/*! \file
Copyright (c) 2003, The Regents of the University of California, through
Lawrence Berkeley National Laboratory (subject to receipt of any required
approvals from U.S. Dept. of Energy)
All rights reserved.
The source code is distributed under BSD license, see the file License.txt
at the top-level directory.
*/
/*! @file zsp_blas2.c
* \brief Sparse BLAS 2, using some dense BLAS 2 operations
*
*
* -- SuperLU routine (version 5.1) --
* Univ. of California Berkeley, Xerox Palo Alto Research Center,
* and Lawrence Berkeley National Lab.
* October 15, 2003
*
* Last update: December 3, 2015
*
*/
/*
* File name: zsp_blas2.c
* Purpose: Sparse BLAS 2, using some dense BLAS 2 operations.
*/
#include "slu_zdefs.h"
/*
* Function prototypes
*/
void zusolve(int, int, doublecomplex*, doublecomplex*);
void zlsolve(int, int, doublecomplex*, doublecomplex*);
void zmatvec(int, int, int, doublecomplex*, doublecomplex*, doublecomplex*);
/*! \brief Solves one of the systems of equations A*x = b, or A'*x = b
*
*
* Purpose
* =======
*
* sp_ztrsv() solves one of the systems of equations
* A*x = b, or A'*x = b,
* where b and x are n element vectors and A is a sparse unit , or
* non-unit, upper or lower triangular matrix.
* No test for singularity or near-singularity is included in this
* routine. Such tests must be performed before calling this routine.
*
* Parameters
* ==========
*
* uplo - (input) char*
* On entry, uplo specifies whether the matrix is an upper or
* lower triangular matrix as follows:
* uplo = 'U' or 'u' A is an upper triangular matrix.
* uplo = 'L' or 'l' A is a lower triangular matrix.
*
* trans - (input) char*
* On entry, trans specifies the equations to be solved as
* follows:
* trans = 'N' or 'n' A*x = b.
* trans = 'T' or 't' A'*x = b.
* trans = 'C' or 'c' A^H*x = b.
*
* diag - (input) char*
* On entry, diag specifies whether or not A is unit
* triangular as follows:
* diag = 'U' or 'u' A is assumed to be unit triangular.
* diag = 'N' or 'n' A is not assumed to be unit
* triangular.
*
* L - (input) SuperMatrix*
* The factor L from the factorization Pr*A*Pc=L*U. Use
* compressed row subscripts storage for supernodes,
* i.e., L has types: Stype = SC, Dtype = SLU_Z, Mtype = TRLU.
*
* U - (input) SuperMatrix*
* The factor U from the factorization Pr*A*Pc=L*U.
* U has types: Stype = NC, Dtype = SLU_Z, Mtype = TRU.
*
* x - (input/output) doublecomplex*
* Before entry, the incremented array X must contain the n
* element right-hand side vector b. On exit, X is overwritten
* with the solution vector x.
*
* info - (output) int*
* If *info = -i, the i-th argument had an illegal value.
