1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr>
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 "sparse.h"
11 
sparse_permutations(const SparseMatrixType & ref)12 template<int OtherStorage, typename SparseMatrixType> void sparse_permutations(const SparseMatrixType& ref)
13 {
14   typedef typename SparseMatrixType::Index Index;
15 
16   const Index rows = ref.rows();
17   const Index cols = ref.cols();
18   typedef typename SparseMatrixType::Scalar Scalar;
19   typedef typename SparseMatrixType::Index Index;
20   typedef SparseMatrix<Scalar, OtherStorage, Index> OtherSparseMatrixType;
21   typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
22   typedef Matrix<Index,Dynamic,1> VectorI;
23 
24   double density = (std::max)(8./(rows*cols), 0.01);
25 
26   SparseMatrixType mat(rows, cols), up(rows,cols), lo(rows,cols);
27   OtherSparseMatrixType res;
28   DenseMatrix mat_d = DenseMatrix::Zero(rows, cols), up_sym_d, lo_sym_d, res_d;
29 
30   initSparse<Scalar>(density, mat_d, mat, 0);
31 
32   up = mat.template triangularView<Upper>();
33   lo = mat.template triangularView<Lower>();
34 
35   up_sym_d = mat_d.template selfadjointView<Upper>();
36   lo_sym_d = mat_d.template selfadjointView<Lower>();
37 
38   VERIFY_IS_APPROX(mat, mat_d);
39   VERIFY_IS_APPROX(up, DenseMatrix(mat_d.template triangularView<Upper>()));
40   VERIFY_IS_APPROX(lo, DenseMatrix(mat_d.template triangularView<Lower>()));
41 
42   PermutationMatrix<Dynamic> p, p_null;
43   VectorI pi;
44   randomPermutationVector(pi, cols);
45   p.indices() = pi;
46 
47   res = mat*p;
48   res_d = mat_d*p;
49   VERIFY(res.isApprox(res_d) && "mat*p");
50 
51   res = p*mat;
52   res_d = p*mat_d;
53   VERIFY(res.isApprox(res_d) && "p*mat");
54 
55   res = mat*p.inverse();
56   res_d = mat*p.inverse();
57   VERIFY(res.isApprox(res_d) && "mat*inv(p)");
58 
59   res = p.inverse()*mat;
60   res_d = p.inverse()*mat_d;
61   VERIFY(res.isApprox(res_d) && "inv(p)*mat");
62 
63   res = mat.twistedBy(p);
64   res_d = (p * mat_d) * p.inverse();
65   VERIFY(res.isApprox(res_d) && "p*mat*inv(p)");
66 
67 
68   res = mat.template selfadjointView<Upper>().twistedBy(p_null);
69   res_d = up_sym_d;
70   VERIFY(res.isApprox(res_d) && "full selfadjoint upper to full");
71 
72   res = mat.template selfadjointView<Lower>().twistedBy(p_null);
73   res_d = lo_sym_d;
74   VERIFY(res.isApprox(res_d) && "full selfadjoint lower to full");
75 
76 
77   res = up.template selfadjointView<Upper>().twistedBy(p_null);
78   res_d = up_sym_d;
79   VERIFY(res.isApprox(res_d) && "upper selfadjoint to full");
80 
81   res = lo.template selfadjointView<Lower>().twistedBy(p_null);
82   res_d = lo_sym_d;
83   VERIFY(res.isApprox(res_d) && "lower selfadjoint full");
84 
85 
86   res = mat.template selfadjointView<Upper>();
87   res_d = up_sym_d;
88   VERIFY(res.isApprox(res_d) && "full selfadjoint upper to full");
89 
90   res = mat.template selfadjointView<Lower>();
91   res_d = lo_sym_d;
92   VERIFY(res.isApprox(res_d) && "full selfadjoint lower to full");
93 
94   res = up.template selfadjointView<Upper>();
95   res_d = up_sym_d;
96   VERIFY(res.isApprox(res_d) && "upper selfadjoint to full");
97 
98   res = lo.template selfadjointView<Lower>();
99   res_d = lo_sym_d;
100   VERIFY(res.isApprox(res_d) && "lower selfadjoint full");
101 
102 
103   res.template selfadjointView<Upper>() = mat.template selfadjointView<Upper>();
104   res_d = up_sym_d.template triangularView<Upper>();
105   VERIFY(res.isApprox(res_d) && "full selfadjoint upper to upper");
106 
107   res.template selfadjointView<Lower>() = mat.template selfadjointView<Upper>();
108   res_d = up_sym_d.template triangularView<Lower>();
109   VERIFY(res.isApprox(res_d) && "full selfadjoint upper to lower");
110 
111   res.template selfadjointView<Upper>() = mat.template selfadjointView<Lower>();
112   res_d = lo_sym_d.template triangularView<Upper>();
113   VERIFY(res.isApprox(res_d) && "full selfadjoint lower to upper");
