1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
5// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
6//
7// This Source Code Form is subject to the terms of the Mozilla
8// Public License v. 2.0. If a copy of the MPL was not distributed
9// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
10
11// this hack is needed to make this file compiles with -pedantic (gcc)
12#ifdef __GNUC__
13#define throw(X)
14#endif
15
16#ifdef __INTEL_COMPILER
17  // disable "warning #76: argument to macro is empty" produced by the above hack
18  #pragma warning disable 76
19#endif
20
21// discard stack allocation as that too bypasses malloc
22#define EIGEN_STACK_ALLOCATION_LIMIT 0
23// any heap allocation will raise an assert
24#define EIGEN_NO_MALLOC
25
26#include "main.h"
27#include <Eigen/Cholesky>
28#include <Eigen/Eigenvalues>
29#include <Eigen/LU>
30#include <Eigen/QR>
31#include <Eigen/SVD>
32
33template<typename MatrixType> void nomalloc(const MatrixType& m)
34{
35  /* this test check no dynamic memory allocation are issued with fixed-size matrices
36  */
37  typedef typename MatrixType::Index Index;
38  typedef typename MatrixType::Scalar Scalar;
39
40  Index rows = m.rows();
41  Index cols = m.cols();
42
43  MatrixType m1 = MatrixType::Random(rows, cols),
44             m2 = MatrixType::Random(rows, cols),
45             m3(rows, cols);
46
47  Scalar s1 = internal::random<Scalar>();
48
49  Index r = internal::random<Index>(0, rows-1),
50        c = internal::random<Index>(0, cols-1);
51
52  VERIFY_IS_APPROX((m1+m2)*s1,              s1*m1+s1*m2);
53  VERIFY_IS_APPROX((m1+m2)(r,c), (m1(r,c))+(m2(r,c)));
54  VERIFY_IS_APPROX(m1.cwiseProduct(m1.block(0,0,rows,cols)), (m1.array()*m1.array()).matrix());
55  VERIFY_IS_APPROX((m1*m1.transpose())*m2,  m1*(m1.transpose()*m2));
56
57  m2.col(0).noalias() = m1 * m1.col(0);
58  m2.col(0).noalias() -= m1.adjoint() * m1.col(0);
59  m2.col(0).noalias() -= m1 * m1.row(0).adjoint();
60  m2.col(0).noalias() -= m1.adjoint() * m1.row(0).adjoint();
61
62  m2.row(0).noalias() = m1.row(0) * m1;
63  m2.row(0).noalias() -= m1.row(0) * m1.adjoint();
64  m2.row(0).noalias() -= m1.col(0).adjoint() * m1;
65  m2.row(0).noalias() -= m1.col(0).adjoint() * m1.adjoint();
66  VERIFY_IS_APPROX(m2,m2);
67
68  m2.col(0).noalias() = m1.template triangularView<Upper>() * m1.col(0);
69  m2.col(0).noalias() -= m1.adjoint().template triangularView<Upper>() * m1.col(0);
70  m2.col(0).noalias() -= m1.template triangularView<Upper>() * m1.row(0).adjoint();
71  m2.col(0).noalias() -= m1.adjoint().template triangularView<Upper>() * m1.row(0).adjoint();
72
73  m2.row(0).noalias() = m1.row(0) * m1.template triangularView<Upper>();
74  m2.row(0).noalias() -= m1.row(0) * m1.adjoint().template triangularView<Upper>();
75  m2.row(0).noalias() -= m1.col(0).adjoint() * m1.template triangularView<Upper>();
76  m2.row(0).noalias() -= m1.col(0).adjoint() * m1.adjoint().template triangularView<Upper>();
77  VERIFY_IS_APPROX(m2,m2);
78
79  m2.col(0).noalias() = m1.template selfadjointView<Upper>() * m1.col(0);
80  m2.col(0).noalias() -= m1.adjoint().template selfadjointView<Upper>() * m1.col(0);
81  m2.col(0).noalias() -= m1.template selfadjointView<Upper>() * m1.row(0).adjoint();
82  m2.col(0).noalias() -= m1.adjoint().template selfadjointView<Upper>() * m1.row(0).adjoint();
83
84  m2.row(0).noalias() = m1.row(0) * m1.template selfadjointView<Upper>();
85  m2.row(0).noalias() -= m1.row(0) * m1.adjoint().template selfadjointView<Upper>();
86  m2.row(0).noalias() -= m1.col(0).adjoint() * m1.template selfadjointView<Upper>();
87  m2.row(0).noalias() -= m1.col(0).adjoint() * m1.adjoint().template selfadjointView<Upper>();
88  VERIFY_IS_APPROX(m2,m2);
89
90  m2.template selfadjointView<Lower>().rankUpdate(m1.col(0),-1);
91  m2.template selfadjointView<Lower>().rankUpdate(m1.row(0),-1);
92
93  // The following fancy matrix-matrix products are not safe yet regarding static allocation
94//   m1 += m1.template triangularView<Upper>() * m2.col(;
95//   m1.template selfadjointView<Lower>().rankUpdate(m2);
96//   m1 += m1.template triangularView<Upper>() * m2;
97//   m1 += m1.template selfadjointView<Lower>() * m2;
98//   VERIFY_IS_APPROX(m1,m1);
99}
100
101template<typename Scalar>
