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// Copyright (c) 2017-2023, University of Tennessee. All rights reserved.
// SPDX-License-Identifier: BSD-3-Clause
// This program is free software: you can redistribute it and/or modify it under
// the terms of the BSD 3-Clause license. See the accompanying LICENSE file.
#ifndef BLAS_SYRK_HH
#define BLAS_SYRK_HH
#include "blas/util.hh"
#include <limits>
namespace blas {
// =============================================================================
/// Symmetric rank-k update:
/// \[
/// C = \alpha A A^T + \beta C,
/// \]
/// or
/// \[
/// C = \alpha A^T A + \beta C,
/// \]
/// where alpha and beta are scalars, C is an n-by-n symmetric matrix,
/// and A is an n-by-k or k-by-n matrix.
///
/// Generic implementation for arbitrary data types.
///
/// @param[in] layout
/// Matrix storage, Layout::ColMajor or Layout::RowMajor.
///
/// @param[in] uplo
/// What part of the matrix C is referenced,
/// the opposite triangle being assumed from symmetry:
/// - Uplo::Lower: only the lower triangular part of C is referenced.
/// - Uplo::Upper: only the upper triangular part of C is referenced.
///
/// @param[in] trans
/// The operation to be performed:
/// - Op::NoTrans: $C = \alpha A A^T + \beta C$.
/// - Op::Trans: $C = \alpha A^T A + \beta C$.
/// - In the real case, Op::ConjTrans is interpreted as Op::Trans.
/// In the complex case, Op::ConjTrans is illegal (see @ref herk instead).
///
/// @param[in] n
/// Number of rows and columns of the matrix C. n >= 0.
///
/// @param[in] k
/// - If trans = NoTrans: number of columns of the matrix A. k >= 0.
/// - Otherwise: number of rows of the matrix A. k >= 0.
///
/// @param[in] alpha
/// Scalar alpha. If alpha is zero, A is not accessed.
///
/// @param[in] A
/// - If trans = NoTrans:
/// the n-by-k matrix A, stored in an lda-by-k array [RowMajor: n-by-lda].
/// - Otherwise:
/// the k-by-n matrix A, stored in an lda-by-n array [RowMajor: k-by-lda].
///
/// @param[in] lda
/// Leading dimension of A.
/// - If trans = NoTrans: lda >= max(1, n) [RowMajor: lda >= max(1, k)],
/// - Otherwise: lda >= max(1, k) [RowMajor: lda >= max(1, n)].
///
/// @param[in] beta
/// Scalar beta. If beta is zero, C need not be set on input.
///
/// @param[in] C
/// The n-by-n symmetric matrix C,
/// stored in an lda-by-n array [RowMajor: n-by-lda].
///
/// @param[in] ldc
/// Leading dimension of C. ldc >= max(1, n).
