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- /* blas/source_trsv_c.h
- *
- * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
- *
- * 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.
- */
- {
- const int conj = (TransA == CblasConjTrans) ? -1 : 1;
- const int Trans = (TransA != CblasConjTrans) ? TransA : CblasTrans;
- const int nonunit = (Diag == CblasNonUnit);
- INDEX i, j;
- INDEX ix, jx;
- if (N == 0)
- return;
- /* form x := inv( A )*x */
- if ((order == CblasRowMajor && Trans == CblasNoTrans && Uplo == CblasUpper)
- || (order == CblasColMajor && Trans == CblasTrans && Uplo == CblasLower)) {
- ix = OFFSET(N, incX) + incX * (N - 1);
- if (nonunit) {
- const BASE a_real = CONST_REAL(A, lda * (N - 1) + (N - 1));
- const BASE a_imag = conj * CONST_IMAG(A, lda * (N - 1) + (N - 1));
- const BASE x_real = REAL(X, ix);
- const BASE x_imag = IMAG(X, ix);
- const BASE s = xhypot(a_real, a_imag);
- const BASE b_real = a_real / s;
- const BASE b_imag = a_imag / s;
- REAL(X, ix) = (x_real * b_real + x_imag * b_imag) / s;
- IMAG(X, ix) = (x_imag * b_real - b_imag * x_real) / s;
- }
- ix -= incX;
- for (i = N - 1; i > 0 && i--;) {
- BASE tmp_real = REAL(X, ix);
- BASE tmp_imag = IMAG(X, ix);
- jx = ix + incX;
- for (j = i + 1; j < N; j++) {
- const BASE Aij_real = CONST_REAL(A, lda * i + j);
- const BASE Aij_imag = conj * CONST_IMAG(A, lda * i + j);
- const BASE x_real = REAL(X, jx);
- const BASE x_imag = IMAG(X, jx);
- tmp_real -= Aij_real * x_real - Aij_imag * x_imag;
- tmp_imag -= Aij_real * x_imag + Aij_imag * x_real;
- jx += incX;
- }
- if (nonunit) {
- const BASE a_real = CONST_REAL(A, lda * i + i);
- const BASE a_imag = conj * CONST_IMAG(A, lda * i + i);
- const BASE s = xhypot(a_real, a_imag);
- const BASE b_real = a_real / s;
- const BASE b_imag = a_imag / s;
- REAL(X, ix) = (tmp_real * b_real + tmp_imag * b_imag) / s;
- IMAG(X, ix) = (tmp_imag * b_real - tmp_real * b_imag) / s;
- } else {
- REAL(X, ix) = tmp_real;
- IMAG(X, ix) = tmp_imag;
- }
- ix -= incX;
- }
- } else if ((order == CblasRowMajor && Trans == CblasNoTrans && Uplo == CblasLower)
- || (order == CblasColMajor && Trans == CblasTrans && Uplo == CblasUpper)) {
- /* forward substitution */
- ix = OFFSET(N, incX);
- if (nonunit) {
- const BASE a_real = CONST_REAL(A, lda * 0 + 0);
- const BASE a_imag = conj * CONST_IMAG(A, lda * 0 + 0);
- const BASE x_real = REAL(X, ix);
- const BASE x_imag = IMAG(X, ix);
- const BASE s = xhypot(a_real, a_imag);
- const BASE b_real = a_real / s;
- const BASE b_imag = a_imag / s;
- REAL(X, ix) = (x_real * b_real + x_imag * b_imag) / s;
- IMAG(X, ix) = (x_imag * b_real - b_imag * x_real) / s;
- }
- ix += incX;
- for (i = 1; i < N; i++) {
- BASE tmp_real = REAL(X, ix);
- BASE tmp_imag = IMAG(X, ix);
- jx = OFFSET(N, incX);
- for (j = 0; j < i; j++) {
- const BASE Aij_real = CONST_REAL(A, lda * i + j);
- const BASE Aij_imag = conj * CONST_IMAG(A, lda * i + j);
- const BASE x_real = REAL(X, jx);
- const BASE x_imag = IMAG(X, jx);
- tmp_real -= Aij_real * x_real - Aij_imag * x_imag;
- tmp_imag -= Aij_real * x_imag + Aij_imag * x_real;
- jx += incX;
- }
- if (nonunit) {
- const BASE a_real = CONST_REAL(A, lda * i + i);
- const BASE a_imag = conj * CONST_IMAG(A, lda * i + i);
- const BASE s = xhypot(a_real, a_imag);
- const BASE b_real = a_real / s;
- const BASE b_imag = a_imag / s;
- REAL(X, ix) = (tmp_real * b_real + tmp_imag * b_imag) / s;
