], &c__1);
zdscal_(n, &scl, &vl[i__ * vl_dim1 + 1], &c__1);
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
i__3 = k + i__ * vl_dim1;
/* Computing 2nd power */
d__1 = vl[i__3].r;
/* Computing 2nd power */
d__2 = d_imag(&vl[k + i__ * vl_dim1]);
rwork[irwork + k - 1] = d__1 * d__1 + d__2 * d__2;
/* L10: */
}
k = idamax_(n, &rwork[irwork], &c__1);
d_cnjg(&z__2, &vl[k + i__ * vl_dim1]);
d__1 = sqrt(rwork[irwork + k - 1]);
z__1.r = z__2.r / d__1, z__1.i = z__2.i / d__1;
tmp.r = z__1.r, tmp.i = z__1.i;
zscal_(n, &tmp, &vl[i__ * vl_dim1 + 1], &c__1);
i__2 = k + i__ * vl_dim1;
i__3 = k + i__ * vl_dim1;
d__1 = vl[i__3].r;
z__1.r = d__1, z__1.i = 0.;
vl[i__2].r = z__1.r, vl[i__2].i = z__1.i;
/* L20: */
}
}
if (wantvr) {
/*
Undo balancing of right eigenvectors
(CWorkspace: none)
(RWorkspace: need N)
*/
zgebak_("B", "R", n, &ilo, &ihi, &rwork[ibal], n, &vr[vr_offset],
ldvr, &ierr);
/* Normalize right eigenvectors and make largest component real */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
scl = 1. / dznrm2_(n, &vr[i__ * vr_dim1 + 1], &c__1);
zdscal_(n, &scl, &vr[i__ * vr_dim1 + 1], &c__1);
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
i__3 = k + i__ * vr_dim1;
/* Computing 2nd power */
d__1 = vr[i__3].r;
/* Computing 2nd power */
d__2 = d_imag(&vr[k + i__ * vr_dim1]);
rwork[irwork + k - 1] = d__1 * d__1 + d__2 * d__2;
/* L30: */
}
k = idamax_(n, &rwork[irwork], &c__1);
d_cnjg(&z__2, &vr[k + i__ * vr_dim1]);
d__1 = sqrt(rwork[irwork + k - 1]);
z__1.r = z__2.r / d__1, z__1.i = z__2.i / d__1;
tmp.r = z__1.r, tmp.i = z__1.i;
zscal_(n, &tmp, &vr[i__ * vr_dim1 + 1], &c__1);
i__2 = k + i__ * vr_dim1;
i__3 = k + i__ * vr_dim1;
d__1 = vr[i__3].r;
z__1.r = d__1, z__1.i = 0.;
vr[i__2].r = z__1.r, vr[i__2].i = z__1.i;
/* L40: */
}
}
/* Undo scaling if necessary */
L50:
if (scalea) {
i__1 = *n - *info;
/* Computing MAX */
i__3 = *n - *info;
i__2 = max(i__3,1);
zlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &w[*info + 1]
, &i__2, &ierr);
if (*info > 0) {
i__1 = ilo - 1;
zlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &w[1], n,
&ierr);
}
}
work[1].r = (doublereal) maxwrk, work[1].i = 0.;
return 0;
/* End of ZGEEV */
} /* zgeev_ */
/* Subroutine */ int zgehd2_(integer *n, integer *ilo, integer *ihi,
doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
doublecomplex z__1;
/* Builtin functions */
void d_cnjg(doublecomplex *, doublecomplex *);
/* Local variables */
static integer i__;
static doublecomplex alpha;
extern /* Subroutine */ int zlarf_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, doublecomplex *), xerbla_(char *, integer *), zlarfg_(integer *, doublecomplex *, doublecomplex *,
integer *, doublecomplex *);
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZGEHD2 reduces a complex general matrix A to upper Hessenberg form H
by a unitary similarity transformation: Q' * A * Q = H .
Arguments
=========
N (input) INTEGER
The order of the matrix A. N >= 0.
ILO (input) INTEGER
IHI (input) INTEGER
It is assumed that A is already upper triangular in rows
and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally
set by a previous call to ZGEBAL; otherwise they should be
set to 1 and N respectively. See Further Details.
1 <= ILO <= IHI <= max(1,N).
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the n by n general matrix to be reduced.
On exit, the upper triangle and the first subdiagonal of A
are overwritten with the upper Hessenberg matrix H, and the
elements below the first subdiagonal, with the array TAU,
represent the unitary matrix Q as a product of elementary
reflectors. See Further Details.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
TAU (output) COMPLEX*16 array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace) COMPLEX*16 array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
Further Details
===============
The matrix Q is represented as a product of (ihi-ilo) elementary
reflectors
Q = H(ilo) H(ilo+1) . . . H(ihi-1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
exit in A(i+2:ihi,i), and tau in TAU(i).
The contents of A are illustrated by the following example, with
n = 7, ilo = 2 and ihi = 6:
on entry, on exit,
( a a a a a a a ) ( a a h h h h a )
( a a a a a a ) ( a h h h h a )
( a a a a a a ) ( h h h h h h )
( a a a a a a ) ( v2 h h h h h )
( a a a a a a ) ( v2 v3 h h h h )
( a a a a a a ) ( v2 v3 v4 h h h )
( a ) ( a )
where a denotes an element of the original matrix A, h denotes a
modified element of the upper Hessenberg matrix H, and vi denotes an
element of the vector defining H(i).
=====================================================================
Test the input parameters
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
if (*n < 0) {
*info = -1;
} else if (*ilo < 1 || *ilo > max(1,*n)) {
*info = -2;
} else if (*ihi < min(*ilo,*n) || *ihi > *n) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGEHD2", &i__1);
return 0;
}
i__1 = *ihi - 1;
for (i__ = *ilo; i__ <= i__1; ++i__) {
/* Compute elementary reflector H(i) to annihilate A(i+2:ihi,i) */
i__2 = i__ + 1 + i__ * a_dim1;
alpha.r = a[i__2].r, alpha.i = a[i__2].i;
i__2 = *ihi - i__;
/* Computing MIN */
i__3 = i__ + 2;
zlarfg_(&i__2, &alpha, &a[min(i__3,*n) + i__ * a_dim1], &c__1, &tau[
i__]);
i__2 = i__ + 1 + i__ * a_dim1;
a[i__2].r = 1., a[i__2].i = 0.;
/* Apply H(i) to A(1:ihi,i+1:ihi) from the right */
i__2 = *ihi - i__;
zlarf_("Right", ihi, &i__2, &a[i__ + 1 + i__ * a_dim1], &c__1, &tau[
i__], &a[(i__ + 1) * a_dim1 + 1], lda, &work[1]);
/* Apply H(i)' to A(i+1:ihi,i+1:n) from the left */
i__2 = *ihi - i__;
i__3 = *n - i__;
d_cnjg(&z__1, &tau[i__]);
zlarf_("Left", &i__2, &i__3, &a[i__ + 1 + i__ * a_dim1], &c__1, &z__1,
&a[i__ + 1 + (i__ + 1) * a_dim1], lda, &work[1]);
i__2 = i__ + 1 + i__ * a_dim1;
a[i__2].r = alpha.r, a[i__2].i = alpha.i;
/* L10: */
}
return 0;
/* End of ZGEHD2 */
} /* zgehd2_ */
/* Subroutine */ int zgehrd_(integer *n, integer *ilo, integer *ihi,
doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
doublecomplex z__1;
/* Local variables */
static integer i__;
static doublecomplex t[4160] /* was [65][64] */;
static integer ib;
static doublecomplex ei;
static integer nb, nh, nx, iws, nbmin, iinfo;
extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *,
integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *), zgehd2_(integer *, integer *, integer
*, doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *),
zlahrd_(integer *, integer *, integer *, doublecomplex *, integer
*, doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *);
static integer ldwork, lwkopt;
static logical lquery;
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZGEHRD reduces a complex general matrix A to upper Hessenberg form H
by a unitary similarity transformation: Q' * A * Q = H .
Arguments
=========
N (input) INTEGER
The order of the matrix A. N >= 0.
ILO (input) INTEGER
IHI (input) INTEGER
It is assumed that A is already upper triangular in rows
and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally
set by a previous call to ZGEBAL; otherwise they should be
set to 1 and N respectively. See Further Details.
1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the N-by-N general matrix to be reduced.
On exit, the upper triangle and the first subdiagonal of A
are overwritten with the upper Hessenberg matrix H, and the
elements below the first subdiagonal, with the array TAU,
represent the unitary matrix Q as a product of elementary
reflectors. See Further Details.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
TAU (output) COMPLEX*16 array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to
zero.
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The length of the array WORK. LWORK >= max(1,N).
For optimum performance LWORK >= N*NB, where NB is the
optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
Further Details
===============
The matrix Q is represented as a product of (ihi-ilo) elementary
reflectors
Q = H(ilo) H(ilo+1) . . . H(ihi-1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
exit in A(i+2:ihi,i), and tau in TAU(i).
The contents of A are illustrated by the following example, with
n = 7, ilo = 2 and ihi = 6:
on entry, on exit,
( a a a a a a a ) ( a a h h h h a )
( a a a a a a ) ( a h h h h a )
( a a a a a a ) ( h h h h h h )
( a a a a a a ) ( v2 h h h h h )
( a a a a a a ) ( v2 v3 h h h h )
( a a a a a a ) ( v2 v3 v4 h h h )
( a ) ( a )
where a denotes an element of the original matrix A, h denotes a
modified element of the upper Hessenberg matrix H, and vi denotes an
element of the vector defining H(i).
=====================================================================
Test the input parameters
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
/* Computing MIN */
i__1 = 64, i__2 = ilaenv_(&c__1, "ZGEHRD", " ", n, ilo, ihi, &c_n1, (
ftnlen)6, (ftnlen)1);
nb = min(i__1,i__2);
lwkopt = *n * nb;
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
lquery = *lwork == -1;
if (*n < 0) {
*info = -1;
} else if (*ilo < 1 || *ilo > max(1,*n)) {
*info = -2;
} else if (*ihi < min(*ilo,*n) || *ihi > *n) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if ((*lwork < max(1,*n) && ! lquery)) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGEHRD", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Set elements 1:ILO-1 and IHI:N-1 of TAU to zero */
i__1 = *ilo - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
tau[i__2].r = 0., tau[i__2].i = 0.;
/* L10: */
}
i__1 = *n - 1;
for (i__ = max(1,*ihi); i__ <= i__1; ++i__) {
i__2 = i__;
tau[i__2].r = 0., tau[i__2].i = 0.;
/* L20: */
}
/* Quick return if possible */
nh = *ihi - *ilo + 1;
if (nh <= 1) {
work[1].r = 1., work[1].i = 0.;
return 0;
}
nbmin = 2;
iws = 1;
if ((nb > 1 && nb < nh)) {
/*
Determine when to cross over from blocked to unblocked code
(last block is always handled by unblocked code).
Computing MAX
*/
i__1 = nb, i__2 = ilaenv_(&c__3, "ZGEHRD", " ", n, ilo, ihi, &c_n1, (
ftnlen)6, (ftnlen)1);
nx = max(i__1,i__2);
if (nx < nh) {
/* Determine if workspace is large enough for blocked code. */
iws = *n * nb;
if (*lwork < iws) {
/*
Not enough workspace to use optimal NB: determine the
minimum value of NB, and reduce NB or force use of
unblocked code.
Computing MAX
*/
i__1 = 2, i__2 = ilaenv_(&c__2, "ZGEHRD", " ", n, ilo, ihi, &
c_n1, (ftnlen)6, (ftnlen)1);
nbmin = max(i__1,i__2);
if (*lwork >= *n * nbmin) {
nb = *lwork / *n;
} else {
nb = 1;
}
}
}
}
ldwork = *n;
if (nb < nbmin || nb >= nh) {
/* Use unblocked code below */
i__ = *ilo;
} else {
/* Use blocked code */
i__1 = *ihi - 1 - nx;
i__2 = nb;
for (i__ = *ilo; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/* Computing MIN */
i__3 = nb, i__4 = *ihi - i__;
ib = min(i__3,i__4);
/*
Reduce columns i:i+ib-1 to Hessenberg form, returning the
matrices V and T of the block reflector H = I - V*T*V'
which performs the reduction, and also the matrix Y = A*V*T
*/
zlahrd_(ihi, &i__, &ib, &a[i__ * a_dim1 + 1], lda, &tau[i__], t, &
c__65, &work[1], &ldwork);
/*
Apply the block reflector H to A(1:ihi,i+ib:ihi) from the
right, computing A := A - Y * V'. V(i+ib,ib-1) must be set
to 1.
*/
i__3 = i__ + ib + (i__ + ib - 1) * a_dim1;
ei.r = a[i__3].r, ei.i = a[i__3].i;
i__3 = i__ + ib + (i__ + ib - 1) * a_dim1;
a[i__3].r = 1., a[i__3].i = 0.;
i__3 = *ihi - i__ - ib + 1;
z__1.r = -1., z__1.i = -0.;
zgemm_("No transpose", "Conjugate transpose", ihi, &i__3, &ib, &
z__1, &work[1], &ldwork, &a[i__ + ib + i__ * a_dim1], lda,
&c_b60, &a[(i__ + ib) * a_dim1 + 1], lda);
i__3 = i__ + ib + (i__ + ib - 1) * a_dim1;
a[i__3].r = ei.r, a[i__3].i = ei.i;
/*
Apply the block reflector H to A(i+1:ihi,i+ib:n) from the
left
*/
i__3 = *ihi - i__;
i__4 = *n - i__ - ib + 1;
zlarfb_("Left", "Conjugate transpose", "Forward", "Columnwise", &
i__3, &i__4, &ib, &a[i__ + 1 + i__ * a_dim1], lda, t, &
c__65, &a[i__ + 1 + (i__ + ib) * a_dim1], lda, &work[1], &
ldwork);
/* L30: */
}
}
/* Use unblocked code to reduce the rest of the matrix */
zgehd2_(n, &i__, ihi, &a[a_offset], lda, &tau[1], &work[1], &iinfo);
work[1].r = (doublereal) iws, work[1].i = 0.;
return 0;
/* End of ZGEHRD */
} /* zgehrd_ */
/* Subroutine */ int zgelq2_(integer *m, integer *n, doublecomplex *a,
integer *lda, doublecomplex *tau, doublecomplex *work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
/* Local variables */
static integer i__, k;
static doublecomplex alpha;
extern /* Subroutine */ int zlarf_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, doublecomplex *), xerbla_(char *, integer *), zlarfg_(integer *, doublecomplex *, doublecomplex *,
integer *, doublecomplex *), zlacgv_(integer *, doublecomplex *,
integer *);
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZGELQ2 computes an LQ factorization of a complex m by n matrix A:
A = L * Q.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the m by n matrix A.
On exit, the elements on and below the diagonal of the array
contain the m by min(m,n) lower trapezoidal matrix L (L is
lower triangular if m <= n); the elements above the diagonal,
with the array TAU, represent the unitary matrix Q as a
product of elementary reflectors (see Further Details).
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU (output) COMPLEX*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace) COMPLEX*16 array, dimension (M)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Further Details
===============
The matrix Q is represented as a product of elementary reflectors
Q = H(k)' . . . H(2)' H(1)', where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in
A(i,i+1:n), and tau in TAU(i).
=====================================================================
Test the input arguments
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*m)) {
*info = -4;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGELQ2", &i__1);
return 0;
}
k = min(*m,*n);
i__1 = k;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Generate elementary reflector H(i) to annihilate A(i,i+1:n) */
i__2 = *n - i__ + 1;
zlacgv_(&i__2, &a[i__ + i__ * a_dim1], lda);
i__2 = i__ + i__ * a_dim1;
alpha.r = a[i__2].r, alpha.i = a[i__2].i;
i__2 = *n - i__ + 1;
/* Computing MIN */
i__3 = i__ + 1;
zlarfg_(&i__2, &alpha, &a[i__ + min(i__3,*n) * a_dim1], lda, &tau[i__]
);
if (i__ < *m) {
/* Apply H(i) to A(i+1:m,i:n) from the right */
i__2 = i__ + i__ * a_dim1;
a[i__2].r = 1., a[i__2].i = 0.;
i__2 = *m - i__;
i__3 = *n - i__ + 1;
zlarf_("Right", &i__2, &i__3, &a[i__ + i__ * a_dim1], lda, &tau[
i__], &a[i__ + 1 + i__ * a_dim1], lda, &work[1]);
}
i__2 = i__ + i__ * a_dim1;
a[i__2].r = alpha.r, a[i__2].i = alpha.i;
i__2 = *n - i__ + 1;
zlacgv_(&i__2, &a[i__ + i__ * a_dim1], lda);
/* L10: */
}
return 0;
/* End of ZGELQ2 */
} /* zgelq2_ */
/* Subroutine */ int zgelqf_(integer *m, integer *n, doublecomplex *a,
integer *lda, doublecomplex *tau, doublecomplex *work, integer *lwork,
integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
/* Local variables */
static integer i__, k, ib, nb, nx, iws, nbmin, iinfo;
extern /* Subroutine */ int zgelq2_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *), xerbla_(
char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
static integer ldwork;
extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
static integer lwkopt;
static logical lquery;
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZGELQF computes an LQ factorization of a complex M-by-N matrix A:
A = L * Q.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and below the diagonal of the array
contain the m-by-min(m,n) lower trapezoidal matrix L (L is
lower triangular if m <= n); the elements above the diagonal,
with the array TAU, represent the unitary matrix Q as a
product of elementary reflectors (see Further Details).
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU (output) COMPLEX*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,M).
For optimum performance LWORK >= M*NB, where NB is the
optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Further Details
===============
The matrix Q is represented as a product of elementary reflectors
Q = H(k)' . . . H(2)' H(1)', where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in
A(i,i+1:n), and tau in TAU(i).
=====================================================================
Test the input arguments
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
nb = ilaenv_(&c__1, "ZGELQF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)
1);
lwkopt = *m * nb;
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
lquery = *lwork == -1;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*m)) {
*info = -4;
} else if ((*lwork < max(1,*m) && ! lquery)) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGELQF", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
k = min(*m,*n);
if (k == 0) {
work[1].r = 1., work[1].i = 0.;
return 0;
}
nbmin = 2;
nx = 0;
iws = *m;
if ((nb > 1 && nb < k)) {
/*
Determine when to cross over from blocked to unblocked code.
Computing MAX
*/
i__1 = 0, i__2 = ilaenv_(&c__3, "ZGELQF", " ", m, n, &c_n1, &c_n1, (
ftnlen)6, (ftnlen)1);
nx = max(i__1,i__2);
if (nx < k) {
/* Determine if workspace is large enough for blocked code. */
ldwork = *m;
iws = ldwork * nb;
if (*lwork < iws) {
/*
Not enough workspace to use optimal NB: reduce NB and
determine the minimum value of NB.
*/
nb = *lwork / ldwork;
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "ZGELQF", " ", m, n, &c_n1, &
c_n1, (ftnlen)6, (ftnlen)1);
nbmin = max(i__1,i__2);
}
}
}
if (((nb >= nbmin && nb < k) && nx < k)) {
/* Use blocked code initially */
i__1 = k - nx;
i__2 = nb;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/* Computing MIN */
i__3 = k - i__ + 1;
ib = min(i__3,nb);
/*
Compute the LQ factorization of the current block
A(i:i+ib-1,i:n)
*/
i__3 = *n - i__ + 1;
zgelq2_(&ib, &i__3, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[
1], &iinfo);
if (i__ + ib <= *m) {
/*
Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1)
*/
i__3 = *n - i__ + 1;
zlarft_("Forward", "Rowwise", &i__3, &ib, &a[i__ + i__ *
a_dim1], lda, &tau[i__], &work[1], &ldwork);
/* Apply H to A(i+ib:m,i:n) from the right */
i__3 = *m - i__ - ib + 1;
i__4 = *n - i__ + 1;
zlarfb_("Right", "No transpose", "Forward", "Rowwise", &i__3,
&i__4, &ib, &a[i__ + i__ * a_dim1], lda, &work[1], &
ldwork, &a[i__ + ib + i__ * a_dim1], lda, &work[ib +
1], &ldwork);
}
/* L10: */
}
} else {
i__ = 1;
}
/* Use unblocked code to factor the last or only block. */
if (i__ <= k) {
i__2 = *m - i__ + 1;
i__1 = *n - i__ + 1;
zgelq2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1]
, &iinfo);
}
work[1].r = (doublereal) iws, work[1].i = 0.;
return 0;
/* End of ZGELQF */
} /* zgelqf_ */
/* Subroutine */ int zgelsd_(integer *m, integer *n, integer *nrhs,
doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb,
doublereal *s, doublereal *rcond, integer *rank, doublecomplex *work,
integer *lwork, doublereal *rwork, integer *iwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4;
doublereal d__1;
doublecomplex z__1;
/* Local variables */
static integer ie, il, mm;
static doublereal eps, anrm, bnrm;
static integer itau, iascl, ibscl;
static doublereal sfmin;
static integer minmn, maxmn, itaup, itauq, mnthr, nwork;
extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
extern /* Subroutine */ int dlascl_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublereal *,
integer *, integer *), dlaset_(char *, integer *, integer
*, doublereal *, doublereal *, doublereal *, integer *),
xerbla_(char *, integer *), zgebrd_(integer *, integer *,
doublecomplex *, integer *, doublereal *, doublereal *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *,
integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern doublereal zlange_(char *, integer *, integer *, doublecomplex *,
integer *, doublereal *);
static doublereal bignum;
extern /* Subroutine */ int zgelqf_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *, integer *
), zlalsd_(char *, integer *, integer *, integer *, doublereal *,
doublereal *, doublecomplex *, integer *, doublereal *, integer *,
doublecomplex *, doublereal *, integer *, integer *),
zlascl_(char *, integer *, integer *, doublereal *, doublereal *,
integer *, integer *, doublecomplex *, integer *, integer *), zgeqrf_(integer *, integer *, doublecomplex *, integer *,
doublecomplex *, doublecomplex *, integer *, integer *);
static integer ldwork;
extern /* Subroutine */ int zlacpy_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *),
zlaset_(char *, integer *, integer *, doublecomplex *,
doublecomplex *, doublecomplex *, integer *);
static integer minwrk, maxwrk;
static doublereal smlnum;
extern /* Subroutine */ int zunmbr_(char *, char *, char *, integer *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *
);
static logical lquery;
static integer nrwork, smlsiz;
extern /* Subroutine */ int zunmlq_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *), zunmqr_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *);
/*
-- LAPACK driver routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
October 31, 1999
Purpose
=======
ZGELSD computes the minimum-norm solution to a real linear least
squares problem:
minimize 2-norm(| b - A*x |)
using the singular value decomposition (SVD) of A. A is an M-by-N
matrix which may be rank-deficient.
Several right hand side vectors b and solution vectors x can be
handled in a single call; they are stored as the columns of the
M-by-NRHS right hand side matrix B and the N-by-NRHS solution
matrix X.
The problem is solved in three steps:
(1) Reduce the coefficient matrix A to bidiagonal form with
Householder tranformations, reducing the original problem
into a "bidiagonal least squares problem" (BLS)
(2) Solve the BLS using a divide and conquer approach.
(3) Apply back all the Householder tranformations to solve
the original least squares problem.
The effective rank of A is determined by treating as zero those
singular values which are less than RCOND times the largest singular
value.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
A (input) COMPLEX*16 array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, A has been destroyed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
On entry, the M-by-NRHS right hand side matrix B.
On exit, B is overwritten by the N-by-NRHS solution matrix X.
If m >= n and RANK = n, the residual sum-of-squares for
the solution in the i-th column is given by the sum of
squares of elements n+1:m in that column.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,M,N).
S (output) DOUBLE PRECISION array, dimension (min(M,N))
The singular values of A in decreasing order.
The condition number of A in the 2-norm = S(1)/S(min(m,n)).
RCOND (input) DOUBLE PRECISION
RCOND is used to determine the effective rank of A.
Singular values S(i) <= RCOND*S(1) are treated as zero.
If RCOND < 0, machine precision is used instead.
RANK (output) INTEGER
The effective rank of A, i.e., the number of singular values
which are greater than RCOND*S(1).
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK must be at least 1.
The exact minimum amount of workspace needed depends on M,
N and NRHS. As long as LWORK is at least
2 * N + N * NRHS
if M is greater than or equal to N or
2 * M + M * NRHS
if M is less than N, the code will execute correctly.
For good performance, LWORK should generally be larger.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
RWORK (workspace) DOUBLE PRECISION array, dimension at least
10*N + 2*N*SMLSIZ + 8*N*NLVL + 3*SMLSIZ*NRHS +
(SMLSIZ+1)**2
if M is greater than or equal to N or
10*M + 2*M*SMLSIZ + 8*M*NLVL + 3*SMLSIZ*NRHS +
(SMLSIZ+1)**2
if M is less than N, the code will execute correctly.
SMLSIZ is returned by ILAENV and is equal to the maximum
size of the subproblems at the bottom of the computation
tree (usually about 25), and
NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 )
IWORK (workspace) INTEGER array, dimension (LIWORK)
LIWORK >= 3 * MINMN * NLVL + 11 * MINMN,
where MINMN = MIN( M,N ).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: the algorithm for computing the SVD failed to converge;
if INFO = i, i off-diagonal elements of an intermediate
bidiagonal form did not converge to zero.
Further Details
===============
Based on contributions by
Ming Gu and Ren-Cang Li, Computer Science Division, University of
California at Berkeley, USA
Osni Marques, LBNL/NERSC, USA
=====================================================================
Test the input arguments.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
--s;
--work;
--rwork;
--iwork;
/* Function Body */
*info = 0;
minmn = min(*m,*n);
maxmn = max(*m,*n);
mnthr = ilaenv_(&c__6, "ZGELSD", " ", m, n, nrhs, &c_n1, (ftnlen)6, (
ftnlen)1);
lquery = *lwork == -1;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*lda < max(1,*m)) {
*info = -5;
} else if (*ldb < max(1,maxmn)) {
*info = -7;
}
smlsiz = ilaenv_(&c__9, "ZGELSD", " ", &c__0, &c__0, &c__0, &c__0, (
ftnlen)6, (ftnlen)1);
/*
Compute workspace.
(Note: Comments in the code beginning "Workspace:" describe the
minimal amount of workspace needed at that point in the code,
as well as the preferred amount for good performance.
NB refers to the optimal block size for the immediately
following subroutine, as returned by ILAENV.)
*/
minwrk = 1;
if (*info == 0) {
maxwrk = 0;
mm = *m;
if ((*m >= *n && *m >= mnthr)) {
/* Path 1a - overdetermined, with many more rows than columns. */
mm = *n;
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * ilaenv_(&c__1, "ZGEQRF", " ", m, n, &
c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *nrhs * ilaenv_(&c__1, "ZUNMQR", "LC", m,
nrhs, n, &c_n1, (ftnlen)6, (ftnlen)2);
maxwrk = max(i__1,i__2);
}
if (*m >= *n) {
/*
Path 1 - overdetermined or exactly determined.
Computing MAX
*/
i__1 = maxwrk, i__2 = ((*n) << (1)) + (mm + *n) * ilaenv_(&c__1,
"ZGEBRD", " ", &mm, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1)
;
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*n) << (1)) + *nrhs * ilaenv_(&c__1,
"ZUNMBR", "QLC", &mm, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)
3);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*n) << (1)) + (*n - 1) * ilaenv_(&c__1,
"ZUNMBR", "PLN", n, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*n) << (1)) + *n * *nrhs;
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = ((*n) << (1)) + mm, i__2 = ((*n) << (1)) + *n * *nrhs;
minwrk = max(i__1,i__2);
}
if (*n > *m) {
if (*n >= mnthr) {
/*
Path 2a - underdetermined, with many more columns
than rows.
*/
maxwrk = *m + *m * ilaenv_(&c__1, "ZGELQF", " ", m, n, &c_n1,
&c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + ((*m) << (2)) + ((*m) << (1))
* ilaenv_(&c__1, "ZGEBRD", " ", m, m, &c_n1, &c_n1, (
ftnlen)6, (ftnlen)1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + ((*m) << (2)) + *nrhs *
ilaenv_(&c__1, "ZUNMBR", "QLC", m, nrhs, m, &c_n1, (
ftnlen)6, (ftnlen)3);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + ((*m) << (2)) + (*m - 1) *
ilaenv_(&c__1, "ZUNMLQ", "LC", n, nrhs, m, &c_n1, (
ftnlen)6, (ftnlen)2);
maxwrk = max(i__1,i__2);
if (*nrhs > 1) {
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + *m + *m * *nrhs;
maxwrk = max(i__1,i__2);
} else {
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + ((*m) << (1));
maxwrk = max(i__1,i__2);
}
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + ((*m) << (2)) + *m * *nrhs;
maxwrk = max(i__1,i__2);
} else {
/* Path 2 - underdetermined. */
maxwrk = ((*m) << (1)) + (*n + *m) * ilaenv_(&c__1, "ZGEBRD",
" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*m) << (1)) + *nrhs * ilaenv_(&c__1,
"ZUNMBR", "QLC", m, nrhs, m, &c_n1, (ftnlen)6, (
ftnlen)3);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*m) << (1)) + *m * ilaenv_(&c__1,
"ZUNMBR", "PLN", n, nrhs, m, &c_n1, (ftnlen)6, (
ftnlen)3);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*m) << (1)) + *m * *nrhs;
maxwrk = max(i__1,i__2);
}
/* Computing MAX */
i__1 = ((*m) << (1)) + *n, i__2 = ((*m) << (1)) + *m * *nrhs;
minwrk = max(i__1,i__2);
}
minwrk = min(minwrk,maxwrk);
d__1 = (doublereal) maxwrk;
z__1.r = d__1, z__1.i = 0.;
work[1].r = z__1.r, work[1].i = z__1.i;
if ((*lwork < minwrk && ! lquery)) {
*info = -12;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGELSD", &i__1);
return 0;
} else if (lquery) {
goto L10;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0) {
*rank = 0;
return 0;
}
/* Get machine parameters. */
eps = PRECISION;
sfmin = SAFEMINIMUM;
smlnum = sfmin / eps;
bignum = 1. / smlnum;
dlabad_(&smlnum, &bignum);
/* Scale A if max entry outside range [SMLNUM,BIGNUM]. */
anrm = zlange_("M", m, n, &a[a_offset], lda, &rwork[1]);
iascl = 0;
if ((anrm > 0. && anrm < smlnum)) {
/* Scale matrix norm up to SMLNUM */
zlascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda,
info);
iascl = 1;
} else if (anrm > bignum) {
/* Scale matrix norm down to BIGNUM. */
zlascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda,
info);
iascl = 2;
} else if (anrm == 0.) {
/* Matrix all zero. Return zero solution. */
i__1 = max(*m,*n);
zlaset_("F", &i__1, nrhs, &c_b59, &c_b59, &b[b_offset], ldb);
dlaset_("F", &minmn, &c__1, &c_b324, &c_b324, &s[1], &c__1)
;
*rank = 0;
goto L10;
}
/* Scale B if max entry outside range [SMLNUM,BIGNUM]. */
bnrm = zlange_("M", m, nrhs, &b[b_offset], ldb, &rwork[1]);
ibscl = 0;
if ((bnrm > 0. && bnrm < smlnum)) {
/* Scale matrix norm up to SMLNUM. */
zlascl_("G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb,
info);
ibscl = 1;
} else if (bnrm > bignum) {
/* Scale matrix norm down to BIGNUM. */
zlascl_("G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb,
info);
ibscl = 2;
}
/* If M < N make sure B(M+1:N,:) = 0 */
if (*m < *n) {
i__1 = *n - *m;
zlaset_("F", &i__1, nrhs, &c_b59, &c_b59, &b[*m + 1 + b_dim1], ldb);
}
/* Overdetermined case. */
if (*m >= *n) {
/* Path 1 - overdetermined or exactly determined. */
mm = *m;
if (*m >= mnthr) {
/* Path 1a - overdetermined, with many more rows than columns */
mm = *n;
itau = 1;
nwork = itau + *n;
/*
Compute A=Q*R.
(RWorkspace: need N)
(CWorkspace: need N, prefer N*NB)
*/
i__1 = *lwork - nwork + 1;
zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1,
info);
/*
Multiply B by transpose(Q).
(RWorkspace: need N)
(CWorkspace: need NRHS, prefer NRHS*NB)
*/
i__1 = *lwork - nwork + 1;
zunmqr_("L", "C", m, nrhs, n, &a[a_offset], lda, &work[itau], &b[
b_offset], ldb, &work[nwork], &i__1, info);
/* Zero out below R. */
if (*n > 1) {
i__1 = *n - 1;
i__2 = *n - 1;
zlaset_("L", &i__1, &i__2, &c_b59, &c_b59, &a[a_dim1 + 2],
lda);
}
}
itauq = 1;
itaup = itauq + *n;
nwork = itaup + *n;
ie = 1;
nrwork = ie + *n;
/*
Bidiagonalize R in A.
(RWorkspace: need N)
(CWorkspace: need 2*N+MM, prefer 2*N+(MM+N)*NB)
*/
i__1 = *lwork - nwork + 1;
zgebrd_(&mm, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq], &
work[itaup], &work[nwork], &i__1, info);
/*
Multiply B by transpose of left bidiagonalizing vectors of R.
(CWorkspace: need 2*N+NRHS, prefer 2*N+NRHS*NB)
*/
i__1 = *lwork - nwork + 1;
zunmbr_("Q", "L", "C", &mm, nrhs, n, &a[a_offset], lda, &work[itauq],
&b[b_offset], ldb, &work[nwork], &i__1, info);
/* Solve the bidiagonal least squares problem. */
zlalsd_("U", &smlsiz, n, nrhs, &s[1], &rwork[ie], &b[b_offset], ldb,
rcond, rank, &work[nwork], &rwork[nrwork], &iwork[1], info);
if (*info != 0) {
goto L10;
}
/* Multiply B by right bidiagonalizing vectors of R. */
i__1 = *lwork - nwork + 1;
zunmbr_("P", "L", "N", n, nrhs, n, &a[a_offset], lda, &work[itaup], &
b[b_offset], ldb, &work[nwork], &i__1, info);
} else /* if(complicated condition) */ {
/* Computing MAX */
i__1 = *m, i__2 = ((*m) << (1)) - 4, i__1 = max(i__1,i__2), i__1 =
max(i__1,*nrhs), i__2 = *n - *m * 3;
if ((*n >= mnthr && *lwork >= ((*m) << (2)) + *m * *m + max(i__1,i__2)
)) {
/*
Path 2a - underdetermined, with many more columns than rows
and sufficient workspace for an efficient algorithm.
*/
ldwork = *m;
/*
Computing MAX
Computing MAX
*/
i__3 = *m, i__4 = ((*m) << (1)) - 4, i__3 = max(i__3,i__4), i__3 =
max(i__3,*nrhs), i__4 = *n - *m * 3;
i__1 = ((*m) << (2)) + *m * *lda + max(i__3,i__4), i__2 = *m * *
lda + *m + *m * *nrhs;
if (*lwork >= max(i__1,i__2)) {
ldwork = *lda;
}
itau = 1;
nwork = *m + 1;
/*
Compute A=L*Q.
(CWorkspace: need 2*M, prefer M+M*NB)
*/
i__1 = *lwork - nwork + 1;
zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1,
info);
il = nwork;
/* Copy L to WORK(IL), zeroing out above its diagonal. */
zlacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwork);
i__1 = *m - 1;
i__2 = *m - 1;
zlaset_("U", &i__1, &i__2, &c_b59, &c_b59, &work[il + ldwork], &
ldwork);
itauq = il + ldwork * *m;
itaup = itauq + *m;
nwork = itaup + *m;
ie = 1;
nrwork = ie + *m;
/*
Bidiagonalize L in WORK(IL).
(RWorkspace: need M)
(CWorkspace: need M*M+4*M, prefer M*M+4*M+2*M*NB)
*/
i__1 = *lwork - nwork + 1;
zgebrd_(m, m, &work[il], &ldwork, &s[1], &rwork[ie], &work[itauq],
&work[itaup], &work[nwork], &i__1, info);
/*
Multiply B by transpose of left bidiagonalizing vectors of L.
(CWorkspace: need M*M+4*M+NRHS, prefer M*M+4*M+NRHS*NB)
*/
i__1 = *lwork - nwork + 1;
zunmbr_("Q", "L", "C", m, nrhs, m, &work[il], &ldwork, &work[
itauq], &b[b_offset], ldb, &work[nwork], &i__1, info);
/* Solve the bidiagonal least squares problem. */
zlalsd_("U", &smlsiz, m, nrhs, &s[1], &rwork[ie], &b[b_offset],
ldb, rcond, rank, &work[nwork], &rwork[nrwork], &iwork[1],
info);
if (*info != 0) {
goto L10;
}
/* Multiply B by right bidiagonalizing vectors of L. */
i__1 = *lwork - nwork + 1;
zunmbr_("P", "L", "N", m, nrhs, m, &work[il], &ldwork, &work[
itaup], &b[b_offset], ldb, &work[nwork], &i__1, info);
/* Zero out below first M rows of B. */
i__1 = *n - *m;
zlaset_("F", &i__1, nrhs, &c_b59, &c_b59, &b[*m + 1 + b_dim1],
ldb);
nwork = itau + *m;
/*
Multiply transpose(Q) by B.
(CWorkspace: need NRHS, prefer NRHS*NB)
*/
i__1 = *lwork - nwork + 1;
zunmlq_("L", "C", n, nrhs, m, &a[a_offset], lda, &work[itau], &b[
b_offset], ldb, &work[nwork], &i__1, info);
} else {
/* Path 2 - remaining underdetermined cases. */
itauq = 1;
itaup = itauq + *m;
nwork = itaup + *m;
ie = 1;
nrwork = ie + *m;
/*
Bidiagonalize A.
(RWorkspace: need M)
(CWorkspace: need 2*M+N, prefer 2*M+(M+N)*NB)
*/
i__1 = *lwork - nwork + 1;
zgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
&work[itaup], &work[nwork], &i__1, info);
/*
Multiply B by transpose of left bidiagonalizing vectors.
(CWorkspace: need 2*M+NRHS, prefer 2*M+NRHS*NB)
*/
i__1 = *lwork - nwork + 1;
zunmbr_("Q", "L", "C", m, nrhs, n, &a[a_offset], lda, &work[itauq]
, &b[b_offset], ldb, &work[nwork], &i__1, info);
/* Solve the bidiagonal least squares problem. */
zlalsd_("L", &smlsiz, m, nrhs, &s[1], &rwork[ie], &b[b_offset],
ldb, rcond, rank, &work[nwork], &rwork[nrwork], &iwork[1],
info);
if (*info != 0) {
goto L10;
}
/* Multiply B by right bidiagonalizing vectors of A. */
i__1 = *lwork - nwork + 1;
zunmbr_("P", "L", "N", n, nrhs, m, &a[a_offset], lda, &work[itaup]
, &b[b_offset], ldb, &work[nwork], &i__1, info);
}
}
/* Undo scaling. */
if (iascl == 1) {
zlascl_("G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb,
info);
dlascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &
minmn, info);
} else if (iascl == 2) {
zlascl_("G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb,
info);
dlascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &
minmn, info);
}
if (ibscl == 1) {
zlascl_("G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb,
info);
} else if (ibscl == 2) {
zlascl_("G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb,
info);
}
L10:
d__1 = (doublereal) maxwrk;
z__1.r = d__1, z__1.i = 0.;
work[1].r = z__1.r, work[1].i = z__1.i;
return 0;
/* End of ZGELSD */
} /* zgelsd_ */
/* Subroutine */ int zgeqr2_(integer *m, integer *n, doublecomplex *a,
integer *lda, doublecomplex *tau, doublecomplex *work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
doublecomplex z__1;
/* Builtin functions */
void d_cnjg(doublecomplex *, doublecomplex *);
/* Local variables */
static integer i__, k;
static doublecomplex alpha;
extern /* Subroutine */ int zlarf_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, doublecomplex *), xerbla_(char *, integer *), zlarfg_(integer *, doublecomplex *, doublecomplex *,
integer *, doublecomplex *);
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZGEQR2 computes a QR factorization of a complex m by n matrix A:
A = Q * R.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the m by n matrix A.
On exit, the elements on and above the diagonal of the array
contain the min(m,n) by n upper trapezoidal matrix R (R is
upper triangular if m >= n); the elements below the diagonal,
with the array TAU, represent the unitary matrix Q as a
product of elementary reflectors (see Further Details).
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU (output) COMPLEX*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace) COMPLEX*16 array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Further Details
===============
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
and tau in TAU(i).
=====================================================================
Test the input arguments
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*m)) {
*info = -4;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGEQR2", &i__1);
return 0;
}
k = min(*m,*n);
i__1 = k;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Generate elementary reflector H(i) to annihilate A(i+1:m,i) */
i__2 = *m - i__ + 1;
/* Computing MIN */
i__3 = i__ + 1;
zlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[min(i__3,*m) + i__ * a_dim1]
, &c__1, &tau[i__]);
if (i__ < *n) {
/* Apply H(i)' to A(i:m,i+1:n) from the left */
i__2 = i__ + i__ * a_dim1;
alpha.r = a[i__2].r, alpha.i = a[i__2].i;
i__2 = i__ + i__ * a_dim1;
a[i__2].r = 1., a[i__2].i = 0.;
i__2 = *m - i__ + 1;
i__3 = *n - i__;
d_cnjg(&z__1, &tau[i__]);
zlarf_("Left", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, &z__1,
&a[i__ + (i__ + 1) * a_dim1], lda, &work[1]);
i__2 = i__ + i__ * a_dim1;
a[i__2].r = alpha.r, a[i__2].i = alpha.i;
}
/* L10: */
}
return 0;
/* End of ZGEQR2 */
} /* zgeqr2_ */
/* Subroutine */ int zgeqrf_(integer *m, integer *n, doublecomplex *a,
integer *lda, doublecomplex *tau, doublecomplex *work, integer *lwork,
integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
/* Local variables */
static integer i__, k, ib, nb, nx, iws, nbmin, iinfo;
extern /* Subroutine */ int zgeqr2_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *), xerbla_(
char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
static integer ldwork;
extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
static integer lwkopt;
static logical lquery;
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZGEQRF computes a QR factorization of a complex M-by-N matrix A:
A = Q * R.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)-by-N upper trapezoidal matrix R (R is
upper triangular if m >= n); the elements below the diagonal,
with the array TAU, represent the unitary matrix Q as a
product of min(m,n) elementary reflectors (see Further
Details).
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU (output) COMPLEX*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,N).
For optimum performance LWORK >= N*NB, where NB is
the optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Further Details
===============
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
and tau in TAU(i).
=====================================================================
Test the input arguments
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
nb = ilaenv_(&c__1, "ZGEQRF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)
1);
lwkopt = *n * nb;
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
lquery = *lwork == -1;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*m)) {
*info = -4;
} else if ((*lwork < max(1,*n) && ! lquery)) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGEQRF", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
k = min(*m,*n);
if (k == 0) {
work[1].r = 1., work[1].i = 0.;
return 0;
}
nbmin = 2;
nx = 0;
iws = *n;
if ((nb > 1 && nb < k)) {
/*
Determine when to cross over from blocked to unblocked code.
Computing MAX
*/
i__1 = 0, i__2 = ilaenv_(&c__3, "ZGEQRF", " ", m, n, &c_n1, &c_n1, (
ftnlen)6, (ftnlen)1);
nx = max(i__1,i__2);
if (nx < k) {
/* Determine if workspace is large enough for blocked code. */
ldwork = *n;
iws = ldwork * nb;
if (*lwork < iws) {
/*
Not enough workspace to use optimal NB: reduce NB and
determine the minimum value of NB.
*/
nb = *lwork / ldwork;
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "ZGEQRF", " ", m, n, &c_n1, &
c_n1, (ftnlen)6, (ftnlen)1);
nbmin = max(i__1,i__2);
}
}
}
if (((nb >= nbmin && nb < k) && nx < k)) {
/* Use blocked code initially */
i__1 = k - nx;
i__2 = nb;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/* Computing MIN */
i__3 = k - i__ + 1;
ib = min(i__3,nb);
/*
Compute the QR factorization of the current block
A(i:m,i:i+ib-1)
*/
i__3 = *m - i__ + 1;
zgeqr2_(&i__3, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[
1], &iinfo);
if (i__ + ib <= *n) {
/*
Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1)
*/
i__3 = *m - i__ + 1;
zlarft_("Forward", "Columnwise", &i__3, &ib, &a[i__ + i__ *
a_dim1], lda, &tau[i__], &work[1], &ldwork);
/* Apply H' to A(i:m,i+ib:n) from the left */
i__3 = *m - i__ + 1;
i__4 = *n - i__ - ib + 1;
zlarfb_("Left", "Conjugate transpose", "Forward", "Columnwise"
, &i__3, &i__4, &ib, &a[i__ + i__ * a_dim1], lda, &
work[1], &ldwork, &a[i__ + (i__ + ib) * a_dim1], lda,
&work[ib + 1], &ldwork);
}
/* L10: */
}
} else {
i__ = 1;
}
/* Use unblocked code to factor the last or only block. */
if (i__ <= k) {
i__2 = *m - i__ + 1;
i__1 = *n - i__ + 1;
zgeqr2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1]
, &iinfo);
}
work[1].r = (doublereal) iws, work[1].i = 0.;
return 0;
/* End of ZGEQRF */
} /* zgeqrf_ */
/* Subroutine */ int zgesdd_(char *jobz, integer *m, integer *n,
doublecomplex *a, integer *lda, doublereal *s, doublecomplex *u,
integer *ldu, doublecomplex *vt, integer *ldvt, doublecomplex *work,
integer *lwork, doublereal *rwork, integer *iwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1,
i__2, i__3;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static integer i__, ie, il, ir, iu, blk;
static doublereal dum[1], eps;
static integer iru, ivt, iscl;
static doublereal anrm;
static integer idum[1], ierr, itau, irvt;
extern logical lsame_(char *, char *);
static integer chunk, minmn;
extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *,
integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
static integer wrkbl, itaup, itauq;
static logical wntqa;
static integer nwork;
static logical wntqn, wntqo, wntqs;
extern /* Subroutine */ int zlacp2_(char *, integer *, integer *,
doublereal *, integer *, doublecomplex *, integer *);
static integer mnthr1, mnthr2;
extern /* Subroutine */ int dbdsdc_(char *, char *, integer *, doublereal
*, doublereal *, doublereal *, integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, integer *, integer *);
extern /* Subroutine */ int dlascl_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublereal *,
integer *, integer *), xerbla_(char *, integer *),
zgebrd_(integer *, integer *, doublecomplex *, integer *,
doublereal *, doublereal *, doublecomplex *, doublecomplex *,
doublecomplex *, integer *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
static doublereal bignum;
extern doublereal zlange_(char *, integer *, integer *, doublecomplex *,
integer *, doublereal *);
extern /* Subroutine */ int zgelqf_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *, integer *
), zlacrm_(integer *, integer *, doublecomplex *, integer *,
doublereal *, integer *, doublecomplex *, integer *, doublereal *)
, zlarcm_(integer *, integer *, doublereal *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *), zlascl_(char *, integer *, integer *, doublereal *,
doublereal *, integer *, integer *, doublecomplex *, integer *,
integer *), zgeqrf_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *, integer *
);
static integer ldwrkl;
extern /* Subroutine */ int zlacpy_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *),
zlaset_(char *, integer *, integer *, doublecomplex *,
doublecomplex *, doublecomplex *, integer *);
static integer ldwrkr, minwrk, ldwrku, maxwrk;
extern /* Subroutine */ int zungbr_(char *, integer *, integer *, integer
*, doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, integer *);
static integer ldwkvt;
static doublereal smlnum;
static logical wntqas;
extern /* Subroutine */ int zunmbr_(char *, char *, char *, integer *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *
), zunglq_(integer *, integer *, integer *
, doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, integer *);
static logical lquery;
static integer nrwork;
extern /* Subroutine */ int zungqr_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, integer *);
/*
-- LAPACK driver routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
October 31, 1999
Purpose
=======
ZGESDD computes the singular value decomposition (SVD) of a complex
M-by-N matrix A, optionally computing the left and/or right singular
vectors, by using divide-and-conquer method. The SVD is written
A = U * SIGMA * conjugate-transpose(V)
where SIGMA is an M-by-N matrix which is zero except for its
min(m,n) diagonal elements, U is an M-by-M unitary matrix, and
V is an N-by-N unitary matrix. The diagonal elements of SIGMA
are the singular values of A; they are real and non-negative, and
are returned in descending order. The first min(m,n) columns of
U and V are the left and right singular vectors of A.
Note that the routine returns VT = V**H, not V.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Arguments
=========
JOBZ (input) CHARACTER*1
Specifies options for computing all or part of the matrix U:
= 'A': all M columns of U and all N rows of V**H are
returned in the arrays U and VT;
= 'S': the first min(M,N) columns of U and the first
min(M,N) rows of V**H are returned in the arrays U
and VT;
= 'O': If M >= N, the first N columns of U are overwritten
on the array A and all rows of V**H are returned in
the array VT;
otherwise, all columns of U are returned in the
array U and the first M rows of V**H are overwritten
in the array VT;
= 'N': no columns of U or rows of V**H are computed.
M (input) INTEGER
The number of rows of the input matrix A. M >= 0.
N (input) INTEGER
The number of columns of the input matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit,
if JOBZ = 'O', A is overwritten with the first N columns
of U (the left singular vectors, stored
columnwise) if M >= N;
A is overwritten with the first M rows
of V**H (the right singular vectors, stored
rowwise) otherwise.
if JOBZ .ne. 'O', the contents of A are destroyed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
S (output) DOUBLE PRECISION array, dimension (min(M,N))
The singular values of A, sorted so that S(i) >= S(i+1).
U (output) COMPLEX*16 array, dimension (LDU,UCOL)
UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N;
UCOL = min(M,N) if JOBZ = 'S'.
If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M
unitary matrix U;
if JOBZ = 'S', U contains the first min(M,N) columns of U
(the left singular vectors, stored columnwise);
if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced.
LDU (input) INTEGER
The leading dimension of the array U. LDU >= 1; if
JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M.
VT (output) COMPLEX*16 array, dimension (LDVT,N)
If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the
N-by-N unitary matrix V**H;
if JOBZ = 'S', VT contains the first min(M,N) rows of
V**H (the right singular vectors, stored rowwise);
if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced.
LDVT (input) INTEGER
The leading dimension of the array VT. LDVT >= 1; if
JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N;
if JOBZ = 'S', LDVT >= min(M,N).
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= 1.
if JOBZ = 'N', LWORK >= 2*min(M,N)+max(M,N).
if JOBZ = 'O',
LWORK >= 2*min(M,N)*min(M,N)+2*min(M,N)+max(M,N).
if JOBZ = 'S' or 'A',
LWORK >= min(M,N)*min(M,N)+2*min(M,N)+max(M,N).
For good performance, LWORK should generally be larger.
If LWORK < 0 but other input arguments are legal, WORK(1)
returns the optimal LWORK.
RWORK (workspace) DOUBLE PRECISION array, dimension (LRWORK)
If JOBZ = 'N', LRWORK >= 7*min(M,N).
Otherwise, LRWORK >= 5*min(M,N)*min(M,N) + 5*min(M,N)
IWORK (workspace) INTEGER array, dimension (8*min(M,N))
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: The updating process of DBDSDC did not converge.
Further Details
===============
Based on contributions by
Ming Gu and Huan Ren, Computer Science Division, University of
California at Berkeley, USA
=====================================================================
Test the input arguments
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--s;
u_dim1 = *ldu;
u_offset = 1 + u_dim1 * 1;
u -= u_offset;
vt_dim1 = *ldvt;
vt_offset = 1 + vt_dim1 * 1;
vt -= vt_offset;
--work;
--rwork;
--iwork;
/* Function Body */
*info = 0;
minmn = min(*m,*n);
mnthr1 = (integer) (minmn * 17. / 9.);
mnthr2 = (integer) (minmn * 5. / 3.);
wntqa = lsame_(jobz, "A");
wntqs = lsame_(jobz, "S");
wntqas = wntqa || wntqs;
wntqo = lsame_(jobz, "O");
wntqn = lsame_(jobz, "N");
minwrk = 1;
maxwrk = 1;
lquery = *lwork == -1;
if (! (wntqa || wntqs || wntqo || wntqn)) {
*info = -1;
} else if (*m < 0) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*lda < max(1,*m)) {
*info = -5;
} else if (*ldu < 1 || (wntqas && *ldu < *m) || ((wntqo && *m < *n) && *
ldu < *m)) {
*info = -8;
} else if (*ldvt < 1 || (wntqa && *ldvt < *n) || (wntqs && *ldvt < minmn)
|| ((wntqo && *m >= *n) && *ldvt < *n)) {
*info = -10;
}
/*
Compute workspace
(Note: Comments in the code beginning "Workspace:" describe the
minimal amount of workspace needed at that point in the code,
as well as the preferred amount for good performance.
CWorkspace refers to complex workspace, and RWorkspace to
real workspace. NB refers to the optimal block size for the
immediately following subroutine, as returned by ILAENV.)
*/
if (((*info == 0 && *m > 0) && *n > 0)) {
if (*m >= *n) {
/*
There is no complex work space needed for bidiagonal SVD
The real work space needed for bidiagonal SVD is BDSPAC,
BDSPAC = 3*N*N + 4*N
*/
if (*m >= mnthr1) {
if (wntqn) {
/* Path 1 (M much larger than N, JOBZ='N') */
wrkbl = *n + *n * ilaenv_(&c__1, "ZGEQRF", " ", m, n, &
c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
i__1 = wrkbl, i__2 = ((*n) << (1)) + ((*n) << (1)) *
ilaenv_(&c__1, "ZGEBRD", " ", n, n, &c_n1, &c_n1,
(ftnlen)6, (ftnlen)1);
wrkbl = max(i__1,i__2);
maxwrk = wrkbl;
minwrk = *n * 3;
} else if (wntqo) {
/* Path 2 (M much larger than N, JOBZ='O') */
wrkbl = *n + *n * ilaenv_(&c__1, "ZGEQRF", " ", m, n, &
c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n + *n * ilaenv_(&c__1, "ZUNGQR",
" ", m, n, n, &c_n1, (ftnlen)6, (ftnlen)1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = ((*n) << (1)) + ((*n) << (1)) *
ilaenv_(&c__1, "ZGEBRD", " ", n, n, &c_n1, &c_n1,
(ftnlen)6, (ftnlen)1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = ((*n) << (1)) + *n * ilaenv_(&c__1,
"ZUNMBR", "QLN", n, n, n, &c_n1, (ftnlen)6, (
ftnlen)3);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = ((*n) << (1)) + *n * ilaenv_(&c__1,
"ZUNMBR", "PRC", n, n, n, &c_n1, (ftnlen)6, (
ftnlen)3);
wrkbl = max(i__1,i__2);
maxwrk = *m * *n + *n * *n + wrkbl;
minwrk = ((*n) << (1)) * *n + *n * 3;
} else if (wntqs) {
/* Path 3 (M much larger than N, JOBZ='S') */
wrkbl = *n + *n * ilaenv_(&c__1, "ZGEQRF", " ", m, n, &
c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n + *n * ilaenv_(&c__1, "ZUNGQR",
" ", m, n, n, &c_n1, (ftnlen)6, (ftnlen)1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = ((*n) << (1)) + ((*n) << (1)) *
ilaenv_(&c__1, "ZGEBRD", " ", n, n, &c_n1, &c_n1,
(ftnlen)6, (ftnlen)1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = ((*n) << (1)) + *n * ilaenv_(&c__1,
"ZUNMBR", "QLN", n, n, n, &c_n1, (ftnlen)6, (
ftnlen)3);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = ((*n) << (1)) + *n * ilaenv_(&c__1,
"ZUNMBR", "PRC", n, n, n, &c_n1, (ftnlen)6, (
ftnlen)3);
wrkbl = max(i__1,i__2);
maxwrk = *n * *n + wrkbl;
minwrk = *n * *n + *n * 3;
} else if (wntqa) {
/* Path 4 (M much larger than N, JOBZ='A') */
wrkbl = *n + *n * ilaenv_(&c__1, "ZGEQRF", " ", m, n, &
c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n + *m * ilaenv_(&c__1, "ZUNGQR",
" ", m, m, n, &c_n1, (ftnlen)6, (ftnlen)1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = ((*n) << (1)) + ((*n) << (1)) *
ilaenv_(&c__1, "ZGEBRD", " ", n, n, &c_n1, &c_n1,
(ftnlen)6, (ftnlen)1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = ((*n) << (1)) + *n * ilaenv_(&c__1,
"ZUNMBR", "QLN", n, n, n, &c_n1, (ftnlen)6, (
ftnlen)3);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = ((*n) << (1)) + *n * ilaenv_(&c__1,
"ZUNMBR", "PRC", n, n, n, &c_n1, (ftnlen)6, (
ftnlen)3);
wrkbl = max(i__1,i__2);
maxwrk = *n * *n + wrkbl;
minwrk = *n * *n + ((*n) << (1)) + *m;
}
} else if (*m >= mnthr2) {
/* Path 5 (M much larger than N, but not as much as MNTHR1) */
maxwrk = ((*n) << (1)) + (*m + *n) * ilaenv_(&c__1, "ZGEBRD",
" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
minwrk = ((*n) << (1)) + *m;
if (wntqo) {
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*n) << (1)) + *n * ilaenv_(&c__1,
"ZUNGBR", "P", n, n, n, &c_n1, (ftnlen)6, (ftnlen)
1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*n) << (1)) + *n * ilaenv_(&c__1,
"ZUNGBR", "Q", m, n, n, &c_n1, (ftnlen)6, (ftnlen)
1);
maxwrk = max(i__1,i__2);
maxwrk += *m * *n;
minwrk += *n * *n;
} else if (wntqs) {
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*n) << (1)) + *n * ilaenv_(&c__1,
"ZUNGBR", "P", n, n, n, &c_n1, (ftnlen)6, (ftnlen)
1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*n) << (1)) + *n * ilaenv_(&c__1,
"ZUNGBR", "Q", m, n, n, &c_n1, (ftnlen)6, (ftnlen)
1);
maxwrk = max(i__1,i__2);
} else if (wntqa) {
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*n) << (1)) + *n * ilaenv_(&c__1,
"ZUNGBR", "P", n, n, n, &c_n1, (ftnlen)6, (ftnlen)
1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*n) << (1)) + *m * ilaenv_(&c__1,
"ZUNGBR", "Q", m, m, n, &c_n1, (ftnlen)6, (ftnlen)
1);
maxwrk = max(i__1,i__2);
}
} else {
/* Path 6 (M at least N, but not much larger) */
maxwrk = ((*n) << (1)) + (*m + *n) * ilaenv_(&c__1, "ZGEBRD",
" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
minwrk = ((*n) << (1)) + *m;
if (wntqo) {
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*n) << (1)) + *n * ilaenv_(&c__1,
"ZUNMBR", "PRC", n, n, n, &c_n1, (ftnlen)6, (
ftnlen)3);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*n) << (1)) + *n * ilaenv_(&c__1,
"ZUNMBR", "QLN", m, n, n, &c_n1, (ftnlen)6, (
ftnlen)3);
maxwrk = max(i__1,i__2);
maxwrk += *m * *n;
minwrk += *n * *n;
} else if (wntqs) {
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*n) << (1)) + *n * ilaenv_(&c__1,
"ZUNMBR", "PRC", n, n, n, &c_n1, (ftnlen)6, (
ftnlen)3);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*n) << (1)) + *n * ilaenv_(&c__1,
"ZUNMBR", "QLN", m, n, n, &c_n1, (ftnlen)6, (
ftnlen)3);
maxwrk = max(i__1,i__2);
} else if (wntqa) {
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*n) << (1)) + *n * ilaenv_(&c__1,
"ZUNGBR", "PRC", n, n, n, &c_n1, (ftnlen)6, (
ftnlen)3);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*n) << (1)) + *m * ilaenv_(&c__1,
"ZUNGBR", "QLN", m, m, n, &c_n1, (ftnlen)6, (
ftnlen)3);
maxwrk = max(i__1,i__2);
}
}
} else {
/*
There is no complex work space needed for bidiagonal SVD
The real work space needed for bidiagonal SVD is BDSPAC,
BDSPAC = 3*M*M + 4*M
*/
if (*n >= mnthr1) {
if (wntqn) {
/* Path 1t (N much larger than M, JOBZ='N') */
maxwrk = *m + *m * ilaenv_(&c__1, "ZGELQF", " ", m, n, &
c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*m) << (1)) + ((*m) << (1)) *
ilaenv_(&c__1, "ZGEBRD", " ", m, m, &c_n1, &c_n1,
(ftnlen)6, (ftnlen)1);
maxwrk = max(i__1,i__2);
minwrk = *m * 3;
} else if (wntqo) {
/* Path 2t (N much larger than M, JOBZ='O') */
wrkbl = *m + *m * ilaenv_(&c__1, "ZGELQF", " ", m, n, &
c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m + *m * ilaenv_(&c__1, "ZUNGLQ",
" ", m, n, m, &c_n1, (ftnlen)6, (ftnlen)1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = ((*m) << (1)) + ((*m) << (1)) *
ilaenv_(&c__1, "ZGEBRD", " ", m, m, &c_n1, &c_n1,
(ftnlen)6, (ftnlen)1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = ((*m) << (1)) + *m * ilaenv_(&c__1,
"ZUNMBR", "PRC", m, m, m, &c_n1, (ftnlen)6, (
ftnlen)3);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = ((*m) << (1)) + *m * ilaenv_(&c__1,
"ZUNMBR", "QLN", m, m, m, &c_n1, (ftnlen)6, (
ftnlen)3);
wrkbl = max(i__1,i__2);
maxwrk = *m * *n + *m * *m + wrkbl;
minwrk = ((*m) << (1)) * *m + *m * 3;
} else if (wntqs) {
/* Path 3t (N much larger than M, JOBZ='S') */
wrkbl = *m + *m * ilaenv_(&c__1, "ZGELQF", " ", m, n, &
c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m + *m * ilaenv_(&c__1, "ZUNGLQ",
" ", m, n, m, &c_n1, (ftnlen)6, (ftnlen)1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = ((*m) << (1)) + ((*m) << (1)) *
ilaenv_(&c__1, "ZGEBRD", " ", m, m, &c_n1, &c_n1,
(ftnlen)6, (ftnlen)1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = ((*m) << (1)) + *m * ilaenv_(&c__1,
"ZUNMBR", "PRC", m, m, m, &c_n1, (ftnlen)6, (
ftnlen)3);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = ((*m) << (1)) + *m * ilaenv_(&c__1,
"ZUNMBR", "QLN", m, m, m, &c_n1, (ftnlen)6, (
ftnlen)3);
wrkbl = max(i__1,i__2);
maxwrk = *m * *m + wrkbl;
minwrk = *m * *m + *m * 3;
} else if (wntqa) {
/* Path 4t (N much larger than M, JOBZ='A') */
wrkbl = *m + *m * ilaenv_(&c__1, "ZGELQF", " ", m, n, &
c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m + *n * ilaenv_(&c__1, "ZUNGLQ",
" ", n, n, m, &c_n1, (ftnlen)6, (ftnlen)1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = ((*m) << (1)) + ((*m) << (1)) *
ilaenv_(&c__1, "ZGEBRD", " ", m, m, &c_n1, &c_n1,
(ftnlen)6, (ftnlen)1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = ((*m) << (1)) + *m * ilaenv_(&c__1,
"ZUNMBR", "PRC", m, m, m, &c_n1, (ftnlen)6, (
ftnlen)3);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = ((*m) << (1)) + *m * ilaenv_(&c__1,
"ZUNMBR", "QLN", m, m, m, &c_n1, (ftnlen)6, (
ftnlen)3);
wrkbl = max(i__1,i__2);
maxwrk = *m * *m + wrkbl;
minwrk = *m * *m + ((*m) << (1)) + *n;
}
} else if (*n >= mnthr2) {
/* Path 5t (N much larger than M, but not as much as MNTHR1) */
maxwrk = ((*m) << (1)) + (*m + *n) * ilaenv_(&c__1, "ZGEBRD",
" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
minwrk = ((*m) << (1)) + *n;
if (wntqo) {
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*m) << (1)) + *m * ilaenv_(&c__1,
"ZUNGBR", "P", m, n, m, &c_n1, (ftnlen)6, (ftnlen)
1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*m) << (1)) + *m * ilaenv_(&c__1,
"ZUNGBR", "Q", m, m, n, &c_n1, (ftnlen)6, (ftnlen)
1);
maxwrk = max(i__1,i__2);
maxwrk += *m * *n;
minwrk += *m * *m;
} else if (wntqs) {
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*m) << (1)) + *m * ilaenv_(&c__1,
"ZUNGBR", "P", m, n, m, &c_n1, (ftnlen)6, (ftnlen)
1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*m) << (1)) + *m * ilaenv_(&c__1,
"ZUNGBR", "Q", m, m, n, &c_n1, (ftnlen)6, (ftnlen)
1);
maxwrk = max(i__1,i__2);
} else if (wntqa) {
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*m) << (1)) + *n * ilaenv_(&c__1,
"ZUNGBR", "P", n, n, m, &c_n1, (ftnlen)6, (ftnlen)
1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*m) << (1)) + *m * ilaenv_(&c__1,
"ZUNGBR", "Q", m, m, n, &c_n1, (ftnlen)6, (ftnlen)
1);
maxwrk = max(i__1,i__2);
}
} else {
/* Path 6t (N greater than M, but not much larger) */
maxwrk = ((*m) << (1)) + (*m + *n) * ilaenv_(&c__1, "ZGEBRD",
" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
minwrk = ((*m) << (1)) + *n;
if (wntqo) {
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*m) << (1)) + *m * ilaenv_(&c__1,
"ZUNMBR", "PRC", m, n, m, &c_n1, (ftnlen)6, (
ftnlen)3);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*m) << (1)) + *m * ilaenv_(&c__1,
"ZUNMBR", "QLN", m, m, n, &c_n1, (ftnlen)6, (
ftnlen)3);
maxwrk = max(i__1,i__2);
maxwrk += *m * *n;
minwrk += *m * *m;
} else if (wntqs) {
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*m) << (1)) + *m * ilaenv_(&c__1,
"ZUNGBR", "PRC", m, n, m, &c_n1, (ftnlen)6, (
ftnlen)3);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*m) << (1)) + *m * ilaenv_(&c__1,
"ZUNGBR", "QLN", m, m, n, &c_n1, (ftnlen)6, (
ftnlen)3);
maxwrk = max(i__1,i__2);
} else if (wntqa) {
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*m) << (1)) + *n * ilaenv_(&c__1,
"ZUNGBR", "PRC", n, n, m, &c_n1, (ftnlen)6, (
ftnlen)3);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = ((*m) << (1)) + *m * ilaenv_(&c__1,
"ZUNGBR", "QLN", m, m, n, &c_n1, (ftnlen)6, (
ftnlen)3);
maxwrk = max(i__1,i__2);
}
}
}
maxwrk = max(maxwrk,minwrk);
work[1].r = (doublereal) maxwrk, work[1].i = 0.;
}
if ((*lwork < minwrk && ! lquery)) {
*info = -13;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGESDD", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0) {
if (*lwork >= 1) {
work[1].r = 1., work[1].i = 0.;
}
return 0;
}
/* Get machine constants */
eps = PRECISION;
smlnum = sqrt(SAFEMINIMUM) / eps;
bignum = 1. / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
anrm = zlange_("M", m, n, &a[a_offset], lda, dum);
iscl = 0;
if ((anrm > 0. && anrm < smlnum)) {
iscl = 1;
zlascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, &
ierr);
} else if (anrm > bignum) {
iscl = 1;
zlascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, &
ierr);
}
if (*m >= *n) {
/*
A has at least as many rows as columns. If A has sufficiently
more rows than columns, first reduce using the QR
decomposition (if sufficient workspace available)
*/
if (*m >= mnthr1) {
if (wntqn) {
/*
Path 1 (M much larger than N, JOBZ='N')
No singular vectors to be computed
*/
itau = 1;
nwork = itau + *n;
/*
Compute A=Q*R
(CWorkspace: need 2*N, prefer N+N*NB)
(RWorkspace: need 0)
*/
i__1 = *lwork - nwork + 1;
zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
i__1, &ierr);
/* Zero out below R */
i__1 = *n - 1;
i__2 = *n - 1;
zlaset_("L", &i__1, &i__2, &c_b59, &c_b59, &a[a_dim1 + 2],
lda);
ie = 1;
itauq = 1;
itaup = itauq + *n;
nwork = itaup + *n;
/*
Bidiagonalize R in A
(CWorkspace: need 3*N, prefer 2*N+2*N*NB)
(RWorkspace: need N)
*/
i__1 = *lwork - nwork + 1;
zgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[
itauq], &work[itaup], &work[nwork], &i__1, &ierr);
nrwork = ie + *n;
/*
Perform bidiagonal SVD, compute singular values only
(CWorkspace: 0)
(RWorkspace: need BDSPAC)
*/
dbdsdc_("U", "N", n, &s[1], &rwork[ie], dum, &c__1, dum, &
c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
} else if (wntqo) {
/*
Path 2 (M much larger than N, JOBZ='O')
N left singular vectors to be overwritten on A and
N right singular vectors to be computed in VT
*/
iu = 1;
/* WORK(IU) is N by N */
ldwrku = *n;
ir = iu + ldwrku * *n;
if (*lwork >= *m * *n + *n * *n + *n * 3) {
/* WORK(IR) is M by N */
ldwrkr = *m;
} else {
ldwrkr = (*lwork - *n * *n - *n * 3) / *n;
}
itau = ir + ldwrkr * *n;
nwork = itau + *n;
/*
Compute A=Q*R
(CWorkspace: need N*N+2*N, prefer M*N+N+N*NB)
(RWorkspace: 0)
*/
i__1 = *lwork - nwork + 1;
zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
i__1, &ierr);
/* Copy R to WORK( IR ), zeroing out below it */
zlacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr);
i__1 = *n - 1;
i__2 = *n - 1;
zlaset_("L", &i__1, &i__2, &c_b59, &c_b59, &work[ir + 1], &
ldwrkr);
/*
Generate Q in A
(CWorkspace: need 2*N, prefer N+N*NB)
(RWorkspace: 0)
*/
i__1 = *lwork - nwork + 1;
zungqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[nwork],
&i__1, &ierr);
ie = 1;
itauq = itau;
itaup = itauq + *n;
nwork = itaup + *n;
/*
Bidiagonalize R in WORK(IR)
(CWorkspace: need N*N+3*N, prefer M*N+2*N+2*N*NB)
(RWorkspace: need N)
*/
i__1 = *lwork - nwork + 1;
zgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &rwork[ie], &work[
itauq], &work[itaup], &work[nwork], &i__1, &ierr);
/*
Perform bidiagonal SVD, computing left singular vectors
of R in WORK(IRU) and computing right singular vectors
of R in WORK(IRVT)
(CWorkspace: need 0)
(RWorkspace: need BDSPAC)
*/
iru = ie + *n;
irvt = iru + *n * *n;
nrwork = irvt + *n * *n;
dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
info);
/*
Copy real matrix RWORK(IRU) to complex matrix WORK(IU)
Overwrite WORK(IU) by the left singular vectors of R
(CWorkspace: need 2*N*N+3*N, prefer M*N+N*N+2*N+N*NB)
(RWorkspace: 0)
*/
zlacp2_("F", n, n, &rwork[iru], n, &work[iu], &ldwrku);
i__1 = *lwork - nwork + 1;
zunmbr_("Q", "L", "N", n, n, n, &work[ir], &ldwrkr, &work[
itauq], &work[iu], &ldwrku, &work[nwork], &i__1, &
ierr);
/*
Copy real matrix RWORK(IRVT) to complex matrix VT
Overwrite VT by the right singular vectors of R
(CWorkspace: need N*N+3*N, prefer M*N+2*N+N*NB)
(RWorkspace: 0)
*/
zlacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
i__1 = *lwork - nwork + 1;
zunmbr_("P", "R", "C", n, n, n, &work[ir], &ldwrkr, &work[
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
ierr);
/*
Multiply Q in A by left singular vectors of R in
WORK(IU), storing result in WORK(IR) and copying to A
(CWorkspace: need 2*N*N, prefer N*N+M*N)
(RWorkspace: 0)
*/
i__1 = *m;
i__2 = ldwrkr;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
i__2) {
/* Computing MIN */
i__3 = *m - i__ + 1;
chunk = min(i__3,ldwrkr);
zgemm_("N", "N", &chunk, n, n, &c_b60, &a[i__ + a_dim1],
lda, &work[iu], &ldwrku, &c_b59, &work[ir], &
ldwrkr);
zlacpy_("F", &chunk, n, &work[ir], &ldwrkr, &a[i__ +
a_dim1], lda);
/* L10: */
}
} else if (wntqs) {
/*
Path 3 (M much larger than N, JOBZ='S')
N left singular vectors to be computed in U and
N right singular vectors to be computed in VT
*/
ir = 1;
/* WORK(IR) is N by N */
ldwrkr = *n;
itau = ir + ldwrkr * *n;
nwork = itau + *n;
/*
Compute A=Q*R
(CWorkspace: need N*N+2*N, prefer N*N+N+N*NB)
(RWorkspace: 0)
*/
i__2 = *lwork - nwork + 1;
zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
i__2, &ierr);
/* Copy R to WORK(IR), zeroing out below it */
zlacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr);
i__2 = *n - 1;
i__1 = *n - 1;
zlaset_("L", &i__2, &i__1, &c_b59, &c_b59, &work[ir + 1], &
ldwrkr);
/*
Generate Q in A
(CWorkspace: need 2*N, prefer N+N*NB)
(RWorkspace: 0)
*/
i__2 = *lwork - nwork + 1;
zungqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[nwork],
&i__2, &ierr);
ie = 1;
itauq = itau;
itaup = itauq + *n;
nwork = itaup + *n;
/*
Bidiagonalize R in WORK(IR)
(CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB)
(RWorkspace: need N)
*/
i__2 = *lwork - nwork + 1;
zgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &rwork[ie], &work[
itauq], &work[itaup], &work[nwork], &i__2, &ierr);
/*
Perform bidiagonal SVD, computing left singular vectors
of bidiagonal matrix in RWORK(IRU) and computing right
singular vectors of bidiagonal matrix in RWORK(IRVT)
(CWorkspace: need 0)
(RWorkspace: need BDSPAC)
*/
iru = ie + *n;
irvt = iru + *n * *n;
nrwork = irvt + *n * *n;
dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
info);
/*
Copy real matrix RWORK(IRU) to complex matrix U
Overwrite U by left singular vectors of R
(CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB)
(RWorkspace: 0)
*/
zlacp2_("F", n, n, &rwork[iru], n, &u[u_offset], ldu);
i__2 = *lwork - nwork + 1;
zunmbr_("Q", "L", "N", n, n, n, &work[ir], &ldwrkr, &work[
itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
/*
Copy real matrix RWORK(IRVT) to complex matrix VT
Overwrite VT by right singular vectors of R
(CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB)
(RWorkspace: 0)
*/
zlacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
i__2 = *lwork - nwork + 1;
zunmbr_("P", "R", "C", n, n, n, &work[ir], &ldwrkr, &work[
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
ierr);
/*
Multiply Q in A by left singular vectors of R in
WORK(IR), storing result in U
(CWorkspace: need N*N)
(RWorkspace: 0)
*/
zlacpy_("F", n, n, &u[u_offset], ldu, &work[ir], &ldwrkr);
zgemm_("N", "N", m, n, n, &c_b60, &a[a_offset], lda, &work[ir]
, &ldwrkr, &c_b59, &u[u_offset], ldu);
} else if (wntqa) {
/*
Path 4 (M much larger than N, JOBZ='A')
M left singular vectors to be computed in U and
N right singular vectors to be computed in VT
*/
iu = 1;
/* WORK(IU) is N by N */
ldwrku = *n;
itau = iu + ldwrku * *n;
nwork = itau + *n;
/*
Compute A=Q*R, copying result to U
(CWorkspace: need 2*N, prefer N+N*NB)
(RWorkspace: 0)
*/
i__2 = *lwork - nwork + 1;
zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
i__2, &ierr);
zlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu);
/*
Generate Q in U
(CWorkspace: need N+M, prefer N+M*NB)
(RWorkspace: 0)
*/
i__2 = *lwork - nwork + 1;
zungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &work[nwork],
&i__2, &ierr);
/* Produce R in A, zeroing out below it */
i__2 = *n - 1;
i__1 = *n - 1;
zlaset_("L", &i__2, &i__1, &c_b59, &c_b59, &a[a_dim1 + 2],
lda);
ie = 1;
itauq = itau;
itaup = itauq + *n;
nwork = itaup + *n;
/*
Bidiagonalize R in A
(CWorkspace: need 3*N, prefer 2*N+2*N*NB)
(RWorkspace: need N)
*/
i__2 = *lwork - nwork + 1;
zgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[
itauq], &work[itaup], &work[nwork], &i__2, &ierr);
iru = ie + *n;
irvt = iru + *n * *n;
nrwork = irvt + *n * *n;
/*
Perform bidiagonal SVD, computing left singular vectors
of bidiagonal matrix in RWORK(IRU) and computing right
singular vectors of bidiagonal matrix in RWORK(IRVT)
(CWorkspace: need 0)
(RWorkspace: need BDSPAC)
*/
dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
info);
/*
Copy real matrix RWORK(IRU) to complex matrix WORK(IU)
Overwrite WORK(IU) by left singular vectors of R
(CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB)
(RWorkspace: 0)
*/
zlacp2_("F", n, n, &rwork[iru], n, &work[iu], &ldwrku);
i__2 = *lwork - nwork + 1;
zunmbr_("Q", "L", "N", n, n, n, &a[a_offset], lda, &work[
itauq], &work[iu], &ldwrku, &work[nwork], &i__2, &
ierr);
/*
Copy real matrix RWORK(IRVT) to complex matrix VT
Overwrite VT by right singular vectors of R
(CWorkspace: need 3*N, prefer 2*N+N*NB)
(RWorkspace: 0)
*/
zlacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
i__2 = *lwork - nwork + 1;
zunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
ierr);
/*
Multiply Q in U by left singular vectors of R in
WORK(IU), storing result in A
(CWorkspace: need N*N)
(RWorkspace: 0)
*/
zgemm_("N", "N", m, n, n, &c_b60, &u[u_offset], ldu, &work[iu]
, &ldwrku, &c_b59, &a[a_offset], lda);
/* Copy left singular vectors of A from A to U */
zlacpy_("F", m, n, &a[a_offset], lda, &u[u_offset], ldu);
}
} else if (*m >= mnthr2) {
/*
MNTHR2 <= M < MNTHR1
Path 5 (M much larger than N, but not as much as MNTHR1)
Reduce to bidiagonal form without QR decomposition, use
ZUNGBR and matrix multiplication to compute singular vectors
*/
ie = 1;
nrwork = ie + *n;
itauq = 1;
itaup = itauq + *n;
nwork = itaup + *n;
/*
Bidiagonalize A
(CWorkspace: need 2*N+M, prefer 2*N+(M+N)*NB)
(RWorkspace: need N)
*/
i__2 = *lwork - nwork + 1;
zgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
&work[itaup], &work[nwork], &i__2, &ierr);
if (wntqn) {
/*
Compute singular values only
