/* blas/source_her2k.h
*
* Copyright (C) 2001, 2007 Brian Gough
*
* 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.
*/
{
INDEX i, j, k;
int uplo, trans;
CHECK_ARGS13(HER2K,Order,Uplo,Trans,N,K,alpha,A,lda,B,ldb,beta,C,ldc);
{
const BASE alpha_real = CONST_REAL0(alpha);
BASE alpha_imag = CONST_IMAG0(alpha);
if (beta == 1.0 && ((alpha_real == 0.0 && alpha_imag == 0.0) || K == 0))
return;
if (Order == CblasRowMajor) {
uplo = Uplo;
trans = Trans;
} else {
uplo = (Uplo == CblasUpper) ? CblasLower : CblasUpper;
trans = (Trans == CblasNoTrans) ? CblasConjTrans : CblasNoTrans;
alpha_imag *= -1; /* conjugate alpha */
}
/* form C := beta*C */
if (beta == 0.0) {
if (uplo == CblasUpper) {
for (i = 0; i < N; i++) {
for (j = i; j < N; j++) {
REAL(C, ldc * i + j) = 0.0;
IMAG(C, ldc * i + j) = 0.0;
}
}
} else {
for (i = 0; i < N; i++) {
for (j = 0; j <= i; j++) {
REAL(C, ldc * i + j) = 0.0;
IMAG(C, ldc * i + j) = 0.0;
}
}
}
} else if (beta != 1.0) {
if (uplo == CblasUpper) {
for (i = 0; i < N; i++) {
REAL(C, ldc * i + i) *= beta;
IMAG(C, ldc * i + i) = 0.0;
for (j = i + 1; j < N; j++) {
REAL(C, ldc * i + j) *= beta;
IMAG(C, ldc * i + j) *= beta;
}
}
} else {
for (i = 0; i < N; i++) {
for (j = 0; j < i; j++) {
REAL(C, ldc * i + j) *= beta;
IMAG(C, ldc * i + j) *= beta;
}
REAL(C, ldc * i + i) *= beta;
IMAG(C, ldc * i + i) = 0.0;
}
}
} else {
for (i = 0; i < N; i++) {
IMAG(C, ldc * i + i) = 0.0;
}
}
if (alpha_real == 0.0 && alpha_imag == 0.0)
return;
if (uplo == CblasUpper && trans == CblasNoTrans) {
for (i = 0; i < N; i++) {
/* Cii += alpha Aik conj(Bik) + conj(alpha) Bik conj(Aik) */
{
BASE temp_real = 0.0;
/* BASE temp_imag = 0.0; */
for (k = 0; k < K; k++) {
const BASE Aik_real = CONST_REAL(A, i * lda + k);
const BASE Aik_imag = CONST_IMAG(A, i * lda + k);
/* temp1 = alpha * Aik */
const BASE temp1_real = alpha_real * Aik_real - alpha_imag * Aik_imag;
const BASE temp1_imag = alpha_real * Aik_imag + alpha_imag * Aik_real;
const BASE Bik_real = CONST_REAL(B, i * ldb + k);
const BASE Bik_imag = CONST_IMAG(B, i * ldb + k);
temp_real += temp1_real * Bik_real + temp1_imag * Bik_imag;
}
REAL(C, i * ldc + i) += 2 * temp_real;
IMAG(C, i * ldc + i) = 0.0;
}
/* Cij += alpha Aik conj(Bjk) + conj(alpha) Bik conj(Ajk) */
for (j = i + 1; j < N; j++) {
BASE temp_real = 0.0;
BASE temp_imag = 0.0;
for (k = 0; k < K; k++) {
const BASE Aik_real = CONST_REAL(A, i * lda + k);
const BASE Aik_imag = CONST_IMAG(A, i * lda + k);
/* temp1 = alpha * Aik */
const BASE temp1_real = alpha_real * Aik_real - alpha_imag * Aik_imag;
const BASE temp1_imag = alpha_real * Aik_imag + alpha_imag * Aik_real;
const BASE Bik_real = CONST_REAL(B, i * ldb + k);
const BASE Bik_imag = CONST_IMAG(B, i * ldb + k);
