1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2011 Kolja Brix <brix@igpm.rwth-aachen.de>
5 // Copyright (C) 2011 Andreas Platen <andiplaten@gmx.de>
6 // Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>
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 #ifdef EIGEN_TEST_PART_1
13
14 #include "sparse.h"
15 #include <Eigen/SparseExtra>
16 #include <Eigen/KroneckerProduct>
17
18 template<typename MatrixType>
check_dimension(const MatrixType & ab,const int rows,const int cols)19 void check_dimension(const MatrixType& ab, const int rows, const int cols)
20 {
21 VERIFY_IS_EQUAL(ab.rows(), rows);
22 VERIFY_IS_EQUAL(ab.cols(), cols);
23 }
24
25
26 template<typename MatrixType>
check_kronecker_product(const MatrixType & ab)27 void check_kronecker_product(const MatrixType& ab)
28 {
29 VERIFY_IS_EQUAL(ab.rows(), 6);
30 VERIFY_IS_EQUAL(ab.cols(), 6);
31 VERIFY_IS_EQUAL(ab.nonZeros(), 36);
32 VERIFY_IS_APPROX(ab.coeff(0,0), -0.4017367630386106);
33 VERIFY_IS_APPROX(ab.coeff(0,1), 0.1056863433932735);
34 VERIFY_IS_APPROX(ab.coeff(0,2), -0.7255206194554212);
35 VERIFY_IS_APPROX(ab.coeff(0,3), 0.1908653336744706);
36 VERIFY_IS_APPROX(ab.coeff(0,4), 0.350864567234111);
37 VERIFY_IS_APPROX(ab.coeff(0,5), -0.0923032108308013);
38 VERIFY_IS_APPROX(ab.coeff(1,0), 0.415417514804677);
39 VERIFY_IS_APPROX(ab.coeff(1,1), -0.2369227701722048);
40 VERIFY_IS_APPROX(ab.coeff(1,2), 0.7502275131458511);
41 VERIFY_IS_APPROX(ab.coeff(1,3), -0.4278731019742696);
42 VERIFY_IS_APPROX(ab.coeff(1,4), -0.3628129162264507);
43 VERIFY_IS_APPROX(ab.coeff(1,5), 0.2069210808481275);
44 VERIFY_IS_APPROX(ab.coeff(2,0), 0.05465890160863986);
45 VERIFY_IS_APPROX(ab.coeff(2,1), -0.2634092511419858);
46 VERIFY_IS_APPROX(ab.coeff(2,2), 0.09871180285793758);
47 VERIFY_IS_APPROX(ab.coeff(2,3), -0.4757066334017702);
48 VERIFY_IS_APPROX(ab.coeff(2,4), -0.04773740823058334);
49 VERIFY_IS_APPROX(ab.coeff(2,5), 0.2300535609645254);
50 VERIFY_IS_APPROX(ab.coeff(3,0), -0.8172945853260133);
51 VERIFY_IS_APPROX(ab.coeff(3,1), 0.2150086428359221);
52 VERIFY_IS_APPROX(ab.coeff(3,2), 0.5825113847292743);
53 VERIFY_IS_APPROX(ab.coeff(3,3), -0.1532433770097174);
54 VERIFY_IS_APPROX(ab.coeff(3,4), -0.329383387282399);
55 VERIFY_IS_APPROX(ab.coeff(3,5), 0.08665207912033064);
56 VERIFY_IS_APPROX(ab.coeff(4,0), 0.8451267514863225);
57 VERIFY_IS_APPROX(ab.coeff(4,1), -0.481996458918977);
58 VERIFY_IS_APPROX(ab.coeff(4,2), -0.6023482390791535);
59 VERIFY_IS_APPROX(ab.coeff(4,3), 0.3435339347164565);
60 VERIFY_IS_APPROX(ab.coeff(4,4), 0.3406002157428891);
61 VERIFY_IS_APPROX(ab.coeff(4,5), -0.1942526344200915);
62 VERIFY_IS_APPROX(ab.coeff(5,0), 0.1111982482925399);
63 VERIFY_IS_APPROX(ab.coeff(5,1), -0.5358806424754169);
64 VERIFY_IS_APPROX(ab.coeff(5,2), -0.07925446559335647);
65 VERIFY_IS_APPROX(ab.coeff(5,3), 0.3819388757769038);
66 VERIFY_IS_APPROX(ab.coeff(5,4), 0.04481475387219876);
67 VERIFY_IS_APPROX(ab.coeff(5,5), -0.2159688616158057);
68 }
69
70
71 template<typename MatrixType>
check_sparse_kronecker_product(const MatrixType & ab)72 void check_sparse_kronecker_product(const MatrixType& ab)