*
*/
int
sp_ztrsv(char *uplo, char *trans, char *diag, SuperMatrix *L,
SuperMatrix *U, doublecomplex *x, SuperLUStat_t *stat, int *info)
{
#ifdef _CRAY
_fcd ftcs1 = _cptofcd("L", strlen("L")),
ftcs2 = _cptofcd("N", strlen("N")),
ftcs3 = _cptofcd("U", strlen("U"));
#endif
SCformat *Lstore;
NCformat *Ustore;
doublecomplex *Lval, *Uval;
int incx = 1, incy = 1;
doublecomplex temp;
doublecomplex alpha = {1.0, 0.0}, beta = {1.0, 0.0};
doublecomplex comp_zero = {0.0, 0.0};
int nrow;
int fsupc, nsupr, nsupc, luptr, istart, irow;
int i, k, iptr, jcol;
doublecomplex *work;
flops_t solve_ops;
/* Test the input parameters */
*info = 0;
if ( strncmp(uplo,"L", 1)!=0 && strncmp(uplo, "U", 1)!=0 ) *info = -1;
else if ( strncmp(trans, "N", 1)!=0 && strncmp(trans, "T", 1)!=0 &&
strncmp(trans, "C", 1)!=0) *info = -2;
else if ( strncmp(diag, "U", 1)!=0 && strncmp(diag, "N", 1)!=0 )
*info = -3;
else if ( L->nrow != L->ncol || L->nrow < 0 ) *info = -4;
else if ( U->nrow != U->ncol || U->nrow < 0 ) *info = -5;
if ( *info ) {
i = -(*info);
input_error("sp_ztrsv", &i);
return 0;
}
Lstore = L->Store;
Lval = Lstore->nzval;
Ustore = U->Store;
Uval = Ustore->nzval;
solve_ops = 0;
if ( !(work = doublecomplexCalloc(L->nrow)) )
ABORT("Malloc fails for work in sp_ztrsv().");
if ( strncmp(trans, "N", 1)==0 ) { /* Form x := inv(A)*x. */
if ( strncmp(uplo, "L", 1)==0 ) {
/* Form x := inv(L)*x */
if ( L->nrow == 0 ) return 0; /* Quick return */
for (k = 0; k <= Lstore->nsuper; k++) {
fsupc = L_FST_SUPC(k);
istart = L_SUB_START(fsupc);
nsupr = L_SUB_START(fsupc+1) - istart;
nsupc = L_FST_SUPC(k+1) - fsupc;
luptr = L_NZ_START(fsupc);
nrow = nsupr - nsupc;
/* 1 z_div costs 10 flops */
solve_ops += 4 * nsupc * (nsupc - 1) + 10 * nsupc;
solve_ops += 8 * nrow * nsupc;
if ( nsupc == 1 ) {
for (iptr=istart+1; iptr < L_SUB_START(fsupc+1); ++iptr) {
irow = L_SUB(iptr);
++luptr;
zz_mult(&comp_zero, &x[fsupc], &Lval[luptr]);
z_sub(&x[irow], &x[irow], &comp_zero);
}
} else {
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
CTRSV(ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
CGEMV(ftcs2, &nrow, &nsupc, &alpha, &Lval[luptr+nsupc],
&nsupr, &x[fsupc], &incx, &beta, &work[0], &incy);
#else
ztrsv_("L", "N", "U", &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
zgemv_("N", &nrow, &nsupc, &alpha, &Lval[luptr+nsupc],
&nsupr, &x[fsupc], &incx, &beta, &work[0], &incy);
#endif
#else
zlsolve ( nsupr, nsupc, &Lval[luptr], &x[fsupc]);
zmatvec ( nsupr, nsupr-nsupc, nsupc, &Lval[luptr+nsupc],
&x[fsupc], &work[0] );
#endif
iptr = istart + nsupc;
for (i = 0; i < nrow; ++i, ++iptr) {
irow = L_SUB(iptr);
z_sub(&x[irow], &x[irow], &work[i]); /* Scatter */
work[i] = comp_zero;
}
}
} /* for k ... */
} else {
/* Form x := inv(U)*x */
if ( U->nrow == 0 ) return 0; /* Quick return */
for (k = Lstore->nsuper; k >= 0; k--) {
fsupc = L_FST_SUPC(k);
nsupr = L_SUB_START(fsupc+1) - L_SUB_START(fsupc);
nsupc = L_FST_SUPC(k+1) - fsupc;
luptr = L_NZ_START(fsupc);
/* 1 z_div costs 10 flops */
solve_ops += 4 * nsupc * (nsupc + 1) + 10 * nsupc;
if ( nsupc == 1 ) {
z_div(&x[fsupc], &x[fsupc], &Lval[luptr]);
for (i = U_NZ_START(fsupc); i < U_NZ_START(fsupc+1); ++i) {
irow = U_SUB(i);
zz_mult(&comp_zero, &x[fsupc], &Uval[i]);
z_sub(&x[irow], &x[irow], &comp_zero);
