/* ========================================================================== */
/* === Cholesky/t_cholmod_ltsolve =========================================== */
/* ========================================================================== */
/* -----------------------------------------------------------------------------
* CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
* The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
* Lesser General Public License. See lesser.txt for a text of the license.
* CHOLMOD is also available under other licenses; contact authors for details.
* http://www.cise.ufl.edu/research/sparse
* -------------------------------------------------------------------------- */
/* Template routine to solve L'x=b with unit or non-unit diagonal, or
* solve DL'x=b.
*
* The numeric xtype of L and Y must match. Y contains b on input and x on
* output, stored in row-form. Y is nrow-by-n, where nrow must equal 1 for the
* complex or zomplex cases, and nrow <= 4 for the real case.
*
* This file is not compiled separately. It is included in t_cholmod_solve.c
* instead. It contains no user-callable routines.
*
* workspace: none
*
* Supports real, complex, and zomplex factors.
*/
/* undefine all prior definitions */
#undef FORM_NAME
#undef LSOLVE
#undef DIAG
/* -------------------------------------------------------------------------- */
/* define the method */
/* -------------------------------------------------------------------------- */
#ifdef LL
/* LL': solve Lx=b with non-unit diagonal */
#define FORM_NAME(prefix,rank) prefix ## ll_ltsolve_ ## rank
#define DIAG
#elif defined (LD)
/* LDL': solve LDx=b */
#define FORM_NAME(prefix,rank) prefix ## ldl_dltsolve_ ## rank
#define DIAG
#else
/* LDL': solve Lx=b with unit diagonal */
#define FORM_NAME(prefix,rank) prefix ## ldl_ltsolve_ ## rank
#endif
/* LSOLVE(k) defines the name of a routine for an n-by-k right-hand-side. */
#define LSOLVE(prefix,rank) FORM_NAME(prefix,rank)
#ifdef REAL
/* ========================================================================== */
/* === LSOLVE (1) =========================================================== */
/* ========================================================================== */
/* Solve L'x=b, where b has 1 column */
static void LSOLVE (PREFIX,1)
(
cholmod_factor *L,
double X [ ] /* n-by-1 in row form */
)
{
double *Lx = L->x ;
Int *Li = L->i ;
Int *Lp = L->p ;
Int *Lnz = L->nz ;
Int j, n = L->n ;
for (j = n-1 ; j >= 0 ; )
{
/* get the start, end, and length of column j */
Int p = Lp [j] ;
Int lnz = Lnz [j] ;
Int pend = p + lnz ;
/* find a chain of supernodes (up to j, j-1, and j-2) */
if (j < 4 || lnz != Lnz [j-1] - 1 || Li [Lp [j-1]+1] != j)
{
/* -------------------------------------------------------------- */
/* solve with a single column of L */
/* -------------------------------------------------------------- */
