SymmPackMat.hpp

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/*******************************************************************************
 * Copyright (C) 2017-2022 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 SYMMPACKMAT_HPP
#define SYMMPACKMAT_HPP
 
#include "DenseMat.hpp"
 
template<sp_d T> class SymmPackMat final : public DenseMat<T> {
    static constexpr char UPLO = 'U';
 
    static T bin;
 
    int solve_trs(Mat<T>&, Mat<T>&&);
    int solve_trs(Mat<T>&, const Mat<T>&);
 
public:
    explicit SymmPackMat(uword);
 
    unique_ptr<MetaMat<T>> make_copy() override;
 
    void unify(uword) override;
    void nullify(uword) override;
 
    const T& operator()(uword, uword) const 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 SymmPackMat<T>::bin = 0.;
 
template<sp_d T> SymmPackMat<T>::SymmPackMat(const uword in_size)
    : DenseMat<T>(in_size, in_size, (in_size + 1) * in_size / 2) {}
 
template<sp_d T> unique_ptr<MetaMat<T>> SymmPackMat<T>::make_copy() { return std::make_unique<SymmPackMat<T>>(*this); }
 
template<sp_d T> void SymmPackMat<T>::unify(const uword K) {
    nullify(K);
    access::rw(this->memory[(K * K + 3 * K) / 2]) = 1.;
}
 
template<sp_d T> void SymmPackMat<T>::nullify(const uword K) {
    suanpan_for(0llu, K, [&](const uword I) { access::rw(this->memory[(K * K + K) / 2 + I]) = 0.; });
    suanpan_for(K, this->n_rows, [&](const uword I) { access::rw(this->memory[(I * I + I) / 2 + K]) = 0.; });
 
    this->factored = false;
}
 
template<sp_d T> const T& SymmPackMat<T>::operator()(const uword in_row, const uword in_col) const { return this->memory[in_col > in_row ? (in_col * in_col + in_col) / 2 + in_row : (in_row * in_row + in_row) / 2 + in_col]; }
 
template<sp_d T> T& SymmPackMat<T>::at(const uword in_row, const uword in_col) {
    if(in_col < in_row) return bin;
    this->factored = false;
    return access::rw(this->memory[(in_col * in_col + in_col) / 2 + in_row]);
}
 
template<const char S, const char T, sp_d T1> Mat<T1> spmm(const SymmPackMat<T1>& A, const Mat<T1>& B);
 
template<sp_d T> Mat<T> SymmPackMat<T>::operator*(const Mat<T>& X) const {
    if(!X.is_colvec()) return spmm<'R', 'N'>(*this, X);
 
    auto Y = X;
 
    const auto N = static_cast<int>(this->n_rows);
    constexpr auto INC = 1;
    T ALPHA = 1.;
    T BETA = 0.;
 
    if(std::is_same_v<T, float>) {
        using E = float;
        arma_fortran(arma_sspmv)(&UPLO, &N, (E*)&ALPHA, (E*)this->memptr(), (E*)X.memptr(), &INC, (E*)&BETA, (E*)Y.memptr(), &INC);
    }
    else if(std::is_same_v<T, double>) {
        using E = double;
        arma_fortran(arma_dspmv)(&UPLO, &N, (E*)&ALPHA, (E*)this->memptr(), (E*)X.memptr(), &INC, (E*)&BETA, (E*)Y.memptr(), &INC);
    }
 
    return Y;
}
 
template<sp_d T> int SymmPackMat<T>::direct_solve(Mat<T>& X, const Mat<T>& B) {
    if(this->factored) return this->solve_trs(X, B);
 
    const auto N = static_cast<int>(this->n_rows);
    const auto NRHS = static_cast<int>(B.n_cols);
    const auto LDB = static_cast<int>(B.n_rows);
    auto INFO = 0;
 
    this->factored = true;
 
    if(std::is_same_v<T, float>) {
        using E = float;
        X = B;
        arma_fortran(arma_sppsv)(&UPLO, &N, &NRHS, (E*)this->memptr(), (E*)X.memptr(), &LDB, &INFO);
    }
    else if(Precision::FULL == this->setting.precision) {
        using E = double;
        X = B;
        arma_fortran(arma_dppsv)(&UPLO, &N, &NRHS, (E*)this->memptr(), (E*)X.memptr(), &LDB, &INFO);
    }
    else {
        this->s_memory = this->to_float();
        arma_fortran(arma_spptrf)(&UPLO, &N, this->s_memory.memptr(), &INFO);
        if(0 == INFO) INFO = this->solve_trs(X, B);
    }
 