(Cworkspace: 0)
(Rworkspace: need BDSPAC)
*/
dbdsdc_("U", "N", n, &s[1], &rwork[ie], dum, &c__1, dum, &
c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
} else if (wntqo) {
iu = nwork;
iru = nrwork;
irvt = iru + *n * *n;
nrwork = irvt + *n * *n;
/*
Copy A to VT, generate P**H
(Cworkspace: need 2*N, prefer N+N*NB)
(Rworkspace: 0)
*/
zlacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
i__2 = *lwork - nwork + 1;
zungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &
work[nwork], &i__2, &ierr);
/*
Generate Q in A
(CWorkspace: need 2*N, prefer N+N*NB)
(RWorkspace: 0)
*/
i__2 = *lwork - nwork + 1;
zungbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], &work[
nwork], &i__2, &ierr);
if (*lwork >= *m * *n + *n * 3) {
/* WORK( IU ) is M by N */
ldwrku = *m;
} else {
/* WORK(IU) is LDWRKU by N */
ldwrku = (*lwork - *n * 3) / *n;
}
nwork = iu + ldwrku * *n;
/*
Perform bidiagonal SVD, computing left singular vectors
of bidiagonal matrix in RWORK(IRU) and computing right
singular vectors of bidiagonal matrix in RWORK(IRVT)
(CWorkspace: need 0)
(RWorkspace: need BDSPAC)
*/
dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
info);
/*
Multiply real matrix RWORK(IRVT) by P**H in VT,
storing the result in WORK(IU), copying to VT
(Cworkspace: need 0)
(Rworkspace: need 3*N*N)
*/
zlarcm_(n, n, &rwork[irvt], n, &vt[vt_offset], ldvt, &work[iu]
, &ldwrku, &rwork[nrwork]);
zlacpy_("F", n, n, &work[iu], &ldwrku, &vt[vt_offset], ldvt);
/*
Multiply Q in A by real matrix RWORK(IRU), storing the
result in WORK(IU), copying to A
(CWorkspace: need N*N, prefer M*N)
(Rworkspace: need 3*N*N, prefer N*N+2*M*N)
*/
nrwork = irvt;
i__2 = *m;
i__1 = ldwrku;
for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
i__1) {
/* Computing MIN */
i__3 = *m - i__ + 1;
chunk = min(i__3,ldwrku);
zlacrm_(&chunk, n, &a[i__ + a_dim1], lda, &rwork[iru], n,
&work[iu], &ldwrku, &rwork[nrwork]);
zlacpy_("F", &chunk, n, &work[iu], &ldwrku, &a[i__ +
a_dim1], lda);
/* L20: */
}
} else if (wntqs) {
/*
Copy A to VT, generate P**H
(Cworkspace: need 2*N, prefer N+N*NB)
(Rworkspace: 0)
*/
zlacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
i__1 = *lwork - nwork + 1;
zungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &
work[nwork], &i__1, &ierr);
/*
Copy A to U, generate Q
(Cworkspace: need 2*N, prefer N+N*NB)
(Rworkspace: 0)
*/
zlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu);
i__1 = *lwork - nwork + 1;
zungbr_("Q", m, n, n, &u[u_offset], ldu, &work[itauq], &work[
nwork], &i__1, &ierr);
/*
Perform bidiagonal SVD, computing left singular vectors
of bidiagonal matrix in RWORK(IRU) and computing right
singular vectors of bidiagonal matrix in RWORK(IRVT)
(CWorkspace: need 0)
(RWorkspace: need BDSPAC)
*/
iru = nrwork;
irvt = iru + *n * *n;
nrwork = irvt + *n * *n;
dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
info);
/*
Multiply real matrix RWORK(IRVT) by P**H in VT,
storing the result in A, copying to VT
(Cworkspace: need 0)
(Rworkspace: need 3*N*N)
*/
zlarcm_(n, n, &rwork[irvt], n, &vt[vt_offset], ldvt, &a[
a_offset], lda, &rwork[nrwork]);
zlacpy_("F", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
/*
Multiply Q in U by real matrix RWORK(IRU), storing the
result in A, copying to U
(CWorkspace: need 0)
(Rworkspace: need N*N+2*M*N)
*/
nrwork = irvt;
zlacrm_(m, n, &u[u_offset], ldu, &rwork[iru], n, &a[a_offset],
lda, &rwork[nrwork]);
zlacpy_("F", m, n, &a[a_offset], lda, &u[u_offset], ldu);
} else {
/*
Copy A to VT, generate P**H
(Cworkspace: need 2*N, prefer N+N*NB)
(Rworkspace: 0)
*/
zlacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
i__1 = *lwork - nwork + 1;
zungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &
work[nwork], &i__1, &ierr);
/*
Copy A to U, generate Q
(Cworkspace: need 2*N, prefer N+N*NB)
(Rworkspace: 0)
*/
zlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu);
i__1 = *lwork - nwork + 1;
zungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
nwork], &i__1, &ierr);
/*
Perform bidiagonal SVD, computing left singular vectors
of bidiagonal matrix in RWORK(IRU) and computing right
singular vectors of bidiagonal matrix in RWORK(IRVT)
(CWorkspace: need 0)
(RWorkspace: need BDSPAC)
*/
iru = nrwork;
irvt = iru + *n * *n;
nrwork = irvt + *n * *n;
dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
info);
/*
Multiply real matrix RWORK(IRVT) by P**H in VT,
storing the result in A, copying to VT
(Cworkspace: need 0)
(Rworkspace: need 3*N*N)
*/
zlarcm_(n, n, &rwork[irvt], n, &vt[vt_offset], ldvt, &a[
a_offset], lda, &rwork[nrwork]);
zlacpy_("F", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
/*
Multiply Q in U by real matrix RWORK(IRU), storing the
result in A, copying to U
(CWorkspace: 0)
(Rworkspace: need 3*N*N)
*/
nrwork = irvt;
zlacrm_(m, n, &u[u_offset], ldu, &rwork[iru], n, &a[a_offset],
lda, &rwork[nrwork]);
zlacpy_("F", m, n, &a[a_offset], lda, &u[u_offset], ldu);
}
} else {
/*
M .LT. MNTHR2
Path 6 (M at least N, but not much larger)
Reduce to bidiagonal form without QR decomposition
Use ZUNMBR to compute singular vectors
*/
ie = 1;
nrwork = ie + *n;
itauq = 1;
itaup = itauq + *n;
nwork = itaup + *n;
/*
Bidiagonalize A
(CWorkspace: need 2*N+M, prefer 2*N+(M+N)*NB)
(RWorkspace: need N)
*/
i__1 = *lwork - nwork + 1;
zgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
&work[itaup], &work[nwork], &i__1, &ierr);
if (wntqn) {
/*
Compute singular values only
(Cworkspace: 0)
(Rworkspace: need BDSPAC)
*/
dbdsdc_("U", "N", n, &s[1], &rwork[ie], dum, &c__1, dum, &
c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
} else if (wntqo) {
iu = nwork;
iru = nrwork;
irvt = iru + *n * *n;
nrwork = irvt + *n * *n;
if (*lwork >= *m * *n + *n * 3) {
/* WORK( IU ) is M by N */
ldwrku = *m;
} else {
/* WORK( IU ) is LDWRKU by N */
ldwrku = (*lwork - *n * 3) / *n;
}
nwork = iu + ldwrku * *n;
/*
Perform bidiagonal SVD, computing left singular vectors
of bidiagonal matrix in RWORK(IRU) and computing right
singular vectors of bidiagonal matrix in RWORK(IRVT)
(CWorkspace: need 0)
(RWorkspace: need BDSPAC)
*/
dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
info);
/*
Copy real matrix RWORK(IRVT) to complex matrix VT
Overwrite VT by right singular vectors of A
(Cworkspace: need 2*N, prefer N+N*NB)
(Rworkspace: need 0)
*/
zlacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
i__1 = *lwork - nwork + 1;
zunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
ierr);
if (*lwork >= *m * *n + *n * 3) {
/*
Copy real matrix RWORK(IRU) to complex matrix WORK(IU)
Overwrite WORK(IU) by left singular vectors of A, copying
to A
(Cworkspace: need M*N+2*N, prefer M*N+N+N*NB)
(Rworkspace: need 0)
*/
zlaset_("F", m, n, &c_b59, &c_b59, &work[iu], &ldwrku);
zlacp2_("F", n, n, &rwork[iru], n, &work[iu], &ldwrku);
i__1 = *lwork - nwork + 1;
zunmbr_("Q", "L", "N", m, n, n, &a[a_offset], lda, &work[
itauq], &work[iu], &ldwrku, &work[nwork], &i__1, &
ierr);
zlacpy_("F", m, n, &work[iu], &ldwrku, &a[a_offset], lda);
} else {
/*
Generate Q in A
(Cworkspace: need 2*N, prefer N+N*NB)
(Rworkspace: need 0)
*/
i__1 = *lwork - nwork + 1;
zungbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], &
work[nwork], &i__1, &ierr);
/*
Multiply Q in A by real matrix RWORK(IRU), storing the
result in WORK(IU), copying to A
(CWorkspace: need N*N, prefer M*N)
(Rworkspace: need 3*N*N, prefer N*N+2*M*N)
*/
nrwork = irvt;
i__1 = *m;
i__2 = ldwrku;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
i__2) {
/* Computing MIN */
i__3 = *m - i__ + 1;
chunk = min(i__3,ldwrku);
zlacrm_(&chunk, n, &a[i__ + a_dim1], lda, &rwork[iru],
n, &work[iu], &ldwrku, &rwork[nrwork]);
zlacpy_("F", &chunk, n, &work[iu], &ldwrku, &a[i__ +
a_dim1], lda);
/* L30: */
}
}
} else if (wntqs) {
/*
Perform bidiagonal SVD, computing left singular vectors
of bidiagonal matrix in RWORK(IRU) and computing right
singular vectors of bidiagonal matrix in RWORK(IRVT)
(CWorkspace: need 0)
(RWorkspace: need BDSPAC)
*/
iru = nrwork;
irvt = iru + *n * *n;
nrwork = irvt + *n * *n;
dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
info);
/*
Copy real matrix RWORK(IRU) to complex matrix U
Overwrite U by left singular vectors of A
(CWorkspace: need 3*N, prefer 2*N+N*NB)
(RWorkspace: 0)
*/
zlaset_("F", m, n, &c_b59, &c_b59, &u[u_offset], ldu);
zlacp2_("F", n, n, &rwork[iru], n, &u[u_offset], ldu);
i__2 = *lwork - nwork + 1;
zunmbr_("Q", "L", "N", m, n, n, &a[a_offset], lda, &work[
itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
/*
Copy real matrix RWORK(IRVT) to complex matrix VT
Overwrite VT by right singular vectors of A
(CWorkspace: need 3*N, prefer 2*N+N*NB)
(RWorkspace: 0)
*/
zlacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
i__2 = *lwork - nwork + 1;
zunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
ierr);
} else {
/*
Perform bidiagonal SVD, computing left singular vectors
of bidiagonal matrix in RWORK(IRU) and computing right
singular vectors of bidiagonal matrix in RWORK(IRVT)
(CWorkspace: need 0)
(RWorkspace: need BDSPAC)
*/
iru = nrwork;
irvt = iru + *n * *n;
nrwork = irvt + *n * *n;
dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
info);
/* Set the right corner of U to identity matrix */
zlaset_("F", m, m, &c_b59, &c_b59, &u[u_offset], ldu);
i__2 = *m - *n;
i__1 = *m - *n;
zlaset_("F", &i__2, &i__1, &c_b59, &c_b60, &u[*n + 1 + (*n +
1) * u_dim1], ldu);
/*
Copy real matrix RWORK(IRU) to complex matrix U
Overwrite U by left singular vectors of A
(CWorkspace: need 2*N+M, prefer 2*N+M*NB)
(RWorkspace: 0)
*/
zlacp2_("F", n, n, &rwork[iru], n, &u[u_offset], ldu);
i__2 = *lwork - nwork + 1;
zunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
/*
Copy real matrix RWORK(IRVT) to complex matrix VT
Overwrite VT by right singular vectors of A
(CWorkspace: need 3*N, prefer 2*N+N*NB)
(RWorkspace: 0)
*/
zlacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
i__2 = *lwork - nwork + 1;
zunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
ierr);
}
}
} else {
/*
A has more columns than rows. If A has sufficiently more
columns than rows, first reduce using the LQ decomposition
(if sufficient workspace available)
*/
if (*n >= mnthr1) {
if (wntqn) {
/*
Path 1t (N much larger than M, JOBZ='N')
No singular vectors to be computed
*/
itau = 1;
nwork = itau + *m;
/*
Compute A=L*Q
(CWorkspace: need 2*M, prefer M+M*NB)
(RWorkspace: 0)
*/
i__2 = *lwork - nwork + 1;
zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
i__2, &ierr);
/* Zero out above L */
i__2 = *m - 1;
i__1 = *m - 1;
zlaset_("U", &i__2, &i__1, &c_b59, &c_b59, &a[((a_dim1) << (1)
) + 1], lda);
ie = 1;
itauq = 1;
itaup = itauq + *m;
nwork = itaup + *m;
/*
Bidiagonalize L in A
(CWorkspace: need 3*M, prefer 2*M+2*M*NB)
(RWorkspace: need M)
*/
i__2 = *lwork - nwork + 1;
zgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &work[
itauq], &work[itaup], &work[nwork], &i__2, &ierr);
nrwork = ie + *m;
/*
Perform bidiagonal SVD, compute singular values only
(CWorkspace: 0)
(RWorkspace: need BDSPAC)
*/
dbdsdc_("U", "N", m, &s[1], &rwork[ie], dum, &c__1, dum, &
c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
} else if (wntqo) {
/*
Path 2t (N much larger than M, JOBZ='O')
M right singular vectors to be overwritten on A and
M left singular vectors to be computed in U
*/
ivt = 1;
ldwkvt = *m;
/* WORK(IVT) is M by M */
il = ivt + ldwkvt * *m;
if (*lwork >= *m * *n + *m * *m + *m * 3) {
/* WORK(IL) M by N */
ldwrkl = *m;
chunk = *n;
} else {
/* WORK(IL) is M by CHUNK */
ldwrkl = *m;
chunk = (*lwork - *m * *m - *m * 3) / *m;
}
itau = il + ldwrkl * chunk;
nwork = itau + *m;
/*
Compute A=L*Q
(CWorkspace: need 2*M, prefer M+M*NB)
(RWorkspace: 0)
*/
i__2 = *lwork - nwork + 1;
zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
i__2, &ierr);
/* Copy L to WORK(IL), zeroing about above it */
zlacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwrkl);
i__2 = *m - 1;
i__1 = *m - 1;
zlaset_("U", &i__2, &i__1, &c_b59, &c_b59, &work[il + ldwrkl],
&ldwrkl);
/*
Generate Q in A
(CWorkspace: need M*M+2*M, prefer M*M+M+M*NB)
(RWorkspace: 0)
*/
i__2 = *lwork - nwork + 1;
zunglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[nwork],
&i__2, &ierr);
ie = 1;
itauq = itau;
itaup = itauq + *m;
nwork = itaup + *m;
/*
Bidiagonalize L in WORK(IL)
(CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB)
(RWorkspace: need M)
*/
i__2 = *lwork - nwork + 1;
zgebrd_(m, m, &work[il], &ldwrkl, &s[1], &rwork[ie], &work[
itauq], &work[itaup], &work[nwork], &i__2, &ierr);
/*
Perform bidiagonal SVD, computing left singular vectors
of bidiagonal matrix in RWORK(IRU) and computing right
singular vectors of bidiagonal matrix in RWORK(IRVT)
(CWorkspace: need 0)
(RWorkspace: need BDSPAC)
*/
iru = ie + *m;
irvt = iru + *m * *m;
nrwork = irvt + *m * *m;
dbdsdc_("U", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
info);
/*
Copy real matrix RWORK(IRU) to complex matrix WORK(IU)
Overwrite WORK(IU) by the left singular vectors of L
(CWorkspace: need N*N+3*N, prefer M*N+2*N+N*NB)
(RWorkspace: 0)
*/
zlacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
i__2 = *lwork - nwork + 1;
zunmbr_("Q", "L", "N", m, m, m, &work[il], &ldwrkl, &work[
itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
/*
Copy real matrix RWORK(IRVT) to complex matrix WORK(IVT)
Overwrite WORK(IVT) by the right singular vectors of L
(CWorkspace: need N*N+3*N, prefer M*N+2*N+N*NB)
(RWorkspace: 0)
*/
zlacp2_("F", m, m, &rwork[irvt], m, &work[ivt], &ldwkvt);
i__2 = *lwork - nwork + 1;
zunmbr_("P", "R", "C", m, m, m, &work[il], &ldwrkl, &work[
itaup], &work[ivt], &ldwkvt, &work[nwork], &i__2, &
ierr);
/*
Multiply right singular vectors of L in WORK(IL) by Q
in A, storing result in WORK(IL) and copying to A
(CWorkspace: need 2*M*M, prefer M*M+M*N))
(RWorkspace: 0)
*/
i__2 = *n;
i__1 = chunk;
for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
i__1) {
/* Computing MIN */
i__3 = *n - i__ + 1;
blk = min(i__3,chunk);
zgemm_("N", "N", m, &blk, m, &c_b60, &work[ivt], m, &a[
i__ * a_dim1 + 1], lda, &c_b59, &work[il], &
ldwrkl);
zlacpy_("F", m, &blk, &work[il], &ldwrkl, &a[i__ * a_dim1
+ 1], lda);
/* L40: */
}
} else if (wntqs) {
/*
Path 3t (N much larger than M, JOBZ='S')
M right singular vectors to be computed in VT and
M left singular vectors to be computed in U
*/
il = 1;
/* WORK(IL) is M by M */
ldwrkl = *m;
itau = il + ldwrkl * *m;
nwork = itau + *m;
/*
Compute A=L*Q
(CWorkspace: need 2*M, prefer M+M*NB)
(RWorkspace: 0)
*/
i__1 = *lwork - nwork + 1;
zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
i__1, &ierr);
/* Copy L to WORK(IL), zeroing out above it */
zlacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwrkl);
i__1 = *m - 1;
i__2 = *m - 1;
zlaset_("U", &i__1, &i__2, &c_b59, &c_b59, &work[il + ldwrkl],
&ldwrkl);
/*
Generate Q in A
(CWorkspace: need M*M+2*M, prefer M*M+M+M*NB)
(RWorkspace: 0)
*/
i__1 = *lwork - nwork + 1;
zunglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[nwork],
&i__1, &ierr);
ie = 1;
itauq = itau;
itaup = itauq + *m;
nwork = itaup + *m;
/*
Bidiagonalize L in WORK(IL)
(CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB)
(RWorkspace: need M)
*/
i__1 = *lwork - nwork + 1;
zgebrd_(m, m, &work[il], &ldwrkl, &s[1], &rwork[ie], &work[
itauq], &work[itaup], &work[nwork], &i__1, &ierr);
/*
Perform bidiagonal SVD, computing left singular vectors
of bidiagonal matrix in RWORK(IRU) and computing right
singular vectors of bidiagonal matrix in RWORK(IRVT)
(CWorkspace: need 0)
(RWorkspace: need BDSPAC)
*/
iru = ie + *m;
irvt = iru + *m * *m;
nrwork = irvt + *m * *m;
dbdsdc_("U", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
info);
/*
Copy real matrix RWORK(IRU) to complex matrix U
Overwrite U by left singular vectors of L
(CWorkspace: need M*M+3*M, prefer M*M+2*M+M*NB)
(RWorkspace: 0)
*/
zlacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
i__1 = *lwork - nwork + 1;
zunmbr_("Q", "L", "N", m, m, m, &work[il], &ldwrkl, &work[
itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
/*
Copy real matrix RWORK(IRVT) to complex matrix VT
Overwrite VT by left singular vectors of L
(CWorkspace: need M*M+3*M, prefer M*M+2*M+M*NB)
(RWorkspace: 0)
*/
zlacp2_("F", m, m, &rwork[irvt], m, &vt[vt_offset], ldvt);
i__1 = *lwork - nwork + 1;
zunmbr_("P", "R", "C", m, m, m, &work[il], &ldwrkl, &work[
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
ierr);
/*
Copy VT to WORK(IL), multiply right singular vectors of L
in WORK(IL) by Q in A, storing result in VT
(CWorkspace: need M*M)
(RWorkspace: 0)
*/
zlacpy_("F", m, m, &vt[vt_offset], ldvt, &work[il], &ldwrkl);
zgemm_("N", "N", m, n, m, &c_b60, &work[il], &ldwrkl, &a[
a_offset], lda, &c_b59, &vt[vt_offset], ldvt);
} else if (wntqa) {
/*
Path 9t (N much larger than M, JOBZ='A')
N right singular vectors to be computed in VT and
M left singular vectors to be computed in U
*/
ivt = 1;
/* WORK(IVT) is M by M */
ldwkvt = *m;
itau = ivt + ldwkvt * *m;
nwork = itau + *m;
/*
Compute A=L*Q, copying result to VT
(CWorkspace: need 2*M, prefer M+M*NB)
(RWorkspace: 0)
*/
i__1 = *lwork - nwork + 1;
zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
i__1, &ierr);
zlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
/*
Generate Q in VT
(CWorkspace: need M+N, prefer M+N*NB)
(RWorkspace: 0)
*/
i__1 = *lwork - nwork + 1;
zunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &work[
nwork], &i__1, &ierr);
/* Produce L in A, zeroing out above it */
i__1 = *m - 1;
i__2 = *m - 1;
zlaset_("U", &i__1, &i__2, &c_b59, &c_b59, &a[((a_dim1) << (1)
) + 1], lda);
ie = 1;
itauq = itau;
itaup = itauq + *m;
nwork = itaup + *m;
/*
Bidiagonalize L in A
(CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB)
(RWorkspace: need M)
*/
i__1 = *lwork - nwork + 1;
zgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &work[
itauq], &work[itaup], &work[nwork], &i__1, &ierr);
/*
Perform bidiagonal SVD, computing left singular vectors
of bidiagonal matrix in RWORK(IRU) and computing right
singular vectors of bidiagonal matrix in RWORK(IRVT)
(CWorkspace: need 0)
(RWorkspace: need BDSPAC)
*/
iru = ie + *m;
irvt = iru + *m * *m;
nrwork = irvt + *m * *m;
dbdsdc_("U", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
info);
/*
Copy real matrix RWORK(IRU) to complex matrix U
Overwrite U by left singular vectors of L
(CWorkspace: need 3*M, prefer 2*M+M*NB)
(RWorkspace: 0)
*/
zlacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
i__1 = *lwork - nwork + 1;
zunmbr_("Q", "L", "N", m, m, m, &a[a_offset], lda, &work[
itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
/*
Copy real matrix RWORK(IRVT) to complex matrix WORK(IVT)
Overwrite WORK(IVT) by right singular vectors of L
(CWorkspace: need M*M+3*M, prefer M*M+2*M+M*NB)
(RWorkspace: 0)
*/
zlacp2_("F", m, m, &rwork[irvt], m, &work[ivt], &ldwkvt);
i__1 = *lwork - nwork + 1;
zunmbr_("P", "R", "C", m, m, m, &a[a_offset], lda, &work[
itaup], &work[ivt], &ldwkvt, &work[nwork], &i__1, &
ierr);
/*
Multiply right singular vectors of L in WORK(IVT) by
Q in VT, storing result in A
(CWorkspace: need M*M)
(RWorkspace: 0)
*/
zgemm_("N", "N", m, n, m, &c_b60, &work[ivt], &ldwkvt, &vt[
vt_offset], ldvt, &c_b59, &a[a_offset], lda);
/* Copy right singular vectors of A from A to VT */
zlacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
}
} else if (*n >= mnthr2) {
/*
MNTHR2 <= N < MNTHR1
Path 5t (N much larger than M, but not as much as MNTHR1)
Reduce to bidiagonal form without QR decomposition, use
ZUNGBR and matrix multiplication to compute singular vectors
*/
ie = 1;
nrwork = ie + *m;
itauq = 1;
itaup = itauq + *m;
nwork = itaup + *m;
/*
Bidiagonalize A
(CWorkspace: need 2*M+N, prefer 2*M+(M+N)*NB)
(RWorkspace: M)
*/
i__1 = *lwork - nwork + 1;
zgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
&work[itaup], &work[nwork], &i__1, &ierr);
if (wntqn) {
/*
Compute singular values only
(Cworkspace: 0)
(Rworkspace: need BDSPAC)
*/
dbdsdc_("L", "N", m, &s[1], &rwork[ie], dum, &c__1, dum, &
c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
} else if (wntqo) {
irvt = nrwork;
iru = irvt + *m * *m;
nrwork = iru + *m * *m;
ivt = nwork;
/*
Copy A to U, generate Q
(Cworkspace: need 2*M, prefer M+M*NB)
(Rworkspace: 0)
*/
zlacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
i__1 = *lwork - nwork + 1;
zungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
nwork], &i__1, &ierr);
/*
Generate P**H in A
(Cworkspace: need 2*M, prefer M+M*NB)
(Rworkspace: 0)
*/
i__1 = *lwork - nwork + 1;
zungbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &work[
nwork], &i__1, &ierr);
ldwkvt = *m;
if (*lwork >= *m * *n + *m * 3) {
/* WORK( IVT ) is M by N */
nwork = ivt + ldwkvt * *n;
chunk = *n;
} else {
/* WORK( IVT ) is M by CHUNK */
chunk = (*lwork - *m * 3) / *m;
nwork = ivt + ldwkvt * chunk;
}
/*
Perform bidiagonal SVD, computing left singular vectors
of bidiagonal matrix in RWORK(IRU) and computing right
singular vectors of bidiagonal matrix in RWORK(IRVT)
(CWorkspace: need 0)
(RWorkspace: need BDSPAC)
*/
dbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
info);
/*
Multiply Q in U by real matrix RWORK(IRVT)
storing the result in WORK(IVT), copying to U
(Cworkspace: need 0)
(Rworkspace: need 2*M*M)
*/
zlacrm_(m, m, &u[u_offset], ldu, &rwork[iru], m, &work[ivt], &
ldwkvt, &rwork[nrwork]);
zlacpy_("F", m, m, &work[ivt], &ldwkvt, &u[u_offset], ldu);
/*
Multiply RWORK(IRVT) by P**H in A, storing the
result in WORK(IVT), copying to A
(CWorkspace: need M*M, prefer M*N)
(Rworkspace: need 2*M*M, prefer 2*M*N)
*/
nrwork = iru;
i__1 = *n;
i__2 = chunk;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
i__2) {
/* Computing MIN */
i__3 = *n - i__ + 1;
blk = min(i__3,chunk);
zlarcm_(m, &blk, &rwork[irvt], m, &a[i__ * a_dim1 + 1],
lda, &work[ivt], &ldwkvt, &rwork[nrwork]);
zlacpy_("F", m, &blk, &work[ivt], &ldwkvt, &a[i__ *
a_dim1 + 1], lda);
/* L50: */
}
} else if (wntqs) {
/*
Copy A to U, generate Q
(Cworkspace: need 2*M, prefer M+M*NB)
(Rworkspace: 0)
*/
zlacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
i__2 = *lwork - nwork + 1;
zungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
nwork], &i__2, &ierr);
/*
Copy A to VT, generate P**H
(Cworkspace: need 2*M, prefer M+M*NB)
(Rworkspace: 0)
*/
zlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
i__2 = *lwork - nwork + 1;
zungbr_("P", m, n, m, &vt[vt_offset], ldvt, &work[itaup], &
work[nwork], &i__2, &ierr);
/*
Perform bidiagonal SVD, computing left singular vectors
of bidiagonal matrix in RWORK(IRU) and computing right
singular vectors of bidiagonal matrix in RWORK(IRVT)
(CWorkspace: need 0)
(RWorkspace: need BDSPAC)
*/
irvt = nrwork;
iru = irvt + *m * *m;
nrwork = iru + *m * *m;
dbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
info);
/*
Multiply Q in U by real matrix RWORK(IRU), storing the
result in A, copying to U
(CWorkspace: need 0)
(Rworkspace: need 3*M*M)
*/
zlacrm_(m, m, &u[u_offset], ldu, &rwork[iru], m, &a[a_offset],
lda, &rwork[nrwork]);
zlacpy_("F", m, m, &a[a_offset], lda, &u[u_offset], ldu);
/*
Multiply real matrix RWORK(IRVT) by P**H in VT,
storing the result in A, copying to VT
(Cworkspace: need 0)
(Rworkspace: need M*M+2*M*N)
*/
nrwork = iru;
zlarcm_(m, n, &rwork[irvt], m, &vt[vt_offset], ldvt, &a[
a_offset], lda, &rwork[nrwork]);
zlacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
} else {
/*
Copy A to U, generate Q
(Cworkspace: need 2*M, prefer M+M*NB)
(Rworkspace: 0)
*/
zlacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
i__2 = *lwork - nwork + 1;
zungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
nwork], &i__2, &ierr);
/*
Copy A to VT, generate P**H
(Cworkspace: need 2*M, prefer M+M*NB)
(Rworkspace: 0)
*/
zlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
i__2 = *lwork - nwork + 1;
zungbr_("P", n, n, m, &vt[vt_offset], ldvt, &work[itaup], &
work[nwork], &i__2, &ierr);
/*
Perform bidiagonal SVD, computing left singular vectors
of bidiagonal matrix in RWORK(IRU) and computing right
singular vectors of bidiagonal matrix in RWORK(IRVT)
(CWorkspace: need 0)
(RWorkspace: need BDSPAC)
*/
irvt = nrwork;
iru = irvt + *m * *m;
nrwork = iru + *m * *m;
dbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
info);
/*
Multiply Q in U by real matrix RWORK(IRU), storing the
result in A, copying to U
(CWorkspace: need 0)
(Rworkspace: need 3*M*M)
*/
zlacrm_(m, m, &u[u_offset], ldu, &rwork[iru], m, &a[a_offset],
lda, &rwork[nrwork]);
zlacpy_("F", m, m, &a[a_offset], lda, &u[u_offset], ldu);
/*
Multiply real matrix RWORK(IRVT) by P**H in VT,
storing the result in A, copying to VT
(Cworkspace: need 0)
(Rworkspace: need M*M+2*M*N)
*/
zlarcm_(m, n, &rwork[irvt], m, &vt[vt_offset], ldvt, &a[
a_offset], lda, &rwork[nrwork]);
zlacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
}
} else {
/*
N .LT. MNTHR2
Path 6t (N greater than M, but not much larger)
Reduce to bidiagonal form without LQ decomposition
Use ZUNMBR to compute singular vectors
*/
ie = 1;
nrwork = ie + *m;
itauq = 1;
itaup = itauq + *m;
nwork = itaup + *m;
/*
Bidiagonalize A
(CWorkspace: need 2*M+N, prefer 2*M+(M+N)*NB)
(RWorkspace: M)
*/
i__2 = *lwork - nwork + 1;
zgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
&work[itaup], &work[nwork], &i__2, &ierr);
if (wntqn) {
/*
Compute singular values only
(Cworkspace: 0)
(Rworkspace: need BDSPAC)
*/
dbdsdc_("L", "N", m, &s[1], &rwork[ie], dum, &c__1, dum, &
c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
} else if (wntqo) {
ldwkvt = *m;
ivt = nwork;
if (*lwork >= *m * *n + *m * 3) {
/* WORK( IVT ) is M by N */
zlaset_("F", m, n, &c_b59, &c_b59, &work[ivt], &ldwkvt);
nwork = ivt + ldwkvt * *n;
} else {
/* WORK( IVT ) is M by CHUNK */
chunk = (*lwork - *m * 3) / *m;
nwork = ivt + ldwkvt * chunk;
}
/*
Perform bidiagonal SVD, computing left singular vectors
of bidiagonal matrix in RWORK(IRU) and computing right
singular vectors of bidiagonal matrix in RWORK(IRVT)
(CWorkspace: need 0)
(RWorkspace: need BDSPAC)
*/
irvt = nrwork;
iru = irvt + *m * *m;
nrwork = iru + *m * *m;
dbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
info);
/*
Copy real matrix RWORK(IRU) to complex matrix U
Overwrite U by left singular vectors of A
(Cworkspace: need 2*M, prefer M+M*NB)
(Rworkspace: need 0)
*/
zlacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
i__2 = *lwork - nwork + 1;
zunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
if (*lwork >= *m * *n + *m * 3) {
/*
Copy real matrix RWORK(IRVT) to complex matrix WORK(IVT)
Overwrite WORK(IVT) by right singular vectors of A,
copying to A
(Cworkspace: need M*N+2*M, prefer M*N+M+M*NB)
(Rworkspace: need 0)
*/
zlacp2_("F", m, m, &rwork[irvt], m, &work[ivt], &ldwkvt);
i__2 = *lwork - nwork + 1;
zunmbr_("P", "R", "C", m, n, m, &a[a_offset], lda, &work[
itaup], &work[ivt], &ldwkvt, &work[nwork], &i__2,
&ierr);
zlacpy_("F", m, n, &work[ivt], &ldwkvt, &a[a_offset], lda);
} else {
/*
Generate P**H in A
(Cworkspace: need 2*M, prefer M+M*NB)
(Rworkspace: need 0)
*/
i__2 = *lwork - nwork + 1;
zungbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &
work[nwork], &i__2, &ierr);
/*
Multiply Q in A by real matrix RWORK(IRU), storing the
result in WORK(IU), copying to A
(CWorkspace: need M*M, prefer M*N)
(Rworkspace: need 3*M*M, prefer M*M+2*M*N)
*/
nrwork = iru;
i__2 = *n;
i__1 = chunk;
for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
i__1) {
/* Computing MIN */
i__3 = *n - i__ + 1;
blk = min(i__3,chunk);
zlarcm_(m, &blk, &rwork[irvt], m, &a[i__ * a_dim1 + 1]
, lda, &work[ivt], &ldwkvt, &rwork[nrwork]);
zlacpy_("F", m, &blk, &work[ivt], &ldwkvt, &a[i__ *
a_dim1 + 1], lda);
/* L60: */
}
}
} else if (wntqs) {
/*
Perform bidiagonal SVD, computing left singular vectors
of bidiagonal matrix in RWORK(IRU) and computing right
singular vectors of bidiagonal matrix in RWORK(IRVT)
(CWorkspace: need 0)
(RWorkspace: need BDSPAC)
*/
irvt = nrwork;
iru = irvt + *m * *m;
nrwork = iru + *m * *m;
dbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
info);
/*
Copy real matrix RWORK(IRU) to complex matrix U
Overwrite U by left singular vectors of A
(CWorkspace: need 3*M, prefer 2*M+M*NB)
(RWorkspace: M*M)
*/
zlacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
i__1 = *lwork - nwork + 1;
zunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
/*
Copy real matrix RWORK(IRVT) to complex matrix VT
Overwrite VT by right singular vectors of A
(CWorkspace: need 3*M, prefer 2*M+M*NB)
(RWorkspace: M*M)
*/
zlaset_("F", m, n, &c_b59, &c_b59, &vt[vt_offset], ldvt);
zlacp2_("F", m, m, &rwork[irvt], m, &vt[vt_offset], ldvt);
i__1 = *lwork - nwork + 1;
zunmbr_("P", "R", "C", m, n, m, &a[a_offset], lda, &work[
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
ierr);
} else {
/*
Perform bidiagonal SVD, computing left singular vectors
of bidiagonal matrix in RWORK(IRU) and computing right
singular vectors of bidiagonal matrix in RWORK(IRVT)
(CWorkspace: need 0)
(RWorkspace: need BDSPAC)
*/
irvt = nrwork;
iru = irvt + *m * *m;
nrwork = iru + *m * *m;
dbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
info);
/*
Copy real matrix RWORK(IRU) to complex matrix U
Overwrite U by left singular vectors of A
(CWorkspace: need 3*M, prefer 2*M+M*NB)
(RWorkspace: M*M)
*/
zlacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
i__1 = *lwork - nwork + 1;
zunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
/* Set the right corner of VT to identity matrix */
i__1 = *n - *m;
i__2 = *n - *m;
zlaset_("F", &i__1, &i__2, &c_b59, &c_b60, &vt[*m + 1 + (*m +
1) * vt_dim1], ldvt);
/*
Copy real matrix RWORK(IRVT) to complex matrix VT
Overwrite VT by right singular vectors of A
(CWorkspace: need 2*M+N, prefer 2*M+N*NB)
(RWorkspace: M*M)
*/
zlaset_("F", n, n, &c_b59, &c_b59, &vt[vt_offset], ldvt);
zlacp2_("F", m, m, &rwork[irvt], m, &vt[vt_offset], ldvt);
i__1 = *lwork - nwork + 1;
zunmbr_("P", "R", "C", n, n, m, &a[a_offset], lda, &work[
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
ierr);
}
}
}
/* Undo scaling if necessary */
if (iscl == 1) {
if (anrm > bignum) {
dlascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &
minmn, &ierr);
}
if (anrm < smlnum) {
dlascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &
minmn, &ierr);
}
}
/* Return optimal workspace in WORK(1) */
work[1].r = (doublereal) maxwrk, work[1].i = 0.;
return 0;
/* End of ZGESDD */
} /* zgesdd_ */
/* Subroutine */ int zgesv_(integer *n, integer *nrhs, doublecomplex *a,
integer *lda, integer *ipiv, doublecomplex *b, integer *ldb, integer *
info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1;
/* Local variables */
extern /* Subroutine */ int xerbla_(char *, integer *), zgetrf_(
integer *, integer *, doublecomplex *, integer *, integer *,
integer *), zgetrs_(char *, integer *, integer *, doublecomplex *,
integer *, integer *, doublecomplex *, integer *, integer *);
/*
-- LAPACK driver routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
March 31, 1993
Purpose
=======
ZGESV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N matrix and X and B are N-by-NRHS matrices.
The LU decomposition with partial pivoting and row interchanges is
used to factor A as
A = P * L * U,
where P is a permutation matrix, L is unit lower triangular, and U is
upper triangular. The factored form of A is then used to solve the
system of equations A * X = B.
Arguments
=========
N (input) INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the N-by-N coefficient matrix A.
On exit, the factors L and U from the factorization
A = P*L*U; the unit diagonal elements of L are not stored.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
IPIV (output) INTEGER array, dimension (N)
The pivot indices that define the permutation matrix P;
row i of the matrix was interchanged with row IPIV(i).
B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
On entry, the N-by-NRHS matrix of right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS solution matrix X.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, U(i,i) is exactly zero. The factorization
has been completed, but the factor U is exactly
singular, so the solution could not be computed.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--ipiv;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
/* Function Body */
*info = 0;
if (*n < 0) {
*info = -1;
} else if (*nrhs < 0) {
*info = -2;
} else if (*lda < max(1,*n)) {
*info = -4;
} else if (*ldb < max(1,*n)) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGESV ", &i__1);
return 0;
}
/* Compute the LU factorization of A. */
zgetrf_(n, n, &a[a_offset], lda, &ipiv[1], info);
if (*info == 0) {
/* Solve the system A*X = B, overwriting B with X. */
zgetrs_("No transpose", n, nrhs, &a[a_offset], lda, &ipiv[1], &b[
b_offset], ldb, info);
}
return 0;
/* End of ZGESV */
} /* zgesv_ */
/* Subroutine */ int zgetf2_(integer *m, integer *n, doublecomplex *a,
integer *lda, integer *ipiv, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
doublecomplex z__1;
/* Builtin functions */
void z_div(doublecomplex *, doublecomplex *, doublecomplex *);
/* Local variables */
static integer j, jp;
extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
doublecomplex *, integer *), zgeru_(integer *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *), zswap_(integer *,
doublecomplex *, integer *, doublecomplex *, integer *), xerbla_(
char *, integer *);
extern integer izamax_(integer *, doublecomplex *, integer *);
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZGETF2 computes an LU factorization of a general m-by-n matrix A
using partial pivoting with row interchanges.
The factorization has the form
A = P * L * U
where P is a permutation matrix, L is lower triangular with unit
diagonal elements (lower trapezoidal if m > n), and U is upper
triangular (upper trapezoidal if m < n).
This is the right-looking Level 2 BLAS version of the algorithm.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the m by n matrix to be factored.
On exit, the factors L and U from the factorization
A = P*L*U; the unit diagonal elements of L are not stored.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
IPIV (output) INTEGER array, dimension (min(M,N))
The pivot indices; for 1 <= i <= min(M,N), row i of the
matrix was interchanged with row IPIV(i).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -k, the k-th argument had an illegal value
> 0: if INFO = k, U(k,k) is exactly zero. The factorization
has been completed, but the factor U is exactly
singular, and division by zero will occur if it is used
to solve a system of equations.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--ipiv;
/* Function Body */
*info = 0;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*m)) {
*info = -4;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGETF2", &i__1);
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0) {
return 0;
}
i__1 = min(*m,*n);
for (j = 1; j <= i__1; ++j) {
/* Find pivot and test for singularity. */
i__2 = *m - j + 1;
jp = j - 1 + izamax_(&i__2, &a[j + j * a_dim1], &c__1);
ipiv[j] = jp;
i__2 = jp + j * a_dim1;
if (a[i__2].r != 0. || a[i__2].i != 0.) {
/* Apply the interchange to columns 1:N. */
if (jp != j) {
zswap_(n, &a[j + a_dim1], lda, &a[jp + a_dim1], lda);
}
/* Compute elements J+1:M of J-th column. */
if (j < *m) {
i__2 = *m - j;
z_div(&z__1, &c_b60, &a[j + j * a_dim1]);
zscal_(&i__2, &z__1, &a[j + 1 + j * a_dim1], &c__1);
}
} else if (*info == 0) {
*info = j;
}
if (j < min(*m,*n)) {
/* Update trailing submatrix. */
i__2 = *m - j;
i__3 = *n - j;
z__1.r = -1., z__1.i = -0.;
zgeru_(&i__2, &i__3, &z__1, &a[j + 1 + j * a_dim1], &c__1, &a[j +
(j + 1) * a_dim1], lda, &a[j + 1 + (j + 1) * a_dim1], lda)
;
}
/* L10: */
}
return 0;
/* End of ZGETF2 */
} /* zgetf2_ */
/* Subroutine */ int zgetrf_(integer *m, integer *n, doublecomplex *a,
integer *lda, integer *ipiv, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
doublecomplex z__1;
/* Local variables */
static integer i__, j, jb, nb, iinfo;
extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *,
integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *), ztrsm_(char *, char *, char *, char *,
integer *, integer *, doublecomplex *, doublecomplex *, integer *
, doublecomplex *, integer *),
zgetf2_(integer *, integer *, doublecomplex *, integer *, integer
*, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int zlaswp_(integer *, doublecomplex *, integer *,
integer *, integer *, integer *, integer *);
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZGETRF computes an LU factorization of a general M-by-N matrix A
using partial pivoting with row interchanges.
The factorization has the form
A = P * L * U
where P is a permutation matrix, L is lower triangular with unit
diagonal elements (lower trapezoidal if m > n), and U is upper
triangular (upper trapezoidal if m < n).
This is the right-looking Level 3 BLAS version of the algorithm.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the M-by-N matrix to be factored.
On exit, the factors L and U from the factorization
A = P*L*U; the unit diagonal elements of L are not stored.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
IPIV (output) INTEGER array, dimension (min(M,N))
The pivot indices; for 1 <= i <= min(M,N), row i of the
matrix was interchanged with row IPIV(i).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, U(i,i) is exactly zero. The factorization
has been completed, but the factor U is exactly
singular, and division by zero will occur if it is used
to solve a system of equations.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--ipiv;
/* Function Body */
*info = 0;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*m)) {
*info = -4;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGETRF", &i__1);
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0) {
return 0;
}
/* Determine the block size for this environment. */
nb = ilaenv_(&c__1, "ZGETRF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)
1);
if (nb <= 1 || nb >= min(*m,*n)) {
/* Use unblocked code. */
zgetf2_(m, n, &a[a_offset], lda, &ipiv[1], info);
} else {
/* Use blocked code. */
i__1 = min(*m,*n);
i__2 = nb;
for (j = 1; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
/* Computing MIN */
i__3 = min(*m,*n) - j + 1;
jb = min(i__3,nb);
/*
Factor diagonal and subdiagonal blocks and test for exact
singularity.
*/
i__3 = *m - j + 1;
zgetf2_(&i__3, &jb, &a[j + j * a_dim1], lda, &ipiv[j], &iinfo);
/* Adjust INFO and the pivot indices. */
if ((*info == 0 && iinfo > 0)) {
*info = iinfo + j - 1;
}
/* Computing MIN */
i__4 = *m, i__5 = j + jb - 1;
i__3 = min(i__4,i__5);
for (i__ = j; i__ <= i__3; ++i__) {
ipiv[i__] = j - 1 + ipiv[i__];
/* L10: */
}
/* Apply interchanges to columns 1:J-1. */
i__3 = j - 1;
i__4 = j + jb - 1;
zlaswp_(&i__3, &a[a_offset], lda, &j, &i__4, &ipiv[1], &c__1);
if (j + jb <= *n) {
/* Apply interchanges to columns J+JB:N. */
i__3 = *n - j - jb + 1;
i__4 = j + jb - 1;
zlaswp_(&i__3, &a[(j + jb) * a_dim1 + 1], lda, &j, &i__4, &
ipiv[1], &c__1);
/* Compute block row of U. */
i__3 = *n - j - jb + 1;
ztrsm_("Left", "Lower", "No transpose", "Unit", &jb, &i__3, &
c_b60, &a[j + j * a_dim1], lda, &a[j + (j + jb) *
a_dim1], lda);
if (j + jb <= *m) {
/* Update trailing submatrix. */
i__3 = *m - j - jb + 1;
i__4 = *n - j - jb + 1;
z__1.r = -1., z__1.i = -0.;
zgemm_("No transpose", "No transpose", &i__3, &i__4, &jb,
&z__1, &a[j + jb + j * a_dim1], lda, &a[j + (j +
jb) * a_dim1], lda, &c_b60, &a[j + jb + (j + jb) *
a_dim1], lda);
}
}
/* L20: */
}
}
return 0;
/* End of ZGETRF */
} /* zgetrf_ */
/* Subroutine */ int zgetrs_(char *trans, integer *n, integer *nrhs,
doublecomplex *a, integer *lda, integer *ipiv, doublecomplex *b,
integer *ldb, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1;
/* Local variables */
extern logical lsame_(char *, char *);
extern /* Subroutine */ int ztrsm_(char *, char *, char *, char *,
integer *, integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *),
xerbla_(char *, integer *);
static logical notran;
extern /* Subroutine */ int zlaswp_(integer *, doublecomplex *, integer *,
integer *, integer *, integer *, integer *);
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZGETRS solves a system of linear equations
A * X = B, A**T * X = B, or A**H * X = B
with a general N-by-N matrix A using the LU factorization computed
by ZGETRF.
Arguments
=========
TRANS (input) CHARACTER*1
Specifies the form of the system of equations:
= 'N': A * X = B (No transpose)
= 'T': A**T * X = B (Transpose)
= 'C': A**H * X = B (Conjugate transpose)
N (input) INTEGER
The order of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
A (input) COMPLEX*16 array, dimension (LDA,N)
The factors L and U from the factorization A = P*L*U
as computed by ZGETRF.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
IPIV (input) INTEGER array, dimension (N)
The pivot indices from ZGETRF; for 1<=i<=N, row i of the
matrix was interchanged with row IPIV(i).
B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--ipiv;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
/* Function Body */
*info = 0;
notran = lsame_(trans, "N");
if (((! notran && ! lsame_(trans, "T")) && ! lsame_(
trans, "C"))) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if (*ldb < max(1,*n)) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGETRS", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0 || *nrhs == 0) {
return 0;
}
if (notran) {
/*
Solve A * X = B.
Apply row interchanges to the right hand sides.
*/
zlaswp_(nrhs, &b[b_offset], ldb, &c__1, n, &ipiv[1], &c__1);
/* Solve L*X = B, overwriting B with X. */
ztrsm_("Left", "Lower", "No transpose", "Unit", n, nrhs, &c_b60, &a[
a_offset], lda, &b[b_offset], ldb);
/* Solve U*X = B, overwriting B with X. */
ztrsm_("Left", "Upper", "No transpose", "Non-unit", n, nrhs, &c_b60, &
a[a_offset], lda, &b[b_offset], ldb);
} else {
/*
Solve A**T * X = B or A**H * X = B.
Solve U'*X = B, overwriting B with X.
*/
ztrsm_("Left", "Upper", trans, "Non-unit", n, nrhs, &c_b60, &a[
a_offset], lda, &b[b_offset], ldb);
/* Solve L'*X = B, overwriting B with X. */
ztrsm_("Left", "Lower", trans, "Unit", n, nrhs, &c_b60, &a[a_offset],
lda, &b[b_offset], ldb);
/* Apply row interchanges to the solution vectors. */
zlaswp_(nrhs, &b[b_offset], ldb, &c__1, n, &ipiv[1], &c_n1);
}
return 0;
/* End of ZGETRS */
} /* zgetrs_ */
/* Subroutine */ int zheevd_(char *jobz, char *uplo, integer *n,
doublecomplex *a, integer *lda, doublereal *w, doublecomplex *work,
integer *lwork, doublereal *rwork, integer *lrwork, integer *iwork,
integer *liwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
doublereal d__1, d__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static doublereal eps;
static integer inde;
static doublereal anrm;
static integer imax;
static doublereal rmin, rmax;
static integer lopt;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *);
static doublereal sigma;
extern logical lsame_(char *, char *);
static integer iinfo, lwmin, liopt;
static logical lower;
static integer llrwk, lropt;
static logical wantz;
static integer indwk2, llwrk2;
static integer iscale;
static doublereal safmin;
extern /* Subroutine */ int xerbla_(char *, integer *);
static doublereal bignum;
extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *,
integer *, doublereal *);
static integer indtau;
extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *,
integer *), zlascl_(char *, integer *, integer *, doublereal *,
doublereal *, integer *, integer *, doublecomplex *, integer *,
integer *), zstedc_(char *, integer *, doublereal *,
doublereal *, doublecomplex *, integer *, doublecomplex *,
integer *, doublereal *, integer *, integer *, integer *, integer
*);
static integer indrwk, indwrk, liwmin;
extern /* Subroutine */ int zhetrd_(char *, integer *, doublecomplex *,
integer *, doublereal *, doublereal *, doublecomplex *,
doublecomplex *, integer *, integer *), zlacpy_(char *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
integer *);
static integer lrwmin, llwork;
static doublereal smlnum;
static logical lquery;
extern /* Subroutine */ int zunmtr_(char *, char *, char *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *);
/*
-- LAPACK driver routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZHEEVD computes all eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A. If eigenvectors are desired, it uses a
divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Arguments
=========
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA, N)
On entry, the Hermitian matrix A. If UPLO = 'U', the
leading N-by-N upper triangular part of A contains the
upper triangular part of the matrix A. If UPLO = 'L',
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.
On exit, if JOBZ = 'V', then if INFO = 0, A contains the
orthonormal eigenvectors of the matrix A.
If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
or the upper triangle (if UPLO='U') of A, including the
diagonal, is destroyed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
W (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The length of the array WORK.
If N <= 1, LWORK must be at least 1.
If JOBZ = 'N' and N > 1, LWORK must be at least N + 1.
If JOBZ = 'V' and N > 1, LWORK must be at least 2*N + N**2.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
RWORK (workspace/output) DOUBLE PRECISION array,
dimension (LRWORK)
On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
LRWORK (input) INTEGER
The dimension of the array RWORK.
If N <= 1, LRWORK must be at least 1.
If JOBZ = 'N' and N > 1, LRWORK must be at least N.
If JOBZ = 'V' and N > 1, LRWORK must be at least
1 + 5*N + 2*N**2.
If LRWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal size of the RWORK array,
returns this value as the first entry of the RWORK array, and
no error message related to LRWORK is issued by XERBLA.
IWORK (workspace/output) INTEGER array, dimension (LIWORK)
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
LIWORK (input) INTEGER
The dimension of the array IWORK.
If N <= 1, LIWORK must be at least 1.
If JOBZ = 'N' and N > 1, LIWORK must be at least 1.
If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal size of the IWORK array,
returns this value as the first entry of the IWORK array, and
no error message related to LIWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero.
Further Details
===============
Based on contributions by
Jeff Rutter, Computer Science Division, University of California
at Berkeley, USA
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--w;
--work;
--rwork;
--iwork;
/* Function Body */
wantz = lsame_(jobz, "V");
lower = lsame_(uplo, "L");
lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1;
*info = 0;
if (*n <= 1) {
lwmin = 1;
lrwmin = 1;
liwmin = 1;
lopt = lwmin;
lropt = lrwmin;
liopt = liwmin;
} else {
if (wantz) {
lwmin = ((*n) << (1)) + *n * *n;
/* Computing 2nd power */
i__1 = *n;
lrwmin = *n * 5 + 1 + ((i__1 * i__1) << (1));
liwmin = *n * 5 + 3;
} else {
lwmin = *n + 1;
lrwmin = *n;
liwmin = 1;
}
lopt = lwmin;
lropt = lrwmin;
liopt = liwmin;
}
if (! (wantz || lsame_(jobz, "N"))) {
*info = -1;
} else if (! (lower || lsame_(uplo, "U"))) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if ((*lwork < lwmin && ! lquery)) {
*info = -8;
} else if ((*lrwork < lrwmin && ! lquery)) {
*info = -10;
} else if ((*liwork < liwmin && ! lquery)) {
*info = -12;
}
if (*info == 0) {
work[1].r = (doublereal) lopt, work[1].i = 0.;
rwork[1] = (doublereal) lropt;
iwork[1] = liopt;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZHEEVD", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
if (*n == 1) {
i__1 = a_dim1 + 1;
w[1] = a[i__1].r;
if (wantz) {
i__1 = a_dim1 + 1;
a[i__1].r = 1., a[i__1].i = 0.;
}
return 0;
}
/* Get machine constants. */
safmin = SAFEMINIMUM;
eps = PRECISION;
smlnum = safmin / eps;
bignum = 1. / smlnum;
rmin = sqrt(smlnum);
rmax = sqrt(bignum);
/* Scale matrix to allowable range, if necessary. */
anrm = zlanhe_("M", uplo, n, &a[a_offset], lda, &rwork[1]);
iscale = 0;
if ((anrm > 0. && anrm < rmin)) {
iscale = 1;
sigma = rmin / anrm;
} else if (anrm > rmax) {
iscale = 1;
sigma = rmax / anrm;
}
if (iscale == 1) {
zlascl_(uplo, &c__0, &c__0, &c_b1015, &sigma, n, n, &a[a_offset], lda,
info);
}
/* Call ZHETRD to reduce Hermitian matrix to tridiagonal form. */
inde = 1;
indtau = 1;
indwrk = indtau + *n;
indrwk = inde + *n;
indwk2 = indwrk + *n * *n;
llwork = *lwork - indwrk + 1;
llwrk2 = *lwork - indwk2 + 1;
llrwk = *lrwork - indrwk + 1;
zhetrd_(uplo, n, &a[a_offset], lda, &w[1], &rwork[inde], &work[indtau], &
work[indwrk], &llwork, &iinfo);
/* Computing MAX */
i__1 = indwrk;
d__1 = (doublereal) lopt, d__2 = (doublereal) (*n) + work[i__1].r;
lopt = (integer) max(d__1,d__2);
/*
For eigenvalues only, call DSTERF. For eigenvectors, first call
ZSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
tridiagonal matrix, then call ZUNMTR to multiply it to the
Householder transformations represented as Householder vectors in
A.
*/
if (! wantz) {
dsterf_(n, &w[1], &rwork[inde], info);
} else {
zstedc_("I", n, &w[1], &rwork[inde], &work[indwrk], n, &work[indwk2],
&llwrk2, &rwork[indrwk], &llrwk, &iwork[1], liwork, info);
zunmtr_("L", uplo, "N", n, n, &a[a_offset], lda, &work[indtau], &work[
indwrk], n, &work[indwk2], &llwrk2, &iinfo);
zlacpy_("A", n, n, &work[indwrk], n, &a[a_offset], lda);
/*
Computing MAX
Computing 2nd power
*/
i__3 = *n;
i__4 = indwk2;
i__1 = lopt, i__2 = *n + i__3 * i__3 + (integer) work[i__4].r;
lopt = max(i__1,i__2);
}
/* If matrix was scaled, then rescale eigenvalues appropriately. */
if (iscale == 1) {
if (*info == 0) {
imax = *n;
} else {
imax = *info - 1;
}
d__1 = 1. / sigma;
dscal_(&imax, &d__1, &w[1], &c__1);
}
work[1].r = (doublereal) lopt, work[1].i = 0.;
rwork[1] = (doublereal) lropt;
iwork[1] = liopt;
return 0;
/* End of ZHEEVD */
} /* zheevd_ */
/* Subroutine */ int zhetd2_(char *uplo, integer *n, doublecomplex *a,
integer *lda, doublereal *d__, doublereal *e, doublecomplex *tau,
integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
doublereal d__1;
doublecomplex z__1, z__2, z__3, z__4;
/* Local variables */
static integer i__;
static doublecomplex taui;
extern /* Subroutine */ int zher2_(char *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
static doublecomplex alpha;
extern logical lsame_(char *, char *);
extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *);
extern /* Subroutine */ int zhemv_(char *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, doublecomplex *, integer *);
static logical upper;
extern /* Subroutine */ int zaxpy_(integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *), xerbla_(
char *, integer *), zlarfg_(integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *);
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
October 31, 1999
Purpose
=======
ZHETD2 reduces a complex Hermitian matrix A to real symmetric
tridiagonal form T by a unitary similarity transformation:
Q' * A * Q = T.
Arguments
=========
UPLO (input) CHARACTER*1
Specifies whether the upper or lower triangular part of the
Hermitian matrix A is stored:
= 'U': Upper triangular
= 'L': Lower triangular
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading
n-by-n upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading n-by-n lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, if UPLO = 'U', the diagonal and first superdiagonal
of A are overwritten by the corresponding elements of the
tridiagonal matrix T, and the elements above the first
superdiagonal, with the array TAU, represent the unitary
matrix Q as a product of elementary reflectors; if UPLO
= 'L', the diagonal and first subdiagonal of A are over-
written by the corresponding elements of the tridiagonal
matrix T, and the elements below the first subdiagonal, with
the array TAU, represent the unitary matrix Q as a product
of elementary reflectors. See Further Details.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
D (output) DOUBLE PRECISION array, dimension (N)
The diagonal elements of the tridiagonal matrix T:
D(i) = A(i,i).
E (output) DOUBLE PRECISION array, dimension (N-1)
The off-diagonal elements of the tridiagonal matrix T:
E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'.
TAU (output) COMPLEX*16 array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
Further Details
===============
If UPLO = 'U', the matrix Q is represented as a product of elementary
reflectors
Q = H(n-1) . . . H(2) H(1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
A(1:i-1,i+1), and tau in TAU(i).
If UPLO = 'L', the matrix Q is represented as a product of elementary
reflectors
Q = H(1) H(2) . . . H(n-1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
and tau in TAU(i).
The contents of A on exit are illustrated by the following examples
with n = 5:
if UPLO = 'U': if UPLO = 'L':
( d e v2 v3 v4 ) ( d )
( d e v3 v4 ) ( e d )
( d e v4 ) ( v1 e d )
( d e ) ( v1 v2 e d )
( d ) ( v1 v2 v3 e d )
where d and e denote diagonal and off-diagonal elements of T, and vi
denotes an element of the vector defining H(i).
=====================================================================
Test the input parameters
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--d__;
--e;
--tau;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if ((! upper && ! lsame_(uplo, "L"))) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*n)) {
*info = -4;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZHETD2", &i__1);
return 0;
}
/* Quick return if possible */
if (*n <= 0) {
return 0;
}
if (upper) {
/* Reduce the upper triangle of A */
i__1 = *n + *n * a_dim1;
i__2 = *n + *n * a_dim1;
d__1 = a[i__2].r;
a[i__1].r = d__1, a[i__1].i = 0.;
for (i__ = *n - 1; i__ >= 1; --i__) {
/*
Generate elementary reflector H(i) = I - tau * v * v'
to annihilate A(1:i-1,i+1)
*/
i__1 = i__ + (i__ + 1) * a_dim1;
alpha.r = a[i__1].r, alpha.i = a[i__1].i;
zlarfg_(&i__, &alpha, &a[(i__ + 1) * a_dim1 + 1], &c__1, &taui);
i__1 = i__;
e[i__1] = alpha.r;
if (taui.r != 0. || taui.i != 0.) {
/* Apply H(i) from both sides to A(1:i,1:i) */
i__1 = i__ + (i__ + 1) * a_dim1;
a[i__1].r = 1., a[i__1].i = 0.;
/* Compute x := tau * A * v storing x in TAU(1:i) */
zhemv_(uplo, &i__, &taui, &a[a_offset], lda, &a[(i__ + 1) *
a_dim1 + 1], &c__1, &c_b59, &tau[1], &c__1)
;
/* Compute w := x - 1/2 * tau * (x'*v) * v */
z__3.r = -.5, z__3.i = -0.;
z__2.r = z__3.r * taui.r - z__3.i * taui.i, z__2.i = z__3.r *
taui.i + z__3.i * taui.r;
zdotc_(&z__4, &i__, &tau[1], &c__1, &a[(i__ + 1) * a_dim1 + 1]
, &c__1);
z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r *
z__4.i + z__2.i * z__4.r;
alpha.r = z__1.r, alpha.i = z__1.i;
zaxpy_(&i__, &alpha, &a[(i__ + 1) * a_dim1 + 1], &c__1, &tau[
1], &c__1);
/*
Apply the transformation as a rank-2 update:
A := A - v * w' - w * v'
*/
z__1.r = -1., z__1.i = -0.;
zher2_(uplo, &i__, &z__1, &a[(i__ + 1) * a_dim1 + 1], &c__1, &
tau[1], &c__1, &a[a_offset], lda);
} else {
i__1 = i__ + i__ * a_dim1;
i__2 = i__ + i__ * a_dim1;
d__1 = a[i__2].r;
a[i__1].r = d__1, a[i__1].i = 0.;
}
i__1 = i__ + (i__ + 1) * a_dim1;
i__2 = i__;
a[i__1].r = e[i__2], a[i__1].i = 0.;
i__1 = i__ + 1;
i__2 = i__ + 1 + (i__ + 1) * a_dim1;
d__[i__1] = a[i__2].r;
i__1 = i__;
tau[i__1].r = taui.r, tau[i__1].i = taui.i;
/* L10: */
}
i__1 = a_dim1 + 1;
d__[1] = a[i__1].r;
} else {
/* Reduce the lower triangle of A */
i__1 = a_dim1 + 1;
i__2 = a_dim1 + 1;
d__1 = a[i__2].r;
a[i__1].r = d__1, a[i__1].i = 0.;
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
/*
Generate elementary reflector H(i) = I - tau * v * v'
to annihilate A(i+2:n,i)
*/
i__2 = i__ + 1 + i__ * a_dim1;
alpha.r = a[i__2].r, alpha.i = a[i__2].i;
i__2 = *n - i__;
/* Computing MIN */
i__3 = i__ + 2;
zlarfg_(&i__2, &alpha, &a[min(i__3,*n) + i__ * a_dim1], &c__1, &
taui);
i__2 = i__;
e[i__2] = alpha.r;
if (taui.r != 0. || taui.i != 0.) {
/* Apply H(i) from both sides to A(i+1:n,i+1:n) */
i__2 = i__ + 1 + i__ * a_dim1;
a[i__2].r = 1., a[i__2].i = 0.;
/* Compute x := tau * A * v storing y in TAU(i:n-1) */
i__2 = *n - i__;
zhemv_(uplo, &i__2, &taui, &a[i__ + 1 + (i__ + 1) * a_dim1],
lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b59, &tau[
i__], &c__1);
/* Compute w := x - 1/2 * tau * (x'*v) * v */
z__3.r = -.5, z__3.i = -0.;
z__2.r = z__3.r * taui.r - z__3.i * taui.i, z__2.i = z__3.r *
taui.i + z__3.i * taui.r;
i__2 = *n - i__;
zdotc_(&z__4, &i__2, &tau[i__], &c__1, &a[i__ + 1 + i__ *
a_dim1], &c__1);
z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r *
z__4.i + z__2.i * z__4.r;
alpha.r = z__1.r, alpha.i = z__1.i;
i__2 = *n - i__;
zaxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &tau[
i__], &c__1);
/*
Apply the transformation as a rank-2 update:
A := A - v * w' - w * v'
*/
i__2 = *n - i__;
z__1.r = -1., z__1.i = -0.;
zher2_(uplo, &i__2, &z__1, &a[i__ + 1 + i__ * a_dim1], &c__1,
&tau[i__], &c__1, &a[i__ + 1 + (i__ + 1) * a_dim1],
lda);
} else {
i__2 = i__ + 1 + (i__ + 1) * a_dim1;
i__3 = i__ + 1 + (i__ + 1) * a_dim1;
d__1 = a[i__3].r;
a[i__2].r = d__1, a[i__2].i = 0.;
}
i__2 = i__ + 1 + i__ * a_dim1;
i__3 = i__;
a[i__2].r = e[i__3], a[i__2].i = 0.;
i__2 = i__;
i__3 = i__ + i__ * a_dim1;
d__[i__2] = a[i__3].r;
i__2 = i__;
tau[i__2].r = taui.r, tau[i__2].i = taui.i;
/* L20: */
}
i__1 = *n;
i__2 = *n + *n * a_dim1;
d__[i__1] = a[i__2].r;
}
return 0;
/* End of ZHETD2 */
} /* zhetd2_ */
/* Subroutine */ int zhetrd_(char *uplo, integer *n, doublecomplex *a,
integer *lda, doublereal *d__, doublereal *e, doublecomplex *tau,
doublecomplex *work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
doublecomplex z__1;
/* Local variables */
static integer i__, j, nb, kk, nx, iws;
extern logical lsame_(char *, char *);
static integer nbmin, iinfo;
static logical upper;
extern /* Subroutine */ int zhetd2_(char *, integer *, doublecomplex *,
integer *, doublereal *, doublereal *, doublecomplex *, integer *), zher2k_(char *, char *, integer *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, doublereal *, doublecomplex *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int zlatrd_(char *, integer *, integer *,
doublecomplex *, integer *, doublereal *, doublecomplex *,
doublecomplex *, integer *);
static integer ldwork, lwkopt;
static logical lquery;
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZHETRD reduces a complex Hermitian matrix A to real symmetric
tridiagonal form T by a unitary similarity transformation:
Q**H * A * Q = T.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading
N-by-N upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, if UPLO = 'U', the diagonal and first superdiagonal
of A are overwritten by the corresponding elements of the
tridiagonal matrix T, and the elements above the first
superdiagonal, with the array TAU, represent the unitary
matrix Q as a product of elementary reflectors; if UPLO
= 'L', the diagonal and first subdiagonal of A are over-
written by the corresponding elements of the tridiagonal
matrix T, and the elements below the first subdiagonal, with
the array TAU, represent the unitary matrix Q as a product
of elementary reflectors. See Further Details.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
D (output) DOUBLE PRECISION array, dimension (N)
The diagonal elements of the tridiagonal matrix T:
D(i) = A(i,i).
E (output) DOUBLE PRECISION array, dimension (N-1)
The off-diagonal elements of the tridiagonal matrix T:
E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'.
TAU (output) COMPLEX*16 array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= 1.
For optimum performance LWORK >= N*NB, where NB is the
optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Further Details
===============
If UPLO = 'U', the matrix Q is represented as a product of elementary
reflectors
Q = H(n-1) . . . H(2) H(1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
A(1:i-1,i+1), and tau in TAU(i).
If UPLO = 'L', the matrix Q is represented as a product of elementary
reflectors
Q = H(1) H(2) . . . H(n-1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
and tau in TAU(i).
The contents of A on exit are illustrated by the following examples
with n = 5:
if UPLO = 'U': if UPLO = 'L':
( d e v2 v3 v4 ) ( d )
( d e v3 v4 ) ( e d )
( d e v4 ) ( v1 e d )
( d e ) ( v1 v2 e d )
( d ) ( v1 v2 v3 e d )
where d and e denote diagonal and off-diagonal elements of T, and vi
denotes an element of the vector defining H(i).
=====================================================================
Test the input parameters
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--d__;
--e;
--tau;
--work;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
lquery = *lwork == -1;
if ((! upper && ! lsame_(uplo, "L"))) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*n)) {
*info = -4;
} else if ((*lwork < 1 && ! lquery)) {
*info = -9;
}
if (*info == 0) {
/* Determine the block size. */
nb = ilaenv_(&c__1, "ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6,
(ftnlen)1);
lwkopt = *n * nb;
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZHETRD", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
work[1].r = 1., work[1].i = 0.;
return 0;
}
nx = *n;
iws = 1;
if ((nb > 1 && nb < *n)) {
/*
Determine when to cross over from blocked to unblocked code
(last block is always handled by unblocked code).
Computing MAX
*/
i__1 = nb, i__2 = ilaenv_(&c__3, "ZHETRD", uplo, n, &c_n1, &c_n1, &
c_n1, (ftnlen)6, (ftnlen)1);
nx = max(i__1,i__2);
if (nx < *n) {
/* Determine if workspace is large enough for blocked code. */
ldwork = *n;
iws = ldwork * nb;
if (*lwork < iws) {
/*
Not enough workspace to use optimal NB: determine the
minimum value of NB, and reduce NB or force use of
unblocked code by setting NX = N.
Computing MAX
*/
i__1 = *lwork / ldwork;
nb = max(i__1,1);
nbmin = ilaenv_(&c__2, "ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1,
(ftnlen)6, (ftnlen)1);
if (nb < nbmin) {
nx = *n;
}
}
} else {
nx = *n;
}
} else {
nb = 1;
}
if (upper) {
/*
Reduce the upper triangle of A.
Columns 1:kk are handled by the unblocked method.
*/
kk = *n - (*n - nx + nb - 1) / nb * nb;
i__1 = kk + 1;
i__2 = -nb;
for (i__ = *n - nb + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
i__2) {
/*
Reduce columns i:i+nb-1 to tridiagonal form and form the
matrix W which is needed to update the unreduced part of
the matrix
*/
i__3 = i__ + nb - 1;
zlatrd_(uplo, &i__3, &nb, &a[a_offset], lda, &e[1], &tau[1], &
work[1], &ldwork);
/*
Update the unreduced submatrix A(1:i-1,1:i-1), using an
update of the form: A := A - V*W' - W*V'
*/
i__3 = i__ - 1;
z__1.r = -1., z__1.i = -0.;
zher2k_(uplo, "No transpose", &i__3, &nb, &z__1, &a[i__ * a_dim1
+ 1], lda, &work[1], &ldwork, &c_b1015, &a[a_offset], lda);
/*
Copy superdiagonal elements back into A, and diagonal
elements into D
*/
i__3 = i__ + nb - 1;
for (j = i__; j <= i__3; ++j) {
i__4 = j - 1 + j * a_dim1;
i__5 = j - 1;
a[i__4].r = e[i__5], a[i__4].i = 0.;
i__4 = j;
i__5 = j + j * a_dim1;
d__[i__4] = a[i__5].r;
/* L10: */
}
/* L20: */
}
/* Use unblocked code to reduce the last or only block */
zhetd2_(uplo, &kk, &a[a_offset], lda, &d__[1], &e[1], &tau[1], &iinfo);
} else {
/* Reduce the lower triangle of A */
i__2 = *n - nx;
i__1 = nb;
for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) {
/*
Reduce columns i:i+nb-1 to tridiagonal form and form the
matrix W which is needed to update the unreduced part of
the matrix
*/
i__3 = *n - i__ + 1;
zlatrd_(uplo, &i__3, &nb, &a[i__ + i__ * a_dim1], lda, &e[i__], &
tau[i__], &work[1], &ldwork);
/*
Update the unreduced submatrix A(i+nb:n,i+nb:n), using
an update of the form: A := A - V*W' - W*V'
*/
i__3 = *n - i__ - nb + 1;
z__1.r = -1., z__1.i = -0.;
zher2k_(uplo, "No transpose", &i__3, &nb, &z__1, &a[i__ + nb +
i__ * a_dim1], lda, &work[nb + 1], &ldwork, &c_b1015, &a[
i__ + nb + (i__ + nb) * a_dim1], lda);
/*
Copy subdiagonal elements back into A, and diagonal
elements into D
*/
i__3 = i__ + nb - 1;
for (j = i__; j <= i__3; ++j) {
i__4 = j + 1 + j * a_dim1;
i__5 = j;
a[i__4].r = e[i__5], a[i__4].i = 0.;
i__4 = j;
i__5 = j + j * a_dim1;
d__[i__4] = a[i__5].r;
/* L30: */
}
/* L40: */
}
/* Use unblocked code to reduce the last or only block */
i__1 = *n - i__ + 1;
zhetd2_(uplo, &i__1, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[i__],
&tau[i__], &iinfo);
}
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
return 0;
/* End of ZHETRD */
} /* zhetrd_ */
/* Subroutine */ int zhseqr_(char *job, char *compz, integer *n, integer *ilo,
integer *ihi, doublecomplex *h__, integer *ldh, doublecomplex *w,
doublecomplex *z__, integer *ldz, doublecomplex *work, integer *lwork,
integer *info)
{
/* System generated locals */
address a__1[2];
integer h_dim1, h_offset, z_dim1, z_offset, i__1, i__2, i__3, i__4[2],
i__5, i__6;
doublereal d__1, d__2, d__3, d__4;
doublecomplex z__1;
char ch__1[2];
/* Builtin functions */
double d_imag(doublecomplex *);
void d_cnjg(doublecomplex *, doublecomplex *);
/* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen);
/* Local variables */
static integer i__, j, k, l;
static doublecomplex s[225] /* was [15][15] */, v[16];
static integer i1, i2, ii, nh, nr, ns, nv;
static doublecomplex vv[16];
static integer itn;
static doublecomplex tau;
static integer its;
static doublereal ulp, tst1;
static integer maxb, ierr;
static doublereal unfl;
static doublecomplex temp;
static doublereal ovfl;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
doublecomplex *, integer *);
static integer itemp;
static doublereal rtemp;
extern /* Subroutine */ int zgemv_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *);
static logical initz, wantt, wantz;
static doublereal rwork[1];
extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
extern doublereal dlapy2_(doublereal *, doublereal *);
extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int zdscal_(integer *, doublereal *,
doublecomplex *, integer *), zlarfg_(integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *);
extern integer izamax_(integer *, doublecomplex *, integer *);
extern doublereal zlanhs_(char *, integer *, doublecomplex *, integer *,
doublereal *);
extern /* Subroutine */ int zlahqr_(logical *, logical *, integer *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
integer *, integer *, doublecomplex *, integer *, integer *),
zlacpy_(char *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *), zlaset_(char *, integer *,
integer *, doublecomplex *, doublecomplex *, doublecomplex *,
integer *), zlarfx_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *);
static doublereal smlnum;
static logical lquery;
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZHSEQR computes the eigenvalues of a complex upper Hessenberg
matrix H, and, optionally, the matrices T and Z from the Schur
decomposition H = Z T Z**H, where T is an upper triangular matrix
(the Schur form), and Z is the unitary matrix of Schur vectors.
Optionally Z may be postmultiplied into an input unitary matrix Q,
so that this routine can give the Schur factorization of a matrix A
which has been reduced to the Hessenberg form H by the unitary
matrix Q: A = Q*H*Q**H = (QZ)*T*(QZ)**H.
Arguments
=========
JOB (input) CHARACTER*1
= 'E': compute eigenvalues only;
= 'S': compute eigenvalues and the Schur form T.
COMPZ (input) CHARACTER*1
= 'N': no Schur vectors are computed;
= 'I': Z is initialized to the unit matrix and the matrix Z
of Schur vectors of H is returned;
= 'V': Z must contain an unitary matrix Q on entry, and
the product Q*Z is returned.
N (input) INTEGER
The order of the matrix H. N >= 0.
ILO (input) INTEGER
IHI (input) INTEGER
It is assumed that H is already upper triangular in rows
and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally
set by a previous call to ZGEBAL, and then passed to CGEHRD
when the matrix output by ZGEBAL is reduced to Hessenberg
form. Otherwise ILO and IHI should be set to 1 and N
respectively.
1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
H (input/output) COMPLEX*16 array, dimension (LDH,N)
On entry, the upper Hessenberg matrix H.
On exit, if JOB = 'S', H contains the upper triangular matrix
T from the Schur decomposition (the Schur form). If
JOB = 'E', the contents of H are unspecified on exit.
LDH (input) INTEGER
The leading dimension of the array H. LDH >= max(1,N).
W (output) COMPLEX*16 array, dimension (N)
The computed eigenvalues. If JOB = 'S', the eigenvalues are
stored in the same order as on the diagonal of the Schur form
returned in H, with W(i) = H(i,i).
Z (input/output) COMPLEX*16 array, dimension (LDZ,N)
If COMPZ = 'N': Z is not referenced.
If COMPZ = 'I': on entry, Z need not be set, and on exit, Z
contains the unitary matrix Z of the Schur vectors of H.
If COMPZ = 'V': on entry Z must contain an N-by-N matrix Q,
which is assumed to be equal to the unit matrix except for
the submatrix Z(ILO:IHI,ILO:IHI); on exit Z contains Q*Z.
Normally Q is the unitary matrix generated by ZUNGHR after
the call to ZGEHRD which formed the Hessenberg matrix H.
LDZ (input) INTEGER
The leading dimension of the array Z.
LDZ >= max(1,N) if COMPZ = 'I' or 'V'; LDZ >= 1 otherwise.
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,N).
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, ZHSEQR failed to compute all the
eigenvalues in a total of 30*(IHI-ILO+1) iterations;
elements 1:ilo-1 and i+1:n of W contain those
eigenvalues which have been successfully computed.
=====================================================================
Decode and test the input parameters
*/
/* Parameter adjustments */
h_dim1 = *ldh;
h_offset = 1 + h_dim1 * 1;
h__ -= h_offset;
--w;
z_dim1 = *ldz;
z_offset = 1 + z_dim1 * 1;
z__ -= z_offset;
--work;
/* Function Body */
wantt = lsame_(job, "S");
initz = lsame_(compz, "I");
wantz = initz || lsame_(compz, "V");
*info = 0;
i__1 = max(1,*n);
work[1].r = (doublereal) i__1, work[1].i = 0.;
lquery = *lwork == -1;
if ((! lsame_(job, "E") && ! wantt)) {
*info = -1;
} else if ((! lsame_(compz, "N") && ! wantz)) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*ilo < 1 || *ilo > max(1,*n)) {
*info = -4;
} else if (*ihi < min(*ilo,*n) || *ihi > *n) {
*info = -5;
} else if (*ldh < max(1,*n)) {
*info = -7;
} else if (*ldz < 1 || (wantz && *ldz < max(1,*n))) {
*info = -10;
} else if ((*lwork < max(1,*n) && ! lquery)) {
*info = -12;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZHSEQR", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Initialize Z, if necessary */
if (initz) {
zlaset_("Full", n, n, &c_b59, &c_b60, &z__[z_offset], ldz);
}
/* Store the eigenvalues isolated by ZGEBAL. */
i__1 = *ilo - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__ + i__ * h_dim1;
w[i__2].r = h__[i__3].r, w[i__2].i = h__[i__3].i;
/* L10: */
}
i__1 = *n;
for (i__ = *ihi + 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__ + i__ * h_dim1;
w[i__2].r = h__[i__3].r, w[i__2].i = h__[i__3].i;
/* L20: */
}
/* Quick return if possible. */
if (*n == 0) {
return 0;
}
if (*ilo == *ihi) {
i__1 = *ilo;
i__2 = *ilo + *ilo * h_dim1;
w[i__1].r = h__[i__2].r, w[i__1].i = h__[i__2].i;
return 0;
}
/*
Set rows and columns ILO to IHI to zero below the first
subdiagonal.
*/
i__1 = *ihi - 2;
for (j = *ilo; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j + 2; i__ <= i__2; ++i__) {
i__3 = i__ + j * h_dim1;
h__[i__3].r = 0., h__[i__3].i = 0.;
/* L30: */
}
/* L40: */
}
nh = *ihi - *ilo + 1;
/*
I1 and I2 are the indices of the first row and last column of H
to which transformations must be applied. If eigenvalues only are
being computed, I1 and I2 are re-set inside the main loop.
