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eigenvalues: RealSchur
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8 files changed

+134
-10
lines changed

8 files changed

+134
-10
lines changed

‎CMakeLists.txt‎

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@@ -240,6 +240,7 @@ set(${PROJECT_NAME}_DECOMPOSITIONS_HEADERS
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include/eigenpy/decompositions/GeneralizedSelfAdjointEigenSolver.hpp
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include/eigenpy/decompositions/HessenbergDecomposition.hpp
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include/eigenpy/decompositions/RealQZ.hpp
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include/eigenpy/decompositions/RealSchur.hpp
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include/eigenpy/decompositions/ComplexEigenSolver.hpp
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include/eigenpy/decompositions/ComplexSchur.hpp
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include/eigenpy/decompositions/PermutationMatrix.hpp
@@ -335,6 +336,7 @@ set(${PROJECT_NAME}_DECOMPOSITIONS_SOURCES
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src/decompositions/fullpivlu-solver.cpp
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src/decompositions/hessenberg-decomposition.cpp
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src/decompositions/real-qz.cpp
339+
src/decompositions/real-schur.cpp
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src/decompositions/partialpivlu-solver.cpp
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src/decompositions/minres-solver.cpp
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src/decompositions/sparse-lu-solver.cpp

‎include/eigenpy/decompositions/ComplexSchur.hpp‎

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@@ -42,7 +42,7 @@ struct ComplexSchurVisitor
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const Eigen::EigenBase<MatrixType>& matrixQ,
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bool)) &
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Solver::computeFromHessenberg,
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bp::args("self", "matrix", "computeU"),
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bp::args("self", "matrixH", "matrixQ", "computeU"),
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"Compute Schur decomposition from a given Hessenberg matrix. ",
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bp::return_self<>())
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‎include/eigenpy/decompositions/RealQZ.hpp‎

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@@ -16,22 +16,20 @@ namespace eigenpy {
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template <typename _MatrixType>
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struct RealQZVisitor
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: public boost::python::def_visitor<
20-
RealQZVisitor<_MatrixType>> {
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: public boost::python::def_visitor<RealQZVisitor<_MatrixType>> {
2120
typedef _MatrixType MatrixType;
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typedef typename MatrixType::Scalar Scalar;
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typedef Eigen::RealQZ<MatrixType> Solver;
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template <class PyClass>
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void visit(PyClass& cl) const {
27-
cl.def(bp::init<Eigen::DenseIndex>(
28-
bp::arg("size"), "Default constructor. "))
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cl.def(
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bp::init<Eigen::DenseIndex>(bp::arg("size"), "Default constructor. "))
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.def(bp::init<MatrixType, MatrixType, bp::optional<bool>>(
3029
bp::args("A", "B", "computeQZ"),
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"Constructor; computes real QZ decomposition of given matrices. "))
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33-
.def("compute",
34-
&RealQZVisitor::compute_proxy<MatrixType>,
32+
.def("compute", &RealQZVisitor::compute_proxy<MatrixType>,
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bp::args("self", "A", "B"),
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"Computes QZ decomposition of given matrix. ",
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bp::return_self<>())
@@ -40,8 +38,7 @@ struct RealQZVisitor
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(Solver::*)(const MatrixType& A, const MatrixType& B, bool)) &
4139
Solver::compute,
4240
bp::args("self", "A", "B", "computeEigenvectors"),
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"Computes QZ decomposition of given matrix. ",
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bp::return_self<>())
41+
"Computes QZ decomposition of given matrix. ", bp::return_self<>())
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.def("info", &Solver::info, bp::arg("self"),
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"NumericalIssue if the input contains INF or NaN values or "
@@ -70,7 +67,7 @@ struct RealQZVisitor
7067

7168
static void expose() {
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static const std::string classname =
73-
"RealQZVisitorSolver" + scalar_name<Scalar>::shortname();
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"RealQZVisitor" + scalar_name<Scalar>::shortname();
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expose(classname);
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}
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‎include/eigenpy/decompositions/RealSchur.hpp‎

