Squashed 'third_party/eigen/' content from commit 61d72f6
Change-Id: Iccc90fa0b55ab44037f018046d2fcffd90d9d025
git-subtree-dir: third_party/eigen
git-subtree-split: 61d72f6383cfa842868c53e30e087b0258177257
diff --git a/test/eigensolver_complex.cpp b/test/eigensolver_complex.cpp
new file mode 100644
index 0000000..c9d8c08
--- /dev/null
+++ b/test/eigensolver_complex.cpp
@@ -0,0 +1,122 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// 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/.
+
+#include "main.h"
+#include <limits>
+#include <Eigen/Eigenvalues>
+#include <Eigen/LU>
+
+/* Check that two column vectors are approximately equal upto permutations,
+ by checking that the k-th power sums are equal for k = 1, ..., vec1.rows() */
+template<typename VectorType>
+void verify_is_approx_upto_permutation(const VectorType& vec1, const VectorType& vec2)
+{
+ typedef typename NumTraits<typename VectorType::Scalar>::Real RealScalar;
+
+ VERIFY(vec1.cols() == 1);
+ VERIFY(vec2.cols() == 1);
+ VERIFY(vec1.rows() == vec2.rows());
+ for (int k = 1; k <= vec1.rows(); ++k)
+ {
+ VERIFY_IS_APPROX(vec1.array().pow(RealScalar(k)).sum(), vec2.array().pow(RealScalar(k)).sum());
+ }
+}
+
+
+template<typename MatrixType> void eigensolver(const MatrixType& m)
+{
+ typedef typename MatrixType::Index Index;
+ /* this test covers the following files:
+ ComplexEigenSolver.h, and indirectly ComplexSchur.h
+ */
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ MatrixType a = MatrixType::Random(rows,cols);
+ MatrixType symmA = a.adjoint() * a;
+
+ ComplexEigenSolver<MatrixType> ei0(symmA);
+ VERIFY_IS_EQUAL(ei0.info(), Success);
+ VERIFY_IS_APPROX(symmA * ei0.eigenvectors(), ei0.eigenvectors() * ei0.eigenvalues().asDiagonal());
+
+ ComplexEigenSolver<MatrixType> ei1(a);
+ VERIFY_IS_EQUAL(ei1.info(), Success);
+ VERIFY_IS_APPROX(a * ei1.eigenvectors(), ei1.eigenvectors() * ei1.eigenvalues().asDiagonal());
+ // Note: If MatrixType is real then a.eigenvalues() uses EigenSolver and thus
+ // another algorithm so results may differ slightly
+ verify_is_approx_upto_permutation(a.eigenvalues(), ei1.eigenvalues());
+
+ ComplexEigenSolver<MatrixType> ei2;
+ ei2.setMaxIterations(ComplexSchur<MatrixType>::m_maxIterationsPerRow * rows).compute(a);
+ VERIFY_IS_EQUAL(ei2.info(), Success);
+ VERIFY_IS_EQUAL(ei2.eigenvectors(), ei1.eigenvectors());
+ VERIFY_IS_EQUAL(ei2.eigenvalues(), ei1.eigenvalues());
+ if (rows > 2) {
+ ei2.setMaxIterations(1).compute(a);
+ VERIFY_IS_EQUAL(ei2.info(), NoConvergence);
+ VERIFY_IS_EQUAL(ei2.getMaxIterations(), 1);
+ }
+
+ ComplexEigenSolver<MatrixType> eiNoEivecs(a, false);
+ VERIFY_IS_EQUAL(eiNoEivecs.info(), Success);
+ VERIFY_IS_APPROX(ei1.eigenvalues(), eiNoEivecs.eigenvalues());
+
+ // Regression test for issue #66
+ MatrixType z = MatrixType::Zero(rows,cols);
+ ComplexEigenSolver<MatrixType> eiz(z);
+ VERIFY((eiz.eigenvalues().cwiseEqual(0)).all());
+
+ MatrixType id = MatrixType::Identity(rows, cols);
+ VERIFY_IS_APPROX(id.operatorNorm(), RealScalar(1));
+
+ if (rows > 1)
+ {
+ // Test matrix with NaN
+ a(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
+ ComplexEigenSolver<MatrixType> eiNaN(a);
+ VERIFY_IS_EQUAL(eiNaN.info(), NoConvergence);
+ }
+}
+
+template<typename MatrixType> void eigensolver_verify_assert(const MatrixType& m)
+{
+ ComplexEigenSolver<MatrixType> eig;
+ VERIFY_RAISES_ASSERT(eig.eigenvectors());
+ VERIFY_RAISES_ASSERT(eig.eigenvalues());
+
+ MatrixType a = MatrixType::Random(m.rows(),m.cols());
+ eig.compute(a, false);
+ VERIFY_RAISES_ASSERT(eig.eigenvectors());
+}
+
+void test_eigensolver_complex()
+{
+ int s = 0;
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( eigensolver(Matrix4cf()) );
+ s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
+ CALL_SUBTEST_2( eigensolver(MatrixXcd(s,s)) );
+ CALL_SUBTEST_3( eigensolver(Matrix<std::complex<float>, 1, 1>()) );
+ CALL_SUBTEST_4( eigensolver(Matrix3f()) );
+ }
+ CALL_SUBTEST_1( eigensolver_verify_assert(Matrix4cf()) );
+ s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
+ CALL_SUBTEST_2( eigensolver_verify_assert(MatrixXcd(s,s)) );
+ CALL_SUBTEST_3( eigensolver_verify_assert(Matrix<std::complex<float>, 1, 1>()) );
+ CALL_SUBTEST_4( eigensolver_verify_assert(Matrix3f()) );
+
+ // Test problem size constructors
+ CALL_SUBTEST_5(ComplexEigenSolver<MatrixXf> tmp(s));
+
+ TEST_SET_BUT_UNUSED_VARIABLE(s)
+}