*/
if (wantt) {
i1 = 1;
i2 = *n;
} else {
i1 = *ilo;
i2 = *ihi;
}
/* Ensure that the subdiagonal elements are real. */
i__1 = *ihi;
for (i__ = *ilo + 1; i__ <= i__1; ++i__) {
i__2 = i__ + (i__ - 1) * h_dim1;
temp.r = h__[i__2].r, temp.i = h__[i__2].i;
if (d_imag(&temp) != 0.) {
d__1 = temp.r;
d__2 = d_imag(&temp);
rtemp = dlapy2_(&d__1, &d__2);
i__2 = i__ + (i__ - 1) * h_dim1;
h__[i__2].r = rtemp, h__[i__2].i = 0.;
z__1.r = temp.r / rtemp, z__1.i = temp.i / rtemp;
temp.r = z__1.r, temp.i = z__1.i;
if (i2 > i__) {
i__2 = i2 - i__;
d_cnjg(&z__1, &temp);
zscal_(&i__2, &z__1, &h__[i__ + (i__ + 1) * h_dim1], ldh);
}
i__2 = i__ - i1;
zscal_(&i__2, &temp, &h__[i1 + i__ * h_dim1], &c__1);
if (i__ < *ihi) {
i__2 = i__ + 1 + i__ * h_dim1;
i__3 = i__ + 1 + i__ * h_dim1;
z__1.r = temp.r * h__[i__3].r - temp.i * h__[i__3].i, z__1.i =
temp.r * h__[i__3].i + temp.i * h__[i__3].r;
h__[i__2].r = z__1.r, h__[i__2].i = z__1.i;
}
if (wantz) {
zscal_(&nh, &temp, &z__[*ilo + i__ * z_dim1], &c__1);
}
}
/* L50: */
}
/*
Determine the order of the multi-shift QR algorithm to be used.
Writing concatenation
*/
i__4[0] = 1, a__1[0] = job;
i__4[1] = 1, a__1[1] = compz;
s_cat(ch__1, a__1, i__4, &c__2, (ftnlen)2);
ns = ilaenv_(&c__4, "ZHSEQR", ch__1, n, ilo, ihi, &c_n1, (ftnlen)6, (
ftnlen)2);
/* Writing concatenation */
i__4[0] = 1, a__1[0] = job;
i__4[1] = 1, a__1[1] = compz;
s_cat(ch__1, a__1, i__4, &c__2, (ftnlen)2);
maxb = ilaenv_(&c__8, "ZHSEQR", ch__1, n, ilo, ihi, &c_n1, (ftnlen)6, (
ftnlen)2);
if (ns <= 1 || ns > nh || maxb >= nh) {
/* Use the standard double-shift algorithm */
zlahqr_(&wantt, &wantz, n, ilo, ihi, &h__[h_offset], ldh, &w[1], ilo,
ihi, &z__[z_offset], ldz, info);
return 0;
}
maxb = max(2,maxb);
/* Computing MIN */
i__1 = min(ns,maxb);
ns = min(i__1,15);
/*
Now 1 < NS <= MAXB < NH.
Set machine-dependent constants for the stopping criterion.
If norm(H) <= sqrt(OVFL), overflow should not occur.
*/
unfl = SAFEMINIMUM;
ovfl = 1. / unfl;
dlabad_(&unfl, &ovfl);
ulp = PRECISION;
smlnum = unfl * (nh / ulp);
/* ITN is the total number of multiple-shift QR iterations allowed. */
itn = nh * 30;
/*
The main loop begins here. I is the loop index and decreases from
IHI to ILO in steps of at most MAXB. Each iteration of the loop
works with the active submatrix in rows and columns L to I.
Eigenvalues I+1 to IHI have already converged. Either L = ILO, or
H(L,L-1) is negligible so that the matrix splits.
*/
i__ = *ihi;
L60:
if (i__ < *ilo) {
goto L180;
}
/*
Perform multiple-shift QR iterations on rows and columns ILO to I
until a submatrix of order at most MAXB splits off at the bottom
because a subdiagonal element has become negligible.
*/
l = *ilo;
i__1 = itn;
for (its = 0; its <= i__1; ++its) {
/* Look for a single small subdiagonal element. */
i__2 = l + 1;
for (k = i__; k >= i__2; --k) {
i__3 = k - 1 + (k - 1) * h_dim1;
i__5 = k + k * h_dim1;
tst1 = (d__1 = h__[i__3].r, abs(d__1)) + (d__2 = d_imag(&h__[k -
1 + (k - 1) * h_dim1]), abs(d__2)) + ((d__3 = h__[i__5].r,
abs(d__3)) + (d__4 = d_imag(&h__[k + k * h_dim1]), abs(
d__4)));
if (tst1 == 0.) {
i__3 = i__ - l + 1;
tst1 = zlanhs_("1", &i__3, &h__[l + l * h_dim1], ldh, rwork);
}
i__3 = k + (k - 1) * h_dim1;
/* Computing MAX */
d__2 = ulp * tst1;
if ((d__1 = h__[i__3].r, abs(d__1)) <= max(d__2,smlnum)) {
goto L80;
}
/* L70: */
}
L80:
l = k;
if (l > *ilo) {
/* H(L,L-1) is negligible. */
i__2 = l + (l - 1) * h_dim1;
h__[i__2].r = 0., h__[i__2].i = 0.;
}
/* Exit from loop if a submatrix of order <= MAXB has split off. */
if (l >= i__ - maxb + 1) {
goto L170;
}
/*
Now the active submatrix is in rows and columns L to I. If
eigenvalues only are being computed, only the active submatrix
need be transformed.
*/
if (! wantt) {
i1 = l;
i2 = i__;
}
if (its == 20 || its == 30) {
/* Exceptional shifts. */
i__2 = i__;
for (ii = i__ - ns + 1; ii <= i__2; ++ii) {
i__3 = ii;
i__5 = ii + (ii - 1) * h_dim1;
i__6 = ii + ii * h_dim1;
d__3 = ((d__1 = h__[i__5].r, abs(d__1)) + (d__2 = h__[i__6].r,
abs(d__2))) * 1.5;
w[i__3].r = d__3, w[i__3].i = 0.;
/* L90: */
}
} else {
/* Use eigenvalues of trailing submatrix of order NS as shifts. */
zlacpy_("Full", &ns, &ns, &h__[i__ - ns + 1 + (i__ - ns + 1) *
h_dim1], ldh, s, &c__15);
zlahqr_(&c_false, &c_false, &ns, &c__1, &ns, s, &c__15, &w[i__ -
ns + 1], &c__1, &ns, &z__[z_offset], ldz, &ierr);
if (ierr > 0) {
/*
If ZLAHQR failed to compute all NS eigenvalues, use the
unconverged diagonal elements as the remaining shifts.
*/
i__2 = ierr;
for (ii = 1; ii <= i__2; ++ii) {
i__3 = i__ - ns + ii;
i__5 = ii + ii * 15 - 16;
w[i__3].r = s[i__5].r, w[i__3].i = s[i__5].i;
/* L100: */
}
}
}
/*
Form the first column of (G-w(1)) (G-w(2)) . . . (G-w(ns))
where G is the Hessenberg submatrix H(L:I,L:I) and w is
the vector of shifts (stored in W). The result is
stored in the local array V.
*/
v[0].r = 1., v[0].i = 0.;
i__2 = ns + 1;
for (ii = 2; ii <= i__2; ++ii) {
i__3 = ii - 1;
v[i__3].r = 0., v[i__3].i = 0.;
/* L110: */
}
nv = 1;
i__2 = i__;
for (j = i__ - ns + 1; j <= i__2; ++j) {
i__3 = nv + 1;
zcopy_(&i__3, v, &c__1, vv, &c__1);
i__3 = nv + 1;
i__5 = j;
z__1.r = -w[i__5].r, z__1.i = -w[i__5].i;
zgemv_("No transpose", &i__3, &nv, &c_b60, &h__[l + l * h_dim1],
ldh, vv, &c__1, &z__1, v, &c__1);
++nv;
/*
Scale V(1:NV) so that max(abs(V(i))) = 1. If V is zero,
reset it to the unit vector.
*/
itemp = izamax_(&nv, v, &c__1);
i__3 = itemp - 1;
rtemp = (d__1 = v[i__3].r, abs(d__1)) + (d__2 = d_imag(&v[itemp -
1]), abs(d__2));
if (rtemp == 0.) {
v[0].r = 1., v[0].i = 0.;
i__3 = nv;
for (ii = 2; ii <= i__3; ++ii) {
i__5 = ii - 1;
v[i__5].r = 0., v[i__5].i = 0.;
/* L120: */
}
} else {
rtemp = max(rtemp,smlnum);
d__1 = 1. / rtemp;
zdscal_(&nv, &d__1, v, &c__1);
}
/* L130: */
}
/* Multiple-shift QR step */
i__2 = i__ - 1;
for (k = l; k <= i__2; ++k) {
/*
The first iteration of this loop determines a reflection G
from the vector V and applies it from left and right to H,
thus creating a nonzero bulge below the subdiagonal.
Each subsequent iteration determines a reflection G to
restore the Hessenberg form in the (K-1)th column, and thus
chases the bulge one step toward the bottom of the active
submatrix. NR is the order of G.
Computing MIN
*/
i__3 = ns + 1, i__5 = i__ - k + 1;
nr = min(i__3,i__5);
if (k > l) {
zcopy_(&nr, &h__[k + (k - 1) * h_dim1], &c__1, v, &c__1);
}
zlarfg_(&nr, v, &v[1], &c__1, &tau);
if (k > l) {
i__3 = k + (k - 1) * h_dim1;
h__[i__3].r = v[0].r, h__[i__3].i = v[0].i;
i__3 = i__;
for (ii = k + 1; ii <= i__3; ++ii) {
i__5 = ii + (k - 1) * h_dim1;
h__[i__5].r = 0., h__[i__5].i = 0.;
/* L140: */
}
}
v[0].r = 1., v[0].i = 0.;
/*
Apply G' from the left to transform the rows of the matrix
in columns K to I2.
*/
i__3 = i2 - k + 1;
d_cnjg(&z__1, &tau);
zlarfx_("Left", &nr, &i__3, v, &z__1, &h__[k + k * h_dim1], ldh, &
work[1]);
/*
Apply G from the right to transform the columns of the
matrix in rows I1 to min(K+NR,I).
Computing MIN
*/
i__5 = k + nr;
i__3 = min(i__5,i__) - i1 + 1;
zlarfx_("Right", &i__3, &nr, v, &tau, &h__[i1 + k * h_dim1], ldh,
&work[1]);
if (wantz) {
/* Accumulate transformations in the matrix Z */
zlarfx_("Right", &nh, &nr, v, &tau, &z__[*ilo + k * z_dim1],
ldz, &work[1]);
}
/* L150: */
}
/* Ensure that H(I,I-1) is real. */
i__2 = i__ + (i__ - 1) * h_dim1;
temp.r = h__[i__2].r, temp.i = h__[i__2].i;
if (d_imag(&temp) != 0.) {
d__1 = temp.r;
d__2 = d_imag(&temp);
rtemp = dlapy2_(&d__1, &d__2);
i__2 = i__ + (i__ - 1) * h_dim1;
h__[i__2].r = rtemp, h__[i__2].i = 0.;
z__1.r = temp.r / rtemp, z__1.i = temp.i / rtemp;
temp.r = z__1.r, temp.i = z__1.i;
if (i2 > i__) {
i__2 = i2 - i__;
d_cnjg(&z__1, &temp);
zscal_(&i__2, &z__1, &h__[i__ + (i__ + 1) * h_dim1], ldh);
}
i__2 = i__ - i1;
zscal_(&i__2, &temp, &h__[i1 + i__ * h_dim1], &c__1);
if (wantz) {
zscal_(&nh, &temp, &z__[*ilo + i__ * z_dim1], &c__1);
}
}
/* L160: */
}
/* Failure to converge in remaining number of iterations */
*info = i__;
return 0;
L170:
/*
A submatrix of order <= MAXB in rows and columns L to I has split
off. Use the double-shift QR algorithm to handle it.
*/
zlahqr_(&wantt, &wantz, n, &l, &i__, &h__[h_offset], ldh, &w[1], ilo, ihi,
&z__[z_offset], ldz, info);
if (*info > 0) {
return 0;
}
/*
Decrement number of remaining iterations, and return to start of
the main loop with a new value of I.
*/
itn -= its;
i__ = l - 1;
goto L60;
L180:
i__1 = max(1,*n);
work[1].r = (doublereal) i__1, work[1].i = 0.;
return 0;
/* End of ZHSEQR */
} /* zhseqr_ */
/* Subroutine */ int zlabrd_(integer *m, integer *n, integer *nb,
doublecomplex *a, integer *lda, doublereal *d__, doublereal *e,
doublecomplex *tauq, doublecomplex *taup, doublecomplex *x, integer *
ldx, doublecomplex *y, integer *ldy)
{
/* System generated locals */
integer a_dim1, a_offset, x_dim1, x_offset, y_dim1, y_offset, i__1, i__2,
i__3;
doublecomplex z__1;
/* Local variables */
static integer i__;
static doublecomplex alpha;
extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
doublecomplex *, integer *), zgemv_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *),
zlarfg_(integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *), zlacgv_(integer *, doublecomplex *, integer *);
/*
-- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZLABRD reduces the first NB rows and columns of a complex general
m by n matrix A to upper or lower real bidiagonal form by a unitary
transformation Q' * A * P, and returns the matrices X and Y which
are needed to apply the transformation to the unreduced part of A.
If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower
bidiagonal form.
This is an auxiliary routine called by ZGEBRD
Arguments
=========
M (input) INTEGER
The number of rows in the matrix A.
N (input) INTEGER
The number of columns in the matrix A.
NB (input) INTEGER
The number of leading rows and columns of A to be reduced.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the m by n general matrix to be reduced.
On exit, the first NB rows and columns of the matrix are
overwritten; the rest of the array is unchanged.
If m >= n, elements on and below the diagonal in the first NB
columns, with the array TAUQ, represent the unitary
matrix Q as a product of elementary reflectors; and
elements above the diagonal in the first NB rows, with the
array TAUP, represent the unitary matrix P as a product
of elementary reflectors.
If m < n, elements below the diagonal in the first NB
columns, with the array TAUQ, represent the unitary
matrix Q as a product of elementary reflectors, and
elements on and above the diagonal in the first NB rows,
with the array TAUP, represent the unitary matrix P as
a product of elementary reflectors.
See Further Details.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
D (output) DOUBLE PRECISION array, dimension (NB)
The diagonal elements of the first NB rows and columns of
the reduced matrix. D(i) = A(i,i).
E (output) DOUBLE PRECISION array, dimension (NB)
The off-diagonal elements of the first NB rows and columns of
the reduced matrix.
TAUQ (output) COMPLEX*16 array dimension (NB)
The scalar factors of the elementary reflectors which
represent the unitary matrix Q. See Further Details.
TAUP (output) COMPLEX*16 array, dimension (NB)
The scalar factors of the elementary reflectors which
represent the unitary matrix P. See Further Details.
X (output) COMPLEX*16 array, dimension (LDX,NB)
The m-by-nb matrix X required to update the unreduced part
of A.
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,M).
Y (output) COMPLEX*16 array, dimension (LDY,NB)
The n-by-nb matrix Y required to update the unreduced part
of A.
LDY (output) INTEGER
The leading dimension of the array Y. LDY >= max(1,N).
Further Details
===============
The matrices Q and P are represented as products of elementary
reflectors:
Q = H(1) H(2) . . . H(nb) and P = G(1) G(2) . . . G(nb)
Each H(i) and G(i) has the form:
H(i) = I - tauq * v * v' and G(i) = I - taup * u * u'
where tauq and taup are complex scalars, and v and u are complex
vectors.
If m >= n, v(1:i-1) = 0, v(i) = 1, and v(i:m) is stored on exit in
A(i:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+1:n) is stored on exit in
A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
If m < n, v(1:i) = 0, v(i+1) = 1, and v(i+1:m) is stored on exit in
A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i:n) is stored on exit in
A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
The elements of the vectors v and u together form the m-by-nb matrix
V and the nb-by-n matrix U' which are needed, with X and Y, to apply
the transformation to the unreduced part of the matrix, using a block
update of the form: A := A - V*Y' - X*U'.
The contents of A on exit are illustrated by the following examples
with nb = 2:
m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n):
( 1 1 u1 u1 u1 ) ( 1 u1 u1 u1 u1 u1 )
( v1 1 1 u2 u2 ) ( 1 1 u2 u2 u2 u2 )
( v1 v2 a a a ) ( v1 1 a a a a )
( v1 v2 a a a ) ( v1 v2 a a a a )
( v1 v2 a a a ) ( v1 v2 a a a a )
( v1 v2 a a a )
where a denotes an element of the original matrix which is unchanged,
vi denotes an element of the vector defining H(i), and ui an element
of the vector defining G(i).
=====================================================================
Quick return if possible
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--d__;
--e;
--tauq;
--taup;
x_dim1 = *ldx;
x_offset = 1 + x_dim1 * 1;
x -= x_offset;
y_dim1 = *ldy;
y_offset = 1 + y_dim1 * 1;
y -= y_offset;
/* Function Body */
if (*m <= 0 || *n <= 0) {
return 0;
}
if (*m >= *n) {
/* Reduce to upper bidiagonal form */
i__1 = *nb;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Update A(i:m,i) */
i__2 = i__ - 1;
zlacgv_(&i__2, &y[i__ + y_dim1], ldy);
i__2 = *m - i__ + 1;
i__3 = i__ - 1;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__2, &i__3, &z__1, &a[i__ + a_dim1], lda,
&y[i__ + y_dim1], ldy, &c_b60, &a[i__ + i__ * a_dim1], &
c__1);
i__2 = i__ - 1;
zlacgv_(&i__2, &y[i__ + y_dim1], ldy);
i__2 = *m - i__ + 1;
i__3 = i__ - 1;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__2, &i__3, &z__1, &x[i__ + x_dim1], ldx,
&a[i__ * a_dim1 + 1], &c__1, &c_b60, &a[i__ + i__ *
a_dim1], &c__1);
/* Generate reflection Q(i) to annihilate A(i+1:m,i) */
i__2 = i__ + i__ * a_dim1;
alpha.r = a[i__2].r, alpha.i = a[i__2].i;
i__2 = *m - i__ + 1;
/* Computing MIN */
i__3 = i__ + 1;
zlarfg_(&i__2, &alpha, &a[min(i__3,*m) + i__ * a_dim1], &c__1, &
tauq[i__]);
i__2 = i__;
d__[i__2] = alpha.r;
if (i__ < *n) {
i__2 = i__ + i__ * a_dim1;
a[i__2].r = 1., a[i__2].i = 0.;
/* Compute Y(i+1:n,i) */
i__2 = *m - i__ + 1;
i__3 = *n - i__;
zgemv_("Conjugate transpose", &i__2, &i__3, &c_b60, &a[i__ + (
i__ + 1) * a_dim1], lda, &a[i__ + i__ * a_dim1], &
c__1, &c_b59, &y[i__ + 1 + i__ * y_dim1], &c__1);
i__2 = *m - i__ + 1;
i__3 = i__ - 1;
zgemv_("Conjugate transpose", &i__2, &i__3, &c_b60, &a[i__ +
a_dim1], lda, &a[i__ + i__ * a_dim1], &c__1, &c_b59, &
y[i__ * y_dim1 + 1], &c__1);
i__2 = *n - i__;
i__3 = i__ - 1;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__2, &i__3, &z__1, &y[i__ + 1 +
y_dim1], ldy, &y[i__ * y_dim1 + 1], &c__1, &c_b60, &y[
i__ + 1 + i__ * y_dim1], &c__1);
i__2 = *m - i__ + 1;
i__3 = i__ - 1;
zgemv_("Conjugate transpose", &i__2, &i__3, &c_b60, &x[i__ +
x_dim1], ldx, &a[i__ + i__ * a_dim1], &c__1, &c_b59, &
y[i__ * y_dim1 + 1], &c__1);
i__2 = i__ - 1;
i__3 = *n - i__;
z__1.r = -1., z__1.i = -0.;
zgemv_("Conjugate transpose", &i__2, &i__3, &z__1, &a[(i__ +
1) * a_dim1 + 1], lda, &y[i__ * y_dim1 + 1], &c__1, &
c_b60, &y[i__ + 1 + i__ * y_dim1], &c__1);
i__2 = *n - i__;
zscal_(&i__2, &tauq[i__], &y[i__ + 1 + i__ * y_dim1], &c__1);
/* Update A(i,i+1:n) */
i__2 = *n - i__;
zlacgv_(&i__2, &a[i__ + (i__ + 1) * a_dim1], lda);
zlacgv_(&i__, &a[i__ + a_dim1], lda);
i__2 = *n - i__;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__2, &i__, &z__1, &y[i__ + 1 +
y_dim1], ldy, &a[i__ + a_dim1], lda, &c_b60, &a[i__ +
(i__ + 1) * a_dim1], lda);
zlacgv_(&i__, &a[i__ + a_dim1], lda);
i__2 = i__ - 1;
zlacgv_(&i__2, &x[i__ + x_dim1], ldx);
i__2 = i__ - 1;
i__3 = *n - i__;
z__1.r = -1., z__1.i = -0.;
zgemv_("Conjugate transpose", &i__2, &i__3, &z__1, &a[(i__ +
1) * a_dim1 + 1], lda, &x[i__ + x_dim1], ldx, &c_b60,
&a[i__ + (i__ + 1) * a_dim1], lda);
i__2 = i__ - 1;
zlacgv_(&i__2, &x[i__ + x_dim1], ldx);
/* Generate reflection P(i) to annihilate A(i,i+2:n) */
i__2 = i__ + (i__ + 1) * a_dim1;
alpha.r = a[i__2].r, alpha.i = a[i__2].i;
i__2 = *n - i__;
/* Computing MIN */
i__3 = i__ + 2;
zlarfg_(&i__2, &alpha, &a[i__ + min(i__3,*n) * a_dim1], lda, &
taup[i__]);
i__2 = i__;
e[i__2] = alpha.r;
i__2 = i__ + (i__ + 1) * a_dim1;
a[i__2].r = 1., a[i__2].i = 0.;
/* Compute X(i+1:m,i) */
i__2 = *m - i__;
i__3 = *n - i__;
zgemv_("No transpose", &i__2, &i__3, &c_b60, &a[i__ + 1 + (
i__ + 1) * a_dim1], lda, &a[i__ + (i__ + 1) * a_dim1],
lda, &c_b59, &x[i__ + 1 + i__ * x_dim1], &c__1);
i__2 = *n - i__;
zgemv_("Conjugate transpose", &i__2, &i__, &c_b60, &y[i__ + 1
+ y_dim1], ldy, &a[i__ + (i__ + 1) * a_dim1], lda, &
c_b59, &x[i__ * x_dim1 + 1], &c__1);
i__2 = *m - i__;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__2, &i__, &z__1, &a[i__ + 1 +
a_dim1], lda, &x[i__ * x_dim1 + 1], &c__1, &c_b60, &x[
i__ + 1 + i__ * x_dim1], &c__1);
i__2 = i__ - 1;
i__3 = *n - i__;
zgemv_("No transpose", &i__2, &i__3, &c_b60, &a[(i__ + 1) *
a_dim1 + 1], lda, &a[i__ + (i__ + 1) * a_dim1], lda, &
c_b59, &x[i__ * x_dim1 + 1], &c__1);
i__2 = *m - i__;
i__3 = i__ - 1;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__2, &i__3, &z__1, &x[i__ + 1 +
x_dim1], ldx, &x[i__ * x_dim1 + 1], &c__1, &c_b60, &x[
i__ + 1 + i__ * x_dim1], &c__1);
i__2 = *m - i__;
zscal_(&i__2, &taup[i__], &x[i__ + 1 + i__ * x_dim1], &c__1);
i__2 = *n - i__;
zlacgv_(&i__2, &a[i__ + (i__ + 1) * a_dim1], lda);
}
/* L10: */
}
} else {
/* Reduce to lower bidiagonal form */
i__1 = *nb;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Update A(i,i:n) */
i__2 = *n - i__ + 1;
zlacgv_(&i__2, &a[i__ + i__ * a_dim1], lda);
i__2 = i__ - 1;
zlacgv_(&i__2, &a[i__ + a_dim1], lda);
i__2 = *n - i__ + 1;
i__3 = i__ - 1;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__2, &i__3, &z__1, &y[i__ + y_dim1], ldy,
&a[i__ + a_dim1], lda, &c_b60, &a[i__ + i__ * a_dim1],
lda);
i__2 = i__ - 1;
zlacgv_(&i__2, &a[i__ + a_dim1], lda);
i__2 = i__ - 1;
zlacgv_(&i__2, &x[i__ + x_dim1], ldx);
i__2 = i__ - 1;
i__3 = *n - i__ + 1;
z__1.r = -1., z__1.i = -0.;
zgemv_("Conjugate transpose", &i__2, &i__3, &z__1, &a[i__ *
a_dim1 + 1], lda, &x[i__ + x_dim1], ldx, &c_b60, &a[i__ +
i__ * a_dim1], lda);
i__2 = i__ - 1;
zlacgv_(&i__2, &x[i__ + x_dim1], ldx);
/* Generate reflection P(i) to annihilate A(i,i+1:n) */
i__2 = i__ + i__ * a_dim1;
alpha.r = a[i__2].r, alpha.i = a[i__2].i;
i__2 = *n - i__ + 1;
/* Computing MIN */
i__3 = i__ + 1;
zlarfg_(&i__2, &alpha, &a[i__ + min(i__3,*n) * a_dim1], lda, &
taup[i__]);
i__2 = i__;
d__[i__2] = alpha.r;
if (i__ < *m) {
i__2 = i__ + i__ * a_dim1;
a[i__2].r = 1., a[i__2].i = 0.;
/* Compute X(i+1:m,i) */
i__2 = *m - i__;
i__3 = *n - i__ + 1;
zgemv_("No transpose", &i__2, &i__3, &c_b60, &a[i__ + 1 + i__
* a_dim1], lda, &a[i__ + i__ * a_dim1], lda, &c_b59, &
x[i__ + 1 + i__ * x_dim1], &c__1);
i__2 = *n - i__ + 1;
i__3 = i__ - 1;
zgemv_("Conjugate transpose", &i__2, &i__3, &c_b60, &y[i__ +
y_dim1], ldy, &a[i__ + i__ * a_dim1], lda, &c_b59, &x[
i__ * x_dim1 + 1], &c__1);
i__2 = *m - i__;
i__3 = i__ - 1;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__2, &i__3, &z__1, &a[i__ + 1 +
a_dim1], lda, &x[i__ * x_dim1 + 1], &c__1, &c_b60, &x[
i__ + 1 + i__ * x_dim1], &c__1);
i__2 = i__ - 1;
i__3 = *n - i__ + 1;
zgemv_("No transpose", &i__2, &i__3, &c_b60, &a[i__ * a_dim1
+ 1], lda, &a[i__ + i__ * a_dim1], lda, &c_b59, &x[
i__ * x_dim1 + 1], &c__1);
i__2 = *m - i__;
i__3 = i__ - 1;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__2, &i__3, &z__1, &x[i__ + 1 +
x_dim1], ldx, &x[i__ * x_dim1 + 1], &c__1, &c_b60, &x[
i__ + 1 + i__ * x_dim1], &c__1);
i__2 = *m - i__;
zscal_(&i__2, &taup[i__], &x[i__ + 1 + i__ * x_dim1], &c__1);
i__2 = *n - i__ + 1;
zlacgv_(&i__2, &a[i__ + i__ * a_dim1], lda);
/* Update A(i+1:m,i) */
i__2 = i__ - 1;
zlacgv_(&i__2, &y[i__ + y_dim1], ldy);
i__2 = *m - i__;
i__3 = i__ - 1;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__2, &i__3, &z__1, &a[i__ + 1 +
a_dim1], lda, &y[i__ + y_dim1], ldy, &c_b60, &a[i__ +
1 + i__ * a_dim1], &c__1);
i__2 = i__ - 1;
zlacgv_(&i__2, &y[i__ + y_dim1], ldy);
i__2 = *m - i__;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__2, &i__, &z__1, &x[i__ + 1 +
x_dim1], ldx, &a[i__ * a_dim1 + 1], &c__1, &c_b60, &a[
i__ + 1 + i__ * a_dim1], &c__1);
/* Generate reflection Q(i) to annihilate A(i+2:m,i) */
i__2 = i__ + 1 + i__ * a_dim1;
alpha.r = a[i__2].r, alpha.i = a[i__2].i;
i__2 = *m - i__;
/* Computing MIN */
i__3 = i__ + 2;
zlarfg_(&i__2, &alpha, &a[min(i__3,*m) + i__ * a_dim1], &c__1,
&tauq[i__]);
i__2 = i__;
e[i__2] = alpha.r;
i__2 = i__ + 1 + i__ * a_dim1;
a[i__2].r = 1., a[i__2].i = 0.;
/* Compute Y(i+1:n,i) */
i__2 = *m - i__;
i__3 = *n - i__;
zgemv_("Conjugate transpose", &i__2, &i__3, &c_b60, &a[i__ +
1 + (i__ + 1) * a_dim1], lda, &a[i__ + 1 + i__ *
a_dim1], &c__1, &c_b59, &y[i__ + 1 + i__ * y_dim1], &
c__1);
i__2 = *m - i__;
i__3 = i__ - 1;
zgemv_("Conjugate transpose", &i__2, &i__3, &c_b60, &a[i__ +
1 + a_dim1], lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &
c_b59, &y[i__ * y_dim1 + 1], &c__1);
i__2 = *n - i__;
i__3 = i__ - 1;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__2, &i__3, &z__1, &y[i__ + 1 +
y_dim1], ldy, &y[i__ * y_dim1 + 1], &c__1, &c_b60, &y[
i__ + 1 + i__ * y_dim1], &c__1);
i__2 = *m - i__;
zgemv_("Conjugate transpose", &i__2, &i__, &c_b60, &x[i__ + 1
+ x_dim1], ldx, &a[i__ + 1 + i__ * a_dim1], &c__1, &
c_b59, &y[i__ * y_dim1 + 1], &c__1);
i__2 = *n - i__;
z__1.r = -1., z__1.i = -0.;
zgemv_("Conjugate transpose", &i__, &i__2, &z__1, &a[(i__ + 1)
* a_dim1 + 1], lda, &y[i__ * y_dim1 + 1], &c__1, &
c_b60, &y[i__ + 1 + i__ * y_dim1], &c__1);
i__2 = *n - i__;
zscal_(&i__2, &tauq[i__], &y[i__ + 1 + i__ * y_dim1], &c__1);
} else {
i__2 = *n - i__ + 1;
zlacgv_(&i__2, &a[i__ + i__ * a_dim1], lda);
}
/* L20: */
}
}
return 0;
/* End of ZLABRD */
} /* zlabrd_ */
/* Subroutine */ int zlacgv_(integer *n, doublecomplex *x, integer *incx)
{
/* System generated locals */
integer i__1, i__2;
doublecomplex z__1;
/* Builtin functions */
void d_cnjg(doublecomplex *, doublecomplex *);
/* Local variables */
static integer i__, ioff;
/*
-- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
October 31, 1992
Purpose
=======
ZLACGV conjugates a complex vector of length N.
Arguments
=========
N (input) INTEGER
The length of the vector X. N >= 0.
X (input/output) COMPLEX*16 array, dimension
(1+(N-1)*abs(INCX))
On entry, the vector of length N to be conjugated.
On exit, X is overwritten with conjg(X).
INCX (input) INTEGER
The spacing between successive elements of X.
=====================================================================
*/
/* Parameter adjustments */
--x;
/* Function Body */
if (*incx == 1) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
d_cnjg(&z__1, &x[i__]);
x[i__2].r = z__1.r, x[i__2].i = z__1.i;
/* L10: */
}
} else {
ioff = 1;
if (*incx < 0) {
ioff = 1 - (*n - 1) * *incx;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = ioff;
d_cnjg(&z__1, &x[ioff]);
x[i__2].r = z__1.r, x[i__2].i = z__1.i;
ioff += *incx;
/* L20: */
}
}
return 0;
/* End of ZLACGV */
} /* zlacgv_ */
/* Subroutine */ int zlacp2_(char *uplo, integer *m, integer *n, doublereal *
a, integer *lda, doublecomplex *b, integer *ldb)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4;
/* Local variables */
static integer i__, j;
extern logical lsame_(char *, char *);
/*
-- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZLACP2 copies all or part of a real two-dimensional matrix A to a
complex matrix B.
Arguments
=========
UPLO (input) CHARACTER*1
Specifies the part of the matrix A to be copied to B.
= 'U': Upper triangular part
= 'L': Lower triangular part
Otherwise: All of the matrix A
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
A (input) DOUBLE PRECISION array, dimension (LDA,N)
The m by n matrix A. If UPLO = 'U', only the upper trapezium
is accessed; if UPLO = 'L', only the lower trapezium is
accessed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
B (output) COMPLEX*16 array, dimension (LDB,N)
On exit, B = A in the locations specified by UPLO.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,M).
=====================================================================
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
/* Function Body */
if (lsame_(uplo, "U")) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = min(j,*m);
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * a_dim1;
b[i__3].r = a[i__4], b[i__3].i = 0.;
/* L10: */
}
/* L20: */
}
} else if (lsame_(uplo, "L")) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = j; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * a_dim1;
b[i__3].r = a[i__4], b[i__3].i = 0.;
/* L30: */
}
/* L40: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * a_dim1;
b[i__3].r = a[i__4], b[i__3].i = 0.;
/* L50: */
}
/* L60: */
}
}
return 0;
/* End of ZLACP2 */
} /* zlacp2_ */
/* Subroutine */ int zlacpy_(char *uplo, integer *m, integer *n,
doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4;
/* Local variables */
static integer i__, j;
extern logical lsame_(char *, char *);
/*
-- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
February 29, 1992
Purpose
=======
ZLACPY copies all or part of a two-dimensional matrix A to another
matrix B.
Arguments
=========
UPLO (input) CHARACTER*1
Specifies the part of the matrix A to be copied to B.
= 'U': Upper triangular part
= 'L': Lower triangular part
Otherwise: All of the matrix A
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
A (input) COMPLEX*16 array, dimension (LDA,N)
The m by n matrix A. If UPLO = 'U', only the upper trapezium
is accessed; if UPLO = 'L', only the lower trapezium is
accessed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
B (output) COMPLEX*16 array, dimension (LDB,N)
On exit, B = A in the locations specified by UPLO.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,M).
=====================================================================
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
/* Function Body */
if (lsame_(uplo, "U")) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = min(j,*m);
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * a_dim1;
b[i__3].r = a[i__4].r, b[i__3].i = a[i__4].i;
/* L10: */
}
/* L20: */
}
} else if (lsame_(uplo, "L")) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = j; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * a_dim1;
b[i__3].r = a[i__4].r, b[i__3].i = a[i__4].i;
/* L30: */
}
/* L40: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * a_dim1;
b[i__3].r = a[i__4].r, b[i__3].i = a[i__4].i;
/* L50: */
}
/* L60: */
}
}
return 0;
/* End of ZLACPY */
} /* zlacpy_ */
/* Subroutine */ int zlacrm_(integer *m, integer *n, doublecomplex *a,
integer *lda, doublereal *b, integer *ldb, doublecomplex *c__,
integer *ldc, doublereal *rwork)
{
/* System generated locals */
integer b_dim1, b_offset, a_dim1, a_offset, c_dim1, c_offset, i__1, i__2,
i__3, i__4, i__5;
doublereal d__1;
doublecomplex z__1;
/* Builtin functions */
double d_imag(doublecomplex *);
/* Local variables */
static integer i__, j, l;
extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *,
integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *);
/*
-- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZLACRM performs a very simple matrix-matrix multiplication:
C := A * B,
where A is M by N and complex; B is N by N and real;
C is M by N and complex.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A and of the matrix C.
M >= 0.
N (input) INTEGER
The number of columns and rows of the matrix B and
the number of columns of the matrix C.
N >= 0.
A (input) COMPLEX*16 array, dimension (LDA, N)
A contains the M by N matrix A.
LDA (input) INTEGER
The leading dimension of the array A. LDA >=max(1,M).
B (input) DOUBLE PRECISION array, dimension (LDB, N)
B contains the N by N matrix B.
LDB (input) INTEGER
The leading dimension of the array B. LDB >=max(1,N).
C (input) COMPLEX*16 array, dimension (LDC, N)
C contains the M by N matrix C.
LDC (input) INTEGER
The leading dimension of the array C. LDC >=max(1,N).
RWORK (workspace) DOUBLE PRECISION array, dimension (2*M*N)
=====================================================================
Quick return if possible.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1 * 1;
c__ -= c_offset;
--rwork;
/* Function Body */
if (*m == 0 || *n == 0) {
return 0;
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
rwork[(j - 1) * *m + i__] = a[i__3].r;
/* L10: */
}
/* L20: */
}
l = *m * *n + 1;
dgemm_("N", "N", m, n, n, &c_b1015, &rwork[1], m, &b[b_offset], ldb, &
c_b324, &rwork[l], m);
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = l + (j - 1) * *m + i__ - 1;
c__[i__3].r = rwork[i__4], c__[i__3].i = 0.;
/* L30: */
}
/* L40: */
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
rwork[(j - 1) * *m + i__] = d_imag(&a[i__ + j * a_dim1]);
/* L50: */
}
/* L60: */
}
dgemm_("N", "N", m, n, n, &c_b1015, &rwork[1], m, &b[b_offset], ldb, &
c_b324, &rwork[l], m);
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
d__1 = c__[i__4].r;
i__5 = l + (j - 1) * *m + i__ - 1;
z__1.r = d__1, z__1.i = rwork[i__5];
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/* L70: */
}
/* L80: */
}
return 0;
/* End of ZLACRM */
} /* zlacrm_ */
/* Double Complex */ VOID zladiv_(doublecomplex * ret_val, doublecomplex *x,
doublecomplex *y)
{
/* System generated locals */
doublereal d__1, d__2, d__3, d__4;
doublecomplex z__1;
/* Builtin functions */
double d_imag(doublecomplex *);
/* Local variables */
static doublereal zi, zr;
extern /* Subroutine */ int dladiv_(doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *);
/*
-- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
October 31, 1992
Purpose
=======
ZLADIV := X / Y, where X and Y are complex. The computation of X / Y
will not overflow on an intermediary step unless the results
overflows.
Arguments
=========
X (input) COMPLEX*16
Y (input) COMPLEX*16
The complex scalars X and Y.
=====================================================================
*/
d__1 = x->r;
d__2 = d_imag(x);
d__3 = y->r;
d__4 = d_imag(y);
dladiv_(&d__1, &d__2, &d__3, &d__4, &zr, &zi);
z__1.r = zr, z__1.i = zi;
ret_val->r = z__1.r, ret_val->i = z__1.i;
return ;
/* End of ZLADIV */
} /* zladiv_ */
/* Subroutine */ int zlaed0_(integer *qsiz, integer *n, doublereal *d__,
doublereal *e, doublecomplex *q, integer *ldq, doublecomplex *qstore,
integer *ldqs, doublereal *rwork, integer *iwork, integer *info)
{
/* System generated locals */
integer q_dim1, q_offset, qstore_dim1, qstore_offset, i__1, i__2;
doublereal d__1;
/* Builtin functions */
double log(doublereal);
integer pow_ii(integer *, integer *);
/* Local variables */
static integer i__, j, k, ll, iq, lgn, msd2, smm1, spm1, spm2;
static doublereal temp;
static integer curr, iperm;
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *);
static integer indxq, iwrem, iqptr, tlvls;
extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *), zlaed7_(integer *, integer *,
integer *, integer *, integer *, integer *, doublereal *,
doublecomplex *, integer *, doublereal *, integer *, doublereal *,
integer *, integer *, integer *, integer *, integer *,
doublereal *, doublecomplex *, doublereal *, integer *, integer *)
;
static integer igivcl;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int zlacrm_(integer *, integer *, doublecomplex *,
integer *, doublereal *, integer *, doublecomplex *, integer *,
doublereal *);
static integer igivnm, submat, curprb, subpbs, igivpt;
extern /* Subroutine */ int dsteqr_(char *, integer *, doublereal *,
doublereal *, doublereal *, integer *, doublereal *, integer *);
static integer curlvl, matsiz, iprmpt, smlsiz;
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
Using the divide and conquer method, ZLAED0 computes all eigenvalues
of a symmetric tridiagonal matrix which is one diagonal block of
those from reducing a dense or band Hermitian matrix and
corresponding eigenvectors of the dense or band matrix.
Arguments
=========
QSIZ (input) INTEGER
The dimension of the unitary matrix used to reduce
the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.
N (input) INTEGER
The dimension of the symmetric tridiagonal matrix. N >= 0.
D (input/output) DOUBLE PRECISION array, dimension (N)
On entry, the diagonal elements of the tridiagonal matrix.
On exit, the eigenvalues in ascending order.
E (input/output) DOUBLE PRECISION array, dimension (N-1)
On entry, the off-diagonal elements of the tridiagonal matrix.
On exit, E has been destroyed.
Q (input/output) COMPLEX*16 array, dimension (LDQ,N)
On entry, Q must contain an QSIZ x N matrix whose columns
unitarily orthonormal. It is a part of the unitary matrix
that reduces the full dense Hermitian matrix to a
(reducible) symmetric tridiagonal matrix.
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >= max(1,N).
IWORK (workspace) INTEGER array,
the dimension of IWORK must be at least
6 + 6*N + 5*N*lg N
( lg( N ) = smallest integer k
such that 2^k >= N )
RWORK (workspace) DOUBLE PRECISION array,
dimension (1 + 3*N + 2*N*lg N + 3*N**2)
( lg( N ) = smallest integer k
such that 2^k >= N )
QSTORE (workspace) COMPLEX*16 array, dimension (LDQS, N)
Used to store parts of
the eigenvector matrix when the updating matrix multiplies
take place.
LDQS (input) INTEGER
The leading dimension of the array QSTORE.
LDQS >= max(1,N).
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: The algorithm failed to compute an eigenvalue while
working on the submatrix lying in rows and columns
INFO/(N+1) through mod(INFO,N+1).
=====================================================================
Warning: N could be as big as QSIZ!
Test the input parameters.
*/
/* Parameter adjustments */
--d__;
--e;
q_dim1 = *ldq;
q_offset = 1 + q_dim1 * 1;
q -= q_offset;
qstore_dim1 = *ldqs;
qstore_offset = 1 + qstore_dim1 * 1;
qstore -= qstore_offset;
--rwork;
--iwork;
/* Function Body */
*info = 0;
/*
IF( ICOMPQ .LT. 0 .OR. ICOMPQ .GT. 2 ) THEN
INFO = -1
ELSE IF( ( ICOMPQ .EQ. 1 ) .AND. ( QSIZ .LT. MAX( 0, N ) ) )
$ THEN
*/
if (*qsiz < max(0,*n)) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*ldq < max(1,*n)) {
*info = -6;
} else if (*ldqs < max(1,*n)) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZLAED0", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
smlsiz = ilaenv_(&c__9, "ZLAED0", " ", &c__0, &c__0, &c__0, &c__0, (
ftnlen)6, (ftnlen)1);
/*
Determine the size and placement of the submatrices, and save in
the leading elements of IWORK.
*/
iwork[1] = *n;
subpbs = 1;
tlvls = 0;
L10:
if (iwork[subpbs] > smlsiz) {
for (j = subpbs; j >= 1; --j) {
iwork[j * 2] = (iwork[j] + 1) / 2;
iwork[((j) << (1)) - 1] = iwork[j] / 2;
/* L20: */
}
++tlvls;
subpbs <<= 1;
goto L10;
}
i__1 = subpbs;
for (j = 2; j <= i__1; ++j) {
iwork[j] += iwork[j - 1];
/* L30: */
}
/*
Divide the matrix into SUBPBS submatrices of size at most SMLSIZ+1
using rank-1 modifications (cuts).
*/
spm1 = subpbs - 1;
i__1 = spm1;
for (i__ = 1; i__ <= i__1; ++i__) {
submat = iwork[i__] + 1;
smm1 = submat - 1;
d__[smm1] -= (d__1 = e[smm1], abs(d__1));
d__[submat] -= (d__1 = e[smm1], abs(d__1));
/* L40: */
}
indxq = ((*n) << (2)) + 3;
/*
Set up workspaces for eigenvalues only/accumulate new vectors
routine
*/
temp = log((doublereal) (*n)) / log(2.);
lgn = (integer) temp;
if (pow_ii(&c__2, &lgn) < *n) {
++lgn;
}
if (pow_ii(&c__2, &lgn) < *n) {
++lgn;
}
iprmpt = indxq + *n + 1;
iperm = iprmpt + *n * lgn;
iqptr = iperm + *n * lgn;
igivpt = iqptr + *n + 2;
igivcl = igivpt + *n * lgn;
igivnm = 1;
iq = igivnm + ((*n) << (1)) * lgn;
/* Computing 2nd power */
i__1 = *n;
iwrem = iq + i__1 * i__1 + 1;
/* Initialize pointers */
i__1 = subpbs;
for (i__ = 0; i__ <= i__1; ++i__) {
iwork[iprmpt + i__] = 1;
iwork[igivpt + i__] = 1;
/* L50: */
}
iwork[iqptr] = 1;
/*
Solve each submatrix eigenproblem at the bottom of the divide and
conquer tree.
*/
curr = 0;
i__1 = spm1;
for (i__ = 0; i__ <= i__1; ++i__) {
if (i__ == 0) {
submat = 1;
matsiz = iwork[1];
} else {
submat = iwork[i__] + 1;
matsiz = iwork[i__ + 1] - iwork[i__];
}
ll = iq - 1 + iwork[iqptr + curr];
dsteqr_("I", &matsiz, &d__[submat], &e[submat], &rwork[ll], &matsiz, &
rwork[1], info);
zlacrm_(qsiz, &matsiz, &q[submat * q_dim1 + 1], ldq, &rwork[ll], &
matsiz, &qstore[submat * qstore_dim1 + 1], ldqs, &rwork[iwrem]
);
/* Computing 2nd power */
i__2 = matsiz;
iwork[iqptr + curr + 1] = iwork[iqptr + curr] + i__2 * i__2;
++curr;
if (*info > 0) {
*info = submat * (*n + 1) + submat + matsiz - 1;
return 0;
}
k = 1;
i__2 = iwork[i__ + 1];
for (j = submat; j <= i__2; ++j) {
iwork[indxq + j] = k;
++k;
/* L60: */
}
/* L70: */
}
/*
Successively merge eigensystems of adjacent submatrices
into eigensystem for the corresponding larger matrix.
while ( SUBPBS > 1 )
*/
curlvl = 1;
L80:
if (subpbs > 1) {
spm2 = subpbs - 2;
i__1 = spm2;
for (i__ = 0; i__ <= i__1; i__ += 2) {
if (i__ == 0) {
submat = 1;
matsiz = iwork[2];
msd2 = iwork[1];
curprb = 0;
} else {
submat = iwork[i__] + 1;
matsiz = iwork[i__ + 2] - iwork[i__];
msd2 = matsiz / 2;
++curprb;
}
/*
Merge lower order eigensystems (of size MSD2 and MATSIZ - MSD2)
into an eigensystem of size MATSIZ. ZLAED7 handles the case
when the eigenvectors of a full or band Hermitian matrix (which
was reduced to tridiagonal form) are desired.
I am free to use Q as a valuable working space until Loop 150.
*/
zlaed7_(&matsiz, &msd2, qsiz, &tlvls, &curlvl, &curprb, &d__[
submat], &qstore[submat * qstore_dim1 + 1], ldqs, &e[
submat + msd2 - 1], &iwork[indxq + submat], &rwork[iq], &
iwork[iqptr], &iwork[iprmpt], &iwork[iperm], &iwork[
igivpt], &iwork[igivcl], &rwork[igivnm], &q[submat *
q_dim1 + 1], &rwork[iwrem], &iwork[subpbs + 1], info);
if (*info > 0) {
*info = submat * (*n + 1) + submat + matsiz - 1;
return 0;
}
iwork[i__ / 2 + 1] = iwork[i__ + 2];
/* L90: */
}
subpbs /= 2;
++curlvl;
goto L80;
}
/*
end while
Re-merge the eigenvalues/vectors which were deflated at the final
merge step.
*/
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
j = iwork[indxq + i__];
rwork[i__] = d__[j];
zcopy_(qsiz, &qstore[j * qstore_dim1 + 1], &c__1, &q[i__ * q_dim1 + 1]
, &c__1);
/* L100: */
}
dcopy_(n, &rwork[1], &c__1, &d__[1], &c__1);
return 0;
/* End of ZLAED0 */
} /* zlaed0_ */
/* Subroutine */ int zlaed7_(integer *n, integer *cutpnt, integer *qsiz,
integer *tlvls, integer *curlvl, integer *curpbm, doublereal *d__,
doublecomplex *q, integer *ldq, doublereal *rho, integer *indxq,
doublereal *qstore, integer *qptr, integer *prmptr, integer *perm,
integer *givptr, integer *givcol, doublereal *givnum, doublecomplex *
work, doublereal *rwork, integer *iwork, integer *info)
{
/* System generated locals */
integer q_dim1, q_offset, i__1, i__2;
/* Builtin functions */
integer pow_ii(integer *, integer *);
/* Local variables */
static integer i__, k, n1, n2, iq, iw, iz, ptr, ind1, ind2, indx, curr,
indxc, indxp;
extern /* Subroutine */ int dlaed9_(integer *, integer *, integer *,
integer *, doublereal *, doublereal *, integer *, doublereal *,
doublereal *, doublereal *, doublereal *, integer *, integer *),
zlaed8_(integer *, integer *, integer *, doublecomplex *, integer
*, doublereal *, doublereal *, integer *, doublereal *,
doublereal *, doublecomplex *, integer *, doublereal *, integer *,
integer *, integer *, integer *, integer *, integer *,
doublereal *, integer *), dlaeda_(integer *, integer *, integer *,
integer *, integer *, integer *, integer *, integer *,
doublereal *, doublereal *, integer *, doublereal *, doublereal *,
integer *);
static integer idlmda;
extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *,
integer *, integer *, integer *), xerbla_(char *, integer *), zlacrm_(integer *, integer *, doublecomplex *, integer *,
doublereal *, integer *, doublecomplex *, integer *, doublereal *
);
static integer coltyp;
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZLAED7 computes the updated eigensystem of a diagonal
matrix after modification by a rank-one symmetric matrix. This
routine is used only for the eigenproblem which requires all
eigenvalues and optionally eigenvectors of a dense or banded
Hermitian matrix that has been reduced to tridiagonal form.
T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out)
where Z = Q'u, u is a vector of length N with ones in the
CUTPNT and CUTPNT + 1 th elements and zeros elsewhere.
The eigenvectors of the original matrix are stored in Q, and the
eigenvalues are in D. The algorithm consists of three stages:
The first stage consists of deflating the size of the problem
when there are multiple eigenvalues or if there is a zero in
the Z vector. For each such occurence the dimension of the
secular equation problem is reduced by one. This stage is
performed by the routine DLAED2.
The second stage consists of calculating the updated
eigenvalues. This is done by finding the roots of the secular
equation via the routine DLAED4 (as called by SLAED3).
This routine also calculates the eigenvectors of the current
problem.
The final stage consists of computing the updated eigenvectors
directly using the updated eigenvalues. The eigenvectors for
the current problem are multiplied with the eigenvectors from
the overall problem.
Arguments
=========
N (input) INTEGER
The dimension of the symmetric tridiagonal matrix. N >= 0.
CUTPNT (input) INTEGER
Contains the location of the last eigenvalue in the leading
sub-matrix. min(1,N) <= CUTPNT <= N.
QSIZ (input) INTEGER
The dimension of the unitary matrix used to reduce
the full matrix to tridiagonal form. QSIZ >= N.
TLVLS (input) INTEGER
The total number of merging levels in the overall divide and
conquer tree.
CURLVL (input) INTEGER
The current level in the overall merge routine,
0 <= curlvl <= tlvls.
CURPBM (input) INTEGER
The current problem in the current level in the overall
merge routine (counting from upper left to lower right).
D (input/output) DOUBLE PRECISION array, dimension (N)
On entry, the eigenvalues of the rank-1-perturbed matrix.
On exit, the eigenvalues of the repaired matrix.
Q (input/output) COMPLEX*16 array, dimension (LDQ,N)
On entry, the eigenvectors of the rank-1-perturbed matrix.
On exit, the eigenvectors of the repaired tridiagonal matrix.
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >= max(1,N).
RHO (input) DOUBLE PRECISION
Contains the subdiagonal element used to create the rank-1
modification.
INDXQ (output) INTEGER array, dimension (N)
This contains the permutation which will reintegrate the
subproblem just solved back into sorted order,
ie. D( INDXQ( I = 1, N ) ) will be in ascending order.
IWORK (workspace) INTEGER array, dimension (4*N)
RWORK (workspace) DOUBLE PRECISION array,
dimension (3*N+2*QSIZ*N)
WORK (workspace) COMPLEX*16 array, dimension (QSIZ*N)
QSTORE (input/output) DOUBLE PRECISION array, dimension (N**2+1)
Stores eigenvectors of submatrices encountered during
divide and conquer, packed together. QPTR points to
beginning of the submatrices.
QPTR (input/output) INTEGER array, dimension (N+2)
List of indices pointing to beginning of submatrices stored
in QSTORE. The submatrices are numbered starting at the
bottom left of the divide and conquer tree, from left to
right and bottom to top.
PRMPTR (input) INTEGER array, dimension (N lg N)
Contains a list of pointers which indicate where in PERM a
level's permutation is stored. PRMPTR(i+1) - PRMPTR(i)
indicates the size of the permutation and also the size of
the full, non-deflated problem.
PERM (input) INTEGER array, dimension (N lg N)
Contains the permutations (from deflation and sorting) to be
applied to each eigenblock.
GIVPTR (input) INTEGER array, dimension (N lg N)
Contains a list of pointers which indicate where in GIVCOL a
level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i)
indicates the number of Givens rotations.
GIVCOL (input) INTEGER array, dimension (2, N lg N)
Each pair of numbers indicates a pair of columns to take place
in a Givens rotation.
GIVNUM (input) DOUBLE PRECISION array, dimension (2, N lg N)
Each number indicates the S value to be used in the
corresponding Givens rotation.
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = 1, an eigenvalue did not converge
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
--d__;
q_dim1 = *ldq;
q_offset = 1 + q_dim1 * 1;
q -= q_offset;
--indxq;
--qstore;
--qptr;
--prmptr;
--perm;
--givptr;
givcol -= 3;
givnum -= 3;
--work;
--rwork;
--iwork;
/* Function Body */
*info = 0;
/*
IF( ICOMPQ.LT.0 .OR. ICOMPQ.GT.1 ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
*/
if (*n < 0) {
*info = -1;
} else if (min(1,*n) > *cutpnt || *n < *cutpnt) {
*info = -2;
} else if (*qsiz < *n) {
*info = -3;
} else if (*ldq < max(1,*n)) {
*info = -9;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZLAED7", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/*
The following values are for bookkeeping purposes only. They are
integer pointers which indicate the portion of the workspace
used by a particular array in DLAED2 and SLAED3.
*/
iz = 1;
idlmda = iz + *n;
iw = idlmda + *n;
iq = iw + *n;
indx = 1;
indxc = indx + *n;
coltyp = indxc + *n;
indxp = coltyp + *n;
/*
Form the z-vector which consists of the last row of Q_1 and the
first row of Q_2.
*/
ptr = pow_ii(&c__2, tlvls) + 1;
i__1 = *curlvl - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = *tlvls - i__;
ptr += pow_ii(&c__2, &i__2);
/* L10: */
}
curr = ptr + *curpbm;
dlaeda_(n, tlvls, curlvl, curpbm, &prmptr[1], &perm[1], &givptr[1], &
givcol[3], &givnum[3], &qstore[1], &qptr[1], &rwork[iz], &rwork[
iz + *n], info);
/*
When solving the final problem, we no longer need the stored data,
so we will overwrite the data from this level onto the previously
used storage space.
*/
if (*curlvl == *tlvls) {
qptr[curr] = 1;
prmptr[curr] = 1;
givptr[curr] = 1;
}
/* Sort and Deflate eigenvalues. */
zlaed8_(&k, n, qsiz, &q[q_offset], ldq, &d__[1], rho, cutpnt, &rwork[iz],
&rwork[idlmda], &work[1], qsiz, &rwork[iw], &iwork[indxp], &iwork[
indx], &indxq[1], &perm[prmptr[curr]], &givptr[curr + 1], &givcol[
((givptr[curr]) << (1)) + 1], &givnum[((givptr[curr]) << (1)) + 1]
, info);
prmptr[curr + 1] = prmptr[curr] + *n;
givptr[curr + 1] += givptr[curr];
/* Solve Secular Equation. */
if (k != 0) {
dlaed9_(&k, &c__1, &k, n, &d__[1], &rwork[iq], &k, rho, &rwork[idlmda]
, &rwork[iw], &qstore[qptr[curr]], &k, info);
zlacrm_(qsiz, &k, &work[1], qsiz, &qstore[qptr[curr]], &k, &q[
q_offset], ldq, &rwork[iq]);
/* Computing 2nd power */
i__1 = k;
qptr[curr + 1] = qptr[curr] + i__1 * i__1;
if (*info != 0) {
return 0;
}
/* Prepare the INDXQ sorting premutation. */
n1 = k;
n2 = *n - k;
ind1 = 1;
ind2 = *n;
dlamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &indxq[1]);
} else {
qptr[curr + 1] = qptr[curr];
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
indxq[i__] = i__;
/* L20: */
}
}
return 0;
/* End of ZLAED7 */
} /* zlaed7_ */
/* Subroutine */ int zlaed8_(integer *k, integer *n, integer *qsiz,
doublecomplex *q, integer *ldq, doublereal *d__, doublereal *rho,
integer *cutpnt, doublereal *z__, doublereal *dlamda, doublecomplex *
q2, integer *ldq2, doublereal *w, integer *indxp, integer *indx,
integer *indxq, integer *perm, integer *givptr, integer *givcol,
doublereal *givnum, integer *info)
{
/* System generated locals */
integer q_dim1, q_offset, q2_dim1, q2_offset, i__1;
doublereal d__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static doublereal c__;
static integer i__, j;
static doublereal s, t;
static integer k2, n1, n2, jp, n1p1;
static doublereal eps, tau, tol;
static integer jlam, imax, jmax;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *), dcopy_(integer *, doublereal *, integer *, doublereal
*, integer *), zdrot_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, doublereal *), zcopy_(
integer *, doublecomplex *, integer *, doublecomplex *, integer *)
;
extern integer idamax_(integer *, doublereal *, integer *);
extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *,
integer *, integer *, integer *), xerbla_(char *, integer *), zlacpy_(char *, integer *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *);
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Oak Ridge National Lab, Argonne National Lab,
Courant Institute, NAG Ltd., and Rice University
September 30, 1994
Purpose
=======
ZLAED8 merges the two sets of eigenvalues together into a single
sorted set. Then it tries to deflate the size of the problem.
There are two ways in which deflation can occur: when two or more
eigenvalues are close together or if there is a tiny element in the
Z vector. For each such occurrence the order of the related secular
equation problem is reduced by one.
Arguments
=========
K (output) INTEGER
Contains the number of non-deflated eigenvalues.
This is the order of the related secular equation.
N (input) INTEGER
The dimension of the symmetric tridiagonal matrix. N >= 0.
QSIZ (input) INTEGER
The dimension of the unitary matrix used to reduce
the dense or band matrix to tridiagonal form.
QSIZ >= N if ICOMPQ = 1.
Q (input/output) COMPLEX*16 array, dimension (LDQ,N)
On entry, Q contains the eigenvectors of the partially solved
system which has been previously updated in matrix
multiplies with other partially solved eigensystems.
On exit, Q contains the trailing (N-K) updated eigenvectors
(those which were deflated) in its last N-K columns.
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >= max( 1, N ).
D (input/output) DOUBLE PRECISION array, dimension (N)
On entry, D contains the eigenvalues of the two submatrices to
be combined. On exit, D contains the trailing (N-K) updated
eigenvalues (those which were deflated) sorted into increasing
order.
RHO (input/output) DOUBLE PRECISION
Contains the off diagonal element associated with the rank-1
cut which originally split the two submatrices which are now
being recombined. RHO is modified during the computation to
the value required by DLAED3.
CUTPNT (input) INTEGER
Contains the location of the last eigenvalue in the leading
sub-matrix. MIN(1,N) <= CUTPNT <= N.
Z (input) DOUBLE PRECISION array, dimension (N)
On input this vector contains the updating vector (the last
row of the first sub-eigenvector matrix and the first row of
the second sub-eigenvector matrix). The contents of Z are
destroyed during the updating process.
DLAMDA (output) DOUBLE PRECISION array, dimension (N)
Contains a copy of the first K eigenvalues which will be used
by DLAED3 to form the secular equation.
Q2 (output) COMPLEX*16 array, dimension (LDQ2,N)
If ICOMPQ = 0, Q2 is not referenced. Otherwise,
Contains a copy of the first K eigenvectors which will be used
by DLAED7 in a matrix multiply (DGEMM) to update the new
eigenvectors.
LDQ2 (input) INTEGER
The leading dimension of the array Q2. LDQ2 >= max( 1, N ).
W (output) DOUBLE PRECISION array, dimension (N)
This will hold the first k values of the final
deflation-altered z-vector and will be passed to DLAED3.
INDXP (workspace) INTEGER array, dimension (N)
This will contain the permutation used to place deflated
values of D at the end of the array. On output INDXP(1:K)
points to the nondeflated D-values and INDXP(K+1:N)
points to the deflated eigenvalues.
INDX (workspace) INTEGER array, dimension (N)
This will contain the permutation used to sort the contents of
D into ascending order.
INDXQ (input) INTEGER array, dimension (N)
This contains the permutation which separately sorts the two
sub-problems in D into ascending order. Note that elements in
the second half of this permutation must first have CUTPNT
added to their values in order to be accurate.
PERM (output) INTEGER array, dimension (N)
Contains the permutations (from deflation and sorting) to be
applied to each eigenblock.
GIVPTR (output) INTEGER
Contains the number of Givens rotations which took place in
this subproblem.
GIVCOL (output) INTEGER array, dimension (2, N)
Each pair of numbers indicates a pair of columns to take place
in a Givens rotation.
GIVNUM (output) DOUBLE PRECISION array, dimension (2, N)
Each number indicates the S value to be used in the
corresponding Givens rotation.
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
q_dim1 = *ldq;
q_offset = 1 + q_dim1 * 1;
q -= q_offset;
--d__;
--z__;
--dlamda;
q2_dim1 = *ldq2;
q2_offset = 1 + q2_dim1 * 1;
q2 -= q2_offset;
--w;
--indxp;
--indx;
--indxq;
--perm;
givcol -= 3;
givnum -= 3;
/* Function Body */
*info = 0;
if (*n < 0) {
*info = -2;
} else if (*qsiz < *n) {
*info = -3;
} else if (*ldq < max(1,*n)) {
*info = -5;
} else if (*cutpnt < min(1,*n) || *cutpnt > *n) {
*info = -8;
} else if (*ldq2 < max(1,*n)) {
*info = -12;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZLAED8", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
n1 = *cutpnt;
n2 = *n - n1;
n1p1 = n1 + 1;
if (*rho < 0.) {
dscal_(&n2, &c_b1294, &z__[n1p1], &c__1);
}
/* Normalize z so that norm(z) = 1 */
t = 1. / sqrt(2.);
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
indx[j] = j;
/* L10: */
}
dscal_(n, &t, &z__[1], &c__1);
*rho = (d__1 = *rho * 2., abs(d__1));
/* Sort the eigenvalues into increasing order */
i__1 = *n;
for (i__ = *cutpnt + 1; i__ <= i__1; ++i__) {
indxq[i__] += *cutpnt;
/* L20: */
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
dlamda[i__] = d__[indxq[i__]];
w[i__] = z__[indxq[i__]];
/* L30: */
}
i__ = 1;
j = *cutpnt + 1;
dlamrg_(&n1, &n2, &dlamda[1], &c__1, &c__1, &indx[1]);
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
d__[i__] = dlamda[indx[i__]];
z__[i__] = w[indx[i__]];
/* L40: */
}
/* Calculate the allowable deflation tolerance */
imax = idamax_(n, &z__[1], &c__1);
jmax = idamax_(n, &d__[1], &c__1);
eps = EPSILON;
tol = eps * 8. * (d__1 = d__[jmax], abs(d__1));
/*
If the rank-1 modifier is small enough, no more needs to be done
-- except to reorganize Q so that its columns correspond with the
elements in D.
*/
if (*rho * (d__1 = z__[imax], abs(d__1)) <= tol) {
*k = 0;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
perm[j] = indxq[indx[j]];
zcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1]
, &c__1);
/* L50: */
}
zlacpy_("A", qsiz, n, &q2[q2_dim1 + 1], ldq2, &q[q_dim1 + 1], ldq);
return 0;
}
/*
If there are multiple eigenvalues then the problem deflates. Here
the number of equal eigenvalues are found. As each equal
eigenvalue is found, an elementary reflector is computed to rotate
the corresponding eigensubspace so that the corresponding
components of Z are zero in this new basis.
*/
*k = 0;
*givptr = 0;
k2 = *n + 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*rho * (d__1 = z__[j], abs(d__1)) <= tol) {
/* Deflate due to small z component. */
--k2;
indxp[k2] = j;
if (j == *n) {
goto L100;
}
} else {
jlam = j;
goto L70;
}
/* L60: */
}
L70:
++j;
if (j > *n) {
goto L90;
}
if (*rho * (d__1 = z__[j], abs(d__1)) <= tol) {
/* Deflate due to small z component. */
--k2;
indxp[k2] = j;
} else {
/* Check if eigenvalues are close enough to allow deflation. */
s = z__[jlam];
c__ = z__[j];
/*
Find sqrt(a**2+b**2) without overflow or
destructive underflow.
*/
tau = dlapy2_(&c__, &s);
t = d__[j] - d__[jlam];
c__ /= tau;
s = -s / tau;
if ((d__1 = t * c__ * s, abs(d__1)) <= tol) {
/* Deflation is possible. */
z__[j] = tau;
z__[jlam] = 0.;
/* Record the appropriate Givens rotation */
++(*givptr);
givcol[((*givptr) << (1)) + 1] = indxq[indx[jlam]];
givcol[((*givptr) << (1)) + 2] = indxq[indx[j]];
givnum[((*givptr) << (1)) + 1] = c__;
givnum[((*givptr) << (1)) + 2] = s;
zdrot_(qsiz, &q[indxq[indx[jlam]] * q_dim1 + 1], &c__1, &q[indxq[
indx[j]] * q_dim1 + 1], &c__1, &c__, &s);
t = d__[jlam] * c__ * c__ + d__[j] * s * s;
d__[j] = d__[jlam] * s * s + d__[j] * c__ * c__;
d__[jlam] = t;
--k2;
i__ = 1;
L80:
if (k2 + i__ <= *n) {
if (d__[jlam] < d__[indxp[k2 + i__]]) {
indxp[k2 + i__ - 1] = indxp[k2 + i__];
indxp[k2 + i__] = jlam;
++i__;
goto L80;
} else {
indxp[k2 + i__ - 1] = jlam;
}
} else {
indxp[k2 + i__ - 1] = jlam;
}
jlam = j;
} else {
++(*k);
w[*k] = z__[jlam];
dlamda[*k] = d__[jlam];
indxp[*k] = jlam;
jlam = j;
}
}
goto L70;
L90:
/* Record the last eigenvalue. */
++(*k);
w[*k] = z__[jlam];
dlamda[*k] = d__[jlam];
indxp[*k] = jlam;
L100:
/*
Sort the eigenvalues and corresponding eigenvectors into DLAMDA
and Q2 respectively. The eigenvalues/vectors which were not
deflated go into the first K slots of DLAMDA and Q2 respectively,
while those which were deflated go into the last N - K slots.
*/
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
jp = indxp[j];
dlamda[j] = d__[jp];
perm[j] = indxq[indx[jp]];
zcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1], &
c__1);
/* L110: */
}
/*
The deflated eigenvalues and their corresponding vectors go back
into the last N - K slots of D and Q respectively.
*/
if (*k < *n) {
i__1 = *n - *k;
dcopy_(&i__1, &dlamda[*k + 1], &c__1, &d__[*k + 1], &c__1);
i__1 = *n - *k;
zlacpy_("A", qsiz, &i__1, &q2[(*k + 1) * q2_dim1 + 1], ldq2, &q[(*k +
1) * q_dim1 + 1], ldq);
}
return 0;
/* End of ZLAED8 */
} /* zlaed8_ */
/* Subroutine */ int zlahqr_(logical *wantt, logical *wantz, integer *n,
integer *ilo, integer *ihi, doublecomplex *h__, integer *ldh,
doublecomplex *w, integer *iloz, integer *ihiz, doublecomplex *z__,
integer *ldz, integer *info)
{
/* System generated locals */
integer h_dim1, h_offset, z_dim1, z_offset, i__1, i__2, i__3, i__4, i__5;
doublereal d__1, d__2, d__3, d__4, d__5, d__6;
doublecomplex z__1, z__2, z__3, z__4;
/* Builtin functions */
double d_imag(doublecomplex *);
void z_sqrt(doublecomplex *, doublecomplex *), d_cnjg(doublecomplex *,
doublecomplex *);
double z_abs(doublecomplex *);
/* Local variables */
static integer i__, j, k, l, m;
static doublereal s;
static doublecomplex t, u, v[2], x, y;
static integer i1, i2;
static doublecomplex t1;
static doublereal t2;
static doublecomplex v2;
static doublereal h10;
static doublecomplex h11;
static doublereal h21;
static doublecomplex h22;
static integer nh, nz;
static doublecomplex h11s;
static integer itn, its;
static doublereal ulp;
static doublecomplex sum;
static doublereal tst1;
static doublecomplex temp;
extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
doublecomplex *, integer *);
static doublereal rtemp, rwork[1];
extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
extern /* Subroutine */ int zlarfg_(integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *);
extern /* Double Complex */ VOID zladiv_(doublecomplex *, doublecomplex *,
doublecomplex *);
extern doublereal zlanhs_(char *, integer *, doublecomplex *, integer *,
doublereal *);
static doublereal smlnum;
/*
-- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZLAHQR is an auxiliary routine called by ZHSEQR to update the
eigenvalues and Schur decomposition already computed by ZHSEQR, by
dealing with the Hessenberg submatrix in rows and columns ILO to IHI.
Arguments
=========
WANTT (input) LOGICAL
= .TRUE. : the full Schur form T is required;
= .FALSE.: only eigenvalues are required.
WANTZ (input) LOGICAL
= .TRUE. : the matrix of Schur vectors Z is required;
= .FALSE.: Schur vectors are not required.
N (input) INTEGER
The order of the matrix H. N >= 0.
ILO (input) INTEGER
IHI (input) INTEGER
It is assumed that H is already upper triangular in rows and
columns IHI+1:N, and that H(ILO,ILO-1) = 0 (unless ILO = 1).
ZLAHQR works primarily with the Hessenberg submatrix in rows
and columns ILO to IHI, but applies transformations to all of
H if WANTT is .TRUE..
1 <= ILO <= max(1,IHI); IHI <= N.
H (input/output) COMPLEX*16 array, dimension (LDH,N)
On entry, the upper Hessenberg matrix H.
On exit, if WANTT is .TRUE., H is upper triangular in rows
and columns ILO:IHI, with any 2-by-2 diagonal blocks in
standard form. If WANTT is .FALSE., the contents of H are
unspecified on exit.
LDH (input) INTEGER
The leading dimension of the array H. LDH >= max(1,N).
W (output) COMPLEX*16 array, dimension (N)
The computed eigenvalues ILO to IHI are stored in the
corresponding elements of W. If WANTT is .TRUE., the
eigenvalues are stored in the same order as on the diagonal
of the Schur form returned in H, with W(i) = H(i,i).
ILOZ (input) INTEGER
IHIZ (input) INTEGER
Specify the rows of Z to which transformations must be
applied if WANTZ is .TRUE..
1 <= ILOZ <= ILO; IHI <= IHIZ <= N.
Z (input/output) COMPLEX*16 array, dimension (LDZ,N)
If WANTZ is .TRUE., on entry Z must contain the current
matrix Z of transformations accumulated by ZHSEQR, and on
exit Z has been updated; transformations are applied only to
the submatrix Z(ILOZ:IHIZ,ILO:IHI).
If WANTZ is .FALSE., Z is not referenced.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= max(1,N).
INFO (output) INTEGER
= 0: successful exit
> 0: if INFO = i, ZLAHQR failed to compute all the
eigenvalues ILO to IHI in a total of 30*(IHI-ILO+1)
iterations; elements i+1:ihi of W contain those
eigenvalues which have been successfully computed.
=====================================================================
*/
/* Parameter adjustments */
h_dim1 = *ldh;
h_offset = 1 + h_dim1 * 1;
h__ -= h_offset;
--w;
z_dim1 = *ldz;
z_offset = 1 + z_dim1 * 1;
z__ -= z_offset;
/* Function Body */
*info = 0;
/* Quick return if possible */
if (*n == 0) {
return 0;
}
if (*ilo == *ihi) {
i__1 = *ilo;
i__2 = *ilo + *ilo * h_dim1;
w[i__1].r = h__[i__2].r, w[i__1].i = h__[i__2].i;
return 0;
}
nh = *ihi - *ilo + 1;
nz = *ihiz - *iloz + 1;
/*
Set machine-dependent constants for the stopping criterion.
If norm(H) <= sqrt(OVFL), overflow should not occur.
*/
ulp = PRECISION;
smlnum = SAFEMINIMUM / ulp;
/*
I1 and I2 are the indices of the first row and last column of H
to which transformations must be applied. If eigenvalues only are
being computed, I1 and I2 are set inside the main loop.
*/
if (*wantt) {
i1 = 1;
i2 = *n;
}
/* ITN is the total number of QR iterations allowed. */
itn = nh * 30;
/*
The main loop begins here. I is the loop index and decreases from
IHI to ILO in steps of 1. Each iteration of the loop works
with the active submatrix in rows and columns L to I.
Eigenvalues I+1 to IHI have already converged. Either L = ILO, or
H(L,L-1) is negligible so that the matrix splits.
*/
i__ = *ihi;
L10:
if (i__ < *ilo) {
goto L130;
}
/*
Perform QR iterations on rows and columns ILO to I until a
submatrix of order 1 splits off at the bottom because a
subdiagonal element has become negligible.
*/
l = *ilo;
i__1 = itn;
for (its = 0; its <= i__1; ++its) {
/* Look for a single small subdiagonal element. */
i__2 = l + 1;
for (k = i__; k >= i__2; --k) {
i__3 = k - 1 + (k - 1) * h_dim1;
i__4 = k + k * h_dim1;
tst1 = (d__1 = h__[i__3].r, abs(d__1)) + (d__2 = d_imag(&h__[k -
1 + (k - 1) * h_dim1]), abs(d__2)) + ((d__3 = h__[i__4].r,
abs(d__3)) + (d__4 = d_imag(&h__[k + k * h_dim1]), abs(
d__4)));
if (tst1 == 0.) {
i__3 = i__ - l + 1;
tst1 = zlanhs_("1", &i__3, &h__[l + l * h_dim1], ldh, rwork);
}
i__3 = k + (k - 1) * h_dim1;
/* Computing MAX */
d__2 = ulp * tst1;
if ((d__1 = h__[i__3].r, abs(d__1)) <= max(d__2,smlnum)) {
goto L30;
}
/* L20: */
}
L30:
l = k;
if (l > *ilo) {
/* H(L,L-1) is negligible */
i__2 = l + (l - 1) * h_dim1;
h__[i__2].r = 0., h__[i__2].i = 0.;
}
/* Exit from loop if a submatrix of order 1 has split off. */
if (l >= i__) {
goto L120;
}
/*
Now the active submatrix is in rows and columns L to I. If
eigenvalues only are being computed, only the active submatrix
need be transformed.
*/
if (! (*wantt)) {
i1 = l;
i2 = i__;
}
if (its == 10 || its == 20) {
/* Exceptional shift. */
i__2 = i__ + (i__ - 1) * h_dim1;
s = (d__1 = h__[i__2].r, abs(d__1)) * .75;
i__2 = i__ + i__ * h_dim1;
z__1.r = s + h__[i__2].r, z__1.i = h__[i__2].i;
t.r = z__1.r, t.i = z__1.i;
} else {
/* Wilkinson's shift. */
i__2 = i__ + i__ * h_dim1;
t.r = h__[i__2].r, t.i = h__[i__2].i;
i__2 = i__ - 1 + i__ * h_dim1;
i__3 = i__ + (i__ - 1) * h_dim1;
d__1 = h__[i__3].r;
z__1.r = d__1 * h__[i__2].r, z__1.i = d__1 * h__[i__2].i;
u.r = z__1.r, u.i = z__1.i;
if (u.r != 0. || u.i != 0.) {
i__2 = i__ - 1 + (i__ - 1) * h_dim1;
z__2.r = h__[i__2].r - t.r, z__2.i = h__[i__2].i - t.i;
z__1.r = z__2.r * .5, z__1.i = z__2.i * .5;
x.r = z__1.r, x.i = z__1.i;
z__3.r = x.r * x.r - x.i * x.i, z__3.i = x.r * x.i + x.i *
x.r;
z__2.r = z__3.r + u.r, z__2.i = z__3.i + u.i;
z_sqrt(&z__1, &z__2);
y.r = z__1.r, y.i = z__1.i;
if (x.r * y.r + d_imag(&x) * d_imag(&y) < 0.) {
z__1.r = -y.r, z__1.i = -y.i;
y.r = z__1.r, y.i = z__1.i;
}
z__3.r = x.r + y.r, z__3.i = x.i + y.i;
zladiv_(&z__2, &u, &z__3);
z__1.r = t.r - z__2.r, z__1.i = t.i - z__2.i;
t.r = z__1.r, t.i = z__1.i;
}
}
/* Look for two consecutive small subdiagonal elements. */
i__2 = l + 1;
for (m = i__ - 1; m >= i__2; --m) {
/*
Determine the effect of starting the single-shift QR
iteration at row M, and see if this would make H(M,M-1)
negligible.
*/
i__3 = m + m * h_dim1;
h11.r = h__[i__3].r, h11.i = h__[i__3].i;
i__3 = m + 1 + (m + 1) * h_dim1;
h22.r = h__[i__3].r, h22.i = h__[i__3].i;
z__1.r = h11.r - t.r, z__1.i = h11.i - t.i;
h11s.r = z__1.r, h11s.i = z__1.i;
i__3 = m + 1 + m * h_dim1;
h21 = h__[i__3].r;
s = (d__1 = h11s.r, abs(d__1)) + (d__2 = d_imag(&h11s), abs(d__2))
+ abs(h21);
z__1.r = h11s.r / s, z__1.i = h11s.i / s;
h11s.r = z__1.r, h11s.i = z__1.i;
h21 /= s;
v[0].r = h11s.r, v[0].i = h11s.i;
v[1].r = h21, v[1].i = 0.;
i__3 = m + (m - 1) * h_dim1;
h10 = h__[i__3].r;
tst1 = ((d__1 = h11s.r, abs(d__1)) + (d__2 = d_imag(&h11s), abs(
d__2))) * ((d__3 = h11.r, abs(d__3)) + (d__4 = d_imag(&
h11), abs(d__4)) + ((d__5 = h22.r, abs(d__5)) + (d__6 =
d_imag(&h22), abs(d__6))));
if ((d__1 = h10 * h21, abs(d__1)) <= ulp * tst1) {
goto L50;
}
/* L40: */
}
i__2 = l + l * h_dim1;
h11.r = h__[i__2].r, h11.i = h__[i__2].i;
i__2 = l + 1 + (l + 1) * h_dim1;
h22.r = h__[i__2].r, h22.i = h__[i__2].i;
z__1.r = h11.r - t.r, z__1.i = h11.i - t.i;
h11s.r = z__1.r, h11s.i = z__1.i;
i__2 = l + 1 + l * h_dim1;
h21 = h__[i__2].r;
s = (d__1 = h11s.r, abs(d__1)) + (d__2 = d_imag(&h11s), abs(d__2)) +
abs(h21);
z__1.r = h11s.r / s, z__1.i = h11s.i / s;
h11s.r = z__1.r, h11s.i = z__1.i;
h21 /= s;
v[0].r = h11s.r, v[0].i = h11s.i;
v[1].r = h21, v[1].i = 0.;
L50:
/* Single-shift QR step */
i__2 = i__ - 1;
for (k = m; k <= i__2; ++k) {
/*
The first iteration of this loop determines a reflection G
from the vector V and applies it from left and right to H,
thus creating a nonzero bulge below the subdiagonal.
Each subsequent iteration determines a reflection G to
restore the Hessenberg form in the (K-1)th column, and thus
chases the bulge one step toward the bottom of the active
submatrix.
V(2) is always real before the call to ZLARFG, and hence
after the call T2 ( = T1*V(2) ) is also real.
