BandMat.hpp

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/*******************************************************************************
 * Copyright (C) 2017-2023 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.
 *
 * This program is distributed in the hope that it will be useful,
 * 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.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program.  If not, see <http://www.gnu.org/licenses/>.
 ******************************************************************************/
// ReSharper disable CppCStyleCast
#ifndef BANDMAT_HPP
#define BANDMAT_HPP
 
#include "DenseMat.hpp"
 
template<sp_d T> class BandMat final : public DenseMat<T> {
    static constexpr char TRAN = 'N';
 
    static T bin;
 
    const uword l_band;
    const uword u_band;
    const uword s_band;
    const uword m_rows; // memory block layout
 
    int solve_trs(Mat<T>&, Mat<T>&&);
    int solve_trs(Mat<T>&, const Mat<T>&);
 
public:
    BandMat(uword, uword, uword);
 
    unique_ptr<MetaMat<T>> make_copy() override;
 
    void unify(uword) override;
    void nullify(uword) override;
 
    const T& operator()(uword, uword) const override;
    T& unsafe_at(uword, uword) override;
    T& at(uword, uword) override;
 
    Mat<T> operator*(const Mat<T>&) const override;
 
    int direct_solve(Mat<T>&, Mat<T>&&) override;
    int direct_solve(Mat<T>&, const Mat<T>&) override;
};
 
template<sp_d T> T BandMat<T>::bin = 0.;
 
template<sp_d T> BandMat<T>::BandMat(const uword in_size, const uword in_l, const uword in_u)
    : DenseMat<T>(in_size, in_size, (2 * in_l + in_u + 1) * in_size)
    , l_band(in_l)
    , u_band(in_u)
    , s_band(in_l + in_u)
    , m_rows(2 * in_l + in_u + 1) {}
 
template<sp_d T> unique_ptr<MetaMat<T>> BandMat<T>::make_copy() { return std::make_unique<BandMat<T>>(*this); }
 
template<sp_d T> void BandMat<T>::unify(const uword K) {
    nullify(K);
    access::rw(this->memory[s_band + K * m_rows]) = 1.;
}
 
template<sp_d T> void BandMat<T>::nullify(const uword K) {
    suanpan_for(std::max(K, u_band) - u_band, std::min(this->n_rows, K + l_band + 1), [&](const uword I) { access::rw(this->memory[I + s_band + K * (m_rows - 1)]) = 0.; });
    suanpan_for(std::max(K, l_band) - l_band, std::min(this->n_cols, K + u_band + 1), [&](const uword I) { access::rw(this->memory[K + s_band + I * (m_rows - 1)]) = 0.; });
 
    this->factored = false;
}
 
template<sp_d T> const T& BandMat<T>::operator()(const uword in_row, const uword in_col) const {
    if(in_row > in_col + l_band || in_row + u_band < in_col) return bin = 0.;
    return this->memory[in_row + s_band + in_col * (m_rows - 1)];
}
 
template<sp_d T> T& BandMat<T>::unsafe_at(const uword in_row, const uword in_col) {
    this->factored = false;
    return access::rw(this->memory[in_row + s_band + in_col * (m_rows - 1)]);
}
 
template<sp_d T> T& BandMat<T>::at(const uword in_row, const uword in_col) {
    if(in_row > in_col + l_band || in_row + u_band < in_col) return bin = 0.;
    this->factored = false;
    return access::rw(this->memory[in_row + s_band + in_col * (m_rows - 1)]);
}
 
template<sp_d T> Mat<T> BandMat<T>::operator*(const Mat<T>& X) const {
    Mat<T> Y(arma::size(X));
 
    const auto M = static_cast<int>(this->n_rows);
    const auto N = static_cast<int>(this->n_cols);
    const auto KL = static_cast<int>(l_band);
    const auto KU = static_cast<int>(u_band);
    const auto LDA = static_cast<int>(m_rows);
    const auto INC = 1;
    T ALPHA = 1.;
    T BETA = 0.;
 
    if(std::is_same_v<T, float>) {
        using E = float;
        suanpan_for(0llu, X.n_cols, [&](const uword I) { arma_fortran(arma_sgbmv)(&TRAN, &M, &N, &KL, &KU, (E*)&ALPHA, (E*)(this->memptr() + l_band), &LDA, (E*)X.colptr(I), &INC, (E*)&BETA, (E*)Y.colptr(I), &INC); });
    }
    else if(std::is_same_v<T, double>) {
        using E = double;
        suanpan_for(0llu, X.n_cols, [&](const uword I) { arma_fortran(arma_dgbmv)(&TRAN, &M, &N, &KL, &KU, (E*)&ALPHA, (E*)(this->memptr() + l_band), &LDA, (E*)X.colptr(I), &INC, (E*)&BETA, (E*)Y.colptr(I), &INC); });
    }
 
    return Y;
}
 
template<sp_d T> int BandMat<T>::direct_solve(Mat<T>& X, const Mat<T>& B) {
    if(this->factored) return this->solve_trs(X, B);
 
    suanpan_assert([&] { if(this->n_rows != this->n_cols) throw invalid_argument("requires a square matrix"); });
 
    auto INFO = 0;
 
    auto N = static_cast<int>(this->n_rows);
    const auto KL = static_cast<int>(l_band);
    const auto KU = static_cast<int>(u_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->pivot.zeros(N);
    this->factored = true;
 
