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122 lines
4.0 KiB
122 lines
4.0 KiB
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra. Eigen itself is part of the KDE project.
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//
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// Copyright (C) 2008 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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template<typename Derived>
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void doSomeRankPreservingOperations(Eigen::MatrixBase<Derived>& m)
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{
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typedef typename Derived::RealScalar RealScalar;
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for(int a = 0; a < 3*(m.rows()+m.cols()); a++)
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{
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RealScalar d = Eigen::ei_random<RealScalar>(-1,1);
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int i = Eigen::ei_random<int>(0,m.rows()-1); // i is a random row number
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int j;
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do {
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j = Eigen::ei_random<int>(0,m.rows()-1);
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} while (i==j); // j is another one (must be different)
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m.row(i) += d * m.row(j);
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i = Eigen::ei_random<int>(0,m.cols()-1); // i is a random column number
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do {
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j = Eigen::ei_random<int>(0,m.cols()-1);
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} while (i==j); // j is another one (must be different)
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m.col(i) += d * m.col(j);
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}
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}
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template<typename MatrixType> void lu_non_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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// NOTE there seems to be a problem with too small sizes -- could easily lie in the doSomeRankPreservingOperations function
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int rows = ei_random<int>(20,200), cols = ei_random<int>(20,200), cols2 = ei_random<int>(20,200);
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int rank = ei_random<int>(1, std::min(rows, cols)-1);
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MatrixType m1(rows, cols), m2(cols, cols2), m3(rows, cols2), k(1,1);
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m1 = MatrixType::Random(rows,cols);
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if(rows <= cols)
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for(int i = rank; i < rows; i++) m1.row(i).setZero();
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else
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for(int i = rank; i < cols; i++) m1.col(i).setZero();
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doSomeRankPreservingOperations(m1);
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LU<MatrixType> lu(m1);
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typename LU<MatrixType>::KernelResultType m1kernel = lu.kernel();
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typename LU<MatrixType>::ImageResultType m1image = lu.image();
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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() == (lu.rank() == rows));
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VERIFY((m1 * m1kernel).isMuchSmallerThan(m1));
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VERIFY(m1image.lu().rank() == rank);
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MatrixType sidebyside(m1.rows(), m1.cols() + m1image.cols());
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sidebyside << m1, m1image;
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VERIFY(sidebyside.lu().rank() == rank);
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m2 = MatrixType::Random(cols,cols2);
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m3 = m1*m2;
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m2 = MatrixType::Random(cols,cols2);
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lu.solve(m3, &m2);
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VERIFY_IS_APPROX(m3, m1*m2);
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/* solve now always returns true
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m3 = MatrixType::Random(rows,cols2);
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VERIFY(!lu.solve(m3, &m2));
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*/
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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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int size = ei_random<int>(10,200);
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MatrixType m1(size, size), m2(size, size), m3(size, size);
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m1 = MatrixType::Random(size,size);
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if (ei_is_same_type<RealScalar,float>::ret)
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{
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// let's build a matrix more stable to inverse
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MatrixType a = MatrixType::Random(size,size*2);
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m1 += a * a.adjoint();
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}
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LU<MatrixType> lu(m1);
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VERIFY(0 == lu.dimensionOfKernel());
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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().lu().isInvertible());
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m3 = MatrixType::Random(size,size);
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lu.solve(m3, &m2);
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VERIFY_IS_APPROX(m3, m1*m2);
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VERIFY_IS_APPROX(m2, lu.inverse()*m3);
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m3 = MatrixType::Random(size,size);
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VERIFY(lu.solve(m3, &m2));
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}
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void test_eigen2_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<MatrixXf>() );
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CALL_SUBTEST_2( lu_non_invertible<MatrixXd>() );
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CALL_SUBTEST_3( lu_non_invertible<MatrixXcf>() );
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CALL_SUBTEST_4( lu_non_invertible<MatrixXcd>() );
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CALL_SUBTEST_1( lu_invertible<MatrixXf>() );
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CALL_SUBTEST_2( lu_invertible<MatrixXd>() );
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CALL_SUBTEST_3( lu_invertible<MatrixXcf>() );
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CALL_SUBTEST_4( lu_invertible<MatrixXcd>() );
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}
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}
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