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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 DENSE_CHOLESKY_H
#define DENSE_CHOLESKY_H
#include <Eigen/Core>
#include <Eigen/Cholesky>
#include <stdexcept>
#include "../Util/CompInfo.h"
namespace Spectra {
///
/// \ingroup MatOp
///
/// This class defines the operations related to Cholesky decomposition on a
/// positive definite matrix, \f$B=LL'\f$, where \f$L\f$ is a lower triangular
/// matrix. It is mainly used in the SymGEigsSolver generalized eigen solver
/// in the Cholesky decomposition mode.
///
template <typename Scalar, int Uplo = Eigen::Lower>
class DenseCholesky
{
private:
typedef Eigen::Index Index;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> Matrix;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
typedef Eigen::Map<const Matrix> MapConstMat;
typedef Eigen::Map<const Vector> MapConstVec;
typedef Eigen::Map<Vector> MapVec;
typedef const Eigen::Ref<const Matrix> ConstGenericMatrix;
const Index m_n;
Eigen::LLT<Matrix, Uplo> m_decomp;
int m_info; // status of the decomposition
public:
///
/// Constructor to create the matrix operation object.
///
/// \param mat An **Eigen** matrix object, whose type can be
/// `Eigen::Matrix<Scalar, ...>` (e.g. `Eigen::MatrixXd` and
/// `Eigen::MatrixXf`), or its mapped version
/// (e.g. `Eigen::Map<Eigen::MatrixXd>`).
///
DenseCholesky(ConstGenericMatrix& mat) :
m_n(mat.rows()), m_info(NOT_COMPUTED)
{
if(mat.rows() != mat.cols())
throw std::invalid_argument("DenseCholesky: matrix must be square");
m_decomp.compute(mat);
m_info = (m_decomp.info() == Eigen::Success) ?
SUCCESSFUL :
NUMERICAL_ISSUE;
}
///
/// Returns the number of rows of the underlying matrix.
///
Index rows() const { return m_n; }
///
/// Returns the number of columns of the underlying matrix.
///
Index cols() const { return m_n; }
///
/// Returns the status of the computation.
/// The full list of enumeration values can be found in \ref Enumerations.
///
int info() const { return m_info; }
///
/// Performs the lower triangular solving operation \f$y=L^{-1}x\f$.
///
/// \param x_in Pointer to the \f$x\f$ vector.
/// \param y_out Pointer to the \f$y\f$ vector.
///
// 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.matrixL().solve(x);
}
///
/// Performs the upper triangular solving operation \f$y=(L')^{-1}x\f$.
///
/// \param x_in Pointer to the \f$x\f$ vector.
/// \param y_out Pointer to the \f$y\f$ vector.
///
// 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);
}
};
} // namespace Spectra
#endif // DENSE_CHOLESKY_H
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