SparseCholesky.h

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// Copyright (C) 2016-2019 Yixuan Qiu <yixuan.qiu@cos.name>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at https://mozilla.org/MPL/2.0/.

#ifndef SPARSE_CHOLESKY_H
#define SPARSE_CHOLESKY_H

#include <Eigen/Core>
#include <Eigen/SparseCore>
#include <Eigen/SparseCholesky>
#include <stdexcept>
#include "../Util/CompInfo.h"

namespace Spectra {

template <typename Scalar, int Uplo = Eigen::Lower, int Flags = 0, typename StorageIndex = int>
class SparseCholesky
{
private:
    typedef Eigen::Index Index;
    typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
    typedef Eigen::Map<const Vector> MapConstVec;
    typedef Eigen::Map<Vector> MapVec;
    typedef Eigen::SparseMatrix<Scalar, Flags, StorageIndex> SparseMatrix;
    typedef const Eigen::Ref<const SparseMatrix> ConstGenericSparseMatrix;

    const Index m_n;
    Eigen::SimplicialLLT<SparseMatrix, Uplo> m_decomp;
    int m_info;  // status of the decomposition

public:
    SparseCholesky(ConstGenericSparseMatrix& mat) :
        m_n(mat.rows())
    {
        if (mat.rows() != mat.cols())
            throw std::invalid_argument("SparseCholesky: matrix must be square");

        m_decomp.compute(mat);
        m_info = (m_decomp.info() == Eigen::Success) ?
            SUCCESSFUL :
            NUMERICAL_ISSUE;
    }

    Index rows() const { return m_n; }
    Index cols() const { return m_n; }

    int info() const { return m_info; }

    // y_out = inv(L) * x_in
    void lower_triangular_solve(const Scalar* x_in, Scalar* y_out) const
    {
        MapConstVec x(x_in, m_n);
        MapVec y(y_out, m_n);
        y.noalias() = m_decomp.permutationP() * x;
        m_decomp.matrixL().solveInPlace(y);
    }

    // y_out = inv(L') * x_in
    void upper_triangular_solve(const Scalar* x_in, Scalar* y_out) const
    {
        MapConstVec x(x_in, m_n);
        MapVec y(y_out, m_n);
        y.noalias() = m_decomp.matrixU().solve(x);
        y = m_decomp.permutationPinv() * y;
    }
};

}  // namespace Spectra

#endif  // SPARSE_CHOLESKY_H