trmm.hh

// 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_TRMM_HH
#define BLAS_TRMM_HH
 
#include "blas/util.hh"
 
#include <limits>
 
namespace blas {
 
// =============================================================================
 
template <typename TA, typename TB>
void trmm(
    blas::Layout layout,
    blas::Side side,
    blas::Uplo uplo,
    blas::Op trans,
    blas::Diag diag,
    int64_t m,
    int64_t n,
    blas::scalar_type<TA, TB> alpha,
    TA const *A, int64_t lda,
    TB       *B, int64_t ldb )
{
    using std::swap;
    using scalar_t = blas::scalar_type<TA, TB>;
 
    #define A(i_, j_) A[ (i_) + (j_)*lda ]
    #define B(i_, j_) B[ (i_) + (j_)*ldb ]
 
    // constants
    const scalar_t zero = 0;
 
    // check arguments
    blas_error_if( layout != Layout::ColMajor &&
                   layout != Layout::RowMajor );
    blas_error_if( side != Side::Left &&
                   side != Side::Right );
    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( m < 0 );
    blas_error_if( n < 0 );
 
    // adapt if row major
    if (layout == Layout::RowMajor) {
        side = (side == Side::Left)
               ? Side::Right
               : Side::Left;
        if (uplo == Uplo::Lower)
            uplo = Uplo::Upper;
        else if (uplo == Uplo::Upper)
            uplo = Uplo::Lower;
        swap( m, n );
    }
 
    // check remaining arguments
    blas_error_if( lda < ((side == Side::Left) ? m : n) );
    blas_error_if( ldb < m );
 
    // quick return
    if (m == 0 || n == 0)
        return;
 
    // alpha == zero
    if (alpha == zero) {
        for (int64_t j = 0; j < n; ++j) {
            for (int64_t i = 0; i < m; ++i)
                B(i, j) = zero;
        }
        return;
    }
 
    // alpha != zero
    if (side == Side::Left) {
        if (trans == Op::NoTrans) {
            if (uplo == Uplo::Upper) {
                for (int64_t j = 0; j < n; ++j) {
                    for (int64_t k = 0; k < m; ++k) {
                        scalar_t alpha_Bkj = alpha*B(k, j);
                        for (int64_t i = 0; i < k; ++i)
                            B(i, j) += A(i, k)*alpha_Bkj;
                        B(k, j) = (diag == Diag::NonUnit)
                                  ? A(k, k)*alpha_Bkj
                                  : alpha_Bkj;
                    }
                }
            }
            else { // uplo == Uplo::Lower
                for (int64_t j = 0; j < n; ++j) {
                    for (int64_t k = m-1; k >= 0; --k) {
                        scalar_t alpha_Bkj = alpha*B(k, j);
                        B(k, j) = (diag == Diag::NonUnit)
                                  ? A(k, k)*alpha_Bkj
                                  : alpha_Bkj;
                        for (int64_t i = k+1; i < m; ++i)
                            B(i, j) += A(i, k)*alpha_Bkj;
                    }
                }
            }
        }
        else if (trans == Op::Trans) {
            if (uplo == Uplo::Upper) {
                for (int64_t j = 0; j < n; ++j) {
                    for (int64_t i = m-1; i >= 0; --i) {
                        scalar_t sum = (diag == Diag::NonUnit)
                                       ? A(i, i)*B(i, j)
                                       : B(i, j);
                        for (int64_t k = 0; k < i; ++k)
                            sum += A(k, i)*B(k, j);
                        B(i, j) = alpha * sum;
                    }
                }
            }
            else { // uplo == Uplo::Lower
                for (int64_t j = 0; j < n; ++j) {
                    for (int64_t i = 0; i < m; ++i) {
                        scalar_t sum = (diag == Diag::NonUnit)
                                       ? A(i, i)*B(i, j)
                                       : B(i, j);
                        for (int64_t k = i+1; k < m; ++k)
                            sum += A(k, i)*B(k, j);
                        B(i, j) = alpha * sum;
                    }
                }
            }
        }
        else { // trans == Op::ConjTrans
            if (uplo == Uplo::Upper) {
                for (int64_t j = 0; j < n; ++j) {
                    for (int64_t i = m-1; i >= 0; --i) {
                        scalar_t sum = (diag == Diag::NonUnit)
                                       ? conj(A(i, i))*B(i, j)
                                       : B(i, j);
                        for (int64_t k = 0; k < i; ++k)
                            sum += conj(A(k, i))*B(k, j);
                        B(i, j) = alpha * sum;
                    }
                }
            }
            else { // uplo == Uplo::Lower
                for (int64_t j = 0; j < n; ++j) {
                    for (int64_t i = 0; i < m; ++i) {
                        scalar_t sum = (diag == Diag::NonUnit)
                                       ? conj(A(i, i))*B(i, j)
                                       : B(i, j);
                        for (int64_t k = i+1; k < m; ++k)
                            sum += conj(A(k, i))*B(k, j);
                        B(i, j) = alpha * sum;
                    }
                }
            }
        }
    }
    else { // side == Side::Right
        if (trans == Op::NoTrans) {
            if (uplo == Uplo::Upper) {
                for (int64_t j = n-1; j >= 0; --j) {
 
