symm.hpp

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//
// Copyright (c) 2017-2021, University of Tennessee. All rights reserved.
// Copyright (c) 2021-2023, 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_SYMM_HH
#define TLAPACK_BLAS_SYMM_HH
 
#include "tlapack/base/utils.hpp"
 
namespace tlapack {
 
template <TLAPACK_MATRIX matrixA_t,
          TLAPACK_MATRIX matrixB_t,
          TLAPACK_MATRIX matrixC_t,
          TLAPACK_SCALAR alpha_t,
          TLAPACK_SCALAR beta_t,
          class T = type_t<matrixC_t>,
          disable_if_allow_optblas_t<pair<matrixA_t, T>,
                                     pair<matrixB_t, T>,
                                     pair<matrixC_t, T>,
                                     pair<alpha_t, T>,
                                     pair<beta_t, T> > = 0>
void symm(Side side,
          Uplo uplo,
          const alpha_t& alpha,
          const matrixA_t& A,
          const matrixB_t& B,
          const beta_t& beta,
          matrixC_t& C)
{
    // data traits
    using TA = type_t<matrixA_t>;
    using TB = type_t<matrixB_t>;
    using idx_t = size_type<matrixC_t>;
 
    // constants
    const idx_t m = nrows(B);
    const idx_t n = ncols(B);
 
    // check arguments
    tlapack_check_false(side != Side::Left && side != Side::Right);
    tlapack_check_false(uplo != Uplo::Lower && uplo != Uplo::Upper &&
                        uplo != Uplo::General);
    tlapack_check_false(nrows(A) != ncols(A));
    tlapack_check_false(nrows(A) != ((side == Side::Left) ? m : n));
    tlapack_check_false(nrows(C) != m);
    tlapack_check_false(ncols(C) != n);
 
    if (side == Side::Left) {
        if (uplo != Uplo::Lower) {
            // uplo == Uplo::Upper or uplo == Uplo::General
            for (idx_t j = 0; j < n; ++j) {
                for (idx_t i = 0; i < m; ++i) {
                    const scalar_type<alpha_t, TB> alphaTimesBij =
                        alpha * B(i, j);
                    scalar_type<TA, TB> sum(0);
 
                    for (idx_t k = 0; k < i; ++k) {
                        C(k, j) += A(k, i) * alphaTimesBij;
                        sum += A(k, i) * B(k, j);
                    }
                    C(i, j) =
                        beta * C(i, j) + A(i, i) * alphaTimesBij + alpha * sum;
                }
            }
        }
        else {
            // uplo == Uplo::Lower
            for (idx_t j = 0; j < n; ++j) {
                for (idx_t i = m - 1; i != idx_t(-1); --i) {
                    const scalar_type<alpha_t, TB> alphaTimesBij =
                        alpha * B(i, j);
                    scalar_type<TA, TB> sum(0);
 
                    for (idx_t k = i + 1; k < m; ++k) {
                        C(k, j) += A(k, i) * alphaTimesBij;
                        sum += A(k, i) * B(k, j);
                    }
                    C(i, j) =
                        beta * C(i, j) + A(i, i) * alphaTimesBij + alpha * sum;
                }
            }
        }
    }
    else {  // side == Side::Right
 
        using scalar_t = scalar_type<alpha_t, TA>;
 
        if (uplo != Uplo::Lower) {
            // uplo == Uplo::Upper or uplo == Uplo::General
            for (idx_t j = 0; j < n; ++j) {
                {
                    const scalar_t alphaTimesAjj = alpha * A(j, j);
                    for (idx_t i = 0; i < m; ++i)
                        C(i, j) = beta * C(i, j) + B(i, j) * alphaTimesAjj;
                }
 
                for (idx_t k = 0; k < j; ++k) {
                    const scalar_t alphaTimesAkj = alpha * A(k, j);
                    for (idx_t i = 0; i < m; ++i)
                        C(i, j) += B(i, k) * alphaTimesAkj;
                }
 
                for (idx_t k = j + 1; k < n; ++k) {
                    const scalar_t alphaTimesAjk = alpha * A(j, k);
                    for (idx_t i = 0; i < m; ++i)
                        C(i, j) += B(i, k) * alphaTimesAjk;
                }
            }
        }
        else {
            // uplo == Uplo::Lower
            for (idx_t j = 0; j < n; ++j) {
                {
                    const scalar_t alphaTimesAjj = alpha * A(j, j);
                    for (idx_t i = 0; i < m; ++i)
                        C(i, j) = beta * C(i, j) + B(i, j) * alphaTimesAjj;
                }
 
                for (idx_t k = 0; k < j; ++k) {
                    const scalar_t alphaTimesAjk = alpha * A(j, k);
                    for (idx_t i = 0; i < m; ++i)
                        C(i, j) += B(i, k) * alphaTimesAjk;
                }
 
                for (idx_t k = j + 1; k < n; ++k) {
                    const scalar_t alphaTimesAkj = alpha * A(k, j);
                    for (idx_t i = 0; i < m; ++i)
                        C(i, j) += B(i, k) * alphaTimesAkj;
                }
            }
        }
    }
}
 
#ifdef TLAPACK_USE_LAPACKPP
 
template <TLAPACK_LEGACY_MATRIX matrixA_t,
          TLAPACK_LEGACY_MATRIX matrixB_t,
          TLAPACK_LEGACY_MATRIX matrixC_t,
          TLAPACK_SCALAR alpha_t,
          TLAPACK_SCALAR beta_t,
          class T = type_t<matrixC_t>,
          enable_if_allow_optblas_t<pair<matrixA_t, T>,
                                    pair<matrixB_t, T>,
                                    pair<matrixC_t, T>,
                                    pair<alpha_t, T>,
                                    pair<beta_t, T> > = 0>
void symm(Side side,
          Uplo uplo,
          const alpha_t alpha,
          const matrixA_t& A,
          const matrixB_t& B,
          const beta_t beta,
          matrixC_t& C)
{
    // Legacy objects
    auto A_ = legacy_matrix(A);
    auto B_ = legacy_matrix(B);
    auto C_ = legacy_matrix(C);
 
    // Constants to forward
    constexpr Layout L = layout<matrixC_t>;
    const auto& m = C_.m;
    const auto& n = C_.n;
 
    // Warnings for NaNs and Infs
    if (alpha == alpha_t(0))
        tlapack_warning(
            -3, "Infs and NaNs in A or B will not propagate to C on output");
    if (beta == beta_t(0) && !is_same_v<beta_t, StrongZero>)
        tlapack_warning(
            -6,
            "Infs and NaNs in C on input will not propagate to C on output");
 
    return ::blas::symm((::blas::Layout)L, (::blas::Side)side,
                        (::blas::Uplo)uplo, m, n, alpha, A_.ptr, A_.ldim,
                        B_.ptr, B_.ldim, (T)beta, C_.ptr, C_.ldim);
}
 
#endif
 
template <TLAPACK_MATRIX matrixA_t,
          TLAPACK_MATRIX matrixB_t,
          TLAPACK_MATRIX matrixC_t,
          TLAPACK_SCALAR alpha_t>
void symm(Side side,
          Uplo uplo,
          const alpha_t& alpha,
          const matrixA_t& A,
          const matrixB_t& B,
          matrixC_t& C)
{
    return symm(side, uplo, alpha, A, B, StrongZero(), C);
}
 
}  // namespace tlapack
 
#endif  //  #ifndef TLAPACK_BLAS_SYMM_HH