double y = X [j] ;
#ifdef DIAG
double d = Lx [p] ;
#endif
#ifdef LD
y /= d ;
#endif
for (p++ ; p < pend ; p++)
{
y -= Lx [p] * X [Li [p]] ;
}
#ifdef LL
X [j] = y / d ;
#else
X [j] = y ;
#endif
j-- ; /* advance to the next column of L */
}
else if (lnz != Lnz [j-2]-2 || Li [Lp [j-2]+2] != j)
{
/* -------------------------------------------------------------- */
/* solve with a supernode of two columns of L */
/* -------------------------------------------------------------- */
double y [2], t ;
Int q = Lp [j-1] ;
#ifdef DIAG
double d [2] ;
d [0] = Lx [p] ;
d [1] = Lx [q] ;
#endif
t = Lx [q+1] ;
#ifdef LD
y [0] = X [j ] / d [0] ;
y [1] = X [j-1] / d [1] ;
#else
y [0] = X [j ] ;
y [1] = X [j-1] ;
#endif
for (p++, q += 2 ; p < pend ; p++, q++)
{
Int i = Li [p] ;
y [0] -= Lx [p] * X [i] ;
y [1] -= Lx [q] * X [i] ;
}
#ifdef LL
y [0] /= d [0] ;
y [1] = (y [1] - t * y [0]) / d [1] ;
#else
y [1] -= t * y [0] ;
#endif
X [j ] = y [0] ;
X [j-1] = y [1] ;
j -= 2 ; /* advance to the next column of L */
}
else
{
/* -------------------------------------------------------------- */
/* solve with a supernode of three columns of L */
/* -------------------------------------------------------------- */
double y [3], t [3] ;
Int q = Lp [j-1] ;
Int r = Lp [j-2] ;
#ifdef DIAG
double d [3] ;
d [0] = Lx [p] ;
d [1] = Lx [q] ;
d [2] = Lx [r] ;
#endif
t [0] = Lx [q+1] ;
t [1] = Lx [r+1] ;
t [2] = Lx [r+2] ;
#ifdef LD
y [0] = X [j] / d [0] ;
y [1] = X [j-1] / d [1] ;
y [2] = X [j-2] / d [2] ;
#else
y [0] = X [j] ;
y [1] = X [j-1] ;
y [2] = X [j-2] ;
#endif
for (p++, q += 2, r += 3 ; p < pend ; p++, q++, r++)
{
Int i = Li [p] ;
y [0] -= Lx [p] * X [i] ;
y [1] -= Lx [q] * X [i] ;
y [2] -= Lx [r] * X [i] ;
}
#ifdef LL
y [0] /= d [0] ;
y [1] = (y [1] - t [0] * y [0]) / d [1] ;
y [2] = (y [2] - t [2] * y [0] - t [1] * y [1]) / d [2] ;
#else
y [1] -= t [0] * y [0] ;
y [2] -= t [2] * y [0] + t [1] * y [1] ;
#endif
X [j-2] = y [2] ;
X [j-1] = y [1] ;
X [j ] = y [0] ;
j -= 3 ; /* advance to the next column of L */
}
}
}
/* ========================================================================== */
/* === LSOLVE (2) =========================================================== */
/* ========================================================================== */
/* Solve L'x=b, where b has 2 columns */
static void LSOLVE (PREFIX,2)
(
cholmod_factor *L,
double X [ ][2] /* n-by-2 in row form */
)
{
double *Lx = L->x ;
Int *Li = L->i ;
Int *Lp = L->p ;
Int *Lnz = L->nz ;
Int j, n = L->n ;
for (j = n-1 ; j >= 0 ; )
{
/* get the start, end, and length of column j */
Int p = Lp [j] ;
Int lnz = Lnz [j] ;
Int pend = p + lnz ;
/* find a chain of supernodes (up to j, j-1, and j-2) */
if (j < 4 || lnz != Lnz [j-1] - 1 || Li [Lp [j-1]+1] != j)
{
/* -------------------------------------------------------------- */
/* solve with a single column of L */
