[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) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
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| 5 | // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
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| 6 | //
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| 7 | // This Source Code Form is subject to the terms of the Mozilla
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| 8 | // Public License v. 2.0. If a copy of the MPL was not distributed
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| 9 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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| 10 |
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| 11 | // this hack is needed to make this file compiles with -pedantic (gcc)
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| 12 | #ifdef __GNUC__
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| 13 | #define throw(X)
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| 14 | #endif
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| 15 |
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| 16 | #ifdef __INTEL_COMPILER
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| 17 | // disable "warning #76: argument to macro is empty" produced by the above hack
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| 18 | #pragma warning disable 76
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| 19 | #endif
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| 20 |
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| 21 | // discard stack allocation as that too bypasses malloc
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| 22 | #define EIGEN_STACK_ALLOCATION_LIMIT 0
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| 23 | // any heap allocation will raise an assert
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| 24 | #define EIGEN_NO_MALLOC
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| 25 |
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| 26 | #include "main.h"
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| 27 | #include <Eigen/Cholesky>
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| 28 | #include <Eigen/Eigenvalues>
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| 29 | #include <Eigen/LU>
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| 30 | #include <Eigen/QR>
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| 31 | #include <Eigen/SVD>
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| 32 |
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| 33 | template<typename MatrixType> void nomalloc(const MatrixType& m)
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| 34 | {
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| 35 | /* this test check no dynamic memory allocation are issued with fixed-size matrices
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| 36 | */
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| 37 | typedef typename MatrixType::Index Index;
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| 38 | typedef typename MatrixType::Scalar Scalar;
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| 39 |
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| 40 | Index rows = m.rows();
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| 41 | Index cols = m.cols();
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| 42 |
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| 43 | MatrixType m1 = MatrixType::Random(rows, cols),
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| 44 | m2 = MatrixType::Random(rows, cols),
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| 45 | m3(rows, cols);
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| 46 |
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| 47 | Scalar s1 = internal::random<Scalar>();
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| 48 |
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| 49 | Index r = internal::random<Index>(0, rows-1),
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| 50 | c = internal::random<Index>(0, cols-1);
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| 51 |
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| 52 | VERIFY_IS_APPROX((m1+m2)*s1, s1*m1+s1*m2);
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| 53 | VERIFY_IS_APPROX((m1+m2)(r,c), (m1(r,c))+(m2(r,c)));
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| 54 | VERIFY_IS_APPROX(m1.cwiseProduct(m1.block(0,0,rows,cols)), (m1.array()*m1.array()).matrix());
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| 55 | VERIFY_IS_APPROX((m1*m1.transpose())*m2, m1*(m1.transpose()*m2));
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| 56 |
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| 57 | m2.col(0).noalias() = m1 * m1.col(0);
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| 58 | m2.col(0).noalias() -= m1.adjoint() * m1.col(0);
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| 59 | m2.col(0).noalias() -= m1 * m1.row(0).adjoint();
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| 60 | m2.col(0).noalias() -= m1.adjoint() * m1.row(0).adjoint();
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| 61 |
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| 62 | m2.row(0).noalias() = m1.row(0) * m1;
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| 63 | m2.row(0).noalias() -= m1.row(0) * m1.adjoint();
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| 64 | m2.row(0).noalias() -= m1.col(0).adjoint() * m1;
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| 65 | m2.row(0).noalias() -= m1.col(0).adjoint() * m1.adjoint();
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| 66 | VERIFY_IS_APPROX(m2,m2);
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| 67 |
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| 68 | m2.col(0).noalias() = m1.template triangularView<Upper>() * m1.col(0);
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| 69 | m2.col(0).noalias() -= m1.adjoint().template triangularView<Upper>() * m1.col(0);
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| 70 | m2.col(0).noalias() -= m1.template triangularView<Upper>() * m1.row(0).adjoint();
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| 71 | m2.col(0).noalias() -= m1.adjoint().template triangularView<Upper>() * m1.row(0).adjoint();
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| 72 |
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| 73 | m2.row(0).noalias() = m1.row(0) * m1.template triangularView<Upper>();
