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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_HER2K_HH
#define BLAS_HER2K_HH
#include "blas/util.hh"
#include "blas/syr2k.hh"
#include <limits>
namespace blas {
// =============================================================================
/// Hermitian rank-k update:
/// \[
/// C = \alpha A B^H + conj(\alpha) B A^H + \beta C,
/// \]
/// or
/// \[
/// C = \alpha A^H B + conj(\alpha) B^H A + \beta C,
/// \]
/// where alpha and beta are scalars, C is an n-by-n Hermitian matrix,
/// and A and B are n-by-k or k-by-n matrices.
///
/// 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: $C = \alpha A B^H + conj(\alpha) A^H B + \beta C$.
/// - Op::ConjTrans: $C = \alpha A^H B + conj(\alpha) B A^H + \beta C$.
/// - In the real case, Op::Trans is interpreted as Op::ConjTrans.
/// In the complex case, Op::Trans is illegal (see @ref syr2k 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 and B are 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] B
/// - If trans = NoTrans:
/// the n-by-k matrix B, stored in an ldb-by-k array [RowMajor: n-by-ldb].
/// - Otherwise:
/// the k-by-n matrix B, stored in an ldb-by-n array [RowMajor: k-by-ldb].
///
/// @param[in] ldb
/// Leading dimension of B.
/// - If trans = NoTrans: ldb >= max(1, n) [RowMajor: ldb >= max(1, k)],
/// - Otherwise: ldb >= max(1, k) [RowMajor: ldb >= 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 Hermitian 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 her2k
template <typename TA, typename TB, typename TC>
void her2k(
blas::Layout layout,
blas::Uplo uplo,
blas::Op trans,
int64_t n, int64_t k,
scalar_type<TA, TB, TC> alpha, // note: complex
TA const *A, int64_t lda,
TB const *B, int64_t ldb,
real_type<TA, TB, TC> beta, // note: real
TC *C, int64_t ldc )
{
typedef blas::scalar_type<TA, TB, TC> scalar_t;
#define A(i_, j_) A[ (i_) + (j_)*lda ]
#define B(i_, j_) B[ (i_) + (j_)*ldb ]
#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::Trans) {
blas_error_if_msg(
( blas::is_complex<TA>::value ||
blas::is_complex<TB>::value ),
"trans == Op::Trans && "
"( blas::is_complex<TA>::value ||"
" blas::is_complex<TB>::value )" );
trans = Op::ConjTrans;
}
else {
blas_error_if( trans != Op::NoTrans &&
trans != Op::ConjTrans );
}
// 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::ConjTrans
: Op::NoTrans;
alpha = conj(alpha);
}
// check remaining arguments
blas_error_if( lda < ((trans == Op::NoTrans) ? n : k) );
blas_error_if( ldb < ((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;
C(j, j) = beta * real( C(j, j) );
}
}
else if (uplo != Uplo::Lower) {
for (int64_t j = 0; j < n; ++j) {
C(j, j) = beta * real( C(j, j) );
for (int64_t i = j+1; i < n; ++i)
C(i, j) *= beta;
}
}
else {
for (int64_t j = 0; j < n; ++j) {
for (int64_t i = 0; i < j; ++i)
C(i, j) *= beta;
C(j, j) = beta * real( C(j, j) );
for (int64_t i = j+1; 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;
C(j, j) = beta * real( C(j, j) );
for (int64_t l = 0; l < k; ++l) {
scalar_t alpha_conj_Bjl = alpha*conj( B(j, l) );
scalar_t conj_alpha_Ajl = conj( alpha*A(j, l) );
for (int64_t i = 0; i < j; ++i) {
C(i, j) += A(i, l)*alpha_conj_Bjl
+ B(i, l)*conj_alpha_Ajl;
}
C(j, j) += 2 * real( A(j, l) * alpha_conj_Bjl );
}
}
}
else { // uplo == Uplo::Lower
for (int64_t j = 0; j < n; ++j) {
C(j, j) = beta * real( C(j, j) );
for (int64_t i = j+1; i < n; ++i)
C(i, j) *= beta;
for (int64_t l = 0; l < k; ++l) {
scalar_t alpha_conj_Bjl = alpha*conj( B(j, l) );
scalar_t conj_alpha_Ajl = conj( alpha*A(j, l) );
C(j, j) += 2 * real( A(j, l) * alpha_conj_Bjl );
for (int64_t i = j+1; i < n; ++i) {
C(i, j) += A(i, l) * alpha_conj_Bjl
+ B(i, l) * conj_alpha_Ajl;
}
}
}
}
}
else { // trans == Op::ConjTrans
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 sum1 = zero;
scalar_t sum2 = zero;
for (int64_t l = 0; l < k; ++l) {
sum1 += conj( A(l, i) ) * B(l, j);
sum2 += conj( B(l, i) ) * A(l, j);
}
C(i, j) = (i < j)
? alpha*sum1 + conj(alpha)*sum2 + beta*C(i, j)
: real( alpha*sum1 + conj(alpha)*sum2 )
+ beta*real( 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 sum1 = zero;
scalar_t sum2 = zero;
for (int64_t l = 0; l < k; ++l) {
sum1 += conj( A(l, i) ) * B(l, j);
sum2 += conj( B(l, i) ) * A(l, j);
}
C(i, j) = (i > j)
? alpha*sum1 + conj(alpha)*sum2 + beta*C(i, j)
: real( alpha*sum1 + conj(alpha)*sum2 )
+ beta*real( 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) = conj( C(j, i) );
}
}
#undef A
#undef B
#undef C
}
} // namespace blas
#endif // #ifndef BLAS_HER2K_HH
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