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/* blas/source_trsm_c.h
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*
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* Copyright (C) 2001, 2007 Brian Gough
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3 of the License, or (at
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* your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*/
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{
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INDEX i, j, k;
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INDEX n1, n2;
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const int nonunit = (Diag == CblasNonUnit);
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const int conj = (TransA == CblasConjTrans) ? -1 : 1;
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int side, uplo, trans;
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CHECK_ARGS12(TRSM,Order,Side,Uplo,TransA,Diag,M,N,alpha,A,lda,B,ldb);
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{
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const BASE alpha_real = CONST_REAL0(alpha);
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const BASE alpha_imag = CONST_IMAG0(alpha);
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if (Order == CblasRowMajor) {
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n1 = M;
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n2 = N;
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side = Side;
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uplo = Uplo;
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trans = TransA;
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trans = (TransA == CblasNoTrans) ? CblasNoTrans : CblasTrans;
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} else {
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n1 = N;
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n2 = M;
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side = (Side == CblasLeft) ? CblasRight : CblasLeft; /* exchanged */
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uplo = (Uplo == CblasUpper) ? CblasLower : CblasUpper; /* exchanged */
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trans = (TransA == CblasNoTrans) ? CblasNoTrans : CblasTrans; /* same */
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}
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if (side == CblasLeft && uplo == CblasUpper && trans == CblasNoTrans) {
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/* form B := alpha * inv(TriU(A)) *B */
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if (!(alpha_real == 1.0 && alpha_imag == 0.0)) {
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for (i = 0; i < n1; i++) {
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for (j = 0; j < n2; j++) {
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const BASE Bij_real = REAL(B, ldb * i + j);
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const BASE Bij_imag = IMAG(B, ldb * i + j);
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REAL(B, ldb * i + j) = alpha_real * Bij_real - alpha_imag * Bij_imag;
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IMAG(B, ldb * i + j) = alpha_real * Bij_imag + alpha_imag * Bij_real;
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}
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}
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}
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for (i = n1; i > 0 && i--;) {
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if (nonunit) {
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const BASE Aii_real = CONST_REAL(A, lda * i + i);
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const BASE Aii_imag = conj * CONST_IMAG(A, lda * i + i);
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const BASE s = xhypot(Aii_real, Aii_imag);
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const BASE a_real = Aii_real / s;
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const BASE a_imag = Aii_imag / s;
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for (j = 0; j < n2; j++) {
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const BASE Bij_real = REAL(B, ldb * i + j);
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const BASE Bij_imag = IMAG(B, ldb * i + j);
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REAL(B, ldb * i + j) = (Bij_real * a_real + Bij_imag * a_imag) / s;
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IMAG(B, ldb * i + j) = (Bij_imag * a_real - Bij_real * a_imag) / s;
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}
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}
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for (k = 0; k < i; k++) {
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const BASE Aki_real = CONST_REAL(A, k * lda + i);
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const BASE Aki_imag = conj * CONST_IMAG(A, k * lda + i);
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for (j = 0; j < n2; j++) {
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const BASE Bij_real = REAL(B, ldb * i + j);
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const BASE Bij_imag = IMAG(B, ldb * i + j);
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REAL(B, ldb * k + j) -= Aki_real * Bij_real - Aki_imag * Bij_imag;
