BandSymmMat.hpp

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/*******************************************************************************
 * Copyright (C) 2017-2024 Theodore Chang
 *
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
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 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
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// ReSharper disable CppCStyleCast
#ifndef BANDSYMMMAT_HPP
#define BANDSYMMMAT_HPP
 
#include "DenseMat.hpp"
 
template<sp_d T> class BandSymmMat final : public DenseMat<T> {
    static constexpr char UPLO = 'L';
 
    static T bin;
 
    const uword band;
    const uword m_rows; // memory block layout
 
    int solve_trs(Mat<T>&, Mat<T>&&);
 
protected:
    using DenseMat<T>::direct_solve;
 
    int direct_solve(Mat<T>&, Mat<T>&&) override;
 
public:
    BandSymmMat(const uword in_size, const uword in_bandwidth)
        : DenseMat<T>(in_size, in_size, (in_bandwidth + 1) * in_size)
        , band(in_bandwidth)
        , m_rows(in_bandwidth + 1) {}
 
    unique_ptr<MetaMat<T>> make_copy() override { return std::make_unique<BandSymmMat>(*this); }
 
    void nullify(const uword K) override {
        this->factored = false;
        suanpan::for_each(std::max(band, K) - band, K, [&](const uword I) { this->memory[K - I + I * m_rows] = T(0); });
        const auto t_factor = K * m_rows - K;
        suanpan::for_each(K, std::min(this->n_rows, K + band + 1), [&](const uword I) { this->memory[I + t_factor] = T(0); });
    }
 
    T operator()(const uword in_row, const uword in_col) const override {
        if(in_row > band + in_col || in_col > in_row + band) [[unlikely]] return bin = T(0);
        return this->memory[in_row > in_col ? in_row - in_col + in_col * m_rows : in_col - in_row + in_row * m_rows];
    }
 
    T& unsafe_at(const uword in_row, const uword in_col) override {
        this->factored = false;
        return this->memory[in_row - in_col + in_col * m_rows];
    }
 
    T& at(const uword in_row, const uword in_col) override {
        if(in_row > band + in_col || in_row < in_col) [[unlikely]] return bin = T(0);
        return this->unsafe_at(in_row, in_col);
    }
 
    Mat<T> operator*(const Mat<T>&) const override;
};
 
template<sp_d T> T BandSymmMat<T>::bin = T(0);
 
template<sp_d T> Mat<T> BandSymmMat<T>::operator*(const Mat<T>& X) const {
    Mat<T> Y(arma::size(X));
 
    const auto N = static_cast<int>(this->n_cols);
    const auto K = static_cast<int>(band);
    const auto LDA = static_cast<int>(m_rows);
    constexpr auto INC = 1;
    T ALPHA = T(1);
    T BETA = T(0);
 
    if constexpr(std::is_same_v<T, float>) {
        using E = float;
        suanpan::for_each(X.n_cols, [&](const uword I) { arma_fortran(arma_ssbmv)(&UPLO, &N, &K, (E*)&ALPHA, (E*)this->memptr(), &LDA, (E*)X.colptr(I), &INC, (E*)&BETA, (E*)Y.colptr(I), &INC); });
    }
    else {
        using E = double;
        suanpan::for_each(X.n_cols, [&](const uword I) { arma_fortran(arma_dsbmv)(&UPLO, &N, &K, (E*)&ALPHA, (E*)this->memptr(), &LDA, (E*)X.colptr(I), &INC, (E*)&BETA, (E*)Y.colptr(I), &INC); });
    }
 
    return Y;
}
 
template<sp_d T> int BandSymmMat<T>::direct_solve(Mat<T>& X, Mat<T>&& B) {
    if(this->factored) return this->solve_trs(X, std::forward<Mat<T>>(B));
 
    suanpan_assert([&] { if(this->n_rows != this->n_cols) throw invalid_argument("requires a square matrix"); });
 
    auto INFO = 0;
 
    const auto N = static_cast<int>(this->n_rows);
    const auto KD = static_cast<int>(band);
    const auto NRHS = static_cast<int>(B.n_cols);
    const auto LDAB = static_cast<int>(m_rows);
    const auto LDB = static_cast<int>(B.n_rows);
    this->factored = true;
 
    if constexpr(std::is_same_v<T, float>) {
        using E = float;
        arma_fortran(arma_spbsv)(&UPLO, &N, &KD, &NRHS, (E*)this->memptr(), &LDAB, (E*)B.memptr(), &LDB, &INFO);
        X = std::move(B);
    }
    else if(Precision::FULL == this->setting.precision) {
        using E = double;
        arma_fortran(arma_dpbsv)(&UPLO, &N, &KD, &NRHS, (E*)this->memptr(), &LDAB, (E*)B.memptr(), &LDB, &INFO);
        X = std::move(B);
    }
    else {
        this->s_memory = this->to_float();
        arma_fortran(arma_spbtrf)(&UPLO, &N, &KD, this->s_memory.memptr(), &LDAB, &INFO);
        if(0 == INFO) INFO = this->solve_trs(X, std::forward<Mat<T>>(B));
    }
 
    if(0 != INFO)
        suanpan_error("Error code {} received, the matrix is probably singular.\n", INFO);
 
    return INFO;
}
 
template<sp_d T> int BandSymmMat<T>::solve_trs(Mat<T>& X, Mat<T>&& B) {
    auto INFO = 0;
 
    const auto N = static_cast<int>(this->n_rows);
    const auto KD = static_cast<int>(band);
    const auto NRHS = static_cast<int>(B.n_cols);
    const auto LDAB = static_cast<int>(m_rows);
    const auto LDB = static_cast<int>(B.n_rows);
 
    if constexpr(std::is_same_v<T, float>) {
        using E = float;
        arma_fortran(arma_spbtrs)(&UPLO, &N, &KD, &NRHS, (E*)this->memptr(), &LDAB, (E*)B.memptr(), &LDB, &INFO);
        X = std::move(B);
    }
    else if(Precision::FULL == this->setting.precision) {
        using E = double;
        arma_fortran(arma_dpbtrs)(&UPLO, &N, &KD, &NRHS, (E*)this->memptr(), &LDAB, (E*)B.memptr(), &LDB, &INFO);
        X = std::move(B);
    }
    else
        this->mixed_trs(X, std::forward<Mat<T>>(B), [&](fmat& residual) {
            arma_fortran(arma_spbtrs)(&UPLO, &N, &KD, &NRHS, this->s_memory.memptr(), &LDAB, residual.memptr(), &LDB, &INFO);
            return INFO;
        });
 
    if(0 != INFO)
        suanpan_error("Error code {} received, the matrix is probably singular.\n", INFO);
 
    return INFO;
}
 
#endif