Add Spectra.

thirdparty/include/Spectra/MatOp/internal/SymGEigsCayleyOp.h

@@ -0,0 +1,105 @@
+// Copyright (C) 2020-2022 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_SYM_GEIGS_CAYLEY_OP_H
+#define SPECTRA_SYM_GEIGS_CAYLEY_OP_H
+
+#include <Eigen/Core>
+
+#include "../SymShiftInvert.h"
+#include "../SparseSymMatProd.h"
+
+namespace Spectra {
+
+///
+/// \ingroup Operators
+///
+/// This class defines the matrix operation for generalized eigen solver in the
+/// Cayley mode. It computes \f$y=(A-\sigma B)^{-1}(A+\sigma B)x\f$ for any
+/// vector \f$x\f$, where \f$A\f$ is a symmetric matrix, \f$B\f$ is positive definite,
+/// and \f$\sigma\f$ is a real shift.
+/// This class is intended for internal use.
+///
+template <typename OpType = SymShiftInvert<double>,
+          typename BOpType = SparseSymMatProd<double>>
+class SymGEigsCayleyOp
+{
+public:
+    using Scalar = typename OpType::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>;
+
+    OpType& m_op;
+    const BOpType& m_Bop;
+    mutable Vector m_cache;  // temporary working space
+    Scalar m_sigma;
+
+public:
+    ///
+    /// Constructor to create the matrix operation object.
+    ///
+    /// \param op   The \f$(A-\sigma B)^{-1}\f$ matrix operation object.
+    /// \param Bop  The \f$B\f$ matrix operation object.
+    ///
+    SymGEigsCayleyOp(OpType& op, const BOpType& Bop) :
+        m_op(op), m_Bop(Bop), m_cache(op.rows())
+    {}
+
+    ///
+    /// Move constructor.
+    ///
+    SymGEigsCayleyOp(SymGEigsCayleyOp&& other) :
+        m_op(other.m_op), m_Bop(other.m_Bop), m_sigma(other.m_sigma)
+    {
+        // We emulate the move constructor for Vector using Vector::swap()
+        m_cache.swap(other.m_cache);
+    }
+
+    ///
+    /// Return the number of rows of the underlying matrix.
+    ///
+    Index rows() const { return m_op.rows(); }
+    ///
+    /// Return the number of columns of the underlying matrix.
+    ///
+    Index cols() const { return m_op.rows(); }
+
+    ///
+    /// Set the real shift \f$\sigma\f$.
+    ///
+    void set_shift(const Scalar& sigma)
+    {
+        m_op.set_shift(sigma);
+        m_sigma = sigma;
+    }
+
+    ///
+    /// Perform the matrix operation \f$y=(A-\sigma B)^{-1}(A+\sigma B)x\f$.
+    ///
+    /// \param x_in  Pointer to the \f$x\f$ vector.
+    /// \param y_out Pointer to the \f$y\f$ vector.
+    ///
+    // y_out = inv(A - sigma * B) * (A + sigma * B) * x_in
+    void perform_op(const Scalar* x_in, Scalar* y_out) const
+    {
+        //   inv(A - sigma * B) * (A + sigma * B) * x
+        // = inv(A - sigma * B) * (A - sigma * B + 2 * sigma * B) * x
+        // = x + 2 * sigma * inv(A - sigma * B) * B * x
+        m_Bop.perform_op(x_in, m_cache.data());
+        m_op.perform_op(m_cache.data(), y_out);
+        MapConstVec x(x_in, this->rows());
+        MapVec y(y_out, this->rows());
+        y.noalias() = x + (Scalar(2) * m_sigma) * y;
+    }
+};
+
+}  // namespace Spectra
+
+#endif  // SPECTRA_SYM_GEIGS_CAYLEY_OP_H