/* blas/source_tpsv_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;
CHECK_ARGS8(TPSV,order,Uplo,TransA,Diag,N,Ap,X,incX);
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);
if (nonunit) {
const BASE a_real = CONST_REAL(Ap, TPUP(N, (N - 1), (N - 1)));
const BASE a_imag = conj * CONST_IMAG(Ap, TPUP(N, (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);
INDEX jx = ix + incX;
for (j = i + 1; j < N; j++) {
const BASE Aij_real = CONST_REAL(Ap, TPUP(N, i, j));
const BASE Aij_imag = conj * CONST_IMAG(Ap, TPUP(N, 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(Ap, TPUP(N, i, i));
const BASE a_imag = conj * CONST_IMAG(Ap, TPUP(N, 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 */
INDEX ix = OFFSET(N, incX);
if (nonunit) {
const BASE a_real = CONST_REAL(Ap, TPLO(N, 0, 0));
const BASE a_imag = conj * CONST_IMAG(Ap, TPLO(N, 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);
INDEX jx = OFFSET(N, incX);
for (j = 0; j < i; j++) {
const BASE Aij_real = CONST_REAL(Ap, TPLO(N, i, j));
const BASE Aij_imag = conj * CONST_IMAG(Ap, TPLO(N, 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(Ap, TPLO(N, i, i));
const BASE a_imag = conj * CONST_IMAG(Ap, TPLO(N, 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 */
INDEX ix = OFFSET(N, incX);
if (nonunit) {
const BASE a_real = CONST_REAL(Ap, TPUP(N, 0, 0));
const BASE a_imag = conj * CONST_IMAG(Ap, TPUP(N, 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);
INDEX jx = OFFSET(N, incX);
for (j = 0; j < i; j++) {
const BASE Aij_real = CONST_REAL(Ap, TPUP(N, j, i));
const BASE Aij_imag = conj * CONST_IMAG(Ap, TPUP(N, 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(Ap, TPUP(N, i, i));
const BASE a_imag = conj * CONST_IMAG(Ap, TPUP(N, 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 */
INDEX ix = OFFSET(N, incX) + incX * (N - 1);
if (nonunit) {
const BASE a_real = CONST_REAL(Ap, TPLO(N, (N - 1), (N - 1)));
const BASE a_imag = conj * CONST_IMAG(Ap, TPLO(N, (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);
INDEX jx = ix + incX;
for (j = i + 1; j < N; j++) {
const BASE Aij_real = CONST_REAL(Ap, TPLO(N, j, i));
const BASE Aij_imag = conj * CONST_IMAG(Ap, TPLO(N, 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(Ap, TPLO(N, i, i));
const BASE a_imag = conj * CONST_IMAG(Ap, TPLO(N, 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");
}
}