1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2011 Kolja Brix <[email protected]>
5 // Copyright (C) 2011 Andreas Platen <[email protected]>
6 // Copyright (C) 2012 Chen-Pang He <[email protected]>
7 //
8 // This Source Code Form is subject to the terms of the Mozilla
9 // Public License v. 2.0. If a copy of the MPL was not distributed
10 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
11
12
13 #ifdef EIGEN_TEST_PART_1
14
15 #include "sparse.h"
16 #include <Eigen/SparseExtra>
17 #include <Eigen/KroneckerProduct>
18
19 template<typename MatrixType>
check_dimension(const MatrixType & ab,const int rows,const int cols)20 void check_dimension(const MatrixType& ab, const int rows, const int cols)
21 {
22 VERIFY_IS_EQUAL(ab.rows(), rows);
23 VERIFY_IS_EQUAL(ab.cols(), cols);
24 }
25
26
27 template<typename MatrixType>
check_kronecker_product(const MatrixType & ab)28 void check_kronecker_product(const MatrixType& ab)
29 {
30 VERIFY_IS_EQUAL(ab.rows(), 6);
31 VERIFY_IS_EQUAL(ab.cols(), 6);
32 VERIFY_IS_EQUAL(ab.nonZeros(), 36);
33 VERIFY_IS_APPROX(ab.coeff(0,0), -0.4017367630386106);
34 VERIFY_IS_APPROX(ab.coeff(0,1), 0.1056863433932735);
35 VERIFY_IS_APPROX(ab.coeff(0,2), -0.7255206194554212);
36 VERIFY_IS_APPROX(ab.coeff(0,3), 0.1908653336744706);
37 VERIFY_IS_APPROX(ab.coeff(0,4), 0.350864567234111);
38 VERIFY_IS_APPROX(ab.coeff(0,5), -0.0923032108308013);
39 VERIFY_IS_APPROX(ab.coeff(1,0), 0.415417514804677);
40 VERIFY_IS_APPROX(ab.coeff(1,1), -0.2369227701722048);
41 VERIFY_IS_APPROX(ab.coeff(1,2), 0.7502275131458511);
42 VERIFY_IS_APPROX(ab.coeff(1,3), -0.4278731019742696);
43 VERIFY_IS_APPROX(ab.coeff(1,4), -0.3628129162264507);
44 VERIFY_IS_APPROX(ab.coeff(1,5), 0.2069210808481275);
45 VERIFY_IS_APPROX(ab.coeff(2,0), 0.05465890160863986);
46 VERIFY_IS_APPROX(ab.coeff(2,1), -0.2634092511419858);
47 VERIFY_IS_APPROX(ab.coeff(2,2), 0.09871180285793758);
48 VERIFY_IS_APPROX(ab.coeff(2,3), -0.4757066334017702);
49 VERIFY_IS_APPROX(ab.coeff(2,4), -0.04773740823058334);
50 VERIFY_IS_APPROX(ab.coeff(2,5), 0.2300535609645254);
51 VERIFY_IS_APPROX(ab.coeff(3,0), -0.8172945853260133);
52 VERIFY_IS_APPROX(ab.coeff(3,1), 0.2150086428359221);
53 VERIFY_IS_APPROX(ab.coeff(3,2), 0.5825113847292743);
54 VERIFY_IS_APPROX(ab.coeff(3,3), -0.1532433770097174);
55 VERIFY_IS_APPROX(ab.coeff(3,4), -0.329383387282399);
56 VERIFY_IS_APPROX(ab.coeff(3,5), 0.08665207912033064);
57 VERIFY_IS_APPROX(ab.coeff(4,0), 0.8451267514863225);
58 VERIFY_IS_APPROX(ab.coeff(4,1), -0.481996458918977);
59 VERIFY_IS_APPROX(ab.coeff(4,2), -0.6023482390791535);
60 VERIFY_IS_APPROX(ab.coeff(4,3), 0.3435339347164565);
61 VERIFY_IS_APPROX(ab.coeff(4,4), 0.3406002157428891);
62 VERIFY_IS_APPROX(ab.coeff(4,5), -0.1942526344200915);
63 VERIFY_IS_APPROX(ab.coeff(5,0), 0.1111982482925399);
64 VERIFY_IS_APPROX(ab.coeff(5,1), -0.5358806424754169);
65 VERIFY_IS_APPROX(ab.coeff(5,2), -0.07925446559335647);
66 VERIFY_IS_APPROX(ab.coeff(5,3), 0.3819388757769038);
67 VERIFY_IS_APPROX(ab.coeff(5,4), 0.04481475387219876);
68 VERIFY_IS_APPROX(ab.coeff(5,5), -0.2159688616158057);
69 }
70
71
72 template<typename MatrixType>
check_sparse_kronecker_product(const MatrixType & ab)73 void check_sparse_kronecker_product(const MatrixType& ab)
