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