/* blas/source_trsm_c.h
*
* Copyright (C) 2001, 2007 Brian Gough
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 3 of the License, or (at
* your option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
{
INDEX i, j, k;
INDEX n1, n2;
const int nonunit = (Diag == CblasNonUnit);
const int conj = (TransA == CblasConjTrans) ? -1 : 1;
int side, uplo, trans;
CHECK_ARGS12(TRSM,Order,Side,Uplo,TransA,Diag,M,N,alpha,A,lda,B,ldb);
{
const BASE alpha_real = CONST_REAL0(alpha);
const BASE alpha_imag = CONST_IMAG0(alpha);
if (Order == CblasRowMajor) {
n1 = M;
n2 = N;
side = Side;
uplo = Uplo;
trans = TransA;
trans = (TransA == CblasNoTrans) ? CblasNoTrans : CblasTrans;
} else {
n1 = N;
n2 = M;
side = (Side == CblasLeft) ? CblasRight : CblasLeft; /* exchanged */
uplo = (Uplo == CblasUpper) ? CblasLower : CblasUpper; /* exchanged */
trans = (TransA == CblasNoTrans) ? CblasNoTrans : CblasTrans; /* same */
}
if (side == CblasLeft && uplo == CblasUpper && trans == CblasNoTrans) {
/* form B := alpha * inv(TriU(A)) *B */
if (!(alpha_real == 1.0 && alpha_imag == 0.0)) {
for (i = 0; i < n1; i++) {
for (j = 0; j < n2; j++) {
const BASE Bij_real = REAL(B, ldb * i + j);
const BASE Bij_imag = IMAG(B, ldb * i + j);
REAL(B, ldb * i + j) = alpha_real * Bij_real - alpha_imag * Bij_imag;
IMAG(B, ldb * i + j) = alpha_real * Bij_imag + alpha_imag * Bij_real;
}
}
}
for (i = n1; i > 0 && i--;) {
if (nonunit) {
const BASE Aii_real = CONST_REAL(A, lda * i + i);
const BASE Aii_imag = conj * CONST_IMAG(A, lda * i + i);
const BASE s = xhypot(Aii_real, Aii_imag);
const BASE a_real = Aii_real / s;
const BASE a_imag = Aii_imag / s;
for (j = 0; j < n2; j++) {
const BASE Bij_real = REAL(B, ldb * i + j);
const BASE Bij_imag = IMAG(B, ldb * i + j);
REAL(B, ldb * i + j) = (Bij_real * a_real + Bij_imag * a_imag) / s;
IMAG(B, ldb * i + j) = (Bij_imag * a_real - Bij_real * a_imag) / s;
}
}
for (k = 0; k < i; k++) {
const BASE Aki_real = CONST_REAL(A, k * lda + i);
const BASE Aki_imag = conj * CONST_IMAG(A, k * lda + i);
for (j = 0; j < n2; j++) {
const BASE Bij_real = REAL(B, ldb * i + j);
const BASE Bij_imag = IMAG(B, ldb * i + j);
REAL(B, ldb * k + j) -= Aki_real * Bij_real - Aki_imag * Bij_imag;
IMAG(B, ldb * k + j) -= Aki_real * Bij_imag + Aki_imag * Bij_real;
}
}
}
} else if (side == CblasLeft && uplo == CblasUpper && trans == CblasTrans) {
/* form B := alpha * inv(TriU(A))' *B */
if (!(alpha_real == 1.0 && alpha_imag == 0.0)) {
for (i = 0; i < n1; i++) {
for (j = 0; j < n2; j++) {
const BASE Bij_real = REAL(B, ldb * i + j);
const BASE Bij_imag = IMAG(B, ldb * i + j);
REAL(B, ldb * i + j) = alpha_real * Bij_real - alpha_imag * Bij_imag;
IMAG(B, ldb * i + j) = alpha_real * Bij_imag + alpha_imag * Bij_real;
}
}
}
for (i = 0; i < n1; i++) {
if (nonunit) {
const BASE Aii_real = CONST_REAL(A, lda * i + i);
const BASE Aii_imag = conj * CONST_IMAG(A, lda * i + i);
const BASE s = xhypot(Aii_real, Aii_imag);
const BASE a_real = Aii_real / s;
