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ComplexQZ

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This commit is contained in:
Ludwig Striet
2025-10-13 17:35:03 +00:00
committed by Rasmus Munk Larsen
parent e1f1a608be
commit 99f8512985
4 changed files with 749 additions and 0 deletions
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1
test/CMakeLists.txt
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@@ -257,6 +257,7 @@ ei_add_test(eigensolver_selfadjoint)
ei_add_test(eigensolver_generic)
ei_add_test(eigensolver_complex)
ei_add_test(real_qz)
ei_add_test(complex_qz)
ei_add_test(eigensolver_generalized_real)
ei_add_test(jacobi)
ei_add_test(jacobisvd)

86
test/complex_qz.cpp Normal file
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@@ -0,0 +1,86 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 The Eigen Authors
//
// 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 http://mozilla.org/MPL/2.0/.
#define EIGEN_RUNTIME_NO_MALLOC
#include "main.h"
#include <Eigen/Eigenvalues>
/* this test covers the following files:
ComplexQZ.h
*/
template <typename MatrixType>
void generate_random_matrix_pair(const Index dim, MatrixType& A, MatrixType& B) {
A.resize(dim, dim);
B.resize(dim, dim);
A.setRandom();
B.setRandom();
// Set each row of B with a probability of 10% to 0
for (int i = 0; i < dim; i++) {
if (internal::random<int>(0, 10) == 0) B.row(i).setZero();
}
}
template <typename MatrixType>
void complex_qz(const MatrixType& A, const MatrixType& B) {
using std::abs;
const Index dim = A.rows();
ComplexQZ<MatrixType> qz(A, B);
VERIFY_IS_EQUAL(qz.info(), Success);
auto T = qz.matrixT(), S = qz.matrixS();
bool is_all_zero_T = true, is_all_zero_S = true;
using RealScalar = typename MatrixType::RealScalar;
RealScalar tol = dim * 10 * NumTraits<RealScalar>::epsilon();
for (Index j = 0; j < dim; j++) {
for (Index i = j + 1; i < dim; i++) {
if (std::abs(T(i, j)) > tol) {
std::cerr << std::abs(T(i, j)) << std::endl;
is_all_zero_T = false;
}
if (std::abs(S(i, j)) > tol) {
std::cerr << std::abs(S(i, j)) << std::endl;
is_all_zero_S = false;
}
}
}
VERIFY_IS_EQUAL(is_all_zero_T, true);
VERIFY_IS_EQUAL(is_all_zero_S, true);
VERIFY_IS_APPROX(qz.matrixQ() * qz.matrixS() * qz.matrixZ(), A);
VERIFY_IS_APPROX(qz.matrixQ() * qz.matrixT() * qz.matrixZ(), B);
VERIFY_IS_APPROX(qz.matrixQ() * qz.matrixQ().adjoint(), MatrixType::Identity(dim, dim));
VERIFY_IS_APPROX(qz.matrixZ() * qz.matrixZ().adjoint(), MatrixType::Identity(dim, dim));
}
EIGEN_DECLARE_TEST(complex_qz) {
// const Index dim1 = 15;
// const Index dim2 = 80;
for (int i = 0; i < g_repeat; i++) {
// Check for very small, fixed-sized double- and float complex matrices
Eigen::Matrix2cd A_2x2, B_2x2;
A_2x2.setRandom();
B_2x2.setRandom();
B_2x2.row(1).setZero();
Eigen::Matrix3cf A_3x3, B_3x3;
A_3x3.setRandom();
B_3x3.setRandom();
B_3x3.col(i % 3).setRandom();
// Test for small float complex matrices
Eigen::MatrixXcf A_float, B_float;
const Index dim1 = internal::random<Index>(15, 80), dim2 = internal::random<Index>(15, 80);
generate_random_matrix_pair(dim1, A_float, B_float);
// Test for a bit larger double complex matrices
Eigen::MatrixXcd A_double, B_double;
generate_random_matrix_pair(dim2, A_double, B_double);
CALL_SUBTEST_1(complex_qz(A_2x2, B_2x2));
CALL_SUBTEST_2(complex_qz(A_3x3, B_3x3));
CALL_SUBTEST_3(complex_qz(A_float, B_float));
CALL_SUBTEST_4(complex_qz(A_double, B_double));
}
}