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* bug fixes in: Dot, generalized eigen problem, singular matrix detetection in Cholesky

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* fix all numerical instabilies in the unit tests, now all tests can be run 2000 times
  with almost zero failures.
This commit is contained in:
Gael Guennebaud
2008-08-23 15:14:20 +00:00
parent 312013a089
commit 2120fed849
20 changed files with 632 additions and 103 deletions
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8
test/CMakeLists.txt
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@@ -1,5 +1,9 @@
IF(BUILD_TESTS)
find_package(GSL)
if(GSL_FOUND)
add_definitions("-DHAS_GSL")
endif(GSL_FOUND)
IF(CMAKE_COMPILER_IS_GNUCXX)
IF(CMAKE_SYSTEM_NAME MATCHES Linux)
@@ -69,6 +73,10 @@ MACRO(EI_ADD_TEST testname)
target_link_libraries(${targetname} Eigen2)
ENDIF(TEST_LIB)
if(GSL_FOUND)
target_link_libraries(${targetname} ${GSL_LIBRARIES})
endif(GSL_FOUND)
IF(WIN32)
ADD_TEST(${testname} "${targetname}")
ELSE(WIN32)

50
test/adjoint.cpp
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@@ -31,25 +31,29 @@ template<typename MatrixType> void adjoint(const MatrixType& m)
*/
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
int rows = m.rows();
int cols = m.cols();
MatrixType m1 = MatrixType::Random(rows, cols),
m2 = MatrixType::Random(rows, cols),
RealScalar largerEps = test_precision<RealScalar>();
if (ei_is_same_type<RealScalar,float>::ret)
largerEps = 1e-3f;
MatrixType m1 = test_random_matrix<MatrixType>(rows, cols),
m2 = test_random_matrix<MatrixType>(rows, cols),
m3(rows, cols),
mzero = MatrixType::Zero(rows, cols),
identity = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
::Identity(rows, rows),
square = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
::Random(rows, rows);
VectorType v1 = VectorType::Random(rows),
v2 = VectorType::Random(rows),
v3 = VectorType::Random(rows),
identity = SquareMatrixType::Identity(rows, rows),
square = test_random_matrix<SquareMatrixType>(rows, rows);
VectorType v1 = test_random_matrix<VectorType>(rows),
v2 = test_random_matrix<VectorType>(rows),
v3 = test_random_matrix<VectorType>(rows),
vzero = VectorType::Zero(rows);
Scalar s1 = ei_random<Scalar>(),
s2 = ei_random<Scalar>();
Scalar s1 = test_random<Scalar>(),
s2 = test_random<Scalar>();
// check basic compatibility of adjoint, transpose, conjugate
VERIFY_IS_APPROX(m1.transpose().conjugate().adjoint(), m1);
@@ -61,19 +65,18 @@ template<typename MatrixType> void adjoint(const MatrixType& m)
// check basic properties of dot, norm, norm2
typedef typename NumTraits<Scalar>::Real RealScalar;
VERIFY_IS_APPROX((s1 * v1 + s2 * v2).dot(v3), s1 * v1.dot(v3) + s2 * v2.dot(v3));
VERIFY_IS_APPROX(v3.dot(s1 * v1 + s2 * v2), ei_conj(s1)*v3.dot(v1)+ei_conj(s2)*v3.dot(v2));
VERIFY_IS_APPROX(ei_conj(v1.dot(v2)), v2.dot(v1));
VERIFY_IS_APPROX(ei_abs(v1.dot(v1)), v1.norm2());
VERIFY(ei_isApprox((s1 * v1 + s2 * v2).dot(v3), s1 * v1.dot(v3) + s2 * v2.dot(v3), largerEps));
VERIFY(ei_isApprox(v3.dot(s1 * v1 + s2 * v2), ei_conj(s1)*v3.dot(v1)+ei_conj(s2)*v3.dot(v2), largerEps));
VERIFY_IS_APPROX(ei_conj(v1.dot(v2)), v2.dot(v1));
VERIFY_IS_APPROX(ei_abs(v1.dot(v1)), v1.norm2());
if(NumTraits<Scalar>::HasFloatingPoint)
VERIFY_IS_APPROX(v1.norm2(), v1.norm() * v1.norm());
VERIFY_IS_MUCH_SMALLER_THAN(ei_abs(vzero.dot(v1)), static_cast<RealScalar>(1));
VERIFY_IS_APPROX(v1.norm2(), v1.norm() * v1.norm());
VERIFY_IS_MUCH_SMALLER_THAN(ei_abs(vzero.dot(v1)), static_cast<RealScalar>(1));
if(NumTraits<Scalar>::HasFloatingPoint)
VERIFY_IS_MUCH_SMALLER_THAN(vzero.norm(), static_cast<RealScalar>(1));
VERIFY_IS_MUCH_SMALLER_THAN(vzero.norm(), static_cast<RealScalar>(1));
// check compatibility of dot and adjoint
// FIXME this line failed with MSVC and complex<double> in the ei_aligned_free()
VERIFY_IS_APPROX(v1.dot(square * v2), (square.adjoint() * v1).dot(v2));
VERIFY(ei_isApprox(v1.dot(square * v2), (square.adjoint() * v1).dot(v2), largerEps));
// like in testBasicStuff, test operator() to check const-qualification
int r = ei_random<int>(0, rows-1),
@@ -93,10 +96,11 @@ void test_adjoint()
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST( adjoint(Matrix<float, 1, 1>()) );
CALL_SUBTEST( adjoint(Matrix4d()) );
CALL_SUBTEST( adjoint(MatrixXcf(3, 3)) );
CALL_SUBTEST( adjoint(Matrix3d()) );
CALL_SUBTEST( adjoint(Matrix4f()) );
CALL_SUBTEST( adjoint(MatrixXcf(4, 4)) );
CALL_SUBTEST( adjoint(MatrixXi(8, 12)) );
CALL_SUBTEST( adjoint(MatrixXcd(20, 20)) );
CALL_SUBTEST( adjoint(MatrixXf(21, 21)) );
}
// test a large matrix only once
CALL_SUBTEST( adjoint(Matrix<float, 100, 100>()) );

