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86e0ed81f8
* Get rid of code-duplication for real vs. complex matrices. * Fix flipped arguments to select. * Make the condition estimation functions free functions. * Use Vector::Unit() to generate canonical unit vectors. * Misc. cleanup.
282 lines
9.5 KiB
C++
282 lines
9.5 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2008-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#include "main.h"
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#include <Eigen/LU>
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using namespace std;
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template<typename MatrixType>
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typename MatrixType::RealScalar matrix_l1_norm(const MatrixType& m) {
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return m.cwiseAbs().colwise().sum().maxCoeff();
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}
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template<typename MatrixType> void lu_non_invertible()
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{
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typedef typename MatrixType::Index Index;
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typedef typename MatrixType::RealScalar RealScalar;
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/* this test covers the following files:
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LU.h
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*/
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Index rows, cols, cols2;
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if(MatrixType::RowsAtCompileTime==Dynamic)
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{
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rows = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE);
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}
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else
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{
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rows = MatrixType::RowsAtCompileTime;
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}
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if(MatrixType::ColsAtCompileTime==Dynamic)
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{
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cols = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE);
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cols2 = internal::random<int>(2,EIGEN_TEST_MAX_SIZE);
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}
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else
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{
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cols2 = cols = MatrixType::ColsAtCompileTime;
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}
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enum {
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RowsAtCompileTime = MatrixType::RowsAtCompileTime,
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ColsAtCompileTime = MatrixType::ColsAtCompileTime
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};
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typedef typename internal::kernel_retval_base<FullPivLU<MatrixType> >::ReturnType KernelMatrixType;
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typedef typename internal::image_retval_base<FullPivLU<MatrixType> >::ReturnType ImageMatrixType;
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typedef Matrix<typename MatrixType::Scalar, ColsAtCompileTime, ColsAtCompileTime>
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CMatrixType;
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typedef Matrix<typename MatrixType::Scalar, RowsAtCompileTime, RowsAtCompileTime>
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RMatrixType;
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Index rank = internal::random<Index>(1, (std::min)(rows, cols)-1);
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// The image of the zero matrix should consist of a single (zero) column vector
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VERIFY((MatrixType::Zero(rows,cols).fullPivLu().image(MatrixType::Zero(rows,cols)).cols() == 1));
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MatrixType m1(rows, cols), m3(rows, cols2);
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CMatrixType m2(cols, cols2);
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createRandomPIMatrixOfRank(rank, rows, cols, m1);
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FullPivLU<MatrixType> lu;
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// The special value 0.01 below works well in tests. Keep in mind that we're only computing the rank
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// of singular values are either 0 or 1.
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// So it's not clear at all that the epsilon should play any role there.
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lu.setThreshold(RealScalar(0.01));
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lu.compute(m1);
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MatrixType u(rows,cols);
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u = lu.matrixLU().template triangularView<Upper>();
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RMatrixType l = RMatrixType::Identity(rows,rows);
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l.block(0,0,rows,(std::min)(rows,cols)).template triangularView<StrictlyLower>()
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= lu.matrixLU().block(0,0,rows,(std::min)(rows,cols));
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VERIFY_IS_APPROX(lu.permutationP() * m1 * lu.permutationQ(), l*u);
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KernelMatrixType m1kernel = lu.kernel();
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ImageMatrixType m1image = lu.image(m1);
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VERIFY_IS_APPROX(m1, lu.reconstructedMatrix());
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VERIFY(rank == lu.rank());
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VERIFY(cols - lu.rank() == lu.dimensionOfKernel());
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VERIFY(!lu.isInjective());
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VERIFY(!lu.isInvertible());
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VERIFY(!lu.isSurjective());
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VERIFY((m1 * m1kernel).isMuchSmallerThan(m1));
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VERIFY(m1image.fullPivLu().rank() == rank);
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VERIFY_IS_APPROX(m1 * m1.adjoint() * m1image, m1image);
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m2 = CMatrixType::Random(cols,cols2);
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m3 = m1*m2;
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m2 = CMatrixType::Random(cols,cols2);
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// test that the code, which does resize(), may be applied to an xpr
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m2.block(0,0,m2.rows(),m2.cols()) = lu.solve(m3);
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VERIFY_IS_APPROX(m3, m1*m2);
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// test solve with transposed
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m3 = MatrixType::Random(rows,cols2);
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m2 = m1.transpose()*m3;
