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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_TRMV_HH
#define BLAS_TRMV_HH
#include "blas/util.hh"
#include <limits>
namespace blas {
// =============================================================================
/// Triangular matrix-vector multiply:
/// \[
/// x = op(A) x,
/// \]
/// where $op(A)$ is one of
/// $op(A) = A$,
/// $op(A) = A^T$, or
/// $op(A) = A^H$,
/// x is a vector,
/// and A is an n-by-n, unit or non-unit, upper or lower triangular 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 to be zero.
/// - Uplo::Lower: A is lower triangular.
/// - Uplo::Upper: A is upper triangular.
///
/// @param[in] trans
/// The operation to be performed:
/// - Op::NoTrans: $x = A x$,
/// - Op::Trans: $x = A^T x$,
/// - Op::ConjTrans: $x = A^H x$.
///
/// @param[in] diag
/// Whether A has a unit or non-unit diagonal:
/// - Diag::Unit: A is assumed to be unit triangular.
/// The diagonal elements of A are not referenced.
/// - Diag::NonUnit: A is not assumed to be unit triangular.
///
/// @param[in] n
/// Number of rows and columns of the matrix A. n >= 0.
///
/// @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, out] 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).
///
/// @ingroup trmv
template <typename TA, typename TX>
void trmv(
blas::Layout layout,
blas::Uplo uplo,
blas::Op trans,
blas::Diag diag,
int64_t n,
TA const *A, int64_t lda,
TX *x, int64_t incx )
{
#define A(i_, j_) A[ (i_) + (j_)*lda ]
// check arguments
blas_error_if( layout != Layout::ColMajor &&
layout != Layout::RowMajor );
blas_error_if( uplo != Uplo::Lower &&
uplo != Uplo::Upper );
blas_error_if( trans != Op::NoTrans &&
trans != Op::Trans &&
trans != Op::ConjTrans );
blas_error_if( diag != Diag::NonUnit &&
diag != Diag::Unit );
blas_error_if( n < 0 );
blas_error_if( lda < n );
blas_error_if( incx == 0 );
// quick return
if (n == 0)
return;
// for row major, swap lower <=> upper and
// A => A^T; A^T => A; A^H => A & conj
bool doconj = false;
if (layout == Layout::RowMajor) {
uplo = (uplo == Uplo::Lower ? Uplo::Upper : Uplo::Lower);
if (trans == Op::NoTrans) {
trans = Op::Trans;
}
else {
if (trans == Op::ConjTrans) {
doconj = true;
}
trans = Op::NoTrans;
}
}
bool nonunit = (diag == Diag::NonUnit);
int64_t kx = (incx > 0 ? 0 : (-n + 1)*incx);
if (trans == Op::NoTrans && ! doconj) {
// Form x := A*x
if (uplo == Uplo::Upper) {
// upper
if (incx == 1) {
// unit stride
for (int64_t j = 0; j < n; ++j) {
// note: NOT skipping if x[j] is zero, for consistent NAN handling
TX tmp = x[j];
for (int64_t i = 0; i <= j-1; ++i) {
x[i] += tmp * A(i, j);
}
if (nonunit) {
x[j] *= A(j, j);
}
}
}
else {
// non-unit stride
int64_t jx = kx;
for (int64_t j = 0; j < n; ++j) {
// note: NOT skipping if x[j] is zero ...
TX tmp = x[jx];
int64_t ix = kx;
for (int64_t i = 0; i <= j-1; ++i) {
x[ix] += tmp * A(i, j);
ix += incx;
}
if (nonunit) {
x[jx] *= A(j, j);
}
jx += incx;
}
}
}
else {
// lower
if (incx == 1) {
// unit stride
for (int64_t j = n-1; j >= 0; --j) {
// note: NOT skipping if x[j] is zero ...
TX tmp = x[j];
for (int64_t i = n-1; i >= j+1; --i) {
x[i] += tmp * A(i, j);
}
if (nonunit) {
x[j] *= A(j, j);
}
}
}
else {
// non-unit stride
kx += (n - 1)*incx;
int64_t jx = kx;
for (int64_t j = n-1; j >= 0; --j) {
// note: NOT skipping if x[j] is zero ...
TX tmp = x[jx];
int64_t ix = kx;
for (int64_t i = n-1; i >= j+1; --i) {
x[ix] += tmp * A(i, j);
ix -= incx;
}
if (nonunit) {
x[jx] *= A(j, j);
}
jx -= incx;
}
}
}
}
else if (trans == Op::NoTrans && doconj) {
// Form x := A*x
if (uplo == Uplo::Upper) {
// upper
if (incx == 1) {
// unit stride
for (int64_t j = 0; j < n; ++j) {
// note: NOT skipping if x[j] is zero, for consistent NAN handling
TX tmp = x[j];
for (int64_t i = 0; i <= j-1; ++i) {
x[i] += tmp * conj( A(i, j) );
}
if (nonunit) {
x[j] *= conj( A(j, j) );
}
}
}
else {
// non-unit stride
int64_t jx = kx;
for (int64_t j = 0; j < n; ++j) {
// note: NOT skipping if x[j] is zero ...