12
test/array.cpp
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@@ -32,17 +32,18 @@ template<typename MatrixType> void scalarAdd(const MatrixType& m)
*/
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
int rows = m.rows();
int cols = m.cols();
MatrixType m1 = MatrixType::Random(rows, cols),
m2 = MatrixType::Random(rows, cols),
MatrixType m1 = test_random_matrix<MatrixType>(rows, cols),
m2 = test_random_matrix<MatrixType>(rows, cols),
m3(rows, cols);
Scalar s1 = ei_random<Scalar>(),
s2 = ei_random<Scalar>();
Scalar s1 = test_random<Scalar>(),
s2 = test_random<Scalar>();
VERIFY_IS_APPROX(m1.cwise() + s1, s1 + m1.cwise());
VERIFY_IS_APPROX(m1.cwise() + s1, MatrixType::Constant(rows,cols,s1) + m1);
@@ -56,7 +57,8 @@ template<typename MatrixType> void scalarAdd(const MatrixType& m)
VERIFY_IS_APPROX(m1.colwise().sum().sum(), m1.sum());
VERIFY_IS_APPROX(m1.rowwise().sum().sum(), m1.sum());
VERIFY_IS_NOT_APPROX((m1.rowwise().sum()*2).sum(), m1.sum());
if (!ei_isApprox(m1.sum(), (m1+m2).sum()))
VERIFY_IS_NOT_APPROX(((m1+m2).rowwise().sum()).sum(), m1.sum());
VERIFY_IS_APPROX(m1.colwise().sum(), m1.colwise().redux(ei_scalar_sum_op<Scalar>()));
}