*/
if (k > m) {
zcopy_(&c__2, &h__[k + (k - 1) * h_dim1], &c__1, v, &c__1);
}
zlarfg_(&c__2, v, &v[1], &c__1, &t1);
if (k > m) {
i__3 = k + (k - 1) * h_dim1;
h__[i__3].r = v[0].r, h__[i__3].i = v[0].i;
i__3 = k + 1 + (k - 1) * h_dim1;
h__[i__3].r = 0., h__[i__3].i = 0.;
}
v2.r = v[1].r, v2.i = v[1].i;
z__1.r = t1.r * v2.r - t1.i * v2.i, z__1.i = t1.r * v2.i + t1.i *
v2.r;
t2 = z__1.r;
/*
Apply G from the left to transform the rows of the matrix
in columns K to I2.
*/
i__3 = i2;
for (j = k; j <= i__3; ++j) {
d_cnjg(&z__3, &t1);
i__4 = k + j * h_dim1;
z__2.r = z__3.r * h__[i__4].r - z__3.i * h__[i__4].i, z__2.i =
z__3.r * h__[i__4].i + z__3.i * h__[i__4].r;
i__5 = k + 1 + j * h_dim1;
z__4.r = t2 * h__[i__5].r, z__4.i = t2 * h__[i__5].i;
z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
sum.r = z__1.r, sum.i = z__1.i;
i__4 = k + j * h_dim1;
i__5 = k + j * h_dim1;
z__1.r = h__[i__5].r - sum.r, z__1.i = h__[i__5].i - sum.i;
h__[i__4].r = z__1.r, h__[i__4].i = z__1.i;
i__4 = k + 1 + j * h_dim1;
i__5 = k + 1 + j * h_dim1;
z__2.r = sum.r * v2.r - sum.i * v2.i, z__2.i = sum.r * v2.i +
sum.i * v2.r;
z__1.r = h__[i__5].r - z__2.r, z__1.i = h__[i__5].i - z__2.i;
h__[i__4].r = z__1.r, h__[i__4].i = z__1.i;
/* L60: */
}
/*
Apply G from the right to transform the columns of the
matrix in rows I1 to min(K+2,I).
Computing MIN
*/
i__4 = k + 2;
i__3 = min(i__4,i__);
for (j = i1; j <= i__3; ++j) {
i__4 = j + k * h_dim1;
z__2.r = t1.r * h__[i__4].r - t1.i * h__[i__4].i, z__2.i =
t1.r * h__[i__4].i + t1.i * h__[i__4].r;
i__5 = j + (k + 1) * h_dim1;
z__3.r = t2 * h__[i__5].r, z__3.i = t2 * h__[i__5].i;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
sum.r = z__1.r, sum.i = z__1.i;
i__4 = j + k * h_dim1;
i__5 = j + k * h_dim1;
z__1.r = h__[i__5].r - sum.r, z__1.i = h__[i__5].i - sum.i;
h__[i__4].r = z__1.r, h__[i__4].i = z__1.i;
i__4 = j + (k + 1) * h_dim1;
i__5 = j + (k + 1) * h_dim1;
d_cnjg(&z__3, &v2);
z__2.r = sum.r * z__3.r - sum.i * z__3.i, z__2.i = sum.r *
z__3.i + sum.i * z__3.r;
z__1.r = h__[i__5].r - z__2.r, z__1.i = h__[i__5].i - z__2.i;
h__[i__4].r = z__1.r, h__[i__4].i = z__1.i;
/* L70: */
}
if (*wantz) {
/* Accumulate transformations in the matrix Z */
i__3 = *ihiz;
for (j = *iloz; j <= i__3; ++j) {
i__4 = j + k * z_dim1;
z__2.r = t1.r * z__[i__4].r - t1.i * z__[i__4].i, z__2.i =
t1.r * z__[i__4].i + t1.i * z__[i__4].r;
i__5 = j + (k + 1) * z_dim1;
z__3.r = t2 * z__[i__5].r, z__3.i = t2 * z__[i__5].i;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
sum.r = z__1.r, sum.i = z__1.i;
i__4 = j + k * z_dim1;
i__5 = j + k * z_dim1;
z__1.r = z__[i__5].r - sum.r, z__1.i = z__[i__5].i -
sum.i;
z__[i__4].r = z__1.r, z__[i__4].i = z__1.i;
i__4 = j + (k + 1) * z_dim1;
i__5 = j + (k + 1) * z_dim1;
d_cnjg(&z__3, &v2);
z__2.r = sum.r * z__3.r - sum.i * z__3.i, z__2.i = sum.r *
z__3.i + sum.i * z__3.r;
z__1.r = z__[i__5].r - z__2.r, z__1.i = z__[i__5].i -
z__2.i;
z__[i__4].r = z__1.r, z__[i__4].i = z__1.i;
/* L80: */
}
}
if ((k == m && m > l)) {
/*
If the QR step was started at row M > L because two
consecutive small subdiagonals were found, then extra
scaling must be performed to ensure that H(M,M-1) remains
real.
*/
z__1.r = 1. - t1.r, z__1.i = 0. - t1.i;
temp.r = z__1.r, temp.i = z__1.i;
d__1 = z_abs(&temp);
z__1.r = temp.r / d__1, z__1.i = temp.i / d__1;
temp.r = z__1.r, temp.i = z__1.i;
i__3 = m + 1 + m * h_dim1;
i__4 = m + 1 + m * h_dim1;
d_cnjg(&z__2, &temp);
z__1.r = h__[i__4].r * z__2.r - h__[i__4].i * z__2.i, z__1.i =
h__[i__4].r * z__2.i + h__[i__4].i * z__2.r;
h__[i__3].r = z__1.r, h__[i__3].i = z__1.i;
if (m + 2 <= i__) {
i__3 = m + 2 + (m + 1) * h_dim1;
i__4 = m + 2 + (m + 1) * h_dim1;
z__1.r = h__[i__4].r * temp.r - h__[i__4].i * temp.i,
z__1.i = h__[i__4].r * temp.i + h__[i__4].i *
temp.r;
h__[i__3].r = z__1.r, h__[i__3].i = z__1.i;
}
i__3 = i__;
for (j = m; j <= i__3; ++j) {
if (j != m + 1) {
if (i2 > j) {
i__4 = i2 - j;
zscal_(&i__4, &temp, &h__[j + (j + 1) * h_dim1],
ldh);
}
i__4 = j - i1;
d_cnjg(&z__1, &temp);
zscal_(&i__4, &z__1, &h__[i1 + j * h_dim1], &c__1);
if (*wantz) {
d_cnjg(&z__1, &temp);
zscal_(&nz, &z__1, &z__[*iloz + j * z_dim1], &
c__1);
}
}
/* L90: */
}
}
/* L100: */
}
/* Ensure that H(I,I-1) is real. */
i__2 = i__ + (i__ - 1) * h_dim1;
temp.r = h__[i__2].r, temp.i = h__[i__2].i;
if (d_imag(&temp) != 0.) {
rtemp = z_abs(&temp);
i__2 = i__ + (i__ - 1) * h_dim1;
h__[i__2].r = rtemp, h__[i__2].i = 0.;
z__1.r = temp.r / rtemp, z__1.i = temp.i / rtemp;
temp.r = z__1.r, temp.i = z__1.i;
if (i2 > i__) {
i__2 = i2 - i__;
d_cnjg(&z__1, &temp);
zscal_(&i__2, &z__1, &h__[i__ + (i__ + 1) * h_dim1], ldh);
}
i__2 = i__ - i1;
zscal_(&i__2, &temp, &h__[i1 + i__ * h_dim1], &c__1);
if (*wantz) {
zscal_(&nz, &temp, &z__[*iloz + i__ * z_dim1], &c__1);
}
}
/* L110: */
}
/* Failure to converge in remaining number of iterations */
*info = i__;
return 0;
L120:
/* H(I,I-1) is negligible: one eigenvalue has converged. */
i__1 = i__;
i__2 = i__ + i__ * h_dim1;
w[i__1].r = h__[i__2].r, w[i__1].i = h__[i__2].i;
/*
Decrement number of remaining iterations, and return to start of
the main loop with new value of I.
*/
itn -= its;
i__ = l - 1;
goto L10;
L130:
return 0;
/* End of ZLAHQR */
} /* zlahqr_ */
/* Subroutine */ int zlahrd_(integer *n, integer *k, integer *nb,
doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *t,
integer *ldt, doublecomplex *y, integer *ldy)
{
/* System generated locals */
integer a_dim1, a_offset, t_dim1, t_offset, y_dim1, y_offset, i__1, i__2,
i__3;
doublecomplex z__1;
/* Local variables */
static integer i__;
static doublecomplex ei;
extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
doublecomplex *, integer *), zgemv_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *),
zcopy_(integer *, doublecomplex *, integer *, doublecomplex *,
integer *), zaxpy_(integer *, doublecomplex *, doublecomplex *,
integer *, doublecomplex *, integer *), ztrmv_(char *, char *,
char *, integer *, doublecomplex *, integer *, doublecomplex *,
integer *), zlarfg_(integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *),
zlacgv_(integer *, doublecomplex *, integer *);
/*
-- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZLAHRD reduces the first NB columns of a complex general n-by-(n-k+1)
matrix A so that elements below the k-th subdiagonal are zero. The
reduction is performed by a unitary similarity transformation
Q' * A * Q. The routine returns the matrices V and T which determine
Q as a block reflector I - V*T*V', and also the matrix Y = A * V * T.
This is an auxiliary routine called by ZGEHRD.
Arguments
=========
N (input) INTEGER
The order of the matrix A.
K (input) INTEGER
The offset for the reduction. Elements below the k-th
subdiagonal in the first NB columns are reduced to zero.
NB (input) INTEGER
The number of columns to be reduced.
A (input/output) COMPLEX*16 array, dimension (LDA,N-K+1)
On entry, the n-by-(n-k+1) general matrix A.
On exit, the elements on and above the k-th subdiagonal in
the first NB columns are overwritten with the corresponding
elements of the reduced matrix; the elements below the k-th
subdiagonal, with the array TAU, represent the matrix Q as a
product of elementary reflectors. The other columns of A are
unchanged. See Further Details.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
TAU (output) COMPLEX*16 array, dimension (NB)
The scalar factors of the elementary reflectors. See Further
Details.
T (output) COMPLEX*16 array, dimension (LDT,NB)
The upper triangular matrix T.
LDT (input) INTEGER
The leading dimension of the array T. LDT >= NB.
Y (output) COMPLEX*16 array, dimension (LDY,NB)
The n-by-nb matrix Y.
LDY (input) INTEGER
The leading dimension of the array Y. LDY >= max(1,N).
Further Details
===============
The matrix Q is represented as a product of nb elementary reflectors
Q = H(1) H(2) . . . H(nb).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(1:i+k-1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in
A(i+k+1:n,i), and tau in TAU(i).
The elements of the vectors v together form the (n-k+1)-by-nb matrix
V which is needed, with T and Y, to apply the transformation to the
unreduced part of the matrix, using an update of the form:
A := (I - V*T*V') * (A - Y*V').
The contents of A on exit are illustrated by the following example
with n = 7, k = 3 and nb = 2:
( a h a a a )
( a h a a a )
( a h a a a )
( h h a a a )
( v1 h a a a )
( v1 v2 a a a )
( v1 v2 a a a )
where a denotes an element of the original matrix A, h denotes a
modified element of the upper Hessenberg matrix H, and vi denotes an
element of the vector defining H(i).
=====================================================================
Quick return if possible
*/
/* Parameter adjustments */
--tau;
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
t_dim1 = *ldt;
t_offset = 1 + t_dim1 * 1;
t -= t_offset;
y_dim1 = *ldy;
y_offset = 1 + y_dim1 * 1;
y -= y_offset;
/* Function Body */
if (*n <= 1) {
return 0;
}
i__1 = *nb;
for (i__ = 1; i__ <= i__1; ++i__) {
if (i__ > 1) {
/*
Update A(1:n,i)
Compute i-th column of A - Y * V'
*/
i__2 = i__ - 1;
zlacgv_(&i__2, &a[*k + i__ - 1 + a_dim1], lda);
i__2 = i__ - 1;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", n, &i__2, &z__1, &y[y_offset], ldy, &a[*k
+ i__ - 1 + a_dim1], lda, &c_b60, &a[i__ * a_dim1 + 1], &
c__1);
i__2 = i__ - 1;
zlacgv_(&i__2, &a[*k + i__ - 1 + a_dim1], lda);
/*
Apply I - V * T' * V' to this column (call it b) from the
left, using the last column of T as workspace
Let V = ( V1 ) and b = ( b1 ) (first I-1 rows)
( V2 ) ( b2 )
where V1 is unit lower triangular
w := V1' * b1
*/
i__2 = i__ - 1;
zcopy_(&i__2, &a[*k + 1 + i__ * a_dim1], &c__1, &t[*nb * t_dim1 +
1], &c__1);
i__2 = i__ - 1;
ztrmv_("Lower", "Conjugate transpose", "Unit", &i__2, &a[*k + 1 +
a_dim1], lda, &t[*nb * t_dim1 + 1], &c__1);
/* w := w + V2'*b2 */
i__2 = *n - *k - i__ + 1;
i__3 = i__ - 1;
zgemv_("Conjugate transpose", &i__2, &i__3, &c_b60, &a[*k + i__ +
a_dim1], lda, &a[*k + i__ + i__ * a_dim1], &c__1, &c_b60,
&t[*nb * t_dim1 + 1], &c__1);
/* w := T'*w */
i__2 = i__ - 1;
ztrmv_("Upper", "Conjugate transpose", "Non-unit", &i__2, &t[
t_offset], ldt, &t[*nb * t_dim1 + 1], &c__1);
/* b2 := b2 - V2*w */
i__2 = *n - *k - i__ + 1;
i__3 = i__ - 1;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__2, &i__3, &z__1, &a[*k + i__ + a_dim1],
lda, &t[*nb * t_dim1 + 1], &c__1, &c_b60, &a[*k + i__ +
i__ * a_dim1], &c__1);
/* b1 := b1 - V1*w */
i__2 = i__ - 1;
ztrmv_("Lower", "No transpose", "Unit", &i__2, &a[*k + 1 + a_dim1]
, lda, &t[*nb * t_dim1 + 1], &c__1);
i__2 = i__ - 1;
z__1.r = -1., z__1.i = -0.;
zaxpy_(&i__2, &z__1, &t[*nb * t_dim1 + 1], &c__1, &a[*k + 1 + i__
* a_dim1], &c__1);
i__2 = *k + i__ - 1 + (i__ - 1) * a_dim1;
a[i__2].r = ei.r, a[i__2].i = ei.i;
}
/*
Generate the elementary reflector H(i) to annihilate
A(k+i+1:n,i)
*/
i__2 = *k + i__ + i__ * a_dim1;
ei.r = a[i__2].r, ei.i = a[i__2].i;
i__2 = *n - *k - i__ + 1;
/* Computing MIN */
i__3 = *k + i__ + 1;
zlarfg_(&i__2, &ei, &a[min(i__3,*n) + i__ * a_dim1], &c__1, &tau[i__])
;
i__2 = *k + i__ + i__ * a_dim1;
a[i__2].r = 1., a[i__2].i = 0.;
/* Compute Y(1:n,i) */
i__2 = *n - *k - i__ + 1;
zgemv_("No transpose", n, &i__2, &c_b60, &a[(i__ + 1) * a_dim1 + 1],
lda, &a[*k + i__ + i__ * a_dim1], &c__1, &c_b59, &y[i__ *
y_dim1 + 1], &c__1);
i__2 = *n - *k - i__ + 1;
i__3 = i__ - 1;
zgemv_("Conjugate transpose", &i__2, &i__3, &c_b60, &a[*k + i__ +
a_dim1], lda, &a[*k + i__ + i__ * a_dim1], &c__1, &c_b59, &t[
i__ * t_dim1 + 1], &c__1);
i__2 = i__ - 1;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", n, &i__2, &z__1, &y[y_offset], ldy, &t[i__ *
t_dim1 + 1], &c__1, &c_b60, &y[i__ * y_dim1 + 1], &c__1);
zscal_(n, &tau[i__], &y[i__ * y_dim1 + 1], &c__1);
/* Compute T(1:i,i) */
i__2 = i__ - 1;
i__3 = i__;
z__1.r = -tau[i__3].r, z__1.i = -tau[i__3].i;
zscal_(&i__2, &z__1, &t[i__ * t_dim1 + 1], &c__1);
i__2 = i__ - 1;
ztrmv_("Upper", "No transpose", "Non-unit", &i__2, &t[t_offset], ldt,
&t[i__ * t_dim1 + 1], &c__1)
;
i__2 = i__ + i__ * t_dim1;
i__3 = i__;
t[i__2].r = tau[i__3].r, t[i__2].i = tau[i__3].i;
/* L10: */
}
i__1 = *k + *nb + *nb * a_dim1;
a[i__1].r = ei.r, a[i__1].i = ei.i;
return 0;
/* End of ZLAHRD */
} /* zlahrd_ */
/* Subroutine */ int zlals0_(integer *icompq, integer *nl, integer *nr,
integer *sqre, integer *nrhs, doublecomplex *b, integer *ldb,
doublecomplex *bx, integer *ldbx, integer *perm, integer *givptr,
integer *givcol, integer *ldgcol, doublereal *givnum, integer *ldgnum,
doublereal *poles, doublereal *difl, doublereal *difr, doublereal *
z__, integer *k, doublereal *c__, doublereal *s, doublereal *rwork,
integer *info)
{
/* System generated locals */
integer givcol_dim1, givcol_offset, difr_dim1, difr_offset, givnum_dim1,
givnum_offset, poles_dim1, poles_offset, b_dim1, b_offset,
bx_dim1, bx_offset, i__1, i__2, i__3, i__4, i__5;
doublereal d__1;
doublecomplex z__1;
/* Builtin functions */
double d_imag(doublecomplex *);
/* Local variables */
static integer i__, j, m, n;
static doublereal dj;
static integer nlp1, jcol;
static doublereal temp;
static integer jrow;
extern doublereal dnrm2_(integer *, doublereal *, integer *);
static doublereal diflj, difrj, dsigj;
extern /* Subroutine */ int dgemv_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *), zdrot_(integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, doublereal *);
extern doublereal dlamc3_(doublereal *, doublereal *);
extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *), xerbla_(char *, integer *);
static doublereal dsigjp;
extern /* Subroutine */ int zdscal_(integer *, doublereal *,
doublecomplex *, integer *), zlascl_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublecomplex *
, integer *, integer *), zlacpy_(char *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *);
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
December 1, 1999
Purpose
=======
ZLALS0 applies back the multiplying factors of either the left or the
right singular vector matrix of a diagonal matrix appended by a row
to the right hand side matrix B in solving the least squares problem
using the divide-and-conquer SVD approach.
For the left singular vector matrix, three types of orthogonal
matrices are involved:
(1L) Givens rotations: the number of such rotations is GIVPTR; the
pairs of columns/rows they were applied to are stored in GIVCOL;
and the C- and S-values of these rotations are stored in GIVNUM.
(2L) Permutation. The (NL+1)-st row of B is to be moved to the first
row, and for J=2:N, PERM(J)-th row of B is to be moved to the
J-th row.
(3L) The left singular vector matrix of the remaining matrix.
For the right singular vector matrix, four types of orthogonal
matrices are involved:
(1R) The right singular vector matrix of the remaining matrix.
(2R) If SQRE = 1, one extra Givens rotation to generate the right
null space.
(3R) The inverse transformation of (2L).
(4R) The inverse transformation of (1L).
Arguments
=========
ICOMPQ (input) INTEGER
Specifies whether singular vectors are to be computed in
factored form:
= 0: Left singular vector matrix.
= 1: Right singular vector matrix.
NL (input) INTEGER
The row dimension of the upper block. NL >= 1.
NR (input) INTEGER
The row dimension of the lower block. NR >= 1.
SQRE (input) INTEGER
= 0: the lower block is an NR-by-NR square matrix.
= 1: the lower block is an NR-by-(NR+1) rectangular matrix.
The bidiagonal matrix has row dimension N = NL + NR + 1,
and column dimension M = N + SQRE.
NRHS (input) INTEGER
The number of columns of B and BX. NRHS must be at least 1.
B (input/output) COMPLEX*16 array, dimension ( LDB, NRHS )
On input, B contains the right hand sides of the least
squares problem in rows 1 through M. On output, B contains
the solution X in rows 1 through N.
LDB (input) INTEGER
The leading dimension of B. LDB must be at least
max(1,MAX( M, N ) ).
BX (workspace) COMPLEX*16 array, dimension ( LDBX, NRHS )
LDBX (input) INTEGER
The leading dimension of BX.
PERM (input) INTEGER array, dimension ( N )
The permutations (from deflation and sorting) applied
to the two blocks.
GIVPTR (input) INTEGER
The number of Givens rotations which took place in this
subproblem.
GIVCOL (input) INTEGER array, dimension ( LDGCOL, 2 )
Each pair of numbers indicates a pair of rows/columns
involved in a Givens rotation.
LDGCOL (input) INTEGER
The leading dimension of GIVCOL, must be at least N.
GIVNUM (input) DOUBLE PRECISION array, dimension ( LDGNUM, 2 )
Each number indicates the C or S value used in the
corresponding Givens rotation.
LDGNUM (input) INTEGER
The leading dimension of arrays DIFR, POLES and
GIVNUM, must be at least K.
POLES (input) DOUBLE PRECISION array, dimension ( LDGNUM, 2 )
On entry, POLES(1:K, 1) contains the new singular
values obtained from solving the secular equation, and
POLES(1:K, 2) is an array containing the poles in the secular
equation.
DIFL (input) DOUBLE PRECISION array, dimension ( K ).
On entry, DIFL(I) is the distance between I-th updated
(undeflated) singular value and the I-th (undeflated) old
singular value.
DIFR (input) DOUBLE PRECISION array, dimension ( LDGNUM, 2 ).
On entry, DIFR(I, 1) contains the distances between I-th
updated (undeflated) singular value and the I+1-th
(undeflated) old singular value. And DIFR(I, 2) is the
normalizing factor for the I-th right singular vector.
Z (input) DOUBLE PRECISION array, dimension ( K )
Contain the components of the deflation-adjusted updating row
vector.
K (input) INTEGER
Contains the dimension of the non-deflated matrix,
This is the order of the related secular equation. 1 <= K <=N.
C (input) DOUBLE PRECISION
C contains garbage if SQRE =0 and the C-value of a Givens
rotation related to the right null space if SQRE = 1.
S (input) DOUBLE PRECISION
S contains garbage if SQRE =0 and the S-value of a Givens
rotation related to the right null space if SQRE = 1.
RWORK (workspace) DOUBLE PRECISION array, dimension
( K*(1+NRHS) + 2*NRHS )
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
Further Details
===============
Based on contributions by
Ming Gu and Ren-Cang Li, Computer Science Division, University of
California at Berkeley, USA
Osni Marques, LBNL/NERSC, USA
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
bx_dim1 = *ldbx;
bx_offset = 1 + bx_dim1 * 1;
bx -= bx_offset;
--perm;
givcol_dim1 = *ldgcol;
givcol_offset = 1 + givcol_dim1 * 1;
givcol -= givcol_offset;
difr_dim1 = *ldgnum;
difr_offset = 1 + difr_dim1 * 1;
difr -= difr_offset;
poles_dim1 = *ldgnum;
poles_offset = 1 + poles_dim1 * 1;
poles -= poles_offset;
givnum_dim1 = *ldgnum;
givnum_offset = 1 + givnum_dim1 * 1;
givnum -= givnum_offset;
--difl;
--z__;
--rwork;
/* Function Body */
*info = 0;
if (*icompq < 0 || *icompq > 1) {
*info = -1;
} else if (*nl < 1) {
*info = -2;
} else if (*nr < 1) {
*info = -3;
} else if (*sqre < 0 || *sqre > 1) {
*info = -4;
}
n = *nl + *nr + 1;
if (*nrhs < 1) {
*info = -5;
} else if (*ldb < n) {
*info = -7;
} else if (*ldbx < n) {
*info = -9;
} else if (*givptr < 0) {
*info = -11;
} else if (*ldgcol < n) {
*info = -13;
} else if (*ldgnum < n) {
*info = -15;
} else if (*k < 1) {
*info = -20;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZLALS0", &i__1);
return 0;
}
m = n + *sqre;
nlp1 = *nl + 1;
if (*icompq == 0) {
/*
Apply back orthogonal transformations from the left.
Step (1L): apply back the Givens rotations performed.
*/
i__1 = *givptr;
for (i__ = 1; i__ <= i__1; ++i__) {
zdrot_(nrhs, &b[givcol[i__ + ((givcol_dim1) << (1))] + b_dim1],
ldb, &b[givcol[i__ + givcol_dim1] + b_dim1], ldb, &givnum[
i__ + ((givnum_dim1) << (1))], &givnum[i__ + givnum_dim1])
;
/* L10: */
}
/* Step (2L): permute rows of B. */
zcopy_(nrhs, &b[nlp1 + b_dim1], ldb, &bx[bx_dim1 + 1], ldbx);
i__1 = n;
for (i__ = 2; i__ <= i__1; ++i__) {
zcopy_(nrhs, &b[perm[i__] + b_dim1], ldb, &bx[i__ + bx_dim1],
ldbx);
/* L20: */
}
/*
Step (3L): apply the inverse of the left singular vector
matrix to BX.
*/
if (*k == 1) {
zcopy_(nrhs, &bx[bx_offset], ldbx, &b[b_offset], ldb);
if (z__[1] < 0.) {
zdscal_(nrhs, &c_b1294, &b[b_offset], ldb);
}
} else {
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
diflj = difl[j];
dj = poles[j + poles_dim1];
dsigj = -poles[j + ((poles_dim1) << (1))];
if (j < *k) {
difrj = -difr[j + difr_dim1];
dsigjp = -poles[j + 1 + ((poles_dim1) << (1))];
}
if (z__[j] == 0. || poles[j + ((poles_dim1) << (1))] == 0.) {
rwork[j] = 0.;
} else {
rwork[j] = -poles[j + ((poles_dim1) << (1))] * z__[j] /
diflj / (poles[j + ((poles_dim1) << (1))] + dj);
}
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
if (z__[i__] == 0. || poles[i__ + ((poles_dim1) << (1))]
== 0.) {
rwork[i__] = 0.;
} else {
rwork[i__] = poles[i__ + ((poles_dim1) << (1))] * z__[
i__] / (dlamc3_(&poles[i__ + ((poles_dim1) <<
(1))], &dsigj) - diflj) / (poles[i__ + ((
poles_dim1) << (1))] + dj);
}
/* L30: */
}
i__2 = *k;
for (i__ = j + 1; i__ <= i__2; ++i__) {
if (z__[i__] == 0. || poles[i__ + ((poles_dim1) << (1))]
== 0.) {
rwork[i__] = 0.;
} else {
rwork[i__] = poles[i__ + ((poles_dim1) << (1))] * z__[
i__] / (dlamc3_(&poles[i__ + ((poles_dim1) <<
(1))], &dsigjp) + difrj) / (poles[i__ + ((
poles_dim1) << (1))] + dj);
}
/* L40: */
}
rwork[1] = -1.;
temp = dnrm2_(k, &rwork[1], &c__1);
/*
Since B and BX are complex, the following call to DGEMV
is performed in two steps (real and imaginary parts).
CALL DGEMV( 'T', K, NRHS, ONE, BX, LDBX, WORK, 1, ZERO,
$ B( J, 1 ), LDB )
*/
i__ = *k + ((*nrhs) << (1));
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = *k;
for (jrow = 1; jrow <= i__3; ++jrow) {
++i__;
i__4 = jrow + jcol * bx_dim1;
rwork[i__] = bx[i__4].r;
/* L50: */
}
/* L60: */
}
dgemv_("T", k, nrhs, &c_b1015, &rwork[*k + 1 + ((*nrhs) << (1)
)], k, &rwork[1], &c__1, &c_b324, &rwork[*k + 1], &
c__1);
i__ = *k + ((*nrhs) << (1));
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = *k;
for (jrow = 1; jrow <= i__3; ++jrow) {
++i__;
rwork[i__] = d_imag(&bx[jrow + jcol * bx_dim1]);
/* L70: */
}
/* L80: */
}
dgemv_("T", k, nrhs, &c_b1015, &rwork[*k + 1 + ((*nrhs) << (1)
)], k, &rwork[1], &c__1, &c_b324, &rwork[*k + 1 + *
nrhs], &c__1);
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = j + jcol * b_dim1;
i__4 = jcol + *k;
i__5 = jcol + *k + *nrhs;
z__1.r = rwork[i__4], z__1.i = rwork[i__5];
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L90: */
}
zlascl_("G", &c__0, &c__0, &temp, &c_b1015, &c__1, nrhs, &b[j
+ b_dim1], ldb, info);
/* L100: */
}
}
/* Move the deflated rows of BX to B also. */
if (*k < max(m,n)) {
i__1 = n - *k;
zlacpy_("A", &i__1, nrhs, &bx[*k + 1 + bx_dim1], ldbx, &b[*k + 1
+ b_dim1], ldb);
}
} else {
/*
Apply back the right orthogonal transformations.
Step (1R): apply back the new right singular vector matrix
to B.
*/
if (*k == 1) {
zcopy_(nrhs, &b[b_offset], ldb, &bx[bx_offset], ldbx);
} else {
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
dsigj = poles[j + ((poles_dim1) << (1))];
if (z__[j] == 0.) {
rwork[j] = 0.;
} else {
rwork[j] = -z__[j] / difl[j] / (dsigj + poles[j +
poles_dim1]) / difr[j + ((difr_dim1) << (1))];
}
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
if (z__[j] == 0.) {
rwork[i__] = 0.;
} else {
d__1 = -poles[i__ + 1 + ((poles_dim1) << (1))];
rwork[i__] = z__[j] / (dlamc3_(&dsigj, &d__1) - difr[
i__ + difr_dim1]) / (dsigj + poles[i__ +
poles_dim1]) / difr[i__ + ((difr_dim1) << (1))
];
}
/* L110: */
}
i__2 = *k;
for (i__ = j + 1; i__ <= i__2; ++i__) {
if (z__[j] == 0.) {
rwork[i__] = 0.;
} else {
d__1 = -poles[i__ + ((poles_dim1) << (1))];
rwork[i__] = z__[j] / (dlamc3_(&dsigj, &d__1) - difl[
i__]) / (dsigj + poles[i__ + poles_dim1]) /
difr[i__ + ((difr_dim1) << (1))];
}
/* L120: */
}
/*
Since B and BX are complex, the following call to DGEMV
is performed in two steps (real and imaginary parts).
CALL DGEMV( 'T', K, NRHS, ONE, B, LDB, WORK, 1, ZERO,
$ BX( J, 1 ), LDBX )
*/
i__ = *k + ((*nrhs) << (1));
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = *k;
for (jrow = 1; jrow <= i__3; ++jrow) {
++i__;
i__4 = jrow + jcol * b_dim1;
rwork[i__] = b[i__4].r;
/* L130: */
}
/* L140: */
}
dgemv_("T", k, nrhs, &c_b1015, &rwork[*k + 1 + ((*nrhs) << (1)
)], k, &rwork[1], &c__1, &c_b324, &rwork[*k + 1], &
c__1);
i__ = *k + ((*nrhs) << (1));
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = *k;
for (jrow = 1; jrow <= i__3; ++jrow) {
++i__;
rwork[i__] = d_imag(&b[jrow + jcol * b_dim1]);
/* L150: */
}
/* L160: */
}
dgemv_("T", k, nrhs, &c_b1015, &rwork[*k + 1 + ((*nrhs) << (1)
)], k, &rwork[1], &c__1, &c_b324, &rwork[*k + 1 + *
nrhs], &c__1);
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = j + jcol * bx_dim1;
i__4 = jcol + *k;
i__5 = jcol + *k + *nrhs;
z__1.r = rwork[i__4], z__1.i = rwork[i__5];
bx[i__3].r = z__1.r, bx[i__3].i = z__1.i;
/* L170: */
}
/* L180: */
}
}
/*
Step (2R): if SQRE = 1, apply back the rotation that is
related to the right null space of the subproblem.
*/
if (*sqre == 1) {
zcopy_(nrhs, &b[m + b_dim1], ldb, &bx[m + bx_dim1], ldbx);
zdrot_(nrhs, &bx[bx_dim1 + 1], ldbx, &bx[m + bx_dim1], ldbx, c__,
s);
}
if (*k < max(m,n)) {
i__1 = n - *k;
zlacpy_("A", &i__1, nrhs, &b[*k + 1 + b_dim1], ldb, &bx[*k + 1 +
bx_dim1], ldbx);
}
/* Step (3R): permute rows of B. */
zcopy_(nrhs, &bx[bx_dim1 + 1], ldbx, &b[nlp1 + b_dim1], ldb);
if (*sqre == 1) {
zcopy_(nrhs, &bx[m + bx_dim1], ldbx, &b[m + b_dim1], ldb);
}
i__1 = n;
for (i__ = 2; i__ <= i__1; ++i__) {
zcopy_(nrhs, &bx[i__ + bx_dim1], ldbx, &b[perm[i__] + b_dim1],
ldb);
/* L190: */
}
/* Step (4R): apply back the Givens rotations performed. */
for (i__ = *givptr; i__ >= 1; --i__) {
d__1 = -givnum[i__ + givnum_dim1];
zdrot_(nrhs, &b[givcol[i__ + ((givcol_dim1) << (1))] + b_dim1],
ldb, &b[givcol[i__ + givcol_dim1] + b_dim1], ldb, &givnum[
i__ + ((givnum_dim1) << (1))], &d__1);
/* L200: */
}
}
return 0;
/* End of ZLALS0 */
} /* zlals0_ */
/* Subroutine */ int zlalsa_(integer *icompq, integer *smlsiz, integer *n,
integer *nrhs, doublecomplex *b, integer *ldb, doublecomplex *bx,
integer *ldbx, doublereal *u, integer *ldu, doublereal *vt, integer *
k, doublereal *difl, doublereal *difr, doublereal *z__, doublereal *
poles, integer *givptr, integer *givcol, integer *ldgcol, integer *
perm, doublereal *givnum, doublereal *c__, doublereal *s, doublereal *
rwork, integer *iwork, integer *info)
{
/* System generated locals */
integer givcol_dim1, givcol_offset, perm_dim1, perm_offset, difl_dim1,
difl_offset, difr_dim1, difr_offset, givnum_dim1, givnum_offset,
poles_dim1, poles_offset, u_dim1, u_offset, vt_dim1, vt_offset,
z_dim1, z_offset, b_dim1, b_offset, bx_dim1, bx_offset, i__1,
i__2, i__3, i__4, i__5, i__6;
doublecomplex z__1;
/* Builtin functions */
double d_imag(doublecomplex *);
integer pow_ii(integer *, integer *);
/* Local variables */
static integer i__, j, i1, ic, lf, nd, ll, nl, nr, im1, nlf, nrf, lvl,
ndb1, nlp1, lvl2, nrp1, jcol, nlvl, sqre, jrow, jimag;
extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *,
integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *);
static integer jreal, inode, ndiml, ndimr;
extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *), zlals0_(integer *, integer *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, integer *, integer *, integer *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
doublereal *, doublereal *, integer *, doublereal *, doublereal *,
doublereal *, integer *), dlasdt_(integer *, integer *, integer *
, integer *, integer *, integer *, integer *), xerbla_(char *,
integer *);
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZLALSA is an itermediate step in solving the least squares problem
by computing the SVD of the coefficient matrix in compact form (The
singular vectors are computed as products of simple orthorgonal
matrices.).
If ICOMPQ = 0, ZLALSA applies the inverse of the left singular vector
matrix of an upper bidiagonal matrix to the right hand side; and if
ICOMPQ = 1, ZLALSA applies the right singular vector matrix to the
right hand side. The singular vector matrices were generated in
compact form by ZLALSA.
Arguments
=========
ICOMPQ (input) INTEGER
Specifies whether the left or the right singular vector
matrix is involved.
= 0: Left singular vector matrix
= 1: Right singular vector matrix
SMLSIZ (input) INTEGER
The maximum size of the subproblems at the bottom of the
computation tree.
N (input) INTEGER
The row and column dimensions of the upper bidiagonal matrix.
NRHS (input) INTEGER
The number of columns of B and BX. NRHS must be at least 1.
B (input) COMPLEX*16 array, dimension ( LDB, NRHS )
On input, B contains the right hand sides of the least
squares problem in rows 1 through M. On output, B contains
the solution X in rows 1 through N.
LDB (input) INTEGER
The leading dimension of B in the calling subprogram.
LDB must be at least max(1,MAX( M, N ) ).
BX (output) COMPLEX*16 array, dimension ( LDBX, NRHS )
On exit, the result of applying the left or right singular
vector matrix to B.
LDBX (input) INTEGER
The leading dimension of BX.
U (input) DOUBLE PRECISION array, dimension ( LDU, SMLSIZ ).
On entry, U contains the left singular vector matrices of all
subproblems at the bottom level.
LDU (input) INTEGER, LDU = > N.
The leading dimension of arrays U, VT, DIFL, DIFR,
POLES, GIVNUM, and Z.
VT (input) DOUBLE PRECISION array, dimension ( LDU, SMLSIZ+1 ).
On entry, VT' contains the right singular vector matrices of
all subproblems at the bottom level.
K (input) INTEGER array, dimension ( N ).
DIFL (input) DOUBLE PRECISION array, dimension ( LDU, NLVL ).
where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1.
DIFR (input) DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ).
On entry, DIFL(*, I) and DIFR(*, 2 * I -1) record
distances between singular values on the I-th level and
singular values on the (I -1)-th level, and DIFR(*, 2 * I)
record the normalizing factors of the right singular vectors
matrices of subproblems on I-th level.
Z (input) DOUBLE PRECISION array, dimension ( LDU, NLVL ).
On entry, Z(1, I) contains the components of the deflation-
adjusted updating row vector for subproblems on the I-th
level.
POLES (input) DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ).
On entry, POLES(*, 2 * I -1: 2 * I) contains the new and old
singular values involved in the secular equations on the I-th
level.
GIVPTR (input) INTEGER array, dimension ( N ).
On entry, GIVPTR( I ) records the number of Givens
rotations performed on the I-th problem on the computation
tree.
GIVCOL (input) INTEGER array, dimension ( LDGCOL, 2 * NLVL ).
On entry, for each I, GIVCOL(*, 2 * I - 1: 2 * I) records the
locations of Givens rotations performed on the I-th level on
the computation tree.
LDGCOL (input) INTEGER, LDGCOL = > N.
The leading dimension of arrays GIVCOL and PERM.
PERM (input) INTEGER array, dimension ( LDGCOL, NLVL ).
On entry, PERM(*, I) records permutations done on the I-th
level of the computation tree.
GIVNUM (input) DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ).
On entry, GIVNUM(*, 2 *I -1 : 2 * I) records the C- and S-
values of Givens rotations performed on the I-th level on the
computation tree.
C (input) DOUBLE PRECISION array, dimension ( N ).
On entry, if the I-th subproblem is not square,
C( I ) contains the C-value of a Givens rotation related to
the right null space of the I-th subproblem.
S (input) DOUBLE PRECISION array, dimension ( N ).
On entry, if the I-th subproblem is not square,
S( I ) contains the S-value of a Givens rotation related to
the right null space of the I-th subproblem.
RWORK (workspace) DOUBLE PRECISION array, dimension at least
max ( N, (SMLSZ+1)*NRHS*3 ).
IWORK (workspace) INTEGER array.
The dimension must be at least 3 * N
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
Further Details
===============
Based on contributions by
Ming Gu and Ren-Cang Li, Computer Science Division, University of
California at Berkeley, USA
Osni Marques, LBNL/NERSC, USA
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
bx_dim1 = *ldbx;
bx_offset = 1 + bx_dim1 * 1;
bx -= bx_offset;
givnum_dim1 = *ldu;
givnum_offset = 1 + givnum_dim1 * 1;
givnum -= givnum_offset;
poles_dim1 = *ldu;
poles_offset = 1 + poles_dim1 * 1;
poles -= poles_offset;
z_dim1 = *ldu;
z_offset = 1 + z_dim1 * 1;
z__ -= z_offset;
difr_dim1 = *ldu;
difr_offset = 1 + difr_dim1 * 1;
difr -= difr_offset;
difl_dim1 = *ldu;
difl_offset = 1 + difl_dim1 * 1;
difl -= difl_offset;
vt_dim1 = *ldu;
vt_offset = 1 + vt_dim1 * 1;
vt -= vt_offset;
u_dim1 = *ldu;
u_offset = 1 + u_dim1 * 1;
u -= u_offset;
--k;
--givptr;
perm_dim1 = *ldgcol;
perm_offset = 1 + perm_dim1 * 1;
perm -= perm_offset;
givcol_dim1 = *ldgcol;
givcol_offset = 1 + givcol_dim1 * 1;
givcol -= givcol_offset;
--c__;
--s;
--rwork;
--iwork;
/* Function Body */
*info = 0;
if (*icompq < 0 || *icompq > 1) {
*info = -1;
} else if (*smlsiz < 3) {
*info = -2;
} else if (*n < *smlsiz) {
*info = -3;
} else if (*nrhs < 1) {
*info = -4;
} else if (*ldb < *n) {
*info = -6;
} else if (*ldbx < *n) {
*info = -8;
} else if (*ldu < *n) {
*info = -10;
} else if (*ldgcol < *n) {
*info = -19;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZLALSA", &i__1);
return 0;
}
/* Book-keeping and setting up the computation tree. */
inode = 1;
ndiml = inode + *n;
ndimr = ndiml + *n;
dlasdt_(n, &nlvl, &nd, &iwork[inode], &iwork[ndiml], &iwork[ndimr],
smlsiz);
/*
The following code applies back the left singular vector factors.
For applying back the right singular vector factors, go to 170.
*/
if (*icompq == 1) {
goto L170;
}
/*
The nodes on the bottom level of the tree were solved
by DLASDQ. The corresponding left and right singular vector
matrices are in explicit form. First apply back the left
singular vector matrices.
*/
ndb1 = (nd + 1) / 2;
i__1 = nd;
for (i__ = ndb1; i__ <= i__1; ++i__) {
/*
IC : center row of each node
NL : number of rows of left subproblem
NR : number of rows of right subproblem
NLF: starting row of the left subproblem
NRF: starting row of the right subproblem
*/
i1 = i__ - 1;
ic = iwork[inode + i1];
nl = iwork[ndiml + i1];
nr = iwork[ndimr + i1];
nlf = ic - nl;
nrf = ic + 1;
/*
Since B and BX are complex, the following call to DGEMM
is performed in two steps (real and imaginary parts).
CALL DGEMM( 'T', 'N', NL, NRHS, NL, ONE, U( NLF, 1 ), LDU,
$ B( NLF, 1 ), LDB, ZERO, BX( NLF, 1 ), LDBX )
*/
j = (nl * *nrhs) << (1);
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = nlf + nl - 1;
for (jrow = nlf; jrow <= i__3; ++jrow) {
++j;
i__4 = jrow + jcol * b_dim1;
rwork[j] = b[i__4].r;
/* L10: */
}
/* L20: */
}
dgemm_("T", "N", &nl, nrhs, &nl, &c_b1015, &u[nlf + u_dim1], ldu, &
rwork[((nl * *nrhs) << (1)) + 1], &nl, &c_b324, &rwork[1], &
nl);
j = (nl * *nrhs) << (1);
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = nlf + nl - 1;
for (jrow = nlf; jrow <= i__3; ++jrow) {
++j;
rwork[j] = d_imag(&b[jrow + jcol * b_dim1]);
/* L30: */
}
/* L40: */
}
dgemm_("T", "N", &nl, nrhs, &nl, &c_b1015, &u[nlf + u_dim1], ldu, &
rwork[((nl * *nrhs) << (1)) + 1], &nl, &c_b324, &rwork[nl * *
nrhs + 1], &nl);
jreal = 0;
jimag = nl * *nrhs;
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = nlf + nl - 1;
for (jrow = nlf; jrow <= i__3; ++jrow) {
++jreal;
++jimag;
i__4 = jrow + jcol * bx_dim1;
i__5 = jreal;
i__6 = jimag;
z__1.r = rwork[i__5], z__1.i = rwork[i__6];
bx[i__4].r = z__1.r, bx[i__4].i = z__1.i;
/* L50: */
}
/* L60: */
}
/*
Since B and BX are complex, the following call to DGEMM
is performed in two steps (real and imaginary parts).
CALL DGEMM( 'T', 'N', NR, NRHS, NR, ONE, U( NRF, 1 ), LDU,
$ B( NRF, 1 ), LDB, ZERO, BX( NRF, 1 ), LDBX )
*/
j = (nr * *nrhs) << (1);
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = nrf + nr - 1;
for (jrow = nrf; jrow <= i__3; ++jrow) {
++j;
i__4 = jrow + jcol * b_dim1;
rwork[j] = b[i__4].r;
/* L70: */
}
/* L80: */
}
dgemm_("T", "N", &nr, nrhs, &nr, &c_b1015, &u[nrf + u_dim1], ldu, &
rwork[((nr * *nrhs) << (1)) + 1], &nr, &c_b324, &rwork[1], &
nr);
j = (nr * *nrhs) << (1);
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = nrf + nr - 1;
for (jrow = nrf; jrow <= i__3; ++jrow) {
++j;
rwork[j] = d_imag(&b[jrow + jcol * b_dim1]);
/* L90: */
}
/* L100: */
}
dgemm_("T", "N", &nr, nrhs, &nr, &c_b1015, &u[nrf + u_dim1], ldu, &
rwork[((nr * *nrhs) << (1)) + 1], &nr, &c_b324, &rwork[nr * *
nrhs + 1], &nr);
jreal = 0;
jimag = nr * *nrhs;
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = nrf + nr - 1;
for (jrow = nrf; jrow <= i__3; ++jrow) {
++jreal;
++jimag;
i__4 = jrow + jcol * bx_dim1;
i__5 = jreal;
i__6 = jimag;
z__1.r = rwork[i__5], z__1.i = rwork[i__6];
bx[i__4].r = z__1.r, bx[i__4].i = z__1.i;
/* L110: */
}
/* L120: */
}
/* L130: */
}
/*
Next copy the rows of B that correspond to unchanged rows
in the bidiagonal matrix to BX.
*/
i__1 = nd;
for (i__ = 1; i__ <= i__1; ++i__) {
ic = iwork[inode + i__ - 1];
zcopy_(nrhs, &b[ic + b_dim1], ldb, &bx[ic + bx_dim1], ldbx);
/* L140: */
}
/*
Finally go through the left singular vector matrices of all
the other subproblems bottom-up on the tree.
*/
j = pow_ii(&c__2, &nlvl);
sqre = 0;
for (lvl = nlvl; lvl >= 1; --lvl) {
lvl2 = ((lvl) << (1)) - 1;
/*
find the first node LF and last node LL on
the current level LVL
*/
if (lvl == 1) {
lf = 1;
ll = 1;
} else {
i__1 = lvl - 1;
lf = pow_ii(&c__2, &i__1);
ll = ((lf) << (1)) - 1;
}
i__1 = ll;
for (i__ = lf; i__ <= i__1; ++i__) {
im1 = i__ - 1;
ic = iwork[inode + im1];
nl = iwork[ndiml + im1];
nr = iwork[ndimr + im1];
nlf = ic - nl;
nrf = ic + 1;
--j;
zlals0_(icompq, &nl, &nr, &sqre, nrhs, &bx[nlf + bx_dim1], ldbx, &
b[nlf + b_dim1], ldb, &perm[nlf + lvl * perm_dim1], &
givptr[j], &givcol[nlf + lvl2 * givcol_dim1], ldgcol, &
givnum[nlf + lvl2 * givnum_dim1], ldu, &poles[nlf + lvl2 *
poles_dim1], &difl[nlf + lvl * difl_dim1], &difr[nlf +
lvl2 * difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[
j], &s[j], &rwork[1], info);
/* L150: */
}
/* L160: */
}
goto L330;
/* ICOMPQ = 1: applying back the right singular vector factors. */
L170:
/*
First now go through the right singular vector matrices of all
the tree nodes top-down.
*/
j = 0;
i__1 = nlvl;
for (lvl = 1; lvl <= i__1; ++lvl) {
lvl2 = ((lvl) << (1)) - 1;
/*
Find the first node LF and last node LL on
the current level LVL.
*/
if (lvl == 1) {
lf = 1;
ll = 1;
} else {
i__2 = lvl - 1;
lf = pow_ii(&c__2, &i__2);
ll = ((lf) << (1)) - 1;
}
i__2 = lf;
for (i__ = ll; i__ >= i__2; --i__) {
im1 = i__ - 1;
ic = iwork[inode + im1];
nl = iwork[ndiml + im1];
nr = iwork[ndimr + im1];
nlf = ic - nl;
nrf = ic + 1;
if (i__ == ll) {
sqre = 0;
} else {
sqre = 1;
}
++j;
zlals0_(icompq, &nl, &nr, &sqre, nrhs, &b[nlf + b_dim1], ldb, &bx[
nlf + bx_dim1], ldbx, &perm[nlf + lvl * perm_dim1], &
givptr[j], &givcol[nlf + lvl2 * givcol_dim1], ldgcol, &
givnum[nlf + lvl2 * givnum_dim1], ldu, &poles[nlf + lvl2 *
poles_dim1], &difl[nlf + lvl * difl_dim1], &difr[nlf +
lvl2 * difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[
j], &s[j], &rwork[1], info);
/* L180: */
}
/* L190: */
}
/*
The nodes on the bottom level of the tree were solved
by DLASDQ. The corresponding right singular vector
matrices are in explicit form. Apply them back.
*/
ndb1 = (nd + 1) / 2;
i__1 = nd;
for (i__ = ndb1; i__ <= i__1; ++i__) {
i1 = i__ - 1;
ic = iwork[inode + i1];
nl = iwork[ndiml + i1];
nr = iwork[ndimr + i1];
nlp1 = nl + 1;
if (i__ == nd) {
nrp1 = nr;
} else {
nrp1 = nr + 1;
}
nlf = ic - nl;
nrf = ic + 1;
/*
Since B and BX are complex, the following call to DGEMM is
performed in two steps (real and imaginary parts).
CALL DGEMM( 'T', 'N', NLP1, NRHS, NLP1, ONE, VT( NLF, 1 ), LDU,
$ B( NLF, 1 ), LDB, ZERO, BX( NLF, 1 ), LDBX )
*/
j = (nlp1 * *nrhs) << (1);
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = nlf + nlp1 - 1;
for (jrow = nlf; jrow <= i__3; ++jrow) {
++j;
i__4 = jrow + jcol * b_dim1;
rwork[j] = b[i__4].r;
/* L200: */
}
/* L210: */
}
dgemm_("T", "N", &nlp1, nrhs, &nlp1, &c_b1015, &vt[nlf + vt_dim1],
ldu, &rwork[((nlp1 * *nrhs) << (1)) + 1], &nlp1, &c_b324, &
rwork[1], &nlp1);
j = (nlp1 * *nrhs) << (1);
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = nlf + nlp1 - 1;
for (jrow = nlf; jrow <= i__3; ++jrow) {
++j;
rwork[j] = d_imag(&b[jrow + jcol * b_dim1]);
/* L220: */
}
/* L230: */
}
dgemm_("T", "N", &nlp1, nrhs, &nlp1, &c_b1015, &vt[nlf + vt_dim1],
ldu, &rwork[((nlp1 * *nrhs) << (1)) + 1], &nlp1, &c_b324, &
rwork[nlp1 * *nrhs + 1], &nlp1);
jreal = 0;
jimag = nlp1 * *nrhs;
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = nlf + nlp1 - 1;
for (jrow = nlf; jrow <= i__3; ++jrow) {
++jreal;
++jimag;
i__4 = jrow + jcol * bx_dim1;
i__5 = jreal;
i__6 = jimag;
z__1.r = rwork[i__5], z__1.i = rwork[i__6];
bx[i__4].r = z__1.r, bx[i__4].i = z__1.i;
/* L240: */
}
/* L250: */
}
/*
Since B and BX are complex, the following call to DGEMM is
performed in two steps (real and imaginary parts).
CALL DGEMM( 'T', 'N', NRP1, NRHS, NRP1, ONE, VT( NRF, 1 ), LDU,
$ B( NRF, 1 ), LDB, ZERO, BX( NRF, 1 ), LDBX )
*/
j = (nrp1 * *nrhs) << (1);
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = nrf + nrp1 - 1;
for (jrow = nrf; jrow <= i__3; ++jrow) {
++j;
i__4 = jrow + jcol * b_dim1;
rwork[j] = b[i__4].r;
/* L260: */
}
/* L270: */
}
dgemm_("T", "N", &nrp1, nrhs, &nrp1, &c_b1015, &vt[nrf + vt_dim1],
ldu, &rwork[((nrp1 * *nrhs) << (1)) + 1], &nrp1, &c_b324, &
rwork[1], &nrp1);
j = (nrp1 * *nrhs) << (1);
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = nrf + nrp1 - 1;
for (jrow = nrf; jrow <= i__3; ++jrow) {
++j;
rwork[j] = d_imag(&b[jrow + jcol * b_dim1]);
/* L280: */
}
/* L290: */
}
dgemm_("T", "N", &nrp1, nrhs, &nrp1, &c_b1015, &vt[nrf + vt_dim1],
ldu, &rwork[((nrp1 * *nrhs) << (1)) + 1], &nrp1, &c_b324, &
rwork[nrp1 * *nrhs + 1], &nrp1);
jreal = 0;
jimag = nrp1 * *nrhs;
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = nrf + nrp1 - 1;
for (jrow = nrf; jrow <= i__3; ++jrow) {
++jreal;
++jimag;
i__4 = jrow + jcol * bx_dim1;
i__5 = jreal;
i__6 = jimag;
z__1.r = rwork[i__5], z__1.i = rwork[i__6];
bx[i__4].r = z__1.r, bx[i__4].i = z__1.i;
/* L300: */
}
/* L310: */
}
/* L320: */
}
L330:
return 0;
/* End of ZLALSA */
} /* zlalsa_ */
/* Subroutine */ int zlalsd_(char *uplo, integer *smlsiz, integer *n, integer
*nrhs, doublereal *d__, doublereal *e, doublecomplex *b, integer *ldb,
doublereal *rcond, integer *rank, doublecomplex *work, doublereal *
rwork, integer *iwork, integer *info)
{
/* System generated locals */
integer b_dim1, b_offset, i__1, i__2, i__3, i__4, i__5, i__6;
doublereal d__1;
doublecomplex z__1;
/* Builtin functions */
double d_imag(doublecomplex *), log(doublereal), d_sign(doublereal *,
doublereal *);
/* Local variables */
static integer c__, i__, j, k;
static doublereal r__;
static integer s, u, z__;
static doublereal cs;
static integer bx;
static doublereal sn;
static integer st, vt, nm1, st1;
static doublereal eps;
static integer iwk;
static doublereal tol;
static integer difl, difr, jcol, irwb, perm, nsub, nlvl, sqre, bxst, jrow,
irwu, jimag;
extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *,
integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *);
static integer jreal, irwib, poles, sizei, irwrb, nsize;
extern /* Subroutine */ int zdrot_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, doublereal *), zcopy_(
integer *, doublecomplex *, integer *, doublecomplex *, integer *)
;
static integer irwvt, icmpq1, icmpq2;
extern /* Subroutine */ int dlasda_(integer *, integer *, integer *,
integer *, doublereal *, doublereal *, doublereal *, integer *,
doublereal *, integer *, doublereal *, doublereal *, doublereal *,
doublereal *, integer *, integer *, integer *, integer *,
doublereal *, doublereal *, doublereal *, doublereal *, integer *,
integer *), dlascl_(char *, integer *, integer *, doublereal *,
doublereal *, integer *, integer *, doublereal *, integer *,
integer *);
extern integer idamax_(integer *, doublereal *, integer *);
extern /* Subroutine */ int dlasdq_(char *, integer *, integer *, integer
*, integer *, integer *, doublereal *, doublereal *, doublereal *,
integer *, doublereal *, integer *, doublereal *, integer *,
doublereal *, integer *), dlaset_(char *, integer *,
integer *, doublereal *, doublereal *, doublereal *, integer *), dlartg_(doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *), xerbla_(char *, integer *);
static integer givcol;
extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *);
extern /* Subroutine */ int zlalsa_(integer *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
doublereal *, doublereal *, doublereal *, integer *, integer *,
integer *, integer *, doublereal *, doublereal *, doublereal *,
doublereal *, integer *, integer *), zlascl_(char *, integer *,
integer *, doublereal *, doublereal *, integer *, integer *,
doublecomplex *, integer *, integer *), dlasrt_(char *,
integer *, doublereal *, integer *), zlacpy_(char *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
integer *), zlaset_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *);
static doublereal orgnrm;
static integer givnum, givptr, nrwork, irwwrk, smlszp;
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
October 31, 1999
Purpose
=======
ZLALSD uses the singular value decomposition of A to solve the least
squares problem of finding X to minimize the Euclidean norm of each
column of A*X-B, where A is N-by-N upper bidiagonal, and X and B
are N-by-NRHS. The solution X overwrites B.
The singular values of A smaller than RCOND times the largest
singular value are treated as zero in solving the least squares
problem; in this case a minimum norm solution is returned.
The actual singular values are returned in D in ascending order.
This code makes very mild assumptions about floating point
arithmetic. It will work on machines with a guard digit in
add/subtract, or on those binary machines without guard digits
which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2.
It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': D and E define an upper bidiagonal matrix.
= 'L': D and E define a lower bidiagonal matrix.
SMLSIZ (input) INTEGER
The maximum size of the subproblems at the bottom of the
computation tree.
N (input) INTEGER
The dimension of the bidiagonal matrix. N >= 0.
NRHS (input) INTEGER
The number of columns of B. NRHS must be at least 1.
D (input/output) DOUBLE PRECISION array, dimension (N)
On entry D contains the main diagonal of the bidiagonal
matrix. On exit, if INFO = 0, D contains its singular values.
E (input) DOUBLE PRECISION array, dimension (N-1)
Contains the super-diagonal entries of the bidiagonal matrix.
On exit, E has been destroyed.
B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
On input, B contains the right hand sides of the least
squares problem. On output, B contains the solution X.
LDB (input) INTEGER
The leading dimension of B in the calling subprogram.
LDB must be at least max(1,N).
RCOND (input) DOUBLE PRECISION
The singular values of A less than or equal to RCOND times
the largest singular value are treated as zero in solving
the least squares problem. If RCOND is negative,
machine precision is used instead.
For example, if diag(S)*X=B were the least squares problem,
where diag(S) is a diagonal matrix of singular values, the
solution would be X(i) = B(i) / S(i) if S(i) is greater than
RCOND*max(S), and X(i) = 0 if S(i) is less than or equal to
RCOND*max(S).
RANK (output) INTEGER
The number of singular values of A greater than RCOND times
the largest singular value.
WORK (workspace) COMPLEX*16 array, dimension at least
(N * NRHS).
RWORK (workspace) DOUBLE PRECISION array, dimension at least
(9*N + 2*N*SMLSIZ + 8*N*NLVL + 3*SMLSIZ*NRHS + (SMLSIZ+1)**2),
where
NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 )
IWORK (workspace) INTEGER array, dimension at least
(3*N*NLVL + 11*N).
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: The algorithm failed to compute an singular value while
working on the submatrix lying in rows and columns
INFO/(N+1) through MOD(INFO,N+1).
Further Details
===============
Based on contributions by
Ming Gu and Ren-Cang Li, Computer Science Division, University of
California at Berkeley, USA
Osni Marques, LBNL/NERSC, USA
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
--d__;
--e;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
--work;
--rwork;
--iwork;
/* Function Body */
*info = 0;
if (*n < 0) {
*info = -3;
} else if (*nrhs < 1) {
*info = -4;
} else if (*ldb < 1 || *ldb < *n) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZLALSD", &i__1);
return 0;
}
eps = EPSILON;
/* Set up the tolerance. */
if (*rcond <= 0. || *rcond >= 1.) {
*rcond = eps;
}
*rank = 0;
/* Quick return if possible. */
if (*n == 0) {
return 0;
} else if (*n == 1) {
if (d__[1] == 0.) {
zlaset_("A", &c__1, nrhs, &c_b59, &c_b59, &b[b_offset], ldb);
} else {
*rank = 1;
zlascl_("G", &c__0, &c__0, &d__[1], &c_b1015, &c__1, nrhs, &b[
b_offset], ldb, info);
d__[1] = abs(d__[1]);
}
return 0;
}
/* Rotate the matrix if it is lower bidiagonal. */
if (*(unsigned char *)uplo == 'L') {
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
dlartg_(&d__[i__], &e[i__], &cs, &sn, &r__);
d__[i__] = r__;
e[i__] = sn * d__[i__ + 1];
d__[i__ + 1] = cs * d__[i__ + 1];
if (*nrhs == 1) {
zdrot_(&c__1, &b[i__ + b_dim1], &c__1, &b[i__ + 1 + b_dim1], &
c__1, &cs, &sn);
} else {
rwork[((i__) << (1)) - 1] = cs;
rwork[i__ * 2] = sn;
}
/* L10: */
}
if (*nrhs > 1) {
i__1 = *nrhs;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = *n - 1;
for (j = 1; j <= i__2; ++j) {
cs = rwork[((j) << (1)) - 1];
sn = rwork[j * 2];
zdrot_(&c__1, &b[j + i__ * b_dim1], &c__1, &b[j + 1 + i__
* b_dim1], &c__1, &cs, &sn);
/* L20: */
}
/* L30: */
}
}
}
/* Scale. */
nm1 = *n - 1;
orgnrm = dlanst_("M", n, &d__[1], &e[1]);
if (orgnrm == 0.) {
zlaset_("A", n, nrhs, &c_b59, &c_b59, &b[b_offset], ldb);
return 0;
}
dlascl_("G", &c__0, &c__0, &orgnrm, &c_b1015, n, &c__1, &d__[1], n, info);
dlascl_("G", &c__0, &c__0, &orgnrm, &c_b1015, &nm1, &c__1, &e[1], &nm1,
info);
/*
If N is smaller than the minimum divide size SMLSIZ, then solve
the problem with another solver.
*/
if (*n <= *smlsiz) {
irwu = 1;
irwvt = irwu + *n * *n;
irwwrk = irwvt + *n * *n;
irwrb = irwwrk;
irwib = irwrb + *n * *nrhs;
irwb = irwib + *n * *nrhs;
dlaset_("A", n, n, &c_b324, &c_b1015, &rwork[irwu], n);
dlaset_("A", n, n, &c_b324, &c_b1015, &rwork[irwvt], n);
dlasdq_("U", &c__0, n, n, n, &c__0, &d__[1], &e[1], &rwork[irwvt], n,
&rwork[irwu], n, &rwork[irwwrk], &c__1, &rwork[irwwrk], info);
if (*info != 0) {
return 0;
}
/*
In the real version, B is passed to DLASDQ and multiplied
internally by Q'. Here B is complex and that product is
computed below in two steps (real and imaginary parts).
*/
j = irwb - 1;
i__1 = *nrhs;
for (jcol = 1; jcol <= i__1; ++jcol) {
i__2 = *n;
for (jrow = 1; jrow <= i__2; ++jrow) {
++j;
i__3 = jrow + jcol * b_dim1;
rwork[j] = b[i__3].r;
/* L40: */
}
/* L50: */
}
dgemm_("T", "N", n, nrhs, n, &c_b1015, &rwork[irwu], n, &rwork[irwb],
n, &c_b324, &rwork[irwrb], n);
j = irwb - 1;
i__1 = *nrhs;
for (jcol = 1; jcol <= i__1; ++jcol) {
i__2 = *n;
for (jrow = 1; jrow <= i__2; ++jrow) {
++j;
rwork[j] = d_imag(&b[jrow + jcol * b_dim1]);
/* L60: */
}
/* L70: */
}
dgemm_("T", "N", n, nrhs, n, &c_b1015, &rwork[irwu], n, &rwork[irwb],
n, &c_b324, &rwork[irwib], n);
jreal = irwrb - 1;
jimag = irwib - 1;
i__1 = *nrhs;
for (jcol = 1; jcol <= i__1; ++jcol) {
i__2 = *n;
for (jrow = 1; jrow <= i__2; ++jrow) {
++jreal;
++jimag;
i__3 = jrow + jcol * b_dim1;
i__4 = jreal;
i__5 = jimag;
z__1.r = rwork[i__4], z__1.i = rwork[i__5];
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L80: */
}
/* L90: */
}
tol = *rcond * (d__1 = d__[idamax_(n, &d__[1], &c__1)], abs(d__1));
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (d__[i__] <= tol) {
zlaset_("A", &c__1, nrhs, &c_b59, &c_b59, &b[i__ + b_dim1],
ldb);
} else {
zlascl_("G", &c__0, &c__0, &d__[i__], &c_b1015, &c__1, nrhs, &
b[i__ + b_dim1], ldb, info);
++(*rank);
}
/* L100: */
}
/*
Since B is complex, the following call to DGEMM is performed
in two steps (real and imaginary parts). That is for V * B
(in the real version of the code V' is stored in WORK).
CALL DGEMM( 'T', 'N', N, NRHS, N, ONE, WORK, N, B, LDB, ZERO,
$ WORK( NWORK ), N )
*/
j = irwb - 1;
i__1 = *nrhs;
for (jcol = 1; jcol <= i__1; ++jcol) {
i__2 = *n;
for (jrow = 1; jrow <= i__2; ++jrow) {
++j;
i__3 = jrow + jcol * b_dim1;
rwork[j] = b[i__3].r;
/* L110: */
}
/* L120: */
}
dgemm_("T", "N", n, nrhs, n, &c_b1015, &rwork[irwvt], n, &rwork[irwb],
n, &c_b324, &rwork[irwrb], n);
j = irwb - 1;
i__1 = *nrhs;
for (jcol = 1; jcol <= i__1; ++jcol) {
i__2 = *n;
for (jrow = 1; jrow <= i__2; ++jrow) {
++j;
rwork[j] = d_imag(&b[jrow + jcol * b_dim1]);
/* L130: */
}
/* L140: */
}
dgemm_("T", "N", n, nrhs, n, &c_b1015, &rwork[irwvt], n, &rwork[irwb],
n, &c_b324, &rwork[irwib], n);
jreal = irwrb - 1;
jimag = irwib - 1;
i__1 = *nrhs;
for (jcol = 1; jcol <= i__1; ++jcol) {
i__2 = *n;
for (jrow = 1; jrow <= i__2; ++jrow) {
++jreal;
++jimag;
i__3 = jrow + jcol * b_dim1;
i__4 = jreal;
i__5 = jimag;
z__1.r = rwork[i__4], z__1.i = rwork[i__5];
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L150: */
}
/* L160: */
}
/* Unscale. */
dlascl_("G", &c__0, &c__0, &c_b1015, &orgnrm, n, &c__1, &d__[1], n,
info);
dlasrt_("D", n, &d__[1], info);
zlascl_("G", &c__0, &c__0, &orgnrm, &c_b1015, n, nrhs, &b[b_offset],
ldb, info);
return 0;
}
/* Book-keeping and setting up some constants. */
nlvl = (integer) (log((doublereal) (*n) / (doublereal) (*smlsiz + 1)) /
log(2.)) + 1;
smlszp = *smlsiz + 1;
u = 1;
vt = *smlsiz * *n + 1;
difl = vt + smlszp * *n;
difr = difl + nlvl * *n;
z__ = difr + ((nlvl * *n) << (1));
c__ = z__ + nlvl * *n;
s = c__ + *n;
poles = s + *n;
givnum = poles + ((nlvl) << (1)) * *n;
nrwork = givnum + ((nlvl) << (1)) * *n;
bx = 1;
irwrb = nrwork;
irwib = irwrb + *smlsiz * *nrhs;
irwb = irwib + *smlsiz * *nrhs;
sizei = *n + 1;
k = sizei + *n;
givptr = k + *n;
perm = givptr + *n;
givcol = perm + nlvl * *n;
iwk = givcol + ((nlvl * *n) << (1));
st = 1;
sqre = 0;
icmpq1 = 1;
icmpq2 = 0;
nsub = 0;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if ((d__1 = d__[i__], abs(d__1)) < eps) {
d__[i__] = d_sign(&eps, &d__[i__]);
}
/* L170: */
}
i__1 = nm1;
for (i__ = 1; i__ <= i__1; ++i__) {
if ((d__1 = e[i__], abs(d__1)) < eps || i__ == nm1) {
++nsub;
iwork[nsub] = st;
/*
Subproblem found. First determine its size and then
apply divide and conquer on it.
*/
if (i__ < nm1) {
/* A subproblem with E(I) small for I < NM1. */
nsize = i__ - st + 1;
iwork[sizei + nsub - 1] = nsize;
} else if ((d__1 = e[i__], abs(d__1)) >= eps) {
/* A subproblem with E(NM1) not too small but I = NM1. */
nsize = *n - st + 1;
iwork[sizei + nsub - 1] = nsize;
} else {
/*
A subproblem with E(NM1) small. This implies an
1-by-1 subproblem at D(N), which is not solved
explicitly.
*/
nsize = i__ - st + 1;
iwork[sizei + nsub - 1] = nsize;
++nsub;
iwork[nsub] = *n;
iwork[sizei + nsub - 1] = 1;
zcopy_(nrhs, &b[*n + b_dim1], ldb, &work[bx + nm1], n);
}
st1 = st - 1;
if (nsize == 1) {
/*
This is a 1-by-1 subproblem and is not solved
explicitly.
*/
zcopy_(nrhs, &b[st + b_dim1], ldb, &work[bx + st1], n);
} else if (nsize <= *smlsiz) {
/* This is a small subproblem and is solved by DLASDQ. */
dlaset_("A", &nsize, &nsize, &c_b324, &c_b1015, &rwork[vt +
st1], n);
dlaset_("A", &nsize, &nsize, &c_b324, &c_b1015, &rwork[u +
st1], n);
dlasdq_("U", &c__0, &nsize, &nsize, &nsize, &c__0, &d__[st], &
e[st], &rwork[vt + st1], n, &rwork[u + st1], n, &
rwork[nrwork], &c__1, &rwork[nrwork], info)
;
if (*info != 0) {
return 0;
}
/*
In the real version, B is passed to DLASDQ and multiplied
internally by Q'. Here B is complex and that product is
computed below in two steps (real and imaginary parts).
*/
j = irwb - 1;
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = st + nsize - 1;
for (jrow = st; jrow <= i__3; ++jrow) {
++j;
i__4 = jrow + jcol * b_dim1;
rwork[j] = b[i__4].r;
/* L180: */
}
/* L190: */
}
dgemm_("T", "N", &nsize, nrhs, &nsize, &c_b1015, &rwork[u +
st1], n, &rwork[irwb], &nsize, &c_b324, &rwork[irwrb],
&nsize);
j = irwb - 1;
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = st + nsize - 1;
for (jrow = st; jrow <= i__3; ++jrow) {
++j;
rwork[j] = d_imag(&b[jrow + jcol * b_dim1]);
/* L200: */
}
/* L210: */
}
dgemm_("T", "N", &nsize, nrhs, &nsize, &c_b1015, &rwork[u +
st1], n, &rwork[irwb], &nsize, &c_b324, &rwork[irwib],
&nsize);
jreal = irwrb - 1;
jimag = irwib - 1;
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = st + nsize - 1;
for (jrow = st; jrow <= i__3; ++jrow) {
++jreal;
++jimag;
i__4 = jrow + jcol * b_dim1;
i__5 = jreal;
i__6 = jimag;
z__1.r = rwork[i__5], z__1.i = rwork[i__6];
b[i__4].r = z__1.r, b[i__4].i = z__1.i;
/* L220: */
}
/* L230: */
}
zlacpy_("A", &nsize, nrhs, &b[st + b_dim1], ldb, &work[bx +
st1], n);
} else {
/* A large problem. Solve it using divide and conquer. */
dlasda_(&icmpq1, smlsiz, &nsize, &sqre, &d__[st], &e[st], &
rwork[u + st1], n, &rwork[vt + st1], &iwork[k + st1],
&rwork[difl + st1], &rwork[difr + st1], &rwork[z__ +
st1], &rwork[poles + st1], &iwork[givptr + st1], &
iwork[givcol + st1], n, &iwork[perm + st1], &rwork[
givnum + st1], &rwork[c__ + st1], &rwork[s + st1], &
rwork[nrwork], &iwork[iwk], info);
if (*info != 0) {
return 0;
}
bxst = bx + st1;
zlalsa_(&icmpq2, smlsiz, &nsize, nrhs, &b[st + b_dim1], ldb, &
work[bxst], n, &rwork[u + st1], n, &rwork[vt + st1], &
iwork[k + st1], &rwork[difl + st1], &rwork[difr + st1]
, &rwork[z__ + st1], &rwork[poles + st1], &iwork[
givptr + st1], &iwork[givcol + st1], n, &iwork[perm +
st1], &rwork[givnum + st1], &rwork[c__ + st1], &rwork[
s + st1], &rwork[nrwork], &iwork[iwk], info);
if (*info != 0) {
return 0;
}
}
st = i__ + 1;
}
/* L240: */
}
/* Apply the singular values and treat the tiny ones as zero. */
tol = *rcond * (d__1 = d__[idamax_(n, &d__[1], &c__1)], abs(d__1));
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
/*
Some of the elements in D can be negative because 1-by-1
subproblems were not solved explicitly.
*/
if ((d__1 = d__[i__], abs(d__1)) <= tol) {
zlaset_("A", &c__1, nrhs, &c_b59, &c_b59, &work[bx + i__ - 1], n);
} else {
++(*rank);
zlascl_("G", &c__0, &c__0, &d__[i__], &c_b1015, &c__1, nrhs, &
work[bx + i__ - 1], n, info);
}
d__[i__] = (d__1 = d__[i__], abs(d__1));
/* L250: */
}
/* Now apply back the right singular vectors. */
icmpq2 = 1;
i__1 = nsub;
for (i__ = 1; i__ <= i__1; ++i__) {
st = iwork[i__];
st1 = st - 1;
nsize = iwork[sizei + i__ - 1];
bxst = bx + st1;
if (nsize == 1) {
zcopy_(nrhs, &work[bxst], n, &b[st + b_dim1], ldb);
} else if (nsize <= *smlsiz) {
/*
Since B and BX are complex, the following call to DGEMM
is performed in two steps (real and imaginary parts).
CALL DGEMM( 'T', 'N', NSIZE, NRHS, NSIZE, ONE,
$ RWORK( VT+ST1 ), N, RWORK( BXST ), N, ZERO,
$ B( ST, 1 ), LDB )
*/
j = bxst - *n - 1;
jreal = irwb - 1;
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
j += *n;
i__3 = nsize;
for (jrow = 1; jrow <= i__3; ++jrow) {
++jreal;
i__4 = j + jrow;
rwork[jreal] = work[i__4].r;
/* L260: */
}
/* L270: */
}
dgemm_("T", "N", &nsize, nrhs, &nsize, &c_b1015, &rwork[vt + st1],
n, &rwork[irwb], &nsize, &c_b324, &rwork[irwrb], &nsize);
j = bxst - *n - 1;
jimag = irwb - 1;
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
j += *n;
i__3 = nsize;
for (jrow = 1; jrow <= i__3; ++jrow) {
++jimag;
rwork[jimag] = d_imag(&work[j + jrow]);
/* L280: */
}
/* L290: */
}
dgemm_("T", "N", &nsize, nrhs, &nsize, &c_b1015, &rwork[vt + st1],
n, &rwork[irwb], &nsize, &c_b324, &rwork[irwib], &nsize);
jreal = irwrb - 1;
jimag = irwib - 1;
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = st + nsize - 1;
for (jrow = st; jrow <= i__3; ++jrow) {
++jreal;
++jimag;
i__4 = jrow + jcol * b_dim1;
i__5 = jreal;
i__6 = jimag;
z__1.r = rwork[i__5], z__1.i = rwork[i__6];
b[i__4].r = z__1.r, b[i__4].i = z__1.i;
/* L300: */
}
/* L310: */
}
} else {
zlalsa_(&icmpq2, smlsiz, &nsize, nrhs, &work[bxst], n, &b[st +
b_dim1], ldb, &rwork[u + st1], n, &rwork[vt + st1], &
iwork[k + st1], &rwork[difl + st1], &rwork[difr + st1], &
rwork[z__ + st1], &rwork[poles + st1], &iwork[givptr +
st1], &iwork[givcol + st1], n, &iwork[perm + st1], &rwork[
givnum + st1], &rwork[c__ + st1], &rwork[s + st1], &rwork[
nrwork], &iwork[iwk], info);
if (*info != 0) {
return 0;
}
}
/* L320: */
}
/* Unscale and sort the singular values. */
dlascl_("G", &c__0, &c__0, &c_b1015, &orgnrm, n, &c__1, &d__[1], n, info);
dlasrt_("D", n, &d__[1], info);
zlascl_("G", &c__0, &c__0, &orgnrm, &c_b1015, n, nrhs, &b[b_offset], ldb,
info);
return 0;
/* End of ZLALSD */
} /* zlalsd_ */
doublereal zlange_(char *norm, integer *m, integer *n, doublecomplex *a,
integer *lda, doublereal *work)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
doublereal ret_val, d__1, d__2;
/* Builtin functions */
double z_abs(doublecomplex *), sqrt(doublereal);
/* Local variables */
static integer i__, j;
static doublereal sum, scale;
extern logical lsame_(char *, char *);
static doublereal value;
extern /* Subroutine */ int zlassq_(integer *, doublecomplex *, integer *,
doublereal *, doublereal *);
/*
-- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
October 31, 1992
Purpose
=======
ZLANGE returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
complex matrix A.
Description
===========
ZLANGE returns the value
ZLANGE = ( max(abs(A(i,j))), NORM = 'M' or 'm'
(
( norm1(A), NORM = '1', 'O' or 'o'
(
( normI(A), NORM = 'I' or 'i'
(
( normF(A), NORM = 'F', 'f', 'E' or 'e'
where norm1 denotes the one norm of a matrix (maximum column sum),
normI denotes the infinity norm of a matrix (maximum row sum) and
normF denotes the Frobenius norm of a matrix (square root of sum of
squares). Note that max(abs(A(i,j))) is not a matrix norm.
Arguments
=========
NORM (input) CHARACTER*1
Specifies the value to be returned in ZLANGE as described
above.
M (input) INTEGER
The number of rows of the matrix A. M >= 0. When M = 0,
ZLANGE is set to zero.
N (input) INTEGER
The number of columns of the matrix A. N >= 0. When N = 0,
ZLANGE is set to zero.
A (input) COMPLEX*16 array, dimension (LDA,N)
The m by n matrix A.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(M,1).
WORK (workspace) DOUBLE PRECISION array, dimension (LWORK),
where LWORK >= M when NORM = 'I'; otherwise, WORK is not
referenced.
=====================================================================
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--work;
/* Function Body */
if (min(*m,*n) == 0) {
value = 0.;
} else if (lsame_(norm, "M")) {
/* Find max(abs(A(i,j))). */
value = 0.;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__1 = value, d__2 = z_abs(&a[i__ + j * a_dim1]);
value = max(d__1,d__2);
/* L10: */
}
/* L20: */
}
} else if (lsame_(norm, "O") || *(unsigned char *)
norm == '1') {
/* Find norm1(A). */
value = 0.;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
sum = 0.;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
sum += z_abs(&a[i__ + j * a_dim1]);
/* L30: */
}
value = max(value,sum);
/* L40: */
}
} else if (lsame_(norm, "I")) {
/* Find normI(A). */
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
work[i__] = 0.;
/* L50: */
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
work[i__] += z_abs(&a[i__ + j * a_dim1]);
/* L60: */
}
/* L70: */
}
value = 0.;
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MAX */
d__1 = value, d__2 = work[i__];
value = max(d__1,d__2);
/* L80: */
}
} else if (lsame_(norm, "F") || lsame_(norm, "E")) {
/* Find normF(A). */
scale = 0.;
sum = 1.;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
zlassq_(m, &a[j * a_dim1 + 1], &c__1, &scale, &sum);
/* L90: */
}
value = scale * sqrt(sum);
}
ret_val = value;
return ret_val;
/* End of ZLANGE */
} /* zlange_ */
doublereal zlanhe_(char *norm, char *uplo, integer *n, doublecomplex *a,
integer *lda, doublereal *work)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
doublereal ret_val, d__1, d__2, d__3;
/* Builtin functions */
double z_abs(doublecomplex *), sqrt(doublereal);
/* Local variables */
static integer i__, j;
static doublereal sum, absa, scale;
extern logical lsame_(char *, char *);
static doublereal value;
extern /* Subroutine */ int zlassq_(integer *, doublecomplex *, integer *,
doublereal *, doublereal *);
/*
-- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
October 31, 1992
Purpose
=======
ZLANHE returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
complex hermitian matrix A.
