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192 lines
6.5 KiB
C++
192 lines
6.5 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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// Eigen is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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// License as published by the Free Software Foundation; either
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// version 3 of the License, or (at your option) any later version.
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//
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// Alternatively, you can redistribute it and/or
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// modify it under the terms of the GNU General Public License as
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// published by the Free Software Foundation; either version 2 of
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// the License, or (at your option) any later version.
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//
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// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
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// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
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// GNU General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public
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// License and a copy of the GNU General Public License along with
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// Eigen. If not, see <http://www.gnu.org/licenses/>.
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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> void lu_non_invertible()
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{
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typedef typename MatrixType::Scalar Scalar;
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/* this test covers the following files:
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LU.h
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*/
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int rows, cols, cols2;
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if(MatrixType::RowsAtCompileTime==Dynamic)
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{
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rows = ei_random<int>(2,200);
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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 = ei_random<int>(2,200);
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cols2 = ei_random<int>(2,200);
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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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typedef typename ei_kernel_retval_base<FullPivLU<MatrixType> >::ReturnMatrixType KernelMatrixType;
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typedef typename ei_image_retval_base<FullPivLU<MatrixType> >::ReturnMatrixType ImageMatrixType;
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typedef Matrix<typename MatrixType::Scalar, Dynamic, Dynamic> DynamicMatrixType;
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typedef Matrix<typename MatrixType::Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime>
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CMatrixType;
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int rank = ei_random<int>(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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createRandomMatrixOfRank(rank, rows, cols, m1);
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FullPivLU<MatrixType> lu(m1);
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// FIXME need better way to construct trapezoid matrices. extend triangularView to support rectangular.
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DynamicMatrixType u(rows,cols);
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for(int i = 0; i < rows; i++)
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for(int j = 0; j < cols; j++)
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u(i,j) = i>j ? Scalar(0) : lu.matrixLU()(i,j);
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DynamicMatrixType l(rows,rows);
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for(int i = 0; i < rows; i++)
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for(int j = 0; j < rows; j++)
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l(i,j) = (i<j || j>=cols) ? Scalar(0)
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: i==j ? Scalar(1)
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: lu.matrixLU()(i,j);
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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(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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DynamicMatrixType sidebyside(m1.rows(), m1.cols() + m1image.cols());
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sidebyside << m1, m1image;
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VERIFY(sidebyside.fullPivLu().rank() == rank);
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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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}
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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>(1,200);
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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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FullPivLU<MatrixType> lu(m1);
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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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VERIFY_IS_APPROX(m2, lu.inverse()*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_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_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_verify_assert<MatrixXcd>() );
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CALL_SUBTEST_7(( lu_non_invertible<Matrix<float,Dynamic,16> >() ));
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}
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}
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