const BASE Ajk_real = CONST_REAL(A, j * lda + k);
const BASE Ajk_imag = CONST_IMAG(A, j * lda + k);
/* temp2 = alpha * Ajk */
const BASE temp2_real = alpha_real * Ajk_real - alpha_imag * Ajk_imag;
const BASE temp2_imag = alpha_real * Ajk_imag + alpha_imag * Ajk_real;
const BASE Bjk_real = CONST_REAL(B, j * ldb + k);
const BASE Bjk_imag = CONST_IMAG(B, j * ldb + k);
/* Cij += alpha * Aik * conj(Bjk) + conj(alpha) * Bik * conj(Ajk) */
temp_real += ((temp1_real * Bjk_real + temp1_imag * Bjk_imag)
+ (Bik_real * temp2_real + Bik_imag * temp2_imag));
temp_imag += ((temp1_real * (-Bjk_imag) + temp1_imag * Bjk_real)
+ (Bik_real * (-temp2_imag) + Bik_imag * temp2_real));
}
REAL(C, i * ldc + j) += temp_real;
IMAG(C, i * ldc + j) += temp_imag;
}
}
} else if (uplo == CblasUpper && trans == CblasConjTrans) {
for (k = 0; k < K; k++) {
for (i = 0; i < N; i++) {
BASE Aki_real = CONST_REAL(A, k * lda + i);
BASE Aki_imag = CONST_IMAG(A, k * lda + i);
BASE Bki_real = CONST_REAL(B, k * ldb + i);
BASE Bki_imag = CONST_IMAG(B, k * ldb + i);
/* temp1 = alpha * conj(Aki) */
BASE temp1_real = alpha_real * Aki_real - alpha_imag * (-Aki_imag);
BASE temp1_imag = alpha_real * (-Aki_imag) + alpha_imag * Aki_real;
/* temp2 = conj(alpha) * conj(Bki) */
BASE temp2_real = alpha_real * Bki_real - alpha_imag * Bki_imag;
BASE temp2_imag = -(alpha_real * Bki_imag + alpha_imag * Bki_real);
/* Cii += alpha * conj(Aki) * Bki + conj(alpha) * conj(Bki) * Aki */
{
REAL(C, i * lda + i) += 2 * (temp1_real * Bki_real - temp1_imag * Bki_imag);
IMAG(C, i * lda + i) = 0.0;
}
for (j = i + 1; j < N; j++) {
BASE Akj_real = CONST_REAL(A, k * lda + j);
BASE Akj_imag = CONST_IMAG(A, k * lda + j);
BASE Bkj_real = CONST_REAL(B, k * ldb + j);
BASE Bkj_imag = CONST_IMAG(B, k * ldb + j);
/* Cij += alpha * conj(Aki) * Bkj + conj(alpha) * conj(Bki) * Akj */
REAL(C, i * lda + j) += (temp1_real * Bkj_real - temp1_imag * Bkj_imag)
+ (temp2_real * Akj_real - temp2_imag * Akj_imag);
IMAG(C, i * lda + j) += (temp1_real * Bkj_imag + temp1_imag * Bkj_real)
+ (temp2_real * Akj_imag + temp2_imag * Akj_real);
}
}
}
} else if (uplo == CblasLower && trans == CblasNoTrans) {
for (i = 0; i < N; i++) {
/* Cij += alpha Aik conj(Bjk) + conj(alpha) Bik conj(Ajk) */
for (j = 0; j < i; j++) {
BASE temp_real = 0.0;
BASE temp_imag = 0.0;
for (k = 0; k < K; k++) {
const BASE Aik_real = CONST_REAL(A, i * lda + k);
const BASE Aik_imag = CONST_IMAG(A, i * lda + k);
/* temp1 = alpha * Aik */
const BASE temp1_real = alpha_real * Aik_real - alpha_imag * Aik_imag;
const BASE temp1_imag = alpha_real * Aik_imag + alpha_imag * Aik_real;
const BASE Bik_real = CONST_REAL(B, i * ldb + k);
const BASE Bik_imag = CONST_IMAG(B, i * ldb + k);
const BASE Ajk_real = CONST_REAL(A, j * lda + k);
