mirror of
https://gitlab.com/libeigen/eigen.git
synced 2024-12-21 07:19:46 +08:00
211 lines
6.9 KiB
C++
211 lines
6.9 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
|
|
// for linear algebra.
|
|
//
|
|
// Copyright (C) 2008-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
|
|
//
|
|
// 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 <Eigen/LU>
|
|
using namespace std;
|
|
|
|
template<typename MatrixType> void lu_non_invertible()
|
|
{
|
|
typedef typename MatrixType::Index Index;
|
|
typedef typename MatrixType::RealScalar RealScalar;
|
|
/* this test covers the following files:
|
|
LU.h
|
|
*/
|
|
Index rows, cols, cols2;
|
|
if(MatrixType::RowsAtCompileTime==Dynamic)
|
|
{
|
|
rows = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE);
|
|
}
|
|
else
|
|
{
|
|
rows = MatrixType::RowsAtCompileTime;
|
|
}
|
|
if(MatrixType::ColsAtCompileTime==Dynamic)
|
|
{
|
|
cols = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE);
|
|
cols2 = internal::random<int>(2,EIGEN_TEST_MAX_SIZE);
|
|
}
|
|
else
|
|
{
|
|
cols2 = cols = MatrixType::ColsAtCompileTime;
|
|
}
|
|
|
|
enum {
|
|
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
|
ColsAtCompileTime = MatrixType::ColsAtCompileTime
|
|
};
|
|
typedef typename internal::kernel_retval_base<FullPivLU<MatrixType> >::ReturnType KernelMatrixType;
|
|
typedef typename internal::image_retval_base<FullPivLU<MatrixType> >::ReturnType ImageMatrixType;
|
|
typedef Matrix<typename MatrixType::Scalar, ColsAtCompileTime, ColsAtCompileTime>
|
|
CMatrixType;
|
|
typedef Matrix<typename MatrixType::Scalar, RowsAtCompileTime, RowsAtCompileTime>
|
|
RMatrixType;
|
|
|
|
Index rank = internal::random<Index>(1, (std::min)(rows, cols)-1);
|
|
|
|
// The image of the zero matrix should consist of a single (zero) column vector
|
|
VERIFY((MatrixType::Zero(rows,cols).fullPivLu().image(MatrixType::Zero(rows,cols)).cols() == 1));
|
|
|
|
MatrixType m1(rows, cols), m3(rows, cols2);
|
|
CMatrixType m2(cols, cols2);
|
|
createRandomPIMatrixOfRank(rank, rows, cols, m1);
|
|
|
|
FullPivLU<MatrixType> lu;
|
|
|
|
// The special value 0.01 below works well in tests. Keep in mind that we're only computing the rank
|
|
// of singular values are either 0 or 1.
|
|
// So it's not clear at all that the epsilon should play any role there.
|
|
lu.setThreshold(RealScalar(0.01));
|
|
lu.compute(m1);
|
|
|
|
MatrixType u(rows,cols);
|
|
u = lu.matrixLU().template triangularView<Upper>();
|
|
RMatrixType l = RMatrixType::Identity(rows,rows);
|
|
l.block(0,0,rows,(std::min)(rows,cols)).template triangularView<StrictlyLower>()
|
|
= lu.matrixLU().block(0,0,rows,(std::min)(rows,cols));
|
|
|
|
VERIFY_IS_APPROX(lu.permutationP() * m1 * lu.permutationQ(), l*u);
|
|
|
|
KernelMatrixType m1kernel = lu.kernel();
|
|
ImageMatrixType m1image = lu.image(m1);
|
|
|
|
VERIFY_IS_APPROX(m1, lu.reconstructedMatrix());
|
|
VERIFY(rank == lu.rank());
|
|
VERIFY(cols - lu.rank() == lu.dimensionOfKernel());
|
|
VERIFY(!lu.isInjective());
|
|
VERIFY(!lu.isInvertible());
|
|
VERIFY(!lu.isSurjective());
|
|
VERIFY((m1 * m1kernel).isMuchSmallerThan(m1));
|
|
VERIFY(m1image.fullPivLu().rank() == rank);
|
|
VERIFY_IS_APPROX(m1 * m1.adjoint() * m1image, m1image);
|
|
|
|
m2 = CMatrixType::Random(cols,cols2);
|
|
m3 = m1*m2;
|
|
m2 = CMatrixType::Random(cols,cols2);
|
|
// test that the code, which does resize(), may be applied to an xpr
|
|
m2.block(0,0,m2.rows(),m2.cols()) = lu.solve(m3);
|
|
VERIFY_IS_APPROX(m3, m1*m2);
|
|
}
|
|
|
|
template<typename MatrixType> void lu_invertible()
|
|
{
|
|
/* this test covers the following files:
|
|
LU.h
|
|
*/
|
|
typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
|
|
