/* comlr2.f -- translated by f2c (version 19961017).
You must link the resulting object file with the libraries:
-lf2c -lm (in that order)
*/
#include "f2c.h"
/* Subroutine */ int comlr2_(integer *nm, integer *n, integer *low, integer *
igh, integer *int__, doublereal *hr, doublereal *hi, doublereal *wr,
doublereal *wi, doublereal *zr, doublereal *zi, integer *ierr)
{
/* System generated locals */
integer hr_dim1, hr_offset, hi_dim1, hi_offset, zr_dim1, zr_offset,
zi_dim1, zi_offset, i__1, i__2, i__3;
doublereal d__1, d__2, d__3, d__4;
/* Local variables */
static integer iend;
extern /* Subroutine */ int cdiv_(doublereal *, doublereal *, doublereal *
, doublereal *, doublereal *, doublereal *);
static doublereal norm;
static integer i__, j, k, l, m, ii, en, jj, ll, mm, nn;
static doublereal si, ti, xi, yi, sr, tr, xr, yr;
static integer im1;
extern /* Subroutine */ int csroot_(doublereal *, doublereal *,
doublereal *, doublereal *);
static integer ip1, mp1, itn, its;
static doublereal zzi, zzr;
static integer enm1;
static doublereal tst1, tst2;
/* THIS SUBROUTINE IS A TRANSLATION OF THE ALGOL PROCEDURE COMLR2, */
/* NUM. MATH. 16, 181-204(1970) BY PETERS AND WILKINSON. */
/* HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 372-395(1971). */
/* THIS SUBROUTINE FINDS THE EIGENVALUES AND EIGENVECTORS */
/* OF A COMPLEX UPPER HESSENBERG MATRIX BY THE MODIFIED LR */
/* METHOD. THE EIGENVECTORS OF A COMPLEX GENERAL MATRIX */
/* CAN ALSO BE FOUND IF COMHES HAS BEEN USED TO REDUCE */
/* THIS GENERAL MATRIX TO HESSENBERG FORM. */
/* ON INPUT */
/* NM MUST BE SET TO THE ROW DIMENSION OF TWO-DIMENSIONAL */
/* ARRAY PARAMETERS AS DECLARED IN THE CALLING PROGRAM */
/* DIMENSION STATEMENT. */
/* N IS THE ORDER OF THE MATRIX. */
/* LOW AND IGH ARE INTEGERS DETERMINED BY THE BALANCING */
/* SUBROUTINE CBAL. IF CBAL HAS NOT BEEN USED, */
/* SET LOW=1, IGH=N. */
/* INT CONTAINS INFORMATION ON THE ROWS AND COLUMNS INTERCHANGED */
/* IN THE REDUCTION BY COMHES, IF PERFORMED. ONLY ELEMENTS */
/* LOW THROUGH IGH ARE USED. IF THE EIGENVECTORS OF THE HESSEN-
*/
/* BERG MATRIX ARE DESIRED, SET INT(J)=J FOR THESE ELEMENTS. */
/* HR AND HI CONTAIN THE REAL AND IMAGINARY PARTS, */
/* RESPECTIVELY, OF THE COMPLEX UPPER HESSENBERG MATRIX. */
/* THEIR LOWER TRIANGLES BELOW THE SUBDIAGONAL CONTAIN THE */
/* MULTIPLIERS WHICH WERE USED IN THE REDUCTION BY COMHES, */
/* IF PERFORMED. IF THE EIGENVECTORS OF THE HESSENBERG */
/* MATRIX ARE DESIRED, THESE ELEMENTS MUST BE SET TO ZERO. */
/* ON OUTPUT */
/* THE UPPER HESSENBERG PORTIONS OF HR AND HI HAVE BEEN */
/* DESTROYED, BUT THE LOCATION HR(1,1) CONTAINS THE NORM */
/* OF THE TRIANGULARIZED MATRIX. */
/* WR AND WI CONTAIN THE REAL AND IMAGINARY PARTS, */
/* RESPECTIVELY, OF THE EIGENVALUES. IF AN ERROR */