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m3 = MatrixType::Random(rows,cols2);
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lu.template _solve_impl_transposed<false>(m2, m3);
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VERIFY_IS_APPROX(m2, m1.transpose()*m3);
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m3 = MatrixType::Random(rows,cols2);
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m3 = lu.transpose().solve(m2);
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VERIFY_IS_APPROX(m2, m1.transpose()*m3);
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// test solve with conjugate transposed
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m3 = MatrixType::Random(rows,cols2);
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m2 = m1.adjoint()*m3;
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m3 = MatrixType::Random(rows,cols2);
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lu.template _solve_impl_transposed<true>(m2, m3);
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VERIFY_IS_APPROX(m2, m1.adjoint()*m3);
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m3 = MatrixType::Random(rows,cols2);
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m3 = lu.adjoint().solve(m2);
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VERIFY_IS_APPROX(m2, m1.adjoint()*m3);
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}
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template<typename MatrixType> void lu_invertible()
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{
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/* this test covers the following files:
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LU.h
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*/
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typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
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Index size = MatrixType::RowsAtCompileTime;
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if( size==Dynamic)
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size = internal::random<Index>(1,EIGEN_TEST_MAX_SIZE);
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MatrixType m1(size, size), m2(size, size), m3(size, size);
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FullPivLU<MatrixType> lu;
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lu.setThreshold(RealScalar(0.01));
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do {
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m1 = MatrixType::Random(size,size);
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lu.compute(m1);
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} while(!lu.isInvertible());
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VERIFY_IS_APPROX(m1, lu.reconstructedMatrix());
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VERIFY(0 == lu.dimensionOfKernel());
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VERIFY(lu.kernel().cols() == 1); // the kernel() should consist of a single (zero) column vector
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VERIFY(size == lu.rank());
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VERIFY(lu.isInjective());
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VERIFY(lu.isSurjective());
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VERIFY(lu.isInvertible());
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VERIFY(lu.image(m1).fullPivLu().isInvertible());
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m3 = MatrixType::Random(size,size);
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m2 = lu.solve(m3);
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VERIFY_IS_APPROX(m3, m1*m2);
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MatrixType m1_inverse = lu.inverse();
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VERIFY_IS_APPROX(m2, m1_inverse*m3);
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RealScalar rcond = (RealScalar(1) / matrix_l1_norm(m1)) / matrix_l1_norm(m1_inverse);
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const RealScalar rcond_est = lu.rcond();
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// Verify that the estimated condition number is within a factor of 10 of the
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// truth.
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VERIFY(rcond_est > rcond / 10 && rcond_est < rcond * 10);
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// test solve with transposed
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lu.template _solve_impl_transposed<false>(m3, m2);
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VERIFY_IS_APPROX(m3, m1.transpose()*m2);
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m3 = MatrixType::Random(size,size);
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m3 = lu.transpose().solve(m2);
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VERIFY_IS_APPROX(m2, m1.transpose()*m3);
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// test solve with conjugate transposed
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lu.template _solve_impl_transposed<true>(m3, m2);
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VERIFY_IS_APPROX(m3, m1.adjoint()*m2);
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m3 = MatrixType::Random(size,size);
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m3 = lu.adjoint().solve(m2);
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VERIFY_IS_APPROX(m2, m1.adjoint()*m3);
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// Regression test for Bug 302
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MatrixType m4 = MatrixType::Random(size,size);
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VERIFY_IS_APPROX(lu.solve(m3*m4), lu.solve(m3)*m4);
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}
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template<typename MatrixType> void lu_partial_piv()
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{
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/* this test covers the following files:
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PartialPivLU.h
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*/
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typedef typename MatrixType::Index Index;
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typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
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Index size = internal::random<Index>(1,4);
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MatrixType m1(size, size), m2(size, size), m3(size, size);
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m1.setRandom();
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PartialPivLU<MatrixType> plu(m1);
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VERIFY_IS_APPROX(m1, plu.reconstructedMatrix());
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m3 = MatrixType::Random(size,size);
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m2 = plu.solve(m3);
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VERIFY_IS_APPROX(m3, m1*m2);
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MatrixType m1_inverse = plu.inverse();
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VERIFY_IS_APPROX(m2, m1_inverse*m3);
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RealScalar rcond = (RealScalar(1) / matrix_l1_norm(m1)) / matrix_l1_norm(m1_inverse);
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const RealScalar rcond_est = plu.rcond();
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// Verify that the estimate is within a factor of 10 of the truth.