Description
===========
ZLANHE returns the value
ZLANHE = ( max(abs(A(i,j))), NORM = 'M' or 'm'
(
( norm1(A), NORM = '1', 'O' or 'o'
(
( normI(A), NORM = 'I' or 'i'
(
( normF(A), NORM = 'F', 'f', 'E' or 'e'
where norm1 denotes the one norm of a matrix (maximum column sum),
normI denotes the infinity norm of a matrix (maximum row sum) and
normF denotes the Frobenius norm of a matrix (square root of sum of
squares). Note that max(abs(A(i,j))) is not a matrix norm.
Arguments
=========
NORM (input) CHARACTER*1
Specifies the value to be returned in ZLANHE as described
above.
UPLO (input) CHARACTER*1
Specifies whether the upper or lower triangular part of the
hermitian matrix A is to be referenced.
= 'U': Upper triangular part of A is referenced
= 'L': Lower triangular part of A is referenced
N (input) INTEGER
The order of the matrix A. N >= 0. When N = 0, ZLANHE is
set to zero.
A (input) COMPLEX*16 array, dimension (LDA,N)
The hermitian matrix A. If UPLO = 'U', the leading n by n
upper triangular part of A contains the upper triangular part
of the matrix A, and the strictly lower triangular part of A
is not referenced. If UPLO = 'L', the leading n by n lower
triangular part of A contains the lower triangular part of
the matrix A, and the strictly upper triangular part of A is
not referenced. Note that the imaginary parts of the diagonal
elements need not be set and are assumed to be zero.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(N,1).
WORK (workspace) DOUBLE PRECISION array, dimension (LWORK),
where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
WORK is not referenced.
=====================================================================
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--work;
/* Function Body */
if (*n == 0) {
value = 0.;
} else if (lsame_(norm, "M")) {
/* Find max(abs(A(i,j))). */
value = 0.;
if (lsame_(uplo, "U")) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__1 = value, d__2 = z_abs(&a[i__ + j * a_dim1]);
value = max(d__1,d__2);
/* L10: */
}
/* Computing MAX */
i__2 = j + j * a_dim1;
d__2 = value, d__3 = (d__1 = a[i__2].r, abs(d__1));
value = max(d__2,d__3);
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = j + j * a_dim1;
d__2 = value, d__3 = (d__1 = a[i__2].r, abs(d__1));
value = max(d__2,d__3);
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__1 = value, d__2 = z_abs(&a[i__ + j * a_dim1]);
value = max(d__1,d__2);
/* L30: */
}
/* L40: */
}
}
} else if (lsame_(norm, "I") || lsame_(norm, "O") || *(unsigned char *)norm == '1') {
/* Find normI(A) ( = norm1(A), since A is hermitian). */
value = 0.;
if (lsame_(uplo, "U")) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
sum = 0.;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
absa = z_abs(&a[i__ + j * a_dim1]);
sum += absa;
work[i__] += absa;
/* L50: */
}
i__2 = j + j * a_dim1;
work[j] = sum + (d__1 = a[i__2].r, abs(d__1));
/* L60: */
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MAX */
d__1 = value, d__2 = work[i__];
value = max(d__1,d__2);
/* L70: */
}
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
work[i__] = 0.;
/* L80: */
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j + j * a_dim1;
sum = work[j] + (d__1 = a[i__2].r, abs(d__1));
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
absa = z_abs(&a[i__ + j * a_dim1]);
sum += absa;
work[i__] += absa;
/* L90: */
}
value = max(value,sum);
/* L100: */
}
}
} else if (lsame_(norm, "F") || lsame_(norm, "E")) {
/* Find normF(A). */
scale = 0.;
sum = 1.;
if (lsame_(uplo, "U")) {
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
i__2 = j - 1;
zlassq_(&i__2, &a[j * a_dim1 + 1], &c__1, &scale, &sum);
/* L110: */
}
} else {
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
i__2 = *n - j;
zlassq_(&i__2, &a[j + 1 + j * a_dim1], &c__1, &scale, &sum);
/* L120: */
}
}
sum *= 2;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + i__ * a_dim1;
if (a[i__2].r != 0.) {
i__2 = i__ + i__ * a_dim1;
absa = (d__1 = a[i__2].r, abs(d__1));
if (scale < absa) {
/* Computing 2nd power */
d__1 = scale / absa;
sum = sum * (d__1 * d__1) + 1.;
scale = absa;
} else {
/* Computing 2nd power */
d__1 = absa / scale;
sum += d__1 * d__1;
}
}
/* L130: */
}
value = scale * sqrt(sum);
}
ret_val = value;
return ret_val;
/* End of ZLANHE */
} /* zlanhe_ */
doublereal zlanhs_(char *norm, integer *n, doublecomplex *a, integer *lda,
doublereal *work)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
doublereal ret_val, d__1, d__2;
/* Builtin functions */
double z_abs(doublecomplex *), sqrt(doublereal);
/* Local variables */
static integer i__, j;
static doublereal sum, scale;
extern logical lsame_(char *, char *);
static doublereal value;
extern /* Subroutine */ int zlassq_(integer *, doublecomplex *, integer *,
doublereal *, doublereal *);
/*
-- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
October 31, 1992
Purpose
=======
ZLANHS returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
Hessenberg matrix A.
Description
===========
ZLANHS returns the value
ZLANHS = ( max(abs(A(i,j))), NORM = 'M' or 'm'
(
( norm1(A), NORM = '1', 'O' or 'o'
(
( normI(A), NORM = 'I' or 'i'
(
( normF(A), NORM = 'F', 'f', 'E' or 'e'
where norm1 denotes the one norm of a matrix (maximum column sum),
normI denotes the infinity norm of a matrix (maximum row sum) and
normF denotes the Frobenius norm of a matrix (square root of sum of
squares). Note that max(abs(A(i,j))) is not a matrix norm.
Arguments
=========
NORM (input) CHARACTER*1
Specifies the value to be returned in ZLANHS as described
above.
N (input) INTEGER
The order of the matrix A. N >= 0. When N = 0, ZLANHS is
set to zero.
A (input) COMPLEX*16 array, dimension (LDA,N)
The n by n upper Hessenberg matrix A; the part of A below the
first sub-diagonal is not referenced.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(N,1).
WORK (workspace) DOUBLE PRECISION array, dimension (LWORK),
where LWORK >= N when NORM = 'I'; otherwise, WORK is not
referenced.
=====================================================================
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--work;
/* Function Body */
if (*n == 0) {
value = 0.;
} else if (lsame_(norm, "M")) {
/* Find max(abs(A(i,j))). */
value = 0.;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__3 = *n, i__4 = j + 1;
i__2 = min(i__3,i__4);
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__1 = value, d__2 = z_abs(&a[i__ + j * a_dim1]);
value = max(d__1,d__2);
/* L10: */
}
/* L20: */
}
} else if (lsame_(norm, "O") || *(unsigned char *)
norm == '1') {
/* Find norm1(A). */
value = 0.;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
sum = 0.;
/* Computing MIN */
i__3 = *n, i__4 = j + 1;
i__2 = min(i__3,i__4);
for (i__ = 1; i__ <= i__2; ++i__) {
sum += z_abs(&a[i__ + j * a_dim1]);
/* L30: */
}
value = max(value,sum);
/* L40: */
}
} else if (lsame_(norm, "I")) {
/* Find normI(A). */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
work[i__] = 0.;
/* L50: */
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__3 = *n, i__4 = j + 1;
i__2 = min(i__3,i__4);
for (i__ = 1; i__ <= i__2; ++i__) {
work[i__] += z_abs(&a[i__ + j * a_dim1]);
/* L60: */
}
/* L70: */
}
value = 0.;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MAX */
d__1 = value, d__2 = work[i__];
value = max(d__1,d__2);
/* L80: */
}
} else if (lsame_(norm, "F") || lsame_(norm, "E")) {
/* Find normF(A). */
scale = 0.;
sum = 1.;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__3 = *n, i__4 = j + 1;
i__2 = min(i__3,i__4);
zlassq_(&i__2, &a[j * a_dim1 + 1], &c__1, &scale, &sum);
/* L90: */
}
value = scale * sqrt(sum);
}
ret_val = value;
return ret_val;
/* End of ZLANHS */
} /* zlanhs_ */
/* Subroutine */ int zlarcm_(integer *m, integer *n, doublereal *a, integer *
lda, doublecomplex *b, integer *ldb, doublecomplex *c__, integer *ldc,
doublereal *rwork)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2,
i__3, i__4, i__5;
doublereal d__1;
doublecomplex z__1;
/* Builtin functions */
double d_imag(doublecomplex *);
/* Local variables */
static integer i__, j, l;
extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *,
integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *);
/*
-- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZLARCM performs a very simple matrix-matrix multiplication:
C := A * B,
where A is M by M and real; B is M by N and complex;
C is M by N and complex.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A and of the matrix C.
M >= 0.
N (input) INTEGER
The number of columns and rows of the matrix B and
the number of columns of the matrix C.
N >= 0.
A (input) DOUBLE PRECISION array, dimension (LDA, M)
A contains the M by M matrix A.
LDA (input) INTEGER
The leading dimension of the array A. LDA >=max(1,M).
B (input) DOUBLE PRECISION array, dimension (LDB, N)
B contains the M by N matrix B.
LDB (input) INTEGER
The leading dimension of the array B. LDB >=max(1,M).
C (input) COMPLEX*16 array, dimension (LDC, N)
C contains the M by N matrix C.
LDC (input) INTEGER
The leading dimension of the array C. LDC >=max(1,M).
RWORK (workspace) DOUBLE PRECISION array, dimension (2*M*N)
=====================================================================
Quick return if possible.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1 * 1;
c__ -= c_offset;
--rwork;
/* Function Body */
if (*m == 0 || *n == 0) {
return 0;
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
rwork[(j - 1) * *m + i__] = b[i__3].r;
/* L10: */
}
/* L20: */
}
l = *m * *n + 1;
dgemm_("N", "N", m, n, m, &c_b1015, &a[a_offset], lda, &rwork[1], m, &
c_b324, &rwork[l], m);
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = l + (j - 1) * *m + i__ - 1;
c__[i__3].r = rwork[i__4], c__[i__3].i = 0.;
/* L30: */
}
/* L40: */
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
rwork[(j - 1) * *m + i__] = d_imag(&b[i__ + j * b_dim1]);
/* L50: */
}
/* L60: */
}
dgemm_("N", "N", m, n, m, &c_b1015, &a[a_offset], lda, &rwork[1], m, &
c_b324, &rwork[l], m);
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
d__1 = c__[i__4].r;
i__5 = l + (j - 1) * *m + i__ - 1;
z__1.r = d__1, z__1.i = rwork[i__5];
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/* L70: */
}
/* L80: */
}
return 0;
/* End of ZLARCM */
} /* zlarcm_ */
/* Subroutine */ int zlarf_(char *side, integer *m, integer *n, doublecomplex
*v, integer *incv, doublecomplex *tau, doublecomplex *c__, integer *
ldc, doublecomplex *work)
{
/* System generated locals */
integer c_dim1, c_offset;
doublecomplex z__1;
/* Local variables */
extern logical lsame_(char *, char *);
extern /* Subroutine */ int zgerc_(integer *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *), zgemv_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *);
/*
-- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZLARF applies a complex elementary reflector H to a complex M-by-N
matrix C, from either the left or the right. H is represented in the
form
H = I - tau * v * v'
where tau is a complex scalar and v is a complex vector.
If tau = 0, then H is taken to be the unit matrix.
To apply H' (the conjugate transpose of H), supply conjg(tau) instead
tau.
Arguments
=========
SIDE (input) CHARACTER*1
= 'L': form H * C
= 'R': form C * H
M (input) INTEGER
The number of rows of the matrix C.
N (input) INTEGER
The number of columns of the matrix C.
V (input) COMPLEX*16 array, dimension
(1 + (M-1)*abs(INCV)) if SIDE = 'L'
or (1 + (N-1)*abs(INCV)) if SIDE = 'R'
The vector v in the representation of H. V is not used if
TAU = 0.
INCV (input) INTEGER
The increment between elements of v. INCV <> 0.
TAU (input) COMPLEX*16
The value tau in the representation of H.
C (input/output) COMPLEX*16 array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by the matrix H * C if SIDE = 'L',
or C * H if SIDE = 'R'.
LDC (input) INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK (workspace) COMPLEX*16 array, dimension
(N) if SIDE = 'L'
or (M) if SIDE = 'R'
=====================================================================
*/
/* Parameter adjustments */
--v;
c_dim1 = *ldc;
c_offset = 1 + c_dim1 * 1;
c__ -= c_offset;
--work;
/* Function Body */
if (lsame_(side, "L")) {
/* Form H * C */
if (tau->r != 0. || tau->i != 0.) {
/* w := C' * v */
zgemv_("Conjugate transpose", m, n, &c_b60, &c__[c_offset], ldc, &
v[1], incv, &c_b59, &work[1], &c__1);
/* C := C - v * w' */
z__1.r = -tau->r, z__1.i = -tau->i;
zgerc_(m, n, &z__1, &v[1], incv, &work[1], &c__1, &c__[c_offset],
ldc);
}
} else {
/* Form C * H */
if (tau->r != 0. || tau->i != 0.) {
/* w := C * v */
zgemv_("No transpose", m, n, &c_b60, &c__[c_offset], ldc, &v[1],
incv, &c_b59, &work[1], &c__1);
/* C := C - w * v' */
z__1.r = -tau->r, z__1.i = -tau->i;
zgerc_(m, n, &z__1, &work[1], &c__1, &v[1], incv, &c__[c_offset],
ldc);
}
}
return 0;
/* End of ZLARF */
} /* zlarf_ */
/* Subroutine */ int zlarfb_(char *side, char *trans, char *direct, char *
storev, integer *m, integer *n, integer *k, doublecomplex *v, integer
*ldv, doublecomplex *t, integer *ldt, doublecomplex *c__, integer *
ldc, doublecomplex *work, integer *ldwork)
{
/* System generated locals */
integer c_dim1, c_offset, t_dim1, t_offset, v_dim1, v_offset, work_dim1,
work_offset, i__1, i__2, i__3, i__4, i__5;
doublecomplex z__1, z__2;
/* Builtin functions */
void d_cnjg(doublecomplex *, doublecomplex *);
/* Local variables */
static integer i__, j;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *,
integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *), zcopy_(integer *, doublecomplex *,
integer *, doublecomplex *, integer *), ztrmm_(char *, char *,
char *, char *, integer *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *), zlacgv_(integer *, doublecomplex *,
integer *);
static char transt[1];
/*
-- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZLARFB applies a complex block reflector H or its transpose H' to a
complex M-by-N matrix C, from either the left or the right.
Arguments
=========
SIDE (input) CHARACTER*1
= 'L': apply H or H' from the Left
= 'R': apply H or H' from the Right
TRANS (input) CHARACTER*1
= 'N': apply H (No transpose)
= 'C': apply H' (Conjugate transpose)
DIRECT (input) CHARACTER*1
Indicates how H is formed from a product of elementary
reflectors
= 'F': H = H(1) H(2) . . . H(k) (Forward)
= 'B': H = H(k) . . . H(2) H(1) (Backward)
STOREV (input) CHARACTER*1
Indicates how the vectors which define the elementary
reflectors are stored:
= 'C': Columnwise
= 'R': Rowwise
M (input) INTEGER
The number of rows of the matrix C.
N (input) INTEGER
The number of columns of the matrix C.
K (input) INTEGER
The order of the matrix T (= the number of elementary
reflectors whose product defines the block reflector).
V (input) COMPLEX*16 array, dimension
(LDV,K) if STOREV = 'C'
(LDV,M) if STOREV = 'R' and SIDE = 'L'
(LDV,N) if STOREV = 'R' and SIDE = 'R'
The matrix V. See further details.
LDV (input) INTEGER
The leading dimension of the array V.
If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M);
if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N);
if STOREV = 'R', LDV >= K.
T (input) COMPLEX*16 array, dimension (LDT,K)
The triangular K-by-K matrix T in the representation of the
block reflector.
LDT (input) INTEGER
The leading dimension of the array T. LDT >= K.
C (input/output) COMPLEX*16 array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by H*C or H'*C or C*H or C*H'.
LDC (input) INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK (workspace) COMPLEX*16 array, dimension (LDWORK,K)
LDWORK (input) INTEGER
The leading dimension of the array WORK.
If SIDE = 'L', LDWORK >= max(1,N);
if SIDE = 'R', LDWORK >= max(1,M).
=====================================================================
Quick return if possible
*/
/* Parameter adjustments */
v_dim1 = *ldv;
v_offset = 1 + v_dim1 * 1;
v -= v_offset;
t_dim1 = *ldt;
t_offset = 1 + t_dim1 * 1;
t -= t_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1 * 1;
c__ -= c_offset;
work_dim1 = *ldwork;
work_offset = 1 + work_dim1 * 1;
work -= work_offset;
/* Function Body */
if (*m <= 0 || *n <= 0) {
return 0;
}
if (lsame_(trans, "N")) {
*(unsigned char *)transt = 'C';
} else {
*(unsigned char *)transt = 'N';
}
if (lsame_(storev, "C")) {
if (lsame_(direct, "F")) {
/*
Let V = ( V1 ) (first K rows)
( V2 )
where V1 is unit lower triangular.
*/
if (lsame_(side, "L")) {
/*
Form H * C or H' * C where C = ( C1 )
( C2 )
W := C' * V = (C1'*V1 + C2'*V2) (stored in WORK)
W := C1'
*/
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
zcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1],
&c__1);
zlacgv_(n, &work[j * work_dim1 + 1], &c__1);
/* L10: */
}
/* W := W * V1 */
ztrmm_("Right", "Lower", "No transpose", "Unit", n, k, &c_b60,
&v[v_offset], ldv, &work[work_offset], ldwork);
if (*m > *k) {
/* W := W + C2'*V2 */
i__1 = *m - *k;
zgemm_("Conjugate transpose", "No transpose", n, k, &i__1,
&c_b60, &c__[*k + 1 + c_dim1], ldc, &v[*k + 1 +
v_dim1], ldv, &c_b60, &work[work_offset], ldwork);
}
/* W := W * T' or W * T */
ztrmm_("Right", "Upper", transt, "Non-unit", n, k, &c_b60, &t[
t_offset], ldt, &work[work_offset], ldwork);
/* C := C - V * W' */
if (*m > *k) {
/* C2 := C2 - V2 * W' */
i__1 = *m - *k;
z__1.r = -1., z__1.i = -0.;
zgemm_("No transpose", "Conjugate transpose", &i__1, n, k,
&z__1, &v[*k + 1 + v_dim1], ldv, &work[
work_offset], ldwork, &c_b60, &c__[*k + 1 +
c_dim1], ldc);
}
/* W := W * V1' */
ztrmm_("Right", "Lower", "Conjugate transpose", "Unit", n, k,
&c_b60, &v[v_offset], ldv, &work[work_offset], ldwork);
/* C1 := C1 - W' */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = j + i__ * c_dim1;
i__4 = j + i__ * c_dim1;
d_cnjg(&z__2, &work[i__ + j * work_dim1]);
z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i -
z__2.i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/* L20: */
}
/* L30: */
}
} else if (lsame_(side, "R")) {
/*
Form C * H or C * H' where C = ( C1 C2 )
W := C * V = (C1*V1 + C2*V2) (stored in WORK)
W := C1
*/
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
zcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j *
work_dim1 + 1], &c__1);
/* L40: */
}
/* W := W * V1 */
ztrmm_("Right", "Lower", "No transpose", "Unit", m, k, &c_b60,
&v[v_offset], ldv, &work[work_offset], ldwork);
if (*n > *k) {
/* W := W + C2 * V2 */
i__1 = *n - *k;
zgemm_("No transpose", "No transpose", m, k, &i__1, &
c_b60, &c__[(*k + 1) * c_dim1 + 1], ldc, &v[*k +
1 + v_dim1], ldv, &c_b60, &work[work_offset],
ldwork);
}
/* W := W * T or W * T' */
ztrmm_("Right", "Upper", trans, "Non-unit", m, k, &c_b60, &t[
t_offset], ldt, &work[work_offset], ldwork);
/* C := C - W * V' */
if (*n > *k) {
/* C2 := C2 - W * V2' */
i__1 = *n - *k;
z__1.r = -1., z__1.i = -0.;
zgemm_("No transpose", "Conjugate transpose", m, &i__1, k,
&z__1, &work[work_offset], ldwork, &v[*k + 1 +
v_dim1], ldv, &c_b60, &c__[(*k + 1) * c_dim1 + 1],
ldc);
}
/* W := W * V1' */
ztrmm_("Right", "Lower", "Conjugate transpose", "Unit", m, k,
&c_b60, &v[v_offset], ldv, &work[work_offset], ldwork);
/* C1 := C1 - W */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
i__5 = i__ + j * work_dim1;
z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[
i__4].i - work[i__5].i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/* L50: */
}
/* L60: */
}
}
} else {
/*
Let V = ( V1 )
( V2 ) (last K rows)
where V2 is unit upper triangular.
*/
if (lsame_(side, "L")) {
/*
Form H * C or H' * C where C = ( C1 )
( C2 )
W := C' * V = (C1'*V1 + C2'*V2) (stored in WORK)
W := C2'
*/
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
zcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j *
work_dim1 + 1], &c__1);
zlacgv_(n, &work[j * work_dim1 + 1], &c__1);
/* L70: */
}
/* W := W * V2 */
ztrmm_("Right", "Upper", "No transpose", "Unit", n, k, &c_b60,
&v[*m - *k + 1 + v_dim1], ldv, &work[work_offset],
ldwork);
if (*m > *k) {
/* W := W + C1'*V1 */
i__1 = *m - *k;
zgemm_("Conjugate transpose", "No transpose", n, k, &i__1,
&c_b60, &c__[c_offset], ldc, &v[v_offset], ldv, &
c_b60, &work[work_offset], ldwork);
}
/* W := W * T' or W * T */
ztrmm_("Right", "Lower", transt, "Non-unit", n, k, &c_b60, &t[
t_offset], ldt, &work[work_offset], ldwork);
/* C := C - V * W' */
if (*m > *k) {
/* C1 := C1 - V1 * W' */
i__1 = *m - *k;
z__1.r = -1., z__1.i = -0.;
zgemm_("No transpose", "Conjugate transpose", &i__1, n, k,
&z__1, &v[v_offset], ldv, &work[work_offset],
ldwork, &c_b60, &c__[c_offset], ldc);
}
/* W := W * V2' */
ztrmm_("Right", "Upper", "Conjugate transpose", "Unit", n, k,
&c_b60, &v[*m - *k + 1 + v_dim1], ldv, &work[
work_offset], ldwork);
/* C2 := C2 - W' */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = *m - *k + j + i__ * c_dim1;
i__4 = *m - *k + j + i__ * c_dim1;
d_cnjg(&z__2, &work[i__ + j * work_dim1]);
z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i -
z__2.i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/* L80: */
}
/* L90: */
}
} else if (lsame_(side, "R")) {
/*
Form C * H or C * H' where C = ( C1 C2 )
W := C * V = (C1*V1 + C2*V2) (stored in WORK)
W := C2
*/
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
zcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[
j * work_dim1 + 1], &c__1);
/* L100: */
}
/* W := W * V2 */
ztrmm_("Right", "Upper", "No transpose", "Unit", m, k, &c_b60,
&v[*n - *k + 1 + v_dim1], ldv, &work[work_offset],
ldwork);
if (*n > *k) {
/* W := W + C1 * V1 */
i__1 = *n - *k;
zgemm_("No transpose", "No transpose", m, k, &i__1, &
c_b60, &c__[c_offset], ldc, &v[v_offset], ldv, &
c_b60, &work[work_offset], ldwork);
}
/* W := W * T or W * T' */
ztrmm_("Right", "Lower", trans, "Non-unit", m, k, &c_b60, &t[
t_offset], ldt, &work[work_offset], ldwork);
/* C := C - W * V' */
if (*n > *k) {
/* C1 := C1 - W * V1' */
i__1 = *n - *k;
z__1.r = -1., z__1.i = -0.;
zgemm_("No transpose", "Conjugate transpose", m, &i__1, k,
&z__1, &work[work_offset], ldwork, &v[v_offset],
ldv, &c_b60, &c__[c_offset], ldc);
}
/* W := W * V2' */
ztrmm_("Right", "Upper", "Conjugate transpose", "Unit", m, k,
&c_b60, &v[*n - *k + 1 + v_dim1], ldv, &work[
work_offset], ldwork);
/* C2 := C2 - W */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + (*n - *k + j) * c_dim1;
i__4 = i__ + (*n - *k + j) * c_dim1;
i__5 = i__ + j * work_dim1;
z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[
i__4].i - work[i__5].i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/* L110: */
}
/* L120: */
}
}
}
} else if (lsame_(storev, "R")) {
if (lsame_(direct, "F")) {
/*
Let V = ( V1 V2 ) (V1: first K columns)
where V1 is unit upper triangular.
*/
if (lsame_(side, "L")) {
/*
Form H * C or H' * C where C = ( C1 )
( C2 )
W := C' * V' = (C1'*V1' + C2'*V2') (stored in WORK)
W := C1'
*/
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
zcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1],
&c__1);
zlacgv_(n, &work[j * work_dim1 + 1], &c__1);
/* L130: */
}
/* W := W * V1' */
ztrmm_("Right", "Upper", "Conjugate transpose", "Unit", n, k,
&c_b60, &v[v_offset], ldv, &work[work_offset], ldwork);
if (*m > *k) {
/* W := W + C2'*V2' */
i__1 = *m - *k;
zgemm_("Conjugate transpose", "Conjugate transpose", n, k,
&i__1, &c_b60, &c__[*k + 1 + c_dim1], ldc, &v[(*
k + 1) * v_dim1 + 1], ldv, &c_b60, &work[
work_offset], ldwork);
}
/* W := W * T' or W * T */
ztrmm_("Right", "Upper", transt, "Non-unit", n, k, &c_b60, &t[
t_offset], ldt, &work[work_offset], ldwork);
/* C := C - V' * W' */
if (*m > *k) {
/* C2 := C2 - V2' * W' */
i__1 = *m - *k;
z__1.r = -1., z__1.i = -0.;
zgemm_("Conjugate transpose", "Conjugate transpose", &
i__1, n, k, &z__1, &v[(*k + 1) * v_dim1 + 1], ldv,
&work[work_offset], ldwork, &c_b60, &c__[*k + 1
+ c_dim1], ldc);
}
/* W := W * V1 */
ztrmm_("Right", "Upper", "No transpose", "Unit", n, k, &c_b60,
&v[v_offset], ldv, &work[work_offset], ldwork);
/* C1 := C1 - W' */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = j + i__ * c_dim1;
i__4 = j + i__ * c_dim1;
d_cnjg(&z__2, &work[i__ + j * work_dim1]);
z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i -
z__2.i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/* L140: */
}
/* L150: */
}
} else if (lsame_(side, "R")) {
/*
Form C * H or C * H' where C = ( C1 C2 )
W := C * V' = (C1*V1' + C2*V2') (stored in WORK)
W := C1
*/
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
zcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j *
work_dim1 + 1], &c__1);
/* L160: */
}
/* W := W * V1' */
ztrmm_("Right", "Upper", "Conjugate transpose", "Unit", m, k,
&c_b60, &v[v_offset], ldv, &work[work_offset], ldwork);
if (*n > *k) {
/* W := W + C2 * V2' */
i__1 = *n - *k;
zgemm_("No transpose", "Conjugate transpose", m, k, &i__1,
&c_b60, &c__[(*k + 1) * c_dim1 + 1], ldc, &v[(*k
+ 1) * v_dim1 + 1], ldv, &c_b60, &work[
work_offset], ldwork);
}
/* W := W * T or W * T' */
ztrmm_("Right", "Upper", trans, "Non-unit", m, k, &c_b60, &t[
t_offset], ldt, &work[work_offset], ldwork);
/* C := C - W * V */
if (*n > *k) {
/* C2 := C2 - W * V2 */
i__1 = *n - *k;
z__1.r = -1., z__1.i = -0.;
zgemm_("No transpose", "No transpose", m, &i__1, k, &z__1,
&work[work_offset], ldwork, &v[(*k + 1) * v_dim1
+ 1], ldv, &c_b60, &c__[(*k + 1) * c_dim1 + 1],
ldc);
}
/* W := W * V1 */
ztrmm_("Right", "Upper", "No transpose", "Unit", m, k, &c_b60,
&v[v_offset], ldv, &work[work_offset], ldwork);
/* C1 := C1 - W */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
i__5 = i__ + j * work_dim1;
z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[
i__4].i - work[i__5].i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/* L170: */
}
/* L180: */
}
}
} else {
/*
Let V = ( V1 V2 ) (V2: last K columns)
where V2 is unit lower triangular.
*/
if (lsame_(side, "L")) {
/*
Form H * C or H' * C where C = ( C1 )
( C2 )
W := C' * V' = (C1'*V1' + C2'*V2') (stored in WORK)
W := C2'
*/
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
zcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j *
work_dim1 + 1], &c__1);
zlacgv_(n, &work[j * work_dim1 + 1], &c__1);
/* L190: */
}
/* W := W * V2' */
ztrmm_("Right", "Lower", "Conjugate transpose", "Unit", n, k,
&c_b60, &v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[
work_offset], ldwork);
if (*m > *k) {
/* W := W + C1'*V1' */
i__1 = *m - *k;
zgemm_("Conjugate transpose", "Conjugate transpose", n, k,
&i__1, &c_b60, &c__[c_offset], ldc, &v[v_offset],
ldv, &c_b60, &work[work_offset], ldwork);
}
/* W := W * T' or W * T */
ztrmm_("Right", "Lower", transt, "Non-unit", n, k, &c_b60, &t[
t_offset], ldt, &work[work_offset], ldwork);
/* C := C - V' * W' */
if (*m > *k) {
/* C1 := C1 - V1' * W' */
i__1 = *m - *k;
z__1.r = -1., z__1.i = -0.;
zgemm_("Conjugate transpose", "Conjugate transpose", &
i__1, n, k, &z__1, &v[v_offset], ldv, &work[
work_offset], ldwork, &c_b60, &c__[c_offset], ldc);
}
/* W := W * V2 */
ztrmm_("Right", "Lower", "No transpose", "Unit", n, k, &c_b60,
&v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[
work_offset], ldwork);
/* C2 := C2 - W' */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = *m - *k + j + i__ * c_dim1;
i__4 = *m - *k + j + i__ * c_dim1;
d_cnjg(&z__2, &work[i__ + j * work_dim1]);
z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i -
z__2.i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/* L200: */
}
/* L210: */
}
} else if (lsame_(side, "R")) {
/*
Form C * H or C * H' where C = ( C1 C2 )
W := C * V' = (C1*V1' + C2*V2') (stored in WORK)
W := C2
*/
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
zcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[
j * work_dim1 + 1], &c__1);
/* L220: */
}
/* W := W * V2' */
ztrmm_("Right", "Lower", "Conjugate transpose", "Unit", m, k,
&c_b60, &v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[
work_offset], ldwork);
if (*n > *k) {
/* W := W + C1 * V1' */
i__1 = *n - *k;
zgemm_("No transpose", "Conjugate transpose", m, k, &i__1,
&c_b60, &c__[c_offset], ldc, &v[v_offset], ldv, &
c_b60, &work[work_offset], ldwork);
}
/* W := W * T or W * T' */
ztrmm_("Right", "Lower", trans, "Non-unit", m, k, &c_b60, &t[
t_offset], ldt, &work[work_offset], ldwork);
/* C := C - W * V */
if (*n > *k) {
/* C1 := C1 - W * V1 */
i__1 = *n - *k;
z__1.r = -1., z__1.i = -0.;
zgemm_("No transpose", "No transpose", m, &i__1, k, &z__1,
&work[work_offset], ldwork, &v[v_offset], ldv, &
c_b60, &c__[c_offset], ldc);
}
/* W := W * V2 */
ztrmm_("Right", "Lower", "No transpose", "Unit", m, k, &c_b60,
&v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[
work_offset], ldwork);
/* C1 := C1 - W */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + (*n - *k + j) * c_dim1;
i__4 = i__ + (*n - *k + j) * c_dim1;
i__5 = i__ + j * work_dim1;
z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[
i__4].i - work[i__5].i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/* L230: */
}
/* L240: */
}
}
}
}
return 0;
/* End of ZLARFB */
} /* zlarfb_ */
/* Subroutine */ int zlarfg_(integer *n, doublecomplex *alpha, doublecomplex *
x, integer *incx, doublecomplex *tau)
{
/* System generated locals */
integer i__1;
doublereal d__1, d__2;
doublecomplex z__1, z__2;
/* Builtin functions */
double d_imag(doublecomplex *), d_sign(doublereal *, doublereal *);
/* Local variables */
static integer j, knt;
static doublereal beta, alphi, alphr;
extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
doublecomplex *, integer *);
static doublereal xnorm;
extern doublereal dlapy3_(doublereal *, doublereal *, doublereal *),
dznrm2_(integer *, doublecomplex *, integer *), dlamch_(char *);
static doublereal safmin;
extern /* Subroutine */ int zdscal_(integer *, doublereal *,
doublecomplex *, integer *);
static doublereal rsafmn;
extern /* Double Complex */ VOID zladiv_(doublecomplex *, doublecomplex *,
doublecomplex *);
/*
-- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZLARFG generates a complex elementary reflector H of order n, such
that
H' * ( alpha ) = ( beta ), H' * H = I.
( x ) ( 0 )
where alpha and beta are scalars, with beta real, and x is an
(n-1)-element complex vector. H is represented in the form
H = I - tau * ( 1 ) * ( 1 v' ) ,
( v )
where tau is a complex scalar and v is a complex (n-1)-element
vector. Note that H is not hermitian.
If the elements of x are all zero and alpha is real, then tau = 0
and H is taken to be the unit matrix.
Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1 .
Arguments
=========
N (input) INTEGER
The order of the elementary reflector.
ALPHA (input/output) COMPLEX*16
On entry, the value alpha.
On exit, it is overwritten with the value beta.
X (input/output) COMPLEX*16 array, dimension
(1+(N-2)*abs(INCX))
On entry, the vector x.
On exit, it is overwritten with the vector v.
INCX (input) INTEGER
The increment between elements of X. INCX > 0.
TAU (output) COMPLEX*16
The value tau.
=====================================================================
*/
/* Parameter adjustments */
--x;
/* Function Body */
if (*n <= 0) {
tau->r = 0., tau->i = 0.;
return 0;
}
i__1 = *n - 1;
xnorm = dznrm2_(&i__1, &x[1], incx);
alphr = alpha->r;
alphi = d_imag(alpha);
if ((xnorm == 0. && alphi == 0.)) {
/* H = I */
tau->r = 0., tau->i = 0.;
} else {
/* general case */
d__1 = dlapy3_(&alphr, &alphi, &xnorm);
beta = -d_sign(&d__1, &alphr);
safmin = SAFEMINIMUM / EPSILON;
rsafmn = 1. / safmin;
if (abs(beta) < safmin) {
/* XNORM, BETA may be inaccurate; scale X and recompute them */
knt = 0;
L10:
++knt;
i__1 = *n - 1;
zdscal_(&i__1, &rsafmn, &x[1], incx);
beta *= rsafmn;
alphi *= rsafmn;
alphr *= rsafmn;
if (abs(beta) < safmin) {
goto L10;
}
/* New BETA is at most 1, at least SAFMIN */
i__1 = *n - 1;
xnorm = dznrm2_(&i__1, &x[1], incx);
z__1.r = alphr, z__1.i = alphi;
alpha->r = z__1.r, alpha->i = z__1.i;
d__1 = dlapy3_(&alphr, &alphi, &xnorm);
beta = -d_sign(&d__1, &alphr);
d__1 = (beta - alphr) / beta;
d__2 = -alphi / beta;
z__1.r = d__1, z__1.i = d__2;
tau->r = z__1.r, tau->i = z__1.i;
z__2.r = alpha->r - beta, z__2.i = alpha->i;
zladiv_(&z__1, &c_b60, &z__2);
alpha->r = z__1.r, alpha->i = z__1.i;
i__1 = *n - 1;
zscal_(&i__1, alpha, &x[1], incx);
/* If ALPHA is subnormal, it may lose relative accuracy */
alpha->r = beta, alpha->i = 0.;
i__1 = knt;
for (j = 1; j <= i__1; ++j) {
z__1.r = safmin * alpha->r, z__1.i = safmin * alpha->i;
alpha->r = z__1.r, alpha->i = z__1.i;
/* L20: */
}
} else {
d__1 = (beta - alphr) / beta;
d__2 = -alphi / beta;
z__1.r = d__1, z__1.i = d__2;
tau->r = z__1.r, tau->i = z__1.i;
z__2.r = alpha->r - beta, z__2.i = alpha->i;
zladiv_(&z__1, &c_b60, &z__2);
alpha->r = z__1.r, alpha->i = z__1.i;
i__1 = *n - 1;
zscal_(&i__1, alpha, &x[1], incx);
alpha->r = beta, alpha->i = 0.;
}
}
return 0;
/* End of ZLARFG */
} /* zlarfg_ */
/* Subroutine */ int zlarft_(char *direct, char *storev, integer *n, integer *
k, doublecomplex *v, integer *ldv, doublecomplex *tau, doublecomplex *
t, integer *ldt)
{
/* System generated locals */
integer t_dim1, t_offset, v_dim1, v_offset, i__1, i__2, i__3, i__4;
doublecomplex z__1;
/* Local variables */
static integer i__, j;
static doublecomplex vii;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int zgemv_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *),
ztrmv_(char *, char *, char *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *),
zlacgv_(integer *, doublecomplex *, integer *);
/*
-- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZLARFT forms the triangular factor T of a complex block reflector H
of order n, which is defined as a product of k elementary reflectors.
If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;
If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.
If STOREV = 'C', the vector which defines the elementary reflector
H(i) is stored in the i-th column of the array V, and
H = I - V * T * V'
If STOREV = 'R', the vector which defines the elementary reflector
H(i) is stored in the i-th row of the array V, and
H = I - V' * T * V
Arguments
=========
DIRECT (input) CHARACTER*1
Specifies the order in which the elementary reflectors are
multiplied to form the block reflector:
= 'F': H = H(1) H(2) . . . H(k) (Forward)
= 'B': H = H(k) . . . H(2) H(1) (Backward)
STOREV (input) CHARACTER*1
Specifies how the vectors which define the elementary
reflectors are stored (see also Further Details):
= 'C': columnwise
= 'R': rowwise
N (input) INTEGER
The order of the block reflector H. N >= 0.
K (input) INTEGER
The order of the triangular factor T (= the number of
elementary reflectors). K >= 1.
V (input/output) COMPLEX*16 array, dimension
(LDV,K) if STOREV = 'C'
(LDV,N) if STOREV = 'R'
The matrix V. See further details.
LDV (input) INTEGER
The leading dimension of the array V.
If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.
TAU (input) COMPLEX*16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i).
T (output) COMPLEX*16 array, dimension (LDT,K)
The k by k triangular factor T of the block reflector.
If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is
lower triangular. The rest of the array is not used.
LDT (input) INTEGER
The leading dimension of the array T. LDT >= K.
Further Details
===============
The shape of the matrix V and the storage of the vectors which define
the H(i) is best illustrated by the following example with n = 5 and
k = 3. The elements equal to 1 are not stored; the corresponding
array elements are modified but restored on exit. The rest of the
array is not used.
DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R':
V = ( 1 ) V = ( 1 v1 v1 v1 v1 )
( v1 1 ) ( 1 v2 v2 v2 )
( v1 v2 1 ) ( 1 v3 v3 )
( v1 v2 v3 )
( v1 v2 v3 )
DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R':
V = ( v1 v2 v3 ) V = ( v1 v1 1 )
( v1 v2 v3 ) ( v2 v2 v2 1 )
( 1 v2 v3 ) ( v3 v3 v3 v3 1 )
( 1 v3 )
( 1 )
=====================================================================
Quick return if possible
*/
/* Parameter adjustments */
v_dim1 = *ldv;
v_offset = 1 + v_dim1 * 1;
v -= v_offset;
--tau;
t_dim1 = *ldt;
t_offset = 1 + t_dim1 * 1;
t -= t_offset;
/* Function Body */
if (*n == 0) {
return 0;
}
if (lsame_(direct, "F")) {
i__1 = *k;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
if ((tau[i__2].r == 0. && tau[i__2].i == 0.)) {
/* H(i) = I */
i__2 = i__;
for (j = 1; j <= i__2; ++j) {
i__3 = j + i__ * t_dim1;
t[i__3].r = 0., t[i__3].i = 0.;
/* L10: */
}
} else {
/* general case */
i__2 = i__ + i__ * v_dim1;
vii.r = v[i__2].r, vii.i = v[i__2].i;
i__2 = i__ + i__ * v_dim1;
v[i__2].r = 1., v[i__2].i = 0.;
if (lsame_(storev, "C")) {
/* T(1:i-1,i) := - tau(i) * V(i:n,1:i-1)' * V(i:n,i) */
i__2 = *n - i__ + 1;
i__3 = i__ - 1;
i__4 = i__;
z__1.r = -tau[i__4].r, z__1.i = -tau[i__4].i;
zgemv_("Conjugate transpose", &i__2, &i__3, &z__1, &v[i__
+ v_dim1], ldv, &v[i__ + i__ * v_dim1], &c__1, &
c_b59, &t[i__ * t_dim1 + 1], &c__1);
} else {
/* T(1:i-1,i) := - tau(i) * V(1:i-1,i:n) * V(i,i:n)' */
if (i__ < *n) {
i__2 = *n - i__;
zlacgv_(&i__2, &v[i__ + (i__ + 1) * v_dim1], ldv);
}
i__2 = i__ - 1;
i__3 = *n - i__ + 1;
i__4 = i__;
z__1.r = -tau[i__4].r, z__1.i = -tau[i__4].i;
zgemv_("No transpose", &i__2, &i__3, &z__1, &v[i__ *
v_dim1 + 1], ldv, &v[i__ + i__ * v_dim1], ldv, &
c_b59, &t[i__ * t_dim1 + 1], &c__1);
if (i__ < *n) {
i__2 = *n - i__;
zlacgv_(&i__2, &v[i__ + (i__ + 1) * v_dim1], ldv);
}
}
i__2 = i__ + i__ * v_dim1;
v[i__2].r = vii.r, v[i__2].i = vii.i;
/* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) */
i__2 = i__ - 1;
ztrmv_("Upper", "No transpose", "Non-unit", &i__2, &t[
t_offset], ldt, &t[i__ * t_dim1 + 1], &c__1);
i__2 = i__ + i__ * t_dim1;
i__3 = i__;
t[i__2].r = tau[i__3].r, t[i__2].i = tau[i__3].i;
}
/* L20: */
}
} else {
for (i__ = *k; i__ >= 1; --i__) {
i__1 = i__;
if ((tau[i__1].r == 0. && tau[i__1].i == 0.)) {
/* H(i) = I */
i__1 = *k;
for (j = i__; j <= i__1; ++j) {
i__2 = j + i__ * t_dim1;
t[i__2].r = 0., t[i__2].i = 0.;
/* L30: */
}
} else {
/* general case */
if (i__ < *k) {
if (lsame_(storev, "C")) {
i__1 = *n - *k + i__ + i__ * v_dim1;
vii.r = v[i__1].r, vii.i = v[i__1].i;
i__1 = *n - *k + i__ + i__ * v_dim1;
v[i__1].r = 1., v[i__1].i = 0.;
/*
T(i+1:k,i) :=
- tau(i) * V(1:n-k+i,i+1:k)' * V(1:n-k+i,i)
*/
i__1 = *n - *k + i__;
i__2 = *k - i__;
i__3 = i__;
z__1.r = -tau[i__3].r, z__1.i = -tau[i__3].i;
zgemv_("Conjugate transpose", &i__1, &i__2, &z__1, &v[
(i__ + 1) * v_dim1 + 1], ldv, &v[i__ * v_dim1
+ 1], &c__1, &c_b59, &t[i__ + 1 + i__ *
t_dim1], &c__1);
i__1 = *n - *k + i__ + i__ * v_dim1;
v[i__1].r = vii.r, v[i__1].i = vii.i;
} else {
i__1 = i__ + (*n - *k + i__) * v_dim1;
vii.r = v[i__1].r, vii.i = v[i__1].i;
i__1 = i__ + (*n - *k + i__) * v_dim1;
v[i__1].r = 1., v[i__1].i = 0.;
/*
T(i+1:k,i) :=
- tau(i) * V(i+1:k,1:n-k+i) * V(i,1:n-k+i)'
*/
i__1 = *n - *k + i__ - 1;
zlacgv_(&i__1, &v[i__ + v_dim1], ldv);
i__1 = *k - i__;
i__2 = *n - *k + i__;
i__3 = i__;
z__1.r = -tau[i__3].r, z__1.i = -tau[i__3].i;
zgemv_("No transpose", &i__1, &i__2, &z__1, &v[i__ +
1 + v_dim1], ldv, &v[i__ + v_dim1], ldv, &
c_b59, &t[i__ + 1 + i__ * t_dim1], &c__1);
i__1 = *n - *k + i__ - 1;
zlacgv_(&i__1, &v[i__ + v_dim1], ldv);
i__1 = i__ + (*n - *k + i__) * v_dim1;
v[i__1].r = vii.r, v[i__1].i = vii.i;
}
/* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) */
i__1 = *k - i__;
ztrmv_("Lower", "No transpose", "Non-unit", &i__1, &t[i__
+ 1 + (i__ + 1) * t_dim1], ldt, &t[i__ + 1 + i__ *
t_dim1], &c__1)
;
}
i__1 = i__ + i__ * t_dim1;
i__2 = i__;
t[i__1].r = tau[i__2].r, t[i__1].i = tau[i__2].i;
}
/* L40: */
}
}
return 0;
/* End of ZLARFT */
} /* zlarft_ */
/* Subroutine */ int zlarfx_(char *side, integer *m, integer *n,
doublecomplex *v, doublecomplex *tau, doublecomplex *c__, integer *
ldc, doublecomplex *work)
{
/* System generated locals */
integer c_dim1, c_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7, i__8,
i__9, i__10, i__11;
doublecomplex z__1, z__2, z__3, z__4, z__5, z__6, z__7, z__8, z__9, z__10,
z__11, z__12, z__13, z__14, z__15, z__16, z__17, z__18, z__19;
/* Builtin functions */
void d_cnjg(doublecomplex *, doublecomplex *);
/* Local variables */
static integer j;
static doublecomplex t1, t2, t3, t4, t5, t6, t7, t8, t9, v1, v2, v3, v4,
v5, v6, v7, v8, v9, t10, v10, sum;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int zgerc_(integer *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *), zgemv_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *);
/*
-- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZLARFX applies a complex elementary reflector H to a complex m by n
matrix C, from either the left or the right. H is represented in the
form
H = I - tau * v * v'
where tau is a complex scalar and v is a complex vector.
If tau = 0, then H is taken to be the unit matrix
This version uses inline code if H has order < 11.
Arguments
=========
SIDE (input) CHARACTER*1
= 'L': form H * C
= 'R': form C * H
M (input) INTEGER
The number of rows of the matrix C.
N (input) INTEGER
The number of columns of the matrix C.
V (input) COMPLEX*16 array, dimension (M) if SIDE = 'L'
or (N) if SIDE = 'R'
The vector v in the representation of H.
TAU (input) COMPLEX*16
The value tau in the representation of H.
C (input/output) COMPLEX*16 array, dimension (LDC,N)
On entry, the m by n matrix C.
On exit, C is overwritten by the matrix H * C if SIDE = 'L',
or C * H if SIDE = 'R'.
LDC (input) INTEGER
The leading dimension of the array C. LDA >= max(1,M).
WORK (workspace) COMPLEX*16 array, dimension (N) if SIDE = 'L'
or (M) if SIDE = 'R'
WORK is not referenced if H has order < 11.
=====================================================================
*/
/* Parameter adjustments */
--v;
c_dim1 = *ldc;
c_offset = 1 + c_dim1 * 1;
c__ -= c_offset;
--work;
/* Function Body */
if ((tau->r == 0. && tau->i == 0.)) {
return 0;
}
if (lsame_(side, "L")) {
/* Form H * C, where H has order m. */
switch (*m) {
case 1: goto L10;
case 2: goto L30;
case 3: goto L50;
case 4: goto L70;
case 5: goto L90;
case 6: goto L110;
case 7: goto L130;
case 8: goto L150;
case 9: goto L170;
case 10: goto L190;
}
/*
Code for general M
w := C'*v
*/
zgemv_("Conjugate transpose", m, n, &c_b60, &c__[c_offset], ldc, &v[1]
, &c__1, &c_b59, &work[1], &c__1);
/* C := C - tau * v * w' */
z__1.r = -tau->r, z__1.i = -tau->i;
zgerc_(m, n, &z__1, &v[1], &c__1, &work[1], &c__1, &c__[c_offset],
ldc);
goto L410;
L10:
/* Special code for 1 x 1 Householder */
z__3.r = tau->r * v[1].r - tau->i * v[1].i, z__3.i = tau->r * v[1].i
+ tau->i * v[1].r;
d_cnjg(&z__4, &v[1]);
z__2.r = z__3.r * z__4.r - z__3.i * z__4.i, z__2.i = z__3.r * z__4.i
+ z__3.i * z__4.r;
z__1.r = 1. - z__2.r, z__1.i = 0. - z__2.i;
t1.r = z__1.r, t1.i = z__1.i;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j * c_dim1 + 1;
i__3 = j * c_dim1 + 1;
z__1.r = t1.r * c__[i__3].r - t1.i * c__[i__3].i, z__1.i = t1.r *
c__[i__3].i + t1.i * c__[i__3].r;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
/* L20: */
}
goto L410;
L30:
/* Special code for 2 x 2 Householder */
d_cnjg(&z__1, &v[1]);
v1.r = z__1.r, v1.i = z__1.i;
d_cnjg(&z__2, &v1);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t1.r = z__1.r, t1.i = z__1.i;
d_cnjg(&z__1, &v[2]);
v2.r = z__1.r, v2.i = z__1.i;
d_cnjg(&z__2, &v2);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t2.r = z__1.r, t2.i = z__1.i;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j * c_dim1 + 1;
z__2.r = v1.r * c__[i__2].r - v1.i * c__[i__2].i, z__2.i = v1.r *
c__[i__2].i + v1.i * c__[i__2].r;
i__3 = j * c_dim1 + 2;
z__3.r = v2.r * c__[i__3].r - v2.i * c__[i__3].i, z__3.i = v2.r *
c__[i__3].i + v2.i * c__[i__3].r;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
sum.r = z__1.r, sum.i = z__1.i;
i__2 = j * c_dim1 + 1;
i__3 = j * c_dim1 + 1;
z__2.r = sum.r * t1.r - sum.i * t1.i, z__2.i = sum.r * t1.i +
sum.i * t1.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 2;
i__3 = j * c_dim1 + 2;
z__2.r = sum.r * t2.r - sum.i * t2.i, z__2.i = sum.r * t2.i +
sum.i * t2.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
/* L40: */
}
goto L410;
L50:
/* Special code for 3 x 3 Householder */
d_cnjg(&z__1, &v[1]);
v1.r = z__1.r, v1.i = z__1.i;
d_cnjg(&z__2, &v1);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t1.r = z__1.r, t1.i = z__1.i;
d_cnjg(&z__1, &v[2]);
v2.r = z__1.r, v2.i = z__1.i;
d_cnjg(&z__2, &v2);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t2.r = z__1.r, t2.i = z__1.i;
d_cnjg(&z__1, &v[3]);
v3.r = z__1.r, v3.i = z__1.i;
d_cnjg(&z__2, &v3);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t3.r = z__1.r, t3.i = z__1.i;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j * c_dim1 + 1;
z__3.r = v1.r * c__[i__2].r - v1.i * c__[i__2].i, z__3.i = v1.r *
c__[i__2].i + v1.i * c__[i__2].r;
i__3 = j * c_dim1 + 2;
z__4.r = v2.r * c__[i__3].r - v2.i * c__[i__3].i, z__4.i = v2.r *
c__[i__3].i + v2.i * c__[i__3].r;
z__2.r = z__3.r + z__4.r, z__2.i = z__3.i + z__4.i;
i__4 = j * c_dim1 + 3;
z__5.r = v3.r * c__[i__4].r - v3.i * c__[i__4].i, z__5.i = v3.r *
c__[i__4].i + v3.i * c__[i__4].r;
z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + z__5.i;
sum.r = z__1.r, sum.i = z__1.i;
i__2 = j * c_dim1 + 1;
i__3 = j * c_dim1 + 1;
z__2.r = sum.r * t1.r - sum.i * t1.i, z__2.i = sum.r * t1.i +
sum.i * t1.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 2;
i__3 = j * c_dim1 + 2;
z__2.r = sum.r * t2.r - sum.i * t2.i, z__2.i = sum.r * t2.i +
sum.i * t2.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 3;
i__3 = j * c_dim1 + 3;
z__2.r = sum.r * t3.r - sum.i * t3.i, z__2.i = sum.r * t3.i +
sum.i * t3.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
/* L60: */
}
goto L410;
L70:
/* Special code for 4 x 4 Householder */
d_cnjg(&z__1, &v[1]);
v1.r = z__1.r, v1.i = z__1.i;
d_cnjg(&z__2, &v1);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t1.r = z__1.r, t1.i = z__1.i;
d_cnjg(&z__1, &v[2]);
v2.r = z__1.r, v2.i = z__1.i;
d_cnjg(&z__2, &v2);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t2.r = z__1.r, t2.i = z__1.i;
d_cnjg(&z__1, &v[3]);
v3.r = z__1.r, v3.i = z__1.i;
d_cnjg(&z__2, &v3);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t3.r = z__1.r, t3.i = z__1.i;
d_cnjg(&z__1, &v[4]);
v4.r = z__1.r, v4.i = z__1.i;
d_cnjg(&z__2, &v4);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t4.r = z__1.r, t4.i = z__1.i;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j * c_dim1 + 1;
z__4.r = v1.r * c__[i__2].r - v1.i * c__[i__2].i, z__4.i = v1.r *
c__[i__2].i + v1.i * c__[i__2].r;
i__3 = j * c_dim1 + 2;
z__5.r = v2.r * c__[i__3].r - v2.i * c__[i__3].i, z__5.i = v2.r *
c__[i__3].i + v2.i * c__[i__3].r;
z__3.r = z__4.r + z__5.r, z__3.i = z__4.i + z__5.i;
i__4 = j * c_dim1 + 3;
z__6.r = v3.r * c__[i__4].r - v3.i * c__[i__4].i, z__6.i = v3.r *
c__[i__4].i + v3.i * c__[i__4].r;
z__2.r = z__3.r + z__6.r, z__2.i = z__3.i + z__6.i;
i__5 = j * c_dim1 + 4;
z__7.r = v4.r * c__[i__5].r - v4.i * c__[i__5].i, z__7.i = v4.r *
c__[i__5].i + v4.i * c__[i__5].r;
z__1.r = z__2.r + z__7.r, z__1.i = z__2.i + z__7.i;
sum.r = z__1.r, sum.i = z__1.i;
i__2 = j * c_dim1 + 1;
i__3 = j * c_dim1 + 1;
z__2.r = sum.r * t1.r - sum.i * t1.i, z__2.i = sum.r * t1.i +
sum.i * t1.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 2;
i__3 = j * c_dim1 + 2;
z__2.r = sum.r * t2.r - sum.i * t2.i, z__2.i = sum.r * t2.i +
sum.i * t2.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 3;
i__3 = j * c_dim1 + 3;
z__2.r = sum.r * t3.r - sum.i * t3.i, z__2.i = sum.r * t3.i +
sum.i * t3.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 4;
i__3 = j * c_dim1 + 4;
z__2.r = sum.r * t4.r - sum.i * t4.i, z__2.i = sum.r * t4.i +
sum.i * t4.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
/* L80: */
}
goto L410;
L90:
/* Special code for 5 x 5 Householder */
d_cnjg(&z__1, &v[1]);
v1.r = z__1.r, v1.i = z__1.i;
d_cnjg(&z__2, &v1);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t1.r = z__1.r, t1.i = z__1.i;
d_cnjg(&z__1, &v[2]);
v2.r = z__1.r, v2.i = z__1.i;
d_cnjg(&z__2, &v2);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t2.r = z__1.r, t2.i = z__1.i;
d_cnjg(&z__1, &v[3]);
v3.r = z__1.r, v3.i = z__1.i;
d_cnjg(&z__2, &v3);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t3.r = z__1.r, t3.i = z__1.i;
d_cnjg(&z__1, &v[4]);
v4.r = z__1.r, v4.i = z__1.i;
d_cnjg(&z__2, &v4);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t4.r = z__1.r, t4.i = z__1.i;
d_cnjg(&z__1, &v[5]);
v5.r = z__1.r, v5.i = z__1.i;
d_cnjg(&z__2, &v5);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t5.r = z__1.r, t5.i = z__1.i;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j * c_dim1 + 1;
z__5.r = v1.r * c__[i__2].r - v1.i * c__[i__2].i, z__5.i = v1.r *
c__[i__2].i + v1.i * c__[i__2].r;
i__3 = j * c_dim1 + 2;
z__6.r = v2.r * c__[i__3].r - v2.i * c__[i__3].i, z__6.i = v2.r *
c__[i__3].i + v2.i * c__[i__3].r;
z__4.r = z__5.r + z__6.r, z__4.i = z__5.i + z__6.i;
i__4 = j * c_dim1 + 3;
z__7.r = v3.r * c__[i__4].r - v3.i * c__[i__4].i, z__7.i = v3.r *
c__[i__4].i + v3.i * c__[i__4].r;
z__3.r = z__4.r + z__7.r, z__3.i = z__4.i + z__7.i;
i__5 = j * c_dim1 + 4;
z__8.r = v4.r * c__[i__5].r - v4.i * c__[i__5].i, z__8.i = v4.r *
c__[i__5].i + v4.i * c__[i__5].r;
z__2.r = z__3.r + z__8.r, z__2.i = z__3.i + z__8.i;
i__6 = j * c_dim1 + 5;
z__9.r = v5.r * c__[i__6].r - v5.i * c__[i__6].i, z__9.i = v5.r *
c__[i__6].i + v5.i * c__[i__6].r;
z__1.r = z__2.r + z__9.r, z__1.i = z__2.i + z__9.i;
sum.r = z__1.r, sum.i = z__1.i;
i__2 = j * c_dim1 + 1;
i__3 = j * c_dim1 + 1;
z__2.r = sum.r * t1.r - sum.i * t1.i, z__2.i = sum.r * t1.i +
sum.i * t1.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 2;
i__3 = j * c_dim1 + 2;
z__2.r = sum.r * t2.r - sum.i * t2.i, z__2.i = sum.r * t2.i +
sum.i * t2.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 3;
i__3 = j * c_dim1 + 3;
z__2.r = sum.r * t3.r - sum.i * t3.i, z__2.i = sum.r * t3.i +
sum.i * t3.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 4;
i__3 = j * c_dim1 + 4;
z__2.r = sum.r * t4.r - sum.i * t4.i, z__2.i = sum.r * t4.i +
sum.i * t4.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 5;
i__3 = j * c_dim1 + 5;
z__2.r = sum.r * t5.r - sum.i * t5.i, z__2.i = sum.r * t5.i +
sum.i * t5.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
/* L100: */
}
goto L410;
L110:
/* Special code for 6 x 6 Householder */
d_cnjg(&z__1, &v[1]);
v1.r = z__1.r, v1.i = z__1.i;
d_cnjg(&z__2, &v1);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t1.r = z__1.r, t1.i = z__1.i;
d_cnjg(&z__1, &v[2]);
v2.r = z__1.r, v2.i = z__1.i;
d_cnjg(&z__2, &v2);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t2.r = z__1.r, t2.i = z__1.i;
d_cnjg(&z__1, &v[3]);
v3.r = z__1.r, v3.i = z__1.i;
d_cnjg(&z__2, &v3);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t3.r = z__1.r, t3.i = z__1.i;
d_cnjg(&z__1, &v[4]);
v4.r = z__1.r, v4.i = z__1.i;
d_cnjg(&z__2, &v4);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t4.r = z__1.r, t4.i = z__1.i;
d_cnjg(&z__1, &v[5]);
v5.r = z__1.r, v5.i = z__1.i;
d_cnjg(&z__2, &v5);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t5.r = z__1.r, t5.i = z__1.i;
d_cnjg(&z__1, &v[6]);
v6.r = z__1.r, v6.i = z__1.i;
d_cnjg(&z__2, &v6);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t6.r = z__1.r, t6.i = z__1.i;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j * c_dim1 + 1;
z__6.r = v1.r * c__[i__2].r - v1.i * c__[i__2].i, z__6.i = v1.r *
c__[i__2].i + v1.i * c__[i__2].r;
i__3 = j * c_dim1 + 2;
z__7.r = v2.r * c__[i__3].r - v2.i * c__[i__3].i, z__7.i = v2.r *
c__[i__3].i + v2.i * c__[i__3].r;
z__5.r = z__6.r + z__7.r, z__5.i = z__6.i + z__7.i;
i__4 = j * c_dim1 + 3;
z__8.r = v3.r * c__[i__4].r - v3.i * c__[i__4].i, z__8.i = v3.r *
c__[i__4].i + v3.i * c__[i__4].r;
z__4.r = z__5.r + z__8.r, z__4.i = z__5.i + z__8.i;
i__5 = j * c_dim1 + 4;
z__9.r = v4.r * c__[i__5].r - v4.i * c__[i__5].i, z__9.i = v4.r *
c__[i__5].i + v4.i * c__[i__5].r;
z__3.r = z__4.r + z__9.r, z__3.i = z__4.i + z__9.i;
i__6 = j * c_dim1 + 5;
z__10.r = v5.r * c__[i__6].r - v5.i * c__[i__6].i, z__10.i = v5.r
* c__[i__6].i + v5.i * c__[i__6].r;
z__2.r = z__3.r + z__10.r, z__2.i = z__3.i + z__10.i;
i__7 = j * c_dim1 + 6;
z__11.r = v6.r * c__[i__7].r - v6.i * c__[i__7].i, z__11.i = v6.r
* c__[i__7].i + v6.i * c__[i__7].r;
z__1.r = z__2.r + z__11.r, z__1.i = z__2.i + z__11.i;
sum.r = z__1.r, sum.i = z__1.i;
i__2 = j * c_dim1 + 1;
i__3 = j * c_dim1 + 1;
z__2.r = sum.r * t1.r - sum.i * t1.i, z__2.i = sum.r * t1.i +
sum.i * t1.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 2;
i__3 = j * c_dim1 + 2;
z__2.r = sum.r * t2.r - sum.i * t2.i, z__2.i = sum.r * t2.i +
sum.i * t2.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 3;
i__3 = j * c_dim1 + 3;
z__2.r = sum.r * t3.r - sum.i * t3.i, z__2.i = sum.r * t3.i +
sum.i * t3.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 4;
i__3 = j * c_dim1 + 4;
z__2.r = sum.r * t4.r - sum.i * t4.i, z__2.i = sum.r * t4.i +
sum.i * t4.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 5;
i__3 = j * c_dim1 + 5;
z__2.r = sum.r * t5.r - sum.i * t5.i, z__2.i = sum.r * t5.i +
sum.i * t5.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 6;
i__3 = j * c_dim1 + 6;
z__2.r = sum.r * t6.r - sum.i * t6.i, z__2.i = sum.r * t6.i +
sum.i * t6.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
/* L120: */
}
goto L410;
L130:
/* Special code for 7 x 7 Householder */
d_cnjg(&z__1, &v[1]);
v1.r = z__1.r, v1.i = z__1.i;
d_cnjg(&z__2, &v1);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t1.r = z__1.r, t1.i = z__1.i;
d_cnjg(&z__1, &v[2]);
v2.r = z__1.r, v2.i = z__1.i;
d_cnjg(&z__2, &v2);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t2.r = z__1.r, t2.i = z__1.i;
d_cnjg(&z__1, &v[3]);
v3.r = z__1.r, v3.i = z__1.i;
d_cnjg(&z__2, &v3);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t3.r = z__1.r, t3.i = z__1.i;
d_cnjg(&z__1, &v[4]);
v4.r = z__1.r, v4.i = z__1.i;
d_cnjg(&z__2, &v4);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t4.r = z__1.r, t4.i = z__1.i;
d_cnjg(&z__1, &v[5]);
v5.r = z__1.r, v5.i = z__1.i;
d_cnjg(&z__2, &v5);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t5.r = z__1.r, t5.i = z__1.i;
d_cnjg(&z__1, &v[6]);
v6.r = z__1.r, v6.i = z__1.i;
d_cnjg(&z__2, &v6);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t6.r = z__1.r, t6.i = z__1.i;
d_cnjg(&z__1, &v[7]);
v7.r = z__1.r, v7.i = z__1.i;
d_cnjg(&z__2, &v7);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t7.r = z__1.r, t7.i = z__1.i;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j * c_dim1 + 1;
z__7.r = v1.r * c__[i__2].r - v1.i * c__[i__2].i, z__7.i = v1.r *
c__[i__2].i + v1.i * c__[i__2].r;
i__3 = j * c_dim1 + 2;
z__8.r = v2.r * c__[i__3].r - v2.i * c__[i__3].i, z__8.i = v2.r *
c__[i__3].i + v2.i * c__[i__3].r;
z__6.r = z__7.r + z__8.r, z__6.i = z__7.i + z__8.i;
i__4 = j * c_dim1 + 3;
z__9.r = v3.r * c__[i__4].r - v3.i * c__[i__4].i, z__9.i = v3.r *
c__[i__4].i + v3.i * c__[i__4].r;
z__5.r = z__6.r + z__9.r, z__5.i = z__6.i + z__9.i;
i__5 = j * c_dim1 + 4;
z__10.r = v4.r * c__[i__5].r - v4.i * c__[i__5].i, z__10.i = v4.r
* c__[i__5].i + v4.i * c__[i__5].r;
z__4.r = z__5.r + z__10.r, z__4.i = z__5.i + z__10.i;
i__6 = j * c_dim1 + 5;
z__11.r = v5.r * c__[i__6].r - v5.i * c__[i__6].i, z__11.i = v5.r
* c__[i__6].i + v5.i * c__[i__6].r;
z__3.r = z__4.r + z__11.r, z__3.i = z__4.i + z__11.i;
i__7 = j * c_dim1 + 6;
z__12.r = v6.r * c__[i__7].r - v6.i * c__[i__7].i, z__12.i = v6.r
* c__[i__7].i + v6.i * c__[i__7].r;
z__2.r = z__3.r + z__12.r, z__2.i = z__3.i + z__12.i;
i__8 = j * c_dim1 + 7;
z__13.r = v7.r * c__[i__8].r - v7.i * c__[i__8].i, z__13.i = v7.r
* c__[i__8].i + v7.i * c__[i__8].r;
z__1.r = z__2.r + z__13.r, z__1.i = z__2.i + z__13.i;
sum.r = z__1.r, sum.i = z__1.i;
i__2 = j * c_dim1 + 1;
i__3 = j * c_dim1 + 1;
z__2.r = sum.r * t1.r - sum.i * t1.i, z__2.i = sum.r * t1.i +
sum.i * t1.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 2;
i__3 = j * c_dim1 + 2;
z__2.r = sum.r * t2.r - sum.i * t2.i, z__2.i = sum.r * t2.i +
sum.i * t2.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 3;
i__3 = j * c_dim1 + 3;
z__2.r = sum.r * t3.r - sum.i * t3.i, z__2.i = sum.r * t3.i +
sum.i * t3.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 4;
i__3 = j * c_dim1 + 4;
z__2.r = sum.r * t4.r - sum.i * t4.i, z__2.i = sum.r * t4.i +
sum.i * t4.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 5;
i__3 = j * c_dim1 + 5;
z__2.r = sum.r * t5.r - sum.i * t5.i, z__2.i = sum.r * t5.i +
sum.i * t5.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 6;
i__3 = j * c_dim1 + 6;
z__2.r = sum.r * t6.r - sum.i * t6.i, z__2.i = sum.r * t6.i +
sum.i * t6.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 7;
i__3 = j * c_dim1 + 7;
z__2.r = sum.r * t7.r - sum.i * t7.i, z__2.i = sum.r * t7.i +
sum.i * t7.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
/* L140: */
}
goto L410;
L150:
/* Special code for 8 x 8 Householder */
d_cnjg(&z__1, &v[1]);
v1.r = z__1.r, v1.i = z__1.i;
d_cnjg(&z__2, &v1);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t1.r = z__1.r, t1.i = z__1.i;
d_cnjg(&z__1, &v[2]);
v2.r = z__1.r, v2.i = z__1.i;
d_cnjg(&z__2, &v2);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t2.r = z__1.r, t2.i = z__1.i;
d_cnjg(&z__1, &v[3]);
v3.r = z__1.r, v3.i = z__1.i;
d_cnjg(&z__2, &v3);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t3.r = z__1.r, t3.i = z__1.i;
d_cnjg(&z__1, &v[4]);
v4.r = z__1.r, v4.i = z__1.i;
d_cnjg(&z__2, &v4);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t4.r = z__1.r, t4.i = z__1.i;
d_cnjg(&z__1, &v[5]);
v5.r = z__1.r, v5.i = z__1.i;
d_cnjg(&z__2, &v5);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t5.r = z__1.r, t5.i = z__1.i;
d_cnjg(&z__1, &v[6]);
v6.r = z__1.r, v6.i = z__1.i;
d_cnjg(&z__2, &v6);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t6.r = z__1.r, t6.i = z__1.i;
d_cnjg(&z__1, &v[7]);
v7.r = z__1.r, v7.i = z__1.i;
d_cnjg(&z__2, &v7);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t7.r = z__1.r, t7.i = z__1.i;
d_cnjg(&z__1, &v[8]);
v8.r = z__1.r, v8.i = z__1.i;
d_cnjg(&z__2, &v8);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t8.r = z__1.r, t8.i = z__1.i;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j * c_dim1 + 1;
z__8.r = v1.r * c__[i__2].r - v1.i * c__[i__2].i, z__8.i = v1.r *
c__[i__2].i + v1.i * c__[i__2].r;
i__3 = j * c_dim1 + 2;
z__9.r = v2.r * c__[i__3].r - v2.i * c__[i__3].i, z__9.i = v2.r *
c__[i__3].i + v2.i * c__[i__3].r;
z__7.r = z__8.r + z__9.r, z__7.i = z__8.i + z__9.i;
i__4 = j * c_dim1 + 3;
z__10.r = v3.r * c__[i__4].r - v3.i * c__[i__4].i, z__10.i = v3.r
* c__[i__4].i + v3.i * c__[i__4].r;
z__6.r = z__7.r + z__10.r, z__6.i = z__7.i + z__10.i;
i__5 = j * c_dim1 + 4;
z__11.r = v4.r * c__[i__5].r - v4.i * c__[i__5].i, z__11.i = v4.r
* c__[i__5].i + v4.i * c__[i__5].r;
z__5.r = z__6.r + z__11.r, z__5.i = z__6.i + z__11.i;
i__6 = j * c_dim1 + 5;
z__12.r = v5.r * c__[i__6].r - v5.i * c__[i__6].i, z__12.i = v5.r
* c__[i__6].i + v5.i * c__[i__6].r;
z__4.r = z__5.r + z__12.r, z__4.i = z__5.i + z__12.i;
i__7 = j * c_dim1 + 6;
z__13.r = v6.r * c__[i__7].r - v6.i * c__[i__7].i, z__13.i = v6.r
* c__[i__7].i + v6.i * c__[i__7].r;
z__3.r = z__4.r + z__13.r, z__3.i = z__4.i + z__13.i;
i__8 = j * c_dim1 + 7;
z__14.r = v7.r * c__[i__8].r - v7.i * c__[i__8].i, z__14.i = v7.r
* c__[i__8].i + v7.i * c__[i__8].r;
z__2.r = z__3.r + z__14.r, z__2.i = z__3.i + z__14.i;
i__9 = j * c_dim1 + 8;
z__15.r = v8.r * c__[i__9].r - v8.i * c__[i__9].i, z__15.i = v8.r
* c__[i__9].i + v8.i * c__[i__9].r;
z__1.r = z__2.r + z__15.r, z__1.i = z__2.i + z__15.i;
sum.r = z__1.r, sum.i = z__1.i;
i__2 = j * c_dim1 + 1;
i__3 = j * c_dim1 + 1;
z__2.r = sum.r * t1.r - sum.i * t1.i, z__2.i = sum.r * t1.i +
sum.i * t1.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 2;
i__3 = j * c_dim1 + 2;
z__2.r = sum.r * t2.r - sum.i * t2.i, z__2.i = sum.r * t2.i +
sum.i * t2.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 3;
i__3 = j * c_dim1 + 3;
z__2.r = sum.r * t3.r - sum.i * t3.i, z__2.i = sum.r * t3.i +
sum.i * t3.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 4;
i__3 = j * c_dim1 + 4;
z__2.r = sum.r * t4.r - sum.i * t4.i, z__2.i = sum.r * t4.i +
sum.i * t4.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 5;
i__3 = j * c_dim1 + 5;
z__2.r = sum.r * t5.r - sum.i * t5.i, z__2.i = sum.r * t5.i +
sum.i * t5.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 6;
i__3 = j * c_dim1 + 6;
z__2.r = sum.r * t6.r - sum.i * t6.i, z__2.i = sum.r * t6.i +
sum.i * t6.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 7;
i__3 = j * c_dim1 + 7;
z__2.r = sum.r * t7.r - sum.i * t7.i, z__2.i = sum.r * t7.i +
sum.i * t7.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 8;
i__3 = j * c_dim1 + 8;
z__2.r = sum.r * t8.r - sum.i * t8.i, z__2.i = sum.r * t8.i +
sum.i * t8.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
/* L160: */
}
goto L410;
L170:
/* Special code for 9 x 9 Householder */
d_cnjg(&z__1, &v[1]);
v1.r = z__1.r, v1.i = z__1.i;
d_cnjg(&z__2, &v1);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t1.r = z__1.r, t1.i = z__1.i;
d_cnjg(&z__1, &v[2]);
v2.r = z__1.r, v2.i = z__1.i;
d_cnjg(&z__2, &v2);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t2.r = z__1.r, t2.i = z__1.i;
d_cnjg(&z__1, &v[3]);
v3.r = z__1.r, v3.i = z__1.i;
d_cnjg(&z__2, &v3);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t3.r = z__1.r, t3.i = z__1.i;
d_cnjg(&z__1, &v[4]);
v4.r = z__1.r, v4.i = z__1.i;
d_cnjg(&z__2, &v4);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t4.r = z__1.r, t4.i = z__1.i;
d_cnjg(&z__1, &v[5]);
v5.r = z__1.r, v5.i = z__1.i;
d_cnjg(&z__2, &v5);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t5.r = z__1.r, t5.i = z__1.i;
d_cnjg(&z__1, &v[6]);
v6.r = z__1.r, v6.i = z__1.i;
d_cnjg(&z__2, &v6);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t6.r = z__1.r, t6.i = z__1.i;
d_cnjg(&z__1, &v[7]);
v7.r = z__1.r, v7.i = z__1.i;
d_cnjg(&z__2, &v7);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t7.r = z__1.r, t7.i = z__1.i;
d_cnjg(&z__1, &v[8]);
v8.r = z__1.r, v8.i = z__1.i;
d_cnjg(&z__2, &v8);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t8.r = z__1.r, t8.i = z__1.i;
d_cnjg(&z__1, &v[9]);
v9.r = z__1.r, v9.i = z__1.i;
d_cnjg(&z__2, &v9);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t9.r = z__1.r, t9.i = z__1.i;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j * c_dim1 + 1;
z__9.r = v1.r * c__[i__2].r - v1.i * c__[i__2].i, z__9.i = v1.r *
c__[i__2].i + v1.i * c__[i__2].r;
i__3 = j * c_dim1 + 2;
z__10.r = v2.r * c__[i__3].r - v2.i * c__[i__3].i, z__10.i = v2.r
* c__[i__3].i + v2.i * c__[i__3].r;
z__8.r = z__9.r + z__10.r, z__8.i = z__9.i + z__10.i;
i__4 = j * c_dim1 + 3;
z__11.r = v3.r * c__[i__4].r - v3.i * c__[i__4].i, z__11.i = v3.r
* c__[i__4].i + v3.i * c__[i__4].r;
z__7.r = z__8.r + z__11.r, z__7.i = z__8.i + z__11.i;
i__5 = j * c_dim1 + 4;
z__12.r = v4.r * c__[i__5].r - v4.i * c__[i__5].i, z__12.i = v4.r
* c__[i__5].i + v4.i * c__[i__5].r;
z__6.r = z__7.r + z__12.r, z__6.i = z__7.i + z__12.i;
i__6 = j * c_dim1 + 5;
z__13.r = v5.r * c__[i__6].r - v5.i * c__[i__6].i, z__13.i = v5.r
* c__[i__6].i + v5.i * c__[i__6].r;
z__5.r = z__6.r + z__13.r, z__5.i = z__6.i + z__13.i;
i__7 = j * c_dim1 + 6;
z__14.r = v6.r * c__[i__7].r - v6.i * c__[i__7].i, z__14.i = v6.r
* c__[i__7].i + v6.i * c__[i__7].r;
z__4.r = z__5.r + z__14.r, z__4.i = z__5.i + z__14.i;
i__8 = j * c_dim1 + 7;
z__15.r = v7.r * c__[i__8].r - v7.i * c__[i__8].i, z__15.i = v7.r
* c__[i__8].i + v7.i * c__[i__8].r;
z__3.r = z__4.r + z__15.r, z__3.i = z__4.i + z__15.i;
i__9 = j * c_dim1 + 8;
z__16.r = v8.r * c__[i__9].r - v8.i * c__[i__9].i, z__16.i = v8.r
* c__[i__9].i + v8.i * c__[i__9].r;
z__2.r = z__3.r + z__16.r, z__2.i = z__3.i + z__16.i;
i__10 = j * c_dim1 + 9;
z__17.r = v9.r * c__[i__10].r - v9.i * c__[i__10].i, z__17.i =
v9.r * c__[i__10].i + v9.i * c__[i__10].r;
z__1.r = z__2.r + z__17.r, z__1.i = z__2.i + z__17.i;
sum.r = z__1.r, sum.i = z__1.i;
i__2 = j * c_dim1 + 1;
i__3 = j * c_dim1 + 1;
z__2.r = sum.r * t1.r - sum.i * t1.i, z__2.i = sum.r * t1.i +
sum.i * t1.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 2;
i__3 = j * c_dim1 + 2;
z__2.r = sum.r * t2.r - sum.i * t2.i, z__2.i = sum.r * t2.i +
sum.i * t2.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 3;
i__3 = j * c_dim1 + 3;
z__2.r = sum.r * t3.r - sum.i * t3.i, z__2.i = sum.r * t3.i +
sum.i * t3.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 4;
i__3 = j * c_dim1 + 4;
z__2.r = sum.r * t4.r - sum.i * t4.i, z__2.i = sum.r * t4.i +
sum.i * t4.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 5;
i__3 = j * c_dim1 + 5;
z__2.r = sum.r * t5.r - sum.i * t5.i, z__2.i = sum.r * t5.i +
sum.i * t5.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 6;
i__3 = j * c_dim1 + 6;
z__2.r = sum.r * t6.r - sum.i * t6.i, z__2.i = sum.r * t6.i +
sum.i * t6.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 7;
i__3 = j * c_dim1 + 7;
z__2.r = sum.r * t7.r - sum.i * t7.i, z__2.i = sum.r * t7.i +
sum.i * t7.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 8;
i__3 = j * c_dim1 + 8;
z__2.r = sum.r * t8.r - sum.i * t8.i, z__2.i = sum.r * t8.i +
sum.i * t8.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 9;
i__3 = j * c_dim1 + 9;
z__2.r = sum.r * t9.r - sum.i * t9.i, z__2.i = sum.r * t9.i +
sum.i * t9.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
/* L180: */
}
goto L410;
L190:
/* Special code for 10 x 10 Householder */
d_cnjg(&z__1, &v[1]);
v1.r = z__1.r, v1.i = z__1.i;
d_cnjg(&z__2, &v1);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t1.r = z__1.r, t1.i = z__1.i;
d_cnjg(&z__1, &v[2]);