const BASE a_imag = Aii_imag / s;
for (j = 0; j < n2; j++) {
const BASE Bij_real = REAL(B, ldb * i + j);
const BASE Bij_imag = IMAG(B, ldb * i + j);
REAL(B, ldb * i + j) = (Bij_real * a_real + Bij_imag * a_imag) / s;
IMAG(B, ldb * i + j) = (Bij_imag * a_real - Bij_real * a_imag) / s;
}
}
for (k = i + 1; k < n1; k++) {
const BASE Aik_real = CONST_REAL(A, i * lda + k);
const BASE Aik_imag = conj * CONST_IMAG(A, i * lda + k);
for (j = 0; j < n2; j++) {
const BASE Bij_real = REAL(B, ldb * i + j);
const BASE Bij_imag = IMAG(B, ldb * i + j);
REAL(B, ldb * k + j) -= Aik_real * Bij_real - Aik_imag * Bij_imag;
IMAG(B, ldb * k + j) -= Aik_real * Bij_imag + Aik_imag * Bij_real;
}
}
}
} else if (side == CblasLeft && uplo == CblasLower && trans == CblasNoTrans) {
/* form B := alpha * inv(TriL(A))*B */
if (!(alpha_real == 1.0 && alpha_imag == 0.0)) {
for (i = 0; i < n1; i++) {
for (j = 0; j < n2; j++) {
const BASE Bij_real = REAL(B, ldb * i + j);
const BASE Bij_imag = IMAG(B, ldb * i + j);
REAL(B, ldb * i + j) = alpha_real * Bij_real - alpha_imag * Bij_imag;
IMAG(B, ldb * i + j) = alpha_real * Bij_imag + alpha_imag * Bij_real;
}
}
}
for (i = 0; i < n1; i++) {
if (nonunit) {
const BASE Aii_real = CONST_REAL(A, lda * i + i);
const BASE Aii_imag = conj * CONST_IMAG(A, lda * i + i);
const BASE s = xhypot(Aii_real, Aii_imag);
const BASE a_real = Aii_real / s;
const BASE a_imag = Aii_imag / s;
for (j = 0; j < n2; j++) {
const BASE Bij_real = REAL(B, ldb * i + j);
const BASE Bij_imag = IMAG(B, ldb * i + j);
REAL(B, ldb * i + j) = (Bij_real * a_real + Bij_imag * a_imag) / s;
IMAG(B, ldb * i + j) = (Bij_imag * a_real - Bij_real * a_imag) / s;
}
}
for (k = i + 1; k < n1; k++) {
const BASE Aki_real = CONST_REAL(A, k * lda + i);
const BASE Aki_imag = conj * CONST_IMAG(A, k * lda + i);
for (j = 0; j < n2; j++) {
const BASE Bij_real = REAL(B, ldb * i + j);
const BASE Bij_imag = IMAG(B, ldb * i + j);
REAL(B, ldb * k + j) -= Aki_real * Bij_real - Aki_imag * Bij_imag;
IMAG(B, ldb * k + j) -= Aki_real * Bij_imag + Aki_imag * Bij_real;
}
}
}
} else if (side == CblasLeft && uplo == CblasLower && trans == CblasTrans) {
/* form B := alpha * TriL(A)' *B */
if (!(alpha_real == 1.0 && alpha_imag == 0.0)) {
for (i = 0; i < n1; i++) {
for (j = 0; j < n2; j++) {
const BASE Bij_real = REAL(B, ldb * i + j);
const BASE Bij_imag = IMAG(B, ldb * i + j);
REAL(B, ldb * i + j) = alpha_real * Bij_real - alpha_imag * Bij_imag;
IMAG(B, ldb * i + j) = alpha_real * Bij_imag + alpha_imag * Bij_real;
}
}
}
for (i = n1; i > 0 && i--;) {
if (nonunit) {
const BASE Aii_real = CONST_REAL(A, lda * i + i);
const BASE Aii_imag = conj * CONST_IMAG(A, lda * i + i);
const BASE s = xhypot(Aii_real, Aii_imag);
const BASE a_real = Aii_real / s;
const BASE a_imag = Aii_imag / s;
for (j = 0; j < n2; j++) {
const BASE Bij_real = REAL(B, ldb * i + j);
const BASE Bij_imag = IMAG(B, ldb * i + j);
REAL(B, ldb * i + j) = (Bij_real * a_real + Bij_imag * a_imag) / s;