    if(0 != INFO) suanpan_error("solve() receives error code %u from the base driver, the matrix is probably singular.\n", INFO);
 
    return INFO;
}
 
template<sp_d T> int SymmPackMat<T>::solve_trs(Mat<T>& X, const Mat<T>& B) {
    const auto N = static_cast<int>(this->n_rows);
    const auto NRHS = static_cast<int>(B.n_cols);
    const auto LDB = static_cast<int>(B.n_rows);
    auto INFO = 0;
 
    if(std::is_same_v<T, float>) {
        using E = float;
        X = B;
        arma_fortran(arma_spptrs)(&UPLO, &N, &NRHS, (E*)this->memptr(), (E*)X.memptr(), &LDB, &INFO);
    }
    else if(Precision::FULL == this->setting.precision) {
        using E = double;
        X = B;
        arma_fortran(arma_dpptrs)(&UPLO, &N, &NRHS, (E*)this->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_spptrs)(&UPLO, &N, &NRHS, this->s_memory.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 = norm(full_residual -= this->operator*(incre)));
        }
    }
 
    if(INFO != 0) suanpan_error("solve() receives error code %u from base driver, the matrix is probably singular.\n", INFO);
 
    return INFO;
}
 
template<sp_d T> int SymmPackMat<T>::direct_solve(Mat<T>& X, Mat<T>&& B) {
    if(this->factored) return this->solve_trs(X, std::forward<Mat<T>>(B));
 
    const auto N = static_cast<int>(this->n_rows);
    const auto NRHS = static_cast<int>(B.n_cols);
    const auto LDB = static_cast<int>(B.n_rows);
    auto INFO = 0;
 
    this->factored = true;
 
    if(std::is_same_v<T, float>) {
        using E = float;
        arma_fortran(arma_sppsv)(&UPLO, &N, &NRHS, (E*)this->memptr(), (E*)B.memptr(), &LDB, &INFO);
        X = std::move(B);
    }
    else if(Precision::FULL == this->setting.precision) {
        using E = double;
        arma_fortran(arma_dppsv)(&UPLO, &N, &NRHS, (E*)this->memptr(), (E*)B.memptr(), &LDB, &INFO);
        X = std::move(B);
    }
    else {
        this->s_memory = this->to_float();
        arma_fortran(arma_spptrf)(&UPLO, &N, this->s_memory.memptr(), &INFO);
        if(0 == INFO) INFO = this->solve_trs(X, std::forward<Mat<T>>(B));
    }
 
    if(0 != INFO) suanpan_error("solve() receives error code %u from the base driver, the matrix is probably singular.\n", INFO);
 
    return INFO;
}
 
template<sp_d T> int SymmPackMat<T>::solve_trs(Mat<T>& X, Mat<T>&& B) {
    const auto N = static_cast<int>(this->n_rows);
    const auto NRHS = static_cast<int>(B.n_cols);
    const auto LDB = static_cast<int>(B.n_rows);
    auto INFO = 0;
 
    if(std::is_same_v<T, float>) {
        using E = float;
        arma_fortran(arma_spptrs)(&UPLO, &N, &NRHS, (E*)this->memptr(), (E*)B.memptr(), &LDB, &INFO);
        X = std::move(B);
    }
    else if(Precision::FULL == this->setting.precision) {
        using E = double;
        arma_fortran(arma_dpptrs)(&UPLO, &N, &NRHS, (E*)this->memptr(), (E*)B.memptr(), &LDB, &INFO);
        X = std::move(B);
    }
    else {
        X = arma::zeros(B.n_rows, B.n_cols);
 
        auto multiplier = arma::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_spptrs)(&UPLO, &N, &NRHS, this->s_memory.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 = norm(B -= this->operator*(incre)));
        }
    }
 
    if(INFO != 0) suanpan_error("solve() receives error code %u from base driver, the matrix is probably singular.\n", INFO);
 
    return INFO;
}
 
#endif