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cs440-acg/ext/eigen/test/eigensolver_complex.cpp
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cs440-acg/ext/eigen/test/eigensolver_complex.cpp
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// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
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// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#include "main.h"
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#include <limits>
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#include <Eigen/Eigenvalues>
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#include <Eigen/LU>
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template<typename MatrixType> bool find_pivot(typename MatrixType::Scalar tol, MatrixType &diffs, Index col=0)
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{
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bool match = diffs.diagonal().sum() <= tol;
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if(match || col==diffs.cols())
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{
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return match;
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}
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else
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{
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Index n = diffs.cols();
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std::vector<std::pair<Index,Index> > transpositions;
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for(Index i=col; i<n; ++i)
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{
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Index best_index(0);
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if(diffs.col(col).segment(col,n-i).minCoeff(&best_index) > tol)
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break;
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best_index += col;
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diffs.row(col).swap(diffs.row(best_index));
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if(find_pivot(tol,diffs,col+1)) return true;
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diffs.row(col).swap(diffs.row(best_index));
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// move current pivot to the end
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diffs.row(n-(i-col)-1).swap(diffs.row(best_index));
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transpositions.push_back(std::pair<Index,Index>(n-(i-col)-1,best_index));
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}
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// restore
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for(Index k=transpositions.size()-1; k>=0; --k)
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diffs.row(transpositions[k].first).swap(diffs.row(transpositions[k].second));
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}
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return false;
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}
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/* Check that two column vectors are approximately equal upto permutations.
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* Initially, this method checked that the k-th power sums are equal for all k = 1, ..., vec1.rows(),
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* however this strategy is numerically inacurate because of numerical cancellation issues.
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*/
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template<typename VectorType>
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void verify_is_approx_upto_permutation(const VectorType& vec1, const VectorType& vec2)
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{
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typedef typename VectorType::Scalar Scalar;
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typedef typename NumTraits<Scalar>::Real RealScalar;
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VERIFY(vec1.cols() == 1);
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VERIFY(vec2.cols() == 1);
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VERIFY(vec1.rows() == vec2.rows());
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Index n = vec1.rows();
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RealScalar tol = test_precision<RealScalar>()*test_precision<RealScalar>()*numext::maxi(vec1.squaredNorm(),vec2.squaredNorm());
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Matrix<RealScalar,Dynamic,Dynamic> diffs = (vec1.rowwise().replicate(n) - vec2.rowwise().replicate(n).transpose()).cwiseAbs2();
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VERIFY( find_pivot(tol, diffs) );
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}
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template<typename MatrixType> void eigensolver(const MatrixType& m)
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{
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/* this test covers the following files:
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ComplexEigenSolver.h, and indirectly ComplexSchur.h
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*/
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Index rows = m.rows();
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Index cols = m.cols();
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typedef typename MatrixType::Scalar Scalar;
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typedef typename NumTraits<Scalar>::Real RealScalar;
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MatrixType a = MatrixType::Random(rows,cols);
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MatrixType symmA = a.adjoint() * a;
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ComplexEigenSolver<MatrixType> ei0(symmA);
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VERIFY_IS_EQUAL(ei0.info(), Success);
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VERIFY_IS_APPROX(symmA * ei0.eigenvectors(), ei0.eigenvectors() * ei0.eigenvalues().asDiagonal());
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ComplexEigenSolver<MatrixType> ei1(a);
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VERIFY_IS_EQUAL(ei1.info(), Success);
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VERIFY_IS_APPROX(a * ei1.eigenvectors(), ei1.eigenvectors() * ei1.eigenvalues().asDiagonal());
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// Note: If MatrixType is real then a.eigenvalues() uses EigenSolver and thus
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// another algorithm so results may differ slightly
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verify_is_approx_upto_permutation(a.eigenvalues(), ei1.eigenvalues());
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ComplexEigenSolver<MatrixType> ei2;
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ei2.setMaxIterations(ComplexSchur<MatrixType>::m_maxIterationsPerRow * rows).compute(a);
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VERIFY_IS_EQUAL(ei2.info(), Success);
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VERIFY_IS_EQUAL(ei2.eigenvectors(), ei1.eigenvectors());
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VERIFY_IS_EQUAL(ei2.eigenvalues(), ei1.eigenvalues());
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if (rows > 2) {
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ei2.setMaxIterations(1).compute(a);
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VERIFY_IS_EQUAL(ei2.info(), NoConvergence);
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VERIFY_IS_EQUAL(ei2.getMaxIterations(), 1);
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}
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ComplexEigenSolver<MatrixType> eiNoEivecs(a, false);
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VERIFY_IS_EQUAL(eiNoEivecs.info(), Success);
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VERIFY_IS_APPROX(ei1.eigenvalues(), eiNoEivecs.eigenvalues());
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// Regression test for issue #66
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MatrixType z = MatrixType::Zero(rows,cols);
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ComplexEigenSolver<MatrixType> eiz(z);
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VERIFY((eiz.eigenvalues().cwiseEqual(0)).all());
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MatrixType id = MatrixType::Identity(rows, cols);
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VERIFY_IS_APPROX(id.operatorNorm(), RealScalar(1));
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if (rows > 1 && rows < 20)
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{
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// Test matrix with NaN
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a(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
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ComplexEigenSolver<MatrixType> eiNaN(a);
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VERIFY_IS_EQUAL(eiNaN.info(), NoConvergence);
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}
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// regression test for bug 1098
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{
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ComplexEigenSolver<MatrixType> eig(a.adjoint() * a);
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eig.compute(a.adjoint() * a);
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}
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// regression test for bug 478
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{
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a.setZero();
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ComplexEigenSolver<MatrixType> ei3(a);
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VERIFY_IS_EQUAL(ei3.info(), Success);
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VERIFY_IS_MUCH_SMALLER_THAN(ei3.eigenvalues().norm(),RealScalar(1));
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VERIFY((ei3.eigenvectors().transpose()*ei3.eigenvectors().transpose()).eval().isIdentity());
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}
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}
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template<typename MatrixType> void eigensolver_verify_assert(const MatrixType& m)
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{
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ComplexEigenSolver<MatrixType> eig;
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VERIFY_RAISES_ASSERT(eig.eigenvectors());
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VERIFY_RAISES_ASSERT(eig.eigenvalues());
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MatrixType a = MatrixType::Random(m.rows(),m.cols());
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eig.compute(a, false);
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VERIFY_RAISES_ASSERT(eig.eigenvectors());
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}
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void test_eigensolver_complex()
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{
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int s = 0;
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for(int i = 0; i < g_repeat; i++) {
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CALL_SUBTEST_1( eigensolver(Matrix4cf()) );
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s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
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CALL_SUBTEST_2( eigensolver(MatrixXcd(s,s)) );
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CALL_SUBTEST_3( eigensolver(Matrix<std::complex<float>, 1, 1>()) );
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CALL_SUBTEST_4( eigensolver(Matrix3f()) );
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TEST_SET_BUT_UNUSED_VARIABLE(s)
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}
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CALL_SUBTEST_1( eigensolver_verify_assert(Matrix4cf()) );
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s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
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CALL_SUBTEST_2( eigensolver_verify_assert(MatrixXcd(s,s)) );
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CALL_SUBTEST_3( eigensolver_verify_assert(Matrix<std::complex<float>, 1, 1>()) );
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CALL_SUBTEST_4( eigensolver_verify_assert(Matrix3f()) );
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// Test problem size constructors
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CALL_SUBTEST_5(ComplexEigenSolver<MatrixXf> tmp(s));
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TEST_SET_BUT_UNUSED_VARIABLE(s)
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}
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