IMAG(B, ldb * i + j) = (Bij_imag * a_real - Bij_real * a_imag) / s;
}
}
for (k = 0; k < i; k++) {
const BASE Aik_real = CONST_REAL(A, i * lda + k);
const BASE Aik_imag = conj * CONST_IMAG(A, i * lda + k);
for (j = 0; j < n2; j++) {
const BASE Bij_real = REAL(B, ldb * i + j);
const BASE Bij_imag = IMAG(B, ldb * i + j);
REAL(B, ldb * k + j) -= Aik_real * Bij_real - Aik_imag * Bij_imag;
IMAG(B, ldb * k + j) -= Aik_real * Bij_imag + Aik_imag * Bij_real;
}
}
}
} else if (side == CblasRight && uplo == CblasUpper && trans == CblasNoTrans) {
/* form B := alpha * B * inv(TriU(A)) */
if (!(alpha_real == 1.0 && alpha_imag == 0.0)) {
for (i = 0; i < n1; i++) {
for (j = 0; j < n2; j++) {
const BASE Bij_real = REAL(B, ldb * i + j);
const BASE Bij_imag = IMAG(B, ldb * i + j);
REAL(B, ldb * i + j) = alpha_real * Bij_real - alpha_imag * Bij_imag;
IMAG(B, ldb * i + j) = alpha_real * Bij_imag + alpha_imag * Bij_real;
}
}
}
for (i = 0; i < n1; i++) {
for (j = 0; j < n2; j++) {
if (nonunit) {
const BASE Ajj_real = CONST_REAL(A, lda * j + j);
const BASE Ajj_imag = conj * CONST_IMAG(A, lda * j + j);
const BASE s = xhypot(Ajj_real, Ajj_imag);
const BASE a_real = Ajj_real / s;
const BASE a_imag = Ajj_imag / s;
const BASE Bij_real = REAL(B, ldb * i + j);
const BASE Bij_imag = IMAG(B, ldb * i + j);
REAL(B, ldb * i + j) = (Bij_real * a_real + Bij_imag * a_imag) / s;
IMAG(B, ldb * i + j) = (Bij_imag * a_real - Bij_real * a_imag) / s;
}
{
const BASE Bij_real = REAL(B, ldb * i + j);
const BASE Bij_imag = IMAG(B, ldb * i + j);
for (k = j + 1; k < n2; k++) {
const BASE Ajk_real = CONST_REAL(A, j * lda + k);
const BASE Ajk_imag = conj * CONST_IMAG(A, j * lda + k);
REAL(B, ldb * i + k) -= Ajk_real * Bij_real - Ajk_imag * Bij_imag;
IMAG(B, ldb * i + k) -= Ajk_real * Bij_imag + Ajk_imag * Bij_real;
}
}
}
}
} else if (side == CblasRight && uplo == CblasUpper && trans == CblasTrans) {
/* form B := alpha * B * inv(TriU(A))' */
if (!(alpha_real == 1.0 && alpha_imag == 0.0)) {
for (i = 0; i < n1; i++) {
for (j = 0; j < n2; j++) {
const BASE Bij_real = REAL(B, ldb * i + j);
const BASE Bij_imag = IMAG(B, ldb * i + j);
REAL(B, ldb * i + j) = alpha_real * Bij_real - alpha_imag * Bij_imag;
IMAG(B, ldb * i + j) = alpha_real * Bij_imag + alpha_imag * Bij_real;
}
}
}
for (i = 0; i < n1; i++) {
for (j = n2; j > 0 && j--;) {
if (nonunit) {
const BASE Ajj_real = CONST_REAL(A, lda * j + j);
const BASE Ajj_imag = conj * CONST_IMAG(A, lda * j + j);
const BASE s = xhypot(Ajj_real, Ajj_imag);
const BASE a_real = Ajj_real / s;
const BASE a_imag = Ajj_imag / s;
const BASE Bij_real = REAL(B, ldb * i + j);
const BASE Bij_imag = IMAG(B, ldb * i + j);
REAL(B, ldb * i + j) = (Bij_real * a_real + Bij_imag * a_imag) / s;
IMAG(B, ldb * i + j) = (Bij_imag * a_real - Bij_real * a_imag) / s;
}
{
const BASE Bij_real = REAL(B, ldb * i + j);
const BASE Bij_imag = IMAG(B, ldb * i + j);
for (k = 0; k < j; k++) {
const BASE Akj_real = CONST_REAL(A, k * lda + j);