114 
115   res.template selfadjointView<Lower>() = mat.template selfadjointView<Lower>();
116   res_d = lo_sym_d.template triangularView<Lower>();
117   VERIFY(res.isApprox(res_d) && "full selfadjoint lower to lower");
118 
119 
120 
121   res.template selfadjointView<Upper>() = mat.template selfadjointView<Upper>().twistedBy(p);
122   res_d = ((p * up_sym_d) * p.inverse()).eval().template triangularView<Upper>();
123   VERIFY(res.isApprox(res_d) && "full selfadjoint upper twisted to upper");
124 
125   res.template selfadjointView<Upper>() = mat.template selfadjointView<Lower>().twistedBy(p);
126   res_d = ((p * lo_sym_d) * p.inverse()).eval().template triangularView<Upper>();
127   VERIFY(res.isApprox(res_d) && "full selfadjoint lower twisted to upper");
128 
129   res.template selfadjointView<Lower>() = mat.template selfadjointView<Lower>().twistedBy(p);
130   res_d = ((p * lo_sym_d) * p.inverse()).eval().template triangularView<Lower>();
131   VERIFY(res.isApprox(res_d) && "full selfadjoint lower twisted to lower");
132 
133   res.template selfadjointView<Lower>() = mat.template selfadjointView<Upper>().twistedBy(p);
134   res_d = ((p * up_sym_d) * p.inverse()).eval().template triangularView<Lower>();
135   VERIFY(res.isApprox(res_d) && "full selfadjoint upper twisted to lower");
136 
137 
138   res.template selfadjointView<Upper>() = up.template selfadjointView<Upper>().twistedBy(p);
139   res_d = ((p * up_sym_d) * p.inverse()).eval().template triangularView<Upper>();
140   VERIFY(res.isApprox(res_d) && "upper selfadjoint twisted to upper");
141 
142   res.template selfadjointView<Upper>() = lo.template selfadjointView<Lower>().twistedBy(p);
143   res_d = ((p * lo_sym_d) * p.inverse()).eval().template triangularView<Upper>();
144   VERIFY(res.isApprox(res_d) && "lower selfadjoint twisted to upper");
145 
146   res.template selfadjointView<Lower>() = lo.template selfadjointView<Lower>().twistedBy(p);
147   res_d = ((p * lo_sym_d) * p.inverse()).eval().template triangularView<Lower>();
148   VERIFY(res.isApprox(res_d) && "lower selfadjoint twisted to lower");
149 
150   res.template selfadjointView<Lower>() = up.template selfadjointView<Upper>().twistedBy(p);
151   res_d = ((p * up_sym_d) * p.inverse()).eval().template triangularView<Lower>();
152   VERIFY(res.isApprox(res_d) && "upper selfadjoint twisted to lower");
153 
154 
155   res = mat.template selfadjointView<Upper>().twistedBy(p);
156   res_d = (p * up_sym_d) * p.inverse();
157   VERIFY(res.isApprox(res_d) && "full selfadjoint upper twisted to full");
158 
159   res = mat.template selfadjointView<Lower>().twistedBy(p);
160   res_d = (p * lo_sym_d) * p.inverse();
161   VERIFY(res.isApprox(res_d) && "full selfadjoint lower twisted to full");
162 
163   res = up.template selfadjointView<Upper>().twistedBy(p);
164   res_d = (p * up_sym_d) * p.inverse();
165   VERIFY(res.isApprox(res_d) && "upper selfadjoint twisted to full");
166 
167   res = lo.template selfadjointView<Lower>().twistedBy(p);
168   res_d = (p * lo_sym_d) * p.inverse();
169   VERIFY(res.isApprox(res_d) && "lower selfadjoint twisted to full");
170 }
171 
sparse_permutations_all(int size)172 template<typename Scalar> void sparse_permutations_all(int size)
173 {
174   CALL_SUBTEST(( sparse_permutations<ColMajor>(SparseMatrix<Scalar, ColMajor>(size,size)) ));
175   CALL_SUBTEST(( sparse_permutations<ColMajor>(SparseMatrix<Scalar, RowMajor>(size,size)) ));
176   CALL_SUBTEST(( sparse_permutations<RowMajor>(SparseMatrix<Scalar, ColMajor>(size,size)) ));
177   CALL_SUBTEST(( sparse_permutations<RowMajor>(SparseMatrix<Scalar, RowMajor>(size,size)) ));
178 }
179 
test_sparse_permutations()180 void test_sparse_permutations()
181 {
182   for(int i = 0; i < g_repeat; i++) {
183     int s = Eigen::internal::random<int>(1,50);
184     CALL_SUBTEST_1((  sparse_permutations_all<double>(s) ));
185     CALL_SUBTEST_2((  sparse_permutations_all<std::complex<double> >(s) ));
186   }
187 }
188