const BASE Ajk_imag = CONST_IMAG(A, j * lda + k);
/* temp2 = alpha * Ajk */
const BASE temp2_real = alpha_real * Ajk_real - alpha_imag * Ajk_imag;
const BASE temp2_imag = alpha_real * Ajk_imag + alpha_imag * Ajk_real;
const BASE Bjk_real = CONST_REAL(B, j * ldb + k);
const BASE Bjk_imag = CONST_IMAG(B, j * ldb + k);
/* Cij += alpha * Aik * conj(Bjk) + conj(alpha) * Bik * conj(Ajk) */
temp_real += ((temp1_real * Bjk_real + temp1_imag * Bjk_imag)
+ (Bik_real * temp2_real + Bik_imag * temp2_imag));
temp_imag += ((temp1_real * (-Bjk_imag) + temp1_imag * Bjk_real)
+ (Bik_real * (-temp2_imag) + Bik_imag * temp2_real));
}
REAL(C, i * ldc + j) += temp_real;
IMAG(C, i * ldc + j) += temp_imag;
}
/* Cii += alpha Aik conj(Bik) + conj(alpha) Bik conj(Aik) */
{
BASE temp_real = 0.0;
/* BASE temp_imag = 0.0; */
for (k = 0; k < K; k++) {
const BASE Aik_real = CONST_REAL(A, i * lda + k);
const BASE Aik_imag = CONST_IMAG(A, i * lda + k);
/* temp1 = alpha * Aik */
const BASE temp1_real = alpha_real * Aik_real - alpha_imag * Aik_imag;
const BASE temp1_imag = alpha_real * Aik_imag + alpha_imag * Aik_real;
const BASE Bik_real = CONST_REAL(B, i * ldb + k);
const BASE Bik_imag = CONST_IMAG(B, i * ldb + k);
temp_real += temp1_real * Bik_real + temp1_imag * Bik_imag;
}
REAL(C, i * ldc + i) += 2 * temp_real;
IMAG(C, i * ldc + i) = 0.0;
}
}
} else if (uplo == CblasLower && trans == CblasConjTrans) {
for (k = 0; k < K; k++) {
for (i = 0; i < N; i++) {
BASE Aki_real = CONST_REAL(A, k * lda + i);
BASE Aki_imag = CONST_IMAG(A, k * lda + i);
BASE Bki_real = CONST_REAL(B, k * ldb + i);
BASE Bki_imag = CONST_IMAG(B, k * ldb + i);
/* temp1 = alpha * conj(Aki) */
BASE temp1_real = alpha_real * Aki_real - alpha_imag * (-Aki_imag);
BASE temp1_imag = alpha_real * (-Aki_imag) + alpha_imag * Aki_real;
/* temp2 = conj(alpha) * conj(Bki) */
BASE temp2_real = alpha_real * Bki_real - alpha_imag * Bki_imag;
BASE temp2_imag = -(alpha_real * Bki_imag + alpha_imag * Bki_real);
for (j = 0; j < i; j++) {
BASE Akj_real = CONST_REAL(A, k * lda + j);
BASE Akj_imag = CONST_IMAG(A, k * lda + j);
BASE Bkj_real = CONST_REAL(B, k * ldb + j);
BASE Bkj_imag = CONST_IMAG(B, k * ldb + j);
/* Cij += alpha * conj(Aki) * Bkj + conj(alpha) * conj(Bki) * Akj */
REAL(C, i * lda + j) += (temp1_real * Bkj_real - temp1_imag * Bkj_imag)
+ (temp2_real * Akj_real - temp2_imag * Akj_imag);
IMAG(C, i * lda + j) += (temp1_real * Bkj_imag + temp1_imag * Bkj_real)
+ (temp2_real * Akj_imag + temp2_imag * Akj_real);
}
/* Cii += alpha * conj(Aki) * Bki + conj(alpha) * conj(Bki) * Aki */
{
REAL(C, i * lda + i) += 2 * (temp1_real * Bki_real - temp1_imag * Bki_imag);
IMAG(C, i * lda + i) = 0.0;
}
}
}
} else {
BLAS_ERROR("unrecognized operation");
}
}
}