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| 74 | m2.row(0).noalias() -= m1.row(0) * m1.adjoint().template triangularView<Upper>();
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| 75 | m2.row(0).noalias() -= m1.col(0).adjoint() * m1.template triangularView<Upper>();
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| 76 | m2.row(0).noalias() -= m1.col(0).adjoint() * m1.adjoint().template triangularView<Upper>();
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| 77 | VERIFY_IS_APPROX(m2,m2);
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| 78 |
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| 79 | m2.col(0).noalias() = m1.template selfadjointView<Upper>() * m1.col(0);
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| 80 | m2.col(0).noalias() -= m1.adjoint().template selfadjointView<Upper>() * m1.col(0);
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| 81 | m2.col(0).noalias() -= m1.template selfadjointView<Upper>() * m1.row(0).adjoint();
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| 82 | m2.col(0).noalias() -= m1.adjoint().template selfadjointView<Upper>() * m1.row(0).adjoint();
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| 83 |
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| 84 | m2.row(0).noalias() = m1.row(0) * m1.template selfadjointView<Upper>();
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| 85 | m2.row(0).noalias() -= m1.row(0) * m1.adjoint().template selfadjointView<Upper>();
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| 86 | m2.row(0).noalias() -= m1.col(0).adjoint() * m1.template selfadjointView<Upper>();
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| 87 | m2.row(0).noalias() -= m1.col(0).adjoint() * m1.adjoint().template selfadjointView<Upper>();
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| 88 | VERIFY_IS_APPROX(m2,m2);
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| 89 |
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| 90 | m2.template selfadjointView<Lower>().rankUpdate(m1.col(0),-1);
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| 91 | m2.template selfadjointView<Lower>().rankUpdate(m1.row(0),-1);
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| 92 |
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| 93 | // The following fancy matrix-matrix products are not safe yet regarding static allocation
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| 94 | // m1 += m1.template triangularView<Upper>() * m2.col(;
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| 95 | // m1.template selfadjointView<Lower>().rankUpdate(m2);
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| 96 | // m1 += m1.template triangularView<Upper>() * m2;
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| 97 | // m1 += m1.template selfadjointView<Lower>() * m2;
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| 98 | // VERIFY_IS_APPROX(m1,m1);
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| 99 | }
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| 100 |
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| 101 | template<typename Scalar>
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| 102 | void ctms_decompositions()
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| 103 | {
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| 104 | const int maxSize = 16;
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| 105 | const int size = 12;
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| 106 |
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| 107 | typedef Eigen::Matrix<Scalar,
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| 108 | Eigen::Dynamic, Eigen::Dynamic,
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| 109 | 0,
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| 110 | maxSize, maxSize> Matrix;
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| 111 |
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| 112 | typedef Eigen::Matrix<Scalar,
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| 113 | Eigen::Dynamic, 1,
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| 114 | 0,
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| 115 | maxSize, 1> Vector;
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| 116 |
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| 117 | typedef Eigen::Matrix<std::complex<Scalar>,
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| 118 | Eigen::Dynamic, Eigen::Dynamic,
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| 119 | 0,
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| 120 | maxSize, maxSize> ComplexMatrix;
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| 121 |
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| 122 | const Matrix A(Matrix::Random(size, size)), B(Matrix::Random(size, size));
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| 123 | Matrix X(size,size);
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| 124 | const ComplexMatrix complexA(ComplexMatrix::Random(size, size));
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| 125 | const Matrix saA = A.adjoint() * A;
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| 126 | const Vector b(Vector::Random(size));
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| 127 | Vector x(size);
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| 128 |
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| 129 | // Cholesky module
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| 130 | Eigen::LLT<Matrix> LLT; LLT.compute(A);
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| 131 | X = LLT.solve(B);
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| 132 | x = LLT.solve(b);
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| 133 | Eigen::LDLT<Matrix> LDLT; LDLT.compute(A);
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| 134 | X = LDLT.solve(B);
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| 135 | x = LDLT.solve(b);
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| 136 |
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| 137 | // Eigenvalues module
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| 138 | Eigen::HessenbergDecomposition<ComplexMatrix> hessDecomp; hessDecomp.compute(complexA);
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| 139 | Eigen::ComplexSchur<ComplexMatrix> cSchur(size); cSchur.compute(complexA);
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| 140 | Eigen::ComplexEigenSolver<ComplexMatrix> cEigSolver; cEigSolver.compute(complexA);
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| 141 | Eigen::EigenSolver<Matrix> eigSolver; eigSolver.compute(A);
