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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_GEMV_HH
#define BLAS_GEMV_HH
#include "blas/util.hh"
#include <limits>
namespace blas {
// =============================================================================
/// General matrix-vector multiply:
/// \[
/// y = \alpha op(A) x + \beta y,
/// \]
/// where $op(A)$ is one of
/// $op(A) = A$,
/// $op(A) = A^T$, or
/// $op(A) = A^H$,
/// alpha and beta are scalars, x and y are vectors,
/// and A is an m-by-n matrix.
///
/// Generic implementation for arbitrary data types.
///
/// @param[in] layout
/// Matrix storage, Layout::ColMajor or Layout::RowMajor.
///
/// @param[in] trans
/// The operation to be performed:
/// - Op::NoTrans: $y = \alpha A x + \beta y$,
/// - Op::Trans: $y = \alpha A^T x + \beta y$,
/// - Op::ConjTrans: $y = \alpha A^H x + \beta y$.
///
/// @param[in] m
/// Number of rows of the matrix A. m >= 0.
///
/// @param[in] n
/// Number of 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 m-by-n matrix A, stored in an lda-by-n array [RowMajor: m-by-lda].
///
/// @param[in] lda
/// Leading dimension of A. lda >= max(1, m) [RowMajor: lda >= max(1, n)].
///
/// @param[in] x
/// - If trans = NoTrans:
/// the n-element vector x, in an array of length (n-1)*abs(incx) + 1.
/// - Otherwise:
/// the m-element vector x, in an array of length (m-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
/// - If trans = NoTrans:
/// the m-element vector y, in an array of length (m-1)*abs(incy) + 1.
/// - Otherwise:
/// 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 gemv
template <typename TA, typename TX, typename TY>
void gemv(
blas::Layout layout,
blas::Op trans,
int64_t m, 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 )
{
using std::swap;
using scalar_t = blas::scalar_type<TA, TX, TY>;
#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( trans != Op::NoTrans &&
trans != Op::Trans &&
trans != Op::ConjTrans );
blas_error_if( m < 0 );
blas_error_if( n < 0 );
if (layout == Layout::ColMajor)
blas_error_if( lda < m );
else
blas_error_if( lda < n );
blas_error_if( incx == 0 );
blas_error_if( incy == 0 );
// quick return
if (m == 0 || n == 0 || (alpha == zero && beta == one))
return;
bool doconj = false;
if (layout == Layout::RowMajor) {
// A => A^T; A^T => A; A^H => A & conj
swap( m, n );
if (trans == Op::NoTrans) {
trans = Op::Trans;
}
else {
if (trans == Op::ConjTrans) {
doconj = true;
}
trans = Op::NoTrans;
}
}
int64_t lenx = (trans == Op::NoTrans ? n : m);
int64_t leny = (trans == Op::NoTrans ? m : n);
int64_t kx = (incx > 0 ? 0 : (-lenx + 1)*incx);
int64_t ky = (incy > 0 ? 0 : (-leny + 1)*incy);
// ----------
// form y = beta*y
if (beta != one) {
if (incy == 1) {
if (beta == zero) {
for (int64_t i = 0; i < leny; ++i) {
y[i] = zero;
}
}
else {
for (int64_t i = 0; i < leny; ++i) {
y[i] *= beta;
}
}
}
else {
int64_t iy = ky;
if (beta == zero) {
for (int64_t i = 0; i < leny; ++i) {
y[iy] = zero;
iy += incy;
}
}
else {
for (int64_t i = 0; i < leny; ++i) {
y[iy] *= beta;
iy += incy;
}
}
}
}
if (alpha == zero)
return;
// ----------
if (trans == Op::NoTrans && ! doconj) {
// form y += alpha * A * x
int64_t jx = kx;
if (incy == 1) {
for (int64_t j = 0; j < n; ++j) {
scalar_t tmp = alpha*x[jx];
jx += incx;
for (int64_t i = 0; i < m; ++i) {
y[i] += tmp * A(i, j);
}
}
}
else {
for (int64_t j = 0; j < n; ++j) {
scalar_t tmp = alpha*x[jx];
jx += incx;
int64_t iy = ky;
for (int64_t i = 0; i < m; ++i) {
y[iy] += tmp * A(i, j);
iy += incy;
}
}
}
}
else if (trans == Op::NoTrans && doconj) {
// form y += alpha * conj( A ) * x
// this occurs for row-major A^H * x
int64_t jx = kx;
if (incy == 1) {
for (int64_t j = 0; j < n; ++j) {
scalar_t tmp = alpha*x[jx];
jx += incx;
for (int64_t i = 0; i < m; ++i) {
y[i] += tmp * conj(A(i, j));
}
}
}
else {
for (int64_t j = 0; j < n; ++j) {
scalar_t tmp = alpha*x[jx];
jx += incx;
int64_t iy = ky;
for (int64_t i = 0; i < m; ++i) {
y[iy] += tmp * conj(A(i, j));
iy += incy;
}
}
}
}
else if (trans == Op::Trans) {
// form y += alpha * A^T * x
int64_t jy = ky;
if (incx == 1) {
for (int64_t j = 0; j < n; ++j) {
scalar_t tmp = zero;
for (int64_t i = 0; i < m; ++i) {
tmp += A(i, j) * x[i];
}
y[jy] += alpha*tmp;
jy += incy;
}
}
else {
for (int64_t j = 0; j < n; ++j) {
scalar_t tmp = zero;
int64_t ix = kx;
for (int64_t i = 0; i < m; ++i) {
tmp += A(i, j) * x[ix];
ix += incx;
}
y[jy] += alpha*tmp;
jy += incy;
}
}
}
else {
// form y += alpha * A^H * x
int64_t jy = ky;
if (incx == 1) {
for (int64_t j = 0; j < n; ++j) {
scalar_t tmp = zero;
for (int64_t i = 0; i < m; ++i) {
tmp += conj(A(i, j)) * x[i];
}
y[jy] += alpha*tmp;
jy += incy;
}
}
else {
for (int64_t j = 0; j < n; ++j) {
scalar_t tmp = zero;
int64_t ix = kx;
for (int64_t i = 0; i < m; ++i) {
tmp += conj(A(i, j)) * x[ix];
ix += incx;
}
y[jy] += alpha*tmp;
jy += incy;
}
}
}
#undef A
}
} // namespace blas
#endif // #ifndef BLAS_GEMV_HH
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