/* -------------------------------------------------------------- */
double y [2] ;
#ifdef DIAG
double d = Lx [p] ;
#endif
#ifdef LD
y [0] = X [j][0] / d ;
y [1] = X [j][1] / d ;
#else
y [0] = X [j][0] ;
y [1] = X [j][1] ;
#endif
for (p++ ; p < pend ; p++)
{
Int i = Li [p] ;
y [0] -= Lx [p] * X [i][0] ;
y [1] -= Lx [p] * X [i][1] ;
}
#ifdef LL
X [j][0] = y [0] / d ;
X [j][1] = y [1] / d ;
#else
X [j][0] = y [0] ;
X [j][1] = y [1] ;
#endif
j-- ; /* advance to the next column of L */
}
else if (lnz != Lnz [j-2]-2 || Li [Lp [j-2]+2] != j)
{
/* -------------------------------------------------------------- */
/* solve with a supernode of two columns of L */
/* -------------------------------------------------------------- */
double y [2][2], t ;
Int q = Lp [j-1] ;
#ifdef DIAG
double d [2] ;
d [0] = Lx [p] ;
d [1] = Lx [q] ;
#endif
t = Lx [q+1] ;
#ifdef LD
y [0][0] = X [j ][0] / d [0] ;
y [0][1] = X [j ][1] / d [0] ;
y [1][0] = X [j-1][0] / d [1] ;
y [1][1] = X [j-1][1] / d [1] ;
#else
y [0][0] = X [j ][0] ;
y [0][1] = X [j ][1] ;
y [1][0] = X [j-1][0] ;
y [1][1] = X [j-1][1] ;
#endif
for (p++, q += 2 ; p < pend ; p++, q++)
{
Int i = Li [p] ;
y [0][0] -= Lx [p] * X [i][0] ;
y [0][1] -= Lx [p] * X [i][1] ;
y [1][0] -= Lx [q] * X [i][0] ;
y [1][1] -= Lx [q] * X [i][1] ;
}
#ifdef LL
y [0][0] /= d [0] ;
y [0][1] /= d [0] ;
y [1][0] = (y [1][0] - t * y [0][0]) / d [1] ;
y [1][1] = (y [1][1] - t * y [0][1]) / d [1] ;
#else
y [1][0] -= t * y [0][0] ;
y [1][1] -= t * y [0][1] ;
#endif
X [j ][0] = y [0][0] ;
X [j ][1] = y [0][1] ;
X [j-1][0] = y [1][0] ;
X [j-1][1] = y [1][1] ;
j -= 2 ; /* advance to the next column of L */
}
else
{
/* -------------------------------------------------------------- */
/* solve with a supernode of three columns of L */
/* -------------------------------------------------------------- */
double y [3][2], t [3] ;
Int q = Lp [j-1] ;
Int r = Lp [j-2] ;
#ifdef DIAG
double d [3] ;
d [0] = Lx [p] ;
d [1] = Lx [q] ;
d [2] = Lx [r] ;
#endif
t [0] = Lx [q+1] ;
t [1] = Lx [r+1] ;
t [2] = Lx [r+2] ;
#ifdef LD
y [0][0] = X [j ][0] / d [0] ;
y [0][1] = X [j ][1] / d [0] ;
y [1][0] = X [j-1][0] / d [1] ;
y [1][1] = X [j-1][1] / d [1] ;
y [2][0] = X [j-2][0] / d [2] ;
y [2][1] = X [j-2][1] / d [2] ;
#else
y [0][0] = X [j ][0] ;
y [0][1] = X [j ][1] ;
y [1][0] = X [j-1][0] ;
y [1][1] = X [j-1][1] ;
y [2][0] = X [j-2][0] ;
y [2][1] = X [j-2][1] ;
#endif
for (p++, q += 2, r += 3 ; p < pend ; p++, q++, r++)
{
Int i = Li [p] ;
y [0][0] -= Lx [p] * X [i][0] ;
y [0][1] -= Lx [p] * X [i][1] ;
y [1][0] -= Lx [q] * X [i][0] ;
y [1][1] -= Lx [q] * X [i][1] ;
y [2][0] -= Lx [r] * X [i][0] ;
y [2][1] -= Lx [r] * X [i][1] ;
}
#ifdef LL
y [0][0] /= d [0] ;
y [0][1] /= d [0] ;
y [1][0] = (y [1][0] - t [0] * y [0][0]) / d [1] ;
y [1][1] = (y [1][1] - t [0] * y [0][1]) / d [1] ;
y [2][0] = (y [2][0] - t [2] * y [0][0] - t [1] * y [1][0]) / d [2];