///
/// @ingroup syrk
template <typename TA, typename TC>
void syrk(
blas::Layout layout,
blas::Uplo uplo,
blas::Op trans,
int64_t n, int64_t k,
scalar_type<TA, TC> alpha,
TA const *A, int64_t lda,
scalar_type<TA, TC> beta,
TC *C, int64_t ldc )
{
typedef blas::scalar_type<TA, TC> scalar_t;
#define A(i_, j_) A[ (i_) + (j_)*lda ]
#define C(i_, j_) C[ (i_) + (j_)*ldc ]
// constants
const scalar_t zero = 0;
const scalar_t one = 1;
// check arguments
blas_error_if( layout != Layout::ColMajor &&
layout != Layout::RowMajor );
blas_error_if( uplo != Uplo::Lower &&
uplo != Uplo::Upper &&
uplo != Uplo::General );
blas_error_if( n < 0 );
blas_error_if( k < 0 );
// check and interpret argument trans
if (trans == Op::ConjTrans) {
blas_error_if_msg(
blas::is_complex<TA>::value,
"trans == Op::ConjTrans && "
"blas::is_complex<TA>::value" );
trans = Op::Trans;
}
else {
blas_error_if( trans != Op::NoTrans &&
trans != Op::Trans );
}
// adapt if row major
if (layout == Layout::RowMajor) {
if (uplo == Uplo::Lower)
uplo = Uplo::Upper;
else if (uplo == Uplo::Upper)
uplo = Uplo::Lower;
trans = (trans == Op::NoTrans)
? Op::Trans
: Op::NoTrans;
}
// check remaining arguments
blas_error_if( lda < ((trans == Op::NoTrans) ? n : k) );
blas_error_if( ldc < n );
// quick return
if (n == 0 || k == 0)
return;
// alpha == zero
if (alpha == zero) {
if (beta == zero) {
if (uplo != Uplo::Upper) {
for (int64_t j = 0; j < n; ++j) {
for (int64_t i = 0; i <= j; ++i)
C(i, j) = zero;
}
}
else if (uplo != Uplo::Lower) {
for (int64_t j = 0; j < n; ++j) {
for (int64_t i = j; i < n; ++i)
C(i, j) = zero;
}
}
else {
for (int64_t j = 0; j < n; ++j) {
for (int64_t i = 0; i < n; ++i)
C(i, j) = zero;
}
}
}
else if (beta != one) {
if (uplo != Uplo::Upper) {
for (int64_t j = 0; j < n; ++j) {
for (int64_t i = 0; i <= j; ++i)
C(i, j) *= beta;
}
}
else if (uplo != Uplo::Lower) {
for (int64_t j = 0; j < n; ++j) {
for (int64_t i = j; i < n; ++i)
C(i, j) *= beta;
}
}
else {
for (int64_t j = 0; j < n; ++j) {
for (int64_t i = 0; i < n; ++i)
C(i, j) *= beta;
}
}
}
return;
}
// alpha != zero
if (trans == Op::NoTrans) {
if (uplo != Uplo::Lower) {
// uplo == Uplo::Upper or uplo == Uplo::General
for (int64_t j = 0; j < n; ++j) {
for (int64_t i = 0; i <= j; ++i)
C(i, j) *= beta;
for (int64_t l = 0; l < k; ++l) {
scalar_t alpha_Ajl = alpha*A(j, l);
for (int64_t i = 0; i <= j; ++i)
C(i, j) += A(i, l)*alpha_Ajl;
}
}
}
else { // uplo == Uplo::Lower
for (int64_t j = 0; j < n; ++j) {
for (int64_t i = j; i < n; ++i)
C(i, j) *= beta;
for (int64_t l = 0; l < k; ++l) {
scalar_t alpha_Ajl = alpha*A(j, l);
for (int64_t i = j; i < n; ++i)
C(i, j) += A(i, l)*alpha_Ajl;
}
}
}
}
else { // trans == Op::Trans
if (uplo != Uplo::Lower) {
// uplo == Uplo::Upper or uplo == Uplo::General
for (int64_t j = 0; j < n; ++j) {
for (int64_t i = 0; i <= j; ++i) {
scalar_t sum = zero;
for (int64_t l = 0; l < k; ++l)
sum += A(l, i) * A(l, j);
C(i, j) = alpha*sum + beta*C(i, j);
}
}
}
else { // uplo == Uplo::Lower
for (int64_t j = 0; j < n; ++j) {
for (int64_t i = j; i < n; ++i) {
scalar_t sum = zero;
for (int64_t l = 0; l < k; ++l) {
sum += A(l, i) * A(l, j);
}
C(i, j) = alpha*sum + beta*C(i, j);
}
}
}
}
if (uplo == Uplo::General) {
for (int64_t j = 0; j < n; ++j) {
for (int64_t i = j+1; i < n; ++i)
C(i, j) = C(j, i);
}
}
#undef A
#undef C
}
} // namespace blas
#endif // #ifndef BLAS_SYMM_HH
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