1 /* blas/source_tbsv_c.h
3 * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
5 * This program is free software; you can redistribute it and/or modify
6 * it under the terms of the GNU General Public License as published by
7 * the Free Software Foundation; either version 3 of the License, or (at
8 * your option) any later version.
10 * This program is distributed in the hope that it will be useful, but
11 * WITHOUT ANY WARRANTY; without even the implied warranty of
12 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 * General Public License for more details.
15 * You should have received a copy of the GNU General Public License
16 * along with this program; if not, write to the Free Software
17 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
21 const int conj = (TransA == CblasConjTrans) ? -1 : 1;
22 const int Trans = (TransA != CblasConjTrans) ? TransA : CblasTrans;
23 const int nonunit = (Diag == CblasNonUnit);
29 /* form x := inv( A )*x */
31 if ((order == CblasRowMajor && Trans == CblasNoTrans && Uplo == CblasUpper)
32 || (order == CblasColMajor && Trans == CblasTrans && Uplo == CblasLower)) {
34 INDEX ix = OFFSET(N, incX) + incX * (N - 1);
36 for (i = N; i > 0 && i--;) {
37 BASE tmp_real = REAL(X, ix);
38 BASE tmp_imag = IMAG(X, ix);
39 const INDEX j_min = i + 1;
40 const INDEX j_max = GSL_MIN(N, i + K + 1);
41 INDEX jx = OFFSET(N, incX) + j_min * incX;
42 for (j = j_min; j < j_max; j++) {
43 const BASE Aij_real = CONST_REAL(A, lda * i + (j - i));
44 const BASE Aij_imag = conj * CONST_IMAG(A, lda * i + (j - i));
45 const BASE x_real = REAL(X, jx);
46 const BASE x_imag = IMAG(X, jx);
47 tmp_real -= Aij_real * x_real - Aij_imag * x_imag;
48 tmp_imag -= Aij_real * x_imag + Aij_imag * x_real;
53 const BASE a_real = CONST_REAL(A, lda * i + 0);
54 const BASE a_imag = conj * CONST_IMAG(A, lda * i + 0);
55 const BASE s = xhypot(a_real, a_imag);
56 const BASE b_real = a_real / s;
57 const BASE b_imag = a_imag / s;
58 REAL(X, ix) = (tmp_real * b_real + tmp_imag * b_imag) / s;
59 IMAG(X, ix) = (tmp_imag * b_real - tmp_real * b_imag) / s;
61 REAL(X, ix) = tmp_real;
62 IMAG(X, ix) = tmp_imag;
67 } else if ((order == CblasRowMajor && Trans == CblasNoTrans && Uplo == CblasLower)
68 || (order == CblasColMajor && Trans == CblasTrans && Uplo == CblasUpper)) {
69 /* forward substitution */
71 INDEX ix = OFFSET(N, incX);
73 for (i = 0; i < N; i++) {
74 BASE tmp_real = REAL(X, ix);
75 BASE tmp_imag = IMAG(X, ix);
76 const INDEX j_min = (K > i ? 0 : i - K);
77 const INDEX j_max = i;
78 INDEX jx = OFFSET(N, incX) + j_min * incX;
79 for (j = j_min; j < j_max; j++) {
80 const BASE Aij_real = CONST_REAL(A, lda * i + (K + j - i));
81 const BASE Aij_imag = conj * CONST_IMAG(A, lda * i + (K + j - i));
82 const BASE x_real = REAL(X, jx);
83 const BASE x_imag = IMAG(X, jx);
84 tmp_real -= Aij_real * x_real - Aij_imag * x_imag;
85 tmp_imag -= Aij_real * x_imag + Aij_imag * x_real;