y [2][1] = (y [2][1] - t [2] * y [0][1] - t [1] * y [1][1]) / d [2];
#else
y [1][0] -= t [0] * y [0][0] ;
y [1][1] -= t [0] * y [0][1] ;
y [2][0] -= t [2] * y [0][0] + t [1] * y [1][0] ;
y [2][1] -= t [2] * y [0][1] + t [1] * y [1][1] ;
#endif
X [j ][0] = y [0][0] ;
X [j ][1] = y [0][1] ;
X [j-1][0] = y [1][0] ;
X [j-1][1] = y [1][1] ;
X [j-2][0] = y [2][0] ;
X [j-2][1] = y [2][1] ;
j -= 3 ; /* advance to the next column of L */
}
}
}
/* ========================================================================== */
/* === LSOLVE (3) =========================================================== */
/* ========================================================================== */
/* Solve L'x=b, where b has 3 columns */
static void LSOLVE (PREFIX,3)
(
cholmod_factor *L,
double X [ ][3] /* n-by-3 in row form */
)
{
double *Lx = L->x ;
Int *Li = L->i ;
Int *Lp = L->p ;
Int *Lnz = L->nz ;
Int j, n = L->n ;
for (j = n-1 ; j >= 0 ; )
{
/* get the start, end, and length of column j */
Int p = Lp [j] ;
Int lnz = Lnz [j] ;
Int pend = p + lnz ;
/* find a chain of supernodes (up to j, j-1, and j-2) */
if (j < 4 || lnz != Lnz [j-1] - 1 || Li [Lp [j-1]+1] != j)
{
/* -------------------------------------------------------------- */
/* solve with a single column of L */
/* -------------------------------------------------------------- */
double y [3] ;
#ifdef DIAG
double d = Lx [p] ;
#endif
#ifdef LD
y [0] = X [j][0] / d ;
y [1] = X [j][1] / d ;
y [2] = X [j][2] / d ;
#else
y [0] = X [j][0] ;
y [1] = X [j][1] ;
y [2] = X [j][2] ;
#endif
for (p++ ; p < pend ; p++)
{
Int i = Li [p] ;
y [0] -= Lx [p] * X [i][0] ;
y [1] -= Lx [p] * X [i][1] ;
y [2] -= Lx [p] * X [i][2] ;
}
#ifdef LL
X [j][0] = y [0] / d ;
X [j][1] = y [1] / d ;
X [j][2] = y [2] / d ;
#else
X [j][0] = y [0] ;
X [j][1] = y [1] ;
X [j][2] = y [2] ;
#endif
j-- ; /* advance to the next column of L */
}
else if (lnz != Lnz [j-2]-2 || Li [Lp [j-2]+2] != j)
{
/* -------------------------------------------------------------- */
/* solve with a supernode of two columns of L */
/* -------------------------------------------------------------- */
double y [2][3], t ;
Int q = Lp [j-1] ;
#ifdef DIAG
double d [2] ;
d [0] = Lx [p] ;
d [1] = Lx [q] ;
#endif
t = Lx [q+1] ;
#ifdef LD
y [0][0] = X [j ][0] / d [0] ;
y [0][1] = X [j ][1] / d [0] ;
y [0][2] = X [j ][2] / d [0] ;
y [1][0] = X [j-1][0] / d [1] ;
y [1][1] = X [j-1][1] / d [1] ;
y [1][2] = X [j-1][2] / d [1] ;
#else
y [0][0] = X [j ][0] ;
y [0][1] = X [j ][1] ;
y [0][2] = X [j ][2] ;
y [1][0] = X [j-1][0] ;
y [1][1] = X [j-1][1] ;
y [1][2] = X [j-1][2] ;
#endif
for (p++, q += 2 ; p < pend ; p++, q++)
{
Int i = Li [p] ;
y [0][0] -= Lx [p] * X [i][0] ;
y [0][1] -= Lx [p] * X [i][1] ;
y [0][2] -= Lx [p] * X [i][2] ;
y [1][0] -= Lx [q] * X [i][0] ;
y [1][1] -= Lx [q] * X [i][1] ;
y [1][2] -= Lx [q] * X [i][2] ;
}
