Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 1 | // This file is part of Eigen, a lightweight C++ template library |
| 2 | // for linear algebra. |
| 3 | // |
| 4 | // Copyright (C) 2009 Hauke Heibel <hauke.heibel@gmail.com> |
| 5 | // |
| 6 | // This Source Code Form is subject to the terms of the Mozilla |
| 7 | // Public License v. 2.0. If a copy of the MPL was not distributed |
| 8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. |
| 9 | |
| 10 | #include "main.h" |
| 11 | |
| 12 | #include <Eigen/Core> |
| 13 | #include <Eigen/Geometry> |
| 14 | |
| 15 | #include <Eigen/LU> // required for MatrixBase::determinant |
| 16 | #include <Eigen/SVD> // required for SVD |
| 17 | |
| 18 | using namespace Eigen; |
| 19 | |
| 20 | // Constructs a random matrix from the unitary group U(size). |
| 21 | template <typename T> |
| 22 | Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> randMatrixUnitary(int size) |
| 23 | { |
| 24 | typedef T Scalar; |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 25 | typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> MatrixType; |
| 26 | |
| 27 | MatrixType Q; |
| 28 | |
| 29 | int max_tries = 40; |
| 30 | double is_unitary = false; |
| 31 | |
| 32 | while (!is_unitary && max_tries > 0) |
| 33 | { |
| 34 | // initialize random matrix |
| 35 | Q = MatrixType::Random(size, size); |
| 36 | |
| 37 | // orthogonalize columns using the Gram-Schmidt algorithm |
| 38 | for (int col = 0; col < size; ++col) |
| 39 | { |
| 40 | typename MatrixType::ColXpr colVec = Q.col(col); |
| 41 | for (int prevCol = 0; prevCol < col; ++prevCol) |
| 42 | { |
| 43 | typename MatrixType::ColXpr prevColVec = Q.col(prevCol); |
| 44 | colVec -= colVec.dot(prevColVec)*prevColVec; |
| 45 | } |
| 46 | Q.col(col) = colVec.normalized(); |
| 47 | } |
| 48 | |
| 49 | // this additional orthogonalization is not necessary in theory but should enhance |
| 50 | // the numerical orthogonality of the matrix |
| 51 | for (int row = 0; row < size; ++row) |
| 52 | { |
| 53 | typename MatrixType::RowXpr rowVec = Q.row(row); |
| 54 | for (int prevRow = 0; prevRow < row; ++prevRow) |
| 55 | { |
| 56 | typename MatrixType::RowXpr prevRowVec = Q.row(prevRow); |
| 57 | rowVec -= rowVec.dot(prevRowVec)*prevRowVec; |
| 58 | } |
| 59 | Q.row(row) = rowVec.normalized(); |
| 60 | } |
| 61 | |
| 62 | // final check |
| 63 | is_unitary = Q.isUnitary(); |
| 64 | --max_tries; |
| 65 | } |
| 66 | |
| 67 | if (max_tries == 0) |
| 68 | eigen_assert(false && "randMatrixUnitary: Could not construct unitary matrix!"); |
| 69 | |
| 70 | return Q; |
| 71 | } |
| 72 | |
| 73 | // Constructs a random matrix from the special unitary group SU(size). |
| 74 | template <typename T> |
| 75 | Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> randMatrixSpecialUnitary(int size) |
| 76 | { |
| 77 | typedef T Scalar; |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 78 | |
| 79 | typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> MatrixType; |
| 80 | |
| 81 | // initialize unitary matrix |
| 82 | MatrixType Q = randMatrixUnitary<Scalar>(size); |
| 83 | |
| 84 | // tweak the first column to make the determinant be 1 |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 85 | Q.col(0) *= numext::conj(Q.determinant()); |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 86 | |
| 87 | return Q; |
| 88 | } |
| 89 | |
| 90 | template <typename MatrixType> |
| 91 | void run_test(int dim, int num_elements) |
| 92 | { |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 93 | using std::abs; |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 94 | typedef typename internal::traits<MatrixType>::Scalar Scalar; |
| 95 | typedef Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> MatrixX; |
| 96 | typedef Matrix<Scalar, Eigen::Dynamic, 1> VectorX; |
| 97 | |
| 98 | // MUST be positive because in any other case det(cR_t) may become negative for |
| 99 | // odd dimensions! |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 100 | const Scalar c = abs(internal::random<Scalar>()); |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 101 | |