89
test/cholesky.cpp
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@@ -21,11 +21,15 @@
// 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/>.
#define EIGEN_DONT_VECTORIZE
#include "main.h"
#include <Eigen/Cholesky>
#include <Eigen/LU>
#ifdef HAS_GSL
#include "gsl_helper.h"
#endif
template<typename MatrixType> void cholesky(const MatrixType& m)
{
/* this test covers the following files:
@@ -39,38 +43,79 @@ template<typename MatrixType> void cholesky(const MatrixType& m)
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
MatrixType a = test_random_matrix<MatrixType>(rows,cols);
MatrixType a0 = test_random_matrix<MatrixType>(rows,cols);
VectorType vecB = test_random_matrix<VectorType>(rows);
MatrixType matB = test_random_matrix<MatrixType>(rows,cols);
SquareMatrixType covMat = a * a.adjoint();
SquareMatrixType symm = a0 * a0.adjoint();
// let's make sure the matrix is not singular or near singular
MatrixType a1 = test_random_matrix<MatrixType>(rows,cols);
symm += a1 * a1.adjoint();
#ifdef HAS_GSL
if (ei_is_same_type<RealScalar,double>::ret)
{
typedef GslTraits<Scalar> Gsl;
typename Gsl::Matrix gMatA=0, gSymm=0;
typename Gsl::Vector gVecB=0, gVecX=0;
convert<MatrixType>(symm, gSymm);
convert<MatrixType>(symm, gMatA);
convert<VectorType>(vecB, gVecB);
convert<VectorType>(vecB, gVecX);
Gsl::cholesky(gMatA);
Gsl::cholesky_solve(gMatA, gVecB, gVecX);
VectorType vecX, _vecX, _vecB;
convert(gVecX, _vecX);
vecX = symm.cholesky().solve(vecB);
Gsl::prod(gSymm, gVecX, gVecB);
convert(gVecB, _vecB);
// test gsl itself !
VERIFY_IS_APPROX(vecB, _vecB);
VERIFY_IS_APPROX(vecX, _vecX);
Gsl::free(gMatA);
Gsl::free(gSymm);
Gsl::free(gVecB);
Gsl::free(gVecX);
}
#endif
if (rows>1)
{
CholeskyWithoutSquareRoot<SquareMatrixType> cholnosqrt(covMat);
VERIFY_IS_APPROX(covMat, cholnosqrt.matrixL() * cholnosqrt.vectorD().asDiagonal() * cholnosqrt.matrixL().adjoint());
// cout << (covMat * cholnosqrt.solve(vecB)).transpose().format(6) << endl;
// cout << vecB.transpose().format(6) << endl << "----------" << endl;
VERIFY((covMat * cholnosqrt.solve(vecB)).isApprox(vecB, test_precision<RealScalar>()*RealScalar(100))); // FIXME
VERIFY((covMat * cholnosqrt.solve(matB)).isApprox(matB, test_precision<RealScalar>()*RealScalar(100))); // FIXME
CholeskyWithoutSquareRoot<SquareMatrixType> cholnosqrt(symm);
VERIFY(cholnosqrt.isPositiveDefinite());
VERIFY_IS_APPROX(symm, cholnosqrt.matrixL() * cholnosqrt.vectorD().asDiagonal() * cholnosqrt.matrixL().adjoint());
VERIFY_IS_APPROX(symm * cholnosqrt.solve(vecB), vecB);
VERIFY_IS_APPROX(symm * cholnosqrt.solve(matB), matB);
}
Cholesky<SquareMatrixType> chol(covMat);
VERIFY_IS_APPROX(covMat, chol.matrixL() * chol.matrixL().adjoint());
// cout << (covMat * chol.solve(vecB)).transpose().format(6) << endl;
// cout << vecB.transpose().format(6) << endl << "----------" << endl;
VERIFY((covMat * chol.solve(vecB)).isApprox(vecB, test_precision<RealScalar>()*RealScalar(100))); // FIXME
VERIFY((covMat * chol.solve(matB)).isApprox(matB, test_precision<RealScalar>()*RealScalar(100))); // FIXME
{
Cholesky<SquareMatrixType> chol(symm);
VERIFY(chol.isPositiveDefinite());
VERIFY_IS_APPROX(symm, chol.matrixL() * chol.matrixL().adjoint());
VERIFY_IS_APPROX(symm * chol.solve(vecB), vecB);
VERIFY_IS_APPROX(symm * chol.solve(matB), matB);
}
// test isPositiveDefinite on non definite matrix
if (rows>4)
{
SquareMatrixType symm = a0.block(0,0,rows,cols-4) * a0.block(0,0,rows,cols-4).adjoint();
Cholesky<SquareMatrixType> chol(symm);
VERIFY(!chol.isPositiveDefinite());
CholeskyWithoutSquareRoot<SquareMatrixType> cholnosqrt(symm);
VERIFY(!cholnosqrt.isPositiveDefinite());
}
}
void test_cholesky()
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST( cholesky(Matrix<float,1,1>()) );
CALL_SUBTEST( cholesky(Matrix<float,2,2>()) );
// CALL_SUBTEST( cholesky(Matrix3f()) );
// CALL_SUBTEST( cholesky(Matrix4d()) );
// CALL_SUBTEST( cholesky(MatrixXcd(7,7)) );
// CALL_SUBTEST( cholesky(MatrixXf(19,19)) );
// CALL_SUBTEST( cholesky(MatrixXd(33,33)) );
CALL_SUBTEST( cholesky(Matrix<double,1,1>()) );
CALL_SUBTEST( cholesky(Matrix2d()) );
CALL_SUBTEST( cholesky(Matrix3f()) );
CALL_SUBTEST( cholesky(Matrix4d()) );
CALL_SUBTEST( cholesky(MatrixXcd(7,7)) );
CALL_SUBTEST( cholesky(MatrixXf(17,17)) );
CALL_SUBTEST( cholesky(MatrixXd(33,33)) );
}
}