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IMAG(B, ldb * k + j) -= Aki_real * Bij_imag + Aki_imag * Bij_real;
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}
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}
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}
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} else if (side == CblasLeft && uplo == CblasUpper && trans == CblasTrans) {
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/* form B := alpha * inv(TriU(A))' *B */
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if (!(alpha_real == 1.0 && alpha_imag == 0.0)) {
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for (i = 0; i < n1; i++) {
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for (j = 0; j < n2; j++) {
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const BASE Bij_real = REAL(B, ldb * i + j);
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const BASE Bij_imag = IMAG(B, ldb * i + j);
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REAL(B, ldb * i + j) = alpha_real * Bij_real - alpha_imag * Bij_imag;
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IMAG(B, ldb * i + j) = alpha_real * Bij_imag + alpha_imag * Bij_real;
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}
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}
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}
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for (i = 0; i < n1; i++) {
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if (nonunit) {
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const BASE Aii_real = CONST_REAL(A, lda * i + i);
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const BASE Aii_imag = conj * CONST_IMAG(A, lda * i + i);
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const BASE s = xhypot(Aii_real, Aii_imag);
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const BASE a_real = Aii_real / s;
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const BASE a_imag = Aii_imag / s;
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for (j = 0; j < n2; j++) {
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const BASE Bij_real = REAL(B, ldb * i + j);
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const BASE Bij_imag = IMAG(B, ldb * i + j);
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REAL(B, ldb * i + j) = (Bij_real * a_real + Bij_imag * a_imag) / s;
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IMAG(B, ldb * i + j) = (Bij_imag * a_real - Bij_real * a_imag) / s;
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}
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}
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for (k = i + 1; k < n1; k++) {
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const BASE Aik_real = CONST_REAL(A, i * lda + k);
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const BASE Aik_imag = conj * CONST_IMAG(A, i * lda + k);
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for (j = 0; j < n2; j++) {
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const BASE Bij_real = REAL(B, ldb * i + j);
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const BASE Bij_imag = IMAG(B, ldb * i + j);
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REAL(B, ldb * k + j) -= Aik_real * Bij_real - Aik_imag * Bij_imag;
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IMAG(B, ldb * k + j) -= Aik_real * Bij_imag + Aik_imag * Bij_real;
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}
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}
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}
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} else if (side == CblasLeft && uplo == CblasLower && trans == CblasNoTrans) {
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/* form B := alpha * inv(TriL(A))*B */
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if (!(alpha_real == 1.0 && alpha_imag == 0.0)) {
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for (i = 0; i < n1; i++) {
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for (j = 0; j < n2; j++) {
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const BASE Bij_real = REAL(B, ldb * i + j);
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const BASE Bij_imag = IMAG(B, ldb * i + j);
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REAL(B, ldb * i + j) = alpha_real * Bij_real - alpha_imag * Bij_imag;
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IMAG(B, ldb * i + j) = alpha_real * Bij_imag + alpha_imag * Bij_real;
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}
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}
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}
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for (i = 0; i < n1; i++) {
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if (nonunit) {
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const BASE Aii_real = CONST_REAL(A, lda * i + i);
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const BASE Aii_imag = conj * CONST_IMAG(A, lda * i + i);
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const BASE s = xhypot(Aii_real, Aii_imag);
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const BASE a_real = Aii_real / s;
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const BASE a_imag = Aii_imag / s;
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for (j = 0; j < n2; j++) {