74 {
75 VERIFY_IS_EQUAL(ab.rows(), 12);
76 VERIFY_IS_EQUAL(ab.cols(), 10);
77 VERIFY_IS_EQUAL(ab.nonZeros(), 3*2);
78 VERIFY_IS_APPROX(ab.coeff(3,0), -0.04);
79 VERIFY_IS_APPROX(ab.coeff(5,1), 0.05);
80 VERIFY_IS_APPROX(ab.coeff(0,6), -0.08);
81 VERIFY_IS_APPROX(ab.coeff(2,7), 0.10);
82 VERIFY_IS_APPROX(ab.coeff(6,8), 0.12);
83 VERIFY_IS_APPROX(ab.coeff(8,9), -0.15);
84 }
85
86
EIGEN_DECLARE_TEST(kronecker_product)87 EIGEN_DECLARE_TEST(kronecker_product)
88 {
89 // DM = dense matrix; SM = sparse matrix
90
91 Matrix<double, 2, 3> DM_a;
92 SparseMatrix<double> SM_a(2,3);
93 SM_a.insert(0,0) = DM_a.coeffRef(0,0) = -0.4461540300782201;
94 SM_a.insert(0,1) = DM_a.coeffRef(0,1) = -0.8057364375283049;
95 SM_a.insert(0,2) = DM_a.coeffRef(0,2) = 0.3896572459516341;
96 SM_a.insert(1,0) = DM_a.coeffRef(1,0) = -0.9076572187376921;
97 SM_a.insert(1,1) = DM_a.coeffRef(1,1) = 0.6469156566545853;
98 SM_a.insert(1,2) = DM_a.coeffRef(1,2) = -0.3658010398782789;
99
100 MatrixXd DM_b(3,2);
101 SparseMatrix<double> SM_b(3,2);
102 SM_b.insert(0,0) = DM_b.coeffRef(0,0) = 0.9004440976767099;
103 SM_b.insert(0,1) = DM_b.coeffRef(0,1) = -0.2368830858139832;
104 SM_b.insert(1,0) = DM_b.coeffRef(1,0) = -0.9311078389941825;
105 SM_b.insert(1,1) = DM_b.coeffRef(1,1) = 0.5310335762980047;
106 SM_b.insert(2,0) = DM_b.coeffRef(2,0) = -0.1225112806872035;
107 SM_b.insert(2,1) = DM_b.coeffRef(2,1) = 0.5903998022741264;
108
109 SparseMatrix<double,RowMajor> SM_row_a(SM_a), SM_row_b(SM_b);
110
111 // test DM_fixedSize = kroneckerProduct(DM_block,DM)
112 Matrix<double, 6, 6> DM_fix_ab = kroneckerProduct(DM_a.topLeftCorner<2,3>(),DM_b);
113
114 CALL_SUBTEST(check_kronecker_product(DM_fix_ab));
115 CALL_SUBTEST(check_kronecker_product(kroneckerProduct(DM_a.topLeftCorner<2,3>(),DM_b)));
116
117 for(int i=0;i<DM_fix_ab.rows();++i)
118 for(int j=0;j<DM_fix_ab.cols();++j)
119 VERIFY_IS_APPROX(kroneckerProduct(DM_a,DM_b).coeff(i,j), DM_fix_ab(i,j));
120
121 // test DM_block = kroneckerProduct(DM,DM)
122 MatrixXd DM_block_ab(10,15);
123 DM_block_ab.block<6,6>(2,5) = kroneckerProduct(DM_a,DM_b);
124 CALL_SUBTEST(check_kronecker_product(DM_block_ab.block<6,6>(2,5)));
125
126 // test DM = kroneckerProduct(DM,DM)
127 MatrixXd DM_ab = kroneckerProduct(DM_a,DM_b);
128 CALL_SUBTEST(check_kronecker_product(DM_ab));
129 CALL_SUBTEST(check_kronecker_product(kroneckerProduct(DM_a,DM_b)));
130
131 // test SM = kroneckerProduct(SM,DM)
132 SparseMatrix<double> SM_ab = kroneckerProduct(SM_a,DM_b);
133 CALL_SUBTEST(check_kronecker_product(SM_ab));
134 SparseMatrix<double,RowMajor> SM_ab2 = kroneckerProduct(SM_a,DM_b);
135 CALL_SUBTEST(check_kronecker_product(SM_ab2));
136 CALL_SUBTEST(check_kronecker_product(kroneckerProduct(SM_a,DM_b)));
137
138 // test SM = kroneckerProduct(DM,SM)
139 SM_ab.setZero();
140 SM_ab.insert(0,0)=37.0;
141 SM_ab = kroneckerProduct(DM_a,SM_b);
142 CALL_SUBTEST(check_kronecker_product(SM_ab));
143 SM_ab2.setZero();
144 SM_ab2.insert(0,0)=37.0;
145 SM_ab2 = kroneckerProduct(DM_a,SM_b);
146 CALL_SUBTEST(check_kronecker_product(SM_ab2));
147 CALL_SUBTEST(check_kronecker_product(kroneckerProduct(DM_a,SM_b)));
148
149 // test SM = kroneckerProduct(SM,SM)