81
test/eigensolver.cpp
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@@ -25,6 +25,10 @@
#include "main.h"
#include <Eigen/QR>
#ifdef HAS_GSL
#include "gsl_helper.h"
#endif
template<typename MatrixType> void eigensolver(const MatrixType& m)
{
/* this test covers the following files:
@@ -33,19 +37,76 @@ template<typename MatrixType> void eigensolver(const MatrixType& m)
int rows = m.rows();
int cols = m.cols();
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, 1> RealVectorType;
typedef typename std::complex<typename NumTraits<typename MatrixType::Scalar>::Real> Complex;
MatrixType a = MatrixType::Random(rows,cols);
MatrixType symmA = a.adjoint() * a;
RealScalar largerEps = 10*test_precision<RealScalar>();
MatrixType a = test_random_matrix<MatrixType>(rows,cols);
MatrixType a1 = test_random_matrix<MatrixType>(rows,cols);
MatrixType symmA = a.adjoint() * a + a1.adjoint() * a1;
MatrixType b = test_random_matrix<MatrixType>(rows,cols);
MatrixType b1 = test_random_matrix<MatrixType>(rows,cols);
MatrixType symmB = b.adjoint() * b + b1.adjoint() * b1;
SelfAdjointEigenSolver<MatrixType> eiSymm(symmA);
VERIFY_IS_APPROX(symmA * eiSymm.eigenvectors(), (eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal().eval()));
// generalized eigen pb
SelfAdjointEigenSolver<MatrixType> eiSymmGen(symmA, symmB);
#ifdef HAS_GSL
if (ei_is_same_type<RealScalar,double>::ret)
{
typedef GslTraits<Scalar> Gsl;
typename Gsl::Matrix gEvec=0, gSymmA=0, gSymmB=0;
typename GslTraits<RealScalar>::Vector gEval=0;
RealVectorType _eval;
MatrixType _evec;
convert<MatrixType>(symmA, gSymmA);
convert<MatrixType>(symmB, gSymmB);
convert<MatrixType>(symmA, gEvec);
gEval = GslTraits<RealScalar>::createVector(rows);
Gsl::eigen_symm(gSymmA, gEval, gEvec);
convert(gEval, _eval);
convert(gEvec, _evec);
// test gsl itself !
VERIFY((symmA * _evec).isApprox(_evec * _eval.asDiagonal().eval(), largerEps));
// compare with eigen
VERIFY_IS_APPROX(_eval, eiSymm.eigenvalues());
VERIFY_IS_APPROX(_evec.cwise().abs(), eiSymm.eigenvectors().cwise().abs());
// generalized pb
Gsl::eigen_symm_gen(gSymmA, gSymmB, gEval, gEvec);
convert(gEval, _eval);
convert(gEvec, _evec);
// test GSL itself:
VERIFY((symmA * _evec).isApprox(symmB * (_evec * _eval.asDiagonal().eval()), largerEps));
// compare with eigen
// std::cerr << _eval.transpose() << "\n" << eiSymmGen.eigenvalues().transpose() << "\n\n";
// std::cerr << _evec.format(6) << "\n\n" << eiSymmGen.eigenvectors().format(6) << "\n\n\n";
VERIFY_IS_APPROX(_eval, eiSymmGen.eigenvalues());
VERIFY_IS_APPROX(_evec.cwise().abs(), eiSymmGen.eigenvectors().cwise().abs());
Gsl::free(gSymmA);
Gsl::free(gSymmB);
GslTraits<RealScalar>::free(gEval);
Gsl::free(gEvec);
}
#endif
VERIFY((symmA * eiSymm.eigenvectors()).isApprox(
eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal().eval(), largerEps));
// generalized eigen problem Ax = lBx
MatrixType b = MatrixType::Random(rows,cols);
MatrixType symmB = b.adjoint() * b;
eiSymm.compute(symmA,symmB);
VERIFY_IS_APPROX(symmA * eiSymm.eigenvectors(), symmB * (eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal().eval()));
VERIFY((symmA * eiSymmGen.eigenvectors()).isApprox(
symmB * (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal().eval()), largerEps));
// EigenSolver<MatrixType> eiNotSymmButSymm(covMat);
// VERIFY_IS_APPROX((covMat.template cast<Complex>()) * (eiNotSymmButSymm.eigenvectors().template cast<Complex>()),
@@ -59,12 +120,12 @@ template<typename MatrixType> void eigensolver(const MatrixType& m)
void test_eigensolver()
{
for(int i = 0; i < 1; i++) {
for(int i = 0; i < g_repeat; i++) {
// very important to test a 3x3 matrix since we provide a special path for it
CALL_SUBTEST( eigensolver(Matrix3f()) );
CALL_SUBTEST( eigensolver(Matrix4d()) );
CALL_SUBTEST( eigensolver(MatrixXf(7,7)) );
CALL_SUBTEST( eigensolver(MatrixXcd(6,6)) );
CALL_SUBTEST( eigensolver(MatrixXcf(3,3)) );
CALL_SUBTEST( eigensolver(MatrixXcd(5,5)) );
CALL_SUBTEST( eigensolver(MatrixXd(19,19)) );
}
}