}
} else {
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
CTRSV(ftcs3, ftcs2, ftcs2, &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#else
ztrsv_("U", "N", "N", &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#endif
#else
zusolve ( nsupr, nsupc, &Lval[luptr], &x[fsupc] );
#endif
for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
solve_ops += 8*(U_NZ_START(jcol+1) - U_NZ_START(jcol));
for (i = U_NZ_START(jcol); i < U_NZ_START(jcol+1);
i++) {
irow = U_SUB(i);
zz_mult(&comp_zero, &x[jcol], &Uval[i]);
z_sub(&x[irow], &x[irow], &comp_zero);
}
}
}
} /* for k ... */
}
} else if ( strncmp(trans, "T", 1)==0 ) { /* Form x := inv(A')*x */
if ( strncmp(uplo, "L", 1)==0 ) {
/* Form x := inv(L')*x */
if ( L->nrow == 0 ) return 0; /* Quick return */
for (k = Lstore->nsuper; k >= 0; --k) {
fsupc = L_FST_SUPC(k);
istart = L_SUB_START(fsupc);
nsupr = L_SUB_START(fsupc+1) - istart;
nsupc = L_FST_SUPC(k+1) - fsupc;
luptr = L_NZ_START(fsupc);
solve_ops += 8 * (nsupr - nsupc) * nsupc;
for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
iptr = istart + nsupc;
for (i = L_NZ_START(jcol) + nsupc;
i < L_NZ_START(jcol+1); i++) {
irow = L_SUB(iptr);
zz_mult(&comp_zero, &x[irow], &Lval[i]);
z_sub(&x[jcol], &x[jcol], &comp_zero);
iptr++;
}
}
if ( nsupc > 1 ) {
solve_ops += 4 * nsupc * (nsupc - 1);
#ifdef _CRAY
ftcs1 = _cptofcd("L", strlen("L"));
ftcs2 = _cptofcd("T", strlen("T"));
ftcs3 = _cptofcd("U", strlen("U"));
CTRSV(ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#else
ztrsv_("L", "T", "U", &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#endif
}
}
} else {
/* Form x := inv(U')*x */
if ( U->nrow == 0 ) return 0; /* Quick return */
for (k = 0; k <= Lstore->nsuper; k++) {
fsupc = L_FST_SUPC(k);
nsupr = L_SUB_START(fsupc+1) - L_SUB_START(fsupc);
nsupc = L_FST_SUPC(k+1) - fsupc;
luptr = L_NZ_START(fsupc);
for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
solve_ops += 8*(U_NZ_START(jcol+1) - U_NZ_START(jcol));
for (i = U_NZ_START(jcol); i < U_NZ_START(jcol+1); i++) {
irow = U_SUB(i);
zz_mult(&comp_zero, &x[irow], &Uval[i]);
z_sub(&x[jcol], &x[jcol], &comp_zero);
}
}
/* 1 z_div costs 10 flops */
solve_ops += 4 * nsupc * (nsupc + 1) + 10 * nsupc;
if ( nsupc == 1 ) {
z_div(&x[fsupc], &x[fsupc], &Lval[luptr]);
} else {
#ifdef _CRAY
ftcs1 = _cptofcd("U", strlen("U"));
ftcs2 = _cptofcd("T", strlen("T"));
ftcs3 = _cptofcd("N", strlen("N"));
CTRSV( ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#else
ztrsv_("U", "T", "N", &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#endif
}
} /* for k ... */
}
} else { /* Form x := conj(inv(A'))*x */
if ( strncmp(uplo, "L", 1)==0 ) {
/* Form x := conj(inv(L'))*x */
if ( L->nrow == 0 ) return 0; /* Quick return */
for (k = Lstore->nsuper; k >= 0; --k) {
fsupc = L_FST_SUPC(k);
istart = L_SUB_START(fsupc);
nsupr = L_SUB_START(fsupc+1) - istart;
nsupc = L_FST_SUPC(k+1) - fsupc;
luptr = L_NZ_START(fsupc);
solve_ops += 8 * (nsupr - nsupc) * nsupc;
for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
iptr = istart + nsupc;
for (i = L_NZ_START(jcol) + nsupc;
i < L_NZ_START(jcol+1); i++) {
irow = L_SUB(iptr);
zz_conj(&temp, &Lval[i]);
zz_mult(&comp_zero, &x[irow], &temp);
z_sub(&x[jcol], &x[jcol], &comp_zero);
