1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2011 Gael Guennebaud <g.gael@free.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 #include <Eigen/SparseCore>
12
13 template<typename Solver, typename Rhs, typename DenseMat, typename DenseRhs>
check_sparse_solving(Solver & solver,const typename Solver::MatrixType & A,const Rhs & b,const DenseMat & dA,const DenseRhs & db)14 void check_sparse_solving(Solver& solver, const typename Solver::MatrixType& A, const Rhs& b, const DenseMat& dA, const DenseRhs& db)
15 {
16 typedef typename Solver::MatrixType Mat;
17 typedef typename Mat::Scalar Scalar;
18
19 DenseRhs refX = dA.lu().solve(db);
20
21 Rhs x(b.rows(), b.cols());
22 Rhs oldb = b;
23
24 solver.compute(A);
25 if (solver.info() != Success)
26 {
27 std::cerr << "sparse solver testing: factorization failed (check_sparse_solving)\n";
28 exit(0);
29 return;
30 }
31 x = solver.solve(b);
32 if (solver.info() != Success)
33 {
34 std::cerr << "sparse solver testing: solving failed\n";
35 return;
36 }
37 VERIFY(oldb.isApprox(b) && "sparse solver testing: the rhs should not be modified!");
38
39 VERIFY(x.isApprox(refX,test_precision<Scalar>()));
40
41 x.setZero();
42 // test the analyze/factorize API
43 solver.analyzePattern(A);
44 solver.factorize(A);
45 if (solver.info() != Success)
46 {
47 std::cerr << "sparse solver testing: factorization failed (check_sparse_solving)\n";
48 exit(0);
49 return;
50 }
51 x = solver.solve(b);
52 if (solver.info() != Success)
53 {
54 std::cerr << "sparse solver testing: solving failed\n";
55 return;
56 }
57 VERIFY(oldb.isApprox(b) && "sparse solver testing: the rhs should not be modified!");
58
59 VERIFY(x.isApprox(refX,test_precision<Scalar>()));
60
61 // test Block as the result and rhs:
62 {
63 DenseRhs x(db.rows(), db.cols());
64 DenseRhs b(db), oldb(db);
65 x.setZero();
66 x.block(0,0,x.rows(),x.cols()) = solver.solve(b.block(0,0,b.rows(),b.cols()));
67 VERIFY(oldb.isApprox(b) && "sparse solver testing: the rhs should not be modified!");
68 VERIFY(x.isApprox(refX,test_precision<Scalar>()));
69 }
70 }
71
72 template<typename Solver, typename Rhs>
check_sparse_solving_real_cases(Solver & solver,const typename Solver::MatrixType & A,const Rhs & b,const Rhs & refX)73 void check_sparse_solving_real_cases(Solver& solver, const typename Solver::MatrixType& A, const Rhs& b, const Rhs& refX)
74 {
75 typedef typename Solver::MatrixType Mat;
76 typedef typename Mat::Scalar Scalar;
77 typedef typename Mat::RealScalar RealScalar;
78
79 Rhs x(b.rows(), b.cols());
80
81 solver.compute(A);
82 if (solver.info() != Success)
83 {
84 std::cerr << "sparse solver testing: factorization failed (check_sparse_solving_real_cases)\n";
85 exit(0);
86 return;
87 }
88 x = solver.solve(b);
89 if (solver.info() != Success)
90 {
91 std::cerr << "sparse solver testing: solving failed\n";
92 return;
93 }
94
95 RealScalar res_error;
96 // Compute the norm of the relative error
97 if(refX.size() != 0)
98 res_error = (refX - x).norm()/refX.norm();
99 else
100 {
101 // Compute the relative residual norm
102 res_error = (b - A * x).norm()/b.norm();
103 }
104 if (res_error > test_precision<Scalar>() ){
105 std::cerr << "Test " << g_test_stack.back() << " failed in "EI_PP_MAKE_STRING(__FILE__)
106 << " (" << EI_PP_MAKE_STRING(__LINE__) << ")" << std::endl << std::endl;
107 abort();
108 }
109
110 }
111 template<typename Solver, typename DenseMat>