#ifdef LL
y [0][0] /= d [0] ;
y [0][1] /= d [0] ;
y [0][2] /= d [0] ;
y [1][0] = (y [1][0] - t * y [0][0]) / d [1] ;
y [1][1] = (y [1][1] - t * y [0][1]) / d [1] ;
y [1][2] = (y [1][2] - t * y [0][2]) / d [1] ;
#else
y [1][0] -= t * y [0][0] ;
y [1][1] -= t * y [0][1] ;
y [1][2] -= t * y [0][2] ;
#endif
X [j ][0] = y [0][0] ;
X [j ][1] = y [0][1] ;
X [j ][2] = y [0][2] ;
X [j-1][0] = y [1][0] ;
X [j-1][1] = y [1][1] ;
X [j-1][2] = y [1][2] ;
j -= 2 ; /* advance to the next column of L */
}
else
{
/* -------------------------------------------------------------- */
/* solve with a supernode of three columns of L */
/* -------------------------------------------------------------- */
double y [3][3], t [3] ;
Int q = Lp [j-1] ;
Int r = Lp [j-2] ;
#ifdef DIAG
double d [3] ;
d [0] = Lx [p] ;
d [1] = Lx [q] ;
d [2] = Lx [r] ;
#endif
t [0] = Lx [q+1] ;
t [1] = Lx [r+1] ;
t [2] = Lx [r+2] ;
#ifdef LD
y [0][0] = X [j ][0] / d [0] ;
y [0][1] = X [j ][1] / d [0] ;
y [0][2] = X [j ][2] / d [0] ;
y [1][0] = X [j-1][0] / d [1] ;
y [1][1] = X [j-1][1] / d [1] ;
y [1][2] = X [j-1][2] / d [1] ;
y [2][0] = X [j-2][0] / d [2] ;
y [2][1] = X [j-2][1] / d [2] ;
y [2][2] = X [j-2][2] / d [2] ;
#else
y [0][0] = X [j ][0] ;
y [0][1] = X [j ][1] ;
y [0][2] = X [j ][2] ;
y [1][0] = X [j-1][0] ;
y [1][1] = X [j-1][1] ;
y [1][2] = X [j-1][2] ;
y [2][0] = X [j-2][0] ;
y [2][1] = X [j-2][1] ;
y [2][2] = X [j-2][2] ;
#endif
for (p++, q += 2, r += 3 ; p < pend ; p++, q++, r++)
{
Int i = Li [p] ;
y [0][0] -= Lx [p] * X [i][0] ;
y [0][1] -= Lx [p] * X [i][1] ;
y [0][2] -= Lx [p] * X [i][2] ;
y [1][0] -= Lx [q] * X [i][0] ;
y [1][1] -= Lx [q] * X [i][1] ;
y [1][2] -= Lx [q] * X [i][2] ;
y [2][0] -= Lx [r] * X [i][0] ;
y [2][1] -= Lx [r] * X [i][1] ;
y [2][2] -= Lx [r] * X [i][2] ;
}
#ifdef LL
y [0][0] /= d [0] ;
y [0][1] /= d [0] ;
y [0][2] /= d [0] ;
y [1][0] = (y [1][0] - t [0] * y [0][0]) / d [1] ;
y [1][1] = (y [1][1] - t [0] * y [0][1]) / d [1] ;
y [1][2] = (y [1][2] - t [0] * y [0][2]) / d [1] ;
y [2][0] = (y [2][0] - t [2] * y [0][0] - t [1] * y [1][0]) / d [2];
y [2][1] = (y [2][1] - t [2] * y [0][1] - t [1] * y [1][1]) / d [2];
y [2][2] = (y [2][2] - t [2] * y [0][2] - t [1] * y [1][2]) / d [2];
#else
y [1][0] -= t [0] * y [0][0] ;
y [1][1] -= t [0] * y [0][1] ;
y [1][2] -= t [0] * y [0][2] ;
y [2][0] -= t [2] * y [0][0] + t [1] * y [1][0] ;
y [2][1] -= t [2] * y [0][1] + t [1] * y [1][1] ;
y [2][2] -= t [2] * y [0][2] + t [1] * y [1][2] ;
#endif
X [j ][0] = y [0][0] ;
X [j ][1] = y [0][1] ;
X [j ][2] = y [0][2] ;
X [j-1][0] = y [1][0] ;
X [j-1][1] = y [1][1] ;
X [j-1][2] = y [1][2] ;
X [j-2][0] = y [2][0] ;
X [j-2][1] = y [2][1] ;
X [j-2][2] = y [2][2] ;
j -= 3 ; /* advance to the next column of L */
}
}
}
/* ========================================================================== */
/* === LSOLVE (4) =========================================================== */