/* EXIT IS MADE, THE EIGENVALUES SHOULD BE CORRECT */
/* FOR INDICES IERR+1,...,N. */
/* ZR AND ZI CONTAIN THE REAL AND IMAGINARY PARTS, */
/* RESPECTIVELY, OF THE EIGENVECTORS. THE EIGENVECTORS */
/* ARE UNNORMALIZED. IF AN ERROR EXIT IS MADE, NONE OF */
/* THE EIGENVECTORS HAS BEEN FOUND. */
/* IERR IS SET TO */
/* ZERO FOR NORMAL RETURN, */
/* J IF THE LIMIT OF 30*N ITERATIONS IS EXHAUSTED */
/* WHILE THE J-TH EIGENVALUE IS BEING SOUGHT. */
/* CALLS CDIV FOR COMPLEX DIVISION. */
/* CALLS CSROOT FOR COMPLEX SQUARE ROOT. */
/* QUESTIONS AND COMMENTS SHOULD BE DIRECTED TO BURTON S. GARBOW, */
/* MATHEMATICS AND COMPUTER SCIENCE DIV, ARGONNE NATIONAL LABORATORY
*/
/* THIS VERSION DATED AUGUST 1983. */
/* ------------------------------------------------------------------
*/
/* Parameter adjustments */
zi_dim1 = *nm;
zi_offset = zi_dim1 + 1;
zi -= zi_offset;
zr_dim1 = *nm;
zr_offset = zr_dim1 + 1;
zr -= zr_offset;
--wi;
--wr;
hi_dim1 = *nm;
hi_offset = hi_dim1 + 1;
hi -= hi_offset;
hr_dim1 = *nm;
hr_offset = hr_dim1 + 1;
hr -= hr_offset;
--int__;
/* Function Body */
*ierr = 0;
/* .......... INITIALIZE EIGENVECTOR MATRIX .......... */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
zr[i__ + j * zr_dim1] = 0.;
zi[i__ + j * zi_dim1] = 0.;
if (i__ == j) {
zr[i__ + j * zr_dim1] = 1.;
}
/* L100: */
}
}
/* .......... FORM THE MATRIX OF ACCUMULATED TRANSFORMATIONS */
/* FROM THE INFORMATION LEFT BY COMHES .......... */
iend = *igh - *low - 1;
if (iend <= 0) {
goto L180;
}
/* .......... FOR I=IGH-1 STEP -1 UNTIL LOW+1 DO -- .......... */
i__2 = iend;
for (ii = 1; ii <= i__2; ++ii) {
i__ = *igh - ii;
ip1 = i__ + 1;
i__1 = *igh;
for (k = ip1; k <= i__1; ++k) {
zr[k + i__ * zr_dim1] = hr[k + (i__ - 1) * hr_dim1];
zi[k + i__ * zi_dim1] = hi[k + (i__ - 1) * hi_dim1];
/* L120: */
}
j = int__[i__];
if (i__ == j) {
goto L160;
}
i__1 = *igh;
for (k = i__; k <= i__1; ++k) {
zr[i__ + k * zr_dim1] = zr[j + k * zr_dim1];
zi[i__ + k * zi_dim1] = zi[j + k * zi_dim1];
zr[j + k * zr_dim1] = 0.;
zi[j + k * zi_dim1] = 0.;
/* L140: */
}
zr[j + i__ * zr_dim1] = 1.;
L160:
;
}
/* .......... STORE ROOTS ISOLATED BY CBAL .......... */
L180:
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (i__ >= *low && i__ <= *igh) {
goto L200;
}
wr[i__] = hr[i__ + i__ * hr_dim1];
wi[i__] = hi[i__ + i__ * hi_dim1];
L200:
;
}
en = *igh;
tr = 0.;
ti = 0.;
itn = *n * 30;
/* .......... SEARCH FOR NEXT EIGENVALUE .......... */
L220:
if (en < *low) {
goto L680;
}
its = 0;
enm1 = en - 1;
/* .......... LOOK FOR SINGLE SMALL SUB-DIAGONAL ELEMENT */
/* FOR L=EN STEP -1 UNTIL LOW DO -- .......... */
L240:
i__2 = en;
for (ll = *low; ll <= i__2; ++ll) {
l = en + *low - ll;
if (l == *low) {
goto L300;
}
tst1 = (d__1 = hr[l - 1 + (l - 1) * hr_dim1], abs(d__1)) + (d__2 = hi[