13
test/geometry.cpp
View File

@@ -69,8 +69,8 @@ template<typename Scalar> void geometry(void)
VERIFY_IS_APPROX(q1 * v2, q1.toRotationMatrix() * v2);
VERIFY_IS_APPROX(q1 * q2 * v2,
q1.toRotationMatrix() * q2.toRotationMatrix() * v2);
VERIFY_IS_NOT_APPROX(q2 * q1 * v2,
q1.toRotationMatrix() * q2.toRotationMatrix() * v2);
VERIFY( !(q2 * q1 * v2).isApprox(
q1.toRotationMatrix() * q2.toRotationMatrix() * v2));
q2 = q1.toRotationMatrix();
VERIFY_IS_APPROX(q1*v1,q2*v1);
@@ -126,7 +126,7 @@ template<typename Scalar> void geometry(void)
t1.prescale(v0);
VERIFY_IS_APPROX( (t0 * Vector3(1,0,0)).norm(), v0.x());
VERIFY_IS_NOT_APPROX((t1 * Vector3(1,0,0)).norm(), v0.x());
VERIFY(!ei_isApprox((t1 * Vector3(1,0,0)).norm(), v0.x()));
t0.setIdentity();
t1.setIdentity();
@@ -138,7 +138,7 @@ template<typename Scalar> void geometry(void)
t1.prescale(v1.cwise().inverse());
t1.translate(-v0);
VERIFY((t0.matrix() * t1.matrix()).isIdentity());
VERIFY((t0.matrix() * t1.matrix()).isIdentity(test_precision<Scalar>()));
t1.fromPositionOrientationScale(v0, q1, v1);
VERIFY_IS_APPROX(t1.matrix(), t0.matrix());
@@ -147,6 +147,8 @@ template<typename Scalar> void geometry(void)
Transform2 t20, t21;
Vector2 v20 = test_random_matrix<Vector2>();
Vector2 v21 = test_random_matrix<Vector2>();
for (int k=0; k<2; ++k)
if (ei_abs(v21[k])<1e-3) v21[k] = 1e-3;
t21.setIdentity();
t21.linear() = Rotation2D<Scalar>(a).toRotationMatrix();
VERIFY_IS_APPROX(t20.fromPositionOrientationScale(v20,a,v21).matrix(),
@@ -154,7 +156,8 @@ template<typename Scalar> void geometry(void)
t21.setIdentity();
t21.linear() = Rotation2D<Scalar>(-a).toRotationMatrix();
VERIFY( (t20.fromPositionOrientationScale(v20,a,v21) * (t21.prescale(v21.cwise().inverse()).translate(-v20))).isIdentity() );
VERIFY( (t20.fromPositionOrientationScale(v20,a,v21)
* (t21.prescale(v21.cwise().inverse()).translate(-v20))).isIdentity(test_precision<Scalar>()) );
}
void test_geometry()