const BASE Akj_imag = conj * CONST_IMAG(A, k * lda + j);
REAL(B, ldb * i + k) -= Akj_real * Bij_real - Akj_imag * Bij_imag;
IMAG(B, ldb * i + k) -= Akj_real * Bij_imag + Akj_imag * Bij_real;
}
}
}
}
} else if (side == CblasRight && uplo == CblasLower && trans == CblasNoTrans) {
/* form B := alpha * B * inv(TriL(A)) */
if (!(alpha_real == 1.0 && alpha_imag == 0.0)) {
for (i = 0; i < n1; i++) {
for (j = 0; j < n2; j++) {
const BASE Bij_real = REAL(B, ldb * i + j);
const BASE Bij_imag = IMAG(B, ldb * i + j);
REAL(B, ldb * i + j) = alpha_real * Bij_real - alpha_imag * Bij_imag;
IMAG(B, ldb * i + j) = alpha_real * Bij_imag + alpha_imag * Bij_real;
}
}
}
for (i = 0; i < n1; i++) {
for (j = n2; j > 0 && j--;) {
if (nonunit) {
const BASE Ajj_real = CONST_REAL(A, lda * j + j);
const BASE Ajj_imag = conj * CONST_IMAG(A, lda * j + j);
const BASE s = xhypot(Ajj_real, Ajj_imag);
const BASE a_real = Ajj_real / s;
const BASE a_imag = Ajj_imag / s;
const BASE Bij_real = REAL(B, ldb * i + j);
const BASE Bij_imag = IMAG(B, ldb * i + j);
REAL(B, ldb * i + j) = (Bij_real * a_real + Bij_imag * a_imag) / s;
IMAG(B, ldb * i + j) = (Bij_imag * a_real - Bij_real * a_imag) / s;
}
{
const BASE Bij_real = REAL(B, ldb * i + j);
const BASE Bij_imag = IMAG(B, ldb * i + j);
for (k = 0; k < j; k++) {
const BASE Ajk_real = CONST_REAL(A, j * lda + k);
const BASE Ajk_imag = conj * CONST_IMAG(A, j * lda + k);
REAL(B, ldb * i + k) -= Ajk_real * Bij_real - Ajk_imag * Bij_imag;
IMAG(B, ldb * i + k) -= Ajk_real * Bij_imag + Ajk_imag * Bij_real;
}
}
}
}
} else if (side == CblasRight && uplo == CblasLower && trans == CblasTrans) {
/* form B := alpha * B * inv(TriL(A))' */
if (!(alpha_real == 1.0 && alpha_imag == 0.0)) {
for (i = 0; i < n1; i++) {
for (j = 0; j < n2; j++) {
const BASE Bij_real = REAL(B, ldb * i + j);
const BASE Bij_imag = IMAG(B, ldb * i + j);
REAL(B, ldb * i + j) = alpha_real * Bij_real - alpha_imag * Bij_imag;
IMAG(B, ldb * i + j) = alpha_real * Bij_imag + alpha_imag * Bij_real;
}
}
}
for (i = 0; i < n1; i++) {
for (j = 0; j < n2; j++) {
if (nonunit) {
const BASE Ajj_real = CONST_REAL(A, lda * j + j);
const BASE Ajj_imag = conj * CONST_IMAG(A, lda * j + j);
const BASE s = xhypot(Ajj_real, Ajj_imag);
const BASE a_real = Ajj_real / s;
const BASE a_imag = Ajj_imag / s;
const BASE Bij_real = REAL(B, ldb * i + j);
const BASE Bij_imag = IMAG(B, ldb * i + j);
REAL(B, ldb * i + j) = (Bij_real * a_real + Bij_imag * a_imag) / s;
IMAG(B, ldb * i + j) = (Bij_imag * a_real - Bij_real * a_imag) / s;
}
{
const BASE Bij_real = REAL(B, ldb * i + j);
const BASE Bij_imag = IMAG(B, ldb * i + j);
for (k = j + 1; k < n2; k++) {
const BASE Akj_real = CONST_REAL(A, k * lda + j);
const BASE Akj_imag = conj * CONST_IMAG(A, k * lda + j);
REAL(B, ldb * i + k) -= Akj_real * Bij_real - Akj_imag * Bij_imag;
IMAG(B, ldb * i + k) -= Akj_real * Bij_imag + Akj_imag * Bij_real;
}
}
}
}
} else {
BLAS_ERROR("unrecognized operation");
}
}
}