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| 142 | Eigen::SelfAdjointEigenSolver<Matrix> saEigSolver(size); saEigSolver.compute(saA);
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| 143 | Eigen::Tridiagonalization<Matrix> tridiag; tridiag.compute(saA);
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| 144 |
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| 145 | // LU module
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| 146 | Eigen::PartialPivLU<Matrix> ppLU; ppLU.compute(A);
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| 147 | X = ppLU.solve(B);
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| 148 | x = ppLU.solve(b);
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| 149 | Eigen::FullPivLU<Matrix> fpLU; fpLU.compute(A);
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| 150 | X = fpLU.solve(B);
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| 151 | x = fpLU.solve(b);
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| 152 |
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| 153 | // QR module
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| 154 | Eigen::HouseholderQR<Matrix> hQR; hQR.compute(A);
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| 155 | X = hQR.solve(B);
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| 156 | x = hQR.solve(b);
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| 157 | Eigen::ColPivHouseholderQR<Matrix> cpQR; cpQR.compute(A);
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| 158 | X = cpQR.solve(B);
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| 159 | x = cpQR.solve(b);
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| 160 | Eigen::FullPivHouseholderQR<Matrix> fpQR; fpQR.compute(A);
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| 161 | // FIXME X = fpQR.solve(B);
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| 162 | x = fpQR.solve(b);
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| 163 |
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| 164 | // SVD module
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| 165 | Eigen::JacobiSVD<Matrix> jSVD; jSVD.compute(A, ComputeFullU | ComputeFullV);
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| 166 | }
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| 167 |
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| 168 | void test_zerosized() {
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| 169 | // default constructors:
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| 170 | Eigen::MatrixXd A;
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| 171 | Eigen::VectorXd v;
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| 172 | // explicit zero-sized:
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| 173 | Eigen::ArrayXXd A0(0,0);
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| 174 | Eigen::ArrayXd v0(std::ptrdiff_t(0)); // FIXME ArrayXd(0) is ambiguous
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| 175 |
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| 176 | // assigning empty objects to each other:
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| 177 | A=A0;
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| 178 | v=v0;
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| 179 | }
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| 180 |
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| 181 | template<typename MatrixType> void test_reference(const MatrixType& m) {
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| 182 | typedef typename MatrixType::Scalar Scalar;
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| 183 | enum { Flag = MatrixType::IsRowMajor ? Eigen::RowMajor : Eigen::ColMajor};
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| 184 | enum { TransposeFlag = !MatrixType::IsRowMajor ? Eigen::RowMajor : Eigen::ColMajor};
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| 185 | typename MatrixType::Index rows = m.rows(), cols=m.cols();
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| 186 | // Dynamic reference:
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| 187 | typedef Eigen::Ref<const Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, Flag > > Ref;
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| 188 | typedef Eigen::Ref<const Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, TransposeFlag> > RefT;
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| 189 |
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| 190 | Ref r1(m);
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| 191 | Ref r2(m.block(rows/3, cols/4, rows/2, cols/2));
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| 192 | RefT r3(m.transpose());
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| 193 | RefT r4(m.topLeftCorner(rows/2, cols/2).transpose());
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| 194 |
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| 195 | VERIFY_RAISES_ASSERT(RefT r5(m));
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| 196 | VERIFY_RAISES_ASSERT(Ref r6(m.transpose()));
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| 197 | VERIFY_RAISES_ASSERT(Ref r7(Scalar(2) * m));
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| 198 | }
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| 199 |
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| 200 | void test_nomalloc()
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| 201 | {
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| 202 | // check that our operator new is indeed called:
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| 203 | VERIFY_RAISES_ASSERT(MatrixXd dummy(MatrixXd::Random(3,3)));
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| 204 | CALL_SUBTEST_1(nomalloc(Matrix<float, 1, 1>()) );
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| 205 | CALL_SUBTEST_2(nomalloc(Matrix4d()) );
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| 206 | CALL_SUBTEST_3(nomalloc(Matrix<float,32,32>()) );
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| 207 |
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| 208 | // Check decomposition modules with dynamic matrices that have a known compile-time max size (ctms)
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| 209 | CALL_SUBTEST_4(ctms_decompositions<float>());
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| 210 | CALL_SUBTEST_5(test_zerosized());
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| 211 | CALL_SUBTEST_6(test_reference(Matrix<float,32,32>()));
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| 212 | }
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