| 102 | MatrixX R = randMatrixSpecialUnitary<Scalar>(dim); |
| 103 | VectorX t = Scalar(50)*VectorX::Random(dim,1); |
| 104 | |
| 105 | MatrixX cR_t = MatrixX::Identity(dim+1,dim+1); |
| 106 | cR_t.block(0,0,dim,dim) = c*R; |
| 107 | cR_t.block(0,dim,dim,1) = t; |
| 108 | |
| 109 | MatrixX src = MatrixX::Random(dim+1, num_elements); |
| 110 | src.row(dim) = Matrix<Scalar, 1, Dynamic>::Constant(num_elements, Scalar(1)); |
| 111 | |
| 112 | MatrixX dst = cR_t*src; |
| 113 | |
| 114 | MatrixX cR_t_umeyama = umeyama(src.block(0,0,dim,num_elements), dst.block(0,0,dim,num_elements)); |
| 115 | |
| 116 | const Scalar error = ( cR_t_umeyama*src - dst ).norm() / dst.norm(); |
| 117 | VERIFY(error < Scalar(40)*std::numeric_limits<Scalar>::epsilon()); |
| 118 | } |
| 119 | |
| 120 | template<typename Scalar, int Dimension> |
| 121 | void run_fixed_size_test(int num_elements) |
| 122 | { |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 123 | using std::abs; |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 124 | typedef Matrix<Scalar, Dimension+1, Dynamic> MatrixX; |
| 125 | typedef Matrix<Scalar, Dimension+1, Dimension+1> HomMatrix; |
| 126 | typedef Matrix<Scalar, Dimension, Dimension> FixedMatrix; |
| 127 | typedef Matrix<Scalar, Dimension, 1> FixedVector; |
| 128 | |
| 129 | const int dim = Dimension; |
| 130 | |
| 131 | // MUST be positive because in any other case det(cR_t) may become negative for |
| 132 | // odd dimensions! |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 133 | // Also if c is to small compared to t.norm(), problem is ill-posed (cf. Bug 744) |
| 134 | const Scalar c = internal::random<Scalar>(0.5, 2.0); |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 135 | |
| 136 | FixedMatrix R = randMatrixSpecialUnitary<Scalar>(dim); |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 137 | FixedVector t = Scalar(32)*FixedVector::Random(dim,1); |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 138 | |
| 139 | HomMatrix cR_t = HomMatrix::Identity(dim+1,dim+1); |
| 140 | cR_t.block(0,0,dim,dim) = c*R; |
| 141 | cR_t.block(0,dim,dim,1) = t; |
| 142 | |
| 143 | MatrixX src = MatrixX::Random(dim+1, num_elements); |
| 144 | src.row(dim) = Matrix<Scalar, 1, Dynamic>::Constant(num_elements, Scalar(1)); |
| 145 | |
| 146 | MatrixX dst = cR_t*src; |
| 147 | |
| 148 | Block<MatrixX, Dimension, Dynamic> src_block(src,0,0,dim,num_elements); |
| 149 | Block<MatrixX, Dimension, Dynamic> dst_block(dst,0,0,dim,num_elements); |
| 150 | |
| 151 | HomMatrix cR_t_umeyama = umeyama(src_block, dst_block); |
| 152 | |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 153 | const Scalar error = ( cR_t_umeyama*src - dst ).squaredNorm(); |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 154 | |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 155 | VERIFY(error < Scalar(16)*std::numeric_limits<Scalar>::epsilon()); |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 156 | } |
| 157 | |
| 158 | void test_umeyama() |
| 159 | { |
| 160 | for (int i=0; i<g_repeat; ++i) |
| 161 | { |
| 162 | const int num_elements = internal::random<int>(40,500); |
| 163 | |
| 164 | // works also for dimensions bigger than 3... |
| 165 | for (int dim=2; dim<8; ++dim) |
| 166 | { |
| 167 | CALL_SUBTEST_1(run_test<MatrixXd>(dim, num_elements)); |
| 168 | CALL_SUBTEST_2(run_test<MatrixXf>(dim, num_elements)); |
| 169 | } |
| 170 | |
| 171 | CALL_SUBTEST_3((run_fixed_size_test<float, 2>(num_elements))); |
| 172 | CALL_SUBTEST_4((run_fixed_size_test<float, 3>(num_elements))); |
| 173 | CALL_SUBTEST_5((run_fixed_size_test<float, 4>(num_elements))); |
| 174 | |
| 175 | CALL_SUBTEST_6((run_fixed_size_test<double, 2>(num_elements))); |
| 176 | CALL_SUBTEST_7((run_fixed_size_test<double, 3>(num_elements))); |
| 177 | CALL_SUBTEST_8((run_fixed_size_test<double, 4>(num_elements))); |
| 178 | } |
| 179 | |
| 180 | // Those two calls don't compile and result in meaningful error messages! |
| 181 | // umeyama(MatrixXcf(),MatrixXcf()); |
| 182 | // umeyama(MatrixXcd(),MatrixXcd()); |
| 183 | } |