v2.r = z__1.r, v2.i = z__1.i;
d_cnjg(&z__2, &v2);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t2.r = z__1.r, t2.i = z__1.i;
d_cnjg(&z__1, &v[3]);
v3.r = z__1.r, v3.i = z__1.i;
d_cnjg(&z__2, &v3);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t3.r = z__1.r, t3.i = z__1.i;
d_cnjg(&z__1, &v[4]);
v4.r = z__1.r, v4.i = z__1.i;
d_cnjg(&z__2, &v4);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t4.r = z__1.r, t4.i = z__1.i;
d_cnjg(&z__1, &v[5]);
v5.r = z__1.r, v5.i = z__1.i;
d_cnjg(&z__2, &v5);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t5.r = z__1.r, t5.i = z__1.i;
d_cnjg(&z__1, &v[6]);
v6.r = z__1.r, v6.i = z__1.i;
d_cnjg(&z__2, &v6);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t6.r = z__1.r, t6.i = z__1.i;
d_cnjg(&z__1, &v[7]);
v7.r = z__1.r, v7.i = z__1.i;
d_cnjg(&z__2, &v7);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t7.r = z__1.r, t7.i = z__1.i;
d_cnjg(&z__1, &v[8]);
v8.r = z__1.r, v8.i = z__1.i;
d_cnjg(&z__2, &v8);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t8.r = z__1.r, t8.i = z__1.i;
d_cnjg(&z__1, &v[9]);
v9.r = z__1.r, v9.i = z__1.i;
d_cnjg(&z__2, &v9);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t9.r = z__1.r, t9.i = z__1.i;
d_cnjg(&z__1, &v[10]);
v10.r = z__1.r, v10.i = z__1.i;
d_cnjg(&z__2, &v10);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t10.r = z__1.r, t10.i = z__1.i;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j * c_dim1 + 1;
z__10.r = v1.r * c__[i__2].r - v1.i * c__[i__2].i, z__10.i = v1.r
* c__[i__2].i + v1.i * c__[i__2].r;
i__3 = j * c_dim1 + 2;
z__11.r = v2.r * c__[i__3].r - v2.i * c__[i__3].i, z__11.i = v2.r
* c__[i__3].i + v2.i * c__[i__3].r;
z__9.r = z__10.r + z__11.r, z__9.i = z__10.i + z__11.i;
i__4 = j * c_dim1 + 3;
z__12.r = v3.r * c__[i__4].r - v3.i * c__[i__4].i, z__12.i = v3.r
* c__[i__4].i + v3.i * c__[i__4].r;
z__8.r = z__9.r + z__12.r, z__8.i = z__9.i + z__12.i;
i__5 = j * c_dim1 + 4;
z__13.r = v4.r * c__[i__5].r - v4.i * c__[i__5].i, z__13.i = v4.r
* c__[i__5].i + v4.i * c__[i__5].r;
z__7.r = z__8.r + z__13.r, z__7.i = z__8.i + z__13.i;
i__6 = j * c_dim1 + 5;
z__14.r = v5.r * c__[i__6].r - v5.i * c__[i__6].i, z__14.i = v5.r
* c__[i__6].i + v5.i * c__[i__6].r;
z__6.r = z__7.r + z__14.r, z__6.i = z__7.i + z__14.i;
i__7 = j * c_dim1 + 6;
z__15.r = v6.r * c__[i__7].r - v6.i * c__[i__7].i, z__15.i = v6.r
* c__[i__7].i + v6.i * c__[i__7].r;
z__5.r = z__6.r + z__15.r, z__5.i = z__6.i + z__15.i;
i__8 = j * c_dim1 + 7;
z__16.r = v7.r * c__[i__8].r - v7.i * c__[i__8].i, z__16.i = v7.r
* c__[i__8].i + v7.i * c__[i__8].r;
z__4.r = z__5.r + z__16.r, z__4.i = z__5.i + z__16.i;
i__9 = j * c_dim1 + 8;
z__17.r = v8.r * c__[i__9].r - v8.i * c__[i__9].i, z__17.i = v8.r
* c__[i__9].i + v8.i * c__[i__9].r;
z__3.r = z__4.r + z__17.r, z__3.i = z__4.i + z__17.i;
i__10 = j * c_dim1 + 9;
z__18.r = v9.r * c__[i__10].r - v9.i * c__[i__10].i, z__18.i =
v9.r * c__[i__10].i + v9.i * c__[i__10].r;
z__2.r = z__3.r + z__18.r, z__2.i = z__3.i + z__18.i;
i__11 = j * c_dim1 + 10;
z__19.r = v10.r * c__[i__11].r - v10.i * c__[i__11].i, z__19.i =
v10.r * c__[i__11].i + v10.i * c__[i__11].r;
z__1.r = z__2.r + z__19.r, z__1.i = z__2.i + z__19.i;
sum.r = z__1.r, sum.i = z__1.i;
i__2 = j * c_dim1 + 1;
i__3 = j * c_dim1 + 1;
z__2.r = sum.r * t1.r - sum.i * t1.i, z__2.i = sum.r * t1.i +
sum.i * t1.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 2;
i__3 = j * c_dim1 + 2;
z__2.r = sum.r * t2.r - sum.i * t2.i, z__2.i = sum.r * t2.i +
sum.i * t2.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 3;
i__3 = j * c_dim1 + 3;
z__2.r = sum.r * t3.r - sum.i * t3.i, z__2.i = sum.r * t3.i +
sum.i * t3.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 4;
i__3 = j * c_dim1 + 4;
z__2.r = sum.r * t4.r - sum.i * t4.i, z__2.i = sum.r * t4.i +
sum.i * t4.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 5;
i__3 = j * c_dim1 + 5;
z__2.r = sum.r * t5.r - sum.i * t5.i, z__2.i = sum.r * t5.i +
sum.i * t5.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 6;
i__3 = j * c_dim1 + 6;
z__2.r = sum.r * t6.r - sum.i * t6.i, z__2.i = sum.r * t6.i +
sum.i * t6.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 7;
i__3 = j * c_dim1 + 7;
z__2.r = sum.r * t7.r - sum.i * t7.i, z__2.i = sum.r * t7.i +
sum.i * t7.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 8;
i__3 = j * c_dim1 + 8;
z__2.r = sum.r * t8.r - sum.i * t8.i, z__2.i = sum.r * t8.i +
sum.i * t8.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 9;
i__3 = j * c_dim1 + 9;
z__2.r = sum.r * t9.r - sum.i * t9.i, z__2.i = sum.r * t9.i +
sum.i * t9.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j * c_dim1 + 10;
i__3 = j * c_dim1 + 10;
z__2.r = sum.r * t10.r - sum.i * t10.i, z__2.i = sum.r * t10.i +
sum.i * t10.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
/* L200: */
}
goto L410;
} else {
/* Form C * H, where H has order n. */
switch (*n) {
case 1: goto L210;
case 2: goto L230;
case 3: goto L250;
case 4: goto L270;
case 5: goto L290;
case 6: goto L310;
case 7: goto L330;
case 8: goto L350;
case 9: goto L370;
case 10: goto L390;
}
/*
Code for general N
w := C * v
*/
zgemv_("No transpose", m, n, &c_b60, &c__[c_offset], ldc, &v[1], &
c__1, &c_b59, &work[1], &c__1);
/* C := C - tau * w * v' */
z__1.r = -tau->r, z__1.i = -tau->i;
zgerc_(m, n, &z__1, &work[1], &c__1, &v[1], &c__1, &c__[c_offset],
ldc);
goto L410;
L210:
/* Special code for 1 x 1 Householder */
z__3.r = tau->r * v[1].r - tau->i * v[1].i, z__3.i = tau->r * v[1].i
+ tau->i * v[1].r;
d_cnjg(&z__4, &v[1]);
z__2.r = z__3.r * z__4.r - z__3.i * z__4.i, z__2.i = z__3.r * z__4.i
+ z__3.i * z__4.r;
z__1.r = 1. - z__2.r, z__1.i = 0. - z__2.i;
t1.r = z__1.r, t1.i = z__1.i;
i__1 = *m;
for (j = 1; j <= i__1; ++j) {
i__2 = j + c_dim1;
i__3 = j + c_dim1;
z__1.r = t1.r * c__[i__3].r - t1.i * c__[i__3].i, z__1.i = t1.r *
c__[i__3].i + t1.i * c__[i__3].r;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
/* L220: */
}
goto L410;
L230:
/* Special code for 2 x 2 Householder */
v1.r = v[1].r, v1.i = v[1].i;
d_cnjg(&z__2, &v1);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t1.r = z__1.r, t1.i = z__1.i;
v2.r = v[2].r, v2.i = v[2].i;
d_cnjg(&z__2, &v2);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t2.r = z__1.r, t2.i = z__1.i;
i__1 = *m;
for (j = 1; j <= i__1; ++j) {
i__2 = j + c_dim1;
z__2.r = v1.r * c__[i__2].r - v1.i * c__[i__2].i, z__2.i = v1.r *
c__[i__2].i + v1.i * c__[i__2].r;
i__3 = j + ((c_dim1) << (1));
z__3.r = v2.r * c__[i__3].r - v2.i * c__[i__3].i, z__3.i = v2.r *
c__[i__3].i + v2.i * c__[i__3].r;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
sum.r = z__1.r, sum.i = z__1.i;
i__2 = j + c_dim1;
i__3 = j + c_dim1;
z__2.r = sum.r * t1.r - sum.i * t1.i, z__2.i = sum.r * t1.i +
sum.i * t1.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + ((c_dim1) << (1));
i__3 = j + ((c_dim1) << (1));
z__2.r = sum.r * t2.r - sum.i * t2.i, z__2.i = sum.r * t2.i +
sum.i * t2.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
/* L240: */
}
goto L410;
L250:
/* Special code for 3 x 3 Householder */
v1.r = v[1].r, v1.i = v[1].i;
d_cnjg(&z__2, &v1);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t1.r = z__1.r, t1.i = z__1.i;
v2.r = v[2].r, v2.i = v[2].i;
d_cnjg(&z__2, &v2);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t2.r = z__1.r, t2.i = z__1.i;
v3.r = v[3].r, v3.i = v[3].i;
d_cnjg(&z__2, &v3);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t3.r = z__1.r, t3.i = z__1.i;
i__1 = *m;
for (j = 1; j <= i__1; ++j) {
i__2 = j + c_dim1;
z__3.r = v1.r * c__[i__2].r - v1.i * c__[i__2].i, z__3.i = v1.r *
c__[i__2].i + v1.i * c__[i__2].r;
i__3 = j + ((c_dim1) << (1));
z__4.r = v2.r * c__[i__3].r - v2.i * c__[i__3].i, z__4.i = v2.r *
c__[i__3].i + v2.i * c__[i__3].r;
z__2.r = z__3.r + z__4.r, z__2.i = z__3.i + z__4.i;
i__4 = j + c_dim1 * 3;
z__5.r = v3.r * c__[i__4].r - v3.i * c__[i__4].i, z__5.i = v3.r *
c__[i__4].i + v3.i * c__[i__4].r;
z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + z__5.i;
sum.r = z__1.r, sum.i = z__1.i;
i__2 = j + c_dim1;
i__3 = j + c_dim1;
z__2.r = sum.r * t1.r - sum.i * t1.i, z__2.i = sum.r * t1.i +
sum.i * t1.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + ((c_dim1) << (1));
i__3 = j + ((c_dim1) << (1));
z__2.r = sum.r * t2.r - sum.i * t2.i, z__2.i = sum.r * t2.i +
sum.i * t2.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + c_dim1 * 3;
i__3 = j + c_dim1 * 3;
z__2.r = sum.r * t3.r - sum.i * t3.i, z__2.i = sum.r * t3.i +
sum.i * t3.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
/* L260: */
}
goto L410;
L270:
/* Special code for 4 x 4 Householder */
v1.r = v[1].r, v1.i = v[1].i;
d_cnjg(&z__2, &v1);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t1.r = z__1.r, t1.i = z__1.i;
v2.r = v[2].r, v2.i = v[2].i;
d_cnjg(&z__2, &v2);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t2.r = z__1.r, t2.i = z__1.i;
v3.r = v[3].r, v3.i = v[3].i;
d_cnjg(&z__2, &v3);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t3.r = z__1.r, t3.i = z__1.i;
v4.r = v[4].r, v4.i = v[4].i;
d_cnjg(&z__2, &v4);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t4.r = z__1.r, t4.i = z__1.i;
i__1 = *m;
for (j = 1; j <= i__1; ++j) {
i__2 = j + c_dim1;
z__4.r = v1.r * c__[i__2].r - v1.i * c__[i__2].i, z__4.i = v1.r *
c__[i__2].i + v1.i * c__[i__2].r;
i__3 = j + ((c_dim1) << (1));
z__5.r = v2.r * c__[i__3].r - v2.i * c__[i__3].i, z__5.i = v2.r *
c__[i__3].i + v2.i * c__[i__3].r;
z__3.r = z__4.r + z__5.r, z__3.i = z__4.i + z__5.i;
i__4 = j + c_dim1 * 3;
z__6.r = v3.r * c__[i__4].r - v3.i * c__[i__4].i, z__6.i = v3.r *
c__[i__4].i + v3.i * c__[i__4].r;
z__2.r = z__3.r + z__6.r, z__2.i = z__3.i + z__6.i;
i__5 = j + ((c_dim1) << (2));
z__7.r = v4.r * c__[i__5].r - v4.i * c__[i__5].i, z__7.i = v4.r *
c__[i__5].i + v4.i * c__[i__5].r;
z__1.r = z__2.r + z__7.r, z__1.i = z__2.i + z__7.i;
sum.r = z__1.r, sum.i = z__1.i;
i__2 = j + c_dim1;
i__3 = j + c_dim1;
z__2.r = sum.r * t1.r - sum.i * t1.i, z__2.i = sum.r * t1.i +
sum.i * t1.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + ((c_dim1) << (1));
i__3 = j + ((c_dim1) << (1));
z__2.r = sum.r * t2.r - sum.i * t2.i, z__2.i = sum.r * t2.i +
sum.i * t2.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + c_dim1 * 3;
i__3 = j + c_dim1 * 3;
z__2.r = sum.r * t3.r - sum.i * t3.i, z__2.i = sum.r * t3.i +
sum.i * t3.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + ((c_dim1) << (2));
i__3 = j + ((c_dim1) << (2));
z__2.r = sum.r * t4.r - sum.i * t4.i, z__2.i = sum.r * t4.i +
sum.i * t4.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
/* L280: */
}
goto L410;
L290:
/* Special code for 5 x 5 Householder */
v1.r = v[1].r, v1.i = v[1].i;
d_cnjg(&z__2, &v1);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t1.r = z__1.r, t1.i = z__1.i;
v2.r = v[2].r, v2.i = v[2].i;
d_cnjg(&z__2, &v2);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t2.r = z__1.r, t2.i = z__1.i;
v3.r = v[3].r, v3.i = v[3].i;
d_cnjg(&z__2, &v3);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t3.r = z__1.r, t3.i = z__1.i;
v4.r = v[4].r, v4.i = v[4].i;
d_cnjg(&z__2, &v4);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t4.r = z__1.r, t4.i = z__1.i;
v5.r = v[5].r, v5.i = v[5].i;
d_cnjg(&z__2, &v5);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t5.r = z__1.r, t5.i = z__1.i;
i__1 = *m;
for (j = 1; j <= i__1; ++j) {
i__2 = j + c_dim1;
z__5.r = v1.r * c__[i__2].r - v1.i * c__[i__2].i, z__5.i = v1.r *
c__[i__2].i + v1.i * c__[i__2].r;
i__3 = j + ((c_dim1) << (1));
z__6.r = v2.r * c__[i__3].r - v2.i * c__[i__3].i, z__6.i = v2.r *
c__[i__3].i + v2.i * c__[i__3].r;
z__4.r = z__5.r + z__6.r, z__4.i = z__5.i + z__6.i;
i__4 = j + c_dim1 * 3;
z__7.r = v3.r * c__[i__4].r - v3.i * c__[i__4].i, z__7.i = v3.r *
c__[i__4].i + v3.i * c__[i__4].r;
z__3.r = z__4.r + z__7.r, z__3.i = z__4.i + z__7.i;
i__5 = j + ((c_dim1) << (2));
z__8.r = v4.r * c__[i__5].r - v4.i * c__[i__5].i, z__8.i = v4.r *
c__[i__5].i + v4.i * c__[i__5].r;
z__2.r = z__3.r + z__8.r, z__2.i = z__3.i + z__8.i;
i__6 = j + c_dim1 * 5;
z__9.r = v5.r * c__[i__6].r - v5.i * c__[i__6].i, z__9.i = v5.r *
c__[i__6].i + v5.i * c__[i__6].r;
z__1.r = z__2.r + z__9.r, z__1.i = z__2.i + z__9.i;
sum.r = z__1.r, sum.i = z__1.i;
i__2 = j + c_dim1;
i__3 = j + c_dim1;
z__2.r = sum.r * t1.r - sum.i * t1.i, z__2.i = sum.r * t1.i +
sum.i * t1.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + ((c_dim1) << (1));
i__3 = j + ((c_dim1) << (1));
z__2.r = sum.r * t2.r - sum.i * t2.i, z__2.i = sum.r * t2.i +
sum.i * t2.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + c_dim1 * 3;
i__3 = j + c_dim1 * 3;
z__2.r = sum.r * t3.r - sum.i * t3.i, z__2.i = sum.r * t3.i +
sum.i * t3.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + ((c_dim1) << (2));
i__3 = j + ((c_dim1) << (2));
z__2.r = sum.r * t4.r - sum.i * t4.i, z__2.i = sum.r * t4.i +
sum.i * t4.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + c_dim1 * 5;
i__3 = j + c_dim1 * 5;
z__2.r = sum.r * t5.r - sum.i * t5.i, z__2.i = sum.r * t5.i +
sum.i * t5.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
/* L300: */
}
goto L410;
L310:
/* Special code for 6 x 6 Householder */
v1.r = v[1].r, v1.i = v[1].i;
d_cnjg(&z__2, &v1);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t1.r = z__1.r, t1.i = z__1.i;
v2.r = v[2].r, v2.i = v[2].i;
d_cnjg(&z__2, &v2);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t2.r = z__1.r, t2.i = z__1.i;
v3.r = v[3].r, v3.i = v[3].i;
d_cnjg(&z__2, &v3);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t3.r = z__1.r, t3.i = z__1.i;
v4.r = v[4].r, v4.i = v[4].i;
d_cnjg(&z__2, &v4);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t4.r = z__1.r, t4.i = z__1.i;
v5.r = v[5].r, v5.i = v[5].i;
d_cnjg(&z__2, &v5);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t5.r = z__1.r, t5.i = z__1.i;
v6.r = v[6].r, v6.i = v[6].i;
d_cnjg(&z__2, &v6);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t6.r = z__1.r, t6.i = z__1.i;
i__1 = *m;
for (j = 1; j <= i__1; ++j) {
i__2 = j + c_dim1;
z__6.r = v1.r * c__[i__2].r - v1.i * c__[i__2].i, z__6.i = v1.r *
c__[i__2].i + v1.i * c__[i__2].r;
i__3 = j + ((c_dim1) << (1));
z__7.r = v2.r * c__[i__3].r - v2.i * c__[i__3].i, z__7.i = v2.r *
c__[i__3].i + v2.i * c__[i__3].r;
z__5.r = z__6.r + z__7.r, z__5.i = z__6.i + z__7.i;
i__4 = j + c_dim1 * 3;
z__8.r = v3.r * c__[i__4].r - v3.i * c__[i__4].i, z__8.i = v3.r *
c__[i__4].i + v3.i * c__[i__4].r;
z__4.r = z__5.r + z__8.r, z__4.i = z__5.i + z__8.i;
i__5 = j + ((c_dim1) << (2));
z__9.r = v4.r * c__[i__5].r - v4.i * c__[i__5].i, z__9.i = v4.r *
c__[i__5].i + v4.i * c__[i__5].r;
z__3.r = z__4.r + z__9.r, z__3.i = z__4.i + z__9.i;
i__6 = j + c_dim1 * 5;
z__10.r = v5.r * c__[i__6].r - v5.i * c__[i__6].i, z__10.i = v5.r
* c__[i__6].i + v5.i * c__[i__6].r;
z__2.r = z__3.r + z__10.r, z__2.i = z__3.i + z__10.i;
i__7 = j + c_dim1 * 6;
z__11.r = v6.r * c__[i__7].r - v6.i * c__[i__7].i, z__11.i = v6.r
* c__[i__7].i + v6.i * c__[i__7].r;
z__1.r = z__2.r + z__11.r, z__1.i = z__2.i + z__11.i;
sum.r = z__1.r, sum.i = z__1.i;
i__2 = j + c_dim1;
i__3 = j + c_dim1;
z__2.r = sum.r * t1.r - sum.i * t1.i, z__2.i = sum.r * t1.i +
sum.i * t1.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + ((c_dim1) << (1));
i__3 = j + ((c_dim1) << (1));
z__2.r = sum.r * t2.r - sum.i * t2.i, z__2.i = sum.r * t2.i +
sum.i * t2.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + c_dim1 * 3;
i__3 = j + c_dim1 * 3;
z__2.r = sum.r * t3.r - sum.i * t3.i, z__2.i = sum.r * t3.i +
sum.i * t3.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + ((c_dim1) << (2));
i__3 = j + ((c_dim1) << (2));
z__2.r = sum.r * t4.r - sum.i * t4.i, z__2.i = sum.r * t4.i +
sum.i * t4.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + c_dim1 * 5;
i__3 = j + c_dim1 * 5;
z__2.r = sum.r * t5.r - sum.i * t5.i, z__2.i = sum.r * t5.i +
sum.i * t5.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + c_dim1 * 6;
i__3 = j + c_dim1 * 6;
z__2.r = sum.r * t6.r - sum.i * t6.i, z__2.i = sum.r * t6.i +
sum.i * t6.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
/* L320: */
}
goto L410;
L330:
/* Special code for 7 x 7 Householder */
v1.r = v[1].r, v1.i = v[1].i;
d_cnjg(&z__2, &v1);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t1.r = z__1.r, t1.i = z__1.i;
v2.r = v[2].r, v2.i = v[2].i;
d_cnjg(&z__2, &v2);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t2.r = z__1.r, t2.i = z__1.i;
v3.r = v[3].r, v3.i = v[3].i;
d_cnjg(&z__2, &v3);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t3.r = z__1.r, t3.i = z__1.i;
v4.r = v[4].r, v4.i = v[4].i;
d_cnjg(&z__2, &v4);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t4.r = z__1.r, t4.i = z__1.i;
v5.r = v[5].r, v5.i = v[5].i;
d_cnjg(&z__2, &v5);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t5.r = z__1.r, t5.i = z__1.i;
v6.r = v[6].r, v6.i = v[6].i;
d_cnjg(&z__2, &v6);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t6.r = z__1.r, t6.i = z__1.i;
v7.r = v[7].r, v7.i = v[7].i;
d_cnjg(&z__2, &v7);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t7.r = z__1.r, t7.i = z__1.i;
i__1 = *m;
for (j = 1; j <= i__1; ++j) {
i__2 = j + c_dim1;
z__7.r = v1.r * c__[i__2].r - v1.i * c__[i__2].i, z__7.i = v1.r *
c__[i__2].i + v1.i * c__[i__2].r;
i__3 = j + ((c_dim1) << (1));
z__8.r = v2.r * c__[i__3].r - v2.i * c__[i__3].i, z__8.i = v2.r *
c__[i__3].i + v2.i * c__[i__3].r;
z__6.r = z__7.r + z__8.r, z__6.i = z__7.i + z__8.i;
i__4 = j + c_dim1 * 3;
z__9.r = v3.r * c__[i__4].r - v3.i * c__[i__4].i, z__9.i = v3.r *
c__[i__4].i + v3.i * c__[i__4].r;
z__5.r = z__6.r + z__9.r, z__5.i = z__6.i + z__9.i;
i__5 = j + ((c_dim1) << (2));
z__10.r = v4.r * c__[i__5].r - v4.i * c__[i__5].i, z__10.i = v4.r
* c__[i__5].i + v4.i * c__[i__5].r;
z__4.r = z__5.r + z__10.r, z__4.i = z__5.i + z__10.i;
i__6 = j + c_dim1 * 5;
z__11.r = v5.r * c__[i__6].r - v5.i * c__[i__6].i, z__11.i = v5.r
* c__[i__6].i + v5.i * c__[i__6].r;
z__3.r = z__4.r + z__11.r, z__3.i = z__4.i + z__11.i;
i__7 = j + c_dim1 * 6;
z__12.r = v6.r * c__[i__7].r - v6.i * c__[i__7].i, z__12.i = v6.r
* c__[i__7].i + v6.i * c__[i__7].r;
z__2.r = z__3.r + z__12.r, z__2.i = z__3.i + z__12.i;
i__8 = j + c_dim1 * 7;
z__13.r = v7.r * c__[i__8].r - v7.i * c__[i__8].i, z__13.i = v7.r
* c__[i__8].i + v7.i * c__[i__8].r;
z__1.r = z__2.r + z__13.r, z__1.i = z__2.i + z__13.i;
sum.r = z__1.r, sum.i = z__1.i;
i__2 = j + c_dim1;
i__3 = j + c_dim1;
z__2.r = sum.r * t1.r - sum.i * t1.i, z__2.i = sum.r * t1.i +
sum.i * t1.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + ((c_dim1) << (1));
i__3 = j + ((c_dim1) << (1));
z__2.r = sum.r * t2.r - sum.i * t2.i, z__2.i = sum.r * t2.i +
sum.i * t2.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + c_dim1 * 3;
i__3 = j + c_dim1 * 3;
z__2.r = sum.r * t3.r - sum.i * t3.i, z__2.i = sum.r * t3.i +
sum.i * t3.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + ((c_dim1) << (2));
i__3 = j + ((c_dim1) << (2));
z__2.r = sum.r * t4.r - sum.i * t4.i, z__2.i = sum.r * t4.i +
sum.i * t4.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + c_dim1 * 5;
i__3 = j + c_dim1 * 5;
z__2.r = sum.r * t5.r - sum.i * t5.i, z__2.i = sum.r * t5.i +
sum.i * t5.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + c_dim1 * 6;
i__3 = j + c_dim1 * 6;
z__2.r = sum.r * t6.r - sum.i * t6.i, z__2.i = sum.r * t6.i +
sum.i * t6.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + c_dim1 * 7;
i__3 = j + c_dim1 * 7;
z__2.r = sum.r * t7.r - sum.i * t7.i, z__2.i = sum.r * t7.i +
sum.i * t7.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
/* L340: */
}
goto L410;
L350:
/* Special code for 8 x 8 Householder */
v1.r = v[1].r, v1.i = v[1].i;
d_cnjg(&z__2, &v1);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t1.r = z__1.r, t1.i = z__1.i;
v2.r = v[2].r, v2.i = v[2].i;
d_cnjg(&z__2, &v2);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t2.r = z__1.r, t2.i = z__1.i;
v3.r = v[3].r, v3.i = v[3].i;
d_cnjg(&z__2, &v3);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t3.r = z__1.r, t3.i = z__1.i;
v4.r = v[4].r, v4.i = v[4].i;
d_cnjg(&z__2, &v4);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t4.r = z__1.r, t4.i = z__1.i;
v5.r = v[5].r, v5.i = v[5].i;
d_cnjg(&z__2, &v5);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t5.r = z__1.r, t5.i = z__1.i;
v6.r = v[6].r, v6.i = v[6].i;
d_cnjg(&z__2, &v6);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t6.r = z__1.r, t6.i = z__1.i;
v7.r = v[7].r, v7.i = v[7].i;
d_cnjg(&z__2, &v7);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t7.r = z__1.r, t7.i = z__1.i;
v8.r = v[8].r, v8.i = v[8].i;
d_cnjg(&z__2, &v8);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t8.r = z__1.r, t8.i = z__1.i;
i__1 = *m;
for (j = 1; j <= i__1; ++j) {
i__2 = j + c_dim1;
z__8.r = v1.r * c__[i__2].r - v1.i * c__[i__2].i, z__8.i = v1.r *
c__[i__2].i + v1.i * c__[i__2].r;
i__3 = j + ((c_dim1) << (1));
z__9.r = v2.r * c__[i__3].r - v2.i * c__[i__3].i, z__9.i = v2.r *
c__[i__3].i + v2.i * c__[i__3].r;
z__7.r = z__8.r + z__9.r, z__7.i = z__8.i + z__9.i;
i__4 = j + c_dim1 * 3;
z__10.r = v3.r * c__[i__4].r - v3.i * c__[i__4].i, z__10.i = v3.r
* c__[i__4].i + v3.i * c__[i__4].r;
z__6.r = z__7.r + z__10.r, z__6.i = z__7.i + z__10.i;
i__5 = j + ((c_dim1) << (2));
z__11.r = v4.r * c__[i__5].r - v4.i * c__[i__5].i, z__11.i = v4.r
* c__[i__5].i + v4.i * c__[i__5].r;
z__5.r = z__6.r + z__11.r, z__5.i = z__6.i + z__11.i;
i__6 = j + c_dim1 * 5;
z__12.r = v5.r * c__[i__6].r - v5.i * c__[i__6].i, z__12.i = v5.r
* c__[i__6].i + v5.i * c__[i__6].r;
z__4.r = z__5.r + z__12.r, z__4.i = z__5.i + z__12.i;
i__7 = j + c_dim1 * 6;
z__13.r = v6.r * c__[i__7].r - v6.i * c__[i__7].i, z__13.i = v6.r
* c__[i__7].i + v6.i * c__[i__7].r;
z__3.r = z__4.r + z__13.r, z__3.i = z__4.i + z__13.i;
i__8 = j + c_dim1 * 7;
z__14.r = v7.r * c__[i__8].r - v7.i * c__[i__8].i, z__14.i = v7.r
* c__[i__8].i + v7.i * c__[i__8].r;
z__2.r = z__3.r + z__14.r, z__2.i = z__3.i + z__14.i;
i__9 = j + ((c_dim1) << (3));
z__15.r = v8.r * c__[i__9].r - v8.i * c__[i__9].i, z__15.i = v8.r
* c__[i__9].i + v8.i * c__[i__9].r;
z__1.r = z__2.r + z__15.r, z__1.i = z__2.i + z__15.i;
sum.r = z__1.r, sum.i = z__1.i;
i__2 = j + c_dim1;
i__3 = j + c_dim1;
z__2.r = sum.r * t1.r - sum.i * t1.i, z__2.i = sum.r * t1.i +
sum.i * t1.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + ((c_dim1) << (1));
i__3 = j + ((c_dim1) << (1));
z__2.r = sum.r * t2.r - sum.i * t2.i, z__2.i = sum.r * t2.i +
sum.i * t2.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + c_dim1 * 3;
i__3 = j + c_dim1 * 3;
z__2.r = sum.r * t3.r - sum.i * t3.i, z__2.i = sum.r * t3.i +
sum.i * t3.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + ((c_dim1) << (2));
i__3 = j + ((c_dim1) << (2));
z__2.r = sum.r * t4.r - sum.i * t4.i, z__2.i = sum.r * t4.i +
sum.i * t4.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + c_dim1 * 5;
i__3 = j + c_dim1 * 5;
z__2.r = sum.r * t5.r - sum.i * t5.i, z__2.i = sum.r * t5.i +
sum.i * t5.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + c_dim1 * 6;
i__3 = j + c_dim1 * 6;
z__2.r = sum.r * t6.r - sum.i * t6.i, z__2.i = sum.r * t6.i +
sum.i * t6.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + c_dim1 * 7;
i__3 = j + c_dim1 * 7;
z__2.r = sum.r * t7.r - sum.i * t7.i, z__2.i = sum.r * t7.i +
sum.i * t7.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + ((c_dim1) << (3));
i__3 = j + ((c_dim1) << (3));
z__2.r = sum.r * t8.r - sum.i * t8.i, z__2.i = sum.r * t8.i +
sum.i * t8.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
/* L360: */
}
goto L410;
L370:
/* Special code for 9 x 9 Householder */
v1.r = v[1].r, v1.i = v[1].i;
d_cnjg(&z__2, &v1);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t1.r = z__1.r, t1.i = z__1.i;
v2.r = v[2].r, v2.i = v[2].i;
d_cnjg(&z__2, &v2);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t2.r = z__1.r, t2.i = z__1.i;
v3.r = v[3].r, v3.i = v[3].i;
d_cnjg(&z__2, &v3);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t3.r = z__1.r, t3.i = z__1.i;
v4.r = v[4].r, v4.i = v[4].i;
d_cnjg(&z__2, &v4);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t4.r = z__1.r, t4.i = z__1.i;
v5.r = v[5].r, v5.i = v[5].i;
d_cnjg(&z__2, &v5);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t5.r = z__1.r, t5.i = z__1.i;
v6.r = v[6].r, v6.i = v[6].i;
d_cnjg(&z__2, &v6);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t6.r = z__1.r, t6.i = z__1.i;
v7.r = v[7].r, v7.i = v[7].i;
d_cnjg(&z__2, &v7);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t7.r = z__1.r, t7.i = z__1.i;
v8.r = v[8].r, v8.i = v[8].i;
d_cnjg(&z__2, &v8);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t8.r = z__1.r, t8.i = z__1.i;
v9.r = v[9].r, v9.i = v[9].i;
d_cnjg(&z__2, &v9);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t9.r = z__1.r, t9.i = z__1.i;
i__1 = *m;
for (j = 1; j <= i__1; ++j) {
i__2 = j + c_dim1;
z__9.r = v1.r * c__[i__2].r - v1.i * c__[i__2].i, z__9.i = v1.r *
c__[i__2].i + v1.i * c__[i__2].r;
i__3 = j + ((c_dim1) << (1));
z__10.r = v2.r * c__[i__3].r - v2.i * c__[i__3].i, z__10.i = v2.r
* c__[i__3].i + v2.i * c__[i__3].r;
z__8.r = z__9.r + z__10.r, z__8.i = z__9.i + z__10.i;
i__4 = j + c_dim1 * 3;
z__11.r = v3.r * c__[i__4].r - v3.i * c__[i__4].i, z__11.i = v3.r
* c__[i__4].i + v3.i * c__[i__4].r;
z__7.r = z__8.r + z__11.r, z__7.i = z__8.i + z__11.i;
i__5 = j + ((c_dim1) << (2));
z__12.r = v4.r * c__[i__5].r - v4.i * c__[i__5].i, z__12.i = v4.r
* c__[i__5].i + v4.i * c__[i__5].r;
z__6.r = z__7.r + z__12.r, z__6.i = z__7.i + z__12.i;
i__6 = j + c_dim1 * 5;
z__13.r = v5.r * c__[i__6].r - v5.i * c__[i__6].i, z__13.i = v5.r
* c__[i__6].i + v5.i * c__[i__6].r;
z__5.r = z__6.r + z__13.r, z__5.i = z__6.i + z__13.i;
i__7 = j + c_dim1 * 6;
z__14.r = v6.r * c__[i__7].r - v6.i * c__[i__7].i, z__14.i = v6.r
* c__[i__7].i + v6.i * c__[i__7].r;
z__4.r = z__5.r + z__14.r, z__4.i = z__5.i + z__14.i;
i__8 = j + c_dim1 * 7;
z__15.r = v7.r * c__[i__8].r - v7.i * c__[i__8].i, z__15.i = v7.r
* c__[i__8].i + v7.i * c__[i__8].r;
z__3.r = z__4.r + z__15.r, z__3.i = z__4.i + z__15.i;
i__9 = j + ((c_dim1) << (3));
z__16.r = v8.r * c__[i__9].r - v8.i * c__[i__9].i, z__16.i = v8.r
* c__[i__9].i + v8.i * c__[i__9].r;
z__2.r = z__3.r + z__16.r, z__2.i = z__3.i + z__16.i;
i__10 = j + c_dim1 * 9;
z__17.r = v9.r * c__[i__10].r - v9.i * c__[i__10].i, z__17.i =
v9.r * c__[i__10].i + v9.i * c__[i__10].r;
z__1.r = z__2.r + z__17.r, z__1.i = z__2.i + z__17.i;
sum.r = z__1.r, sum.i = z__1.i;
i__2 = j + c_dim1;
i__3 = j + c_dim1;
z__2.r = sum.r * t1.r - sum.i * t1.i, z__2.i = sum.r * t1.i +
sum.i * t1.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + ((c_dim1) << (1));
i__3 = j + ((c_dim1) << (1));
z__2.r = sum.r * t2.r - sum.i * t2.i, z__2.i = sum.r * t2.i +
sum.i * t2.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + c_dim1 * 3;
i__3 = j + c_dim1 * 3;
z__2.r = sum.r * t3.r - sum.i * t3.i, z__2.i = sum.r * t3.i +
sum.i * t3.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + ((c_dim1) << (2));
i__3 = j + ((c_dim1) << (2));
z__2.r = sum.r * t4.r - sum.i * t4.i, z__2.i = sum.r * t4.i +
sum.i * t4.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + c_dim1 * 5;
i__3 = j + c_dim1 * 5;
z__2.r = sum.r * t5.r - sum.i * t5.i, z__2.i = sum.r * t5.i +
sum.i * t5.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + c_dim1 * 6;
i__3 = j + c_dim1 * 6;
z__2.r = sum.r * t6.r - sum.i * t6.i, z__2.i = sum.r * t6.i +
sum.i * t6.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + c_dim1 * 7;
i__3 = j + c_dim1 * 7;
z__2.r = sum.r * t7.r - sum.i * t7.i, z__2.i = sum.r * t7.i +
sum.i * t7.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + ((c_dim1) << (3));
i__3 = j + ((c_dim1) << (3));
z__2.r = sum.r * t8.r - sum.i * t8.i, z__2.i = sum.r * t8.i +
sum.i * t8.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + c_dim1 * 9;
i__3 = j + c_dim1 * 9;
z__2.r = sum.r * t9.r - sum.i * t9.i, z__2.i = sum.r * t9.i +
sum.i * t9.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
/* L380: */
}
goto L410;
L390:
/* Special code for 10 x 10 Householder */
v1.r = v[1].r, v1.i = v[1].i;
d_cnjg(&z__2, &v1);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t1.r = z__1.r, t1.i = z__1.i;
v2.r = v[2].r, v2.i = v[2].i;
d_cnjg(&z__2, &v2);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t2.r = z__1.r, t2.i = z__1.i;
v3.r = v[3].r, v3.i = v[3].i;
d_cnjg(&z__2, &v3);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t3.r = z__1.r, t3.i = z__1.i;
v4.r = v[4].r, v4.i = v[4].i;
d_cnjg(&z__2, &v4);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t4.r = z__1.r, t4.i = z__1.i;
v5.r = v[5].r, v5.i = v[5].i;
d_cnjg(&z__2, &v5);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t5.r = z__1.r, t5.i = z__1.i;
v6.r = v[6].r, v6.i = v[6].i;
d_cnjg(&z__2, &v6);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t6.r = z__1.r, t6.i = z__1.i;
v7.r = v[7].r, v7.i = v[7].i;
d_cnjg(&z__2, &v7);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t7.r = z__1.r, t7.i = z__1.i;
v8.r = v[8].r, v8.i = v[8].i;
d_cnjg(&z__2, &v8);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t8.r = z__1.r, t8.i = z__1.i;
v9.r = v[9].r, v9.i = v[9].i;
d_cnjg(&z__2, &v9);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t9.r = z__1.r, t9.i = z__1.i;
v10.r = v[10].r, v10.i = v[10].i;
d_cnjg(&z__2, &v10);
z__1.r = tau->r * z__2.r - tau->i * z__2.i, z__1.i = tau->r * z__2.i
+ tau->i * z__2.r;
t10.r = z__1.r, t10.i = z__1.i;
i__1 = *m;
for (j = 1; j <= i__1; ++j) {
i__2 = j + c_dim1;
z__10.r = v1.r * c__[i__2].r - v1.i * c__[i__2].i, z__10.i = v1.r
* c__[i__2].i + v1.i * c__[i__2].r;
i__3 = j + ((c_dim1) << (1));
z__11.r = v2.r * c__[i__3].r - v2.i * c__[i__3].i, z__11.i = v2.r
* c__[i__3].i + v2.i * c__[i__3].r;
z__9.r = z__10.r + z__11.r, z__9.i = z__10.i + z__11.i;
i__4 = j + c_dim1 * 3;
z__12.r = v3.r * c__[i__4].r - v3.i * c__[i__4].i, z__12.i = v3.r
* c__[i__4].i + v3.i * c__[i__4].r;
z__8.r = z__9.r + z__12.r, z__8.i = z__9.i + z__12.i;
i__5 = j + ((c_dim1) << (2));
z__13.r = v4.r * c__[i__5].r - v4.i * c__[i__5].i, z__13.i = v4.r
* c__[i__5].i + v4.i * c__[i__5].r;
z__7.r = z__8.r + z__13.r, z__7.i = z__8.i + z__13.i;
i__6 = j + c_dim1 * 5;
z__14.r = v5.r * c__[i__6].r - v5.i * c__[i__6].i, z__14.i = v5.r
* c__[i__6].i + v5.i * c__[i__6].r;
z__6.r = z__7.r + z__14.r, z__6.i = z__7.i + z__14.i;
i__7 = j + c_dim1 * 6;
z__15.r = v6.r * c__[i__7].r - v6.i * c__[i__7].i, z__15.i = v6.r
* c__[i__7].i + v6.i * c__[i__7].r;
z__5.r = z__6.r + z__15.r, z__5.i = z__6.i + z__15.i;
i__8 = j + c_dim1 * 7;
z__16.r = v7.r * c__[i__8].r - v7.i * c__[i__8].i, z__16.i = v7.r
* c__[i__8].i + v7.i * c__[i__8].r;
z__4.r = z__5.r + z__16.r, z__4.i = z__5.i + z__16.i;
i__9 = j + ((c_dim1) << (3));
z__17.r = v8.r * c__[i__9].r - v8.i * c__[i__9].i, z__17.i = v8.r
* c__[i__9].i + v8.i * c__[i__9].r;
z__3.r = z__4.r + z__17.r, z__3.i = z__4.i + z__17.i;
i__10 = j + c_dim1 * 9;
z__18.r = v9.r * c__[i__10].r - v9.i * c__[i__10].i, z__18.i =
v9.r * c__[i__10].i + v9.i * c__[i__10].r;
z__2.r = z__3.r + z__18.r, z__2.i = z__3.i + z__18.i;
i__11 = j + c_dim1 * 10;
z__19.r = v10.r * c__[i__11].r - v10.i * c__[i__11].i, z__19.i =
v10.r * c__[i__11].i + v10.i * c__[i__11].r;
z__1.r = z__2.r + z__19.r, z__1.i = z__2.i + z__19.i;
sum.r = z__1.r, sum.i = z__1.i;
i__2 = j + c_dim1;
i__3 = j + c_dim1;
z__2.r = sum.r * t1.r - sum.i * t1.i, z__2.i = sum.r * t1.i +
sum.i * t1.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + ((c_dim1) << (1));
i__3 = j + ((c_dim1) << (1));
z__2.r = sum.r * t2.r - sum.i * t2.i, z__2.i = sum.r * t2.i +
sum.i * t2.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + c_dim1 * 3;
i__3 = j + c_dim1 * 3;
z__2.r = sum.r * t3.r - sum.i * t3.i, z__2.i = sum.r * t3.i +
sum.i * t3.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + ((c_dim1) << (2));
i__3 = j + ((c_dim1) << (2));
z__2.r = sum.r * t4.r - sum.i * t4.i, z__2.i = sum.r * t4.i +
sum.i * t4.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + c_dim1 * 5;
i__3 = j + c_dim1 * 5;
z__2.r = sum.r * t5.r - sum.i * t5.i, z__2.i = sum.r * t5.i +
sum.i * t5.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + c_dim1 * 6;
i__3 = j + c_dim1 * 6;
z__2.r = sum.r * t6.r - sum.i * t6.i, z__2.i = sum.r * t6.i +
sum.i * t6.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + c_dim1 * 7;
i__3 = j + c_dim1 * 7;
z__2.r = sum.r * t7.r - sum.i * t7.i, z__2.i = sum.r * t7.i +
sum.i * t7.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + ((c_dim1) << (3));
i__3 = j + ((c_dim1) << (3));
z__2.r = sum.r * t8.r - sum.i * t8.i, z__2.i = sum.r * t8.i +
sum.i * t8.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + c_dim1 * 9;
i__3 = j + c_dim1 * 9;
z__2.r = sum.r * t9.r - sum.i * t9.i, z__2.i = sum.r * t9.i +
sum.i * t9.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
i__2 = j + c_dim1 * 10;
i__3 = j + c_dim1 * 10;
z__2.r = sum.r * t10.r - sum.i * t10.i, z__2.i = sum.r * t10.i +
sum.i * t10.r;
z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
/* L400: */
}
goto L410;
}
L410:
return 0;
/* End of ZLARFX */
} /* zlarfx_ */
/* Subroutine */ int zlascl_(char *type__, integer *kl, integer *ku,
doublereal *cfrom, doublereal *cto, integer *m, integer *n,
doublecomplex *a, integer *lda, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
doublecomplex z__1;
/* Local variables */
static integer i__, j, k1, k2, k3, k4;
static doublereal mul, cto1;
static logical done;
static doublereal ctoc;
extern logical lsame_(char *, char *);
static integer itype;
static doublereal cfrom1;
static doublereal cfromc;
extern /* Subroutine */ int xerbla_(char *, integer *);
static doublereal bignum, smlnum;
/*
-- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
February 29, 1992
Purpose
=======
ZLASCL multiplies the M by N complex matrix A by the real scalar
CTO/CFROM. This is done without over/underflow as long as the final
result CTO*A(I,J)/CFROM does not over/underflow. TYPE specifies that
A may be full, upper triangular, lower triangular, upper Hessenberg,
or banded.
Arguments
=========
TYPE (input) CHARACTER*1
TYPE indices the storage type of the input matrix.
= 'G': A is a full matrix.
= 'L': A is a lower triangular matrix.
= 'U': A is an upper triangular matrix.
= 'H': A is an upper Hessenberg matrix.
= 'B': A is a symmetric band matrix with lower bandwidth KL
and upper bandwidth KU and with the only the lower
half stored.
= 'Q': A is a symmetric band matrix with lower bandwidth KL
and upper bandwidth KU and with the only the upper
half stored.
= 'Z': A is a band matrix with lower bandwidth KL and upper
bandwidth KU.
KL (input) INTEGER
The lower bandwidth of A. Referenced only if TYPE = 'B',
'Q' or 'Z'.
KU (input) INTEGER
The upper bandwidth of A. Referenced only if TYPE = 'B',
'Q' or 'Z'.
CFROM (input) DOUBLE PRECISION
CTO (input) DOUBLE PRECISION
The matrix A is multiplied by CTO/CFROM. A(I,J) is computed
without over/underflow if the final result CTO*A(I,J)/CFROM
can be represented without over/underflow. CFROM must be
nonzero.
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,M)
The matrix to be multiplied by CTO/CFROM. See TYPE for the
storage type.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
INFO (output) INTEGER
0 - successful exit
<0 - if INFO = -i, the i-th argument had an illegal value.
=====================================================================
Test the input arguments
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
/* Function Body */
*info = 0;
if (lsame_(type__, "G")) {
itype = 0;
} else if (lsame_(type__, "L")) {
itype = 1;
} else if (lsame_(type__, "U")) {
itype = 2;
} else if (lsame_(type__, "H")) {
itype = 3;
} else if (lsame_(type__, "B")) {
itype = 4;
} else if (lsame_(type__, "Q")) {
itype = 5;
} else if (lsame_(type__, "Z")) {
itype = 6;
} else {
itype = -1;
}
if (itype == -1) {
*info = -1;
} else if (*cfrom == 0.) {
*info = -4;
} else if (*m < 0) {
*info = -6;
} else if (*n < 0 || (itype == 4 && *n != *m) || (itype == 5 && *n != *m))
{
*info = -7;
} else if ((itype <= 3 && *lda < max(1,*m))) {
*info = -9;
} else if (itype >= 4) {
/* Computing MAX */
i__1 = *m - 1;
if (*kl < 0 || *kl > max(i__1,0)) {
*info = -2;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__1 = *n - 1;
if (*ku < 0 || *ku > max(i__1,0) || ((itype == 4 || itype == 5) &&
*kl != *ku)) {
*info = -3;
} else if ((itype == 4 && *lda < *kl + 1) || (itype == 5 && *lda <
*ku + 1) || (itype == 6 && *lda < ((*kl) << (1)) + *ku +
1)) {
*info = -9;
}
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZLASCL", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0 || *m == 0) {
return 0;
}
/* Get machine parameters */
smlnum = SAFEMINIMUM;
bignum = 1. / smlnum;
cfromc = *cfrom;
ctoc = *cto;
L10:
cfrom1 = cfromc * smlnum;
cto1 = ctoc / bignum;
if ((abs(cfrom1) > abs(ctoc) && ctoc != 0.)) {
mul = smlnum;
done = FALSE_;
cfromc = cfrom1;
} else if (abs(cto1) > abs(cfromc)) {
mul = bignum;
done = FALSE_;
ctoc = cto1;
} else {
mul = ctoc / cfromc;
done = TRUE_;
}
if (itype == 0) {
/* Full matrix */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__ + j * a_dim1;
z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
/* L20: */
}
/* L30: */
}
} else if (itype == 1) {
/* Lower triangular matrix */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = j; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__ + j * a_dim1;
z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
/* L40: */
}
/* L50: */
}
} else if (itype == 2) {
/* Upper triangular matrix */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = min(j,*m);
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__ + j * a_dim1;
z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
/* L60: */
}
/* L70: */
}
} else if (itype == 3) {
/* Upper Hessenberg matrix */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__3 = j + 1;
i__2 = min(i__3,*m);
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__ + j * a_dim1;
z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
/* L80: */
}
/* L90: */
}
} else if (itype == 4) {
/* Lower half of a symmetric band matrix */
k3 = *kl + 1;
k4 = *n + 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__3 = k3, i__4 = k4 - j;
i__2 = min(i__3,i__4);
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__ + j * a_dim1;
z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
/* L100: */
}
/* L110: */
}
} else if (itype == 5) {
/* Upper half of a symmetric band matrix */
k1 = *ku + 2;
k3 = *ku + 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = k1 - j;
i__3 = k3;
for (i__ = max(i__2,1); i__ <= i__3; ++i__) {
i__2 = i__ + j * a_dim1;
i__4 = i__ + j * a_dim1;
z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
/* L120: */
}
/* L130: */
}
} else if (itype == 6) {
/* Band matrix */
k1 = *kl + *ku + 2;
k2 = *kl + 1;
k3 = ((*kl) << (1)) + *ku + 1;
k4 = *kl + *ku + 1 + *m;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__3 = k1 - j;
/* Computing MIN */
i__4 = k3, i__5 = k4 - j;
i__2 = min(i__4,i__5);
for (i__ = max(i__3,k2); i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__ + j * a_dim1;
z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
/* L140: */
}
/* L150: */
}
}
if (! done) {
goto L10;
}
return 0;
/* End of ZLASCL */
} /* zlascl_ */
/* Subroutine */ int zlaset_(char *uplo, integer *m, integer *n,
doublecomplex *alpha, doublecomplex *beta, doublecomplex *a, integer *
lda)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
/* Local variables */
static integer i__, j;
extern logical lsame_(char *, char *);
/*
-- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
October 31, 1992
Purpose
=======
ZLASET initializes a 2-D array A to BETA on the diagonal and
ALPHA on the offdiagonals.
Arguments
=========
UPLO (input) CHARACTER*1
Specifies the part of the matrix A to be set.
= 'U': Upper triangular part is set. The lower triangle
is unchanged.
= 'L': Lower triangular part is set. The upper triangle
is unchanged.
Otherwise: All of the matrix A is set.
M (input) INTEGER
On entry, M specifies the number of rows of A.
N (input) INTEGER
On entry, N specifies the number of columns of A.
ALPHA (input) COMPLEX*16
All the offdiagonal array elements are set to ALPHA.
BETA (input) COMPLEX*16
All the diagonal array elements are set to BETA.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the m by n matrix A.
On exit, A(i,j) = ALPHA, 1 <= i <= m, 1 <= j <= n, i.ne.j;
A(i,i) = BETA , 1 <= i <= min(m,n)
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
=====================================================================
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
/* Function Body */
if (lsame_(uplo, "U")) {
/*
Set the diagonal to BETA and the strictly upper triangular
part of the array to ALPHA.
*/
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
/* Computing MIN */
i__3 = j - 1;
i__2 = min(i__3,*m);
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
a[i__3].r = alpha->r, a[i__3].i = alpha->i;
/* L10: */
}
/* L20: */
}
i__1 = min(*n,*m);
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + i__ * a_dim1;
a[i__2].r = beta->r, a[i__2].i = beta->i;
/* L30: */
}
} else if (lsame_(uplo, "L")) {
/*
Set the diagonal to BETA and the strictly lower triangular
part of the array to ALPHA.
*/
i__1 = min(*m,*n);
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
a[i__3].r = alpha->r, a[i__3].i = alpha->i;
/* L40: */
}
/* L50: */
}
i__1 = min(*n,*m);
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + i__ * a_dim1;
a[i__2].r = beta->r, a[i__2].i = beta->i;
/* L60: */
}
} else {
/*
Set the array to BETA on the diagonal and ALPHA on the
offdiagonal.
*/
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
a[i__3].r = alpha->r, a[i__3].i = alpha->i;
/* L70: */
}
/* L80: */
}
i__1 = min(*m,*n);
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + i__ * a_dim1;
a[i__2].r = beta->r, a[i__2].i = beta->i;
/* L90: */
}
}
return 0;
/* End of ZLASET */
} /* zlaset_ */
/* Subroutine */ int zlasr_(char *side, char *pivot, char *direct, integer *m,
integer *n, doublereal *c__, doublereal *s, doublecomplex *a,
integer *lda)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
doublecomplex z__1, z__2, z__3;
/* Local variables */
static integer i__, j, info;
static doublecomplex temp;
extern logical lsame_(char *, char *);
static doublereal ctemp, stemp;
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
-- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
October 31, 1992
Purpose
=======
ZLASR performs the transformation
A := P*A, when SIDE = 'L' or 'l' ( Left-hand side )
A := A*P', when SIDE = 'R' or 'r' ( Right-hand side )
where A is an m by n complex matrix and P is an orthogonal matrix,
consisting of a sequence of plane rotations determined by the
parameters PIVOT and DIRECT as follows ( z = m when SIDE = 'L' or 'l'
and z = n when SIDE = 'R' or 'r' ):
When DIRECT = 'F' or 'f' ( Forward sequence ) then
P = P( z - 1 )*...*P( 2 )*P( 1 ),
and when DIRECT = 'B' or 'b' ( Backward sequence ) then
P = P( 1 )*P( 2 )*...*P( z - 1 ),
where P( k ) is a plane rotation matrix for the following planes:
when PIVOT = 'V' or 'v' ( Variable pivot ),
the plane ( k, k + 1 )
when PIVOT = 'T' or 't' ( Top pivot ),
the plane ( 1, k + 1 )
when PIVOT = 'B' or 'b' ( Bottom pivot ),
the plane ( k, z )
c( k ) and s( k ) must contain the cosine and sine that define the
matrix P( k ). The two by two plane rotation part of the matrix
P( k ), R( k ), is assumed to be of the form
R( k ) = ( c( k ) s( k ) ).
( -s( k ) c( k ) )
Arguments
=========
SIDE (input) CHARACTER*1
Specifies whether the plane rotation matrix P is applied to
A on the left or the right.
= 'L': Left, compute A := P*A
= 'R': Right, compute A:= A*P'
DIRECT (input) CHARACTER*1
Specifies whether P is a forward or backward sequence of
plane rotations.
= 'F': Forward, P = P( z - 1 )*...*P( 2 )*P( 1 )
= 'B': Backward, P = P( 1 )*P( 2 )*...*P( z - 1 )
PIVOT (input) CHARACTER*1
Specifies the plane for which P(k) is a plane rotation
matrix.
= 'V': Variable pivot, the plane (k,k+1)
= 'T': Top pivot, the plane (1,k+1)
= 'B': Bottom pivot, the plane (k,z)
M (input) INTEGER
The number of rows of the matrix A. If m <= 1, an immediate
return is effected.
N (input) INTEGER
The number of columns of the matrix A. If n <= 1, an
immediate return is effected.
C, S (input) DOUBLE PRECISION arrays, dimension
(M-1) if SIDE = 'L'
(N-1) if SIDE = 'R'
c(k) and s(k) contain the cosine and sine that define the
matrix P(k). The two by two plane rotation part of the
matrix P(k), R(k), is assumed to be of the form
R( k ) = ( c( k ) s( k ) ).
( -s( k ) c( k ) )
A (input/output) COMPLEX*16 array, dimension (LDA,N)
The m by n matrix A. On exit, A is overwritten by P*A if
SIDE = 'R' or by A*P' if SIDE = 'L'.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
=====================================================================
Test the input parameters
*/
/* Parameter adjustments */
--c__;
--s;
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
/* Function Body */
info = 0;
if (! (lsame_(side, "L") || lsame_(side, "R"))) {
info = 1;
} else if (! (lsame_(pivot, "V") || lsame_(pivot,
"T") || lsame_(pivot, "B"))) {
info = 2;
} else if (! (lsame_(direct, "F") || lsame_(direct,
"B"))) {
info = 3;
} else if (*m < 0) {
info = 4;
} else if (*n < 0) {
info = 5;
} else if (*lda < max(1,*m)) {
info = 9;
}
if (info != 0) {
xerbla_("ZLASR ", &info);
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0) {
return 0;
}
if (lsame_(side, "L")) {
/* Form P * A */
if (lsame_(pivot, "V")) {
if (lsame_(direct, "F")) {
i__1 = *m - 1;
for (j = 1; j <= i__1; ++j) {
ctemp = c__[j];
stemp = s[j];
if (ctemp != 1. || stemp != 0.) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = j + 1 + i__ * a_dim1;
temp.r = a[i__3].r, temp.i = a[i__3].i;
i__3 = j + 1 + i__ * a_dim1;
z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i;
i__4 = j + i__ * a_dim1;
z__3.r = stemp * a[i__4].r, z__3.i = stemp * a[
i__4].i;
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i -
z__3.i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
i__3 = j + i__ * a_dim1;
z__2.r = stemp * temp.r, z__2.i = stemp * temp.i;
i__4 = j + i__ * a_dim1;
z__3.r = ctemp * a[i__4].r, z__3.i = ctemp * a[
i__4].i;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i +
z__3.i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
/* L10: */
}
}
/* L20: */
}
} else if (lsame_(direct, "B")) {
for (j = *m - 1; j >= 1; --j) {
ctemp = c__[j];
stemp = s[j];
if (ctemp != 1. || stemp != 0.) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = j + 1 + i__ * a_dim1;
temp.r = a[i__2].r, temp.i = a[i__2].i;
i__2 = j + 1 + i__ * a_dim1;
z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i;
i__3 = j + i__ * a_dim1;
z__3.r = stemp * a[i__3].r, z__3.i = stemp * a[
i__3].i;
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i -
z__3.i;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
i__2 = j + i__ * a_dim1;
z__2.r = stemp * temp.r, z__2.i = stemp * temp.i;
i__3 = j + i__ * a_dim1;
z__3.r = ctemp * a[i__3].r, z__3.i = ctemp * a[
i__3].i;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i +
z__3.i;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
/* L30: */
}
}
/* L40: */
}
}
} else if (lsame_(pivot, "T")) {
if (lsame_(direct, "F")) {
i__1 = *m;
for (j = 2; j <= i__1; ++j) {
ctemp = c__[j - 1];
stemp = s[j - 1];
if (ctemp != 1. || stemp != 0.) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = j + i__ * a_dim1;
temp.r = a[i__3].r, temp.i = a[i__3].i;
i__3 = j + i__ * a_dim1;
z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i;
i__4 = i__ * a_dim1 + 1;
z__3.r = stemp * a[i__4].r, z__3.i = stemp * a[
i__4].i;
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i -
z__3.i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
i__3 = i__ * a_dim1 + 1;
z__2.r = stemp * temp.r, z__2.i = stemp * temp.i;
i__4 = i__ * a_dim1 + 1;
z__3.r = ctemp * a[i__4].r, z__3.i = ctemp * a[
i__4].i;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i +
z__3.i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
/* L50: */
}
}
/* L60: */
}
} else if (lsame_(direct, "B")) {
for (j = *m; j >= 2; --j) {
ctemp = c__[j - 1];
stemp = s[j - 1];
if (ctemp != 1. || stemp != 0.) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = j + i__ * a_dim1;
temp.r = a[i__2].r, temp.i = a[i__2].i;
i__2 = j + i__ * a_dim1;
z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i;
i__3 = i__ * a_dim1 + 1;
z__3.r = stemp * a[i__3].r, z__3.i = stemp * a[
i__3].i;
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i -
z__3.i;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
i__2 = i__ * a_dim1 + 1;
z__2.r = stemp * temp.r, z__2.i = stemp * temp.i;
i__3 = i__ * a_dim1 + 1;
z__3.r = ctemp * a[i__3].r, z__3.i = ctemp * a[
i__3].i;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i +
z__3.i;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
/* L70: */
}
}
/* L80: */
}
}
} else if (lsame_(pivot, "B")) {
if (lsame_(direct, "F")) {
i__1 = *m - 1;
for (j = 1; j <= i__1; ++j) {
ctemp = c__[j];
stemp = s[j];
if (ctemp != 1. || stemp != 0.) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = j + i__ * a_dim1;
temp.r = a[i__3].r, temp.i = a[i__3].i;
i__3 = j + i__ * a_dim1;
i__4 = *m + i__ * a_dim1;
z__2.r = stemp * a[i__4].r, z__2.i = stemp * a[
i__4].i;
z__3.r = ctemp * temp.r, z__3.i = ctemp * temp.i;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i +
z__3.i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
i__3 = *m + i__ * a_dim1;
i__4 = *m + i__ * a_dim1;
z__2.r = ctemp * a[i__4].r, z__2.i = ctemp * a[
i__4].i;
z__3.r = stemp * temp.r, z__3.i = stemp * temp.i;
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i -
z__3.i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
/* L90: */
}
}
/* L100: */
}
} else if (lsame_(direct, "B")) {
for (j = *m - 1; j >= 1; --j) {
ctemp = c__[j];
stemp = s[j];
if (ctemp != 1. || stemp != 0.) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = j + i__ * a_dim1;
temp.r = a[i__2].r, temp.i = a[i__2].i;
i__2 = j + i__ * a_dim1;
i__3 = *m + i__ * a_dim1;
z__2.r = stemp * a[i__3].r, z__2.i = stemp * a[
i__3].i;
z__3.r = ctemp * temp.r, z__3.i = ctemp * temp.i;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i +
z__3.i;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
i__2 = *m + i__ * a_dim1;
i__3 = *m + i__ * a_dim1;
z__2.r = ctemp * a[i__3].r, z__2.i = ctemp * a[
i__3].i;
z__3.r = stemp * temp.r, z__3.i = stemp * temp.i;
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i -
z__3.i;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
/* L110: */
}
}
/* L120: */
}
}
}
} else if (lsame_(side, "R")) {
/* Form A * P' */
if (lsame_(pivot, "V")) {
if (lsame_(direct, "F")) {
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
ctemp = c__[j];
stemp = s[j];
if (ctemp != 1. || stemp != 0.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + (j + 1) * a_dim1;
temp.r = a[i__3].r, temp.i = a[i__3].i;
i__3 = i__ + (j + 1) * a_dim1;
z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i;
i__4 = i__ + j * a_dim1;
z__3.r = stemp * a[i__4].r, z__3.i = stemp * a[
i__4].i;
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i -
z__3.i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
i__3 = i__ + j * a_dim1;
z__2.r = stemp * temp.r, z__2.i = stemp * temp.i;
i__4 = i__ + j * a_dim1;
z__3.r = ctemp * a[i__4].r, z__3.i = ctemp * a[
i__4].i;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i +
z__3.i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
/* L130: */
}
}
/* L140: */
}
} else if (lsame_(direct, "B")) {
for (j = *n - 1; j >= 1; --j) {
ctemp = c__[j];
stemp = s[j];
if (ctemp != 1. || stemp != 0.) {
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + (j + 1) * a_dim1;
temp.r = a[i__2].r, temp.i = a[i__2].i;
i__2 = i__ + (j + 1) * a_dim1;
z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i;
i__3 = i__ + j * a_dim1;
z__3.r = stemp * a[i__3].r, z__3.i = stemp * a[
i__3].i;
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i -
z__3.i;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
i__2 = i__ + j * a_dim1;
z__2.r = stemp * temp.r, z__2.i = stemp * temp.i;
i__3 = i__ + j * a_dim1;
z__3.r = ctemp * a[i__3].r, z__3.i = ctemp * a[
i__3].i;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i +
z__3.i;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
/* L150: */
}
}
/* L160: */
}
}
} else if (lsame_(pivot, "T")) {
if (lsame_(direct, "F")) {
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
ctemp = c__[j - 1];
stemp = s[j - 1];
if (ctemp != 1. || stemp != 0.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
temp.r = a[i__3].r, temp.i = a[i__3].i;
i__3 = i__ + j * a_dim1;
z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i;
i__4 = i__ + a_dim1;
z__3.r = stemp * a[i__4].r, z__3.i = stemp * a[
i__4].i;
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i -
z__3.i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
i__3 = i__ + a_dim1;
z__2.r = stemp * temp.r, z__2.i = stemp * temp.i;
i__4 = i__ + a_dim1;
z__3.r = ctemp * a[i__4].r, z__3.i = ctemp * a[
i__4].i;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i +
z__3.i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
/* L170: */
}
}
/* L180: */
}
} else if (lsame_(direct, "B")) {
for (j = *n; j >= 2; --j) {
ctemp = c__[j - 1];
stemp = s[j - 1];
if (ctemp != 1. || stemp != 0.) {
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + j * a_dim1;
temp.r = a[i__2].r, temp.i = a[i__2].i;
i__2 = i__ + j * a_dim1;
z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i;
i__3 = i__ + a_dim1;
z__3.r = stemp * a[i__3].r, z__3.i = stemp * a[
i__3].i;
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i -
z__3.i;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
i__2 = i__ + a_dim1;
z__2.r = stemp * temp.r, z__2.i = stemp * temp.i;
i__3 = i__ + a_dim1;
z__3.r = ctemp * a[i__3].r, z__3.i = ctemp * a[
i__3].i;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i +
z__3.i;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
/* L190: */
}
}
/* L200: */
}
}
} else if (lsame_(pivot, "B")) {
if (lsame_(direct, "F")) {
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
ctemp = c__[j];
stemp = s[j];
if (ctemp != 1. || stemp != 0.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
temp.r = a[i__3].r, temp.i = a[i__3].i;
i__3 = i__ + j * a_dim1;
i__4 = i__ + *n * a_dim1;
z__2.r = stemp * a[i__4].r, z__2.i = stemp * a[
i__4].i;
z__3.r = ctemp * temp.r, z__3.i = ctemp * temp.i;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i +
z__3.i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
i__3 = i__ + *n * a_dim1;
i__4 = i__ + *n * a_dim1;
z__2.r = ctemp * a[i__4].r, z__2.i = ctemp * a[
i__4].i;
z__3.r = stemp * temp.r, z__3.i = stemp * temp.i;
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i -
z__3.i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
/* L210: */
}
}
/* L220: */
}
} else if (lsame_(direct, "B")) {
for (j = *n - 1; j >= 1; --j) {
ctemp = c__[j];
stemp = s[j];
if (ctemp != 1. || stemp != 0.) {
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + j * a_dim1;
temp.r = a[i__2].r, temp.i = a[i__2].i;
i__2 = i__ + j * a_dim1;
i__3 = i__ + *n * a_dim1;
z__2.r = stemp * a[i__3].r, z__2.i = stemp * a[
i__3].i;
z__3.r = ctemp * temp.r, z__3.i = ctemp * temp.i;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i +
z__3.i;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
i__2 = i__ + *n * a_dim1;
i__3 = i__ + *n * a_dim1;
z__2.r = ctemp * a[i__3].r, z__2.i = ctemp * a[
i__3].i;
z__3.r = stemp * temp.r, z__3.i = stemp * temp.i;
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i -
z__3.i;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
/* L230: */
}
}
/* L240: */
}
}
}
}
return 0;
/* End of ZLASR */
} /* zlasr_ */
/* Subroutine */ int zlassq_(integer *n, doublecomplex *x, integer *incx,
doublereal *scale, doublereal *sumsq)
{
/* System generated locals */
integer i__1, i__2, i__3;
doublereal d__1;
/* Builtin functions */
double d_imag(doublecomplex *);
/* Local variables */
static integer ix;
static doublereal temp1;
/*
-- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZLASSQ returns the values scl and ssq such that
( scl**2 )*ssq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,
where x( i ) = abs( X( 1 + ( i - 1 )*INCX ) ). The value of sumsq is
assumed to be at least unity and the value of ssq will then satisfy
1.0 .le. ssq .le. ( sumsq + 2*n ).
scale is assumed to be non-negative and scl returns the value
scl = max( scale, abs( real( x( i ) ) ), abs( aimag( x( i ) ) ) ),
i
scale and sumsq must be supplied in SCALE and SUMSQ respectively.
SCALE and SUMSQ are overwritten by scl and ssq respectively.
The routine makes only one pass through the vector X.
Arguments
=========
N (input) INTEGER
The number of elements to be used from the vector X.
X (input) COMPLEX*16 array, dimension (N)
The vector x as described above.
x( i ) = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n.
INCX (input) INTEGER
The increment between successive values of the vector X.
INCX > 0.
SCALE (input/output) DOUBLE PRECISION
On entry, the value scale in the equation above.
On exit, SCALE is overwritten with the value scl .
SUMSQ (input/output) DOUBLE PRECISION
On entry, the value sumsq in the equation above.
On exit, SUMSQ is overwritten with the value ssq .
=====================================================================
*/
/* Parameter adjustments */
--x;
/* Function Body */
if (*n > 0) {
i__1 = (*n - 1) * *incx + 1;
i__2 = *incx;
for (ix = 1; i__2 < 0 ? ix >= i__1 : ix <= i__1; ix += i__2) {
i__3 = ix;
if (x[i__3].r != 0.) {
i__3 = ix;
temp1 = (d__1 = x[i__3].r, abs(d__1));
if (*scale < temp1) {
/* Computing 2nd power */
d__1 = *scale / temp1;
*sumsq = *sumsq * (d__1 * d__1) + 1;
*scale = temp1;
} else {
/* Computing 2nd power */
d__1 = temp1 / *scale;
*sumsq += d__1 * d__1;
}
}
if (d_imag(&x[ix]) != 0.) {
temp1 = (d__1 = d_imag(&x[ix]), abs(d__1));
if (*scale < temp1) {
/* Computing 2nd power */
d__1 = *scale / temp1;
*sumsq = *sumsq * (d__1 * d__1) + 1;
*scale = temp1;
} else {
/* Computing 2nd power */
d__1 = temp1 / *scale;
*sumsq += d__1 * d__1;
}
}
/* L10: */
}
}
return 0;
/* End of ZLASSQ */
} /* zlassq_ */
/* Subroutine */ int zlaswp_(integer *n, doublecomplex *a, integer *lda,
integer *k1, integer *k2, integer *ipiv, integer *incx)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6;
/* Local variables */
static integer i__, j, k, i1, i2, n32, ip, ix, ix0, inc;
static doublecomplex temp;
/*
-- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZLASWP performs a series of row interchanges on the matrix A.
One row interchange is initiated for each of rows K1 through K2 of A.
Arguments
=========
N (input) INTEGER
The number of columns of the matrix A.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the matrix of column dimension N to which the row
interchanges will be applied.
On exit, the permuted matrix.
LDA (input) INTEGER
The leading dimension of the array A.
K1 (input) INTEGER
The first element of IPIV for which a row interchange will
be done.
K2 (input) INTEGER
The last element of IPIV for which a row interchange will
be done.
IPIV (input) INTEGER array, dimension (M*abs(INCX))
The vector of pivot indices. Only the elements in positions
K1 through K2 of IPIV are accessed.
IPIV(K) = L implies rows K and L are to be interchanged.
INCX (input) INTEGER
The increment between successive values of IPIV. If IPIV
is negative, the pivots are applied in reverse order.
Further Details
===============
Modified by
R. C. Whaley, Computer Science Dept., Univ. of Tenn., Knoxville, USA
=====================================================================
Interchange row I with row IPIV(I) for each of rows K1 through K2.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--ipiv;
/* Function Body */
if (*incx > 0) {
ix0 = *k1;
i1 = *k1;
i2 = *k2;
inc = 1;
} else if (*incx < 0) {
ix0 = (1 - *k2) * *incx + 1;
i1 = *k2;
i2 = *k1;
inc = -1;
} else {
return 0;
}
n32 = (*n / 32) << (5);
if (n32 != 0) {
i__1 = n32;
for (j = 1; j <= i__1; j += 32) {
ix = ix0;
i__2 = i2;
i__3 = inc;
for (i__ = i1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__3)
{
ip = ipiv[ix];
if (ip != i__) {
i__4 = j + 31;
for (k = j; k <= i__4; ++k) {
i__5 = i__ + k * a_dim1;
temp.r = a[i__5].r, temp.i = a[i__5].i;
i__5 = i__ + k * a_dim1;
i__6 = ip + k * a_dim1;
a[i__5].r = a[i__6].r, a[i__5].i = a[i__6].i;
i__5 = ip + k * a_dim1;
a[i__5].r = temp.r, a[i__5].i = temp.i;
/* L10: */
}
}
ix += *incx;
/* L20: */
}
/* L30: */
}
}
if (n32 != *n) {
++n32;
ix = ix0;
i__1 = i2;
i__3 = inc;
for (i__ = i1; i__3 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__3) {
ip = ipiv[ix];
if (ip != i__) {
i__2 = *n;
for (k = n32; k <= i__2; ++k) {
i__4 = i__ + k * a_dim1;
temp.r = a[i__4].r, temp.i = a[i__4].i;
i__4 = i__ + k * a_dim1;
i__5 = ip + k * a_dim1;
a[i__4].r = a[i__5].r, a[i__4].i = a[i__5].i;
i__4 = ip + k * a_dim1;
a[i__4].r = temp.r, a[i__4].i = temp.i;
/* L40: */
}
}
ix += *incx;
/* L50: */
}
}
return 0;
/* End of ZLASWP */
} /* zlaswp_ */
/* Subroutine */ int zlatrd_(char *uplo, integer *n, integer *nb,
doublecomplex *a, integer *lda, doublereal *e, doublecomplex *tau,
doublecomplex *w, integer *ldw)
{
/* System generated locals */
integer a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3;
doublereal d__1;
doublecomplex z__1, z__2, z__3, z__4;
/* Local variables */
static integer i__, iw;
static doublecomplex alpha;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
doublecomplex *, integer *);
extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *);
extern /* Subroutine */ int zgemv_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *),
zhemv_(char *, integer *, doublecomplex *, doublecomplex *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *), zaxpy_(integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *), zlarfg_(integer *, doublecomplex *, doublecomplex *,
integer *, doublecomplex *), zlacgv_(integer *, doublecomplex *,
integer *);
/*
-- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZLATRD reduces NB rows and columns of a complex Hermitian matrix A to
Hermitian tridiagonal form by a unitary similarity
transformation Q' * A * Q, and returns the matrices V and W which are
needed to apply the transformation to the unreduced part of A.
If UPLO = 'U', ZLATRD reduces the last NB rows and columns of a
matrix, of which the upper triangle is supplied;
if UPLO = 'L', ZLATRD reduces the first NB rows and columns of a
matrix, of which the lower triangle is supplied.
This is an auxiliary routine called by ZHETRD.
Arguments
=========
UPLO (input) CHARACTER
Specifies whether the upper or lower triangular part of the
Hermitian matrix A is stored:
= 'U': Upper triangular
= 'L': Lower triangular
N (input) INTEGER
The order of the matrix A.
NB (input) INTEGER
The number of rows and columns to be reduced.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading
n-by-n upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading n-by-n lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit:
if UPLO = 'U', the last NB columns have been reduced to
tridiagonal form, with the diagonal elements overwriting
the diagonal elements of A; the elements above the diagonal
with the array TAU, represent the unitary matrix Q as a
product of elementary reflectors;
if UPLO = 'L', the first NB columns have been reduced to
tridiagonal form, with the diagonal elements overwriting
the diagonal elements of A; the elements below the diagonal
with the array TAU, represent the unitary matrix Q as a
product of elementary reflectors.
See Further Details.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
E (output) DOUBLE PRECISION array, dimension (N-1)
If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal
elements of the last NB columns of the reduced matrix;
if UPLO = 'L', E(1:nb) contains the subdiagonal elements of
the first NB columns of the reduced matrix.
TAU (output) COMPLEX*16 array, dimension (N-1)
The scalar factors of the elementary reflectors, stored in
TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'.
See Further Details.
W (output) COMPLEX*16 array, dimension (LDW,NB)
The n-by-nb matrix W required to update the unreduced part
of A.
LDW (input) INTEGER
The leading dimension of the array W. LDW >= max(1,N).
Further Details
===============
If UPLO = 'U', the matrix Q is represented as a product of elementary
reflectors
Q = H(n) H(n-1) . . . H(n-nb+1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i),
and tau in TAU(i-1).
If UPLO = 'L', the matrix Q is represented as a product of elementary
reflectors
Q = H(1) H(2) . . . H(nb).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),
and tau in TAU(i).
The elements of the vectors v together form the n-by-nb matrix V
which is needed, with W, to apply the transformation to the unreduced
part of the matrix, using a Hermitian rank-2k update of the form:
A := A - V*W' - W*V'.
The contents of A on exit are illustrated by the following examples
with n = 5 and nb = 2:
if UPLO = 'U': if UPLO = 'L':
( a a a v4 v5 ) ( d )
( a a v4 v5 ) ( 1 d )
( a 1 v5 ) ( v1 1 a )
( d 1 ) ( v1 v2 a a )
( d ) ( v1 v2 a a a )
where d denotes a diagonal element of the reduced matrix, a denotes
an element of the original matrix that is unchanged, and vi denotes
an element of the vector defining H(i).