73 {
74 VERIFY_IS_EQUAL(ab.rows(), 12);
75 VERIFY_IS_EQUAL(ab.cols(), 10);
76 VERIFY_IS_EQUAL(ab.nonZeros(), 3*2);
77 VERIFY_IS_APPROX(ab.coeff(3,0), -0.04);
78 VERIFY_IS_APPROX(ab.coeff(5,1), 0.05);
79 VERIFY_IS_APPROX(ab.coeff(0,6), -0.08);
80 VERIFY_IS_APPROX(ab.coeff(2,7), 0.10);
81 VERIFY_IS_APPROX(ab.coeff(6,8), 0.12);
82 VERIFY_IS_APPROX(ab.coeff(8,9), -0.15);
83 }
84
85
test_kronecker_product()86 void test_kronecker_product()
87 {
88 // DM = dense matrix; SM = sparse matrix
89
90 Matrix<double, 2, 3> DM_a;
91 SparseMatrix<double> SM_a(2,3);
92 SM_a.insert(0,0) = DM_a.coeffRef(0,0) = -0.4461540300782201;
93 SM_a.insert(0,1) = DM_a.coeffRef(0,1) = -0.8057364375283049;
94 SM_a.insert(0,2) = DM_a.coeffRef(0,2) = 0.3896572459516341;
95 SM_a.insert(1,0) = DM_a.coeffRef(1,0) = -0.9076572187376921;
96 SM_a.insert(1,1) = DM_a.coeffRef(1,1) = 0.6469156566545853;
97 SM_a.insert(1,2) = DM_a.coeffRef(1,2) = -0.3658010398782789;
98
99 MatrixXd DM_b(3,2);
100 SparseMatrix<double> SM_b(3,2);
101 SM_b.insert(0,0) = DM_b.coeffRef(0,0) = 0.9004440976767099;
102 SM_b.insert(0,1) = DM_b.coeffRef(0,1) = -0.2368830858139832;
103 SM_b.insert(1,0) = DM_b.coeffRef(1,0) = -0.9311078389941825;
104 SM_b.insert(1,1) = DM_b.coeffRef(1,1) = 0.5310335762980047;
105 SM_b.insert(2,0) = DM_b.coeffRef(2,0) = -0.1225112806872035;
106 SM_b.insert(2,1) = DM_b.coeffRef(2,1) = 0.5903998022741264;
107
108 SparseMatrix<double,RowMajor> SM_row_a(SM_a), SM_row_b(SM_b);
109
110 // test DM_fixedSize = kroneckerProduct(DM_block,DM)
111 Matrix<double, 6, 6> DM_fix_ab = kroneckerProduct(DM_a.topLeftCorner<2,3>(),DM_b);
112
113 CALL_SUBTEST(check_kronecker_product(DM_fix_ab));
114 CALL_SUBTEST(check_kronecker_product(kroneckerProduct(DM_a.topLeftCorner<2,3>(),DM_b)));
115
116 for(int i=0;i<DM_fix_ab.rows();++i)
117 for(int j=0;j<DM_fix_ab.cols();++j)
118 VERIFY_IS_APPROX(kroneckerProduct(DM_a,DM_b).coeff(i,j), DM_fix_ab(i,j));
119
120 // test DM_block = kroneckerProduct(DM,DM)
121 MatrixXd DM_block_ab(10,15);
122 DM_block_ab.block<6,6>(2,5) = kroneckerProduct(DM_a,DM_b);
123 CALL_SUBTEST(check_kronecker_product(DM_block_ab.block<6,6>(2,5)));
124
125 // test DM = kroneckerProduct(DM,DM)
126 MatrixXd DM_ab = kroneckerProduct(DM_a,DM_b);
127 CALL_SUBTEST(check_kronecker_product(DM_ab));
128 CALL_SUBTEST(check_kronecker_product(kroneckerProduct(DM_a,DM_b)));
129
130 // test SM = kroneckerProduct(SM,DM)
131 SparseMatrix<double> SM_ab = kroneckerProduct(SM_a,DM_b);
132 CALL_SUBTEST(check_kronecker_product(SM_ab));
133 SparseMatrix<double,RowMajor> SM_ab2 = kroneckerProduct(SM_a,DM_b);
134 CALL_SUBTEST(check_kronecker_product(SM_ab2));
135 CALL_SUBTEST(check_kronecker_product(kroneckerProduct(SM_a,DM_b)));
136
137 // test SM = kroneckerProduct(DM,SM)
138 SM_ab.setZero();
139 SM_ab.insert(0,0)=37.0;
140 SM_ab = kroneckerProduct(DM_a,SM_b);
141 CALL_SUBTEST(check_kronecker_product(SM_ab));
142 SM_ab2.setZero();
143 SM_ab2.insert(0,0)=37.0;
144 SM_ab2 = kroneckerProduct(DM_a,SM_b);
145 CALL_SUBTEST(check_kronecker_product(SM_ab2));
146 CALL_SUBTEST(check_kronecker_product(kroneckerProduct(DM_a,SM_b)));