/* ========================================================================== */
/* Solve L'x=b, where b has 4 columns */
static void LSOLVE (PREFIX,4)
(
cholmod_factor *L,
double X [ ][4] /* n-by-4 in row form */
)
{
double *Lx = L->x ;
Int *Li = L->i ;
Int *Lp = L->p ;
Int *Lnz = L->nz ;
Int j, n = L->n ;
for (j = n-1 ; j >= 0 ; )
{
/* get the start, end, and length of column j */
Int p = Lp [j] ;
Int lnz = Lnz [j] ;
Int pend = p + lnz ;
/* find a chain of supernodes (up to j, j-1, and j-2) */
if (j < 4 || lnz != Lnz [j-1] - 1 || Li [Lp [j-1]+1] != j)
{
/* -------------------------------------------------------------- */
/* solve with a single column of L */
/* -------------------------------------------------------------- */
double y [4] ;
#ifdef DIAG
double d = Lx [p] ;
#endif
#ifdef LD
y [0] = X [j][0] / d ;
y [1] = X [j][1] / d ;
y [2] = X [j][2] / d ;
y [3] = X [j][3] / d ;
#else
y [0] = X [j][0] ;
y [1] = X [j][1] ;
y [2] = X [j][2] ;
y [3] = X [j][3] ;
#endif
for (p++ ; p < pend ; p++)
{
Int i = Li [p] ;
y [0] -= Lx [p] * X [i][0] ;
y [1] -= Lx [p] * X [i][1] ;
y [2] -= Lx [p] * X [i][2] ;
y [3] -= Lx [p] * X [i][3] ;
}
#ifdef LL
X [j][0] = y [0] / d ;
X [j][1] = y [1] / d ;
X [j][2] = y [2] / d ;
X [j][3] = y [3] / d ;
#else
X [j][0] = y [0] ;
X [j][1] = y [1] ;
X [j][2] = y [2] ;
X [j][3] = y [3] ;
#endif
j-- ; /* advance to the next column of L */
}
else /* if (j == 1 || lnz != Lnz [j-2]-2 || Li [Lp [j-2]+2] != j) */
{
/* -------------------------------------------------------------- */
/* solve with a supernode of two columns of L */
/* -------------------------------------------------------------- */
double y [2][4], t ;
Int q = Lp [j-1] ;
#ifdef DIAG
double d [2] ;
d [0] = Lx [p] ;
d [1] = Lx [q] ;
#endif
t = Lx [q+1] ;
#ifdef LD
y [0][0] = X [j ][0] / d [0] ;
y [0][1] = X [j ][1] / d [0] ;
y [0][2] = X [j ][2] / d [0] ;
y [0][3] = X [j ][3] / d [0] ;
y [1][0] = X [j-1][0] / d [1] ;
y [1][1] = X [j-1][1] / d [1] ;
y [1][2] = X [j-1][2] / d [1] ;
y [1][3] = X [j-1][3] / d [1] ;
#else
y [0][0] = X [j ][0] ;
y [0][1] = X [j ][1] ;
y [0][2] = X [j ][2] ;
y [0][3] = X [j ][3] ;
y [1][0] = X [j-1][0] ;
y [1][1] = X [j-1][1] ;
y [1][2] = X [j-1][2] ;
y [1][3] = X [j-1][3] ;
#endif
for (p++, q += 2 ; p < pend ; p++, q++)
{
Int i = Li [p] ;
y [0][0] -= Lx [p] * X [i][0] ;
y [0][1] -= Lx [p] * X [i][1] ;
y [0][2] -= Lx [p] * X [i][2] ;
y [0][3] -= Lx [p] * X [i][3] ;
y [1][0] -= Lx [q] * X [i][0] ;
y [1][1] -= Lx [q] * X [i][1] ;
y [1][2] -= Lx [q] * X [i][2] ;
y [1][3] -= Lx [q] * X [i][3] ;
}
#ifdef LL
y [0][0] /= d [0] ;
y [0][1] /= d [0] ;
y [0][2] /= d [0] ;
y [0][3] /= d [0] ;
y [1][0] = (y [1][0] - t * y [0][0]) / d [1] ;
y [1][1] = (y [1][1] - t * y [0][1]) / d [1] ;
y [1][2] = (y [1][2] - t * y [0][2]) / d [1] ;
y [1][3] = (y [1][3] - t * y [0][3]) / d [1] ;
#else