    if(std::is_same_v<T, float>) {
        using E = float;
        X = B;
        arma_fortran(arma_sgbsv)(&N, &KL, &KU, &NRHS, (E*)this->memptr(), &LDAB, this->pivot.memptr(), (E*)X.memptr(), &LDB, &INFO);
    }
    else if(Precision::FULL == this->setting.precision) {
        using E = double;
        X = B;
        arma_fortran(arma_dgbsv)(&N, &KL, &KU, &NRHS, (E*)this->memptr(), &LDAB, this->pivot.memptr(), (E*)X.memptr(), &LDB, &INFO);
    }
    else {
        this->s_memory = this->to_float();
        arma_fortran(arma_sgbtrf)(&N, &N, &KL, &KU, this->s_memory.memptr(), &LDAB, this->pivot.memptr(), &INFO);
        if(0 == INFO) INFO = this->solve_trs(X, B);
    }
 
    if(0 != INFO)
        suanpan_error("Error code {} received, the matrix is probably singular.\n", INFO);
 
    return INFO;
}
 
template<sp_d T> int BandMat<T>::solve_trs(Mat<T>& X, const Mat<T>& B) {
    auto INFO = 0;
 
    const auto N = static_cast<int>(this->n_rows);
    const auto KL = static_cast<int>(l_band);
    const auto KU = static_cast<int>(u_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(std::is_same_v<T, float>) {
        using E = float;
        X = B;
        arma_fortran(arma_sgbtrs)(&TRAN, &N, &KL, &KU, &NRHS, (E*)this->memptr(), &LDAB, this->pivot.memptr(), (E*)X.memptr(), &LDB, &INFO);
    }
    else if(Precision::FULL == this->setting.precision) {
        using E = double;
        X = B;
        arma_fortran(arma_dgbtrs)(&TRAN, &N, &KL, &KU, &NRHS, (E*)this->memptr(), &LDAB, this->pivot.memptr(), (E*)X.memptr(), &LDB, &INFO);
    }
    else {
        X = arma::zeros(B.n_rows, B.n_cols);
 
        mat full_residual = B;
 
        auto multiplier = norm(full_residual);
 
        auto counter = 0u;
        while(counter++ < this->setting.iterative_refinement) {
            if(multiplier < this->setting.tolerance) break;
 
            auto residual = conv_to<fmat>::from(full_residual / multiplier);
 
            arma_fortran(arma_sgbtrs)(&TRAN, &N, &KL, &KU, &NRHS, this->s_memory.memptr(), &LDAB, this->pivot.memptr(), residual.memptr(), &LDB, &INFO);
            if(0 != INFO) break;
 
            const mat incre = multiplier * conv_to<mat>::from(residual);
 
            X += incre;
 
            suanpan_debug("Mixed precision algorithm multiplier: {:.5E}.\n", multiplier = arma::norm(full_residual -= this->operator*(incre)));
        }
    }
 
    if(0 != INFO)
        suanpan_error("Error code {} received, the matrix is probably singular.\n", INFO);
 
    return INFO;
}
 
template<sp_d T> int BandMat<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;
 
    auto N = static_cast<int>(this->n_rows);
    const auto KL = static_cast<int>(l_band);
    const auto KU = static_cast<int>(u_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->pivot.zeros(N);
    this->factored = true;
 
    if(std::is_same_v<T, float>) {
        using E = float;
        arma_fortran(arma_sgbsv)(&N, &KL, &KU, &NRHS, (E*)this->memptr(), &LDAB, this->pivot.memptr(), (E*)B.memptr(), &LDB, &INFO);
        X = std::move(B);
    }
    else if(Precision::FULL == this->setting.precision) {
        using E = double;
        arma_fortran(arma_dgbsv)(&N, &KL, &KU, &NRHS, (E*)this->memptr(), &LDAB, this->pivot.memptr(), (E*)B.memptr(), &LDB, &INFO);
        X = std::move(B);
    }
    else {
        this->s_memory = this->to_float();
        arma_fortran(arma_sgbtrf)(&N, &N, &KL, &KU, this->s_memory.memptr(), &LDAB, this->pivot.memptr(), &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 BandMat<T>::solve_trs(Mat<T>& X, Mat<T>&& B) {
    auto INFO = 0;
 
    const auto N = static_cast<int>(this->n_rows);
    const auto KL = static_cast<int>(l_band);
    const auto KU = static_cast<int>(u_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(std::is_same_v<T, float>) {
        using E = float;
        arma_fortran(arma_sgbtrs)(&TRAN, &N, &KL, &KU, &NRHS, (E*)this->memptr(), &LDAB, this->pivot.memptr(), (E*)B.memptr(), &LDB, &INFO);
        X = std::move(B);
    }
    else if(Precision::FULL == this->setting.precision) {
        using E = double;
        arma_fortran(arma_dgbtrs)(&TRAN, &N, &KL, &KU, &NRHS, (E*)this->memptr(), &LDAB, this->pivot.memptr(), (E*)B.memptr(), &LDB, &INFO);
        X = std::move(B);
    }
    else {
        X = arma::zeros(B.n_rows, B.n_cols);
 
        auto multiplier = norm(B);
 
        auto counter = 0u;
        while(counter++ < this->setting.iterative_refinement) {
            if(multiplier < this->setting.tolerance) break;
 
            auto residual = conv_to<fmat>::from(B / multiplier);
 
            arma_fortran(arma_sgbtrs)(&TRAN, &N, &KL, &KU, &NRHS, this->s_memory.memptr(), &LDAB, this->pivot.memptr(), residual.memptr(), &LDB, &INFO);
            if(0 != INFO) break;
 
            const mat incre = multiplier * conv_to<mat>::from(residual);
 
            X += incre;
 
            suanpan_debug("Mixed precision algorithm multiplier: {:.5E}.\n", multiplier = arma::norm(B -= this->operator*(incre)));
        }
    }
 
    if(0 != INFO)
        suanpan_error("Error code {} received, the matrix is probably singular.\n", INFO);
 
    return INFO;
}
 
#endif