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Add tests for real and complex Schur; extend test for Hessenberg.

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Make a minor correction to the ComplexSchur class.
This commit is contained in:
Jitse Niesen 2010-04-02 14:32:20 +01:00
parent 3a14a13533
commit a16a36ecf2
5 changed files with 176 additions and 14 deletions
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6
Eigen/src/Eigenvalues/ComplexSchur.h
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@ -86,7 +86,7 @@ template<typename _MatrixType> class ComplexSchur
/** \brief Default constructor.
*
* \param [in] size The size of the matrix whose Schur decomposition will be computed.
* \param [in] size Positive integer, size of the matrix whose Schur decomposition will be computed.
*
* The default constructor is useful in cases in which the user
* intends to perform decompositions via compute(). The \p size
@ -95,7 +95,7 @@ template<typename _MatrixType> class ComplexSchur
*
* \sa compute() for an example.
*/
ComplexSchur(int size = RowsAtCompileTime==Dynamic ? 0 : RowsAtCompileTime)
ComplexSchur(int size = RowsAtCompileTime==Dynamic ? 1 : RowsAtCompileTime)
: m_matT(size,size), m_matU(size,size), m_isInitialized(false), m_matUisUptodate(false)
{}
@ -157,7 +157,7 @@ template<typename _MatrixType> class ComplexSchur
*/
const ComplexMatrixType& matrixT() const
{
ei_assert(m_isInitialized && "ComplexShur is not initialized.");
ei_assert(m_isInitialized && "ComplexSchur is not initialized.");
return m_matT;
}

4
test/CMakeLists.txt
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@ -138,7 +138,9 @@ ei_add_test(qr)
ei_add_test(qr_colpivoting)
ei_add_test(qr_fullpivoting)
ei_add_test(upperbidiagonalization)
ei_add_test(hessenberg " " "${GSL_LIBRARIES}")
ei_add_test(hessenberg)
ei_add_test(schur_real)
ei_add_test(schur_complex)
ei_add_test(eigensolver_selfadjoint " " "${GSL_LIBRARIES}")
ei_add_test(eigensolver_generic " " "${GSL_LIBRARIES}")
ei_add_test(eigensolver_complex)

38
test/hessenberg.cpp
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@ -2,6 +2,7 @@
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <g.gael@free.fr>
// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
@ -28,19 +29,36 @@
template<typename Scalar,int Size> void hessenberg(int size = Size)
{
typedef Matrix<Scalar,Size,Size> MatrixType;
MatrixType m = MatrixType::Random(size,size);
HessenbergDecomposition<MatrixType> hess(m);
VERIFY_IS_APPROX(m, hess.matrixQ() * hess.matrixH() * hess.matrixQ().adjoint());
// Test basic functionality: A = U H U* and H is Hessenberg
for(int counter = 0; counter < g_repeat; ++counter) {
MatrixType m = MatrixType::Random(size,size);
HessenbergDecomposition<MatrixType> hess(m);
VERIFY_IS_APPROX(m, hess.matrixQ() * hess.matrixH() * hess.matrixQ().adjoint());
MatrixType H = hess.matrixH();
for(int row = 2; row < size; ++row) {
for(int col = 0; col < row-1; ++col) {
VERIFY(H(row,col) == (typename MatrixType::Scalar)0);
}
}
}
// Test whether compute() and constructor returns same result
MatrixType A = MatrixType::Random(size, size);
HessenbergDecomposition<MatrixType> cs1;
cs1.compute(A);
HessenbergDecomposition<MatrixType> cs2(A);
VERIFY_IS_EQUAL(cs1.matrixQ(), cs2.matrixQ());
VERIFY_IS_EQUAL(cs1.matrixH(), cs2.matrixH());
// TODO: Add tests for packedMatrix() and householderCoefficients()
}
void test_hessenberg()
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1(( hessenberg<std::complex<double>,1>() ));
CALL_SUBTEST_2(( hessenberg<std::complex<double>,2>() ));
CALL_SUBTEST_3(( hessenberg<std::complex<float>,4>() ));
CALL_SUBTEST_4(( hessenberg<float,Dynamic>(ei_random<int>(1,320)) ));
CALL_SUBTEST_5(( hessenberg<std::complex<double>,Dynamic>(ei_random<int>(1,320)) ));
}
CALL_SUBTEST_1(( hessenberg<std::complex<double>,1>() ));
CALL_SUBTEST_2(( hessenberg<std::complex<double>,2>() ));
CALL_SUBTEST_3(( hessenberg<std::complex<float>,4>() ));
CALL_SUBTEST_4(( hessenberg<float,Dynamic>(ei_random<int>(1,320)) ));
CALL_SUBTEST_5(( hessenberg<std::complex<double>,Dynamic>(ei_random<int>(1,320)) ));
}