150 SM_ab.resize(2,33);
151 SM_ab.insert(0,0)=37.0;
152 SM_ab = kroneckerProduct(SM_a,SM_b);
153 CALL_SUBTEST(check_kronecker_product(SM_ab));
154 SM_ab2.resize(5,11);
155 SM_ab2.insert(0,0)=37.0;
156 SM_ab2 = kroneckerProduct(SM_a,SM_b);
157 CALL_SUBTEST(check_kronecker_product(SM_ab2));
158 CALL_SUBTEST(check_kronecker_product(kroneckerProduct(SM_a,SM_b)));
159
160 // test SM = kroneckerProduct(SM,SM) with sparse pattern
161 SM_a.resize(4,5);
162 SM_b.resize(3,2);
163 SM_a.resizeNonZeros(0);
164 SM_b.resizeNonZeros(0);
165 SM_a.insert(1,0) = -0.1;
166 SM_a.insert(0,3) = -0.2;
167 SM_a.insert(2,4) = 0.3;
168 SM_a.finalize();
169
170 SM_b.insert(0,0) = 0.4;
171 SM_b.insert(2,1) = -0.5;
172 SM_b.finalize();
173 SM_ab.resize(1,1);
174 SM_ab.insert(0,0)=37.0;
175 SM_ab = kroneckerProduct(SM_a,SM_b);
176 CALL_SUBTEST(check_sparse_kronecker_product(SM_ab));
177
178 // test dimension of result of DM = kroneckerProduct(DM,DM)
179 MatrixXd DM_a2(2,1);
180 MatrixXd DM_b2(5,4);
181 MatrixXd DM_ab2 = kroneckerProduct(DM_a2,DM_b2);
182 CALL_SUBTEST(check_dimension(DM_ab2,2*5,1*4));
183 DM_a2.resize(10,9);
184 DM_b2.resize(4,8);
185 DM_ab2 = kroneckerProduct(DM_a2,DM_b2);
186 CALL_SUBTEST(check_dimension(DM_ab2,10*4,9*8));
187
188 for(int i = 0; i < g_repeat; i++)
189 {
190 double density = Eigen::internal::random<double>(0.01,0.5);
191 int ra = Eigen::internal::random<int>(1,50);
192 int ca = Eigen::internal::random<int>(1,50);
193 int rb = Eigen::internal::random<int>(1,50);
194 int cb = Eigen::internal::random<int>(1,50);
195 SparseMatrix<float,ColMajor> sA(ra,ca), sB(rb,cb), sC;
196 SparseMatrix<float,RowMajor> sC2;
197 MatrixXf dA(ra,ca), dB(rb,cb), dC;
198 initSparse(density, dA, sA);
199 initSparse(density, dB, sB);
200
201 sC = kroneckerProduct(sA,sB);
202 dC = kroneckerProduct(dA,dB);
203 VERIFY_IS_APPROX(MatrixXf(sC),dC);
204
205 sC = kroneckerProduct(sA.transpose(),sB);
206 dC = kroneckerProduct(dA.transpose(),dB);
207 VERIFY_IS_APPROX(MatrixXf(sC),dC);
208
209 sC = kroneckerProduct(sA.transpose(),sB.transpose());
210 dC = kroneckerProduct(dA.transpose(),dB.transpose());
211 VERIFY_IS_APPROX(MatrixXf(sC),dC);
212
213 sC = kroneckerProduct(sA,sB.transpose());
214 dC = kroneckerProduct(dA,dB.transpose());
215 VERIFY_IS_APPROX(MatrixXf(sC),dC);
216
217 sC2 = kroneckerProduct(sA,sB);
218 dC = kroneckerProduct(dA,dB);
219 VERIFY_IS_APPROX(MatrixXf(sC2),dC);
220
221 sC2 = kroneckerProduct(dA,sB);
222 dC = kroneckerProduct(dA,dB);
223 VERIFY_IS_APPROX(MatrixXf(sC2),dC);
224
225 sC2 = kroneckerProduct(sA,dB);
226 dC = kroneckerProduct(dA,dB);
227 VERIFY_IS_APPROX(MatrixXf(sC2),dC);
228
229 sC2 = kroneckerProduct(2*sA,sB);
230 dC = kroneckerProduct(2*dA,dB);
231 VERIFY_IS_APPROX(MatrixXf(sC2),dC);
232 }
233 }
234
235 #endif
236
237 #ifdef EIGEN_TEST_PART_2
238
239 // simply check that for a dense kronecker product, sparse module is not needed
240 #include "main.h"
241 #include <Eigen/KroneckerProduct>
242
EIGEN_DECLARE_TEST(kronecker_product)243 EIGEN_DECLARE_TEST(kronecker_product)
244 {
245 MatrixXd a(2,2), b(3,3), c;
246 a.setRandom();
247 b.setRandom();
248 c = kroneckerProduct(a,b);
249 VERIFY_IS_APPROX(c.block(3,3,3,3), a(1,1)*b);
250 }
251
252 #endif
253