89 const BASE a_real = CONST_REAL(A, lda * i + K);
90 const BASE a_imag = conj * CONST_IMAG(A, lda * i + K);
91 const BASE s = xhypot(a_real, a_imag);
92 const BASE b_real = a_real / s;
93 const BASE b_imag = a_imag / s;
94 REAL(X, ix) = (tmp_real * b_real + tmp_imag * b_imag) / s;
95 IMAG(X, ix) = (tmp_imag * b_real - tmp_real * b_imag) / s;
97 REAL(X, ix) = tmp_real;
98 IMAG(X, ix) = tmp_imag;
102 } else if ((order == CblasRowMajor && Trans == CblasTrans && Uplo == CblasUpper)
103 || (order == CblasColMajor && Trans == CblasNoTrans && Uplo == CblasLower)) {
104 /* form x := inv( A' )*x */
106 /* forward substitution */
108 INDEX ix = OFFSET(N, incX);
110 for (i = 0; i < N; i++) {
111 BASE tmp_real = REAL(X, ix);
112 BASE tmp_imag = IMAG(X, ix);
113 const INDEX j_min = (K > i ? 0 : i - K);
114 const INDEX j_max = i;
115 INDEX jx = OFFSET(N, incX) + j_min * incX;
116 for (j = j_min; j < j_max; j++) {
117 const BASE Aij_real = CONST_REAL(A, (i - j) + lda * j);
118 const BASE Aij_imag = conj * CONST_IMAG(A, (i - j) + lda * j);
119 const BASE x_real = REAL(X, jx);
120 const BASE x_imag = IMAG(X, jx);
121 tmp_real -= Aij_real * x_real - Aij_imag * x_imag;
122 tmp_imag -= Aij_real * x_imag + Aij_imag * x_real;
126 const BASE a_real = CONST_REAL(A, 0 + lda * i);
127 const BASE a_imag = conj * CONST_IMAG(A, 0 + lda * i);
128 const BASE s = xhypot(a_real, a_imag);
129 const BASE b_real = a_real / s;
130 const BASE b_imag = a_imag / s;
131 REAL(X, ix) = (tmp_real * b_real + tmp_imag * b_imag) / s;
132 IMAG(X, ix) = (tmp_imag * b_real - tmp_real * b_imag) / s;
134 REAL(X, ix) = tmp_real;
135 IMAG(X, ix) = tmp_imag;
139 } else if ((order == CblasRowMajor && Trans == CblasTrans && Uplo == CblasLower)
140 || (order == CblasColMajor && Trans == CblasNoTrans && Uplo == CblasUpper)) {
142 /* backsubstitution */
144 INDEX ix = OFFSET(N, incX) + incX * (N - 1);
146 for (i = N; i > 0 && i--;) {
147 BASE tmp_real = REAL(X, ix);
148 BASE tmp_imag = IMAG(X, ix);
149 const INDEX j_min = i + 1;
150 const INDEX j_max = GSL_MIN(N, i + K + 1);
151 INDEX jx = OFFSET(N, incX) + j_min * incX;
152 for (j = j_min; j < j_max; j++) {
153 const BASE Aij_real = CONST_REAL(A, (K + i - j) + lda * j);
154 const BASE Aij_imag = conj * CONST_IMAG(A, (K + i - j) + lda * j);
155 const BASE x_real = REAL(X, jx);
156 const BASE x_imag = IMAG(X, jx);
157 tmp_real -= Aij_real * x_real - Aij_imag * x_imag;
158 tmp_imag -= Aij_real * x_imag + Aij_imag * x_real;
163 const BASE a_real = CONST_REAL(A, K + lda * i);
164 const BASE a_imag = conj * CONST_IMAG(A, K + lda * i);
165 const BASE s = xhypot(a_real, a_imag);
166 const BASE b_real = a_real / s;
167 const BASE b_imag = a_imag / s;
168 REAL(X, ix) = (tmp_real * b_real + tmp_imag * b_imag) / s;
169 IMAG(X, ix) = (tmp_imag * b_real - tmp_real * b_imag) / s;
171 REAL(X, ix) = tmp_real;
172 IMAG(X, ix) = tmp_imag;
177 BLAS_ERROR("unrecognized operation");