190
test/gsl_helper.h Normal file
View File

@@ -0,0 +1,190 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
//
// 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/>.
#ifndef EIGEN_GSL_HELPER
#define EIGEN_GSL_HELPER
#include <Eigen/Core>
#include <gsl/gsl_blas.h>
#include <gsl/gsl_multifit.h>
#include <gsl/gsl_eigen.h>
#include <gsl/gsl_linalg.h>
#include <gsl/gsl_complex.h>
#include <gsl/gsl_complex_math.h>
namespace Eigen {
template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex> struct GslTraits
{
typedef gsl_matrix* Matrix;
typedef gsl_vector* Vector;
static Matrix createMatrix(int rows, int cols) { return gsl_matrix_alloc(rows,cols); }
static Vector createVector(int size) { return gsl_vector_alloc(size); }
static void free(Matrix& m) { gsl_matrix_free(m); m=0; }
static void free(Vector& m) { gsl_vector_free(m); m=0; }
static void prod(const Matrix& m, const Vector& v, Vector& x) { gsl_blas_dgemv(CblasNoTrans,1,m,v,0,x); }
static void cholesky(Matrix& m) { gsl_linalg_cholesky_decomp(m); }
static void cholesky_solve(const Matrix& m, const Vector& b, Vector& x) { gsl_linalg_cholesky_solve(m,b,x); }
static void eigen_symm(const Matrix& m, Vector& eval, Matrix& evec)
{
gsl_eigen_symmv_workspace * w = gsl_eigen_symmv_alloc(m->size1);
Matrix a = createMatrix(m->size1, m->size2);
gsl_matrix_memcpy(a, m);
gsl_eigen_symmv(a,eval,evec,w);
gsl_eigen_symmv_sort(eval, evec, GSL_EIGEN_SORT_VAL_ASC);
gsl_eigen_symmv_free(w);
free(a);
}
static void eigen_symm_gen(const Matrix& m, const Matrix& _b, Vector& eval, Matrix& evec)
{
gsl_eigen_gensymmv_workspace * w = gsl_eigen_gensymmv_alloc(m->size1);
Matrix a = createMatrix(m->size1, m->size2);
Matrix b = createMatrix(_b->size1, _b->size2);
gsl_matrix_memcpy(a, m);
gsl_matrix_memcpy(b, _b);
gsl_eigen_gensymmv(a,b,eval,evec,w);
gsl_eigen_symmv_sort(eval, evec, GSL_EIGEN_SORT_VAL_ASC);
gsl_eigen_gensymmv_free(w);
free(a);
}
};
template<typename Scalar> struct GslTraits<Scalar,true>
{
typedef gsl_matrix_complex* Matrix;
typedef gsl_vector_complex* Vector;
static Matrix createMatrix(int rows, int cols) { return gsl_matrix_complex_alloc(rows,cols); }
static Vector createVector(int size) { return gsl_vector_complex_alloc(size); }
static void free(Matrix& m) { gsl_matrix_complex_free(m); m=0; }
static void free(Vector& m) { gsl_vector_complex_free(m); m=0; }
static void cholesky(Matrix& m) { gsl_linalg_complex_cholesky_decomp(m); }
static void cholesky_solve(const Matrix& m, const Vector& b, Vector& x) { gsl_linalg_complex_cholesky_solve(m,b,x); }
static void prod(const Matrix& m, const Vector& v, Vector& x)
{ gsl_blas_zgemv(CblasNoTrans,gsl_complex_rect(1,0),m,v,gsl_complex_rect(0,0),x); }
static void eigen_symm(const Matrix& m, gsl_vector* &eval, Matrix& evec)
{
gsl_eigen_hermv_workspace * w = gsl_eigen_hermv_alloc(m->size1);
Matrix a = createMatrix(m->size1, m->size2);
gsl_matrix_complex_memcpy(a, m);
gsl_eigen_hermv(a,eval,evec,w);
gsl_eigen_hermv_sort(eval, evec, GSL_EIGEN_SORT_VAL_ASC);
gsl_eigen_hermv_free(w);
free(a);
}
static void eigen_symm_gen(const Matrix& m, const Matrix& _b, gsl_vector* &eval, Matrix& evec)
{
gsl_eigen_genhermv_workspace * w = gsl_eigen_genhermv_alloc(m->size1);
Matrix a = createMatrix(m->size1, m->size2);
Matrix b = createMatrix(_b->size1, _b->size2);
gsl_matrix_complex_memcpy(a, m);
gsl_matrix_complex_memcpy(b, _b);
gsl_eigen_genhermv(a,b,eval,evec,w);
gsl_eigen_hermv_sort(eval, evec, GSL_EIGEN_SORT_VAL_ASC);
gsl_eigen_genhermv_free(w);
free(a);
}
};
template<typename MatrixType>
void convert(const MatrixType& m, gsl_matrix* &res)
{
// if (res)
// gsl_matrix_free(res);
res = gsl_matrix_alloc(m.rows(), m.cols());
for (int i=0 ; i<m.rows() ; ++i)
for (int j=0 ; j<m.cols(); ++j)
gsl_matrix_set(res, i, j, m(i,j));
}
template<typename MatrixType>
void convert(const gsl_matrix* m, MatrixType& res)
{
res.resize(int(m->size1), int(m->size2));
for (int i=0 ; i<res.rows() ; ++i)
for (int j=0 ; j<res.cols(); ++j)
res(i,j) = gsl_matrix_get(m,i,j);
}
template<typename VectorType>
void convert(const VectorType& m, gsl_vector* &res)
{
if (res) gsl_vector_free(res);
res = gsl_vector_alloc(m.size());
for (int i=0 ; i<m.size() ; ++i)
gsl_vector_set(res, i, m[i]);
}
template<typename VectorType>
void convert(const gsl_vector* m, VectorType& res)
{
res.resize (m->size);
for (int i=0 ; i<res.rows() ; ++i)
res[i] = gsl_vector_get(m, i);
}
template<typename MatrixType>
void convert(const MatrixType& m, gsl_matrix_complex* &res)
{
res = gsl_matrix_complex_alloc(m.rows(), m.cols());
for (int i=0 ; i<m.rows() ; ++i)
for (int j=0 ; j<m.cols(); ++j)
{
gsl_matrix_complex_set(res, i, j,
gsl_complex_rect(m(i,j).real(), m(i,j).imag()));
}
}
template<typename MatrixType>
void convert(const gsl_matrix_complex* m, MatrixType& res)
{
res.resize(int(m->size1), int(m->size2));
for (int i=0 ; i<res.rows() ; ++i)
for (int j=0 ; j<res.cols(); ++j)
res(i,j) = typename MatrixType::Scalar(
GSL_REAL(gsl_matrix_complex_get(m,i,j)),
GSL_IMAG(gsl_matrix_complex_get(m,i,j)));
}
template<typename VectorType>
void convert(const VectorType& m, gsl_vector_complex* &res)
{
res = gsl_vector_complex_alloc(m.size());
for (int i=0 ; i<m.size() ; ++i)
gsl_vector_complex_set(res, i, gsl_complex_rect(m[i].real(), m[i].imag()));
}
template<typename VectorType>
void convert(const gsl_vector_complex* m, VectorType& res)
{
res.resize(m->size);
for (int i=0 ; i<res.rows() ; ++i)
res[i] = typename VectorType::Scalar(
GSL_REAL(gsl_vector_complex_get(m, i)),
GSL_IMAG(gsl_vector_complex_get(m, i)));
}
}
#endif // EIGEN_GSL_HELPER

10
test/inverse.cpp
View File

@@ -35,13 +35,21 @@ template<typename MatrixType> void inverse(const MatrixType& m)
int cols = m.cols();
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;
MatrixType m1 = test_random_matrix<MatrixType>(rows, cols),
m2 = test_random_matrix<MatrixType>(rows, cols),
m2(rows, cols),
mzero = MatrixType::Zero(rows, cols),
identity = MatrixType::Identity(rows, rows);
if (ei_is_same_type<RealScalar,float>::ret)
{
// let's build a more stable to inverse matrix
MatrixType a = test_random_matrix<MatrixType>(rows,cols);
m1 += m1 * m1.adjoint() + a * a.adjoint();
}
m2 = m1.inverse();
VERIFY_IS_APPROX(m1, m2.inverse() );