Index size = MatrixType::RowsAtCompileTime;
|
|
if( size==Dynamic)
|
|
size = internal::random<Index>(1,EIGEN_TEST_MAX_SIZE);
|
|
|
|
MatrixType m1(size, size), m2(size, size), m3(size, size);
|
|
FullPivLU<MatrixType> lu;
|
|
lu.setThreshold(RealScalar(0.01));
|
|
do {
|
|
m1 = MatrixType::Random(size,size);
|
|
lu.compute(m1);
|
|
} while(!lu.isInvertible());
|
|
|
|
VERIFY_IS_APPROX(m1, lu.reconstructedMatrix());
|
|
VERIFY(0 == lu.dimensionOfKernel());
|
|
VERIFY(lu.kernel().cols() == 1); // the kernel() should consist of a single (zero) column vector
|
|
VERIFY(size == lu.rank());
|
|
VERIFY(lu.isInjective());
|
|
VERIFY(lu.isSurjective());
|
|
VERIFY(lu.isInvertible());
|
|
VERIFY(lu.image(m1).fullPivLu().isInvertible());
|
|
m3 = MatrixType::Random(size,size);
|
|
m2 = lu.solve(m3);
|
|
VERIFY_IS_APPROX(m3, m1*m2);
|
|
VERIFY_IS_APPROX(m2, lu.inverse()*m3);
|
|
|
|
// Regression test for Bug 302
|
|
MatrixType m4 = MatrixType::Random(size,size);
|
|
VERIFY_IS_APPROX(lu.solve(m3*m4), lu.solve(m3)*m4);
|
|
}
|
|
|
|
template<typename MatrixType> void lu_partial_piv()
|
|
{
|
|
/* this test covers the following files:
|
|
PartialPivLU.h
|
|
*/
|
|
typedef typename MatrixType::Index Index;
|
|
Index rows = internal::random<Index>(1,4);
|
|
Index cols = rows;
|
|
|
|
MatrixType m1(cols, rows);
|
|
m1.setRandom();
|
|
PartialPivLU<MatrixType> plu(m1);
|
|
|
|
VERIFY_IS_APPROX(m1, plu.reconstructedMatrix());
|
|
}
|
|
|
|
template<typename MatrixType> void lu_verify_assert()
|
|
{
|
|
MatrixType tmp;
|
|
|
|
FullPivLU<MatrixType> lu;
|
|
VERIFY_RAISES_ASSERT(lu.matrixLU())
|
|
VERIFY_RAISES_ASSERT(lu.permutationP())
|
|
VERIFY_RAISES_ASSERT(lu.permutationQ())
|
|
VERIFY_RAISES_ASSERT(lu.kernel())
|
|
VERIFY_RAISES_ASSERT(lu.image(tmp))
|
|
VERIFY_RAISES_ASSERT(lu.solve(tmp))
|
|
VERIFY_RAISES_ASSERT(lu.determinant())
|
|
VERIFY_RAISES_ASSERT(lu.rank())
|
|
VERIFY_RAISES_ASSERT(lu.dimensionOfKernel())
|
|
VERIFY_RAISES_ASSERT(lu.isInjective())
|
|
VERIFY_RAISES_ASSERT(lu.isSurjective())
|
|
VERIFY_RAISES_ASSERT(lu.isInvertible())
|
|
VERIFY_RAISES_ASSERT(lu.inverse())
|
|
|
|
PartialPivLU<MatrixType> plu;
|
|
VERIFY_RAISES_ASSERT(plu.matrixLU())
|
|
VERIFY_RAISES_ASSERT(plu.permutationP())
|
|
VERIFY_RAISES_ASSERT(plu.solve(tmp))
|
|
VERIFY_RAISES_ASSERT(plu.determinant())
|
|
VERIFY_RAISES_ASSERT(plu.inverse())
|
|
}
|
|
|
|
void test_lu()
|
|
{
|
|
for(int i = 0; i < g_repeat; i++) {
|
|
CALL_SUBTEST_1( lu_non_invertible<Matrix3f>() );
|
|
CALL_SUBTEST_1( lu_invertible<Matrix3f>() );
|
|
CALL_SUBTEST_1( lu_verify_assert<Matrix3f>() );
|
|
|
|
CALL_SUBTEST_2( (lu_non_invertible<Matrix<double, 4, 6> >()) );
|
|
CALL_SUBTEST_2( (lu_verify_assert<Matrix<double, 4, 6> >()) );
|
|
|
|
CALL_SUBTEST_3( lu_non_invertible<MatrixXf>() );
|
|
CALL_SUBTEST_3( lu_invertible<MatrixXf>() );
|
|
CALL_SUBTEST_3( lu_verify_assert<MatrixXf>() );
|
|
|
|
CALL_SUBTEST_4( lu_non_invertible<MatrixXd>() );
|
|
CALL_SUBTEST_4( lu_invertible<MatrixXd>() );
|
|
CALL_SUBTEST_4( lu_partial_piv<MatrixXd>() );
|
|
CALL_SUBTEST_4( lu_verify_assert<MatrixXd>() );
|
|
|
|
CALL_SUBTEST_5( lu_non_invertible<MatrixXcf>() );
|
|
CALL_SUBTEST_5( lu_invertible<MatrixXcf>() );
|
|
CALL_SUBTEST_5( lu_verify_assert<MatrixXcf>() );
|
|
|
|
CALL_SUBTEST_6( lu_non_invertible<MatrixXcd>() );
|
|
CALL_SUBTEST_6( lu_invertible<MatrixXcd>() );
|
|
CALL_SUBTEST_6( lu_partial_piv<MatrixXcd>() );
|
|
CALL_SUBTEST_6( lu_verify_assert<MatrixXcd>() );
|
|
|
|
CALL_SUBTEST_7(( lu_non_invertible<Matrix<float,Dynamic,16> >() ));
|
|
|
|
// Test problem size constructors
|
|
CALL_SUBTEST_9( PartialPivLU<MatrixXf>(10) );
|
|
CALL_SUBTEST_9( FullPivLU<MatrixXf>(10, 20); );
|
|
}
|
|
}
|