147
148 // test SM = kroneckerProduct(SM,SM)
149 SM_ab.resize(2,33);
150 SM_ab.insert(0,0)=37.0;
151 SM_ab = kroneckerProduct(SM_a,SM_b);
152 CALL_SUBTEST(check_kronecker_product(SM_ab));
153 SM_ab2.resize(5,11);
154 SM_ab2.insert(0,0)=37.0;
155 SM_ab2 = kroneckerProduct(SM_a,SM_b);
156 CALL_SUBTEST(check_kronecker_product(SM_ab2));
157 CALL_SUBTEST(check_kronecker_product(kroneckerProduct(SM_a,SM_b)));
158
159 // test SM = kroneckerProduct(SM,SM) with sparse pattern
160 SM_a.resize(4,5);
161 SM_b.resize(3,2);
162 SM_a.resizeNonZeros(0);
163 SM_b.resizeNonZeros(0);
164 SM_a.insert(1,0) = -0.1;
165 SM_a.insert(0,3) = -0.2;
166 SM_a.insert(2,4) = 0.3;
167 SM_a.finalize();
168
169 SM_b.insert(0,0) = 0.4;
170 SM_b.insert(2,1) = -0.5;
171 SM_b.finalize();
172 SM_ab.resize(1,1);
173 SM_ab.insert(0,0)=37.0;
174 SM_ab = kroneckerProduct(SM_a,SM_b);
175 CALL_SUBTEST(check_sparse_kronecker_product(SM_ab));
176
177 // test dimension of result of DM = kroneckerProduct(DM,DM)
178 MatrixXd DM_a2(2,1);
179 MatrixXd DM_b2(5,4);
180 MatrixXd DM_ab2 = kroneckerProduct(DM_a2,DM_b2);
181 CALL_SUBTEST(check_dimension(DM_ab2,2*5,1*4));
182 DM_a2.resize(10,9);
183 DM_b2.resize(4,8);
184 DM_ab2 = kroneckerProduct(DM_a2,DM_b2);
185 CALL_SUBTEST(check_dimension(DM_ab2,10*4,9*8));
186
187 for(int i = 0; i < g_repeat; i++)
188 {
189 double density = Eigen::internal::random<double>(0.01,0.5);
190 int ra = Eigen::internal::random<int>(1,50);
191 int ca = Eigen::internal::random<int>(1,50);
192 int rb = Eigen::internal::random<int>(1,50);
193 int cb = Eigen::internal::random<int>(1,50);
194 SparseMatrix<float,ColMajor> sA(ra,ca), sB(rb,cb), sC;
195 SparseMatrix<float,RowMajor> sC2;
196 MatrixXf dA(ra,ca), dB(rb,cb), dC;
197 initSparse(density, dA, sA);
198 initSparse(density, dB, sB);
199
200 sC = kroneckerProduct(sA,sB);
201 dC = kroneckerProduct(dA,dB);
202 VERIFY_IS_APPROX(MatrixXf(sC),dC);
203
204 sC = kroneckerProduct(sA.transpose(),sB);
205 dC = kroneckerProduct(dA.transpose(),dB);
206 VERIFY_IS_APPROX(MatrixXf(sC),dC);
207
208 sC = kroneckerProduct(sA.transpose(),sB.transpose());
209 dC = kroneckerProduct(dA.transpose(),dB.transpose());
210 VERIFY_IS_APPROX(MatrixXf(sC),dC);
211
212 sC = kroneckerProduct(sA,sB.transpose());
213 dC = kroneckerProduct(dA,dB.transpose());
214 VERIFY_IS_APPROX(MatrixXf(sC),dC);
215
216 sC2 = kroneckerProduct(sA,sB);
217 dC = kroneckerProduct(dA,dB);
218 VERIFY_IS_APPROX(MatrixXf(sC2),dC);
219
220 sC2 = kroneckerProduct(dA,sB);
221 dC = kroneckerProduct(dA,dB);
222 VERIFY_IS_APPROX(MatrixXf(sC2),dC);
223
224 sC2 = kroneckerProduct(sA,dB);
225 dC = kroneckerProduct(dA,dB);
226 VERIFY_IS_APPROX(MatrixXf(sC2),dC);
227
228 sC2 = kroneckerProduct(2*sA,sB);
229 dC = kroneckerProduct(2*dA,dB);
230 VERIFY_IS_APPROX(MatrixXf(sC2),dC);
231 }
232 }
233
234 #endif
235
236 #ifdef EIGEN_TEST_PART_2
237
238 // simply check that for a dense kronecker product, sparse module is not needed
239
240 #include "main.h"
241 #include <Eigen/KroneckerProduct>
242
test_kronecker_product()243 void 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