iptr++;
}
}
if ( nsupc > 1 ) {
solve_ops += 4 * nsupc * (nsupc - 1);
#ifdef _CRAY
ftcs1 = _cptofcd("L", strlen("L"));
ftcs2 = _cptofcd(trans, strlen("T"));
ftcs3 = _cptofcd("U", strlen("U"));
ZTRSV(ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#else
ztrsv_("L", trans, "U", &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#endif
}
}
} else {
/* Form x := conj(inv(U'))*x */
if ( U->nrow == 0 ) return 0; /* Quick return */
for (k = 0; k <= Lstore->nsuper; k++) {
fsupc = L_FST_SUPC(k);
nsupr = L_SUB_START(fsupc+1) - L_SUB_START(fsupc);
nsupc = L_FST_SUPC(k+1) - fsupc;
luptr = L_NZ_START(fsupc);
for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
solve_ops += 8*(U_NZ_START(jcol+1) - U_NZ_START(jcol));
for (i = U_NZ_START(jcol); i < U_NZ_START(jcol+1); i++) {
irow = U_SUB(i);
zz_conj(&temp, &Uval[i]);
zz_mult(&comp_zero, &x[irow], &temp);
z_sub(&x[jcol], &x[jcol], &comp_zero);
}
}
/* 1 z_div costs 10 flops */
solve_ops += 4 * nsupc * (nsupc + 1) + 10 * nsupc;
if ( nsupc == 1 ) {
zz_conj(&temp, &Lval[luptr]);
z_div(&x[fsupc], &x[fsupc], &temp);
} else {
#ifdef _CRAY
ftcs1 = _cptofcd("U", strlen("U"));
ftcs2 = _cptofcd(trans, strlen("T"));
ftcs3 = _cptofcd("N", strlen("N"));
ZTRSV( ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#else
ztrsv_("U", trans, "N", &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#endif
}
} /* for k ... */
}
}
stat->ops[SOLVE] += solve_ops;
SUPERLU_FREE(work);
return 0;
}
/*! \brief Performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y
*
*
* Purpose
* =======
*
* sp_zgemv() performs one of the matrix-vector operations
* y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y,
* where alpha and beta are scalars, x and y are vectors and A is a
* sparse A->nrow by A->ncol matrix.
*
* Parameters
* ==========
*
* TRANS - (input) char*
* On entry, TRANS specifies the operation to be performed as
* follows:
* TRANS = 'N' or 'n' y := alpha*A*x + beta*y.
* TRANS = 'T' or 't' y := alpha*A'*x + beta*y.
* TRANS = 'C' or 'c' y := alpha*A^H*x + beta*y.
*
* ALPHA - (input) doublecomplex
* On entry, ALPHA specifies the scalar alpha.
*
* A - (input) SuperMatrix*
* Before entry, the leading m by n part of the array A must
* contain the matrix of coefficients.
*
* X - (input) doublecomplex*, array of DIMENSION at least
* ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
* and at least
* ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
* Before entry, the incremented array X must contain the
* vector x.
*
* INCX - (input) int
* On entry, INCX specifies the increment for the elements of
* X. INCX must not be zero.
*
* BETA - (input) doublecomplex
* On entry, BETA specifies the scalar beta. When BETA is
* supplied as zero then Y need not be set on input.
*
* Y - (output) doublecomplex*, array of DIMENSION at least
* ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
* and at least
* ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
* Before entry with BETA non-zero, the incremented array Y
* must contain the vector y. On exit, Y is overwritten by the
* updated vector y.
*
* INCY - (input) int
* On entry, INCY specifies the increment for the elements of
* Y. INCY must not be zero.
*
* ==== Sparse Level 2 Blas routine.