- IMAG(X, ix) = (tmp_imag * b_real - tmp_real * b_imag) / s;
- } else {
- REAL(X, ix) = tmp_real;
- IMAG(X, ix) = tmp_imag;
- }
- ix += incX;
- }
- } else if ((order == CblasRowMajor && Trans == CblasTrans && Uplo == CblasUpper)
- || (order == CblasColMajor && Trans == CblasNoTrans && Uplo == CblasLower)) {
- /* form x := inv( A' )*x */
- /* forward substitution */
- ix = OFFSET(N, incX);
- if (nonunit) {
- const BASE a_real = CONST_REAL(A, lda * 0 + 0);
- const BASE a_imag = conj * CONST_IMAG(A, lda * 0 + 0);
- const BASE x_real = REAL(X, ix);
- const BASE x_imag = IMAG(X, ix);
- const BASE s = xhypot(a_real, a_imag);
- const BASE b_real = a_real / s;
- const BASE b_imag = a_imag / s;
- REAL(X, ix) = (x_real * b_real + x_imag * b_imag) / s;
- IMAG(X, ix) = (x_imag * b_real - b_imag * x_real) / s;
- }
- ix += incX;
- for (i = 1; i < N; i++) {
- BASE tmp_real = REAL(X, ix);
- BASE tmp_imag = IMAG(X, ix);
- jx = OFFSET(N, incX);
- for (j = 0; j < i; j++) {
- const BASE Aij_real = CONST_REAL(A, lda * j + i);
- const BASE Aij_imag = conj * CONST_IMAG(A, lda * j + i);
- const BASE x_real = REAL(X, jx);
- const BASE x_imag = IMAG(X, jx);
- tmp_real -= Aij_real * x_real - Aij_imag * x_imag;
- tmp_imag -= Aij_real * x_imag + Aij_imag * x_real;
- jx += incX;
- }
- if (nonunit) {
- const BASE a_real = CONST_REAL(A, lda * i + i);
- const BASE a_imag = conj * CONST_IMAG(A, lda * i + i);
- const BASE s = xhypot(a_real, a_imag);
- const BASE b_real = a_real / s;
- const BASE b_imag = a_imag / s;
- REAL(X, ix) = (tmp_real * b_real + tmp_imag * b_imag) / s;
- IMAG(X, ix) = (tmp_imag * b_real - tmp_real * b_imag) / s;
- } else {
- REAL(X, ix) = tmp_real;
- IMAG(X, ix) = tmp_imag;
- }
- ix += incX;
- }
- } else if ((order == CblasRowMajor && Trans == CblasTrans && Uplo == CblasLower)
- || (order == CblasColMajor && Trans == CblasNoTrans && Uplo == CblasUpper)) {
- /* backsubstitution */
- ix = OFFSET(N, incX) + incX * (N - 1);
- if (nonunit) {
- const BASE a_real = CONST_REAL(A, lda * (N - 1) + (N - 1));
- const BASE a_imag = conj * CONST_IMAG(A, lda * (N - 1) + (N - 1));
- const BASE x_real = REAL(X, ix);
- const BASE x_imag = IMAG(X, ix);
- const BASE s = xhypot(a_real, a_imag);
- const BASE b_real = a_real / s;
- const BASE b_imag = a_imag / s;
- REAL(X, ix) = (x_real * b_real + x_imag * b_imag) / s;
- IMAG(X, ix) = (x_imag * b_real - b_imag * x_real) / s;
- }
- ix -= incX;
- for (i = N - 1; i > 0 && i--;) {
- BASE tmp_real = REAL(X, ix);
- BASE tmp_imag = IMAG(X, ix);
- jx = ix + incX;
- for (j = i + 1; j < N; j++) {
- const BASE Aij_real = CONST_REAL(A, lda * j + i);
- const BASE Aij_imag = conj * CONST_IMAG(A, lda * j + i);
- const BASE x_real = REAL(X, jx);
- const BASE x_imag = IMAG(X, jx);
- tmp_real -= Aij_real * x_real - Aij_imag * x_imag;
- tmp_imag -= Aij_real * x_imag + Aij_imag * x_real;
- jx += incX;
- }
- if (nonunit) {
- const BASE a_real = CONST_REAL(A, lda * i + i);
- const BASE a_imag = conj * CONST_IMAG(A, lda * i + i);
- const BASE s = xhypot(a_real, a_imag);
- const BASE b_real = a_real / s;
- const BASE b_imag = a_imag / s;
- REAL(X, ix) = (tmp_real * b_real + tmp_imag * b_imag) / s;
- IMAG(X, ix) = (tmp_imag * b_real - tmp_real * b_imag) / s;
- } else {
- REAL(X, ix) = tmp_real;
- IMAG(X, ix) = tmp_imag;
- }
- ix -= incX;
- }
- } else {
- BLAS_ERROR("unrecognized operation");
- }
- }
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