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 x.setZero();
41 // test the analyze/factorize API
42 solver.analyzePattern(A);
43 solver.factorize(A);
44 if (solver.info() != Success)
45 {
46 std::cerr << "sparse solver testing: factorization failed (check_sparse_solving)\n";
47 exit(0);
48 return;
49 }
50 x = solver.solve(b);
51 if (solver.info() != Success)
52 {
53 std::cerr << "sparse solver testing: solving failed\n";
54 return;
55 }
56 VERIFY(oldb.isApprox(b) && "sparse solver testing: the rhs should not be modified!");
57
58 VERIFY(x.isApprox(refX,test_precision<Scalar>()));
59 }
60
61 // test dense Block as the result and rhs:
62 {
63 DenseRhs x(db.rows(), db.cols());
64 DenseRhs oldb(db);
65 x.setZero();
66 x.block(0,0,x.rows(),x.cols()) = solver.solve(db.block(0,0,db.rows(),db.cols()));
67 VERIFY(oldb.isApprox(db) && "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
117 solver.compute(A);
118 if (solver.info() != Success)
119 {
120 std::cerr << "sparse solver testing: factorization failed (check_sparse_determinant)\n";
121 return;
122 }
123
124 Scalar refDet = dA.determinant();
125 VERIFY_IS_APPROX(refDet,solver.determinant());
126 }
127 template<typename Solver, typename DenseMat>
check_sparse_abs_determinant(Solver & solver,const typename Solver::MatrixType & A,const DenseMat & dA)128 void check_sparse_abs_determinant(Solver& solver, const typename Solver::MatrixType& A, const DenseMat& dA)
129 {
130 using std::abs;
131 typedef typename Solver::MatrixType Mat;
132 typedef typename Mat::Scalar Scalar;
133
134 solver.compute(A);
135 if (solver.info() != Success)
136 {
137 std::cerr << "sparse solver testing: factorization failed (check_sparse_abs_determinant)\n";
138 return;
139 }
140
141 Scalar refDet = abs(dA.determinant());
142 VERIFY_IS_APPROX(refDet,solver.absDeterminant());
143 }
144
145 template<typename Solver, typename DenseMat>
146 int generate_sparse_spd_problem(Solver& , typename Solver::MatrixType& A, typename Solver::MatrixType& halfA, DenseMat& dA, int maxSize = 300)
147 {
148 typedef typename Solver::MatrixType Mat;
149 typedef typename Mat::Scalar Scalar;
150 typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
151
152 int size = internal::random<int>(1,maxSize);
153 double density = (std::max)(8./(size*size), 0.01);
154
155 Mat M(size, size);
156 DenseMatrix dM(size, size);
157
158 initSparse<Scalar>(density, dM, M, ForceNonZeroDiag);
159
160 A = M * M.adjoint();
161 dA = dM * dM.adjoint();
162
163 halfA.resize(size,size);
164 halfA.template selfadjointView<Solver::UpLo>().rankUpdate(M);
165
166 return size;
167 }
168
169
170 #ifdef TEST_REAL_CASES
171 template<typename Scalar>
get_matrixfolder()172 inline std::string get_matrixfolder()
173 {
174 std::string mat_folder = TEST_REAL_CASES;
175 if( internal::is_same<Scalar, std::complex<float> >::value || internal::is_same<Scalar, std::complex<double> >::value )
176 mat_folder = mat_folder + static_cast<std::string>("/complex/");
177 else
178 mat_folder = mat_folder + static_cast<std::string>("/real/");
179 return mat_folder;
180 }
181 #endif
182
check_sparse_spd_solving(Solver & solver)183 template<typename Solver> void check_sparse_spd_solving(Solver& solver)
184 {
185 typedef typename Solver::MatrixType Mat;
186 typedef typename Mat::Scalar Scalar;
187 typedef SparseMatrix<Scalar,ColMajor> SpMat;
188 typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
189 typedef Matrix<Scalar,Dynamic,1> DenseVector;
190
191 // generate the problem
192 Mat A, halfA;
193 DenseMatrix dA;
194 for (int i = 0; i < g_repeat; i++) {
195 int size = generate_sparse_spd_problem(solver, A, halfA, dA);
196
197 // generate the right hand sides