l - 1 + (l - 1) * hi_dim1], abs(d__2)) + (d__3 = hr[l + l *
hr_dim1], abs(d__3)) + (d__4 = hi[l + l * hi_dim1], abs(d__4))
;
tst2 = tst1 + (d__1 = hr[l + (l - 1) * hr_dim1], abs(d__1)) + (d__2 =
hi[l + (l - 1) * hi_dim1], abs(d__2));
if (tst2 == tst1) {
goto L300;
}
/* L260: */
}
/* .......... FORM SHIFT .......... */
L300:
if (l == en) {
goto L660;
}
if (itn == 0) {
goto L1000;
}
if (its == 10 || its == 20) {
goto L320;
}
sr = hr[en + en * hr_dim1];
si = hi[en + en * hi_dim1];
xr = hr[enm1 + en * hr_dim1] * hr[en + enm1 * hr_dim1] - hi[enm1 + en *
hi_dim1] * hi[en + enm1 * hi_dim1];
xi = hr[enm1 + en * hr_dim1] * hi[en + enm1 * hi_dim1] + hi[enm1 + en *
hi_dim1] * hr[en + enm1 * hr_dim1];
if (xr == 0. && xi == 0.) {
goto L340;
}
yr = (hr[enm1 + enm1 * hr_dim1] - sr) / 2.;
yi = (hi[enm1 + enm1 * hi_dim1] - si) / 2.;
/* Computing 2nd power */
d__2 = yr;
/* Computing 2nd power */
d__3 = yi;
d__1 = d__2 * d__2 - d__3 * d__3 + xr;
d__4 = yr * 2. * yi + xi;
csroot_(&d__1, &d__4, &zzr, &zzi);
if (yr * zzr + yi * zzi >= 0.) {
goto L310;
}
zzr = -zzr;
zzi = -zzi;
L310:
d__1 = yr + zzr;
d__2 = yi + zzi;
cdiv_(&xr, &xi, &d__1, &d__2, &xr, &xi);
sr -= xr;
si -= xi;
goto L340;
/* .......... FORM EXCEPTIONAL SHIFT .......... */
L320:
sr = (d__1 = hr[en + enm1 * hr_dim1], abs(d__1)) + (d__2 = hr[enm1 + (en
- 2) * hr_dim1], abs(d__2));
si = (d__1 = hi[en + enm1 * hi_dim1], abs(d__1)) + (d__2 = hi[enm1 + (en
- 2) * hi_dim1], abs(d__2));
L340:
i__2 = en;
for (i__ = *low; i__ <= i__2; ++i__) {
hr[i__ + i__ * hr_dim1] -= sr;
hi[i__ + i__ * hi_dim1] -= si;
/* L360: */
}
tr += sr;
ti += si;
++its;
--itn;
/* .......... LOOK FOR TWO CONSECUTIVE SMALL */
/* SUB-DIAGONAL ELEMENTS .......... */
xr = (d__1 = hr[enm1 + enm1 * hr_dim1], abs(d__1)) + (d__2 = hi[enm1 +
enm1 * hi_dim1], abs(d__2));
yr = (d__1 = hr[en + enm1 * hr_dim1], abs(d__1)) + (d__2 = hi[en + enm1 *
hi_dim1], abs(d__2));
zzr = (d__1 = hr[en + en * hr_dim1], abs(d__1)) + (d__2 = hi[en + en *
hi_dim1], abs(d__2));
/* .......... FOR M=EN-1 STEP -1 UNTIL L DO -- .......... */
i__2 = enm1;
for (mm = l; mm <= i__2; ++mm) {
m = enm1 + l - mm;
if (m == l) {
goto L420;
}
yi = yr;
yr = (d__1 = hr[m + (m - 1) * hr_dim1], abs(d__1)) + (d__2 = hi[m + (
m - 1) * hi_dim1], abs(d__2));
xi = zzr;
zzr = xr;
xr = (d__1 = hr[m - 1 + (m - 1) * hr_dim1], abs(d__1)) + (d__2 = hi[m
- 1 + (m - 1) * hi_dim1], abs(d__2));
tst1 = zzr / yi * (zzr + xr + xi);
tst2 = tst1 + yr;
if (tst2 == tst1) {
goto L420;
}
/* L380: */
}
/* .......... TRIANGULAR DECOMPOSITION H=L*R .......... */
L420:
mp1 = m + 1;
i__2 = en;
for (i__ = mp1; i__ <= i__2; ++i__) {
im1 = i__ - 1;
xr = hr[im1 + im1 * hr_dim1];
xi = hi[im1 + im1 * hi_dim1];
yr = hr[i__ + im1 * hr_dim1];
yi = hi[i__ + im1 * hi_dim1];
if (abs(xr) + abs(xi) >= abs(yr) + abs(yi)) {
goto L460;
