Add Spectra.

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

@@ -0,0 +1,158 @@
+// Copyright (C) 2018-2022 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_ARNOLDI_OP_H
+#define SPECTRA_ARNOLDI_OP_H
+
+#include <Eigen/Core>
+#include <cmath>  // std::sqrt
+
+namespace Spectra {
+
+///
+/// \ingroup Internals
+/// @{
+///
+
+///
+/// \defgroup Operators Operators
+///
+/// Different types of operators.
+///
+
+///
+/// \ingroup Operators
+///
+/// Operators used in the Arnoldi factorization.
+///
+template <typename Scalar, typename OpType, typename BOpType>
+class ArnoldiOp
+{
+private:
+    using Index = Eigen::Index;
+    using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
+
+    const OpType& m_op;
+    const BOpType& m_Bop;
+    mutable Vector m_cache;
+
+public:
+    ArnoldiOp(const OpType& op, const BOpType& Bop) :
+        m_op(op), m_Bop(Bop), m_cache(op.rows())
+    {}
+
+    // Move constructor
+    ArnoldiOp(ArnoldiOp&& other) :
+        m_op(other.m_op), m_Bop(other.m_Bop)
+    {
+        // We emulate the move constructor for Vector using Vector::swap()
+        m_cache.swap(other.m_cache);
+    }
+
+    inline Index rows() const { return m_op.rows(); }
+
+    // In generalized eigenvalue problem Ax=lambda*Bx, define the inner product to be <x, y> = x'By.
+    // For regular eigenvalue problems, it is the usual inner product <x, y> = x'y
+
+    // Compute <x, y> = x'By
+    // x and y are two vectors
+    template <typename Arg1, typename Arg2>
+    Scalar inner_product(const Arg1& x, const Arg2& y) const
+    {
+        m_Bop.perform_op(y.data(), m_cache.data());
+        return x.dot(m_cache);
+    }
+
+    // Compute res = <X, y> = X'By
+    // X is a matrix, y is a vector, res is a vector
+    template <typename Arg1, typename Arg2>
+    void trans_product(const Arg1& x, const Arg2& y, Eigen::Ref<Vector> res) const
+    {
+        m_Bop.perform_op(y.data(), m_cache.data());
+        res.noalias() = x.transpose() * m_cache;
+    }
+
+    // B-norm of a vector, ||x||_B = sqrt(x'Bx)
+    template <typename Arg>
+    Scalar norm(const Arg& x) const
+    {
+        using std::sqrt;
+        return sqrt(inner_product<Arg, Arg>(x, x));
+    }
+
+    // The "A" operator to generate the Krylov subspace
+    inline void perform_op(const Scalar* x_in, Scalar* y_out) const
+    {
+        m_op.perform_op(x_in, y_out);
+    }
+};
+
+///
+/// \ingroup Operators
+///
+/// Placeholder for the B-operator when \f$B = I\f$.
+///
+class IdentityBOp
+{};
+
+///
+/// \ingroup Operators
+///
+/// Partial specialization for the case \f$B = I\f$.
+///
+template <typename Scalar, typename OpType>
+class ArnoldiOp<Scalar, OpType, IdentityBOp>
+{
+private:
+    using Index = Eigen::Index;
+    using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
+
+    const OpType& m_op;
+
+public:
+    ArnoldiOp(const OpType& op, const IdentityBOp& /*Bop*/) :
+        m_op(op)
+    {}
+
+    inline Index rows() const { return m_op.rows(); }
+
+    // Compute <x, y> = x'y
+    // x and y are two vectors
+    template <typename Arg1, typename Arg2>
+    Scalar inner_product(const Arg1& x, const Arg2& y) const
+    {
+        return x.dot(y);
+    }
+
+    // Compute res = <X, y> = X'y
+    // X is a matrix, y is a vector, res is a vector
+    template <typename Arg1, typename Arg2>
+    void trans_product(const Arg1& x, const Arg2& y, Eigen::Ref<Vector> res) const
+    {
+        res.noalias() = x.transpose() * y;
+    }
+
+    // B-norm of a vector. For regular eigenvalue problems it is simply the L2 norm
+    template <typename Arg>
+    Scalar norm(const Arg& x) const
+    {
+        return x.norm();
+    }
+
+    // The "A" operator to generate the Krylov subspace
+    inline void perform_op(const Scalar* x_in, Scalar* y_out) const
+    {
+        m_op.perform_op(x_in, y_out);
+    }
+};
+
+///
+/// @}
+///
+
+}  // namespace Spectra
+
+#endif  // SPECTRA_ARNOLDI_OP_H