Add Spectra.

thirdparty/include/Spectra/MatOp/SparseCholesky.h

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+// Copyright (C) 2016-2022 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 SPECTRA_SPARSE_CHOLESKY_H
+#define SPECTRA_SPARSE_CHOLESKY_H
+
+#include <Eigen/Core>
+#include <Eigen/SparseCore>
+#include <Eigen/SparseCholesky>
+#include <stdexcept>
+
+#include "../Util/CompInfo.h"
+
+namespace Spectra {
+
+///
+/// \ingroup MatOp
+///
+/// This class defines the operations related to Cholesky decomposition on a
+/// sparse 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.
+///
+/// \tparam Scalar_      The element type of the matrix, for example,
+///                      `float`, `double`, and `long double`.
+/// \tparam Uplo         Either `Eigen::Lower` or `Eigen::Upper`, indicating which
+///                      triangular part of the matrix is used.
+/// \tparam Flags        Either `Eigen::ColMajor` or `Eigen::RowMajor`, indicating
+///                      the storage format of the input matrix.
+/// \tparam StorageIndex The type of the indices for the sparse matrix.
+///
+template <typename Scalar_, int Uplo = Eigen::Lower, int Flags = Eigen::ColMajor, typename StorageIndex = int>
+class SparseCholesky
+{
+public:
+    ///
+    /// Element type of the matrix.
+    ///
+    using Scalar = Scalar_;
+
+private:
+    using Index = Eigen::Index;
+    using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
+    using MapConstVec = Eigen::Map<const Vector>;
+    using MapVec = Eigen::Map<Vector>;
+    using SparseMatrix = Eigen::SparseMatrix<Scalar, Flags, StorageIndex>;
+
+    const Index m_n;
+    Eigen::SimplicialLLT<SparseMatrix, Uplo> m_decomp;
+    CompInfo m_info;  // status of the decomposition
+
+public:
+    ///
+    /// Constructor to create the matrix operation object.
+    ///
+    /// \param mat An **Eigen** sparse matrix object, whose type can be
+    /// `Eigen::SparseMatrix<Scalar, ...>` or its mapped version
+    /// `Eigen::Map<Eigen::SparseMatrix<Scalar, ...> >`.
+    ///
+    template <typename Derived>
+    SparseCholesky(const Eigen::SparseMatrixBase<Derived>& mat) :
+        m_n(mat.rows())
+    {
+        static_assert(
+            static_cast<int>(Derived::PlainObject::IsRowMajor) == static_cast<int>(SparseMatrix::IsRowMajor),
+            "SparseCholesky: the \"Flags\" template parameter does not match the input matrix (Eigen::ColMajor/Eigen::RowMajor)");
+
+        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) ?
+            CompInfo::Successful :
+            CompInfo::NumericalIssue;
+    }
+
+    ///
+    /// 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.
+    ///
+    CompInfo 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.permutationP() * x;
+        m_decomp.matrixL().solveInPlace(y);
+    }
+
+    ///
+    /// 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);
+        y = m_decomp.permutationPinv() * y;
+    }
+};
+
+}  // namespace Spectra
+
+#endif  // SPECTRA_SPARSE_CHOLESKY_H