check_sparse_determinant(Solver & solver,const typename Solver::MatrixType & A,const DenseMat & dA)112 void check_sparse_determinant(Solver& solver, const typename Solver::MatrixType& A, const DenseMat& dA)
113 {
114 typedef typename Solver::MatrixType Mat;
115 typedef typename Mat::Scalar Scalar;
116 typedef typename Mat::RealScalar RealScalar;
117
118 solver.compute(A);
119 if (solver.info() != Success)
120 {
121 std::cerr << "sparse solver testing: factorization failed (check_sparse_determinant)\n";
122 return;
123 }
124
125 Scalar refDet = dA.determinant();
126 VERIFY_IS_APPROX(refDet,solver.determinant());
127 }
128
129
130 template<typename Solver, typename DenseMat>
131 int generate_sparse_spd_problem(Solver& , typename Solver::MatrixType& A, typename Solver::MatrixType& halfA, DenseMat& dA, int maxSize = 300)
132 {
133 typedef typename Solver::MatrixType Mat;
134 typedef typename Mat::Scalar Scalar;
135 typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
136
137 int size = internal::random<int>(1,maxSize);
138 double density = (std::max)(8./(size*size), 0.01);
139
140 Mat M(size, size);
141 DenseMatrix dM(size, size);
142
143 initSparse<Scalar>(density, dM, M, ForceNonZeroDiag);
144
145 A = M * M.adjoint();
146 dA = dM * dM.adjoint();
147
148 halfA.resize(size,size);
149 halfA.template selfadjointView<Solver::UpLo>().rankUpdate(M);
150
151 return size;
152 }
153
154
155 #ifdef TEST_REAL_CASES
156 template<typename Scalar>
get_matrixfolder()157 inline std::string get_matrixfolder()
158 {
159 std::string mat_folder = TEST_REAL_CASES;
160 if( internal::is_same<Scalar, std::complex<float> >::value || internal::is_same<Scalar, std::complex<double> >::value )
161 mat_folder = mat_folder + static_cast<string>("/complex/");
162 else
163 mat_folder = mat_folder + static_cast<string>("/real/");
164 return mat_folder;
165 }
166 #endif
167
check_sparse_spd_solving(Solver & solver)168 template<typename Solver> void check_sparse_spd_solving(Solver& solver)
169 {
170 typedef typename Solver::MatrixType Mat;
171 typedef typename Mat::Scalar Scalar;
172 typedef typename Mat::Index Index;
173 typedef SparseMatrix<Scalar,ColMajor> SpMat;
174 typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
175 typedef Matrix<Scalar,Dynamic,1> DenseVector;
176
177 // generate the problem
178 Mat A, halfA;
179 DenseMatrix dA;
180 int size = generate_sparse_spd_problem(solver, A, halfA, dA);
181
182 // generate the right hand sides
183 int rhsCols = internal::random<int>(1,16);
184 double density = (std::max)(8./(size*rhsCols), 0.1);
185 SpMat B(size,rhsCols);
186 DenseVector b = DenseVector::Random(size);
187 DenseMatrix dB(size,rhsCols);
188 initSparse<Scalar>(density, dB, B, ForceNonZeroDiag);
189
190 for (int i = 0; i < g_repeat; i++) {
191 check_sparse_solving(solver, A, b, dA, b);
192 check_sparse_solving(solver, halfA, b, dA, b);
193 check_sparse_solving(solver, A, dB, dA, dB);
194 check_sparse_solving(solver, halfA, dB, dA, dB);
195 check_sparse_solving(solver, A, B, dA, dB);
196 check_sparse_solving(solver, halfA, B, dA, dB);
197 }
198
199 // First, get the folder
200 #ifdef TEST_REAL_CASES
201 if (internal::is_same<Scalar, float>::value
202 || internal::is_same<Scalar, std::complex<float> >::value)
203 return ;
204
205 std::string mat_folder = get_matrixfolder<Scalar>();
206 MatrixMarketIterator<Scalar> it(mat_folder);
207 for (; it; ++it)
208 {
