| /* blas/source_tbsv_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 2 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; |
| |
| if (N == 0) |
| return; |
| |
| /* form x := inv( A )*x */ |
| |
| if ((order == CblasRowMajor && Trans == CblasNoTrans && Uplo == CblasUpper) |
| || (order == CblasColMajor && Trans == CblasTrans && Uplo == CblasLower)) { |
| |
| INDEX ix = OFFSET(N, incX) + incX * (N - 1); |
| |
| for (i = N; i > 0 && i--;) { |
| BASE tmp_real = REAL(X, ix); |
| BASE tmp_imag = IMAG(X, ix); |
| const INDEX j_min = i + 1; |
| const INDEX j_max = GSL_MIN(N, i + K + 1); |
| INDEX jx = OFFSET(N, incX) + j_min * incX; |
| for (j = j_min; j < j_max; j++) { |
| const BASE Aij_real = CONST_REAL(A, lda * i + (j - i)); |
| const BASE Aij_imag = conj * CONST_IMAG(A, lda * i + (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 + 0); |
| const BASE a_imag = conj * CONST_IMAG(A, lda * i + 0); |
| 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 */ |
| |
| INDEX ix = OFFSET(N, incX); |
| |
| for (i = 0; i < N; i++) { |
| BASE tmp_real = REAL(X, ix); |
| BASE tmp_imag = IMAG(X, ix); |
| const INDEX j_min = (K > i ? 0 : i - K); |
| const INDEX j_max = i; |
| INDEX jx = OFFSET(N, incX) + j_min * incX; |
| for (j = j_min; j < j_max; j++) { |
| const BASE Aij_real = CONST_REAL(A, lda * i + (K + j - i)); |
| const BASE Aij_imag = conj * CONST_IMAG(A, lda * i + (K + 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 + K); |
| const BASE a_imag = conj * CONST_IMAG(A, lda * i + K); |
| 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 */ |
| |
| INDEX ix = OFFSET(N, incX); |
| |
| for (i = 0; i < N; i++) { |
| BASE tmp_real = REAL(X, ix); |
| BASE tmp_imag = IMAG(X, ix); |
| const INDEX j_min = (K > i ? 0 : i - K); |
| const INDEX j_max = i; |
| INDEX jx = OFFSET(N, incX) + j_min * incX; |
| for (j = j_min; j < j_max; j++) { |
| const BASE Aij_real = CONST_REAL(A, (i - j) + lda * j); |
| const BASE Aij_imag = conj * CONST_IMAG(A, (i - j) + lda * 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, 0 + lda * i); |
| const BASE a_imag = conj * CONST_IMAG(A, 0 + lda * 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 */ |
| |
| INDEX ix = OFFSET(N, incX) + incX * (N - 1); |
| |
| for (i = N; i > 0 && i--;) { |
| BASE tmp_real = REAL(X, ix); |
| BASE tmp_imag = IMAG(X, ix); |
| const INDEX j_min = i + 1; |
| const INDEX j_max = GSL_MIN(N, i + K + 1); |
| INDEX jx = OFFSET(N, incX) + j_min * incX; |
| for (j = j_min; j < j_max; j++) { |
| const BASE Aij_real = CONST_REAL(A, (K + i - j) + lda * j); |
| const BASE Aij_imag = conj * CONST_IMAG(A, (K + i - j) + lda * 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, K + lda * i); |
| const BASE a_imag = conj * CONST_IMAG(A, K + lda * 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"); |
| } |
| } |