BandMat.hpp

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/*******************************************************************************
 * Copyright (C) 2017-2025 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 : public DenseMat<T> {
    static constexpr char TRAN = 'N';
 
    static T bin;
 
    const uword s_band;
 
    int solve_trs(Mat<T>&, Mat<T>&&);
 
protected:
    const uword m_rows; // memory block layout
 
    const uword l_band;
    const uword u_band;
 
    using DenseMat<T>::direct_solve;
 
    int direct_solve(Mat<T>&, Mat<T>&&) override;
 
public:
    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)
        , s_band(in_l + in_u)
        , m_rows(2 * in_l + in_u + 1)
        , l_band(in_l)
        , u_band(in_u) {
        if(m_rows >= in_size)
            suanpan_warning("The storage requirement for the banded matrix is larger than that of a full matrix, consider using a full/sparse matrix instead.\n");
    }
 
    unique_ptr<MetaMat<T>> make_copy() override { return std::make_unique<BandMat>(*this); }
 
    void nullify(const uword K) override {
        this->factored = false;
        suanpan::for_each(std::max(K, u_band) - u_band, std::min(this->n_rows, K + l_band + 1), [&](const uword I) { this->memory[I + s_band + K * (m_rows - 1)] = T(0); });
        suanpan::for_each(std::max(K, l_band) - l_band, std::min(this->n_cols, K + u_band + 1), [&](const uword I) { this->memory[K + s_band + I * (m_rows - 1)] = T(0); });
    }
 
    T operator()(const uword in_row, const uword in_col) const override {
        if(in_row > in_col + l_band || in_row + u_band < in_col) [[unlikely]]
            return bin = T(0);
        return this->memory[in_row + s_band + in_col * (m_rows - 1)];
    }
 
    T& unsafe_at(const uword in_row, const uword in_col) override {
        this->factored = false;
        return this->memory[in_row + s_band + in_col * (m_rows - 1)];
    }
 
    T& at(const uword in_row, const uword in_col) override {
        if(in_row > in_col + l_band || in_row + u_band < in_col) [[unlikely]]
            return bin = T(0);
        return this->unsafe_at(in_row, in_col);
    }
 
    Mat<T> operator*(const Mat<T>&) const override;
 
    [[nodiscard]] int sign_det() const override {
        std::function<bool(uword)> neg_diag;
        if(Precision::FULL == this->setting.precision) neg_diag = [&](const uword i) { return this->memory[s_band + i * m_rows] < 0.; };
        else neg_diag = [&](const uword i) { return this->s_memory[s_band + i * m_rows] < 0.f; };
 
        auto det_sign = 1;
        for(unsigned I = 0; I < this->pivot.n_elem; ++I)
            if(neg_diag(I) ^ (static_cast<int>(I) + 1 != this->pivot(I))) det_sign = -det_sign;
        return det_sign;
    }
};
 
template<sp_d T> T BandMat<T>::bin = T(0);
 
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<blas_int>(this->n_rows);
    const auto N = static_cast<blas_int>(this->n_cols);
    const auto KL = static_cast<blas_int>(l_band);
    const auto KU = static_cast<blas_int>(u_band);
    const auto LDA = static_cast<blas_int>(m_rows);
    constexpr blas_int 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_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 {
        using E = double;
        suanpan::for_each(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, Mat<T>&& B) {
    if(this->factored) return this->solve_trs(X, std::move(B));
 
    suanpan_assert([&] { if(this->n_rows != this->n_cols) throw std::invalid_argument("requires a square matrix"); });
 
    blas_int INFO = 0;
 
    auto N = static_cast<blas_int>(this->n_rows);
    const auto KL = static_cast<blas_int>(l_band);
    const auto KU = static_cast<blas_int>(u_band);
    const auto NRHS = static_cast<blas_int>(B.n_cols);
    const auto LDAB = static_cast<blas_int>(m_rows);
    const auto LDB = static_cast<blas_int>(B.n_rows);
    this->pivot.zeros(N);
    this->factored = true;
 
    if constexpr(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::move(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) {
    blas_int INFO = 0;
 
    const auto N = static_cast<blas_int>(this->n_rows);
    const auto KL = static_cast<blas_int>(l_band);
    const auto KU = static_cast<blas_int>(u_band);
    const auto NRHS = static_cast<blas_int>(B.n_cols);
    const auto LDAB = static_cast<blas_int>(m_rows);
    const auto LDB = static_cast<blas_int>(B.n_rows);
 
    if constexpr(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
        this->mixed_trs(X, std::move(B), [&](fmat& residual) {
            arma_fortran(arma_sgbtrs)(&TRAN, &N, &KL, &KU, &NRHS, this->s_memory.memptr(), &LDAB, this->pivot.memptr(), residual.memptr(), &LDB, &INFO);
            return INFO;
        });
 
    if(0 != INFO)
        suanpan_error("Error code {} received, the matrix is probably singular.\n", INFO);
 
    return INFO;
}
 
#endif