1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
|
// Copyright (C) 2016-2025 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_DENSE_GEN_COMPLEX_SHIFT_SOLVE_H
#define SPECTRA_DENSE_GEN_COMPLEX_SHIFT_SOLVE_H
#include <Eigen/Core>
#include <Eigen/LU>
#include <stdexcept>
namespace Spectra {
///
/// \ingroup MatOp
///
/// This class defines the complex shift-solve operation on a general real matrix \f$A\f$,
/// i.e., calculating \f$y=\mathrm{Re}\{(A-\sigma I)^{-1}x\}\f$ for any complex-valued
/// \f$\sigma\f$ and real-valued vector \f$x\f$. It is mainly used in the
/// GenEigsComplexShiftSolver eigen solver.
///
/// \tparam Scalar_ The element type of the matrix, for example,
/// `float`, `double`, and `long double`.
/// \tparam Flags Either `Eigen::ColMajor` or `Eigen::RowMajor`, indicating
/// the storage format of the input matrix.
///
template <typename Scalar_, int Flags = Eigen::ColMajor>
class DenseGenComplexShiftSolve
{
public:
///
/// Element type of the matrix.
///
using Scalar = Scalar_;
private:
using Index = Eigen::Index;
using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, Flags>;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using MapConstVec = Eigen::Map<const Vector>;
using MapVec = Eigen::Map<Vector>;
using ConstGenericMatrix = const Eigen::Ref<const Matrix>;
using Complex = std::complex<Scalar>;
using ComplexMatrix = Eigen::Matrix<Complex, Eigen::Dynamic, Eigen::Dynamic, Flags>;
using ComplexVector = Eigen::Matrix<Complex, Eigen::Dynamic, 1>;
using ComplexSolver = Eigen::PartialPivLU<ComplexMatrix>;
ConstGenericMatrix m_mat;
const Index m_n;
ComplexSolver m_solver;
mutable ComplexVector m_x_cache;
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>`).
///
template <typename Derived>
DenseGenComplexShiftSolve(const Eigen::MatrixBase<Derived>& mat) :
m_mat(mat), m_n(mat.rows())
{
static_assert(
static_cast<int>(Derived::PlainObject::IsRowMajor) == static_cast<int>(Matrix::IsRowMajor),
"DenseGenComplexShiftSolve: the \"Flags\" template parameter does not match the input matrix (Eigen::ColMajor/Eigen::RowMajor)");
if (mat.rows() != mat.cols())
throw std::invalid_argument("DenseGenComplexShiftSolve: matrix must be square");
}
///
/// Return the number of rows of the underlying matrix.
///
Index rows() const { return m_n; }
///
/// Return the number of columns of the underlying matrix.
///
Index cols() const { return m_n; }
///
/// Set the complex shift \f$\sigma\f$.
///
/// \param sigmar Real part of \f$\sigma\f$.
/// \param sigmai Imaginary part of \f$\sigma\f$.
///
void set_shift(const Scalar& sigmar, const Scalar& sigmai)
{
m_solver.compute(m_mat.template cast<Complex>() - Complex(sigmar, sigmai) * ComplexMatrix::Identity(m_n, m_n));
m_x_cache.resize(m_n);
m_x_cache.setZero();
}
///
/// Perform the complex shift-solve operation
/// \f$y=\mathrm{Re}\{(A-\sigma I)^{-1}x\}\f$.
///
/// \param x_in Pointer to the \f$x\f$ vector.
/// \param y_out Pointer to the \f$y\f$ vector.
///
// y_out = Re( inv(A - sigma * I) * x_in )
void perform_op(const Scalar* x_in, Scalar* y_out) const
{
m_x_cache.real() = MapConstVec(x_in, m_n);
MapVec y(y_out, m_n);
y.noalias() = m_solver.solve(m_x_cache).real();
}
};
} // namespace Spectra
#endif // SPECTRA_DENSE_GEN_COMPLEX_SHIFT_SOLVE_H
|