209 if (it.sym() == SPD){
210 Mat halfA;
211 PermutationMatrix<Dynamic, Dynamic, Index> pnull;
212 halfA.template selfadjointView<Solver::UpLo>() = it.matrix().template triangularView<Eigen::Lower>().twistedBy(pnull);
213
214 std::cout<< " ==== SOLVING WITH MATRIX " << it.matname() << " ==== \n";
215 check_sparse_solving_real_cases(solver, it.matrix(), it.rhs(), it.refX());
216 check_sparse_solving_real_cases(solver, halfA, it.rhs(), it.refX());
217 }
218 }
219 #endif
220 }
221
check_sparse_spd_determinant(Solver & solver)222 template<typename Solver> void check_sparse_spd_determinant(Solver& solver)
223 {
224 typedef typename Solver::MatrixType Mat;
225 typedef typename Mat::Scalar Scalar;
226 typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
227
228 // generate the problem
229 Mat A, halfA;
230 DenseMatrix dA;
231 generate_sparse_spd_problem(solver, A, halfA, dA, 30);
232
233 for (int i = 0; i < g_repeat; i++) {
234 check_sparse_determinant(solver, A, dA);
235 check_sparse_determinant(solver, halfA, dA );
236 }
237 }
238
239 template<typename Solver, typename DenseMat>
240 int generate_sparse_square_problem(Solver&, typename Solver::MatrixType& A, DenseMat& dA, int maxSize = 300)
241 {
242 typedef typename Solver::MatrixType Mat;
243 typedef typename Mat::Scalar Scalar;
244 typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
245
246 int size = internal::random<int>(1,maxSize);
247 double density = (std::max)(8./(size*size), 0.01);
248
249 A.resize(size,size);
250 dA.resize(size,size);
251
252 initSparse<Scalar>(density, dA, A, ForceNonZeroDiag);
253
254 return size;
255 }
256
check_sparse_square_solving(Solver & solver)257 template<typename Solver> void check_sparse_square_solving(Solver& solver)
258 {
259 typedef typename Solver::MatrixType Mat;
260 typedef typename Mat::Scalar Scalar;
261 typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
262 typedef Matrix<Scalar,Dynamic,1> DenseVector;
263
264 int rhsCols = internal::random<int>(1,16);
265
266 Mat A;
267 DenseMatrix dA;
268 int size = generate_sparse_square_problem(solver, A, dA);
269
270 DenseVector b = DenseVector::Random(size);
271 DenseMatrix dB = DenseMatrix::Random(size,rhsCols);
272 A.makeCompressed();
273 for (int i = 0; i < g_repeat; i++) {
274 check_sparse_solving(solver, A, b, dA, b);
275 check_sparse_solving(solver, A, dB, dA, dB);
276 }
277
278 // First, get the folder
279 #ifdef TEST_REAL_CASES
280 if (internal::is_same<Scalar, float>::value
281 || internal::is_same<Scalar, std::complex<float> >::value)
282 return ;
283
284 std::string mat_folder = get_matrixfolder<Scalar>();
285 MatrixMarketIterator<Scalar> it(mat_folder);
286 for (; it; ++it)
287 {
288 std::cout<< " ==== SOLVING WITH MATRIX " << it.matname() << " ==== \n";
289 check_sparse_solving_real_cases(solver, it.matrix(), it.rhs(), it.refX());
290 }
291 #endif
292
293 }
294
check_sparse_square_determinant(Solver & solver)295 template<typename Solver> void check_sparse_square_determinant(Solver& solver)
296 {
297 typedef typename Solver::MatrixType Mat;
298 typedef typename Mat::Scalar Scalar;
299 typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
300
301 // generate the problem
302 Mat A;
303 DenseMatrix dA;
304 generate_sparse_square_problem(solver, A, dA, 30);
305 A.makeCompressed();
306 for (int i = 0; i < g_repeat; i++) {
307 check_sparse_determinant(solver, A, dA);
308 }
309 }
310