102void ctms_decompositions()
103{
104  const int maxSize = 16;
105  const int size    = 12;
106
107  typedef Eigen::Matrix<Scalar,
108                        Eigen::Dynamic, Eigen::Dynamic,
109                        0,
110                        maxSize, maxSize> Matrix;
111
112  typedef Eigen::Matrix<Scalar,
113                        Eigen::Dynamic, 1,
114                        0,
115                        maxSize, 1> Vector;
116
117  typedef Eigen::Matrix<std::complex<Scalar>,
118                        Eigen::Dynamic, Eigen::Dynamic,
119                        0,
120                        maxSize, maxSize> ComplexMatrix;
121
122  const Matrix A(Matrix::Random(size, size)), B(Matrix::Random(size, size));
123  Matrix X(size,size);
124  const ComplexMatrix complexA(ComplexMatrix::Random(size, size));
125  const Matrix saA = A.adjoint() * A;
126  const Vector b(Vector::Random(size));
127  Vector x(size);
128
129  // Cholesky module
130  Eigen::LLT<Matrix>  LLT;  LLT.compute(A);
131  X = LLT.solve(B);
132  x = LLT.solve(b);
133  Eigen::LDLT<Matrix> LDLT; LDLT.compute(A);
134  X = LDLT.solve(B);
135  x = LDLT.solve(b);
136
137  // Eigenvalues module
138  Eigen::HessenbergDecomposition<ComplexMatrix> hessDecomp;        hessDecomp.compute(complexA);
139  Eigen::ComplexSchur<ComplexMatrix>            cSchur(size);      cSchur.compute(complexA);
140  Eigen::ComplexEigenSolver<ComplexMatrix>      cEigSolver;        cEigSolver.compute(complexA);
141  Eigen::EigenSolver<Matrix>                    eigSolver;         eigSolver.compute(A);
142  Eigen::SelfAdjointEigenSolver<Matrix>         saEigSolver(size); saEigSolver.compute(saA);
143  Eigen::Tridiagonalization<Matrix>             tridiag;           tridiag.compute(saA);
144
145  // LU module
146  Eigen::PartialPivLU<Matrix> ppLU; ppLU.compute(A);
147  X = ppLU.solve(B);
148  x = ppLU.solve(b);
149  Eigen::FullPivLU<Matrix>    fpLU; fpLU.compute(A);
150  X = fpLU.solve(B);
151  x = fpLU.solve(b);
152
153  // QR module
154  Eigen::HouseholderQR<Matrix>        hQR;  hQR.compute(A);
155  X = hQR.solve(B);
156  x = hQR.solve(b);
157  Eigen::ColPivHouseholderQR<Matrix>  cpQR; cpQR.compute(A);
158  X = cpQR.solve(B);
159  x = cpQR.solve(b);
160  Eigen::FullPivHouseholderQR<Matrix> fpQR; fpQR.compute(A);
161  // FIXME X = fpQR.solve(B);
162  x = fpQR.solve(b);
163
164  // SVD module
165  Eigen::JacobiSVD<Matrix> jSVD; jSVD.compute(A, ComputeFullU | ComputeFullV);
166}
167
168void test_zerosized() {
169  // default constructors:
170  Eigen::MatrixXd A;
171  Eigen::VectorXd v;
172  // explicit zero-sized:
173  Eigen::ArrayXXd A0(0,0);
174  Eigen::ArrayXd v0(std::ptrdiff_t(0)); // FIXME ArrayXd(0) is ambiguous
175
176  // assigning empty objects to each other:
177  A=A0;
178  v=v0;
179}
180
181template<typename MatrixType> void test_reference(const MatrixType& m) {
182  typedef typename MatrixType::Scalar Scalar;
183  enum { Flag          =  MatrixType::IsRowMajor ? Eigen::RowMajor : Eigen::ColMajor};
184  enum { TransposeFlag = !MatrixType::IsRowMajor ? Eigen::RowMajor : Eigen::ColMajor};
185  typename MatrixType::Index rows = m.rows(), cols=m.cols();
186  // Dynamic reference:
187  typedef Eigen::Ref<const Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, Flag         > > Ref;
188  typedef Eigen::Ref<const Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, TransposeFlag> > RefT;
189
190  Ref r1(m);
191  Ref r2(m.block(rows/3, cols/4, rows/2, cols/2));
192  RefT r3(m.transpose());
193  RefT r4(m.topLeftCorner(rows/2, cols/2).transpose());
194
195  VERIFY_RAISES_ASSERT(RefT r5(m));
196  VERIFY_RAISES_ASSERT(Ref r6(m.transpose()));
197  VERIFY_RAISES_ASSERT(Ref r7(Scalar(2) * m));
198}
199
200void test_nomalloc()
201{
202  // check that our operator new is indeed called:
203  VERIFY_RAISES_ASSERT(MatrixXd dummy(MatrixXd::Random(3,3)));
204  CALL_SUBTEST_1(nomalloc(Matrix<float, 1, 1>()) );
205  CALL_SUBTEST_2(nomalloc(Matrix4d()) );
206  CALL_SUBTEST_3(nomalloc(Matrix<float,32,32>()) );
207
208  // Check decomposition modules with dynamic matrices that have a known compile-time max size (ctms)
209  CALL_SUBTEST_4(ctms_decompositions<float>());
210  CALL_SUBTEST_5(test_zerosized());
211  CALL_SUBTEST_6(test_reference(Matrix<float,32,32>()));
212}
213