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const BASE Bij_real = REAL(B, ldb * i + j);
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const BASE Bij_imag = IMAG(B, ldb * i + j);
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REAL(B, ldb * i + j) = (Bij_real * a_real + Bij_imag * a_imag) / s;
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IMAG(B, ldb * i + j) = (Bij_imag * a_real - Bij_real * a_imag) / s;
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}
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}
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for (k = i + 1; k < n1; k++) {
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const BASE Aki_real = CONST_REAL(A, k * lda + i);
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const BASE Aki_imag = conj * CONST_IMAG(A, k * lda + i);
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for (j = 0; j < n2; j++) {
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const BASE Bij_real = REAL(B, ldb * i + j);
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const BASE Bij_imag = IMAG(B, ldb * i + j);
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REAL(B, ldb * k + j) -= Aki_real * Bij_real - Aki_imag * Bij_imag;
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IMAG(B, ldb * k + j) -= Aki_real * Bij_imag + Aki_imag * Bij_real;
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}
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}
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}
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} else if (side == CblasLeft && uplo == CblasLower && trans == CblasTrans) {
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/* form B := alpha * TriL(A)' *B */
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if (!(alpha_real == 1.0 && alpha_imag == 0.0)) {
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for (i = 0; i < n1; i++) {
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for (j = 0; j < n2; j++) {
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const BASE Bij_real = REAL(B, ldb * i + j);
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const BASE Bij_imag = IMAG(B, ldb * i + j);
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REAL(B, ldb * i + j) = alpha_real * Bij_real - alpha_imag * Bij_imag;
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IMAG(B, ldb * i + j) = alpha_real * Bij_imag + alpha_imag * Bij_real;
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}
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}
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}
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for (i = n1; i > 0 && i--;) {
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if (nonunit) {
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const BASE Aii_real = CONST_REAL(A, lda * i + i);
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const BASE Aii_imag = conj * CONST_IMAG(A, lda * i + i);
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const BASE s = xhypot(Aii_real, Aii_imag);
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const BASE a_real = Aii_real / s;
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const BASE a_imag = Aii_imag / s;
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for (j = 0; j < n2; j++) {
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const BASE Bij_real = REAL(B, ldb * i + j);
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const BASE Bij_imag = IMAG(B, ldb * i + j);
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REAL(B, ldb * i + j) = (Bij_real * a_real + Bij_imag * a_imag) / s;
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IMAG(B, ldb * i + j) = (Bij_imag * a_real - Bij_real * a_imag) / s;
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}
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}
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for (k = 0; k < i; k++) {
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const BASE Aik_real = CONST_REAL(A, i * lda + k);
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const BASE Aik_imag = conj * CONST_IMAG(A, i * lda + k);
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for (j = 0; j < n2; j++) {
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const BASE Bij_real = REAL(B, ldb * i + j);
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const BASE Bij_imag = IMAG(B, ldb * i + j);
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REAL(B, ldb * k + j) -= Aik_real * Bij_real - Aik_imag * Bij_imag;
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IMAG(B, ldb * k + j) -= Aik_real * Bij_imag + Aik_imag * Bij_real;
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}
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}
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}
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} else if (side == CblasRight && uplo == CblasUpper && trans == CblasNoTrans) {
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/* form B := alpha * B * inv(TriU(A)) */
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if (!(alpha_real == 1.0 && alpha_imag == 0.0)) {
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for (i = 0; i < n1; i++) {
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for (j = 0; j < n2; j++) {
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const BASE Bij_real = REAL(B, ldb * i + j);
