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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_HER2_HH
#define BLAS_HER2_HH
#include "blas/util.hh"
#include "blas/syr2.hh"
#include <limits>
namespace blas {
// =============================================================================
/// Hermitian matrix rank-2 update:
/// \[
/// A = \alpha x y^H + \text{conj}(\alpha) y x^H + A,
/// \]
/// where alpha is a scalar, x and y are vectors,
/// and A is an n-by-n Hermitian 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 A is referenced,
/// the opposite triangle being assumed from symmetry.
/// - Uplo::Lower: only the lower triangular part of A is referenced.
/// - Uplo::Upper: only the upper triangular part of A is referenced.
///
/// @param[in] n
/// Number of rows and columns of the matrix A. n >= 0.
///
/// @param[in] alpha
/// Scalar alpha. If alpha is zero, A is not updated.
///
/// @param[in] x
/// The n-element vector x, in an array of length (n-1)*abs(incx) + 1.
///
/// @param[in] incx
/// Stride between elements of x. incx must not be zero.
/// If incx < 0, uses elements of x in reverse order: x(n-1), ..., x(0).
///
/// @param[in] y
/// The n-element vector y, in an array of length (n-1)*abs(incy) + 1.
///
/// @param[in] incy
/// Stride between elements of y. incy must not be zero.
/// If incy < 0, uses elements of y in reverse order: y(n-1), ..., y(0).
///
/// @param[in, out] A
/// The n-by-n matrix A, stored in an lda-by-n array [RowMajor: n-by-lda].
/// Imaginary parts of the diagonal elements need not be set,
/// are assumed to be zero on entry, and are set to zero on exit.
///
/// @param[in] lda
/// Leading dimension of A. lda >= max(1, n).
///
/// @ingroup her2
template <typename TA, typename TX, typename TY>
void her2(
blas::Layout layout,
blas::Uplo uplo,
int64_t n,
blas::scalar_type<TA, TX, TY> alpha,
TX const *x, int64_t incx,
TY const *y, int64_t incy,
TA *A, int64_t lda )
{
typedef blas::scalar_type<TA, TX, TY> scalar_t;
#define A(i_, j_) A[ (i_) + (j_)*lda ]
// constants
const scalar_t zero = 0;
// check arguments
blas_error_if( layout != Layout::ColMajor &&
layout != Layout::RowMajor );
blas_error_if( uplo != Uplo::Lower &&
uplo != Uplo::Upper );
blas_error_if( n < 0 );
blas_error_if( incx == 0 );
blas_error_if( incy == 0 );
blas_error_if( lda < n );
// quick return
if (n == 0 || alpha == zero)
return;
// for row major, swap lower <=> upper
if (layout == Layout::RowMajor) {
uplo = (uplo == Uplo::Lower ? Uplo::Upper : Uplo::Lower);
}
int64_t kx = (incx > 0 ? 0 : (-n + 1)*incx);
int64_t ky = (incy > 0 ? 0 : (-n + 1)*incy);
if (uplo == Uplo::Upper) {
if (incx == 1 && incy == 1) {
// unit stride
for (int64_t j = 0; j < n; ++j) {
// note: NOT skipping if x[j] or y[j] is zero, for consistent NAN handling
scalar_t tmp1 = alpha * conj( y[j] );
scalar_t tmp2 = conj( alpha * x[j] );
for (int64_t i = 0; i <= j-1; ++i) {
A(i, j) += x[i]*tmp1 + y[i]*tmp2;
}
A(j, j) = real( A(j, j) ) + real( x[j]*tmp1 + y[j]*tmp2 );
}
}
else {
// non-unit stride
int64_t jx = kx;
int64_t jy = ky;
for (int64_t j = 0; j < n; ++j) {
scalar_t tmp1 = alpha * conj( y[jy] );
scalar_t tmp2 = conj( alpha * x[jx] );
int64_t ix = kx;
int64_t iy = ky;
for (int64_t i = 0; i <= j-1; ++i) {
A(i, j) += x[ix]*tmp1 + y[iy]*tmp2;
ix += incx;
iy += incy;
}
A(j, j) = real( A(j, j) ) + real( x[jx]*tmp1 + y[jy]*tmp2 );
jx += incx;
jy += incy;
}
}
}
else {
// lower triangle
if (incx == 1 && incy == 1) {
// unit stride
for (int64_t j = 0; j < n; ++j) {
scalar_t tmp1 = alpha * conj( y[j] );
scalar_t tmp2 = conj( alpha * x[j] );
A(j, j) = real( A(j, j) ) + real( x[j]*tmp1 + y[j]*tmp2 );
for (int64_t i = j+1; i < n; ++i) {
A(i, j) += x[i]*tmp1 + y[i]*tmp2;
}
}
}
else {
// non-unit stride
int64_t jx = kx;
int64_t jy = ky;
for (int64_t j = 0; j < n; ++j) {
scalar_t tmp1 = alpha * conj( y[jy] );
scalar_t tmp2 = conj( alpha * x[jx] );
A(j, j) = real( A(j, j) ) + real( x[jx]*tmp1 + y[jy]*tmp2 );
int64_t ix = jx;
int64_t iy = jy;
for (int64_t i = j+1; i < n; ++i) {
ix += incx;
iy += incy;
A(i, j) += x[ix]*tmp1 + y[iy]*tmp2;
}
jx += incx;
jy += incy;
}
}
}
#undef A
}
} // namespace blas
#endif // #ifndef BLAS_HER2_HH
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