}
/* .......... INTERCHANGE ROWS OF HR AND HI .......... */
i__1 = *n;
for (j = im1; j <= i__1; ++j) {
zzr = hr[im1 + j * hr_dim1];
hr[im1 + j * hr_dim1] = hr[i__ + j * hr_dim1];
hr[i__ + j * hr_dim1] = zzr;
zzi = hi[im1 + j * hi_dim1];
hi[im1 + j * hi_dim1] = hi[i__ + j * hi_dim1];
hi[i__ + j * hi_dim1] = zzi;
/* L440: */
}
cdiv_(&xr, &xi, &yr, &yi, &zzr, &zzi);
wr[i__] = 1.;
goto L480;
L460:
cdiv_(&yr, &yi, &xr, &xi, &zzr, &zzi);
wr[i__] = -1.;
L480:
hr[i__ + im1 * hr_dim1] = zzr;
hi[i__ + im1 * hi_dim1] = zzi;
i__1 = *n;
for (j = i__; j <= i__1; ++j) {
hr[i__ + j * hr_dim1] = hr[i__ + j * hr_dim1] - zzr * hr[im1 + j *
hr_dim1] + zzi * hi[im1 + j * hi_dim1];
hi[i__ + j * hi_dim1] = hi[i__ + j * hi_dim1] - zzr * hi[im1 + j *
hi_dim1] - zzi * hr[im1 + j * hr_dim1];
/* L500: */
}
/* L520: */
}
/* .......... COMPOSITION R*L=H .......... */
i__2 = en;
for (j = mp1; j <= i__2; ++j) {
xr = hr[j + (j - 1) * hr_dim1];
xi = hi[j + (j - 1) * hi_dim1];
hr[j + (j - 1) * hr_dim1] = 0.;
hi[j + (j - 1) * hi_dim1] = 0.;
/* .......... INTERCHANGE COLUMNS OF HR, HI, ZR, AND ZI, */
/* IF NECESSARY .......... */
if (wr[j] <= 0.) {
goto L580;
}
i__1 = j;
for (i__ = 1; i__ <= i__1; ++i__) {
zzr = hr[i__ + (j - 1) * hr_dim1];
hr[i__ + (j - 1) * hr_dim1] = hr[i__ + j * hr_dim1];
hr[i__ + j * hr_dim1] = zzr;
zzi = hi[i__ + (j - 1) * hi_dim1];
hi[i__ + (j - 1) * hi_dim1] = hi[i__ + j * hi_dim1];
hi[i__ + j * hi_dim1] = zzi;
/* L540: */
}
i__1 = *igh;
for (i__ = *low; i__ <= i__1; ++i__) {
zzr = zr[i__ + (j - 1) * zr_dim1];
zr[i__ + (j - 1) * zr_dim1] = zr[i__ + j * zr_dim1];
zr[i__ + j * zr_dim1] = zzr;
zzi = zi[i__ + (j - 1) * zi_dim1];
zi[i__ + (j - 1) * zi_dim1] = zi[i__ + j * zi_dim1];
zi[i__ + j * zi_dim1] = zzi;
/* L560: */
}
L580:
i__1 = j;
for (i__ = 1; i__ <= i__1; ++i__) {
hr[i__ + (j - 1) * hr_dim1] = hr[i__ + (j - 1) * hr_dim1] + xr *
hr[i__ + j * hr_dim1] - xi * hi[i__ + j * hi_dim1];
hi[i__ + (j - 1) * hi_dim1] = hi[i__ + (j - 1) * hi_dim1] + xr *
hi[i__ + j * hi_dim1] + xi * hr[i__ + j * hr_dim1];
/* L600: */
}
/* .......... ACCUMULATE TRANSFORMATIONS .......... */
i__1 = *igh;
for (i__ = *low; i__ <= i__1; ++i__) {
zr[i__ + (j - 1) * zr_dim1] = zr[i__ + (j - 1) * zr_dim1] + xr *
zr[i__ + j * zr_dim1] - xi * zi[i__ + j * zi_dim1];
zi[i__ + (j - 1) * zi_dim1] = zi[i__ + (j - 1) * zi_dim1] + xr *
zi[i__ + j * zi_dim1] + xi * zr[i__ + j * zr_dim1];
/* L620: */
}
/* L640: */
}
goto L240;
/* .......... A ROOT FOUND .......... */
L660:
hr[en + en * hr_dim1] += tr;
wr[en] = hr[en + en * hr_dim1];
hi[en + en * hi_dim1] += ti;
wi[en] = hi[en + en * hi_dim1];
en = enm1;
goto L220;
/* .......... ALL ROOTS FOUND. BACKSUBSTITUTE TO FIND */
/* VECTORS OF UPPER TRIANGULAR FORM .......... */
L680:
norm = 0.;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__1 = *n;