                    scalar_t alpha_Akj = (diag == Diag::NonUnit)
                                         ? alpha*A(j, j)
                                         : alpha;
                    for (int64_t i = 0; i < m; ++i)
                        B(i, j) *= alpha_Akj;
 
                    for (int64_t k = 0; k < j; ++k) {
                        alpha_Akj = alpha*A(k, j);
                        for (int64_t i = 0; i < m; ++i)
                            B(i, j) += B(i, k)*alpha_Akj;
                    }
                }
            }
            else { // uplo == Uplo::Lower
                for (int64_t j = 0; j < n; ++j) {
 
                    scalar_t alpha_Akj = (diag == Diag::NonUnit)
                                         ? alpha*A(j, j)
                                         : alpha;
                    for (int64_t i = 0; i < m; ++i)
                        B(i, j) *= alpha_Akj;
 
                    for (int64_t k = j+1; k < n; ++k) {
                        alpha_Akj = alpha*A(k, j);
                        for (int64_t i = 0; i < m; ++i)
                            B(i, j) += B(i, k)*alpha_Akj;
                    }
                }
            }
        }
        else if (trans == Op::Trans) {
            if (uplo == Uplo::Upper) {
                for (int64_t k = 0; k < n; ++k) {
                    for (int64_t j = 0; j < k; ++j) {
                        scalar_t alpha_Ajk = alpha*A(j, k);
                        for (int64_t i = 0; i < m; ++i)
                            B(i, j) += B(i, k)*alpha_Ajk;
                    }
 
                    scalar_t alpha_Akk = (diag == Diag::NonUnit)
                                         ? alpha*A(k, k)
                                         : alpha;
                    for (int64_t i = 0; i < m; ++i)
                        B(i, k) *= alpha_Akk;
                }
            }
            else { // uplo == Uplo::Lower
                for (int64_t k = n-1; k >= 0; --k) {
                    for (int64_t j = k+1; j < n; ++j) {
                        scalar_t alpha_Ajk = alpha*A(j, k);
                        for (int64_t i = 0; i < m; ++i)
                            B(i, j) += B(i, k)*alpha_Ajk;
                    }
 
                    scalar_t alpha_Akk = (diag == Diag::NonUnit)
                                         ? alpha*A(k, k)
                                         : alpha;
                    for (int64_t i = 0; i < m; ++i)
                        B(i, k) *= alpha_Akk;
                }
            }
        }
        else { // trans == Op::ConjTrans
            if (uplo == Uplo::Upper) {
                for (int64_t k = 0; k < n; ++k) {
                    for (int64_t j = 0; j < k; ++j) {
                        scalar_t alpha_Ajk = alpha*conj(A(j, k));
                        for (int64_t i = 0; i < m; ++i)
                            B(i, j) += B(i, k)*alpha_Ajk;
                    }
 
                    scalar_t alpha_Akk = (diag == Diag::NonUnit)
                                         ? alpha*conj(A(k, k))
                                         : alpha;
                    for (int64_t i = 0; i < m; ++i)
                        B(i, k) *= alpha_Akk;
                }
            }
            else { // uplo == Uplo::Lower
                for (int64_t k = n-1; k >= 0; --k) {
                    for (int64_t j = k+1; j < n; ++j) {
                        scalar_t alpha_Ajk = alpha*conj(A(j, k));
                        for (int64_t i = 0; i < m; ++i)
                            B(i, j) += B(i, k)*alpha_Ajk;
                    }
 
                    scalar_t alpha_Akk = (diag == Diag::NonUnit)
                                         ? alpha*conj(A(k, k))
                                         : alpha;
                    for (int64_t i = 0; i < m; ++i)
                        B(i, k) *= alpha_Akk;
                }
            }
        }
    }
 
    #undef A
    #undef B
}
 
}  // namespace blas
 
#endif        //  #ifndef BLAS_TRMM_HH