*
*/
int
sp_zgemv(char *trans, doublecomplex alpha, SuperMatrix *A, doublecomplex *x,
int incx, doublecomplex beta, doublecomplex *y, int incy)
{
/* Local variables */
NCformat *Astore;
doublecomplex *Aval;
int info;
doublecomplex temp, temp1;
int lenx, leny, i, j, irow;
int iy, jx, jy, kx, ky;
int notran;
doublecomplex comp_zero = {0.0, 0.0};
doublecomplex comp_one = {1.0, 0.0};
notran = ( strncmp(trans, "N", 1)==0 || strncmp(trans, "n", 1)==0 );
Astore = A->Store;
Aval = Astore->nzval;
/* Test the input parameters */
info = 0;
if ( !notran && strncmp(trans, "T", 1)!=0 && strncmp(trans, "C", 1)!=0)
info = 1;
else if ( A->nrow < 0 || A->ncol < 0 ) info = 3;
else if (incx == 0) info = 5;
else if (incy == 0) info = 8;
if (info != 0) {
input_error("sp_zgemv ", &info);
return 0;
}
/* Quick return if possible. */
if (A->nrow == 0 || A->ncol == 0 ||
z_eq(&alpha, &comp_zero) &&
z_eq(&beta, &comp_one))
return 0;
/* Set LENX and LENY, the lengths of the vectors x and y, and set
up the start points in X and Y. */
if ( notran ) {
lenx = A->ncol;
leny = A->nrow;
} else {
lenx = A->nrow;
leny = A->ncol;
}
if (incx > 0) kx = 0;
else kx = - (lenx - 1) * incx;
if (incy > 0) ky = 0;
else ky = - (leny - 1) * incy;
/* Start the operations. In this version the elements of A are
accessed sequentially with one pass through A. */
/* First form y := beta*y. */
if ( !z_eq(&beta, &comp_one) ) {
if (incy == 1) {
if ( z_eq(&beta, &comp_zero) )
for (i = 0; i < leny; ++i) y[i] = comp_zero;
else
for (i = 0; i < leny; ++i)
zz_mult(&y[i], &beta, &y[i]);
} else {
iy = ky;
if ( z_eq(&beta, &comp_zero) )
for (i = 0; i < leny; ++i) {
y[iy] = comp_zero;
iy += incy;
}
else
for (i = 0; i < leny; ++i) {
zz_mult(&y[iy], &beta, &y[iy]);
iy += incy;
}
}
}
if ( z_eq(&alpha, &comp_zero) ) return 0;
if ( notran ) {
/* Form y := alpha*A*x + y. */
jx = kx;
if (incy == 1) {
for (j = 0; j < A->ncol; ++j) {
if ( !z_eq(&x[jx], &comp_zero) ) {
zz_mult(&temp, &alpha, &x[jx]);
for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
irow = Astore->rowind[i];
zz_mult(&temp1, &temp, &Aval[i]);
z_add(&y[irow], &y[irow], &temp1);
}
}
jx += incx;
}
} else {
ABORT("Not implemented.");
}
} else if (strncmp(trans, "T", 1) == 0 || strncmp(trans, "t", 1) == 0) {
/* Form y := alpha*A'*x + y. */
jy = ky;
if (incx == 1) {
for (j = 0; j < A->ncol; ++j) {
temp = comp_zero;
for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
irow = Astore->rowind[i];
zz_mult(&temp1, &Aval[i], &x[irow]);
z_add(&temp, &temp, &temp1);
}
zz_mult(&temp1, &alpha, &temp);
z_add(&y[jy], &y[jy], &temp1);
jy += incy;
}
} else {
ABORT("Not implemented.");
}
} else { /* trans == 'C' or 'c' */
/* Form y := alpha * conj(A) * x + y. */
doublecomplex temp2;
jy = ky;
if (incx == 1) {
for (j = 0; j < A->ncol; ++j) {
temp = comp_zero;
for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
irow = Astore->rowind[i];
temp2.r = Aval[i].r;
temp2.i = -Aval[i].i; /* conjugation */
zz_mult(&temp1, &temp2, &x[irow]);
z_add(&temp, &temp, &temp1);
}
zz_mult(&temp1, &alpha, &temp);
z_add(&y[jy], &y[jy], &temp1);
jy += incy;
}
} else {
ABORT("Not implemented.");
}
}
return 0;
} /* sp_zgemv */