10
test/linearstructure.cpp
View File

@@ -41,15 +41,10 @@ template<typename MatrixType> void linearStructure(const MatrixType& m)
MatrixType m1 = test_random_matrix<MatrixType>(rows, cols),
m2 = test_random_matrix<MatrixType>(rows, cols),
m3(rows, cols),
mzero = MatrixType::Zero(rows, cols),
identity = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
::Identity(rows, rows),
square = test_random_matrix<Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> >(rows, rows);
VectorType v1 = test_random_matrix<VectorType>(rows),
v2 = test_random_matrix<VectorType>(rows),
vzero = VectorType::Zero(rows);
mzero = MatrixType::Zero(rows, cols);
Scalar s1 = test_random<Scalar>();
while (ei_abs(s1)<1e-3) s1 = test_random<Scalar>();
int r = ei_random<int>(0, rows-1),
c = ei_random<int>(0, cols-1);
@@ -94,6 +89,7 @@ void test_linearstructure()
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST( linearStructure(Matrix<float, 1, 1>()) );
CALL_SUBTEST( linearStructure(Matrix2f()) );
CALL_SUBTEST( linearStructure(Vector3d()) );
CALL_SUBTEST( linearStructure(Matrix4d()) );
CALL_SUBTEST( linearStructure(MatrixXcf(3, 3)) );
CALL_SUBTEST( linearStructure(MatrixXf(8, 12)) );

12
test/lu.cpp
View File

@@ -51,7 +51,8 @@ template<typename MatrixType> void lu_non_invertible()
/* this test covers the following files:
LU.h
*/
int rows = ei_random<int>(10,200), cols = ei_random<int>(10,200), cols2 = ei_random<int>(10,200);
// NOTE lu.dimensionOfKernel() fails most of the time for rows or cols smaller that 11
int rows = ei_random<int>(11,200), cols = ei_random<int>(11,200), cols2 = ei_random<int>(11,200);
int rank = ei_random<int>(1, std::min(rows, cols)-1);
MatrixType m1(rows, cols), m2(cols, cols2), m3(rows, cols2), k(1,1);
@@ -91,6 +92,13 @@ template<typename MatrixType> void lu_invertible()
MatrixType m1(size, size), m2(size, size), m3(size, size);
m1 = test_random_matrix<MatrixType>(size,size);
if (ei_is_same_type<RealScalar,float>::ret)
{
// let's build a matrix more stable to inverse
MatrixType a = test_random_matrix<MatrixType>(size,size*2);
m1 += a * a.adjoint();
}
LU<MatrixType> lu(m1);
VERIFY(0 == lu.dimensionOfKernel());
VERIFY(size == lu.rank());
@@ -99,7 +107,7 @@ template<typename MatrixType> void lu_invertible()
VERIFY(lu.isInvertible());
m3 = test_random_matrix<MatrixType>(size,size);
lu.solve(m3, &m2);
VERIFY(m3.isApprox(m1*m2, test_precision<RealScalar>()*RealScalar(100))); // FIXME
VERIFY_IS_APPROX(m3, m1*m2);
VERIFY_IS_APPROX(m2, lu.inverse()*m3);
m3 = test_random_matrix<MatrixType>(size,size);
VERIFY(lu.solve(m3, &m2));

1
test/product_small.cpp
View File

@@ -29,6 +29,7 @@ void test_product_small()
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST( product(Matrix<float, 3, 2>()) );
CALL_SUBTEST( product(Matrix<int, 3, 5>()) );
CALL_SUBTEST( product(Matrix3d()) );
CALL_SUBTEST( product(Matrix4d()) );
CALL_SUBTEST( product(Matrix4f()) );
}

2
test/runtest.sh
View File

@@ -10,7 +10,7 @@ cyan='\E[36m'
white='\E[37m'
if make test_$1 > /dev/null 2> .runtest.log ; then
if ! ./test_$1 > /dev/null 2> .runtest.log ; then
if ! ./test_$1 r20 > /dev/null 2> .runtest.log ; then
echo -e $red Test $1 failed: $black
echo -e $blue
cat .runtest.log

19
test/svd.cpp
View File

@@ -34,11 +34,16 @@ template<typename MatrixType> void svd(const MatrixType& m)
int cols = m.cols();
typedef typename MatrixType::Scalar Scalar;
MatrixType a = MatrixType::Random(rows,cols);
typedef typename NumTraits<Scalar>::Real RealScalar;
MatrixType a = test_random_matrix<MatrixType>(rows,cols);
Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> b =
Matrix<Scalar, MatrixType::RowsAtCompileTime, 1>::Random(rows,1);
test_random_matrix<Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> >(rows,1);
Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> x(cols,1), x2(cols,1);
RealScalar largerEps = test_precision<RealScalar>();
if (ei_is_same_type<RealScalar,float>::ret)
largerEps = 1e-3f;
SVD<MatrixType> svd(a);
MatrixType sigma = MatrixType::Zero(rows,cols);
MatrixType matU = MatrixType::Zero(rows,rows);
@@ -49,8 +54,14 @@ template<typename MatrixType> void svd(const MatrixType& m)
if (rows==cols)
{
if (ei_is_same_type<RealScalar,float>::ret)
{
MatrixType a1 = test_random_matrix<MatrixType>(rows,cols);
a += a * a.adjoint() + a1 * a1.adjoint();
}
SVD<MatrixType> svd(a);
svd.solve(b, &x);
VERIFY_IS_APPROX(a * x, b);
VERIFY_IS_APPROX(a * x,b);
}
}
@@ -60,7 +71,7 @@ void test_svd()
CALL_SUBTEST( svd(Matrix3f()) );
CALL_SUBTEST( svd(Matrix4d()) );
CALL_SUBTEST( svd(MatrixXf(7,7)) );
CALL_SUBTEST( svd(MatrixXf(14,7)) );
CALL_SUBTEST( svd(MatrixXd(14,7)) );
// complex are not implemented yet
// CALL_SUBTEST( svd(MatrixXcd(6,6)) );
// CALL_SUBTEST( svd(MatrixXcf(3,3)) );