TX tmp = x[jx];
int64_t ix = kx;
for (int64_t i = 0; i <= j-1; ++i) {
x[ix] += tmp * conj( A(i, j) );
ix += incx;
}
if (nonunit) {
x[jx] *= conj( A(j, j) );
}
jx += incx;
}
}
}
else {
// lower
if (incx == 1) {
// unit stride
for (int64_t j = n-1; j >= 0; --j) {
// note: NOT skipping if x[j] is zero ...
TX tmp = x[j];
for (int64_t i = n-1; i >= j+1; --i) {
x[i] += tmp * conj( A(i, j) );
}
if (nonunit) {
x[j] *= conj( A(j, j) );
}
}
}
else {
// non-unit stride
kx += (n - 1)*incx;
int64_t jx = kx;
for (int64_t j = n-1; j >= 0; --j) {
// note: NOT skipping if x[j] is zero ...
TX tmp = x[jx];
int64_t ix = kx;
for (int64_t i = n-1; i >= j+1; --i) {
x[ix] += tmp * conj( A(i, j) );
ix -= incx;
}
if (nonunit) {
x[jx] *= conj( A(j, j) );
}
jx -= incx;
}
}
}
}
else if (trans == Op::Trans) {
// Form x := A^T * x
if (uplo == Uplo::Upper) {
// upper
if (incx == 1) {
// unit stride
for (int64_t j = n-1; j >= 0; --j) {
TX tmp = x[j];
if (nonunit) {
tmp *= A(j, j);
}
for (int64_t i = j - 1; i >= 0; --i) {
tmp += A(i, j) * x[i];
}
x[j] = tmp;
}
}
else {
// non-unit stride
int64_t jx = kx + (n - 1)*incx;
for (int64_t j = n-1; j >= 0; --j) {
TX tmp = x[jx];
int64_t ix = jx;
if (nonunit) {
tmp *= A(j, j);
}
for (int64_t i = j - 1; i >= 0; --i) {
ix -= incx;
tmp += A(i, j) * x[ix];
}
x[jx] = tmp;
jx -= incx;
}
}
}
else {
// lower
if (incx == 1) {
// unit stride
for (int64_t j = 0; j < n; ++j) {
TX tmp = x[j];
if (nonunit) {
tmp *= A(j, j);
}
for (int64_t i = j + 1; i < n; ++i) {
tmp += A(i, j) * x[i];
}
x[j] = tmp;
}
}
else {
// non-unit stride
int64_t jx = kx;
for (int64_t j = 0; j < n; ++j) {
TX tmp = x[jx];
int64_t ix = jx;
if (nonunit) {
tmp *= A(j, j);
}
for (int64_t i = j + 1; i < n; ++i) {
ix += incx;
tmp += A(i, j) * x[ix];
}
x[jx] = tmp;
jx += incx;
}
}
}
}
else {
// Form x := A^H * x
// same code as above A^T * x case, except add conj()
if (uplo == Uplo::Upper) {
// upper
if (incx == 1) {
// unit stride
for (int64_t j = n-1; j >= 0; --j) {
TX tmp = x[j];
if (nonunit) {
tmp *= conj( A(j, j) );
}
for (int64_t i = j - 1; i >= 0; --i) {
tmp += conj( A(i, j) ) * x[i];
}
x[j] = tmp;
}
}
else {
// non-unit stride
int64_t jx = kx + (n - 1)*incx;
for (int64_t j = n-1; j >= 0; --j) {
TX tmp = x[jx];
int64_t ix = jx;
if (nonunit) {
tmp *= conj( A(j, j) );
}
for (int64_t i = j - 1; i >= 0; --i) {
ix -= incx;
tmp += conj( A(i, j) ) * x[ix];
}
x[jx] = tmp;
jx -= incx;
}
}
}
else {
// lower
if (incx == 1) {
// unit stride
for (int64_t j = 0; j < n; ++j) {
TX tmp = x[j];
if (nonunit) {
tmp *= conj( A(j, j) );
}
for (int64_t i = j + 1; i < n; ++i) {
tmp += conj( A(i, j) ) * x[i];
}
x[j] = tmp;
}
}
else {
// non-unit stride
int64_t jx = kx;
for (int64_t j = 0; j < n; ++j) {
TX tmp = x[jx];
int64_t ix = jx;
if (nonunit) {
tmp *= conj( A(j, j) );
}
for (int64_t i = j + 1; i < n; ++i) {
ix += incx;
tmp += conj( A(i, j) ) * x[ix];
}
x[jx] = tmp;
jx += incx;
}
}
}
}
#undef A
}
} // namespace blas
#endif // #ifndef BLAS_TRMV_HH
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