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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_SYMV_HH
#define BLAS_SYMV_HH
#include "blas/util.hh"
#include <limits>
namespace blas {
// =============================================================================
/// Symmetric matrix-vector multiply:
/// \[
/// y = \alpha A x + \beta y,
/// \]
/// where alpha and beta are scalars, x and y are vectors,
/// and A is an n-by-n symmetric 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 and x are not accessed.
///
/// @param[in] A
/// The n-by-n matrix A, stored in an lda-by-n array [RowMajor: n-by-lda].
///
/// @param[in] lda
/// Leading dimension of A. lda >= max(1, n).
///
/// @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] beta
/// Scalar beta. If beta is zero, y need not be set on input.
///
/// @param[in, out] 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).
///
/// @ingroup symv
template <typename TA, typename TX, typename TY>
void symv(
blas::Layout layout,
blas::Uplo uplo,
int64_t n,
blas::scalar_type<TA, TX, TY> alpha,
TA const *A, int64_t lda,
TX const *x, int64_t incx,
blas::scalar_type<TA, TX, TY> beta,
TY *y, int64_t incy )
{
printf( "%s: %s\n", __func__, __PRETTY_FUNCTION__ );
typedef blas::scalar_type<TA, TX, TY> scalar_t;
#define A(i_, j_) A[ (i_) + (j_)*lda ]
// 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 );
blas_error_if( n < 0 );
blas_error_if( lda < n );
blas_error_if( incx == 0 );
blas_error_if( incy == 0 );
// quick return
if (n == 0 || (alpha == zero && beta == one))
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);
// form y = beta*y
if (beta != one) {
if (incy == 1) {
if (beta == zero) {
for (int64_t i = 0; i < n; ++i) {
y[i] = zero;
}
}
else {
for (int64_t i = 0; i < n; ++i) {
y[i] *= beta;
}
}
}
else {
int64_t iy = ky;
if (beta == zero) {
for (int64_t i = 0; i < n; ++i) {
y[iy] = zero;
iy += incy;
}
}
else {
for (int64_t i = 0; i < n; ++i) {
y[iy] *= beta;
iy += incy;
}
}
}
}
if (alpha == zero)
return;
if (uplo == Uplo::Upper) {
// A is stored in upper triangle
// form y += alpha * A * x
if (incx == 1 && incy == 1) {
// unit stride
for (int64_t j = 0; j < n; ++j) {
scalar_t tmp1 = alpha*x[j];
scalar_t tmp2 = zero;
for (int64_t i = 0; i < j; ++i) {
y[i] += tmp1 * A(i, j);
tmp2 += A(i, j) * x[i];
}
y[j] += tmp1 * A(j, j) + alpha * 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*x[jx];
scalar_t tmp2 = zero;
int64_t ix = kx;
int64_t iy = ky;
for (int64_t i = 0; i < j; ++i) {
y[iy] += tmp1 * A(i, j);
tmp2 += A(i, j) * x[ix];
ix += incx;
iy += incy;
}
y[jy] += tmp1 * A(j, j) + alpha * tmp2;
jx += incx;
jy += incy;
}
}
}
else {
// A is stored in lower triangle
// form y += alpha * A * x
if (incx == 1 && incy == 1) {
// unit stride
for (int64_t j = 0; j < n; ++j) {
scalar_t tmp1 = alpha*x[j];
scalar_t tmp2 = zero;
for (int64_t i = j+1; i < n; ++i) {
y[i] += tmp1 * A(i, j);
tmp2 += A(i, j) * x[i];
}
y[j] += tmp1 * A(j, j) + alpha * 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*x[jx];
scalar_t tmp2 = zero;
int64_t ix = jx;
int64_t iy = jy;
for (int64_t i = j+1; i < n; ++i) {
ix += incx;
iy += incy;
y[iy] += tmp1 * A(i, j);
tmp2 += A(i, j) * x[ix];
}
y[jy] += tmp1 * A(j, j) + alpha * tmp2;
jx += incx;
jy += incy;
}
}
}
#undef A
}
} // namespace blas
#endif // #ifndef BLAS_SYMV_HH
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