38
test/triangular.cpp
View File

@@ -30,12 +30,15 @@ template<typename MatrixType> void triangular(const MatrixType& m)
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
RealScalar largerEps = 10*test_precision<RealScalar>();
int rows = m.rows();
int cols = m.cols();
MatrixType m1 = MatrixType::Random(rows, cols),
m2 = MatrixType::Random(rows, cols),
MatrixType m1 = test_random_matrix<MatrixType>(rows, cols),
m2 = test_random_matrix<MatrixType>(rows, cols),
m3(rows, cols),
m4(rows, cols),
r1(rows, cols),
r2(rows, cols),
mzero = MatrixType::Zero(rows, cols),
@@ -44,8 +47,8 @@ template<typename MatrixType> void triangular(const MatrixType& m)
::Identity(rows, rows),
square = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
::Random(rows, rows);
VectorType v1 = VectorType::Random(rows),
v2 = VectorType::Random(rows),
VectorType v1 = test_random_matrix<VectorType>(rows),
v2 = test_random_matrix<VectorType>(rows),
vzero = VectorType::Zero(rows);
MatrixType m1up = m1.template part<Eigen::Upper>();
@@ -78,17 +81,34 @@ template<typename MatrixType> void triangular(const MatrixType& m)
m1.template part<Eigen::Lower>() = (m2.transpose() * m2).lazy();
VERIFY_IS_APPROX(m3.template part<Eigen::Lower>(), m1);
m1 = test_random_matrix<MatrixType>(rows, cols);
for (int i=0; i<rows; ++i)
while (ei_abs2(m1(i,i))<1e-3) m1(i,i) = test_random<Scalar>();
Transpose<MatrixType> trm4(m4);
// test back and forward subsitution
m3 = m1.template part<Eigen::Lower>();
VERIFY(m3.template marked<Eigen::Lower>().solveTriangular(m3).cwise().abs().isIdentity(test_precision<RealScalar>()));
VERIFY(m3.transpose().template marked<Eigen::Upper>()
.solveTriangular(m3.transpose()).cwise().abs().isIdentity(test_precision<RealScalar>()));
// check M * inv(L) using in place API
m4 = m3;
m3.transpose().template marked<Eigen::Upper>().solveTriangularInPlace(trm4);
VERIFY(m4.cwise().abs().isIdentity(test_precision<RealScalar>()));
m3 = m1.template part<Eigen::Upper>();
VERIFY(m3.template marked<Eigen::Upper>().solveTriangular(m3).cwise().abs().isIdentity(test_precision<RealScalar>()));
VERIFY(m3.transpose().template marked<Eigen::Lower>()
.solveTriangular(m3.transpose()).cwise().abs().isIdentity(test_precision<RealScalar>()));
// check M * inv(U) using in place API
m4 = m3;
m3.transpose().template marked<Eigen::Lower>().solveTriangularInPlace(trm4);
VERIFY(m4.cwise().abs().isIdentity(test_precision<RealScalar>()));
// FIXME these tests failed due to numerical issues
// m1 = MatrixType::Random(rows, cols);
// VERIFY_IS_APPROX(m1.template part<Eigen::Upper>().eval() * (m1.template part<Eigen::Upper>().solveTriangular(m2)), m2);
// VERIFY_IS_APPROX(m1.template part<Eigen::Lower>().eval() * (m1.template part<Eigen::Lower>().solveTriangular(m2)), m2);
m3 = m1.template part<Eigen::Upper>();
VERIFY(m2.isApprox(m3 * (m3.template marked<Eigen::Upper>().solveTriangular(m2)), largerEps));
m3 = m1.template part<Eigen::Lower>();
VERIFY(m2.isApprox(m3 * (m3.template marked<Eigen::Lower>().solveTriangular(m2)), largerEps));
VERIFY((m1.template part<Eigen::Upper>() * m2.template part<Eigen::Upper>()).isUpper());
@@ -102,6 +122,6 @@ void test_triangular()
CALL_SUBTEST( triangular(Matrix3d()) );
CALL_SUBTEST( triangular(MatrixXcf(4, 4)) );
CALL_SUBTEST( triangular(Matrix<std::complex<float>,8, 8>()) );
CALL_SUBTEST( triangular(MatrixXf(85,85)) );
CALL_SUBTEST( triangular(MatrixXd(17,17)) );
}
}