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 
nomalloc(const MatrixType & m)33 template<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 
101 template<typename Scalar>
ctms_decompositions()102 void 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 
test_zerosized()168 void 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 
test_reference(const MatrixType & m)181 template<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 
test_nomalloc()200 void 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