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// 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>
#include "solverbase.h"
using namespace std;
template<typename MatrixType>
typename MatrixType::RealScalar matrix_l1_norm(const MatrixType& m) {
return m.cwiseAbs().colwise().sum().maxCoeff();
}
template<typename MatrixType> void lu_non_invertible()
{
STATIC_CHECK(( internal::is_same<typename FullPivLU<MatrixType>::StorageIndex,int>::value ));
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));
// The kernel of the zero matrix is the entire space, and thus is an invertible matrix of dimensions cols.
KernelMatrixType kernel = MatrixType::Zero(rows,cols).fullPivLu().kernel();
VERIFY((kernel.fullPivLu().isInvertible()));
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_IS_MUCH_SMALLER_THAN((m1 * m1kernel), m1);
VERIFY(m1image.fullPivLu().rank() == rank);
VERIFY_IS_APPROX(m1 * m1.adjoint() * m1image, m1image);
check_solverbase<CMatrixType, MatrixType>(m1, lu, rows, cols, cols2);
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:
FullPivLU.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());
check_solverbase<MatrixType, MatrixType>(m1, lu, size, size, size);
MatrixType m1_inverse = lu.inverse();
m3 = MatrixType::Random(size,size);
m2 = lu.solve(m3);
VERIFY_IS_APPROX(m2, m1_inverse*m3);
RealScalar rcond = (RealScalar(1) / matrix_l1_norm(m1)) / matrix_l1_norm(m1_inverse);
const RealScalar rcond_est = lu.rcond();
// Verify that the estimated condition number is within a factor of 10 of the
// truth.
VERIFY(rcond_est > rcond / 10 && rcond_est < rcond * 10);
// 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(Index size = MatrixType::ColsAtCompileTime)
{
/* this test covers the following files:
PartialPivLU.h
*/
typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
MatrixType m1(size, size), m2(size, size), m3(size, size);
m1.setRandom();
PartialPivLU<MatrixType> plu(m1);
STATIC_CHECK(( internal::is_same<typename PartialPivLU<MatrixType>::StorageIndex,int>::value ));
VERIFY_IS_APPROX(m1, plu.reconstructedMatrix());
check_solverbase<MatrixType, MatrixType>(m1, plu, size, size, size);
MatrixType m1_inverse = plu.inverse();
m3 = MatrixType::Random(size,size);
m2 = plu.solve(m3);
VERIFY_IS_APPROX(m2, m1_inverse*m3);
RealScalar rcond = (RealScalar(1) / matrix_l1_norm(m1)) / matrix_l1_norm(m1_inverse);
const RealScalar rcond_est = plu.rcond();
// Verify that the estimate is within a factor of 10 of the truth.
VERIFY(rcond_est > rcond / 10 && rcond_est < rcond * 10);
}
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.transpose().solve(tmp))
VERIFY_RAISES_ASSERT(lu.adjoint().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.transpose().solve(tmp))
VERIFY_RAISES_ASSERT(plu.adjoint().solve(tmp))
VERIFY_RAISES_ASSERT(plu.determinant())
VERIFY_RAISES_ASSERT(plu.inverse())
}
EIGEN_DECLARE_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_1( lu_partial_piv<Matrix3f>() );
CALL_SUBTEST_2( (lu_non_invertible<Matrix<double, 4, 6> >()) );
CALL_SUBTEST_2( (lu_verify_assert<Matrix<double, 4, 6> >()) );
CALL_SUBTEST_2( lu_partial_piv<Matrix2d>() );
CALL_SUBTEST_2( lu_partial_piv<Matrix4d>() );
CALL_SUBTEST_2( (lu_partial_piv<Matrix<double,6,6> >()) );
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>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE)) );
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>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE)) );
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); );
}
}
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