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const BASE Bij_imag = IMAG(B, ldb * i + j);
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REAL(B, ldb * i + j) = alpha_real * Bij_real - alpha_imag * Bij_imag;
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IMAG(B, ldb * i + j) = alpha_real * Bij_imag + alpha_imag * Bij_real;
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}
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}
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}
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for (i = 0; i < n1; i++) {
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for (j = 0; j < n2; j++) {
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if (nonunit) {
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const BASE Ajj_real = CONST_REAL(A, lda * j + j);
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const BASE Ajj_imag = conj * CONST_IMAG(A, lda * j + j);
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const BASE s = xhypot(Ajj_real, Ajj_imag);
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const BASE a_real = Ajj_real / s;
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const BASE a_imag = Ajj_imag / s;
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const BASE Bij_real = REAL(B, ldb * i + j);
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const BASE Bij_imag = IMAG(B, ldb * i + j);
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REAL(B, ldb * i + j) = (Bij_real * a_real + Bij_imag * a_imag) / s;
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IMAG(B, ldb * i + j) = (Bij_imag * a_real - Bij_real * a_imag) / s;
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}
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{
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const BASE Bij_real = REAL(B, ldb * i + j);
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const BASE Bij_imag = IMAG(B, ldb * i + j);
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67cb25 |
for (k = j + 1; k < n2; k++) {
|
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Packit |
67cb25 |
const BASE Ajk_real = CONST_REAL(A, j * lda + k);
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Packit |
67cb25 |
const BASE Ajk_imag = conj * CONST_IMAG(A, j * lda + k);
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Packit |
67cb25 |
REAL(B, ldb * i + k) -= Ajk_real * Bij_real - Ajk_imag * Bij_imag;
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Packit |
67cb25 |
IMAG(B, ldb * i + k) -= Ajk_real * Bij_imag + Ajk_imag * Bij_real;
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Packit |
67cb25 |
}
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Packit |
67cb25 |
}
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Packit |
67cb25 |
}
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Packit |
67cb25 |
}
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Packit |
67cb25 |
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Packit |
67cb25 |
} else if (side == CblasRight && uplo == CblasUpper && trans == CblasTrans) {
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Packit |
67cb25 |
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|
Packit |
67cb25 |
/* form B := alpha * B * inv(TriU(A))' */
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Packit |
67cb25 |
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Packit |
67cb25 |
if (!(alpha_real == 1.0 && alpha_imag == 0.0)) {
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Packit |
67cb25 |
for (i = 0; i < n1; i++) {
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Packit |
67cb25 |
for (j = 0; j < n2; j++) {
|
|
Packit |
67cb25 |
const BASE Bij_real = REAL(B, ldb * i + j);
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Packit |
67cb25 |
const BASE Bij_imag = IMAG(B, ldb * i + j);
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Packit |
67cb25 |
REAL(B, ldb * i + j) = alpha_real * Bij_real - alpha_imag * Bij_imag;
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Packit |
67cb25 |
IMAG(B, ldb * i + j) = alpha_real * Bij_imag + alpha_imag * Bij_real;
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Packit |
67cb25 |
}
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Packit |
67cb25 |
}
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Packit |
67cb25 |
}
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Packit |
67cb25 |
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Packit |
67cb25 |
for (i = 0; i < n1; i++) {
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Packit |
67cb25 |
for (j = n2; j > 0 && j--;) {
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Packit |
67cb25 |
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Packit |
67cb25 |
if (nonunit) {
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Packit |
67cb25 |
const BASE Ajj_real = CONST_REAL(A, lda * j + j);
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Packit |
67cb25 |
const BASE Ajj_imag = conj * CONST_IMAG(A, lda * j + j);
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Packit |
67cb25 |
const BASE s = xhypot(Ajj_real, Ajj_imag);
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Packit |
67cb25 |
const BASE a_real = Ajj_real / s;
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Packit |
67cb25 |
const BASE a_imag = Ajj_imag / s;
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Packit |