=====================================================================
Quick return if possible
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--e;
--tau;
w_dim1 = *ldw;
w_offset = 1 + w_dim1 * 1;
w -= w_offset;
/* Function Body */
if (*n <= 0) {
return 0;
}
if (lsame_(uplo, "U")) {
/* Reduce last NB columns of upper triangle */
i__1 = *n - *nb + 1;
for (i__ = *n; i__ >= i__1; --i__) {
iw = i__ - *n + *nb;
if (i__ < *n) {
/* Update A(1:i,i) */
i__2 = i__ + i__ * a_dim1;
i__3 = i__ + i__ * a_dim1;
d__1 = a[i__3].r;
a[i__2].r = d__1, a[i__2].i = 0.;
i__2 = *n - i__;
zlacgv_(&i__2, &w[i__ + (iw + 1) * w_dim1], ldw);
i__2 = *n - i__;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__, &i__2, &z__1, &a[(i__ + 1) *
a_dim1 + 1], lda, &w[i__ + (iw + 1) * w_dim1], ldw, &
c_b60, &a[i__ * a_dim1 + 1], &c__1);
i__2 = *n - i__;
zlacgv_(&i__2, &w[i__ + (iw + 1) * w_dim1], ldw);
i__2 = *n - i__;
zlacgv_(&i__2, &a[i__ + (i__ + 1) * a_dim1], lda);
i__2 = *n - i__;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__, &i__2, &z__1, &w[(iw + 1) *
w_dim1 + 1], ldw, &a[i__ + (i__ + 1) * a_dim1], lda, &
c_b60, &a[i__ * a_dim1 + 1], &c__1);
i__2 = *n - i__;
zlacgv_(&i__2, &a[i__ + (i__ + 1) * a_dim1], lda);
i__2 = i__ + i__ * a_dim1;
i__3 = i__ + i__ * a_dim1;
d__1 = a[i__3].r;
a[i__2].r = d__1, a[i__2].i = 0.;
}
if (i__ > 1) {
/*
Generate elementary reflector H(i) to annihilate
A(1:i-2,i)
*/
i__2 = i__ - 1 + i__ * a_dim1;
alpha.r = a[i__2].r, alpha.i = a[i__2].i;
i__2 = i__ - 1;
zlarfg_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &tau[i__
- 1]);
i__2 = i__ - 1;
e[i__2] = alpha.r;
i__2 = i__ - 1 + i__ * a_dim1;
a[i__2].r = 1., a[i__2].i = 0.;
/* Compute W(1:i-1,i) */
i__2 = i__ - 1;
zhemv_("Upper", &i__2, &c_b60, &a[a_offset], lda, &a[i__ *
a_dim1 + 1], &c__1, &c_b59, &w[iw * w_dim1 + 1], &
c__1);
if (i__ < *n) {
i__2 = i__ - 1;
i__3 = *n - i__;
zgemv_("Conjugate transpose", &i__2, &i__3, &c_b60, &w[(
iw + 1) * w_dim1 + 1], ldw, &a[i__ * a_dim1 + 1],
&c__1, &c_b59, &w[i__ + 1 + iw * w_dim1], &c__1);
i__2 = i__ - 1;
i__3 = *n - i__;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__2, &i__3, &z__1, &a[(i__ + 1) *
a_dim1 + 1], lda, &w[i__ + 1 + iw * w_dim1], &
c__1, &c_b60, &w[iw * w_dim1 + 1], &c__1);
i__2 = i__ - 1;
i__3 = *n - i__;
zgemv_("Conjugate transpose", &i__2, &i__3, &c_b60, &a[(
i__ + 1) * a_dim1 + 1], lda, &a[i__ * a_dim1 + 1],
&c__1, &c_b59, &w[i__ + 1 + iw * w_dim1], &c__1);
i__2 = i__ - 1;
i__3 = *n - i__;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__2, &i__3, &z__1, &w[(iw + 1) *
w_dim1 + 1], ldw, &w[i__ + 1 + iw * w_dim1], &
c__1, &c_b60, &w[iw * w_dim1 + 1], &c__1);
}
i__2 = i__ - 1;
zscal_(&i__2, &tau[i__ - 1], &w[iw * w_dim1 + 1], &c__1);
z__3.r = -.5, z__3.i = -0.;
i__2 = i__ - 1;
z__2.r = z__3.r * tau[i__2].r - z__3.i * tau[i__2].i, z__2.i =
z__3.r * tau[i__2].i + z__3.i * tau[i__2].r;
i__3 = i__ - 1;
zdotc_(&z__4, &i__3, &w[iw * w_dim1 + 1], &c__1, &a[i__ *
a_dim1 + 1], &c__1);
z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r *
z__4.i + z__2.i * z__4.r;
alpha.r = z__1.r, alpha.i = z__1.i;
i__2 = i__ - 1;
zaxpy_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &w[iw *
w_dim1 + 1], &c__1);
}
/* L10: */
}
} else {
/* Reduce first NB columns of lower triangle */
i__1 = *nb;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Update A(i:n,i) */
i__2 = i__ + i__ * a_dim1;
i__3 = i__ + i__ * a_dim1;
d__1 = a[i__3].r;
a[i__2].r = d__1, a[i__2].i = 0.;
i__2 = i__ - 1;
zlacgv_(&i__2, &w[i__ + w_dim1], ldw);
i__2 = *n - i__ + 1;
i__3 = i__ - 1;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__2, &i__3, &z__1, &a[i__ + a_dim1], lda,
&w[i__ + w_dim1], ldw, &c_b60, &a[i__ + i__ * a_dim1], &
c__1);
i__2 = i__ - 1;
zlacgv_(&i__2, &w[i__ + w_dim1], ldw);
i__2 = i__ - 1;
zlacgv_(&i__2, &a[i__ + a_dim1], lda);
i__2 = *n - i__ + 1;
i__3 = i__ - 1;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__2, &i__3, &z__1, &w[i__ + w_dim1], ldw,
&a[i__ + a_dim1], lda, &c_b60, &a[i__ + i__ * a_dim1], &
c__1);
i__2 = i__ - 1;
zlacgv_(&i__2, &a[i__ + a_dim1], lda);
i__2 = i__ + i__ * a_dim1;
i__3 = i__ + i__ * a_dim1;
d__1 = a[i__3].r;
a[i__2].r = d__1, a[i__2].i = 0.;
if (i__ < *n) {
/*
Generate elementary reflector H(i) to annihilate
A(i+2:n,i)
*/
i__2 = i__ + 1 + i__ * a_dim1;
alpha.r = a[i__2].r, alpha.i = a[i__2].i;
i__2 = *n - i__;
/* Computing MIN */
i__3 = i__ + 2;
zlarfg_(&i__2, &alpha, &a[min(i__3,*n) + i__ * a_dim1], &c__1,
&tau[i__]);
i__2 = i__;
e[i__2] = alpha.r;
i__2 = i__ + 1 + i__ * a_dim1;
a[i__2].r = 1., a[i__2].i = 0.;
/* Compute W(i+1:n,i) */
i__2 = *n - i__;
zhemv_("Lower", &i__2, &c_b60, &a[i__ + 1 + (i__ + 1) *
a_dim1], lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &
c_b59, &w[i__ + 1 + i__ * w_dim1], &c__1);
i__2 = *n - i__;
i__3 = i__ - 1;
zgemv_("Conjugate transpose", &i__2, &i__3, &c_b60, &w[i__ +
1 + w_dim1], ldw, &a[i__ + 1 + i__ * a_dim1], &c__1, &
c_b59, &w[i__ * w_dim1 + 1], &c__1);
i__2 = *n - i__;
i__3 = i__ - 1;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__2, &i__3, &z__1, &a[i__ + 1 +
a_dim1], lda, &w[i__ * w_dim1 + 1], &c__1, &c_b60, &w[
i__ + 1 + i__ * w_dim1], &c__1);
i__2 = *n - i__;
i__3 = i__ - 1;
zgemv_("Conjugate transpose", &i__2, &i__3, &c_b60, &a[i__ +
1 + a_dim1], lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &
c_b59, &w[i__ * w_dim1 + 1], &c__1);
i__2 = *n - i__;
i__3 = i__ - 1;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__2, &i__3, &z__1, &w[i__ + 1 +
w_dim1], ldw, &w[i__ * w_dim1 + 1], &c__1, &c_b60, &w[
i__ + 1 + i__ * w_dim1], &c__1);
i__2 = *n - i__;
zscal_(&i__2, &tau[i__], &w[i__ + 1 + i__ * w_dim1], &c__1);
z__3.r = -.5, z__3.i = -0.;
i__2 = i__;
z__2.r = z__3.r * tau[i__2].r - z__3.i * tau[i__2].i, z__2.i =
z__3.r * tau[i__2].i + z__3.i * tau[i__2].r;
i__3 = *n - i__;
zdotc_(&z__4, &i__3, &w[i__ + 1 + i__ * w_dim1], &c__1, &a[
i__ + 1 + i__ * a_dim1], &c__1);
z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r *
z__4.i + z__2.i * z__4.r;
alpha.r = z__1.r, alpha.i = z__1.i;
i__2 = *n - i__;
zaxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &w[
i__ + 1 + i__ * w_dim1], &c__1);
}
/* L20: */
}
}
return 0;
/* End of ZLATRD */
} /* zlatrd_ */
/* Subroutine */ int zlatrs_(char *uplo, char *trans, char *diag, char *
normin, integer *n, doublecomplex *a, integer *lda, doublecomplex *x,
doublereal *scale, doublereal *cnorm, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
doublereal d__1, d__2, d__3, d__4;
doublecomplex z__1, z__2, z__3, z__4;
/* Builtin functions */
double d_imag(doublecomplex *);
void d_cnjg(doublecomplex *, doublecomplex *);
/* Local variables */
static integer i__, j;
static doublereal xj, rec, tjj;
static integer jinc;
static doublereal xbnd;
static integer imax;
static doublereal tmax;
static doublecomplex tjjs;
static doublereal xmax, grow;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *);
extern logical lsame_(char *, char *);
static doublereal tscal;
static doublecomplex uscal;
static integer jlast;
static doublecomplex csumj;
extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *);
static logical upper;
extern /* Double Complex */ VOID zdotu_(doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *);
extern /* Subroutine */ int zaxpy_(integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *), ztrsv_(
char *, char *, char *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *), dlabad_(
doublereal *, doublereal *);
extern integer idamax_(integer *, doublereal *, integer *);
extern /* Subroutine */ int xerbla_(char *, integer *), zdscal_(
integer *, doublereal *, doublecomplex *, integer *);
static doublereal bignum;
extern integer izamax_(integer *, doublecomplex *, integer *);
extern /* Double Complex */ VOID zladiv_(doublecomplex *, doublecomplex *,
doublecomplex *);
static logical notran;
static integer jfirst;
extern doublereal dzasum_(integer *, doublecomplex *, integer *);
static doublereal smlnum;
static logical nounit;
/*
-- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1992
Purpose
=======
ZLATRS solves one of the triangular systems
A * x = s*b, A**T * x = s*b, or A**H * x = s*b,
with scaling to prevent overflow. Here A is an upper or lower
triangular matrix, A**T denotes the transpose of A, A**H denotes the
conjugate transpose of A, x and b are n-element vectors, and s is a
scaling factor, usually less than or equal to 1, chosen so that the
components of x will be less than the overflow threshold. If the
unscaled problem will not cause overflow, the Level 2 BLAS routine
ZTRSV is called. If the matrix A is singular (A(j,j) = 0 for some j),
then s is set to 0 and a non-trivial solution to A*x = 0 is returned.
Arguments
=========
UPLO (input) CHARACTER*1
Specifies whether the matrix A is upper or lower triangular.
= 'U': Upper triangular
= 'L': Lower triangular
TRANS (input) CHARACTER*1
Specifies the operation applied to A.
= 'N': Solve A * x = s*b (No transpose)
= 'T': Solve A**T * x = s*b (Transpose)
= 'C': Solve A**H * x = s*b (Conjugate transpose)
DIAG (input) CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= 'N': Non-unit triangular
= 'U': Unit triangular
NORMIN (input) CHARACTER*1
Specifies whether CNORM has been set or not.
= 'Y': CNORM contains the column norms on entry
= 'N': CNORM is not set on entry. On exit, the norms will
be computed and stored in CNORM.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input) COMPLEX*16 array, dimension (LDA,N)
The triangular matrix A. If UPLO = 'U', the leading n by n
upper triangular part of the array A contains the upper
triangular matrix, and the strictly lower triangular part of
A is not referenced. If UPLO = 'L', the leading n by n lower
triangular part of the array A contains the lower triangular
matrix, and the strictly upper triangular part of A is not
referenced. If DIAG = 'U', the diagonal elements of A are
also not referenced and are assumed to be 1.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max (1,N).
X (input/output) COMPLEX*16 array, dimension (N)
On entry, the right hand side b of the triangular system.
On exit, X is overwritten by the solution vector x.
SCALE (output) DOUBLE PRECISION
The scaling factor s for the triangular system
A * x = s*b, A**T * x = s*b, or A**H * x = s*b.
If SCALE = 0, the matrix A is singular or badly scaled, and
the vector x is an exact or approximate solution to A*x = 0.
CNORM (input or output) DOUBLE PRECISION array, dimension (N)
If NORMIN = 'Y', CNORM is an input argument and CNORM(j)
contains the norm of the off-diagonal part of the j-th column
of A. If TRANS = 'N', CNORM(j) must be greater than or equal
to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j)
must be greater than or equal to the 1-norm.
If NORMIN = 'N', CNORM is an output argument and CNORM(j)
returns the 1-norm of the offdiagonal part of the j-th column
of A.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -k, the k-th argument had an illegal value
Further Details
======= =======
A rough bound on x is computed; if that is less than overflow, ZTRSV
is called, otherwise, specific code is used which checks for possible
overflow or divide-by-zero at every operation.
A columnwise scheme is used for solving A*x = b. The basic algorithm
if A is lower triangular is
x[1:n] := b[1:n]
for j = 1, ..., n
x(j) := x(j) / A(j,j)
x[j+1:n] := x[j+1:n] - x(j) * A[j+1:n,j]
end
Define bounds on the components of x after j iterations of the loop:
M(j) = bound on x[1:j]
G(j) = bound on x[j+1:n]
Initially, let M(0) = 0 and G(0) = max{x(i), i=1,...,n}.
Then for iteration j+1 we have
M(j+1) <= G(j) / | A(j+1,j+1) |
G(j+1) <= G(j) + M(j+1) * | A[j+2:n,j+1] |
<= G(j) ( 1 + CNORM(j+1) / | A(j+1,j+1) | )
where CNORM(j+1) is greater than or equal to the infinity-norm of
column j+1 of A, not counting the diagonal. Hence
G(j) <= G(0) product ( 1 + CNORM(i) / | A(i,i) | )
1<=i<=j
and
|x(j)| <= ( G(0) / |A(j,j)| ) product ( 1 + CNORM(i) / |A(i,i)| )
1<=i< j
Since |x(j)| <= M(j), we use the Level 2 BLAS routine ZTRSV if the
reciprocal of the largest M(j), j=1,..,n, is larger than
max(underflow, 1/overflow).
The bound on x(j) is also used to determine when a step in the
columnwise method can be performed without fear of overflow. If
the computed bound is greater than a large constant, x is scaled to
prevent overflow, but if the bound overflows, x is set to 0, x(j) to
1, and scale to 0, and a non-trivial solution to A*x = 0 is found.
Similarly, a row-wise scheme is used to solve A**T *x = b or
A**H *x = b. The basic algorithm for A upper triangular is
for j = 1, ..., n
x(j) := ( b(j) - A[1:j-1,j]' * x[1:j-1] ) / A(j,j)
end
We simultaneously compute two bounds
G(j) = bound on ( b(i) - A[1:i-1,i]' * x[1:i-1] ), 1<=i<=j
M(j) = bound on x(i), 1<=i<=j
The initial values are G(0) = 0, M(0) = max{b(i), i=1,..,n}, and we
add the constraint G(j) >= G(j-1) and M(j) >= M(j-1) for j >= 1.
Then the bound on x(j) is
M(j) <= M(j-1) * ( 1 + CNORM(j) ) / | A(j,j) |
<= M(0) * product ( ( 1 + CNORM(i) ) / |A(i,i)| )
1<=i<=j
and we can safely call ZTRSV if 1/M(n) and 1/G(n) are both greater
than max(underflow, 1/overflow).
=====================================================================
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--x;
--cnorm;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
notran = lsame_(trans, "N");
nounit = lsame_(diag, "N");
/* Test the input parameters. */
if ((! upper && ! lsame_(uplo, "L"))) {
*info = -1;
} else if (((! notran && ! lsame_(trans, "T")) && !
lsame_(trans, "C"))) {
*info = -2;
} else if ((! nounit && ! lsame_(diag, "U"))) {
*info = -3;
} else if ((! lsame_(normin, "Y") && ! lsame_(
normin, "N"))) {
*info = -4;
} else if (*n < 0) {
*info = -5;
} else if (*lda < max(1,*n)) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZLATRS", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Determine machine dependent parameters to control overflow. */
smlnum = SAFEMINIMUM;
bignum = 1. / smlnum;
dlabad_(&smlnum, &bignum);
smlnum /= PRECISION;
bignum = 1. / smlnum;
*scale = 1.;
if (lsame_(normin, "N")) {
/* Compute the 1-norm of each column, not including the diagonal. */
if (upper) {
/* A is upper triangular. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j - 1;
cnorm[j] = dzasum_(&i__2, &a[j * a_dim1 + 1], &c__1);
/* L10: */
}
} else {
/* A is lower triangular. */
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
i__2 = *n - j;
cnorm[j] = dzasum_(&i__2, &a[j + 1 + j * a_dim1], &c__1);
/* L20: */
}
cnorm[*n] = 0.;
}
}
/*
Scale the column norms by TSCAL if the maximum element in CNORM is
greater than BIGNUM/2.
*/
imax = idamax_(n, &cnorm[1], &c__1);
tmax = cnorm[imax];
if (tmax <= bignum * .5) {
tscal = 1.;
} else {
tscal = .5 / (smlnum * tmax);
dscal_(n, &tscal, &cnorm[1], &c__1);
}
/*
Compute a bound on the computed solution vector to see if the
Level 2 BLAS routine ZTRSV can be used.
*/
xmax = 0.;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = j;
d__3 = xmax, d__4 = (d__1 = x[i__2].r / 2., abs(d__1)) + (d__2 =
d_imag(&x[j]) / 2., abs(d__2));
xmax = max(d__3,d__4);
/* L30: */
}
xbnd = xmax;
if (notran) {
/* Compute the growth in A * x = b. */
if (upper) {
jfirst = *n;
jlast = 1;
jinc = -1;
} else {
jfirst = 1;
jlast = *n;
jinc = 1;
}
if (tscal != 1.) {
grow = 0.;
goto L60;
}
if (nounit) {
/*
A is non-unit triangular.
Compute GROW = 1/G(j) and XBND = 1/M(j).
Initially, G(0) = max{x(i), i=1,...,n}.
*/
grow = .5 / max(xbnd,smlnum);
xbnd = grow;
i__1 = jlast;
i__2 = jinc;
for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
/* Exit the loop if the growth factor is too small. */
if (grow <= smlnum) {
goto L60;
}
i__3 = j + j * a_dim1;
tjjs.r = a[i__3].r, tjjs.i = a[i__3].i;
tjj = (d__1 = tjjs.r, abs(d__1)) + (d__2 = d_imag(&tjjs), abs(
d__2));
if (tjj >= smlnum) {
/*
M(j) = G(j-1) / abs(A(j,j))
Computing MIN
*/
d__1 = xbnd, d__2 = min(1.,tjj) * grow;
xbnd = min(d__1,d__2);
} else {
/* M(j) could overflow, set XBND to 0. */
xbnd = 0.;
}
if (tjj + cnorm[j] >= smlnum) {
/* G(j) = G(j-1)*( 1 + CNORM(j) / abs(A(j,j)) ) */
grow *= tjj / (tjj + cnorm[j]);
} else {
/* G(j) could overflow, set GROW to 0. */
grow = 0.;
}
/* L40: */
}
grow = xbnd;
} else {
/*
A is unit triangular.
Compute GROW = 1/G(j), where G(0) = max{x(i), i=1,...,n}.
Computing MIN
*/
d__1 = 1., d__2 = .5 / max(xbnd,smlnum);
grow = min(d__1,d__2);
i__2 = jlast;
i__1 = jinc;
for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) {
/* Exit the loop if the growth factor is too small. */
if (grow <= smlnum) {
goto L60;
}
/* G(j) = G(j-1)*( 1 + CNORM(j) ) */
grow *= 1. / (cnorm[j] + 1.);
/* L50: */
}
}
L60:
;
} else {
/* Compute the growth in A**T * x = b or A**H * x = b. */
if (upper) {
jfirst = 1;
jlast = *n;
jinc = 1;
} else {
jfirst = *n;
jlast = 1;
jinc = -1;
}
if (tscal != 1.) {
grow = 0.;
goto L90;
}
if (nounit) {
/*
A is non-unit triangular.
Compute GROW = 1/G(j) and XBND = 1/M(j).
Initially, M(0) = max{x(i), i=1,...,n}.
*/
grow = .5 / max(xbnd,smlnum);
xbnd = grow;
i__1 = jlast;
i__2 = jinc;
for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
/* Exit the loop if the growth factor is too small. */
if (grow <= smlnum) {
goto L90;
}
/* G(j) = max( G(j-1), M(j-1)*( 1 + CNORM(j) ) ) */
xj = cnorm[j] + 1.;
/* Computing MIN */
d__1 = grow, d__2 = xbnd / xj;
grow = min(d__1,d__2);
i__3 = j + j * a_dim1;
tjjs.r = a[i__3].r, tjjs.i = a[i__3].i;
tjj = (d__1 = tjjs.r, abs(d__1)) + (d__2 = d_imag(&tjjs), abs(
d__2));
if (tjj >= smlnum) {
/* M(j) = M(j-1)*( 1 + CNORM(j) ) / abs(A(j,j)) */
if (xj > tjj) {
xbnd *= tjj / xj;
}
} else {
/* M(j) could overflow, set XBND to 0. */
xbnd = 0.;
}
/* L70: */
}
grow = min(grow,xbnd);
} else {
/*
A is unit triangular.
Compute GROW = 1/G(j), where G(0) = max{x(i), i=1,...,n}.
Computing MIN
*/
d__1 = 1., d__2 = .5 / max(xbnd,smlnum);
grow = min(d__1,d__2);
i__2 = jlast;
i__1 = jinc;
for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) {
/* Exit the loop if the growth factor is too small. */
if (grow <= smlnum) {
goto L90;
}
/* G(j) = ( 1 + CNORM(j) )*G(j-1) */
xj = cnorm[j] + 1.;
grow /= xj;
/* L80: */
}
}
L90:
;
}
if (grow * tscal > smlnum) {
/*
Use the Level 2 BLAS solve if the reciprocal of the bound on
elements of X is not too small.
*/
ztrsv_(uplo, trans, diag, n, &a[a_offset], lda, &x[1], &c__1);
} else {
/* Use a Level 1 BLAS solve, scaling intermediate results. */
if (xmax > bignum * .5) {
/*
Scale X so that its components are less than or equal to
BIGNUM in absolute value.
*/
*scale = bignum * .5 / xmax;
zdscal_(n, scale, &x[1], &c__1);
xmax = bignum;
} else {
xmax *= 2.;
}
if (notran) {
/* Solve A * x = b */
i__1 = jlast;
i__2 = jinc;
for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
/* Compute x(j) = b(j) / A(j,j), scaling x if necessary. */
i__3 = j;
xj = (d__1 = x[i__3].r, abs(d__1)) + (d__2 = d_imag(&x[j]),
abs(d__2));
if (nounit) {
i__3 = j + j * a_dim1;
z__1.r = tscal * a[i__3].r, z__1.i = tscal * a[i__3].i;
tjjs.r = z__1.r, tjjs.i = z__1.i;
} else {
tjjs.r = tscal, tjjs.i = 0.;
if (tscal == 1.) {
goto L110;
}
}
tjj = (d__1 = tjjs.r, abs(d__1)) + (d__2 = d_imag(&tjjs), abs(
d__2));
if (tjj > smlnum) {
/* abs(A(j,j)) > SMLNUM: */
if (tjj < 1.) {
if (xj > tjj * bignum) {
/* Scale x by 1/b(j). */
rec = 1. / xj;
zdscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
i__3 = j;
zladiv_(&z__1, &x[j], &tjjs);
x[i__3].r = z__1.r, x[i__3].i = z__1.i;
i__3 = j;
xj = (d__1 = x[i__3].r, abs(d__1)) + (d__2 = d_imag(&x[j])
, abs(d__2));
} else if (tjj > 0.) {
/* 0 < abs(A(j,j)) <= SMLNUM: */
if (xj > tjj * bignum) {
/*
Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM
to avoid overflow when dividing by A(j,j).
*/
rec = tjj * bignum / xj;
if (cnorm[j] > 1.) {
/*
Scale by 1/CNORM(j) to avoid overflow when
multiplying x(j) times column j.
*/
rec /= cnorm[j];
}
zdscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
i__3 = j;
zladiv_(&z__1, &x[j], &tjjs);
x[i__3].r = z__1.r, x[i__3].i = z__1.i;
i__3 = j;
xj = (d__1 = x[i__3].r, abs(d__1)) + (d__2 = d_imag(&x[j])
, abs(d__2));
} else {
/*
A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and
scale = 0, and compute a solution to A*x = 0.
*/
i__3 = *n;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__;
x[i__4].r = 0., x[i__4].i = 0.;
/* L100: */
}
i__3 = j;
x[i__3].r = 1., x[i__3].i = 0.;
xj = 1.;
*scale = 0.;
xmax = 0.;
}
L110:
/*
Scale x if necessary to avoid overflow when adding a
multiple of column j of A.
*/
if (xj > 1.) {
rec = 1. / xj;
if (cnorm[j] > (bignum - xmax) * rec) {
/* Scale x by 1/(2*abs(x(j))). */
rec *= .5;
zdscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
}
} else if (xj * cnorm[j] > bignum - xmax) {
/* Scale x by 1/2. */
zdscal_(n, &c_b2210, &x[1], &c__1);
*scale *= .5;
}
if (upper) {
if (j > 1) {
/*
Compute the update
x(1:j-1) := x(1:j-1) - x(j) * A(1:j-1,j)
*/
i__3 = j - 1;
i__4 = j;
z__2.r = -x[i__4].r, z__2.i = -x[i__4].i;
z__1.r = tscal * z__2.r, z__1.i = tscal * z__2.i;
zaxpy_(&i__3, &z__1, &a[j * a_dim1 + 1], &c__1, &x[1],
&c__1);
i__3 = j - 1;
i__ = izamax_(&i__3, &x[1], &c__1);
i__3 = i__;
xmax = (d__1 = x[i__3].r, abs(d__1)) + (d__2 = d_imag(
&x[i__]), abs(d__2));
}
} else {
if (j < *n) {
/*
Compute the update
x(j+1:n) := x(j+1:n) - x(j) * A(j+1:n,j)
*/
i__3 = *n - j;
i__4 = j;
z__2.r = -x[i__4].r, z__2.i = -x[i__4].i;
z__1.r = tscal * z__2.r, z__1.i = tscal * z__2.i;
zaxpy_(&i__3, &z__1, &a[j + 1 + j * a_dim1], &c__1, &
x[j + 1], &c__1);
i__3 = *n - j;
i__ = j + izamax_(&i__3, &x[j + 1], &c__1);
i__3 = i__;
xmax = (d__1 = x[i__3].r, abs(d__1)) + (d__2 = d_imag(
&x[i__]), abs(d__2));
}
}
/* L120: */
}
} else if (lsame_(trans, "T")) {
/* Solve A**T * x = b */
i__2 = jlast;
i__1 = jinc;
for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) {
/*
Compute x(j) = b(j) - sum A(k,j)*x(k).
k<>j
*/
i__3 = j;
xj = (d__1 = x[i__3].r, abs(d__1)) + (d__2 = d_imag(&x[j]),
abs(d__2));
uscal.r = tscal, uscal.i = 0.;
rec = 1. / max(xmax,1.);
if (cnorm[j] > (bignum - xj) * rec) {
/* If x(j) could overflow, scale x by 1/(2*XMAX). */
rec *= .5;
if (nounit) {
i__3 = j + j * a_dim1;
z__1.r = tscal * a[i__3].r, z__1.i = tscal * a[i__3]
.i;
tjjs.r = z__1.r, tjjs.i = z__1.i;
} else {
tjjs.r = tscal, tjjs.i = 0.;
}
tjj = (d__1 = tjjs.r, abs(d__1)) + (d__2 = d_imag(&tjjs),
abs(d__2));
if (tjj > 1.) {
/*
Divide by A(j,j) when scaling x if A(j,j) > 1.
Computing MIN
*/
d__1 = 1., d__2 = rec * tjj;
rec = min(d__1,d__2);
zladiv_(&z__1, &uscal, &tjjs);
uscal.r = z__1.r, uscal.i = z__1.i;
}
if (rec < 1.) {
zdscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
csumj.r = 0., csumj.i = 0.;
if ((uscal.r == 1. && uscal.i == 0.)) {
/*
If the scaling needed for A in the dot product is 1,
call ZDOTU to perform the dot product.
*/
if (upper) {
i__3 = j - 1;
zdotu_(&z__1, &i__3, &a[j * a_dim1 + 1], &c__1, &x[1],
&c__1);
csumj.r = z__1.r, csumj.i = z__1.i;
} else if (j < *n) {
i__3 = *n - j;
zdotu_(&z__1, &i__3, &a[j + 1 + j * a_dim1], &c__1, &
x[j + 1], &c__1);
csumj.r = z__1.r, csumj.i = z__1.i;
}
} else {
/* Otherwise, use in-line code for the dot product. */
if (upper) {
i__3 = j - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * a_dim1;
z__3.r = a[i__4].r * uscal.r - a[i__4].i *
uscal.i, z__3.i = a[i__4].r * uscal.i + a[
i__4].i * uscal.r;
i__5 = i__;
z__2.r = z__3.r * x[i__5].r - z__3.i * x[i__5].i,
z__2.i = z__3.r * x[i__5].i + z__3.i * x[
i__5].r;
z__1.r = csumj.r + z__2.r, z__1.i = csumj.i +
z__2.i;
csumj.r = z__1.r, csumj.i = z__1.i;
/* L130: */
}
} else if (j < *n) {
i__3 = *n;
for (i__ = j + 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * a_dim1;
z__3.r = a[i__4].r * uscal.r - a[i__4].i *
uscal.i, z__3.i = a[i__4].r * uscal.i + a[
i__4].i * uscal.r;
i__5 = i__;
z__2.r = z__3.r * x[i__5].r - z__3.i * x[i__5].i,
z__2.i = z__3.r * x[i__5].i + z__3.i * x[
i__5].r;
z__1.r = csumj.r + z__2.r, z__1.i = csumj.i +
z__2.i;
csumj.r = z__1.r, csumj.i = z__1.i;
/* L140: */
}
}
}
z__1.r = tscal, z__1.i = 0.;
if ((uscal.r == z__1.r && uscal.i == z__1.i)) {
/*
Compute x(j) := ( x(j) - CSUMJ ) / A(j,j) if 1/A(j,j)
was not used to scale the dotproduct.
*/
i__3 = j;
i__4 = j;
z__1.r = x[i__4].r - csumj.r, z__1.i = x[i__4].i -
csumj.i;
x[i__3].r = z__1.r, x[i__3].i = z__1.i;
i__3 = j;
xj = (d__1 = x[i__3].r, abs(d__1)) + (d__2 = d_imag(&x[j])
, abs(d__2));
if (nounit) {
i__3 = j + j * a_dim1;
z__1.r = tscal * a[i__3].r, z__1.i = tscal * a[i__3]
.i;
tjjs.r = z__1.r, tjjs.i = z__1.i;
} else {
tjjs.r = tscal, tjjs.i = 0.;
if (tscal == 1.) {
goto L160;
}
}
/* Compute x(j) = x(j) / A(j,j), scaling if necessary. */
tjj = (d__1 = tjjs.r, abs(d__1)) + (d__2 = d_imag(&tjjs),
abs(d__2));
if (tjj > smlnum) {
/* abs(A(j,j)) > SMLNUM: */
if (tjj < 1.) {
if (xj > tjj * bignum) {
/* Scale X by 1/abs(x(j)). */
rec = 1. / xj;
zdscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
i__3 = j;
zladiv_(&z__1, &x[j], &tjjs);
x[i__3].r = z__1.r, x[i__3].i = z__1.i;
} else if (tjj > 0.) {
/* 0 < abs(A(j,j)) <= SMLNUM: */
if (xj > tjj * bignum) {
/* Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM. */
rec = tjj * bignum / xj;
zdscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
i__3 = j;
zladiv_(&z__1, &x[j], &tjjs);
x[i__3].r = z__1.r, x[i__3].i = z__1.i;
} else {
/*
A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and
scale = 0 and compute a solution to A**T *x = 0.
*/
i__3 = *n;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__;
x[i__4].r = 0., x[i__4].i = 0.;
/* L150: */
}
i__3 = j;
x[i__3].r = 1., x[i__3].i = 0.;
*scale = 0.;
xmax = 0.;
}
L160:
;
} else {
/*
Compute x(j) := x(j) / A(j,j) - CSUMJ if the dot
product has already been divided by 1/A(j,j).
*/
i__3 = j;
zladiv_(&z__2, &x[j], &tjjs);
z__1.r = z__2.r - csumj.r, z__1.i = z__2.i - csumj.i;
x[i__3].r = z__1.r, x[i__3].i = z__1.i;
}
/* Computing MAX */
i__3 = j;
d__3 = xmax, d__4 = (d__1 = x[i__3].r, abs(d__1)) + (d__2 =
d_imag(&x[j]), abs(d__2));
xmax = max(d__3,d__4);
/* L170: */
}
} else {
/* Solve A**H * x = b */
i__1 = jlast;
i__2 = jinc;
for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
/*
Compute x(j) = b(j) - sum A(k,j)*x(k).
k<>j
*/
i__3 = j;
xj = (d__1 = x[i__3].r, abs(d__1)) + (d__2 = d_imag(&x[j]),
abs(d__2));
uscal.r = tscal, uscal.i = 0.;
rec = 1. / max(xmax,1.);
if (cnorm[j] > (bignum - xj) * rec) {
/* If x(j) could overflow, scale x by 1/(2*XMAX). */
rec *= .5;
if (nounit) {
d_cnjg(&z__2, &a[j + j * a_dim1]);
z__1.r = tscal * z__2.r, z__1.i = tscal * z__2.i;
tjjs.r = z__1.r, tjjs.i = z__1.i;
} else {
tjjs.r = tscal, tjjs.i = 0.;
}
tjj = (d__1 = tjjs.r, abs(d__1)) + (d__2 = d_imag(&tjjs),
abs(d__2));
if (tjj > 1.) {
/*
Divide by A(j,j) when scaling x if A(j,j) > 1.
Computing MIN
*/
d__1 = 1., d__2 = rec * tjj;
rec = min(d__1,d__2);
zladiv_(&z__1, &uscal, &tjjs);
uscal.r = z__1.r, uscal.i = z__1.i;
}
if (rec < 1.) {
zdscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
csumj.r = 0., csumj.i = 0.;
if ((uscal.r == 1. && uscal.i == 0.)) {
/*
If the scaling needed for A in the dot product is 1,
call ZDOTC to perform the dot product.
*/
if (upper) {
i__3 = j - 1;
zdotc_(&z__1, &i__3, &a[j * a_dim1 + 1], &c__1, &x[1],
&c__1);
csumj.r = z__1.r, csumj.i = z__1.i;
} else if (j < *n) {
i__3 = *n - j;
zdotc_(&z__1, &i__3, &a[j + 1 + j * a_dim1], &c__1, &
x[j + 1], &c__1);
csumj.r = z__1.r, csumj.i = z__1.i;
}
} else {
/* Otherwise, use in-line code for the dot product. */
if (upper) {
i__3 = j - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
d_cnjg(&z__4, &a[i__ + j * a_dim1]);
z__3.r = z__4.r * uscal.r - z__4.i * uscal.i,
z__3.i = z__4.r * uscal.i + z__4.i *
uscal.r;
i__4 = i__;
z__2.r = z__3.r * x[i__4].r - z__3.i * x[i__4].i,
z__2.i = z__3.r * x[i__4].i + z__3.i * x[
i__4].r;
z__1.r = csumj.r + z__2.r, z__1.i = csumj.i +
z__2.i;
csumj.r = z__1.r, csumj.i = z__1.i;
/* L180: */
}
} else if (j < *n) {
i__3 = *n;
for (i__ = j + 1; i__ <= i__3; ++i__) {
d_cnjg(&z__4, &a[i__ + j * a_dim1]);
z__3.r = z__4.r * uscal.r - z__4.i * uscal.i,
z__3.i = z__4.r * uscal.i + z__4.i *
uscal.r;
i__4 = i__;
z__2.r = z__3.r * x[i__4].r - z__3.i * x[i__4].i,
z__2.i = z__3.r * x[i__4].i + z__3.i * x[
i__4].r;
z__1.r = csumj.r + z__2.r, z__1.i = csumj.i +
z__2.i;
csumj.r = z__1.r, csumj.i = z__1.i;
/* L190: */
}
}
}
z__1.r = tscal, z__1.i = 0.;
if ((uscal.r == z__1.r && uscal.i == z__1.i)) {
/*
Compute x(j) := ( x(j) - CSUMJ ) / A(j,j) if 1/A(j,j)
was not used to scale the dotproduct.
*/
i__3 = j;
i__4 = j;
z__1.r = x[i__4].r - csumj.r, z__1.i = x[i__4].i -
csumj.i;
x[i__3].r = z__1.r, x[i__3].i = z__1.i;
i__3 = j;
xj = (d__1 = x[i__3].r, abs(d__1)) + (d__2 = d_imag(&x[j])
, abs(d__2));
if (nounit) {
d_cnjg(&z__2, &a[j + j * a_dim1]);
z__1.r = tscal * z__2.r, z__1.i = tscal * z__2.i;
tjjs.r = z__1.r, tjjs.i = z__1.i;
} else {
tjjs.r = tscal, tjjs.i = 0.;
if (tscal == 1.) {
goto L210;
}
}
/* Compute x(j) = x(j) / A(j,j), scaling if necessary. */
tjj = (d__1 = tjjs.r, abs(d__1)) + (d__2 = d_imag(&tjjs),
abs(d__2));
if (tjj > smlnum) {
/* abs(A(j,j)) > SMLNUM: */
if (tjj < 1.) {
if (xj > tjj * bignum) {
/* Scale X by 1/abs(x(j)). */
rec = 1. / xj;
zdscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
i__3 = j;
zladiv_(&z__1, &x[j], &tjjs);
x[i__3].r = z__1.r, x[i__3].i = z__1.i;
} else if (tjj > 0.) {
/* 0 < abs(A(j,j)) <= SMLNUM: */
if (xj > tjj * bignum) {
/* Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM. */
rec = tjj * bignum / xj;
zdscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
i__3 = j;
zladiv_(&z__1, &x[j], &tjjs);
x[i__3].r = z__1.r, x[i__3].i = z__1.i;
} else {
/*
A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and
scale = 0 and compute a solution to A**H *x = 0.
*/
i__3 = *n;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__;
x[i__4].r = 0., x[i__4].i = 0.;
/* L200: */
}
i__3 = j;
x[i__3].r = 1., x[i__3].i = 0.;
*scale = 0.;
xmax = 0.;
}
L210:
;
} else {
/*
Compute x(j) := x(j) / A(j,j) - CSUMJ if the dot
product has already been divided by 1/A(j,j).
*/
i__3 = j;
zladiv_(&z__2, &x[j], &tjjs);
z__1.r = z__2.r - csumj.r, z__1.i = z__2.i - csumj.i;
x[i__3].r = z__1.r, x[i__3].i = z__1.i;
}
/* Computing MAX */
i__3 = j;
d__3 = xmax, d__4 = (d__1 = x[i__3].r, abs(d__1)) + (d__2 =
d_imag(&x[j]), abs(d__2));
xmax = max(d__3,d__4);
/* L220: */
}
}
*scale /= tscal;
}
/* Scale the column norms by 1/TSCAL for return. */
if (tscal != 1.) {
d__1 = 1. / tscal;
dscal_(n, &d__1, &cnorm[1], &c__1);
}
return 0;
/* End of ZLATRS */
} /* zlatrs_ */
/* Subroutine */ int zpotf2_(char *uplo, integer *n, doublecomplex *a,
integer *lda, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
doublereal d__1;
doublecomplex z__1, z__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static integer j;
static doublereal ajj;
extern logical lsame_(char *, char *);
extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *);
extern /* Subroutine */ int zgemv_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *);
static logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *), zdscal_(
integer *, doublereal *, doublecomplex *, integer *), zlacgv_(
integer *, doublecomplex *, integer *);
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZPOTF2 computes the Cholesky factorization of a complex Hermitian
positive definite matrix A.
The factorization has the form
A = U' * U , if UPLO = 'U', or
A = L * L', if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular.
This is the unblocked version of the algorithm, calling Level 2 BLAS.
Arguments
=========
UPLO (input) CHARACTER*1
Specifies whether the upper or lower triangular part of the
Hermitian matrix A is stored.
= 'U': Upper triangular
= 'L': Lower triangular
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading
n by n upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading n by n lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization A = U'*U or A = L*L'.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -k, the k-th argument had an illegal value
> 0: if INFO = k, the leading minor of order k is not
positive definite, and the factorization could not be
completed.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if ((! upper && ! lsame_(uplo, "L"))) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*n)) {
*info = -4;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZPOTF2", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
if (upper) {
/* Compute the Cholesky factorization A = U'*U. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Compute U(J,J) and test for non-positive-definiteness. */
i__2 = j + j * a_dim1;
d__1 = a[i__2].r;
i__3 = j - 1;
zdotc_(&z__2, &i__3, &a[j * a_dim1 + 1], &c__1, &a[j * a_dim1 + 1]
, &c__1);
z__1.r = d__1 - z__2.r, z__1.i = -z__2.i;
ajj = z__1.r;
if (ajj <= 0.) {
i__2 = j + j * a_dim1;
a[i__2].r = ajj, a[i__2].i = 0.;
goto L30;
}
ajj = sqrt(ajj);
i__2 = j + j * a_dim1;
a[i__2].r = ajj, a[i__2].i = 0.;
/* Compute elements J+1:N of row J. */
if (j < *n) {
i__2 = j - 1;
zlacgv_(&i__2, &a[j * a_dim1 + 1], &c__1);
i__2 = j - 1;
i__3 = *n - j;
z__1.r = -1., z__1.i = -0.;
zgemv_("Transpose", &i__2, &i__3, &z__1, &a[(j + 1) * a_dim1
+ 1], lda, &a[j * a_dim1 + 1], &c__1, &c_b60, &a[j + (
j + 1) * a_dim1], lda);
i__2 = j - 1;
zlacgv_(&i__2, &a[j * a_dim1 + 1], &c__1);
i__2 = *n - j;
d__1 = 1. / ajj;
zdscal_(&i__2, &d__1, &a[j + (j + 1) * a_dim1], lda);
}
/* L10: */
}
} else {
/* Compute the Cholesky factorization A = L*L'. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Compute L(J,J) and test for non-positive-definiteness. */
i__2 = j + j * a_dim1;
d__1 = a[i__2].r;
i__3 = j - 1;
zdotc_(&z__2, &i__3, &a[j + a_dim1], lda, &a[j + a_dim1], lda);
z__1.r = d__1 - z__2.r, z__1.i = -z__2.i;
ajj = z__1.r;
if (ajj <= 0.) {
i__2 = j + j * a_dim1;
a[i__2].r = ajj, a[i__2].i = 0.;
goto L30;
}
ajj = sqrt(ajj);
i__2 = j + j * a_dim1;
a[i__2].r = ajj, a[i__2].i = 0.;
/* Compute elements J+1:N of column J. */
if (j < *n) {
i__2 = j - 1;
zlacgv_(&i__2, &a[j + a_dim1], lda);
i__2 = *n - j;
i__3 = j - 1;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__2, &i__3, &z__1, &a[j + 1 + a_dim1]
, lda, &a[j + a_dim1], lda, &c_b60, &a[j + 1 + j *
a_dim1], &c__1);
i__2 = j - 1;
zlacgv_(&i__2, &a[j + a_dim1], lda);
i__2 = *n - j;
d__1 = 1. / ajj;
zdscal_(&i__2, &d__1, &a[j + 1 + j * a_dim1], &c__1);
}
/* L20: */
}
}
goto L40;
L30:
*info = j;
L40:
return 0;
/* End of ZPOTF2 */
} /* zpotf2_ */
/* Subroutine */ int zpotrf_(char *uplo, integer *n, doublecomplex *a,
integer *lda, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
doublecomplex z__1;
/* Local variables */
static integer j, jb, nb;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *,
integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *), zherk_(char *, char *, integer *,
integer *, doublereal *, doublecomplex *, integer *, doublereal *,
doublecomplex *, integer *);
static logical upper;
extern /* Subroutine */ int ztrsm_(char *, char *, char *, char *,
integer *, integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *),
zpotf2_(char *, integer *, doublecomplex *, integer *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZPOTRF computes the Cholesky factorization of a complex Hermitian
positive definite matrix A.
The factorization has the form
A = U**H * U, if UPLO = 'U', or
A = L * L**H, if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular.
This is the block version of the algorithm, calling Level 3 BLAS.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading
N-by-N upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization A = U**H*U or A = L*L**H.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if ((! upper && ! lsame_(uplo, "L"))) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*n)) {
*info = -4;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZPOTRF", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Determine the block size for this environment. */
nb = ilaenv_(&c__1, "ZPOTRF", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (
ftnlen)1);
if (nb <= 1 || nb >= *n) {
/* Use unblocked code. */
zpotf2_(uplo, n, &a[a_offset], lda, info);
} else {
/* Use blocked code. */
if (upper) {
/* Compute the Cholesky factorization A = U'*U. */
i__1 = *n;
i__2 = nb;
for (j = 1; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
/*
Update and factorize the current diagonal block and test
for non-positive-definiteness.
Computing MIN
*/
i__3 = nb, i__4 = *n - j + 1;
jb = min(i__3,i__4);
i__3 = j - 1;
zherk_("Upper", "Conjugate transpose", &jb, &i__3, &c_b1294, &
a[j * a_dim1 + 1], lda, &c_b1015, &a[j + j * a_dim1],
lda);
zpotf2_("Upper", &jb, &a[j + j * a_dim1], lda, info);
if (*info != 0) {
goto L30;
}
if (j + jb <= *n) {
/* Compute the current block row. */
i__3 = *n - j - jb + 1;
i__4 = j - 1;
z__1.r = -1., z__1.i = -0.;
zgemm_("Conjugate transpose", "No transpose", &jb, &i__3,
&i__4, &z__1, &a[j * a_dim1 + 1], lda, &a[(j + jb)
* a_dim1 + 1], lda, &c_b60, &a[j + (j + jb) *
a_dim1], lda);
i__3 = *n - j - jb + 1;
ztrsm_("Left", "Upper", "Conjugate transpose", "Non-unit",
&jb, &i__3, &c_b60, &a[j + j * a_dim1], lda, &a[
j + (j + jb) * a_dim1], lda);
}
/* L10: */
}
} else {
/* Compute the Cholesky factorization A = L*L'. */
i__2 = *n;
i__1 = nb;
for (j = 1; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) {
/*
Update and factorize the current diagonal block and test
for non-positive-definiteness.
Computing MIN
*/
i__3 = nb, i__4 = *n - j + 1;
jb = min(i__3,i__4);
i__3 = j - 1;
zherk_("Lower", "No transpose", &jb, &i__3, &c_b1294, &a[j +
a_dim1], lda, &c_b1015, &a[j + j * a_dim1], lda);
zpotf2_("Lower", &jb, &a[j + j * a_dim1], lda, info);
if (*info != 0) {
goto L30;
}
if (j + jb <= *n) {
/* Compute the current block column. */
i__3 = *n - j - jb + 1;
i__4 = j - 1;
z__1.r = -1., z__1.i = -0.;
zgemm_("No transpose", "Conjugate transpose", &i__3, &jb,
&i__4, &z__1, &a[j + jb + a_dim1], lda, &a[j +
a_dim1], lda, &c_b60, &a[j + jb + j * a_dim1],
lda);
i__3 = *n - j - jb + 1;
ztrsm_("Right", "Lower", "Conjugate transpose", "Non-unit"
, &i__3, &jb, &c_b60, &a[j + j * a_dim1], lda, &a[
j + jb + j * a_dim1], lda);
}
/* L20: */
}
}
}
goto L40;
L30:
*info = *info + j - 1;
L40:
return 0;
/* End of ZPOTRF */
} /* zpotrf_ */
/* Subroutine */ int zstedc_(char *compz, integer *n, doublereal *d__,
doublereal *e, doublecomplex *z__, integer *ldz, doublecomplex *work,
integer *lwork, doublereal *rwork, integer *lrwork, integer *iwork,
integer *liwork, integer *info)
{
/* System generated locals */
integer z_dim1, z_offset, i__1, i__2, i__3, i__4;
doublereal d__1, d__2;
/* Builtin functions */
double log(doublereal);
integer pow_ii(integer *, integer *);
double sqrt(doublereal);
/* Local variables */
static integer i__, j, k, m;
static doublereal p;
static integer ii, ll, end, lgn;
static doublereal eps, tiny;
extern logical lsame_(char *, char *);
static integer lwmin, start;
extern /* Subroutine */ int zswap_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *), zlaed0_(integer *, integer *,
doublereal *, doublereal *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, integer *, integer *);
extern /* Subroutine */ int dlascl_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublereal *,
integer *, integer *), dstedc_(char *, integer *,
doublereal *, doublereal *, doublereal *, integer *, doublereal *,
integer *, integer *, integer *, integer *), dlaset_(
char *, integer *, integer *, doublereal *, doublereal *,
doublereal *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *);
extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *,
integer *), zlacrm_(integer *, integer *, doublecomplex *,
integer *, doublereal *, integer *, doublecomplex *, integer *,
doublereal *);
static integer liwmin, icompz;
extern /* Subroutine */ int dsteqr_(char *, integer *, doublereal *,
doublereal *, doublereal *, integer *, doublereal *, integer *), zlacpy_(char *, integer *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *);
static doublereal orgnrm;
static integer lrwmin;
static logical lquery;
static integer smlsiz;
extern /* Subroutine */ int zsteqr_(char *, integer *, doublereal *,
doublereal *, doublecomplex *, integer *, doublereal *, integer *);
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZSTEDC computes all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the divide and conquer method.
The eigenvectors of a full or band complex Hermitian matrix can also
be found if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this
matrix to tridiagonal form.
This code makes very mild assumptions about floating point
arithmetic. It will work on machines with a guard digit in
add/subtract, or on those binary machines without guard digits
which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none. See DLAED3 for details.
Arguments
=========
COMPZ (input) CHARACTER*1
= 'N': Compute eigenvalues only.
= 'I': Compute eigenvectors of tridiagonal matrix also.
= 'V': Compute eigenvectors of original Hermitian matrix
also. On entry, Z contains the unitary matrix used
to reduce the original matrix to tridiagonal form.
N (input) INTEGER
The dimension of the symmetric tridiagonal matrix. N >= 0.
D (input/output) DOUBLE PRECISION array, dimension (N)
On entry, the diagonal elements of the tridiagonal matrix.
On exit, if INFO = 0, the eigenvalues in ascending order.
E (input/output) DOUBLE PRECISION array, dimension (N-1)
On entry, the subdiagonal elements of the tridiagonal matrix.
On exit, E has been destroyed.
Z (input/output) COMPLEX*16 array, dimension (LDZ,N)
On entry, if COMPZ = 'V', then Z contains the unitary
matrix used in the reduction to tridiagonal form.
On exit, if INFO = 0, then if COMPZ = 'V', Z contains the
orthonormal eigenvectors of the original Hermitian matrix,
and if COMPZ = 'I', Z contains the orthonormal eigenvectors
of the symmetric tridiagonal matrix.
If COMPZ = 'N', then Z is not referenced.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1.
If eigenvectors are desired, then LDZ >= max(1,N).
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK.
If COMPZ = 'N' or 'I', or N <= 1, LWORK must be at least 1.
If COMPZ = 'V' and N > 1, LWORK must be at least N*N.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
RWORK (workspace/output) DOUBLE PRECISION array,
dimension (LRWORK)
On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
LRWORK (input) INTEGER
The dimension of the array RWORK.
If COMPZ = 'N' or N <= 1, LRWORK must be at least 1.
If COMPZ = 'V' and N > 1, LRWORK must be at least
1 + 3*N + 2*N*lg N + 3*N**2 ,
where lg( N ) = smallest integer k such
that 2**k >= N.
If COMPZ = 'I' and N > 1, LRWORK must be at least
1 + 4*N + 2*N**2 .
If LRWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal size of the RWORK array,
returns this value as the first entry of the RWORK array, and
no error message related to LRWORK is issued by XERBLA.
IWORK (workspace/output) INTEGER array, dimension (LIWORK)
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
LIWORK (input) INTEGER
The dimension of the array IWORK.
If COMPZ = 'N' or N <= 1, LIWORK must be at least 1.
If COMPZ = 'V' or N > 1, LIWORK must be at least
6 + 6*N + 5*N*lg N.
If COMPZ = 'I' or N > 1, LIWORK must be at least
3 + 5*N .
If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal size of the IWORK array,
returns this value as the first entry of the IWORK array, and
no error message related to LIWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: The algorithm failed to compute an eigenvalue while
working on the submatrix lying in rows and columns
INFO/(N+1) through mod(INFO,N+1).
Further Details
===============
Based on contributions by
Jeff Rutter, Computer Science Division, University of California
at Berkeley, USA
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
--d__;
--e;
z_dim1 = *ldz;
z_offset = 1 + z_dim1 * 1;
z__ -= z_offset;
--work;
--rwork;
--iwork;
/* Function Body */
*info = 0;
lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1;
if (lsame_(compz, "N")) {
icompz = 0;
} else if (lsame_(compz, "V")) {
icompz = 1;
} else if (lsame_(compz, "I")) {
icompz = 2;
} else {
icompz = -1;
}
if (*n <= 1 || icompz <= 0) {
lwmin = 1;
liwmin = 1;
lrwmin = 1;
} else {
lgn = (integer) (log((doublereal) (*n)) / log(2.));
if (pow_ii(&c__2, &lgn) < *n) {
++lgn;
}
if (pow_ii(&c__2, &lgn) < *n) {
++lgn;
}
if (icompz == 1) {
lwmin = *n * *n;
/* Computing 2nd power */
i__1 = *n;
lrwmin = *n * 3 + 1 + ((*n) << (1)) * lgn + i__1 * i__1 * 3;
liwmin = *n * 6 + 6 + *n * 5 * lgn;
} else if (icompz == 2) {
lwmin = 1;
/* Computing 2nd power */
i__1 = *n;
lrwmin = ((*n) << (2)) + 1 + ((i__1 * i__1) << (1));
liwmin = *n * 5 + 3;
}
}
if (icompz < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*ldz < 1 || (icompz > 0 && *ldz < max(1,*n))) {
*info = -6;
} else if ((*lwork < lwmin && ! lquery)) {
*info = -8;
} else if ((*lrwork < lrwmin && ! lquery)) {
*info = -10;
} else if ((*liwork < liwmin && ! lquery)) {
*info = -12;
}
if (*info == 0) {
work[1].r = (doublereal) lwmin, work[1].i = 0.;
rwork[1] = (doublereal) lrwmin;
iwork[1] = liwmin;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZSTEDC", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
if (*n == 1) {
if (icompz != 0) {
i__1 = z_dim1 + 1;
z__[i__1].r = 1., z__[i__1].i = 0.;
}
return 0;
}
smlsiz = ilaenv_(&c__9, "ZSTEDC", " ", &c__0, &c__0, &c__0, &c__0, (
ftnlen)6, (ftnlen)1);
/*
If the following conditional clause is removed, then the routine
will use the Divide and Conquer routine to compute only the
eigenvalues, which requires (3N + 3N**2) real workspace and
(2 + 5N + 2N lg(N)) integer workspace.
Since on many architectures DSTERF is much faster than any other
algorithm for finding eigenvalues only, it is used here
as the default.
If COMPZ = 'N', use DSTERF to compute the eigenvalues.
*/
if (icompz == 0) {
dsterf_(n, &d__[1], &e[1], info);
return 0;
}
/*
If N is smaller than the minimum divide size (SMLSIZ+1), then
solve the problem with another solver.
*/
if (*n <= smlsiz) {
if (icompz == 0) {
dsterf_(n, &d__[1], &e[1], info);
return 0;
} else if (icompz == 2) {
zsteqr_("I", n, &d__[1], &e[1], &z__[z_offset], ldz, &rwork[1],
info);
return 0;
} else {
zsteqr_("V", n, &d__[1], &e[1], &z__[z_offset], ldz, &rwork[1],
info);
return 0;
}
}
/* If COMPZ = 'I', we simply call DSTEDC instead. */
if (icompz == 2) {
dlaset_("Full", n, n, &c_b324, &c_b1015, &rwork[1], n);
ll = *n * *n + 1;
i__1 = *lrwork - ll + 1;
dstedc_("I", n, &d__[1], &e[1], &rwork[1], n, &rwork[ll], &i__1, &
iwork[1], liwork, info);
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * z_dim1;
i__4 = (j - 1) * *n + i__;
z__[i__3].r = rwork[i__4], z__[i__3].i = 0.;
/* L10: */
}
/* L20: */
}
return 0;
}
/*
From now on, only option left to be handled is COMPZ = 'V',
i.e. ICOMPZ = 1.
Scale.
*/
orgnrm = dlanst_("M", n, &d__[1], &e[1]);
if (orgnrm == 0.) {
return 0;
}
eps = EPSILON;
start = 1;
/* while ( START <= N ) */
L30:
if (start <= *n) {
/*
Let END be the position of the next subdiagonal entry such that
E( END ) <= TINY or END = N if no such subdiagonal exists. The
matrix identified by the elements between START and END
constitutes an independent sub-problem.
*/
end = start;
L40:
if (end < *n) {
tiny = eps * sqrt((d__1 = d__[end], abs(d__1))) * sqrt((d__2 =
d__[end + 1], abs(d__2)));
if ((d__1 = e[end], abs(d__1)) > tiny) {
++end;
goto L40;
}
}
/* (Sub) Problem determined. Compute its size and solve it. */
m = end - start + 1;
if (m > smlsiz) {
*info = smlsiz;
/* Scale. */
orgnrm = dlanst_("M", &m, &d__[start], &e[start]);
dlascl_("G", &c__0, &c__0, &orgnrm, &c_b1015, &m, &c__1, &d__[
start], &m, info);
i__1 = m - 1;
i__2 = m - 1;
dlascl_("G", &c__0, &c__0, &orgnrm, &c_b1015, &i__1, &c__1, &e[
start], &i__2, info);
zlaed0_(n, &m, &d__[start], &e[start], &z__[start * z_dim1 + 1],
ldz, &work[1], n, &rwork[1], &iwork[1], info);
if (*info > 0) {
*info = (*info / (m + 1) + start - 1) * (*n + 1) + *info % (m
+ 1) + start - 1;
return 0;
}
/* Scale back. */
dlascl_("G", &c__0, &c__0, &c_b1015, &orgnrm, &m, &c__1, &d__[
start], &m, info);
} else {
dsteqr_("I", &m, &d__[start], &e[start], &rwork[1], &m, &rwork[m *
m + 1], info);
zlacrm_(n, &m, &z__[start * z_dim1 + 1], ldz, &rwork[1], &m, &
work[1], n, &rwork[m * m + 1]);
zlacpy_("A", n, &m, &work[1], n, &z__[start * z_dim1 + 1], ldz);
if (*info > 0) {
*info = start * (*n + 1) + end;
return 0;
}
}
start = end + 1;
goto L30;
}
/*
endwhile
If the problem split any number of times, then the eigenvalues
will not be properly ordered. Here we permute the eigenvalues
(and the associated eigenvectors) into ascending order.
*/
if (m != *n) {
/* Use Selection Sort to minimize swaps of eigenvectors */
i__1 = *n;
for (ii = 2; ii <= i__1; ++ii) {
i__ = ii - 1;
k = i__;
p = d__[i__];
i__2 = *n;
for (j = ii; j <= i__2; ++j) {
if (d__[j] < p) {
k = j;
p = d__[j];
}
/* L50: */
}
if (k != i__) {
d__[k] = d__[i__];
d__[i__] = p;
zswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + 1],
&c__1);
}
/* L60: */
}
}
work[1].r = (doublereal) lwmin, work[1].i = 0.;
rwork[1] = (doublereal) lrwmin;
iwork[1] = liwmin;
return 0;
/* End of ZSTEDC */
} /* zstedc_ */
/* Subroutine */ int zsteqr_(char *compz, integer *n, doublereal *d__,
doublereal *e, doublecomplex *z__, integer *ldz, doublereal *work,
integer *info)
{
/* System generated locals */
integer z_dim1, z_offset, i__1, i__2;
doublereal d__1, d__2;
/* Builtin functions */
double sqrt(doublereal), d_sign(doublereal *, doublereal *);
/* Local variables */
static doublereal b, c__, f, g;
static integer i__, j, k, l, m;
static doublereal p, r__, s;
static integer l1, ii, mm, lm1, mm1, nm1;
static doublereal rt1, rt2, eps;
static integer lsv;
static doublereal tst, eps2;
static integer lend, jtot;
extern /* Subroutine */ int dlae2_(doublereal *, doublereal *, doublereal
*, doublereal *, doublereal *);
extern logical lsame_(char *, char *);
static doublereal anorm;
extern /* Subroutine */ int zlasr_(char *, char *, char *, integer *,
integer *, doublereal *, doublereal *, doublecomplex *, integer *), zswap_(integer *, doublecomplex *,
integer *, doublecomplex *, integer *), dlaev2_(doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *);
static integer lendm1, lendp1;
static integer iscale;
extern /* Subroutine */ int dlascl_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublereal *,
integer *, integer *);
static doublereal safmin;
extern /* Subroutine */ int dlartg_(doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *);
static doublereal safmax;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *);
extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *,
integer *);
static integer lendsv;
static doublereal ssfmin;
static integer nmaxit, icompz;
static doublereal ssfmax;
extern /* Subroutine */ int zlaset_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *);
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZSTEQR computes all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the implicit QL or QR method.
The eigenvectors of a full or band complex Hermitian matrix can also
be found if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this
matrix to tridiagonal form.
Arguments
=========
COMPZ (input) CHARACTER*1
= 'N': Compute eigenvalues only.
= 'V': Compute eigenvalues and eigenvectors of the original
Hermitian matrix. On entry, Z must contain the
unitary matrix used to reduce the original matrix
to tridiagonal form.
= 'I': Compute eigenvalues and eigenvectors of the
tridiagonal matrix. Z is initialized to the identity
matrix.
N (input) INTEGER
The order of the matrix. N >= 0.
D (input/output) DOUBLE PRECISION array, dimension (N)
On entry, the diagonal elements of the tridiagonal matrix.
On exit, if INFO = 0, the eigenvalues in ascending order.
E (input/output) DOUBLE PRECISION array, dimension (N-1)
On entry, the (n-1) subdiagonal elements of the tridiagonal
matrix.
On exit, E has been destroyed.
Z (input/output) COMPLEX*16 array, dimension (LDZ, N)
On entry, if COMPZ = 'V', then Z contains the unitary
matrix used in the reduction to tridiagonal form.
On exit, if INFO = 0, then if COMPZ = 'V', Z contains the
orthonormal eigenvectors of the original Hermitian matrix,
and if COMPZ = 'I', Z contains the orthonormal eigenvectors
of the symmetric tridiagonal matrix.
If COMPZ = 'N', then Z is not referenced.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
eigenvectors are desired, then LDZ >= max(1,N).
WORK (workspace) DOUBLE PRECISION array, dimension (max(1,2*N-2))
If COMPZ = 'N', then WORK is not referenced.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: the algorithm has failed to find all the eigenvalues in
a total of 30*N iterations; if INFO = i, then i
elements of E have not converged to zero; on exit, D
and E contain the elements of a symmetric tridiagonal
matrix which is unitarily similar to the original
matrix.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
--d__;
--e;
z_dim1 = *ldz;
z_offset = 1 + z_dim1 * 1;
z__ -= z_offset;
--work;
/* Function Body */
*info = 0;
if (lsame_(compz, "N")) {
icompz = 0;
} else if (lsame_(compz, "V")) {
icompz = 1;
} else if (lsame_(compz, "I")) {
icompz = 2;
} else {
icompz = -1;
}
if (icompz < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*ldz < 1 || (icompz > 0 && *ldz < max(1,*n))) {
*info = -6;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZSTEQR", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
if (*n == 1) {
if (icompz == 2) {
i__1 = z_dim1 + 1;
z__[i__1].r = 1., z__[i__1].i = 0.;
}
return 0;
}
/* Determine the unit roundoff and over/underflow thresholds. */
eps = EPSILON;
/* Computing 2nd power */
d__1 = eps;
eps2 = d__1 * d__1;
safmin = SAFEMINIMUM;
safmax = 1. / safmin;
ssfmax = sqrt(safmax) / 3.;
ssfmin = sqrt(safmin) / eps2;
/*
Compute the eigenvalues and eigenvectors of the tridiagonal
matrix.
*/
if (icompz == 2) {
zlaset_("Full", n, n, &c_b59, &c_b60, &z__[z_offset], ldz);
}
nmaxit = *n * 30;
jtot = 0;
/*
Determine where the matrix splits and choose QL or QR iteration
for each block, according to whether top or bottom diagonal
element is smaller.
*/
l1 = 1;
nm1 = *n - 1;
L10:
if (l1 > *n) {
goto L160;
}
if (l1 > 1) {
e[l1 - 1] = 0.;
}
if (l1 <= nm1) {
i__1 = nm1;
for (m = l1; m <= i__1; ++m) {
tst = (d__1 = e[m], abs(d__1));
if (tst == 0.) {
goto L30;
}
if (tst <= sqrt((d__1 = d__[m], abs(d__1))) * sqrt((d__2 = d__[m
+ 1], abs(d__2))) * eps) {
e[m] = 0.;
goto L30;
}
/* L20: */
}
}
m = *n;
L30:
l = l1;
lsv = l;
lend = m;
lendsv = lend;
l1 = m + 1;
if (lend == l) {
goto L10;
}
/* Scale submatrix in rows and columns L to LEND */
i__1 = lend - l + 1;
anorm = dlanst_("I", &i__1, &d__[l], &e[l]);
iscale = 0;
if (anorm == 0.) {
goto L10;
}
if (anorm > ssfmax) {
iscale = 1;
i__1 = lend - l + 1;
dlascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n,
info);
i__1 = lend - l;
dlascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n,
info);
} else if (anorm < ssfmin) {
iscale = 2;
i__1 = lend - l + 1;
dlascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n,
info);
i__1 = lend - l;
dlascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n,
info);
}
/* Choose between QL and QR iteration */
if ((d__1 = d__[lend], abs(d__1)) < (d__2 = d__[l], abs(d__2))) {
lend = lsv;
l = lendsv;
}
if (lend > l) {
/*
QL Iteration
Look for small subdiagonal element.
*/
L40:
if (l != lend) {
lendm1 = lend - 1;
i__1 = lendm1;
for (m = l; m <= i__1; ++m) {
/* Computing 2nd power */
d__2 = (d__1 = e[m], abs(d__1));
tst = d__2 * d__2;
if (tst <= eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m
+ 1], abs(d__2)) + safmin) {
goto L60;
}
/* L50: */
}
}
m = lend;
L60:
if (m < lend) {
e[m] = 0.;
}
p = d__[l];
if (m == l) {
goto L80;
}
/*
If remaining matrix is 2-by-2, use DLAE2 or SLAEV2
to compute its eigensystem.
*/
if (m == l + 1) {
if (icompz > 0) {
dlaev2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2, &c__, &s);
work[l] = c__;
work[*n - 1 + l] = s;
zlasr_("R", "V", "B", n, &c__2, &work[l], &work[*n - 1 + l], &
z__[l * z_dim1 + 1], ldz);
} else {
dlae2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2);
}
d__[l] = rt1;
d__[l + 1] = rt2;
e[l] = 0.;
l += 2;
if (l <= lend) {
goto L40;
}
goto L140;
}
if (jtot == nmaxit) {
goto L140;
}
++jtot;
/* Form shift. */
g = (d__[l + 1] - p) / (e[l] * 2.);
r__ = dlapy2_(&g, &c_b1015);
g = d__[m] - p + e[l] / (g + d_sign(&r__, &g));
s = 1.;
c__ = 1.;
p = 0.;
/* Inner loop */
mm1 = m - 1;
i__1 = l;
for (i__ = mm1; i__ >= i__1; --i__) {
f = s * e[i__];
b = c__ * e[i__];
dlartg_(&g, &f, &c__, &s, &r__);
if (i__ != m - 1) {
e[i__ + 1] = r__;
}
g = d__[i__ + 1] - p;
r__ = (d__[i__] - g) * s + c__ * 2. * b;
p = s * r__;
d__[i__ + 1] = g + p;
g = c__ * r__ - b;
/* If eigenvectors are desired, then save rotations. */
if (icompz > 0) {
work[i__] = c__;
work[*n - 1 + i__] = -s;
}
/* L70: */
}
/* If eigenvectors are desired, then apply saved rotations. */
if (icompz > 0) {
mm = m - l + 1;
zlasr_("R", "V", "B", n, &mm, &work[l], &work[*n - 1 + l], &z__[l
* z_dim1 + 1], ldz);
}
d__[l] -= p;
e[l] = g;
goto L40;
/* Eigenvalue found. */
L80:
d__[l] = p;
++l;
if (l <= lend) {
goto L40;
}
goto L140;
} else {
/*
QR Iteration
Look for small superdiagonal element.
*/
L90:
if (l != lend) {
lendp1 = lend + 1;
i__1 = lendp1;
for (m = l; m >= i__1; --m) {
/* Computing 2nd power */
d__2 = (d__1 = e[m - 1], abs(d__1));
tst = d__2 * d__2;
if (tst <= eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m
- 1], abs(d__2)) + safmin) {
goto L110;
}
/* L100: */
}
}
m = lend;
L110:
if (m > lend) {
e[m - 1] = 0.;
}
p = d__[l];
if (m == l) {
goto L130;
}
/*
If remaining matrix is 2-by-2, use DLAE2 or SLAEV2
to compute its eigensystem.
*/
if (m == l - 1) {
if (icompz > 0) {
dlaev2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2, &c__, &s)
;
work[m] = c__;
work[*n - 1 + m] = s;
zlasr_("R", "V", "F", n, &c__2, &work[m], &work[*n - 1 + m], &
z__[(l - 1) * z_dim1 + 1], ldz);
} else {
dlae2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2);
}
d__[l - 1] = rt1;
d__[l] = rt2;
e[l - 1] = 0.;
l += -2;
if (l >= lend) {
goto L90;
}
goto L140;
}
if (jtot == nmaxit) {
goto L140;
}
++jtot;
/* Form shift. */
g = (d__[l - 1] - p) / (e[l - 1] * 2.);
r__ = dlapy2_(&g, &c_b1015);
g = d__[m] - p + e[l - 1] / (g + d_sign(&r__, &g));
s = 1.;
c__ = 1.;
p = 0.;
/* Inner loop */
lm1 = l - 1;
i__1 = lm1;
for (i__ = m; i__ <= i__1; ++i__) {
f = s * e[i__];
b = c__ * e[i__];
dlartg_(&g, &f, &c__, &s, &r__);
if (i__ != m) {
e[i__ - 1] = r__;
}
g = d__[i__] - p;
r__ = (d__[i__ + 1] - g) * s + c__ * 2. * b;
p = s * r__;
d__[i__] = g + p;
g = c__ * r__ - b;
/* If eigenvectors are desired, then save rotations. */
if (icompz > 0) {
work[i__] = c__;
work[*n - 1 + i__] = s;
}
/* L120: */
}
/* If eigenvectors are desired, then apply saved rotations. */
if (icompz > 0) {
mm = l - m + 1;
zlasr_("R", "V", "F", n, &mm, &work[m], &work[*n - 1 + m], &z__[m
* z_dim1 + 1], ldz);
}
d__[l] -= p;
e[lm1] = g;
goto L90;
/* Eigenvalue found. */
L130:
d__[l] = p;
--l;
if (l >= lend) {
goto L90;
}
goto L140;
}
/* Undo scaling if necessary */
L140:
if (iscale == 1) {
i__1 = lendsv - lsv + 1;
dlascl_("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv],
n, info);
i__1 = lendsv - lsv;
dlascl_("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &e[lsv], n,
info);
} else if (iscale == 2) {
i__1 = lendsv - lsv + 1;
dlascl_("G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv],
n, info);
i__1 = lendsv - lsv;
dlascl_("G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &e[lsv], n,
info);
}
/*
Check for no convergence to an eigenvalue after a total
of N*MAXIT iterations.
*/
if (jtot == nmaxit) {
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
if (e[i__] != 0.) {
++(*info);
}
/* L150: */
}
return 0;
}
goto L10;
/* Order eigenvalues and eigenvectors. */
L160:
if (icompz == 0) {
/* Use Quick Sort */
dlasrt_("I", n, &d__[1], info);
} else {
/* Use Selection Sort to minimize swaps of eigenvectors */
i__1 = *n;
for (ii = 2; ii <= i__1; ++ii) {
i__ = ii - 1;
k = i__;
p = d__[i__];
i__2 = *n;
for (j = ii; j <= i__2; ++j) {
if (d__[j] < p) {
k = j;
p = d__[j];
}
/* L170: */
}
if (k != i__) {
d__[k] = d__[i__];
d__[i__] = p;
zswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + 1],
&c__1);
}
/* L180: */
}
}
return 0;
/* End of ZSTEQR */
} /* zsteqr_ */
/* Subroutine */ int ztrevc_(char *side, char *howmny, logical *select,
integer *n, doublecomplex *t, integer *ldt, doublecomplex *vl,
integer *ldvl, doublecomplex *vr, integer *ldvr, integer *mm, integer
*m, doublecomplex *work, doublereal *rwork, integer *info)
{
/* System generated locals */
integer t_dim1, t_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1,
i__2, i__3, i__4, i__5;
doublereal d__1, d__2, d__3;
doublecomplex z__1, z__2;
/* Builtin functions */
double d_imag(doublecomplex *);
void d_cnjg(doublecomplex *, doublecomplex *);
/* Local variables */
static integer i__, j, k, ii, ki, is;
static doublereal ulp;
static logical allv;
static doublereal unfl, ovfl, smin;
static logical over;
static doublereal scale;
extern logical lsame_(char *, char *);
static doublereal remax;
static logical leftv, bothv;
extern /* Subroutine */ int zgemv_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *);
static logical somev;
extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *), dlabad_(doublereal *, doublereal *);
extern /* Subroutine */ int xerbla_(char *, integer *), zdscal_(
integer *, doublereal *, doublecomplex *, integer *);
extern integer izamax_(integer *, doublecomplex *, integer *);
static logical rightv;
extern doublereal dzasum_(integer *, doublecomplex *, integer *);
static doublereal smlnum;
extern /* Subroutine */ int zlatrs_(char *, char *, char *, char *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublereal *, doublereal *, integer *);
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZTREVC computes some or all of the right and/or left eigenvectors of
a complex upper triangular matrix T.
The right eigenvector x and the left eigenvector y of T corresponding
to an eigenvalue w are defined by:
T*x = w*x, y'*T = w*y'
where y' denotes the conjugate transpose of the vector y.
If all eigenvectors are requested, the routine may either return the
matrices X and/or Y of right or left eigenvectors of T, or the
products Q*X and/or Q*Y, where Q is an input unitary
matrix. If T was obtained from the Schur factorization of an
original matrix A = Q*T*Q', then Q*X and Q*Y are the matrices of
right or left eigenvectors of A.
Arguments
=========
SIDE (input) CHARACTER*1
= 'R': compute right eigenvectors only;
= 'L': compute left eigenvectors only;
= 'B': compute both right and left eigenvectors.
HOWMNY (input) CHARACTER*1
= 'A': compute all right and/or left eigenvectors;
= 'B': compute all right and/or left eigenvectors,
and backtransform them using the input matrices
supplied in VR and/or VL;
= 'S': compute selected right and/or left eigenvectors,
specified by the logical array SELECT.
SELECT (input) LOGICAL array, dimension (N)
If HOWMNY = 'S', SELECT specifies the eigenvectors to be
computed.
If HOWMNY = 'A' or 'B', SELECT is not referenced.
To select the eigenvector corresponding to the j-th
eigenvalue, SELECT(j) must be set to .TRUE..
N (input) INTEGER
The order of the matrix T. N >= 0.
T (input/output) COMPLEX*16 array, dimension (LDT,N)
The upper triangular matrix T. T is modified, but restored
on exit.
LDT (input) INTEGER
The leading dimension of the array T. LDT >= max(1,N).
VL (input/output) COMPLEX*16 array, dimension (LDVL,MM)
On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must
contain an N-by-N matrix Q (usually the unitary matrix Q of
Schur vectors returned by ZHSEQR).
On exit, if SIDE = 'L' or 'B', VL contains:
if HOWMNY = 'A', the matrix Y of left eigenvectors of T;
VL is lower triangular. The i-th column
VL(i) of VL is the eigenvector corresponding
to T(i,i).
if HOWMNY = 'B', the matrix Q*Y;
if HOWMNY = 'S', the left eigenvectors of T specified by
SELECT, stored consecutively in the columns
of VL, in the same order as their
eigenvalues.
If SIDE = 'R', VL is not referenced.
LDVL (input) INTEGER
The leading dimension of the array VL. LDVL >= max(1,N) if
SIDE = 'L' or 'B'; LDVL >= 1 otherwise.
VR (input/output) COMPLEX*16 array, dimension (LDVR,MM)
On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must
contain an N-by-N matrix Q (usually the unitary matrix Q of
Schur vectors returned by ZHSEQR).
On exit, if SIDE = 'R' or 'B', VR contains:
if HOWMNY = 'A', the matrix X of right eigenvectors of T;
VR is upper triangular. The i-th column
VR(i) of VR is the eigenvector corresponding
to T(i,i).
if HOWMNY = 'B', the matrix Q*X;
if HOWMNY = 'S', the right eigenvectors of T specified by
SELECT, stored consecutively in the columns
of VR, in the same order as their
eigenvalues.
If SIDE = 'L', VR is not referenced.
LDVR (input) INTEGER
The leading dimension of the array VR. LDVR >= max(1,N) if
SIDE = 'R' or 'B'; LDVR >= 1 otherwise.
MM (input) INTEGER
The number of columns in the arrays VL and/or VR. MM >= M.
M (output) INTEGER
The number of columns in the arrays VL and/or VR actually
used to store the eigenvectors. If HOWMNY = 'A' or 'B', M
is set to N. Each selected eigenvector occupies one
column.
WORK (workspace) COMPLEX*16 array, dimension (2*N)
RWORK (workspace) DOUBLE PRECISION array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Further Details
===============
The algorithm used in this program is basically backward (forward)
substitution, with scaling to make the the code robust against
possible overflow.
Each eigenvector is normalized so that the element of largest
magnitude has magnitude 1; here the magnitude of a complex number
(x,y) is taken to be |x| + |y|.
=====================================================================
Decode and test the input parameters
*/
/* Parameter adjustments */
--select;
t_dim1 = *ldt;
t_offset = 1 + t_dim1 * 1;
t -= t_offset;
vl_dim1 = *ldvl;
vl_offset = 1 + vl_dim1 * 1;
vl -= vl_offset;
vr_dim1 = *ldvr;
vr_offset = 1 + vr_dim1 * 1;
vr -= vr_offset;
--work;
--rwork;
/* Function Body */
bothv = lsame_(side, "B");
rightv = lsame_(side, "R") || bothv;
leftv = lsame_(side, "L") || bothv;
allv = lsame_(howmny, "A");
over = lsame_(howmny, "B");
somev = lsame_(howmny, "S");
/*
Set M to the number of columns required to store the selected
eigenvectors.
*/
if (somev) {
*m = 0;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (select[j]) {
++(*m);
}
/* L10: */
}
} else {
*m = *n;
}
*info = 0;
if ((! rightv && ! leftv)) {
*info = -1;
} else if (((! allv && ! over) && ! somev)) {
*info = -2;
} else if (*n < 0) {
*info = -4;
} else if (*ldt < max(1,*n)) {
*info = -6;
} else if (*ldvl < 1 || (leftv && *ldvl < *n)) {
*info = -8;
} else if (*ldvr < 1 || (rightv && *ldvr < *n)) {
*info = -10;
} else if (*mm < *m) {
*info = -11;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZTREVC", &i__1);
return 0;
}
/* Quick return if possible. */
if (*n == 0) {
return 0;
}
/* Set the constants to control overflow. */
unfl = SAFEMINIMUM;
ovfl = 1. / unfl;
dlabad_(&unfl, &ovfl);
ulp = PRECISION;
smlnum = unfl * (*n / ulp);
/* Store the diagonal elements of T in working array WORK. */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + *n;
i__3 = i__ + i__ * t_dim1;
work[i__2].r = t[i__3].r, work[i__2].i = t[i__3].i;
/* L20: */
}
/*
Compute 1-norm of each column of strictly upper triangular
part of T to control overflow in triangular solver.
