[136] | 1 | // This file is part of Eigen, a lightweight C++ template library
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| 2 | // for linear algebra. Eigen itself is part of the KDE project.
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| 3 | //
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| 4 | // Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
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| 5 | //
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| 6 | // This Source Code Form is subject to the terms of the Mozilla
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| 7 | // Public License v. 2.0. If a copy of the MPL was not distributed
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| 8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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| 9 |
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| 10 | #include "main.h"
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| 11 | #include <Eigen/SVD>
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| 12 |
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| 13 | template<typename MatrixType> void svd(const MatrixType& m)
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| 14 | {
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| 15 | /* this test covers the following files:
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| 16 | SVD.h
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| 17 | */
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| 18 | int rows = m.rows();
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| 19 | int cols = m.cols();
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| 20 |
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| 21 | typedef typename MatrixType::Scalar Scalar;
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| 22 | typedef typename NumTraits<Scalar>::Real RealScalar;
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| 23 | MatrixType a = MatrixType::Random(rows,cols);
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| 24 | Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> b =
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| 25 | Matrix<Scalar, MatrixType::RowsAtCompileTime, 1>::Random(rows,1);
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| 26 | Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> x(cols,1), x2(cols,1);
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| 27 |
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| 28 | RealScalar largerEps = test_precision<RealScalar>();
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| 29 | if (ei_is_same_type<RealScalar,float>::ret)
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| 30 | largerEps = 1e-3f;
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| 31 |
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| 32 | {
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| 33 | SVD<MatrixType> svd(a);
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| 34 | MatrixType sigma = MatrixType::Zero(rows,cols);
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| 35 | MatrixType matU = MatrixType::Zero(rows,rows);
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| 36 | sigma.block(0,0,cols,cols) = svd.singularValues().asDiagonal();
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| 37 | matU.block(0,0,rows,cols) = svd.matrixU();
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| 38 | VERIFY_IS_APPROX(a, matU * sigma * svd.matrixV().transpose());
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| 39 | }
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| 40 |
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| 41 |
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| 42 | if (rows==cols)
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| 43 | {
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| 44 | if (ei_is_same_type<RealScalar,float>::ret)
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| 45 | {
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| 46 | MatrixType a1 = MatrixType::Random(rows,cols);
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| 47 | a += a * a.adjoint() + a1 * a1.adjoint();
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| 48 | }
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| 49 | SVD<MatrixType> svd(a);
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| 50 | svd.solve(b, &x);
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| 51 | VERIFY_IS_APPROX(a * x,b);
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| 52 | }
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| 53 |
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| 54 |
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| 55 | if(rows==cols)
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| 56 | {
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| 57 | SVD<MatrixType> svd(a);
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| 58 | MatrixType unitary, positive;
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| 59 | svd.computeUnitaryPositive(&unitary, &positive);
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| 60 | VERIFY_IS_APPROX(unitary * unitary.adjoint(), MatrixType::Identity(unitary.rows(),unitary.rows()));
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| 61 | VERIFY_IS_APPROX(positive, positive.adjoint());
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| 62 | for(int i = 0; i < rows; i++) VERIFY(positive.diagonal()[i] >= 0); // cheap necessary (not sufficient) condition for positivity
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| 63 | VERIFY_IS_APPROX(unitary*positive, a);
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| 64 |
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| 65 | svd.computePositiveUnitary(&positive, &unitary);
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| 66 | VERIFY_IS_APPROX(unitary * unitary.adjoint(), MatrixType::Identity(unitary.rows(),unitary.rows()));
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| 67 | VERIFY_IS_APPROX(positive, positive.adjoint());
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| 68 | for(int i = 0; i < rows; i++) VERIFY(positive.diagonal()[i] >= 0); // cheap necessary (not sufficient) condition for positivity
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| 69 | VERIFY_IS_APPROX(positive*unitary, a);
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| 70 | }
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| 71 | }
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| 72 |
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| 73 | void test_eigen2_svd()
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| 74 | {
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| 75 | for(int i = 0; i < g_repeat; i++) {
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| 76 | CALL_SUBTEST_1( svd(Matrix3f()) );
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| 77 | CALL_SUBTEST_2( svd(Matrix4d()) );
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| 78 | CALL_SUBTEST_3( svd(MatrixXf(7,7)) );
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| 79 | CALL_SUBTEST_4( svd(MatrixXd(14,7)) );
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| 80 | // complex are not implemented yet
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| 81 | // CALL_SUBTEST( svd(MatrixXcd(6,6)) );
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| 82 | // CALL_SUBTEST( svd(MatrixXcf(3,3)) );
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| 83 | SVD<MatrixXf> s;
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| 84 | MatrixXf m = MatrixXf::Random(10,1);
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| 85 | s.compute(m);
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| 86 | }
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| 87 | }
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