67cb25 |
const BASE Bij_real = REAL(B, ldb * i + j);
|
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Packit |
67cb25 |
const BASE Bij_imag = IMAG(B, ldb * i + j);
|
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Packit |
67cb25 |
REAL(B, ldb * i + j) = (Bij_real * a_real + Bij_imag * a_imag) / s;
|
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Packit |
67cb25 |
IMAG(B, ldb * i + j) = (Bij_imag * a_real - Bij_real * a_imag) / s;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
const BASE Bij_real = REAL(B, ldb * i + j);
|
|
Packit |
67cb25 |
const BASE Bij_imag = IMAG(B, ldb * i + j);
|
|
Packit |
67cb25 |
for (k = 0; k < j; k++) {
|
|
Packit |
67cb25 |
const BASE Akj_real = CONST_REAL(A, k * lda + j);
|
|
Packit |
67cb25 |
const BASE Akj_imag = conj * CONST_IMAG(A, k * lda + j);
|
|
Packit |
67cb25 |
REAL(B, ldb * i + k) -= Akj_real * Bij_real - Akj_imag * Bij_imag;
|
|
Packit |
67cb25 |
IMAG(B, ldb * i + k) -= Akj_real * Bij_imag + Akj_imag * Bij_real;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
} else if (side == CblasRight && uplo == CblasLower && trans == CblasNoTrans) {
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
/* form B := alpha * B * inv(TriL(A)) */
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
if (!(alpha_real == 1.0 && alpha_imag == 0.0)) {
|
|
Packit |
67cb25 |
for (i = 0; i < n1; i++) {
|
|
Packit |
67cb25 |
for (j = 0; j < n2; j++) {
|
|
Packit |
67cb25 |
const BASE Bij_real = REAL(B, ldb * i + j);
|
|
Packit |
67cb25 |
const BASE Bij_imag = IMAG(B, ldb * i + j);
|
|
Packit |
67cb25 |
REAL(B, ldb * i + j) = alpha_real * Bij_real - alpha_imag * Bij_imag;
|
|
Packit |
67cb25 |
IMAG(B, ldb * i + j) = alpha_real * Bij_imag + alpha_imag * Bij_real;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (i = 0; i < n1; i++) {
|
|
Packit |
67cb25 |
for (j = n2; j > 0 && j--;) {
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
if (nonunit) {
|
|
Packit |
67cb25 |
const BASE Ajj_real = CONST_REAL(A, lda * j + j);
|
|
Packit |
67cb25 |
const BASE Ajj_imag = conj * CONST_IMAG(A, lda * j + j);
|
|
Packit |
67cb25 |
const BASE s = xhypot(Ajj_real, Ajj_imag);
|
|
Packit |
67cb25 |
const BASE a_real = Ajj_real / s;
|
|
Packit |
67cb25 |
const BASE a_imag = Ajj_imag / s;
|
|
Packit |
67cb25 |
const BASE Bij_real = REAL(B, ldb * i + j);
|
|
Packit |
67cb25 |
const BASE Bij_imag = IMAG(B, ldb * i + j);
|
|
Packit |
67cb25 |
REAL(B, ldb * i + j) = (Bij_real * a_real + Bij_imag * a_imag) / s;
|
|
Packit |
67cb25 |
IMAG(B, ldb * i + j) = (Bij_imag * a_real - Bij_real * a_imag) / s;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
const BASE Bij_real = REAL(B, ldb * i + j);
|
|
Packit |
67cb25 |
const BASE Bij_imag = IMAG(B, ldb * i + j);
|
|
Packit |
67cb25 |
for (k = 0; k < j; k++) {
|
|
Packit |
67cb25 |
const BASE Ajk_real = CONST_REAL(A, j * lda + k);
|
|
Packit |
67cb25 |
const BASE Ajk_imag = conj * CONST_IMAG(A, j * lda + k);
|
|
Packit |
67cb25 |
REAL(B, ldb * i + k) -= Ajk_real * Bij_real - Ajk_imag * Bij_imag;
|
|
Packit |
67cb25 |
IMAG(B, ldb * i + k) -= Ajk_real * Bij_imag + Ajk_imag * Bij_real;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
} else if (side == CblasRight && uplo == CblasLower && trans == CblasTrans) {
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
/* form B := alpha * B * inv(TriL(A))' */
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
if (!(alpha_real == 1.0 && alpha_imag == 0.0)) {
|
|
Packit |
67cb25 |
for (i = 0; i < n1; i++) {
|
|
Packit |
67cb25 |
for (j = 0; j < n2; j++) {
|
|
Packit |
67cb25 |
const BASE Bij_real = REAL(B, ldb * i + j);
|
|
Packit |
67cb25 |
const BASE Bij_imag = IMAG(B, ldb * i + j);
|
|
Packit |
67cb25 |
REAL(B, ldb * i + j) = alpha_real * Bij_real - alpha_imag * Bij_imag;
|
|
Packit |
67cb25 |
IMAG(B, ldb * i + j) = alpha_real * Bij_imag + alpha_imag * Bij_real;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (i = 0; i < n1; i++) {
|
|
Packit |
67cb25 |
for (j = 0; j < n2; j++) {
|
|
Packit |
67cb25 |
if (nonunit) {
|
|
Packit |
67cb25 |
const BASE Ajj_real = CONST_REAL(A, lda * j + j);
|
|
Packit |
67cb25 |
const BASE Ajj_imag = conj * CONST_IMAG(A, lda * j + j);
|
|
Packit |
67cb25 |
const BASE s = xhypot(Ajj_real, Ajj_imag);
|
|
Packit |
67cb25 |
const BASE a_real = Ajj_real / s;
|
|
Packit |
67cb25 |
const BASE a_imag = Ajj_imag / s;
|
|
Packit |
67cb25 |
const BASE Bij_real = REAL(B, ldb * i + j);
|
|
Packit |
67cb25 |
const BASE Bij_imag = IMAG(B, ldb * i + j);
|
|
Packit |
67cb25 |
REAL(B, ldb * i + j) = (Bij_real * a_real + Bij_imag * a_imag) / s;
|
|
Packit |
67cb25 |
IMAG(B, ldb * i + j) = (Bij_imag * a_real - Bij_real * a_imag) / s;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
const BASE Bij_real = REAL(B, ldb * i + j);
|
|
Packit |
67cb25 |
const BASE Bij_imag = IMAG(B, ldb * i + j);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (k = j + 1; k < n2; k++) {
|
|
Packit |
67cb25 |
const BASE Akj_real = CONST_REAL(A, k * lda + j);
|
|
Packit |
67cb25 |
const BASE Akj_imag = conj * CONST_IMAG(A, k * lda + j);
|
|
Packit |
67cb25 |
REAL(B, ldb * i + k) -= Akj_real * Bij_real - Akj_imag * Bij_imag;
|
|
Packit |
67cb25 |
IMAG(B, ldb * i + k) -= Akj_real * Bij_imag + Akj_imag * Bij_real;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
} else {
|
|
Packit |
67cb25 |
BLAS_ERROR("unrecognized operation");
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|