her2k.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_HER2K_HH
#define TLAPACK_BLAS_HER2K_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_REAL beta_t,
          enable_if_t<(
                          /* Requires: */
                          is_real<beta_t>),
                      int> = 0,
          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, real_type<T> > > = 0>
void her2k(Uplo uplo,
           Op trans,
           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 TC = type_t<matrixC_t>;
    using idx_t = size_type<matrixA_t>;
 
    // constants
    const idx_t n = (trans == Op::NoTrans) ? nrows(A) : ncols(A);
    const idx_t k = (trans == Op::NoTrans) ? ncols(A) : nrows(A);
 
    // check arguments
    tlapack_check_false(uplo != Uplo::Lower && uplo != Uplo::Upper &&
                        uplo != Uplo::General);
    tlapack_check_false(trans != Op::NoTrans && trans != Op::ConjTrans);
    tlapack_check_false(nrows(B) != nrows(A) || ncols(B) != ncols(A));
    tlapack_check_false(nrows(C) != ncols(C));
    tlapack_check_false(nrows(C) != n);
 
    if (trans == Op::NoTrans) {
        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 < j; ++i)
                    C(i, j) *= beta;
                C(j, j) = TC(beta * real(C(j, j)));
 
                for (idx_t l = 0; l < k; ++l) {
                    const scalar_type<alpha_t, TB> alphaConjBjl =
                        alpha * conj(B(j, l));
                    const scalar_type<alpha_t, TA> conjAlphaAjl =
                        conj(alpha * A(j, l));
 
                    for (idx_t i = 0; i < j; ++i)
                        C(i, j) +=
                            A(i, l) * alphaConjBjl + B(i, l) * conjAlphaAjl;
                    C(j, j) += 2 * (real(A(j, l)) * real(alphaConjBjl) -
                                    imag(A(j, l)) * imag(alphaConjBjl));
                }
            }
        }
        else {  // uplo == Uplo::Lower
            for (idx_t j = 0; j < n; ++j) {
                C(j, j) = TC(beta * real(C(j, j)));
                for (idx_t i = j + 1; i < n; ++i)
                    C(i, j) *= beta;
 
                for (idx_t l = 0; l < k; ++l) {
                    const scalar_type<alpha_t, TB> alphaConjBjl =
                        alpha * conj(B(j, l));
                    const scalar_type<alpha_t, TA> conjAlphaAjl =
                        conj(alpha * A(j, l));
 
                    C(j, j) += 2 * (real(A(j, l)) * real(alphaConjBjl) -
                                    imag(A(j, l)) * imag(alphaConjBjl));
                    for (idx_t i = j + 1; i < n; ++i)
                        C(i, j) +=
                            A(i, l) * alphaConjBjl + B(i, l) * conjAlphaAjl;
                }
            }
        }
    }
    else {  // trans == Op::ConjTrans
        using scalar_t = scalar_type<TA, TB>;
 
        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 <= j; ++i) {
                    scalar_t sum1(0);
                    scalar_t sum2(0);
                    for (idx_t l = 0; l < k; ++l) {
                        sum1 += conj(A(l, i)) * B(l, j);
                        sum2 += conj(B(l, i)) * A(l, j);
                    }
 
                    C(i, j) = (i < j) ? alpha * sum1 + conj(alpha) * sum2 +
                                            beta * C(i, j)
                                      : real(alpha) * real(sum1) -
                                            imag(alpha) * imag(sum1) +
                                            real(alpha) * real(sum2) +
                                            imag(alpha) * imag(sum2) +
                                            beta * real(C(i, j));
                }
            }
        }
        else {  // uplo == Uplo::Lower
            for (idx_t j = 0; j < n; ++j) {
                for (idx_t i = j; i < n; ++i) {
                    scalar_t sum1(0);
                    scalar_t sum2(0);
                    for (idx_t l = 0; l < k; ++l) {
                        sum1 += conj(A(l, i)) * B(l, j);
                        sum2 += conj(B(l, i)) * A(l, j);
                    }
 
                    C(i, j) = (i > j) ? alpha * sum1 + conj(alpha) * sum2 +
                                            beta * C(i, j)
                                      : real(alpha) * real(sum1) -
                                            imag(alpha) * imag(sum1) +
                                            real(alpha) * real(sum2) +
                                            imag(alpha) * imag(sum2) +
                                            beta * real(C(i, j));
                }
            }
        }
    }
 
    if (uplo == Uplo::General) {
        for (idx_t j = 0; j < n; ++j) {
            for (idx_t i = j + 1; i < n; ++i)
                C(i, j) = conj(C(j, i));
        }
    }
}
 
#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_REAL beta_t,
          enable_if_t<(
                          /* Requires: */
                          is_real<beta_t>),
                      int> = 0,
          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, real_type<T> > > = 0>
void her2k(Uplo uplo,
           Op trans,
           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& n = C_.n;
    const auto& k = (trans == Op::NoTrans) ? A_.n : A_.m;
 
    // 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::her2k((::blas::Layout)L, (::blas::Uplo)uplo,
                         (::blas::Op)trans, n, k, alpha, A_.ptr, A_.ldim,
                         B_.ptr, B_.ldim, (real_type<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 her2k(Uplo uplo,
           Op trans,
           const alpha_t& alpha,
           const matrixA_t& A,
           const matrixB_t& B,
           matrixC_t& C)
{
    return her2k(uplo, trans, alpha, A, B, StrongZero(), C);
}
 
}  // namespace tlapack
 
#endif  //  #ifndef TLAPACK_BLAS_HER2K_HH