symv.hpp

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//
// Copyright (c) 2017-2021, University of Tennessee. All rights reserved.
// Copyright (c) 2025, University of Colorado Denver. All rights reserved.
//
// This file is part of <T>LAPACK.
// <T>LAPACK 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 TLAPACK_BLAS_SYMV_HH
#define TLAPACK_BLAS_SYMV_HH
 
#include "tlapack/base/utils.hpp"
 
namespace tlapack {
 
template <TLAPACK_MATRIX matrixA_t,
          TLAPACK_VECTOR vectorX_t,
          TLAPACK_VECTOR vectorY_t,
          TLAPACK_SCALAR alpha_t,
          TLAPACK_SCALAR beta_t,
          class T = type_t<vectorY_t>,
          disable_if_allow_optblas_t<pair<matrixA_t, T>,
                                     pair<vectorX_t, T>,
                                     pair<vectorY_t, T>,
                                     pair<beta_t, T> > = 0>
void symv(Uplo uplo,
          const alpha_t& alpha,
          const matrixA_t& A,
          const vectorX_t& x,
          const beta_t& beta,
          vectorY_t& y)
{
    // data traits
    using TA = type_t<matrixA_t>;
    using TX = type_t<vectorX_t>;
    using idx_t = size_type<matrixA_t>;
 
    // constants
    const idx_t n = nrows(A);
 
    // check arguments
    tlapack_check_false(uplo != Uplo::Lower && uplo != Uplo::Upper);
    tlapack_check_false(ncols(A) != n);
    tlapack_check_false(size(x) != n);
    tlapack_check_false(size(y) != n);
 
    // form y = beta*y
    for (idx_t i = 0; i < n; ++i)
        y[i] *= beta;
 
    if (uplo == Uplo::Upper) {
        // A is stored in upper triangle
        // form y += alpha * A * x
        for (idx_t j = 0; j < n; ++j) {
            const scalar_type<alpha_t, TX> tmp1 = alpha * x[j];
            scalar_type<TA, TX> sum(0);
            for (idx_t i = 0; i < j; ++i) {
                y[i] += tmp1 * A(i, j);
                sum += A(i, j) * x[i];
            }
            y[j] += tmp1 * A(j, j) + alpha * sum;
        }
    }
    else {
        // A is stored in lower triangle
        // form y += alpha * A * x
        for (idx_t j = 0; j < n; ++j) {
            const scalar_type<alpha_t, TX> tmp1 = alpha * x[j];
            scalar_type<TA, TX> sum(0);
            for (idx_t i = j + 1; i < n; ++i) {
                y[i] += tmp1 * A(i, j);
                sum += A(i, j) * x[i];
            }
            y[j] += tmp1 * A(j, j) + alpha * sum;
        }
    }
}
 
#ifdef TLAPACK_USE_LAPACKPP
 
template <TLAPACK_LEGACY_MATRIX matrixA_t,
          TLAPACK_LEGACY_VECTOR vectorX_t,
          TLAPACK_LEGACY_VECTOR vectorY_t,
          TLAPACK_SCALAR alpha_t,
          TLAPACK_SCALAR beta_t,
          class T = type_t<vectorY_t>,
          enable_if_allow_optblas_t<pair<matrixA_t, T>,
                                    pair<vectorX_t, T>,
                                    pair<vectorY_t, T>,
                                    pair<beta_t, T> > = 0>
void symv(Uplo uplo,
          const alpha_t alpha,
          const matrixA_t& A,
          const vectorX_t& x,
          const beta_t beta,
          vectorY_t& y)
{
    // Legacy objects
    auto A_ = legacy_matrix(A);
    auto x_ = legacy_vector(x);
    auto y_ = legacy_vector(y);
 
    // Constants to forward
    constexpr Layout L = layout<matrixA_t>;
    const auto& n = A_.n;
 
    // Warnings for NaNs and Infs
    if (alpha == alpha_t(0))
        tlapack_warning(
            -2, "Infs and NaNs in A or x will not propagate to y on output");
    if (beta == beta_t(0) && !is_same_v<beta_t, StrongZero>)
        tlapack_warning(
            -5,
            "Infs and NaNs in y on input will not propagate to y on output");
 
    return ::blas::symv((::blas::Layout)L, (::blas::Uplo)uplo, n, alpha, A_.ptr,
                        A_.ldim, x_.ptr, x_.inc, (T)beta, y_.ptr, y_.inc);
}
 
#endif
 
template <TLAPACK_MATRIX matrixA_t,
          TLAPACK_VECTOR vectorX_t,
          TLAPACK_VECTOR vectorY_t,
          TLAPACK_SCALAR alpha_t>
void symv(Uplo uplo,
          const alpha_t& alpha,
          const matrixA_t& A,
          const vectorX_t& x,
          vectorY_t& y)
{
    return symv(uplo, alpha, A, x, StrongZero(), y);
}
 
}  // namespace tlapack
 
#endif  //  #ifndef TLAPACK_BLAS_SYMV_HH