for (j = i__; j <= i__1; ++j) {
tr = (d__1 = hr[i__ + j * hr_dim1], abs(d__1)) + (d__2 = hi[i__ +
j * hi_dim1], abs(d__2));
if (tr > norm) {
norm = tr;
}
/* L720: */
}
}
hr[hr_dim1 + 1] = norm;
if (*n == 1 || norm == 0.) {
goto L1001;
}
/* .......... FOR EN=N STEP -1 UNTIL 2 DO -- .......... */
i__1 = *n;
for (nn = 2; nn <= i__1; ++nn) {
en = *n + 2 - nn;
xr = wr[en];
xi = wi[en];
hr[en + en * hr_dim1] = 1.;
hi[en + en * hi_dim1] = 0.;
enm1 = en - 1;
/* .......... FOR I=EN-1 STEP -1 UNTIL 1 DO -- .......... */
i__2 = enm1;
for (ii = 1; ii <= i__2; ++ii) {
i__ = en - ii;
zzr = 0.;
zzi = 0.;
ip1 = i__ + 1;
i__3 = en;
for (j = ip1; j <= i__3; ++j) {
zzr = zzr + hr[i__ + j * hr_dim1] * hr[j + en * hr_dim1] - hi[
i__ + j * hi_dim1] * hi[j + en * hi_dim1];
zzi = zzi + hr[i__ + j * hr_dim1] * hi[j + en * hi_dim1] + hi[
i__ + j * hi_dim1] * hr[j + en * hr_dim1];
/* L740: */
}
yr = xr - wr[i__];
yi = xi - wi[i__];
if (yr != 0. || yi != 0.) {
goto L765;
}
tst1 = norm;
yr = tst1;
L760:
yr *= .01;
tst2 = norm + yr;
if (tst2 > tst1) {
goto L760;
}
L765:
cdiv_(&zzr, &zzi, &yr, &yi, &hr[i__ + en * hr_dim1], &hi[i__ + en
* hi_dim1]);
/* .......... OVERFLOW CONTROL .......... */
tr = (d__1 = hr[i__ + en * hr_dim1], abs(d__1)) + (d__2 = hi[i__
+ en * hi_dim1], abs(d__2));
if (tr == 0.) {
goto L780;
}
tst1 = tr;
tst2 = tst1 + 1. / tst1;
if (tst2 > tst1) {
goto L780;
}
i__3 = en;
for (j = i__; j <= i__3; ++j) {
hr[j + en * hr_dim1] /= tr;
hi[j + en * hi_dim1] /= tr;
/* L770: */
}
L780:
;
}
/* L800: */
}
/* .......... END BACKSUBSTITUTION .......... */
enm1 = *n - 1;
/* .......... VECTORS OF ISOLATED ROOTS .......... */
i__1 = enm1;
for (i__ = 1; i__ <= i__1; ++i__) {
if (i__ >= *low && i__ <= *igh) {
goto L840;
}
ip1 = i__ + 1;
i__2 = *n;
for (j = ip1; j <= i__2; ++j) {
zr[i__ + j * zr_dim1] = hr[i__ + j * hr_dim1];
zi[i__ + j * zi_dim1] = hi[i__ + j * hi_dim1];
/* L820: */
}
L840:
;
}
/* .......... MULTIPLY BY TRANSFORMATION MATRIX TO GIVE */
/* VECTORS OF ORIGINAL FULL MATRIX. */
/* FOR J=N STEP -1 UNTIL LOW+1 DO -- .......... */
i__1 = enm1;
for (jj = *low; jj <= i__1; ++jj) {
j = *n + *low - jj;
m = min(j,*igh);
i__2 = *igh;
for (i__ = *low; i__ <= i__2; ++i__) {
zzr = 0.;
zzi = 0.;
i__3 = m;
for (k = *low; k <= i__3; ++k) {
zzr = zzr + zr[i__ + k * zr_dim1] * hr[k + j * hr_dim1] - zi[
i__ + k * zi_dim1] * hi[k + j * hi_dim1];
zzi = zzi + zr[i__ + k * zr_dim1] * hi[k + j * hi_dim1] + zi[
i__ + k * zi_dim1] * hr[k + j * hr_dim1];
/* L860: */
}
zr[i__ + j * zr_dim1] = zzr;
zi[i__ + j * zi_dim1] = zzi;
/* L880: */
}
}
goto L1001;
/* .......... SET ERROR -- ALL EIGENVALUES HAVE NOT */
/* CONVERGED AFTER 30*N ITERATIONS .......... */
L1000:
*ierr = en;
L1001:
return 0;
} /* comlr2_ */
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