67
test/schur_complex.cpp Normal file
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@ -0,0 +1,67 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#include "main.h"
#include <Eigen/Eigenvalues>
template<typename MatrixType> void schur(int size = MatrixType::ColsAtCompileTime)
{
typedef typename ComplexSchur<MatrixType>::ComplexScalar ComplexScalar;
typedef typename ComplexSchur<MatrixType>::ComplexMatrixType ComplexMatrixType;
// Test basic functionality: T is triangular and A = U T U*
for(int counter = 0; counter < g_repeat; ++counter) {
MatrixType A = MatrixType::Random(size, size);
ComplexSchur<MatrixType> schurOfA(A);
ComplexMatrixType U = schurOfA.matrixU();
ComplexMatrixType T = schurOfA.matrixT();
for(int row = 1; row < size; ++row) {
for(int col = 0; col < row; ++col) {
VERIFY(T(row,col) == (typename MatrixType::Scalar)0);
}
}
VERIFY_IS_APPROX(A.template cast<ComplexScalar>(), U * T * U.adjoint());
}
// Test asserts when not initialized
ComplexSchur<MatrixType> csUninitialized;
VERIFY_RAISES_ASSERT(csUninitialized.matrixT());
VERIFY_RAISES_ASSERT(csUninitialized.matrixU());
// Test whether compute() and constructor returns same result
MatrixType A = MatrixType::Random(size, size);
ComplexSchur<MatrixType> cs1;
cs1.compute(A);
ComplexSchur<MatrixType> cs2(A);
VERIFY_IS_EQUAL(cs1.matrixT(), cs2.matrixT());
VERIFY_IS_EQUAL(cs1.matrixU(), cs2.matrixU());
}
void test_schur_complex()
{
CALL_SUBTEST_1(( schur<Matrix4cd>() ));
CALL_SUBTEST_2(( schur<MatrixXcf>(ei_random<int>(1,50)) ));
CALL_SUBTEST_3(( schur<Matrix<std::complex<float>, 1, 1> >() ));
CALL_SUBTEST_4(( schur<Matrix<float, 3, 3, Eigen::RowMajor> >() ));
}

75
test/schur_real.cpp Normal file
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@ -0,0 +1,75 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#include "main.h"
#include <Eigen/Eigenvalues>
template<typename MatrixType> void verifyIsQuasiTriangular(const MatrixType& T)
{
const int size = T.cols();
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
// The "zeros" in the real Schur decomposition are only approximately zero
RealScalar norm = T.norm();
// Check T is lower Hessenberg
for(int row = 2; row < size; ++row) {
for(int col = 0; col < row - 1; ++col) {
VERIFY_IS_MUCH_SMALLER_THAN(T(row,col), norm);
}
}
// Check that any non-zero on the subdiagonal is followed by a zero and is
// part of a 2x2 diagonal block with imaginary eigenvalues.
for(int row = 1; row < size; ++row) {
if (!test_ei_isMuchSmallerThan(T(row,row-1), norm)) {
VERIFY(row == size-1 || test_ei_isMuchSmallerThan(T(row+1,row), norm));
Scalar tr = T(row-1,row-1) + T(row,row);
Scalar det = T(row-1,row-1) * T(row,row) - T(row-1,row) * T(row,row-1);
VERIFY(4 * det > tr * tr);
}
}
}
template<typename MatrixType> void schur(int size = MatrixType::ColsAtCompileTime)
{
// Test basic functionality: T is quasi-triangular and A = U T U*
for(int counter = 0; counter < g_repeat; ++counter) {
MatrixType A = MatrixType::Random(size, size);
RealSchur<MatrixType> schurOfA(A);
MatrixType U = schurOfA.matrixU();
MatrixType T = schurOfA.matrixT();
verifyIsQuasiTriangular(T);
VERIFY_IS_APPROX(A, U * T * U.transpose());
}
}
void test_schur_real()
{
CALL_SUBTEST_1(( schur<Matrix4f>() ));
CALL_SUBTEST_2(( schur<MatrixXd>(ei_random<int>(1,50)) ));
CALL_SUBTEST_3(( schur<Matrix<float, 1, 1> >() ));
CALL_SUBTEST_4(( schur<Matrix<double, 3, 3, Eigen::RowMajor> >() ));
}