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@@ -0,0 +1,93 @@
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/*
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* Copyright 2020 INRIA
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*/
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#ifndef __eigenpy_decompositions_generalized_real_schur_hpp__
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#define __eigenpy_decompositions_generalized_real_schur_hpp__
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8+
#include <Eigen/Core>
9+
#include <Eigen/Eigenvalues>
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11+
#include "eigenpy/eigen-to-python.hpp"
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#include "eigenpy/eigenpy.hpp"
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#include "eigenpy/utils/scalar-name.hpp"
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namespace eigenpy {
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template <typename _MatrixType>
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struct RealSchurVisitor
19+
: public boost::python::def_visitor<
20+
RealSchurVisitor<_MatrixType>> {
21+
typedef _MatrixType MatrixType;
22+
typedef typename MatrixType::Scalar Scalar;
23+
typedef Eigen::RealSchur<MatrixType> Solver;
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template <class PyClass>
26+
void visit(PyClass& cl) const {
27+
cl.def(bp::init<Eigen::DenseIndex>(
28+
bp::arg("size"), "Default constructor. "))
29+
.def(bp::init<MatrixType, bp::optional<bool>>(
30+
bp::args("matrix", "computeU"),
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"Constructor; computes real Schur decomposition of given matrix. "))
32+
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.def("compute",
34+
&RealSchurVisitor::compute_proxy<MatrixType>,
35+
bp::args("self", "matrix"),
36+
"Computes Schur decomposition of given matrix. ",
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bp::return_self<>())
38+
.def("compute",
39+
(Solver &
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(Solver::*)(const Eigen::EigenBase<MatrixType>& matrix, bool)) &
41+
Solver::compute,
42+
bp::args("self", "matrix", "computeEigenvectors"),
43+
"Computes Schur decomposition of given matrix. ",
44+
bp::return_self<>())
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46+
.def("computeFromHessenberg",
47+
(Solver & (Solver::*)(const MatrixType& matrixH,
48+
const MatrixType& matrixQ,
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bool)) &
50+
Solver::computeFromHessenberg,
51+
bp::args("self", "matrixH", "matrixQ", "computeU"),
52+
"Compute Schur decomposition from a given Hessenberg matrix. ",
53+
bp::return_self<>())
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55+
.def("info", &Solver::info, bp::arg("self"),
56+
"NumericalIssue if the input contains INF or NaN values or "
57+
"overflow occured. Returns Success otherwise.")
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59+
.def("matrixT", &Solver::matrixT, bp::arg("self"),
60+
"Returns the quasi-triangular matrix in the Schur decomposition.",
61+
bp::return_value_policy<bp::copy_const_reference>())
62+
.def("matrixU", &Solver::matrixU, bp::arg("self"),
63+
"Returns the orthogonal matrix in the Schur decomposition. ",
64+
bp::return_value_policy<bp::copy_const_reference>())
65+
66+
.def("setMaxIterations", &Solver::setMaxIterations,
67+
bp::args("self", "max_iter"),
68+
"Sets the maximum number of iterations allowed.",
69+
bp::return_self<>());
70+
}
71+
72+
static void expose() {
73+
static const std::string classname =
74+
"RealSchurVisitor" + scalar_name<Scalar>::shortname();
75+
expose(classname);
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}
77+
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static void expose(const std::string& name) {
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bp::class_<Solver>(name.c_str(), bp::no_init)
80+
.def(RealSchurVisitor())
81+
.def(IdVisitor<Solver>());
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}
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private:
85+
template <typename MatrixType>
86+
static Solver& compute_proxy(Solver& self, const MatrixType& A) {
87+
return self.compute(A);
88+
}
89+
};
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} // namespace eigenpy
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#endif // ifndef __eigenpy_decompositions_generalized_real_schur_hpp__

‎src/decompositions/decompositions.cpp‎

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@@ -14,6 +14,7 @@ void exposeSelfAdjointEigenSolver();
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void exposeGeneralizedSelfAdjointEigenSolver();
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void exposeHessenbergDecomposition();
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void exposeRealQZ();
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void exposeRealSchur();
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void exposeComplexEigenSolver();
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void exposeComplexSchur();
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void exposeLLTSolver();
@@ -39,6 +40,7 @@ void exposeDecompositions() {
3940
exposeGeneralizedSelfAdjointEigenSolver();
4041
exposeHessenbergDecomposition();
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exposeRealQZ();
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exposeRealSchur();
4244
exposeComplexEigenSolver();
4345
exposeComplexSchur();
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exposeLLTSolver();

‎src/decompositions/real-schur.cpp‎

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@@ -0,0 +1,13 @@
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/*
3+
* Copyright 2024 INRIA
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*/
5+
6+
#include "eigenpy/decompositions/RealSchur.hpp"
7+
8+
namespace eigenpy {
9+
void exposeRealSchur() {
10+
using namespace Eigen;
11+
RealSchurVisitor<MatrixXd>::expose("RealSchur");
12+
}
13+
} // namespace eigenpy

‎unittest/CMakeLists.txt‎

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@@ -161,6 +161,9 @@ add_python_eigenpy_lib_unit_test(
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add_python_eigenpy_lib_unit_test("py-real-qz" "unittest/python/test_real_qz.py")
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164+
add_python_eigenpy_lib_unit_test("py-real-schur"
165+
"unittest/python/test_real_schur.py")
166+
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add_python_eigenpy_lib_unit_test("py-LLT" "unittest/python/test_LLT.py")
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add_python_eigenpy_lib_unit_test("py-LDLT" "unittest/python/test_LDLT.py")

‎unittest/python/test_real_schur.py‎

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import numpy as np
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3+
import eigenpy
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dim = 100
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rng = np.random.default_rng()
7+
A = rng.random((dim, dim))
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9+
cs = eigenpy.RealSchur(A)
10+
11+
U = cs.matrixU()
12+
T = cs.matrixT()
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14+
assert eigenpy.is_approx(A.real, (U @ T @ U.T).real)

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