*/
rwork[1] = 0.;
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
i__2 = j - 1;
rwork[j] = dzasum_(&i__2, &t[j * t_dim1 + 1], &c__1);
/* L30: */
}
if (rightv) {
/* Compute right eigenvectors. */
is = *m;
for (ki = *n; ki >= 1; --ki) {
if (somev) {
if (! select[ki]) {
goto L80;
}
}
/* Computing MAX */
i__1 = ki + ki * t_dim1;
d__3 = ulp * ((d__1 = t[i__1].r, abs(d__1)) + (d__2 = d_imag(&t[
ki + ki * t_dim1]), abs(d__2)));
smin = max(d__3,smlnum);
work[1].r = 1., work[1].i = 0.;
/* Form right-hand side. */
i__1 = ki - 1;
for (k = 1; k <= i__1; ++k) {
i__2 = k;
i__3 = k + ki * t_dim1;
z__1.r = -t[i__3].r, z__1.i = -t[i__3].i;
work[i__2].r = z__1.r, work[i__2].i = z__1.i;
/* L40: */
}
/*
Solve the triangular system:
(T(1:KI-1,1:KI-1) - T(KI,KI))*X = SCALE*WORK.
*/
i__1 = ki - 1;
for (k = 1; k <= i__1; ++k) {
i__2 = k + k * t_dim1;
i__3 = k + k * t_dim1;
i__4 = ki + ki * t_dim1;
z__1.r = t[i__3].r - t[i__4].r, z__1.i = t[i__3].i - t[i__4]
.i;
t[i__2].r = z__1.r, t[i__2].i = z__1.i;
i__2 = k + k * t_dim1;
if ((d__1 = t[i__2].r, abs(d__1)) + (d__2 = d_imag(&t[k + k *
t_dim1]), abs(d__2)) < smin) {
i__3 = k + k * t_dim1;
t[i__3].r = smin, t[i__3].i = 0.;
}
/* L50: */
}
if (ki > 1) {
i__1 = ki - 1;
zlatrs_("Upper", "No transpose", "Non-unit", "Y", &i__1, &t[
t_offset], ldt, &work[1], &scale, &rwork[1], info);
i__1 = ki;
work[i__1].r = scale, work[i__1].i = 0.;
}
/* Copy the vector x or Q*x to VR and normalize. */
if (! over) {
zcopy_(&ki, &work[1], &c__1, &vr[is * vr_dim1 + 1], &c__1);
ii = izamax_(&ki, &vr[is * vr_dim1 + 1], &c__1);
i__1 = ii + is * vr_dim1;
remax = 1. / ((d__1 = vr[i__1].r, abs(d__1)) + (d__2 = d_imag(
&vr[ii + is * vr_dim1]), abs(d__2)));
zdscal_(&ki, &remax, &vr[is * vr_dim1 + 1], &c__1);
i__1 = *n;
for (k = ki + 1; k <= i__1; ++k) {
i__2 = k + is * vr_dim1;
vr[i__2].r = 0., vr[i__2].i = 0.;
/* L60: */
}
} else {
if (ki > 1) {
i__1 = ki - 1;
z__1.r = scale, z__1.i = 0.;
zgemv_("N", n, &i__1, &c_b60, &vr[vr_offset], ldvr, &work[
1], &c__1, &z__1, &vr[ki * vr_dim1 + 1], &c__1);
}
ii = izamax_(n, &vr[ki * vr_dim1 + 1], &c__1);
i__1 = ii + ki * vr_dim1;
remax = 1. / ((d__1 = vr[i__1].r, abs(d__1)) + (d__2 = d_imag(
&vr[ii + ki * vr_dim1]), abs(d__2)));
zdscal_(n, &remax, &vr[ki * vr_dim1 + 1], &c__1);
}
/* Set back the original diagonal elements of T. */
i__1 = ki - 1;
for (k = 1; k <= i__1; ++k) {
i__2 = k + k * t_dim1;
i__3 = k + *n;
t[i__2].r = work[i__3].r, t[i__2].i = work[i__3].i;
/* L70: */
}
--is;
L80:
;
}
}
if (leftv) {
/* Compute left eigenvectors. */
is = 1;
i__1 = *n;
for (ki = 1; ki <= i__1; ++ki) {
if (somev) {
if (! select[ki]) {
goto L130;
}
}
/* Computing MAX */
i__2 = ki + ki * t_dim1;
d__3 = ulp * ((d__1 = t[i__2].r, abs(d__1)) + (d__2 = d_imag(&t[
ki + ki * t_dim1]), abs(d__2)));
smin = max(d__3,smlnum);
i__2 = *n;
work[i__2].r = 1., work[i__2].i = 0.;
/* Form right-hand side. */
i__2 = *n;
for (k = ki + 1; k <= i__2; ++k) {
i__3 = k;
d_cnjg(&z__2, &t[ki + k * t_dim1]);
z__1.r = -z__2.r, z__1.i = -z__2.i;
work[i__3].r = z__1.r, work[i__3].i = z__1.i;
/* L90: */
}
/*
Solve the triangular system:
(T(KI+1:N,KI+1:N) - T(KI,KI))'*X = SCALE*WORK.
*/
i__2 = *n;
for (k = ki + 1; k <= i__2; ++k) {
i__3 = k + k * t_dim1;
i__4 = k + k * t_dim1;
i__5 = ki + ki * t_dim1;
z__1.r = t[i__4].r - t[i__5].r, z__1.i = t[i__4].i - t[i__5]
.i;
t[i__3].r = z__1.r, t[i__3].i = z__1.i;
i__3 = k + k * t_dim1;
if ((d__1 = t[i__3].r, abs(d__1)) + (d__2 = d_imag(&t[k + k *
t_dim1]), abs(d__2)) < smin) {
i__4 = k + k * t_dim1;
t[i__4].r = smin, t[i__4].i = 0.;
}
/* L100: */
}
if (ki < *n) {
i__2 = *n - ki;
zlatrs_("Upper", "Conjugate transpose", "Non-unit", "Y", &
i__2, &t[ki + 1 + (ki + 1) * t_dim1], ldt, &work[ki +
1], &scale, &rwork[1], info);
i__2 = ki;
work[i__2].r = scale, work[i__2].i = 0.;
}
/* Copy the vector x or Q*x to VL and normalize. */
if (! over) {
i__2 = *n - ki + 1;
zcopy_(&i__2, &work[ki], &c__1, &vl[ki + is * vl_dim1], &c__1)
;
i__2 = *n - ki + 1;
ii = izamax_(&i__2, &vl[ki + is * vl_dim1], &c__1) + ki - 1;
i__2 = ii + is * vl_dim1;
remax = 1. / ((d__1 = vl[i__2].r, abs(d__1)) + (d__2 = d_imag(
&vl[ii + is * vl_dim1]), abs(d__2)));
i__2 = *n - ki + 1;
zdscal_(&i__2, &remax, &vl[ki + is * vl_dim1], &c__1);
i__2 = ki - 1;
for (k = 1; k <= i__2; ++k) {
i__3 = k + is * vl_dim1;
vl[i__3].r = 0., vl[i__3].i = 0.;
/* L110: */
}
} else {
if (ki < *n) {
i__2 = *n - ki;
z__1.r = scale, z__1.i = 0.;
zgemv_("N", n, &i__2, &c_b60, &vl[(ki + 1) * vl_dim1 + 1],
ldvl, &work[ki + 1], &c__1, &z__1, &vl[ki *
vl_dim1 + 1], &c__1);
}
ii = izamax_(n, &vl[ki * vl_dim1 + 1], &c__1);
i__2 = ii + ki * vl_dim1;
remax = 1. / ((d__1 = vl[i__2].r, abs(d__1)) + (d__2 = d_imag(
&vl[ii + ki * vl_dim1]), abs(d__2)));
zdscal_(n, &remax, &vl[ki * vl_dim1 + 1], &c__1);
}
/* Set back the original diagonal elements of T. */
i__2 = *n;
for (k = ki + 1; k <= i__2; ++k) {
i__3 = k + k * t_dim1;
i__4 = k + *n;
t[i__3].r = work[i__4].r, t[i__3].i = work[i__4].i;
/* L120: */
}
++is;
L130:
;
}
}
return 0;
/* End of ZTREVC */
} /* ztrevc_ */
/* Subroutine */ int zung2r_(integer *m, integer *n, integer *k,
doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
doublecomplex z__1;
/* Local variables */
static integer i__, j, l;
extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
doublecomplex *, integer *), zlarf_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, doublecomplex *), xerbla_(char *, integer *);
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZUNG2R generates an m by n complex matrix Q with orthonormal columns,
which is defined as the first n columns of a product of k elementary
reflectors of order m
Q = H(1) H(2) . . . H(k)
as returned by ZGEQRF.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix Q. M >= 0.
N (input) INTEGER
The number of columns of the matrix Q. M >= N >= 0.
K (input) INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the i-th column must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by ZGEQRF in the first k columns of its array
argument A.
On exit, the m by n matrix Q.
LDA (input) INTEGER
The first dimension of the array A. LDA >= max(1,M).
TAU (input) COMPLEX*16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGEQRF.
WORK (workspace) COMPLEX*16 array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument has an illegal value
=====================================================================
Test the input arguments
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
if (*m < 0) {
*info = -1;
} else if (*n < 0 || *n > *m) {
*info = -2;
} else if (*k < 0 || *k > *n) {
*info = -3;
} else if (*lda < max(1,*m)) {
*info = -5;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZUNG2R", &i__1);
return 0;
}
/* Quick return if possible */
if (*n <= 0) {
return 0;
}
/* Initialise columns k+1:n to columns of the unit matrix */
i__1 = *n;
for (j = *k + 1; j <= i__1; ++j) {
i__2 = *m;
for (l = 1; l <= i__2; ++l) {
i__3 = l + j * a_dim1;
a[i__3].r = 0., a[i__3].i = 0.;
/* L10: */
}
i__2 = j + j * a_dim1;
a[i__2].r = 1., a[i__2].i = 0.;
/* L20: */
}
for (i__ = *k; i__ >= 1; --i__) {
/* Apply H(i) to A(i:m,i:n) from the left */
if (i__ < *n) {
i__1 = i__ + i__ * a_dim1;
a[i__1].r = 1., a[i__1].i = 0.;
i__1 = *m - i__ + 1;
i__2 = *n - i__;
zlarf_("Left", &i__1, &i__2, &a[i__ + i__ * a_dim1], &c__1, &tau[
i__], &a[i__ + (i__ + 1) * a_dim1], lda, &work[1]);
}
if (i__ < *m) {
i__1 = *m - i__;
i__2 = i__;
z__1.r = -tau[i__2].r, z__1.i = -tau[i__2].i;
zscal_(&i__1, &z__1, &a[i__ + 1 + i__ * a_dim1], &c__1);
}
i__1 = i__ + i__ * a_dim1;
i__2 = i__;
z__1.r = 1. - tau[i__2].r, z__1.i = 0. - tau[i__2].i;
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
/* Set A(1:i-1,i) to zero */
i__1 = i__ - 1;
for (l = 1; l <= i__1; ++l) {
i__2 = l + i__ * a_dim1;
a[i__2].r = 0., a[i__2].i = 0.;
/* L30: */
}
/* L40: */
}
return 0;
/* End of ZUNG2R */
} /* zung2r_ */
/* Subroutine */ int zungbr_(char *vect, integer *m, integer *n, integer *k,
doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
/* Local variables */
static integer i__, j, nb, mn;
extern logical lsame_(char *, char *);
static integer iinfo;
static logical wantq;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
static integer lwkopt;
static logical lquery;
extern /* Subroutine */ int zunglq_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, integer *), zungqr_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, integer *);
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZUNGBR generates one of the complex unitary matrices Q or P**H
determined by ZGEBRD when reducing a complex matrix A to bidiagonal
form: A = Q * B * P**H. Q and P**H are defined as products of
elementary reflectors H(i) or G(i) respectively.
If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q
is of order M:
if m >= k, Q = H(1) H(2) . . . H(k) and ZUNGBR returns the first n
columns of Q, where m >= n >= k;
if m < k, Q = H(1) H(2) . . . H(m-1) and ZUNGBR returns Q as an
M-by-M matrix.
If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**H
is of order N:
if k < n, P**H = G(k) . . . G(2) G(1) and ZUNGBR returns the first m
rows of P**H, where n >= m >= k;
if k >= n, P**H = G(n-1) . . . G(2) G(1) and ZUNGBR returns P**H as
an N-by-N matrix.
Arguments
=========
VECT (input) CHARACTER*1
Specifies whether the matrix Q or the matrix P**H is
required, as defined in the transformation applied by ZGEBRD:
= 'Q': generate Q;
= 'P': generate P**H.
M (input) INTEGER
The number of rows of the matrix Q or P**H to be returned.
M >= 0.
N (input) INTEGER
The number of columns of the matrix Q or P**H to be returned.
N >= 0.
If VECT = 'Q', M >= N >= min(M,K);
if VECT = 'P', N >= M >= min(N,K).
K (input) INTEGER
If VECT = 'Q', the number of columns in the original M-by-K
matrix reduced by ZGEBRD.
If VECT = 'P', the number of rows in the original K-by-N
matrix reduced by ZGEBRD.
K >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the vectors which define the elementary reflectors,
as returned by ZGEBRD.
On exit, the M-by-N matrix Q or P**H.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= M.
TAU (input) COMPLEX*16 array, dimension
(min(M,K)) if VECT = 'Q'
(min(N,K)) if VECT = 'P'
TAU(i) must contain the scalar factor of the elementary
reflector H(i) or G(i), which determines Q or P**H, as
returned by ZGEBRD in its array argument TAUQ or TAUP.
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,min(M,N)).
For optimum performance LWORK >= min(M,N)*NB, where NB
is the optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
=====================================================================
Test the input arguments
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
wantq = lsame_(vect, "Q");
mn = min(*m,*n);
lquery = *lwork == -1;
if ((! wantq && ! lsame_(vect, "P"))) {
*info = -1;
} else if (*m < 0) {
*info = -2;
} else if (*n < 0 || (wantq && (*n > *m || *n < min(*m,*k))) || (! wantq
&& (*m > *n || *m < min(*n,*k)))) {
*info = -3;
} else if (*k < 0) {
*info = -4;
} else if (*lda < max(1,*m)) {
*info = -6;
} else if ((*lwork < max(1,mn) && ! lquery)) {
*info = -9;
}
if (*info == 0) {
if (wantq) {
nb = ilaenv_(&c__1, "ZUNGQR", " ", m, n, k, &c_n1, (ftnlen)6, (
ftnlen)1);
} else {
nb = ilaenv_(&c__1, "ZUNGLQ", " ", m, n, k, &c_n1, (ftnlen)6, (
ftnlen)1);
}
lwkopt = max(1,mn) * nb;
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZUNGBR", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0) {
work[1].r = 1., work[1].i = 0.;
return 0;
}
if (wantq) {
/*
Form Q, determined by a call to ZGEBRD to reduce an m-by-k
matrix
*/
if (*m >= *k) {
/* If m >= k, assume m >= n >= k */
zungqr_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], lwork, &
iinfo);
} else {
/*
If m < k, assume m = n
Shift the vectors which define the elementary reflectors one
column to the right, and set the first row and column of Q
to those of the unit matrix
*/
for (j = *m; j >= 2; --j) {
i__1 = j * a_dim1 + 1;
a[i__1].r = 0., a[i__1].i = 0.;
i__1 = *m;
for (i__ = j + 1; i__ <= i__1; ++i__) {
i__2 = i__ + j * a_dim1;
i__3 = i__ + (j - 1) * a_dim1;
a[i__2].r = a[i__3].r, a[i__2].i = a[i__3].i;
/* L10: */
}
/* L20: */
}
i__1 = a_dim1 + 1;
a[i__1].r = 1., a[i__1].i = 0.;
i__1 = *m;
for (i__ = 2; i__ <= i__1; ++i__) {
i__2 = i__ + a_dim1;
a[i__2].r = 0., a[i__2].i = 0.;
/* L30: */
}
if (*m > 1) {
/* Form Q(2:m,2:m) */
i__1 = *m - 1;
i__2 = *m - 1;
i__3 = *m - 1;
zungqr_(&i__1, &i__2, &i__3, &a[((a_dim1) << (1)) + 2], lda, &
tau[1], &work[1], lwork, &iinfo);
}
}
} else {
/*
Form P', determined by a call to ZGEBRD to reduce a k-by-n
matrix
*/
if (*k < *n) {
/* If k < n, assume k <= m <= n */
zunglq_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], lwork, &
iinfo);
} else {
/*
If k >= n, assume m = n
Shift the vectors which define the elementary reflectors one
row downward, and set the first row and column of P' to
those of the unit matrix
*/
i__1 = a_dim1 + 1;
a[i__1].r = 1., a[i__1].i = 0.;
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
i__2 = i__ + a_dim1;
a[i__2].r = 0., a[i__2].i = 0.;
/* L40: */
}
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
for (i__ = j - 1; i__ >= 2; --i__) {
i__2 = i__ + j * a_dim1;
i__3 = i__ - 1 + j * a_dim1;
a[i__2].r = a[i__3].r, a[i__2].i = a[i__3].i;
/* L50: */
}
i__2 = j * a_dim1 + 1;
a[i__2].r = 0., a[i__2].i = 0.;
/* L60: */
}
if (*n > 1) {
/* Form P'(2:n,2:n) */
i__1 = *n - 1;
i__2 = *n - 1;
i__3 = *n - 1;
zunglq_(&i__1, &i__2, &i__3, &a[((a_dim1) << (1)) + 2], lda, &
tau[1], &work[1], lwork, &iinfo);
}
}
}
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
return 0;
/* End of ZUNGBR */
} /* zungbr_ */
/* Subroutine */ int zunghr_(integer *n, integer *ilo, integer *ihi,
doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
/* Local variables */
static integer i__, j, nb, nh, iinfo;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
static integer lwkopt;
static logical lquery;
extern /* Subroutine */ int zungqr_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, integer *);
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZUNGHR generates a complex unitary matrix Q which is defined as the
product of IHI-ILO elementary reflectors of order N, as returned by
ZGEHRD:
Q = H(ilo) H(ilo+1) . . . H(ihi-1).
Arguments
=========
N (input) INTEGER
The order of the matrix Q. N >= 0.
ILO (input) INTEGER
IHI (input) INTEGER
ILO and IHI must have the same values as in the previous call
of ZGEHRD. Q is equal to the unit matrix except in the
submatrix Q(ilo+1:ihi,ilo+1:ihi).
1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the vectors which define the elementary reflectors,
as returned by ZGEHRD.
On exit, the N-by-N unitary matrix Q.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
TAU (input) COMPLEX*16 array, dimension (N-1)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGEHRD.
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= IHI-ILO.
For optimum performance LWORK >= (IHI-ILO)*NB, where NB is
the optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
=====================================================================
Test the input arguments
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
nh = *ihi - *ilo;
lquery = *lwork == -1;
if (*n < 0) {
*info = -1;
} else if (*ilo < 1 || *ilo > max(1,*n)) {
*info = -2;
} else if (*ihi < min(*ilo,*n) || *ihi > *n) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if ((*lwork < max(1,nh) && ! lquery)) {
*info = -8;
}
if (*info == 0) {
nb = ilaenv_(&c__1, "ZUNGQR", " ", &nh, &nh, &nh, &c_n1, (ftnlen)6, (
ftnlen)1);
lwkopt = max(1,nh) * nb;
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZUNGHR", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
work[1].r = 1., work[1].i = 0.;
return 0;
}
/*
Shift the vectors which define the elementary reflectors one
column to the right, and set the first ilo and the last n-ihi
rows and columns to those of the unit matrix
*/
i__1 = *ilo + 1;
for (j = *ihi; j >= i__1; --j) {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
a[i__3].r = 0., a[i__3].i = 0.;
/* L10: */
}
i__2 = *ihi;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__ + (j - 1) * a_dim1;
a[i__3].r = a[i__4].r, a[i__3].i = a[i__4].i;
/* L20: */
}
i__2 = *n;
for (i__ = *ihi + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
a[i__3].r = 0., a[i__3].i = 0.;
/* L30: */
}
/* L40: */
}
i__1 = *ilo;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
a[i__3].r = 0., a[i__3].i = 0.;
/* L50: */
}
i__2 = j + j * a_dim1;
a[i__2].r = 1., a[i__2].i = 0.;
/* L60: */
}
i__1 = *n;
for (j = *ihi + 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
a[i__3].r = 0., a[i__3].i = 0.;
/* L70: */
}
i__2 = j + j * a_dim1;
a[i__2].r = 1., a[i__2].i = 0.;
/* L80: */
}
if (nh > 0) {
/* Generate Q(ilo+1:ihi,ilo+1:ihi) */
zungqr_(&nh, &nh, &nh, &a[*ilo + 1 + (*ilo + 1) * a_dim1], lda, &tau[*
ilo], &work[1], lwork, &iinfo);
}
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
return 0;
/* End of ZUNGHR */
} /* zunghr_ */
/* Subroutine */ int zungl2_(integer *m, integer *n, integer *k,
doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
doublecomplex z__1, z__2;
/* Builtin functions */
void d_cnjg(doublecomplex *, doublecomplex *);
/* Local variables */
static integer i__, j, l;
extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
doublecomplex *, integer *), zlarf_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, doublecomplex *), xerbla_(char *, integer *), zlacgv_(integer *, doublecomplex *, integer *);
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZUNGL2 generates an m-by-n complex matrix Q with orthonormal rows,
which is defined as the first m rows of a product of k elementary
reflectors of order n
Q = H(k)' . . . H(2)' H(1)'
as returned by ZGELQF.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix Q. M >= 0.
N (input) INTEGER
The number of columns of the matrix Q. N >= M.
K (input) INTEGER
The number of elementary reflectors whose product defines the
matrix Q. M >= K >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the i-th row must contain the vector which defines
the elementary reflector H(i), for i = 1,2,...,k, as returned
by ZGELQF in the first k rows of its array argument A.
On exit, the m by n matrix Q.
LDA (input) INTEGER
The first dimension of the array A. LDA >= max(1,M).
TAU (input) COMPLEX*16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGELQF.
WORK (workspace) COMPLEX*16 array, dimension (M)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument has an illegal value
=====================================================================
Test the input arguments
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
if (*m < 0) {
*info = -1;
} else if (*n < *m) {
*info = -2;
} else if (*k < 0 || *k > *m) {
*info = -3;
} else if (*lda < max(1,*m)) {
*info = -5;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZUNGL2", &i__1);
return 0;
}
/* Quick return if possible */
if (*m <= 0) {
return 0;
}
if (*k < *m) {
/* Initialise rows k+1:m to rows of the unit matrix */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (l = *k + 1; l <= i__2; ++l) {
i__3 = l + j * a_dim1;
a[i__3].r = 0., a[i__3].i = 0.;
/* L10: */
}
if ((j > *k && j <= *m)) {
i__2 = j + j * a_dim1;
a[i__2].r = 1., a[i__2].i = 0.;
}
/* L20: */
}
}
for (i__ = *k; i__ >= 1; --i__) {
/* Apply H(i)' to A(i:m,i:n) from the right */
if (i__ < *n) {
i__1 = *n - i__;
zlacgv_(&i__1, &a[i__ + (i__ + 1) * a_dim1], lda);
if (i__ < *m) {
i__1 = i__ + i__ * a_dim1;
a[i__1].r = 1., a[i__1].i = 0.;
i__1 = *m - i__;
i__2 = *n - i__ + 1;
d_cnjg(&z__1, &tau[i__]);
zlarf_("Right", &i__1, &i__2, &a[i__ + i__ * a_dim1], lda, &
z__1, &a[i__ + 1 + i__ * a_dim1], lda, &work[1]);
}
i__1 = *n - i__;
i__2 = i__;
z__1.r = -tau[i__2].r, z__1.i = -tau[i__2].i;
zscal_(&i__1, &z__1, &a[i__ + (i__ + 1) * a_dim1], lda);
i__1 = *n - i__;
zlacgv_(&i__1, &a[i__ + (i__ + 1) * a_dim1], lda);
}
i__1 = i__ + i__ * a_dim1;
d_cnjg(&z__2, &tau[i__]);
z__1.r = 1. - z__2.r, z__1.i = 0. - z__2.i;
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
/* Set A(i,1:i-1) to zero */
i__1 = i__ - 1;
for (l = 1; l <= i__1; ++l) {
i__2 = i__ + l * a_dim1;
a[i__2].r = 0., a[i__2].i = 0.;
/* L30: */
}
/* L40: */
}
return 0;
/* End of ZUNGL2 */
} /* zungl2_ */
/* Subroutine */ int zunglq_(integer *m, integer *n, integer *k,
doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
/* Local variables */
static integer i__, j, l, ib, nb, ki, kk, nx, iws, nbmin, iinfo;
extern /* Subroutine */ int zungl2_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
static integer ldwork;
extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
static logical lquery;
static integer lwkopt;
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZUNGLQ generates an M-by-N complex matrix Q with orthonormal rows,
which is defined as the first M rows of a product of K elementary
reflectors of order N
Q = H(k)' . . . H(2)' H(1)'
as returned by ZGELQF.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix Q. M >= 0.
N (input) INTEGER
The number of columns of the matrix Q. N >= M.
K (input) INTEGER
The number of elementary reflectors whose product defines the
matrix Q. M >= K >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the i-th row must contain the vector which defines
the elementary reflector H(i), for i = 1,2,...,k, as returned
by ZGELQF in the first k rows of its array argument A.
On exit, the M-by-N matrix Q.
LDA (input) INTEGER
The first dimension of the array A. LDA >= max(1,M).
TAU (input) COMPLEX*16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGELQF.
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,M).
For optimum performance LWORK >= M*NB, where NB is
the optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit;
< 0: if INFO = -i, the i-th argument has an illegal value
=====================================================================
Test the input arguments
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
nb = ilaenv_(&c__1, "ZUNGLQ", " ", m, n, k, &c_n1, (ftnlen)6, (ftnlen)1);
lwkopt = max(1,*m) * nb;
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
lquery = *lwork == -1;
if (*m < 0) {
*info = -1;
} else if (*n < *m) {
*info = -2;
} else if (*k < 0 || *k > *m) {
*info = -3;
} else if (*lda < max(1,*m)) {
*info = -5;
} else if ((*lwork < max(1,*m) && ! lquery)) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZUNGLQ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*m <= 0) {
work[1].r = 1., work[1].i = 0.;
return 0;
}
nbmin = 2;
nx = 0;
iws = *m;
if ((nb > 1 && nb < *k)) {
/*
Determine when to cross over from blocked to unblocked code.
Computing MAX
*/
i__1 = 0, i__2 = ilaenv_(&c__3, "ZUNGLQ", " ", m, n, k, &c_n1, (
ftnlen)6, (ftnlen)1);
nx = max(i__1,i__2);
if (nx < *k) {
/* Determine if workspace is large enough for blocked code. */
ldwork = *m;
iws = ldwork * nb;
if (*lwork < iws) {
/*
Not enough workspace to use optimal NB: reduce NB and
determine the minimum value of NB.
*/
nb = *lwork / ldwork;
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "ZUNGLQ", " ", m, n, k, &c_n1,
(ftnlen)6, (ftnlen)1);
nbmin = max(i__1,i__2);
}
}
}
if (((nb >= nbmin && nb < *k) && nx < *k)) {
/*
Use blocked code after the last block.
The first kk rows are handled by the block method.
*/
ki = (*k - nx - 1) / nb * nb;
/* Computing MIN */
i__1 = *k, i__2 = ki + nb;
kk = min(i__1,i__2);
/* Set A(kk+1:m,1:kk) to zero. */
i__1 = kk;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = kk + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
a[i__3].r = 0., a[i__3].i = 0.;
/* L10: */
}
/* L20: */
}
} else {
kk = 0;
}
/* Use unblocked code for the last or only block. */
if (kk < *m) {
i__1 = *m - kk;
i__2 = *n - kk;
i__3 = *k - kk;
zungl2_(&i__1, &i__2, &i__3, &a[kk + 1 + (kk + 1) * a_dim1], lda, &
tau[kk + 1], &work[1], &iinfo);
}
if (kk > 0) {
/* Use blocked code */
i__1 = -nb;
for (i__ = ki + 1; i__1 < 0 ? i__ >= 1 : i__ <= 1; i__ += i__1) {
/* Computing MIN */
i__2 = nb, i__3 = *k - i__ + 1;
ib = min(i__2,i__3);
if (i__ + ib <= *m) {
/*
Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1)
*/
i__2 = *n - i__ + 1;
zlarft_("Forward", "Rowwise", &i__2, &ib, &a[i__ + i__ *
a_dim1], lda, &tau[i__], &work[1], &ldwork);
/* Apply H' to A(i+ib:m,i:n) from the right */
i__2 = *m - i__ - ib + 1;
i__3 = *n - i__ + 1;
zlarfb_("Right", "Conjugate transpose", "Forward", "Rowwise",
&i__2, &i__3, &ib, &a[i__ + i__ * a_dim1], lda, &work[
1], &ldwork, &a[i__ + ib + i__ * a_dim1], lda, &work[
ib + 1], &ldwork);
}
/* Apply H' to columns i:n of current block */
i__2 = *n - i__ + 1;
zungl2_(&ib, &i__2, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &
work[1], &iinfo);
/* Set columns 1:i-1 of current block to zero */
i__2 = i__ - 1;
for (j = 1; j <= i__2; ++j) {
i__3 = i__ + ib - 1;
for (l = i__; l <= i__3; ++l) {
i__4 = l + j * a_dim1;
a[i__4].r = 0., a[i__4].i = 0.;
/* L30: */
}
/* L40: */
}
/* L50: */
}
}
work[1].r = (doublereal) iws, work[1].i = 0.;
return 0;
/* End of ZUNGLQ */
} /* zunglq_ */
/* Subroutine */ int zungqr_(integer *m, integer *n, integer *k,
doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
/* Local variables */
static integer i__, j, l, ib, nb, ki, kk, nx, iws, nbmin, iinfo;
extern /* Subroutine */ int zung2r_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
static integer ldwork;
extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
static integer lwkopt;
static logical lquery;
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZUNGQR generates an M-by-N complex matrix Q with orthonormal columns,
which is defined as the first N columns of a product of K elementary
reflectors of order M
Q = H(1) H(2) . . . H(k)
as returned by ZGEQRF.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix Q. M >= 0.
N (input) INTEGER
The number of columns of the matrix Q. M >= N >= 0.
K (input) INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the i-th column must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by ZGEQRF in the first k columns of its array
argument A.
On exit, the M-by-N matrix Q.
LDA (input) INTEGER
The first dimension of the array A. LDA >= max(1,M).
TAU (input) COMPLEX*16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGEQRF.
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,N).
For optimum performance LWORK >= N*NB, where NB is the
optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument has an illegal value
=====================================================================
Test the input arguments
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
nb = ilaenv_(&c__1, "ZUNGQR", " ", m, n, k, &c_n1, (ftnlen)6, (ftnlen)1);
lwkopt = max(1,*n) * nb;
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
lquery = *lwork == -1;
if (*m < 0) {
*info = -1;
} else if (*n < 0 || *n > *m) {
*info = -2;
} else if (*k < 0 || *k > *n) {
*info = -3;
} else if (*lda < max(1,*m)) {
*info = -5;
} else if ((*lwork < max(1,*n) && ! lquery)) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZUNGQR", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n <= 0) {
work[1].r = 1., work[1].i = 0.;
return 0;
}
nbmin = 2;
nx = 0;
iws = *n;
if ((nb > 1 && nb < *k)) {
/*
Determine when to cross over from blocked to unblocked code.
Computing MAX
*/
i__1 = 0, i__2 = ilaenv_(&c__3, "ZUNGQR", " ", m, n, k, &c_n1, (
ftnlen)6, (ftnlen)1);
nx = max(i__1,i__2);
if (nx < *k) {
/* Determine if workspace is large enough for blocked code. */
ldwork = *n;
iws = ldwork * nb;
if (*lwork < iws) {
/*
Not enough workspace to use optimal NB: reduce NB and
determine the minimum value of NB.
*/
nb = *lwork / ldwork;
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "ZUNGQR", " ", m, n, k, &c_n1,
(ftnlen)6, (ftnlen)1);
nbmin = max(i__1,i__2);
}
}
}
if (((nb >= nbmin && nb < *k) && nx < *k)) {
/*
Use blocked code after the last block.
The first kk columns are handled by the block method.
*/
ki = (*k - nx - 1) / nb * nb;
/* Computing MIN */
i__1 = *k, i__2 = ki + nb;
kk = min(i__1,i__2);
/* Set A(1:kk,kk+1:n) to zero. */
i__1 = *n;
for (j = kk + 1; j <= i__1; ++j) {
i__2 = kk;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
a[i__3].r = 0., a[i__3].i = 0.;
/* L10: */
}
/* L20: */
}
} else {
kk = 0;
}
/* Use unblocked code for the last or only block. */
if (kk < *n) {
i__1 = *m - kk;
i__2 = *n - kk;
i__3 = *k - kk;
zung2r_(&i__1, &i__2, &i__3, &a[kk + 1 + (kk + 1) * a_dim1], lda, &
tau[kk + 1], &work[1], &iinfo);
}
if (kk > 0) {
/* Use blocked code */
i__1 = -nb;
for (i__ = ki + 1; i__1 < 0 ? i__ >= 1 : i__ <= 1; i__ += i__1) {
/* Computing MIN */
i__2 = nb, i__3 = *k - i__ + 1;
ib = min(i__2,i__3);
if (i__ + ib <= *n) {
/*
Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1)
*/
i__2 = *m - i__ + 1;
zlarft_("Forward", "Columnwise", &i__2, &ib, &a[i__ + i__ *
a_dim1], lda, &tau[i__], &work[1], &ldwork);
/* Apply H to A(i:m,i+ib:n) from the left */
i__2 = *m - i__ + 1;
i__3 = *n - i__ - ib + 1;
zlarfb_("Left", "No transpose", "Forward", "Columnwise", &
i__2, &i__3, &ib, &a[i__ + i__ * a_dim1], lda, &work[
1], &ldwork, &a[i__ + (i__ + ib) * a_dim1], lda, &
work[ib + 1], &ldwork);
}
/* Apply H to rows i:m of current block */
i__2 = *m - i__ + 1;
zung2r_(&i__2, &ib, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &
work[1], &iinfo);
/* Set rows 1:i-1 of current block to zero */
i__2 = i__ + ib - 1;
for (j = i__; j <= i__2; ++j) {
i__3 = i__ - 1;
for (l = 1; l <= i__3; ++l) {
i__4 = l + j * a_dim1;
a[i__4].r = 0., a[i__4].i = 0.;
/* L30: */
}
/* L40: */
}
/* L50: */
}
}
work[1].r = (doublereal) iws, work[1].i = 0.;
return 0;
/* End of ZUNGQR */
} /* zungqr_ */
/* Subroutine */ int zunm2l_(char *side, char *trans, integer *m, integer *n,
integer *k, doublecomplex *a, integer *lda, doublecomplex *tau,
doublecomplex *c__, integer *ldc, doublecomplex *work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3;
doublecomplex z__1;
/* Builtin functions */
void d_cnjg(doublecomplex *, doublecomplex *);
/* Local variables */
static integer i__, i1, i2, i3, mi, ni, nq;
static doublecomplex aii;
static logical left;
static doublecomplex taui;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int zlarf_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, doublecomplex *), xerbla_(char *, integer *);
static logical notran;
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZUNM2L overwrites the general complex m-by-n matrix C with
Q * C if SIDE = 'L' and TRANS = 'N', or
Q'* C if SIDE = 'L' and TRANS = 'C', or
C * Q if SIDE = 'R' and TRANS = 'N', or
C * Q' if SIDE = 'R' and TRANS = 'C',
where Q is a complex unitary matrix defined as the product of k
elementary reflectors
Q = H(k) . . . H(2) H(1)
as returned by ZGEQLF. Q is of order m if SIDE = 'L' and of order n
if SIDE = 'R'.
Arguments
=========
SIDE (input) CHARACTER*1
= 'L': apply Q or Q' from the Left
= 'R': apply Q or Q' from the Right
TRANS (input) CHARACTER*1
= 'N': apply Q (No transpose)
= 'C': apply Q' (Conjugate transpose)
M (input) INTEGER
The number of rows of the matrix C. M >= 0.
N (input) INTEGER
The number of columns of the matrix C. N >= 0.
K (input) INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = 'L', M >= K >= 0;
if SIDE = 'R', N >= K >= 0.
A (input) COMPLEX*16 array, dimension (LDA,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
ZGEQLF in the last k columns of its array argument A.
A is modified by the routine but restored on exit.
LDA (input) INTEGER
The leading dimension of the array A.
If SIDE = 'L', LDA >= max(1,M);
if SIDE = 'R', LDA >= max(1,N).
TAU (input) COMPLEX*16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGEQLF.
C (input/output) COMPLEX*16 array, dimension (LDC,N)
On entry, the m-by-n matrix C.
On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
LDC (input) INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK (workspace) COMPLEX*16 array, dimension
(N) if SIDE = 'L',
(M) if SIDE = 'R'
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
=====================================================================
Test the input arguments
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
c_dim1 = *ldc;
c_offset = 1 + c_dim1 * 1;
c__ -= c_offset;
--work;
/* Function Body */
*info = 0;
left = lsame_(side, "L");
notran = lsame_(trans, "N");
/* NQ is the order of Q */
if (left) {
nq = *m;
} else {
nq = *n;
}
if ((! left && ! lsame_(side, "R"))) {
*info = -1;
} else if ((! notran && ! lsame_(trans, "C"))) {
*info = -2;
} else if (*m < 0) {
*info = -3;
} else if (*n < 0) {
*info = -4;
} else if (*k < 0 || *k > nq) {
*info = -5;
} else if (*lda < max(1,nq)) {
*info = -7;
} else if (*ldc < max(1,*m)) {
*info = -10;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZUNM2L", &i__1);
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0 || *k == 0) {
return 0;
}
if ((left && notran) || (! left && ! notran)) {
i1 = 1;
i2 = *k;
i3 = 1;
} else {
i1 = *k;
i2 = 1;
i3 = -1;
}
if (left) {
ni = *n;
} else {
mi = *m;
}
i__1 = i2;
i__2 = i3;
for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
if (left) {
/* H(i) or H(i)' is applied to C(1:m-k+i,1:n) */
mi = *m - *k + i__;
} else {
/* H(i) or H(i)' is applied to C(1:m,1:n-k+i) */
ni = *n - *k + i__;
}
/* Apply H(i) or H(i)' */
if (notran) {
i__3 = i__;
taui.r = tau[i__3].r, taui.i = tau[i__3].i;
} else {
d_cnjg(&z__1, &tau[i__]);
taui.r = z__1.r, taui.i = z__1.i;
}
i__3 = nq - *k + i__ + i__ * a_dim1;
aii.r = a[i__3].r, aii.i = a[i__3].i;
i__3 = nq - *k + i__ + i__ * a_dim1;
a[i__3].r = 1., a[i__3].i = 0.;
zlarf_(side, &mi, &ni, &a[i__ * a_dim1 + 1], &c__1, &taui, &c__[
c_offset], ldc, &work[1]);
i__3 = nq - *k + i__ + i__ * a_dim1;
a[i__3].r = aii.r, a[i__3].i = aii.i;
/* L10: */
}
return 0;
/* End of ZUNM2L */
} /* zunm2l_ */
/* Subroutine */ int zunm2r_(char *side, char *trans, integer *m, integer *n,
integer *k, doublecomplex *a, integer *lda, doublecomplex *tau,
doublecomplex *c__, integer *ldc, doublecomplex *work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3;
doublecomplex z__1;
/* Builtin functions */
void d_cnjg(doublecomplex *, doublecomplex *);
/* Local variables */
static integer i__, i1, i2, i3, ic, jc, mi, ni, nq;
static doublecomplex aii;
static logical left;
static doublecomplex taui;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int zlarf_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, doublecomplex *), xerbla_(char *, integer *);
static logical notran;
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZUNM2R overwrites the general complex m-by-n matrix C with
Q * C if SIDE = 'L' and TRANS = 'N', or
Q'* C if SIDE = 'L' and TRANS = 'C', or
C * Q if SIDE = 'R' and TRANS = 'N', or
C * Q' if SIDE = 'R' and TRANS = 'C',
where Q is a complex unitary matrix defined as the product of k
elementary reflectors
Q = H(1) H(2) . . . H(k)
as returned by ZGEQRF. Q is of order m if SIDE = 'L' and of order n
if SIDE = 'R'.
Arguments
=========
SIDE (input) CHARACTER*1
= 'L': apply Q or Q' from the Left
= 'R': apply Q or Q' from the Right
TRANS (input) CHARACTER*1
= 'N': apply Q (No transpose)
= 'C': apply Q' (Conjugate transpose)
M (input) INTEGER
The number of rows of the matrix C. M >= 0.
N (input) INTEGER
The number of columns of the matrix C. N >= 0.
K (input) INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = 'L', M >= K >= 0;
if SIDE = 'R', N >= K >= 0.
A (input) COMPLEX*16 array, dimension (LDA,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
ZGEQRF in the first k columns of its array argument A.
A is modified by the routine but restored on exit.
LDA (input) INTEGER
The leading dimension of the array A.
If SIDE = 'L', LDA >= max(1,M);
if SIDE = 'R', LDA >= max(1,N).
TAU (input) COMPLEX*16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGEQRF.
C (input/output) COMPLEX*16 array, dimension (LDC,N)
On entry, the m-by-n matrix C.
On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
LDC (input) INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK (workspace) COMPLEX*16 array, dimension
(N) if SIDE = 'L',
(M) if SIDE = 'R'
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
=====================================================================
Test the input arguments
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
c_dim1 = *ldc;
c_offset = 1 + c_dim1 * 1;
c__ -= c_offset;
--work;
/* Function Body */
*info = 0;
left = lsame_(side, "L");
notran = lsame_(trans, "N");
/* NQ is the order of Q */
if (left) {
nq = *m;
} else {
nq = *n;
}
if ((! left && ! lsame_(side, "R"))) {
*info = -1;
} else if ((! notran && ! lsame_(trans, "C"))) {
*info = -2;
} else if (*m < 0) {
*info = -3;
} else if (*n < 0) {
*info = -4;
} else if (*k < 0 || *k > nq) {
*info = -5;
} else if (*lda < max(1,nq)) {
*info = -7;
} else if (*ldc < max(1,*m)) {
*info = -10;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZUNM2R", &i__1);
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0 || *k == 0) {
return 0;
}
if ((left && ! notran) || (! left && notran)) {
i1 = 1;
i2 = *k;
i3 = 1;
} else {
i1 = *k;
i2 = 1;
i3 = -1;
}
if (left) {
ni = *n;
jc = 1;
} else {
mi = *m;
ic = 1;
}
i__1 = i2;
i__2 = i3;
for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
if (left) {
/* H(i) or H(i)' is applied to C(i:m,1:n) */
mi = *m - i__ + 1;
ic = i__;
} else {
/* H(i) or H(i)' is applied to C(1:m,i:n) */
ni = *n - i__ + 1;
jc = i__;
}
/* Apply H(i) or H(i)' */
if (notran) {
i__3 = i__;
taui.r = tau[i__3].r, taui.i = tau[i__3].i;
} else {
d_cnjg(&z__1, &tau[i__]);
taui.r = z__1.r, taui.i = z__1.i;
}
i__3 = i__ + i__ * a_dim1;
aii.r = a[i__3].r, aii.i = a[i__3].i;
i__3 = i__ + i__ * a_dim1;
a[i__3].r = 1., a[i__3].i = 0.;
zlarf_(side, &mi, &ni, &a[i__ + i__ * a_dim1], &c__1, &taui, &c__[ic
+ jc * c_dim1], ldc, &work[1]);
i__3 = i__ + i__ * a_dim1;
a[i__3].r = aii.r, a[i__3].i = aii.i;
/* L10: */
}
return 0;
/* End of ZUNM2R */
} /* zunm2r_ */
/* Subroutine */ int zunmbr_(char *vect, char *side, char *trans, integer *m,
integer *n, integer *k, doublecomplex *a, integer *lda, doublecomplex
*tau, doublecomplex *c__, integer *ldc, doublecomplex *work, integer *
lwork, integer *info)
{
/* System generated locals */
address a__1[2];
integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2];
char ch__1[2];
/* Builtin functions */
/* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen);
/* Local variables */
static integer i1, i2, nb, mi, ni, nq, nw;
static logical left;
extern logical lsame_(char *, char *);
static integer iinfo;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
static logical notran, applyq;
static char transt[1];
static integer lwkopt;
static logical lquery;
extern /* Subroutine */ int zunmlq_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *), zunmqr_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *);
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
If VECT = 'Q', ZUNMBR overwrites the general complex M-by-N matrix C
with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'C': Q**H * C C * Q**H
If VECT = 'P', ZUNMBR overwrites the general complex M-by-N matrix C
with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': P * C C * P
TRANS = 'C': P**H * C C * P**H
Here Q and P**H are the unitary matrices determined by ZGEBRD when
reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q
and P**H are defined as products of elementary reflectors H(i) and
G(i) respectively.
Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
order of the unitary matrix Q or P**H that is applied.
If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
if nq >= k, Q = H(1) H(2) . . . H(k);
if nq < k, Q = H(1) H(2) . . . H(nq-1).
If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
if k < nq, P = G(1) G(2) . . . G(k);
if k >= nq, P = G(1) G(2) . . . G(nq-1).
Arguments
=========
VECT (input) CHARACTER*1
= 'Q': apply Q or Q**H;
= 'P': apply P or P**H.
SIDE (input) CHARACTER*1
= 'L': apply Q, Q**H, P or P**H from the Left;
= 'R': apply Q, Q**H, P or P**H from the Right.
TRANS (input) CHARACTER*1
= 'N': No transpose, apply Q or P;
= 'C': Conjugate transpose, apply Q**H or P**H.
M (input) INTEGER
The number of rows of the matrix C. M >= 0.
N (input) INTEGER
The number of columns of the matrix C. N >= 0.
K (input) INTEGER
If VECT = 'Q', the number of columns in the original
matrix reduced by ZGEBRD.
If VECT = 'P', the number of rows in the original
matrix reduced by ZGEBRD.
K >= 0.
A (input) COMPLEX*16 array, dimension
(LDA,min(nq,K)) if VECT = 'Q'
(LDA,nq) if VECT = 'P'
The vectors which define the elementary reflectors H(i) and
G(i), whose products determine the matrices Q and P, as
returned by ZGEBRD.
LDA (input) INTEGER
The leading dimension of the array A.
If VECT = 'Q', LDA >= max(1,nq);
if VECT = 'P', LDA >= max(1,min(nq,K)).
TAU (input) COMPLEX*16 array, dimension (min(nq,K))
TAU(i) must contain the scalar factor of the elementary
reflector H(i) or G(i) which determines Q or P, as returned
by ZGEBRD in the array argument TAUQ or TAUP.
C (input/output) COMPLEX*16 array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q
or P*C or P**H*C or C*P or C*P**H.
LDC (input) INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK.
If SIDE = 'L', LWORK >= max(1,N);
if SIDE = 'R', LWORK >= max(1,M).
For optimum performance LWORK >= N*NB if SIDE = 'L', and
LWORK >= M*NB if SIDE = 'R', where NB is the optimal
blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
=====================================================================
Test the input arguments
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
c_dim1 = *ldc;
c_offset = 1 + c_dim1 * 1;
c__ -= c_offset;
--work;
/* Function Body */
*info = 0;
applyq = lsame_(vect, "Q");
left = lsame_(side, "L");
notran = lsame_(trans, "N");
lquery = *lwork == -1;
/* NQ is the order of Q or P and NW is the minimum dimension of WORK */
if (left) {
nq = *m;
nw = *n;
} else {
nq = *n;
nw = *m;
}
if ((! applyq && ! lsame_(vect, "P"))) {
*info = -1;
} else if ((! left && ! lsame_(side, "R"))) {
*info = -2;
} else if ((! notran && ! lsame_(trans, "C"))) {
*info = -3;
} else if (*m < 0) {
*info = -4;
} else if (*n < 0) {
*info = -5;
} else if (*k < 0) {
*info = -6;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__1 = 1, i__2 = min(nq,*k);
if ((applyq && *lda < max(1,nq)) || (! applyq && *lda < max(i__1,i__2)
)) {
*info = -8;
} else if (*ldc < max(1,*m)) {
*info = -11;
} else if ((*lwork < max(1,nw) && ! lquery)) {
*info = -13;
}
}
if (*info == 0) {
if (applyq) {
if (left) {
/* Writing concatenation */
i__3[0] = 1, a__1[0] = side;
i__3[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
i__1 = *m - 1;
i__2 = *m - 1;
nb = ilaenv_(&c__1, "ZUNMQR", ch__1, &i__1, n, &i__2, &c_n1, (
ftnlen)6, (ftnlen)2);
} else {
/* Writing concatenation */
i__3[0] = 1, a__1[0] = side;
i__3[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
i__1 = *n - 1;
i__2 = *n - 1;
nb = ilaenv_(&c__1, "ZUNMQR", ch__1, m, &i__1, &i__2, &c_n1, (
ftnlen)6, (ftnlen)2);
}
} else {
if (left) {
/* Writing concatenation */
i__3[0] = 1, a__1[0] = side;
i__3[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
i__1 = *m - 1;
i__2 = *m - 1;
nb = ilaenv_(&c__1, "ZUNMLQ", ch__1, &i__1, n, &i__2, &c_n1, (
ftnlen)6, (ftnlen)2);
} else {
/* Writing concatenation */
i__3[0] = 1, a__1[0] = side;
i__3[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
i__1 = *n - 1;
i__2 = *n - 1;
nb = ilaenv_(&c__1, "ZUNMLQ", ch__1, m, &i__1, &i__2, &c_n1, (
ftnlen)6, (ftnlen)2);
}
}
lwkopt = max(1,nw) * nb;
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZUNMBR", &i__1);
return 0;
} else if (lquery) {
}
/* Quick return if possible */
work[1].r = 1., work[1].i = 0.;
if (*m == 0 || *n == 0) {
return 0;
}
if (applyq) {
/* Apply Q */
if (nq >= *k) {
/* Q was determined by a call to ZGEBRD with nq >= k */
zunmqr_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[
c_offset], ldc, &work[1], lwork, &iinfo);
} else if (nq > 1) {
/* Q was determined by a call to ZGEBRD with nq < k */
if (left) {
mi = *m - 1;
ni = *n;
i1 = 2;
i2 = 1;
} else {
mi = *m;
ni = *n - 1;
i1 = 1;
i2 = 2;
}
i__1 = nq - 1;
zunmqr_(side, trans, &mi, &ni, &i__1, &a[a_dim1 + 2], lda, &tau[1]
, &c__[i1 + i2 * c_dim1], ldc, &work[1], lwork, &iinfo);
}
} else {
/* Apply P */
if (notran) {
*(unsigned char *)transt = 'C';
} else {
*(unsigned char *)transt = 'N';
}
if (nq > *k) {
/* P was determined by a call to ZGEBRD with nq > k */
zunmlq_(side, transt, m, n, k, &a[a_offset], lda, &tau[1], &c__[
c_offset], ldc, &work[1], lwork, &iinfo);
} else if (nq > 1) {
/* P was determined by a call to ZGEBRD with nq <= k */
if (left) {
mi = *m - 1;
ni = *n;
i1 = 2;
i2 = 1;
} else {
mi = *m;
ni = *n - 1;
i1 = 1;
i2 = 2;
}
i__1 = nq - 1;
zunmlq_(side, transt, &mi, &ni, &i__1, &a[((a_dim1) << (1)) + 1],
lda, &tau[1], &c__[i1 + i2 * c_dim1], ldc, &work[1],
lwork, &iinfo);
}
}
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
return 0;
/* End of ZUNMBR */
} /* zunmbr_ */
/* Subroutine */ int zunml2_(char *side, char *trans, integer *m, integer *n,
integer *k, doublecomplex *a, integer *lda, doublecomplex *tau,
doublecomplex *c__, integer *ldc, doublecomplex *work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3;
doublecomplex z__1;
/* Builtin functions */
void d_cnjg(doublecomplex *, doublecomplex *);
/* Local variables */
static integer i__, i1, i2, i3, ic, jc, mi, ni, nq;
static doublecomplex aii;
static logical left;
static doublecomplex taui;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int zlarf_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, doublecomplex *), xerbla_(char *, integer *), zlacgv_(integer *, doublecomplex *, integer *);
static logical notran;
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZUNML2 overwrites the general complex m-by-n matrix C with
Q * C if SIDE = 'L' and TRANS = 'N', or
Q'* C if SIDE = 'L' and TRANS = 'C', or
C * Q if SIDE = 'R' and TRANS = 'N', or
C * Q' if SIDE = 'R' and TRANS = 'C',
where Q is a complex unitary matrix defined as the product of k
elementary reflectors
Q = H(k)' . . . H(2)' H(1)'
as returned by ZGELQF. Q is of order m if SIDE = 'L' and of order n
if SIDE = 'R'.
Arguments
=========
SIDE (input) CHARACTER*1
= 'L': apply Q or Q' from the Left
= 'R': apply Q or Q' from the Right
TRANS (input) CHARACTER*1
= 'N': apply Q (No transpose)
= 'C': apply Q' (Conjugate transpose)
M (input) INTEGER
The number of rows of the matrix C. M >= 0.
N (input) INTEGER
The number of columns of the matrix C. N >= 0.
K (input) INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = 'L', M >= K >= 0;
if SIDE = 'R', N >= K >= 0.
A (input) COMPLEX*16 array, dimension
(LDA,M) if SIDE = 'L',
(LDA,N) if SIDE = 'R'
The i-th row must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
ZGELQF in the first k rows of its array argument A.
A is modified by the routine but restored on exit.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,K).
TAU (input) COMPLEX*16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGELQF.
C (input/output) COMPLEX*16 array, dimension (LDC,N)
On entry, the m-by-n matrix C.
On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
LDC (input) INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK (workspace) COMPLEX*16 array, dimension
(N) if SIDE = 'L',
(M) if SIDE = 'R'
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
=====================================================================
Test the input arguments
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
c_dim1 = *ldc;
c_offset = 1 + c_dim1 * 1;
c__ -= c_offset;
--work;
/* Function Body */
*info = 0;
left = lsame_(side, "L");
notran = lsame_(trans, "N");
/* NQ is the order of Q */
if (left) {
nq = *m;
} else {
nq = *n;
}
if ((! left && ! lsame_(side, "R"))) {
*info = -1;
} else if ((! notran && ! lsame_(trans, "C"))) {
*info = -2;
} else if (*m < 0) {
*info = -3;
} else if (*n < 0) {
*info = -4;
} else if (*k < 0 || *k > nq) {
*info = -5;
} else if (*lda < max(1,*k)) {
*info = -7;
} else if (*ldc < max(1,*m)) {
*info = -10;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZUNML2", &i__1);
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0 || *k == 0) {
return 0;
}
if ((left && notran) || (! left && ! notran)) {
i1 = 1;
i2 = *k;
i3 = 1;
} else {
i1 = *k;
i2 = 1;
i3 = -1;
}
if (left) {
ni = *n;
jc = 1;
} else {
mi = *m;
ic = 1;
}
i__1 = i2;
i__2 = i3;
for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
if (left) {
/* H(i) or H(i)' is applied to C(i:m,1:n) */
mi = *m - i__ + 1;
ic = i__;
} else {
/* H(i) or H(i)' is applied to C(1:m,i:n) */
ni = *n - i__ + 1;
jc = i__;
}
/* Apply H(i) or H(i)' */
if (notran) {
d_cnjg(&z__1, &tau[i__]);
taui.r = z__1.r, taui.i = z__1.i;
} else {
i__3 = i__;
taui.r = tau[i__3].r, taui.i = tau[i__3].i;
}
if (i__ < nq) {
i__3 = nq - i__;
zlacgv_(&i__3, &a[i__ + (i__ + 1) * a_dim1], lda);
}
i__3 = i__ + i__ * a_dim1;
aii.r = a[i__3].r, aii.i = a[i__3].i;
i__3 = i__ + i__ * a_dim1;
a[i__3].r = 1., a[i__3].i = 0.;
zlarf_(side, &mi, &ni, &a[i__ + i__ * a_dim1], lda, &taui, &c__[ic +
jc * c_dim1], ldc, &work[1]);
i__3 = i__ + i__ * a_dim1;
a[i__3].r = aii.r, a[i__3].i = aii.i;
if (i__ < nq) {
i__3 = nq - i__;
zlacgv_(&i__3, &a[i__ + (i__ + 1) * a_dim1], lda);
}
/* L10: */
}
return 0;
/* End of ZUNML2 */
} /* zunml2_ */
/* Subroutine */ int zunmlq_(char *side, char *trans, integer *m, integer *n,
integer *k, doublecomplex *a, integer *lda, doublecomplex *tau,
doublecomplex *c__, integer *ldc, doublecomplex *work, integer *lwork,
integer *info)
{
/* System generated locals */
address a__1[2];
integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4,
i__5;
char ch__1[2];
/* Builtin functions */
/* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen);
/* Local variables */
static integer i__;
static doublecomplex t[4160] /* was [65][64] */;
static integer i1, i2, i3, ib, ic, jc, nb, mi, ni, nq, nw, iws;
static logical left;
extern logical lsame_(char *, char *);
static integer nbmin, iinfo;
extern /* Subroutine */ int zunml2_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
static logical notran;
static integer ldwork;
extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
static char transt[1];
static integer lwkopt;
static logical lquery;
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZUNMLQ overwrites the general complex M-by-N matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'C': Q**H * C C * Q**H
where Q is a complex unitary matrix defined as the product of k
elementary reflectors
Q = H(k)' . . . H(2)' H(1)'
as returned by ZGELQF. Q is of order M if SIDE = 'L' and of order N
if SIDE = 'R'.
Arguments
=========
SIDE (input) CHARACTER*1
= 'L': apply Q or Q**H from the Left;
= 'R': apply Q or Q**H from the Right.
TRANS (input) CHARACTER*1
= 'N': No transpose, apply Q;
= 'C': Conjugate transpose, apply Q**H.
M (input) INTEGER
The number of rows of the matrix C. M >= 0.
N (input) INTEGER
The number of columns of the matrix C. N >= 0.
K (input) INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = 'L', M >= K >= 0;
if SIDE = 'R', N >= K >= 0.
A (input) COMPLEX*16 array, dimension
(LDA,M) if SIDE = 'L',
(LDA,N) if SIDE = 'R'
The i-th row must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
ZGELQF in the first k rows of its array argument A.
A is modified by the routine but restored on exit.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,K).
TAU (input) COMPLEX*16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGELQF.
C (input/output) COMPLEX*16 array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
LDC (input) INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK.
If SIDE = 'L', LWORK >= max(1,N);
if SIDE = 'R', LWORK >= max(1,M).
For optimum performance LWORK >= N*NB if SIDE 'L', and
LWORK >= M*NB if SIDE = 'R', where NB is the optimal
blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
=====================================================================
Test the input arguments
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
c_dim1 = *ldc;
c_offset = 1 + c_dim1 * 1;
c__ -= c_offset;
--work;
/* Function Body */
*info = 0;
left = lsame_(side, "L");
notran = lsame_(trans, "N");
lquery = *lwork == -1;
/* NQ is the order of Q and NW is the minimum dimension of WORK */
if (left) {
nq = *m;
nw = *n;
} else {
nq = *n;
nw = *m;
}
if ((! left && ! lsame_(side, "R"))) {
*info = -1;
} else if ((! notran && ! lsame_(trans, "C"))) {
*info = -2;
} else if (*m < 0) {
*info = -3;
} else if (*n < 0) {
*info = -4;
} else if (*k < 0 || *k > nq) {
*info = -5;
} else if (*lda < max(1,*k)) {
*info = -7;
} else if (*ldc < max(1,*m)) {
*info = -10;
} else if ((*lwork < max(1,nw) && ! lquery)) {
*info = -12;
}
if (*info == 0) {
/*
Determine the block size. NB may be at most NBMAX, where NBMAX
is used to define the local array T.
Computing MIN
Writing concatenation
*/
i__3[0] = 1, a__1[0] = side;
i__3[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
i__1 = 64, i__2 = ilaenv_(&c__1, "ZUNMLQ", ch__1, m, n, k, &c_n1, (
ftnlen)6, (ftnlen)2);
nb = min(i__1,i__2);
lwkopt = max(1,nw) * nb;
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZUNMLQ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0 || *k == 0) {
work[1].r = 1., work[1].i = 0.;
return 0;
}
nbmin = 2;
ldwork = nw;
if ((nb > 1 && nb < *k)) {
iws = nw * nb;
if (*lwork < iws) {
nb = *lwork / ldwork;
/*
Computing MAX
Writing concatenation
*/
i__3[0] = 1, a__1[0] = side;
i__3[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
i__1 = 2, i__2 = ilaenv_(&c__2, "ZUNMLQ", ch__1, m, n, k, &c_n1, (
ftnlen)6, (ftnlen)2);
nbmin = max(i__1,i__2);
}
} else {
iws = nw;
}
if (nb < nbmin || nb >= *k) {
/* Use unblocked code */
zunml2_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[
c_offset], ldc, &work[1], &iinfo);
} else {
/* Use blocked code */
if ((left && notran) || (! left && ! notran)) {
i1 = 1;
i2 = *k;
i3 = nb;
} else {
i1 = (*k - 1) / nb * nb + 1;
i2 = 1;
i3 = -nb;
}
if (left) {
ni = *n;
jc = 1;
} else {
mi = *m;
ic = 1;
}
if (notran) {
*(unsigned char *)transt = 'C';
} else {
*(unsigned char *)transt = 'N';
}
i__1 = i2;
i__2 = i3;
for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/* Computing MIN */
i__4 = nb, i__5 = *k - i__ + 1;
ib = min(i__4,i__5);
/*
Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1)
*/
i__4 = nq - i__ + 1;
zlarft_("Forward", "Rowwise", &i__4, &ib, &a[i__ + i__ * a_dim1],
lda, &tau[i__], t, &c__65);
if (left) {
/* H or H' is applied to C(i:m,1:n) */
mi = *m - i__ + 1;
ic = i__;
} else {
/* H or H' is applied to C(1:m,i:n) */
ni = *n - i__ + 1;
jc = i__;
}
/* Apply H or H' */
zlarfb_(side, transt, "Forward", "Rowwise", &mi, &ni, &ib, &a[i__
+ i__ * a_dim1], lda, t, &c__65, &c__[ic + jc * c_dim1],
ldc, &work[1], &ldwork);
/* L10: */
}
}
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
return 0;
/* End of ZUNMLQ */
} /* zunmlq_ */
/* Subroutine */ int zunmql_(char *side, char *trans, integer *m, integer *n,
integer *k, doublecomplex *a, integer *lda, doublecomplex *tau,
doublecomplex *c__, integer *ldc, doublecomplex *work, integer *lwork,
integer *info)
{
/* System generated locals */
address a__1[2];
integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4,
i__5;
char ch__1[2];
/* Builtin functions */
/* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen);
/* Local variables */
static integer i__;
static doublecomplex t[4160] /* was [65][64] */;
static integer i1, i2, i3, ib, nb, mi, ni, nq, nw, iws;
static logical left;
extern logical lsame_(char *, char *);
static integer nbmin, iinfo;
extern /* Subroutine */ int zunm2l_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
static logical notran;
static integer ldwork;
extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
static integer lwkopt;
static logical lquery;
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZUNMQL overwrites the general complex M-by-N matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'C': Q**H * C C * Q**H
where Q is a complex unitary matrix defined as the product of k
elementary reflectors
Q = H(k) . . . H(2) H(1)
as returned by ZGEQLF. Q is of order M if SIDE = 'L' and of order N
if SIDE = 'R'.
Arguments
=========
SIDE (input) CHARACTER*1
= 'L': apply Q or Q**H from the Left;
= 'R': apply Q or Q**H from the Right.
TRANS (input) CHARACTER*1
= 'N': No transpose, apply Q;
= 'C': Transpose, apply Q**H.
M (input) INTEGER
The number of rows of the matrix C. M >= 0.
N (input) INTEGER
The number of columns of the matrix C. N >= 0.
K (input) INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = 'L', M >= K >= 0;
if SIDE = 'R', N >= K >= 0.
A (input) COMPLEX*16 array, dimension (LDA,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
ZGEQLF in the last k columns of its array argument A.
A is modified by the routine but restored on exit.
LDA (input) INTEGER
The leading dimension of the array A.
If SIDE = 'L', LDA >= max(1,M);
if SIDE = 'R', LDA >= max(1,N).
TAU (input) COMPLEX*16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGEQLF.
C (input/output) COMPLEX*16 array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
LDC (input) INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK.
If SIDE = 'L', LWORK >= max(1,N);
if SIDE = 'R', LWORK >= max(1,M).
For optimum performance LWORK >= N*NB if SIDE = 'L', and
LWORK >= M*NB if SIDE = 'R', where NB is the optimal
blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
=====================================================================
Test the input arguments
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
c_dim1 = *ldc;
c_offset = 1 + c_dim1 * 1;
c__ -= c_offset;
--work;
/* Function Body */
*info = 0;
left = lsame_(side, "L");
notran = lsame_(trans, "N");
lquery = *lwork == -1;
/* NQ is the order of Q and NW is the minimum dimension of WORK */
if (left) {
nq = *m;
nw = *n;
} else {
nq = *n;
nw = *m;
}
if ((! left && ! lsame_(side, "R"))) {
*info = -1;
} else if ((! notran && ! lsame_(trans, "C"))) {
*info = -2;
} else if (*m < 0) {
*info = -3;
} else if (*n < 0) {
*info = -4;
} else if (*k < 0 || *k > nq) {
*info = -5;
} else if (*lda < max(1,nq)) {
*info = -7;
} else if (*ldc < max(1,*m)) {
*info = -10;
} else if ((*lwork < max(1,nw) && ! lquery)) {
*info = -12;
}
if (*info == 0) {
/*
Determine the block size. NB may be at most NBMAX, where NBMAX
is used to define the local array T.
Computing MIN
Writing concatenation
*/
i__3[0] = 1, a__1[0] = side;
i__3[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
i__1 = 64, i__2 = ilaenv_(&c__1, "ZUNMQL", ch__1, m, n, k, &c_n1, (
ftnlen)6, (ftnlen)2);
nb = min(i__1,i__2);
lwkopt = max(1,nw) * nb;
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZUNMQL", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0 || *k == 0) {
work[1].r = 1., work[1].i = 0.;
return 0;
}
nbmin = 2;
ldwork = nw;
if ((nb > 1 && nb < *k)) {
iws = nw * nb;
if (*lwork < iws) {
nb = *lwork / ldwork;
/*
Computing MAX
Writing concatenation
*/
i__3[0] = 1, a__1[0] = side;
i__3[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
i__1 = 2, i__2 = ilaenv_(&c__2, "ZUNMQL", ch__1, m, n, k, &c_n1, (
ftnlen)6, (ftnlen)2);
nbmin = max(i__1,i__2);
}
} else {
iws = nw;
}
if (nb < nbmin || nb >= *k) {
/* Use unblocked code */
zunm2l_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[
c_offset], ldc, &work[1], &iinfo);
} else {
/* Use blocked code */
if ((left && notran) || (! left && ! notran)) {
i1 = 1;
i2 = *k;
i3 = nb;
} else {
i1 = (*k - 1) / nb * nb + 1;
i2 = 1;
i3 = -nb;
}
if (left) {
ni = *n;
} else {
mi = *m;
}
i__1 = i2;
i__2 = i3;
for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/* Computing MIN */
i__4 = nb, i__5 = *k - i__ + 1;
ib = min(i__4,i__5);
/*
Form the triangular factor of the block reflector
H = H(i+ib-1) . . . H(i+1) H(i)
*/
i__4 = nq - *k + i__ + ib - 1;
zlarft_("Backward", "Columnwise", &i__4, &ib, &a[i__ * a_dim1 + 1]
, lda, &tau[i__], t, &c__65);
if (left) {
/* H or H' is applied to C(1:m-k+i+ib-1,1:n) */
mi = *m - *k + i__ + ib - 1;
} else {
/* H or H' is applied to C(1:m,1:n-k+i+ib-1) */
ni = *n - *k + i__ + ib - 1;
}
/* Apply H or H' */
zlarfb_(side, trans, "Backward", "Columnwise", &mi, &ni, &ib, &a[
i__ * a_dim1 + 1], lda, t, &c__65, &c__[c_offset], ldc, &
work[1], &ldwork);
/* L10: */
}
}
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
return 0;
/* End of ZUNMQL */
} /* zunmql_ */
/* Subroutine */ int zunmqr_(char *side, char *trans, integer *m, integer *n,
integer *k, doublecomplex *a, integer *lda, doublecomplex *tau,
doublecomplex *c__, integer *ldc, doublecomplex *work, integer *lwork,
integer *info)
{
/* System generated locals */
address a__1[2];
integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4,
i__5;
char ch__1[2];
/* Builtin functions */
/* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen);
/* Local variables */
static integer i__;
static doublecomplex t[4160] /* was [65][64] */;
static integer i1, i2, i3, ib, ic, jc, nb, mi, ni, nq, nw, iws;
static logical left;
extern logical lsame_(char *, char *);
static integer nbmin, iinfo;
extern /* Subroutine */ int zunm2r_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
static logical notran;
static integer ldwork;
extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
static integer lwkopt;
static logical lquery;
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZUNMQR overwrites the general complex M-by-N matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'C': Q**H * C C * Q**H
where Q is a complex unitary matrix defined as the product of k
elementary reflectors
Q = H(1) H(2) . . . H(k)
as returned by ZGEQRF. Q is of order M if SIDE = 'L' and of order N
if SIDE = 'R'.
Arguments
=========
SIDE (input) CHARACTER*1
= 'L': apply Q or Q**H from the Left;
= 'R': apply Q or Q**H from the Right.
TRANS (input) CHARACTER*1
= 'N': No transpose, apply Q;
= 'C': Conjugate transpose, apply Q**H.
M (input) INTEGER
The number of rows of the matrix C. M >= 0.
N (input) INTEGER
The number of columns of the matrix C. N >= 0.
K (input) INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = 'L', M >= K >= 0;
if SIDE = 'R', N >= K >= 0.
A (input) COMPLEX*16 array, dimension (LDA,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
ZGEQRF in the first k columns of its array argument A.
A is modified by the routine but restored on exit.
LDA (input) INTEGER
The leading dimension of the array A.
If SIDE = 'L', LDA >= max(1,M);
if SIDE = 'R', LDA >= max(1,N).
TAU (input) COMPLEX*16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGEQRF.
C (input/output) COMPLEX*16 array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
LDC (input) INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK.
If SIDE = 'L', LWORK >= max(1,N);
if SIDE = 'R', LWORK >= max(1,M).
For optimum performance LWORK >= N*NB if SIDE = 'L', and
LWORK >= M*NB if SIDE = 'R', where NB is the optimal
blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
=====================================================================
Test the input arguments
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
c_dim1 = *ldc;
c_offset = 1 + c_dim1 * 1;
c__ -= c_offset;
--work;
/* Function Body */
*info = 0;
left = lsame_(side, "L");
notran = lsame_(trans, "N");
lquery = *lwork == -1;
/* NQ is the order of Q and NW is the minimum dimension of WORK */
if (left) {
nq = *m;
nw = *n;
} else {
nq = *n;
nw = *m;
}
if ((! left && ! lsame_(side, "R"))) {
*info = -1;
} else if ((! notran && ! lsame_(trans, "C"))) {
*info = -2;
} else if (*m < 0) {
*info = -3;
} else if (*n < 0) {
*info = -4;
} else if (*k < 0 || *k > nq) {
*info = -5;
} else if (*lda < max(1,nq)) {
*info = -7;
} else if (*ldc < max(1,*m)) {
*info = -10;
} else if ((*lwork < max(1,nw) && ! lquery)) {
*info = -12;
}
if (*info == 0) {
/*
Determine the block size. NB may be at most NBMAX, where NBMAX
is used to define the local array T.
Computing MIN
Writing concatenation
*/
i__3[0] = 1, a__1[0] = side;
i__3[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
i__1 = 64, i__2 = ilaenv_(&c__1, "ZUNMQR", ch__1, m, n, k, &c_n1, (
ftnlen)6, (ftnlen)2);
nb = min(i__1,i__2);
lwkopt = max(1,nw) * nb;
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZUNMQR", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0 || *k == 0) {
work[1].r = 1., work[1].i = 0.;
return 0;
}
nbmin = 2;
ldwork = nw;
if ((nb > 1 && nb < *k)) {
iws = nw * nb;
if (*lwork < iws) {
nb = *lwork / ldwork;
/*
Computing MAX
Writing concatenation
*/
i__3[0] = 1, a__1[0] = side;
i__3[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
i__1 = 2, i__2 = ilaenv_(&c__2, "ZUNMQR", ch__1, m, n, k, &c_n1, (
ftnlen)6, (ftnlen)2);
nbmin = max(i__1,i__2);
}
} else {
iws = nw;
}
if (nb < nbmin || nb >= *k) {
/* Use unblocked code */
zunm2r_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[
c_offset], ldc, &work[1], &iinfo);
} else {
/* Use blocked code */
if ((left && ! notran) || (! left && notran)) {
i1 = 1;
i2 = *k;
i3 = nb;
} else {
i1 = (*k - 1) / nb * nb + 1;
i2 = 1;
i3 = -nb;
}
if (left) {
ni = *n;
jc = 1;
} else {
mi = *m;
ic = 1;
}
i__1 = i2;
i__2 = i3;
for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/* Computing MIN */
i__4 = nb, i__5 = *k - i__ + 1;
ib = min(i__4,i__5);
/*
Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1)
*/
i__4 = nq - i__ + 1;
zlarft_("Forward", "Columnwise", &i__4, &ib, &a[i__ + i__ *
a_dim1], lda, &tau[i__], t, &c__65)
;
if (left) {
/* H or H' is applied to C(i:m,1:n) */
mi = *m - i__ + 1;
ic = i__;
} else {
/* H or H' is applied to C(1:m,i:n) */
ni = *n - i__ + 1;
jc = i__;
}
/* Apply H or H' */
zlarfb_(side, trans, "Forward", "Columnwise", &mi, &ni, &ib, &a[
i__ + i__ * a_dim1], lda, t, &c__65, &c__[ic + jc *
c_dim1], ldc, &work[1], &ldwork);
/* L10: */
}
}
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
return 0;
/* End of ZUNMQR */
} /* zunmqr_ */
/* Subroutine */ int zunmtr_(char *side, char *uplo, char *trans, integer *m,
integer *n, doublecomplex *a, integer *lda, doublecomplex *tau,
doublecomplex *c__, integer *ldc, doublecomplex *work, integer *lwork,
integer *info)
{
/* System generated locals */
address a__1[2];
integer a_dim1, a_offset, c_dim1, c_offset, i__1[2], i__2, i__3;
char ch__1[2];
/* Builtin functions */
/* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen);
/* Local variables */
static integer i1, i2, nb, mi, ni, nq, nw;
static logical left;
extern logical lsame_(char *, char *);
static integer iinfo;
static logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
static integer lwkopt;
static logical lquery;
extern /* Subroutine */ int zunmql_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *), zunmqr_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *);
/*
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZUNMTR overwrites the general complex M-by-N matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'C': Q**H * C C * Q**H
where Q is a complex unitary matrix of order nq, with nq = m if
SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
nq-1 elementary reflectors, as returned by ZHETRD:
if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
Arguments
=========
SIDE (input) CHARACTER*1
= 'L': apply Q or Q**H from the Left;
= 'R': apply Q or Q**H from the Right.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A contains elementary reflectors
from ZHETRD;
= 'L': Lower triangle of A contains elementary reflectors
from ZHETRD.
TRANS (input) CHARACTER*1
= 'N': No transpose, apply Q;
= 'C': Conjugate transpose, apply Q**H.
M (input) INTEGER
The number of rows of the matrix C. M >= 0.
N (input) INTEGER
The number of columns of the matrix C. N >= 0.
A (input) COMPLEX*16 array, dimension
(LDA,M) if SIDE = 'L'
(LDA,N) if SIDE = 'R'
The vectors which define the elementary reflectors, as
returned by ZHETRD.
LDA (input) INTEGER
The leading dimension of the array A.
LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.
TAU (input) COMPLEX*16 array, dimension
(M-1) if SIDE = 'L'
(N-1) if SIDE = 'R'
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZHETRD.
C (input/output) COMPLEX*16 array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
LDC (input) INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK.
If SIDE = 'L', LWORK >= max(1,N);
if SIDE = 'R', LWORK >= max(1,M).
For optimum performance LWORK >= N*NB if SIDE = 'L', and
LWORK >=M*NB if SIDE = 'R', where NB is the optimal
blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
=====================================================================
Test the input arguments
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
c_dim1 = *ldc;
c_offset = 1 + c_dim1 * 1;
c__ -= c_offset;
--work;
/* Function Body */
*info = 0;
left = lsame_(side, "L");
upper = lsame_(uplo, "U");
lquery = *lwork == -1;
/* NQ is the order of Q and NW is the minimum dimension of WORK */
if (left) {
nq = *m;
nw = *n;
} else {
nq = *n;
nw = *m;
}
if ((! left && ! lsame_(side, "R"))) {
*info = -1;
} else if ((! upper && ! lsame_(uplo, "L"))) {
*info = -2;
} else if ((! lsame_(trans, "N") && ! lsame_(trans,
"C"))) {
*info = -3;
} else if (*m < 0) {
*info = -4;
} else if (*n < 0) {
*info = -5;
} else if (*lda < max(1,nq)) {
*info = -7;
} else if (*ldc < max(1,*m)) {
*info = -10;
} else if ((*lwork < max(1,nw) && ! lquery)) {
*info = -12;
}
if (*info == 0) {
if (upper) {
if (left) {
/* Writing concatenation */
i__1[0] = 1, a__1[0] = side;
i__1[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2);
i__2 = *m - 1;
i__3 = *m - 1;
nb = ilaenv_(&c__1, "ZUNMQL", ch__1, &i__2, n, &i__3, &c_n1, (
ftnlen)6, (ftnlen)2);
} else {
/* Writing concatenation */
i__1[0] = 1, a__1[0] = side;
i__1[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2);
i__2 = *n - 1;
i__3 = *n - 1;
nb = ilaenv_(&c__1, "ZUNMQL", ch__1, m, &i__2, &i__3, &c_n1, (
ftnlen)6, (ftnlen)2);
}
} else {
if (left) {
/* Writing concatenation */
i__1[0] = 1, a__1[0] = side;
i__1[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2);
i__2 = *m - 1;
i__3 = *m - 1;
nb = ilaenv_(&c__1, "ZUNMQR", ch__1, &i__2, n, &i__3, &c_n1, (
ftnlen)6, (ftnlen)2);
} else {
/* Writing concatenation */
i__1[0] = 1, a__1[0] = side;
i__1[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2);
i__2 = *n - 1;
i__3 = *n - 1;
nb = ilaenv_(&c__1, "ZUNMQR", ch__1, m, &i__2, &i__3, &c_n1, (
ftnlen)6, (ftnlen)2);
}
}
lwkopt = max(1,nw) * nb;
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
}
if (*info != 0) {
i__2 = -(*info);
xerbla_("ZUNMTR", &i__2);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0 || nq == 1) {
work[1].r = 1., work[1].i = 0.;
return 0;
}
if (left) {
mi = *m - 1;
ni = *n;
} else {
mi = *m;
ni = *n - 1;
}
if (upper) {
/* Q was determined by a call to ZHETRD with UPLO = 'U' */
i__2 = nq - 1;
zunmql_(side, trans, &mi, &ni, &i__2, &a[((a_dim1) << (1)) + 1], lda,
&tau[1], &c__[c_offset], ldc, &work[1], lwork, &iinfo);
} else {
/* Q was determined by a call to ZHETRD with UPLO = 'L' */
if (left) {
i1 = 2;
i2 = 1;
} else {
i1 = 1;
i2 = 2;
}
i__2 = nq - 1;
zunmqr_(side, trans, &mi, &ni, &i__2, &a[a_dim1 + 2], lda, &tau[1], &
c__[i1 + i2 * c_dim1], ldc, &work[1], lwork, &iinfo);
}
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
return 0;
/* End of ZUNMTR */
} /* zunmtr_ */
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