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VERIFY(rcond_est > rcond / 10 && rcond_est < rcond * 10);
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// test solve with transposed
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plu.template _solve_impl_transposed<false>(m3, m2);
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VERIFY_IS_APPROX(m3, m1.transpose()*m2);
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m3 = MatrixType::Random(size,size);
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m3 = plu.transpose().solve(m2);
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VERIFY_IS_APPROX(m2, m1.transpose()*m3);
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// test solve with conjugate transposed
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plu.template _solve_impl_transposed<true>(m3, m2);
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VERIFY_IS_APPROX(m3, m1.adjoint()*m2);
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m3 = MatrixType::Random(size,size);
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m3 = plu.adjoint().solve(m2);
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VERIFY_IS_APPROX(m2, m1.adjoint()*m3);
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}
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template<typename MatrixType> void lu_verify_assert()
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{
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MatrixType tmp;
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FullPivLU<MatrixType> lu;
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VERIFY_RAISES_ASSERT(lu.matrixLU())
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VERIFY_RAISES_ASSERT(lu.permutationP())
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VERIFY_RAISES_ASSERT(lu.permutationQ())
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VERIFY_RAISES_ASSERT(lu.kernel())
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VERIFY_RAISES_ASSERT(lu.image(tmp))
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VERIFY_RAISES_ASSERT(lu.solve(tmp))
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VERIFY_RAISES_ASSERT(lu.determinant())
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VERIFY_RAISES_ASSERT(lu.rank())
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VERIFY_RAISES_ASSERT(lu.dimensionOfKernel())
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VERIFY_RAISES_ASSERT(lu.isInjective())
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VERIFY_RAISES_ASSERT(lu.isSurjective())
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VERIFY_RAISES_ASSERT(lu.isInvertible())
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VERIFY_RAISES_ASSERT(lu.inverse())
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PartialPivLU<MatrixType> plu;
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VERIFY_RAISES_ASSERT(plu.matrixLU())
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VERIFY_RAISES_ASSERT(plu.permutationP())
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VERIFY_RAISES_ASSERT(plu.solve(tmp))
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VERIFY_RAISES_ASSERT(plu.determinant())
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VERIFY_RAISES_ASSERT(plu.inverse())
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}
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void test_lu()
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{
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for(int i = 0; i < g_repeat; i++) {
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CALL_SUBTEST_1( lu_non_invertible<Matrix3f>() );
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CALL_SUBTEST_1( lu_invertible<Matrix3f>() );
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CALL_SUBTEST_1( lu_verify_assert<Matrix3f>() );
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CALL_SUBTEST_2( (lu_non_invertible<Matrix<double, 4, 6> >()) );
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CALL_SUBTEST_2( (lu_verify_assert<Matrix<double, 4, 6> >()) );
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CALL_SUBTEST_3( lu_non_invertible<MatrixXf>() );
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CALL_SUBTEST_3( lu_invertible<MatrixXf>() );
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CALL_SUBTEST_3( lu_verify_assert<MatrixXf>() );
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CALL_SUBTEST_4( lu_non_invertible<MatrixXd>() );
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CALL_SUBTEST_4( lu_invertible<MatrixXd>() );
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CALL_SUBTEST_4( lu_partial_piv<MatrixXd>() );
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CALL_SUBTEST_4( lu_verify_assert<MatrixXd>() );
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CALL_SUBTEST_5( lu_non_invertible<MatrixXcf>() );
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CALL_SUBTEST_5( lu_invertible<MatrixXcf>() );
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CALL_SUBTEST_5( lu_verify_assert<MatrixXcf>() );
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CALL_SUBTEST_6( lu_non_invertible<MatrixXcd>() );
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CALL_SUBTEST_6( lu_invertible<MatrixXcd>() );
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CALL_SUBTEST_6( lu_partial_piv<MatrixXcd>() );
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CALL_SUBTEST_6( lu_verify_assert<MatrixXcd>() );
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CALL_SUBTEST_7(( lu_non_invertible<Matrix<float,Dynamic,16> >() ));
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// Test problem size constructors
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CALL_SUBTEST_9( PartialPivLU<MatrixXf>(10) );
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CALL_SUBTEST_9( FullPivLU<MatrixXf>(10, 20); );
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}
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}
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