y [1][0] -= t * y [0][0] ;
y [1][1] -= t * y [0][1] ;
y [1][2] -= t * y [0][2] ;
y [1][3] -= t * y [0][3] ;
#endif
X [j ][0] = y [0][0] ;
X [j ][1] = y [0][1] ;
X [j ][2] = y [0][2] ;
X [j ][3] = y [0][3] ;
X [j-1][0] = y [1][0] ;
X [j-1][1] = y [1][1] ;
X [j-1][2] = y [1][2] ;
X [j-1][3] = y [1][3] ;
j -= 2 ; /* advance to the next column of L */
}
/* NOTE: with 4 right-hand-sides, it suffices to exploit dynamic
* supernodes of just size 1 and 2. 3-column supernodes are not
* needed. */
}
}
#endif
/* ========================================================================== */
/* === LSOLVE (k) =========================================================== */
/* ========================================================================== */
static void LSOLVE (PREFIX,k)
(
cholmod_factor *L,
cholmod_dense *Y /* nr-by-n where nr is 1 to 4 */
)
{
#ifndef REAL
#ifdef DIAG
double d [1] ;
#endif
double yx [2] ;
#ifdef ZOMPLEX
double yz [1] ;
double *Lz = L->z ;
double *Xz = Y->z ;
#endif
double *Lx = L->x ;
double *Xx = Y->x ;
Int *Li = L->i ;
Int *Lp = L->p ;
Int *Lnz = L->nz ;
Int i, j, n = L->n ;
#endif
ASSERT (L->xtype == Y->xtype) ; /* L and Y must have the same xtype */
ASSERT (L->n == Y->ncol) ; /* dimensions must match */
ASSERT (Y->nrow == Y->d) ; /* leading dimension of Y = # rows of Y */
ASSERT (L->xtype != CHOLMOD_PATTERN) ; /* L is not symbolic */
ASSERT (!(L->is_super)) ; /* L is simplicial LL' or LDL' */
#ifdef REAL
/* ---------------------------------------------------------------------- */
/* solve a real linear system, with 1 to 4 RHS's and dynamic supernodes */
/* ---------------------------------------------------------------------- */
ASSERT (Y->nrow <= 4) ;
switch (Y->nrow)
{
case 1: LSOLVE (PREFIX,1) (L, Y->x) ; break ;
case 2: LSOLVE (PREFIX,2) (L, Y->x) ; break ;
case 3: LSOLVE (PREFIX,3) (L, Y->x) ; break ;
case 4: LSOLVE (PREFIX,4) (L, Y->x) ; break ;
}
#else
/* ---------------------------------------------------------------------- */
/* solve a complex linear system, with just one right-hand-side */
/* ---------------------------------------------------------------------- */
ASSERT (Y->nrow == 1) ;
for (j = n-1 ; j >= 0 ; j--)
{
/* get the start, end, and length of column j */
Int p = Lp [j] ;
Int lnz = Lnz [j] ;
Int pend = p + lnz ;
/* y = X [j] ; */
ASSIGN (yx,yz,0, Xx,Xz,j) ;
#ifdef DIAG
/* d = Lx [p] ; */
ASSIGN_REAL (d,0, Lx,p) ;
#endif
#ifdef LD
/* y /= d ; */
DIV_REAL (yx,yz,0, yx,yz,0, d,0) ;
#endif
for (p++ ; p < pend ; p++)
{
/* y -= conj (Lx [p]) * X [Li [p]] ; */
i = Li [p] ;
MULTSUBCONJ (yx,yz,0, Lx,Lz,p, Xx,Xz,i) ;
}
#ifdef LL
/* X [j] = y / d ; */
DIV_REAL (Xx,Xz,j, yx,yz,0, d,0) ;
#else
/* X [j] = y ; */
ASSIGN (Xx,Xz,j, yx,yz,0) ;
#endif
}
#endif
}
/* prepare for the next inclusion of this file in cholmod_solve.c */
#undef LL
#undef LD
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