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// 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>
template<typename MatrixType> bool find_pivot(typename MatrixType::Scalar tol, MatrixType &diffs, Index col=0)
{
bool match = diffs.diagonal().sum() <= tol;
if(match || col==diffs.cols())
{
return match;
}
else
{
Index n = diffs.cols();
std::vector<std::pair<Index,Index> > transpositions;
for(Index i=col; i<n; ++i)
{
Index best_index(0);
if(diffs.col(col).segment(col,n-i).minCoeff(&best_index) > tol)
break;
best_index += col;
diffs.row(col).swap(diffs.row(best_index));
if(find_pivot(tol,diffs,col+1)) return true;
diffs.row(col).swap(diffs.row(best_index));
// move current pivot to the end
diffs.row(n-(i-col)-1).swap(diffs.row(best_index));
transpositions.push_back(std::pair<Index,Index>(n-(i-col)-1,best_index));
}
// restore
for(Index k=transpositions.size()-1; k>=0; --k)
diffs.row(transpositions[k].first).swap(diffs.row(transpositions[k].second));
}
return false;
}
/* Check that two column vectors are approximately equal upto permutations.
* Initially, this method checked that the k-th power sums are equal for all k = 1, ..., vec1.rows(),
* however this strategy is numerically inacurate because of numerical cancellation issues.
*/
template<typename VectorType>
void verify_is_approx_upto_permutation(const VectorType& vec1, const VectorType& vec2)
{
typedef typename VectorType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
VERIFY(vec1.cols() == 1);
VERIFY(vec2.cols() == 1);
VERIFY(vec1.rows() == vec2.rows());
Index n = vec1.rows();
RealScalar tol = test_precision<RealScalar>()*test_precision<RealScalar>()*numext::maxi(vec1.squaredNorm(),vec2.squaredNorm());
Matrix<RealScalar,Dynamic,Dynamic> diffs = (vec1.rowwise().replicate(n) - vec2.rowwise().replicate(n).transpose()).cwiseAbs2();
VERIFY( find_pivot(tol, diffs) );
}
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 && rows < 20)
{
// 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);
}
// regression test for bug 1098
{
ComplexEigenSolver<MatrixType> eig(a.adjoint() * a);
eig.compute(a.adjoint() * a);
}
// regression test for bug 478
{
a.setZero();
ComplexEigenSolver<MatrixType> ei3(a);
VERIFY_IS_EQUAL(ei3.info(), Success);
VERIFY_IS_MUCH_SMALLER_THAN(ei3.eigenvalues().norm(),RealScalar(1));
VERIFY((ei3.eigenvectors().transpose()*ei3.eigenvectors().transpose()).eval().isIdentity());
}
}
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()) );
TEST_SET_BUT_UNUSED_VARIABLE(s)
}
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)
}
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