198 int rhsCols = internal::random<int>(1,16);
199 double density = (std::max)(8./(size*rhsCols), 0.1);
200 SpMat B(size,rhsCols);
201 DenseVector b = DenseVector::Random(size);
202 DenseMatrix dB(size,rhsCols);
203 initSparse<Scalar>(density, dB, B, ForceNonZeroDiag);
204
205 check_sparse_solving(solver, A, b, dA, b);
206 check_sparse_solving(solver, halfA, b, dA, b);
207 check_sparse_solving(solver, A, dB, dA, dB);
208 check_sparse_solving(solver, halfA, dB, dA, dB);
209 check_sparse_solving(solver, A, B, dA, dB);
210 check_sparse_solving(solver, halfA, B, dA, dB);
211
212 // check only once
213 if(i==0)
214 {
215 b = DenseVector::Zero(size);
216 check_sparse_solving(solver, A, b, dA, b);
217 }
218 }
219
220 // First, get the folder
221 #ifdef TEST_REAL_CASES
222 if (internal::is_same<Scalar, float>::value
223 || internal::is_same<Scalar, std::complex<float> >::value)
224 return ;
225
226 std::string mat_folder = get_matrixfolder<Scalar>();
227 MatrixMarketIterator<Scalar> it(mat_folder);
228 for (; it; ++it)
229 {
230 if (it.sym() == SPD){
231 Mat halfA;
232 PermutationMatrix<Dynamic, Dynamic, Index> pnull;
233 halfA.template selfadjointView<Solver::UpLo>() = it.matrix().template triangularView<Eigen::Lower>().twistedBy(pnull);
234
235 std::cout<< " ==== SOLVING WITH MATRIX " << it.matname() << " ==== \n";
236 check_sparse_solving_real_cases(solver, it.matrix(), it.rhs(), it.refX());
237 check_sparse_solving_real_cases(solver, halfA, it.rhs(), it.refX());
238 }
239 }
240 #endif
241 }
242
check_sparse_spd_determinant(Solver & solver)243 template<typename Solver> void check_sparse_spd_determinant(Solver& solver)
244 {
245 typedef typename Solver::MatrixType Mat;
246 typedef typename Mat::Scalar Scalar;
247 typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
248
249 // generate the problem
250 Mat A, halfA;
251 DenseMatrix dA;
252 generate_sparse_spd_problem(solver, A, halfA, dA, 30);
253
254 for (int i = 0; i < g_repeat; i++) {
255 check_sparse_determinant(solver, A, dA);
256 check_sparse_determinant(solver, halfA, dA );
257 }
258 }
259
260 template<typename Solver, typename DenseMat>
261 int generate_sparse_square_problem(Solver&, typename Solver::MatrixType& A, DenseMat& dA, int maxSize = 300)
262 {
263 typedef typename Solver::MatrixType Mat;
264 typedef typename Mat::Scalar Scalar;
265
266 int size = internal::random<int>(1,maxSize);
267 double density = (std::max)(8./(size*size), 0.01);
268
269 A.resize(size,size);
270 dA.resize(size,size);
271
272 initSparse<Scalar>(density, dA, A, ForceNonZeroDiag);
273
274 return size;
275 }
276
check_sparse_square_solving(Solver & solver)277 template<typename Solver> void check_sparse_square_solving(Solver& solver)
278 {
279 typedef typename Solver::MatrixType Mat;
280 typedef typename Mat::Scalar Scalar;
281 typedef SparseMatrix<Scalar,ColMajor> SpMat;
282 typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
283 typedef Matrix<Scalar,Dynamic,1> DenseVector;
284
285 int rhsCols = internal::random<int>(1,16);
286
287 Mat A;
288 DenseMatrix dA;
289 for (int i = 0; i < g_repeat; i++) {
290 int size = generate_sparse_square_problem(solver, A, dA);
291
292 A.makeCompressed();
293 DenseVector b = DenseVector::Random(size);
294 DenseMatrix dB(size,rhsCols);
295 SpMat B(size,rhsCols);
296 double density = (std::max)(8./(size*rhsCols), 0.1);
297 initSparse<Scalar>(density, dB, B, ForceNonZeroDiag);
298 B.makeCompressed();
299 check_sparse_solving(solver, A, b, dA, b);
300 check_sparse_solving(solver, A, dB, dA, dB);
301 check_sparse_solving(solver, A, B, dA, dB);
302
303 // check only once
304 if(i==0)
305 {
306 b = DenseVector::Zero(size);
307 check_sparse_solving(solver, A, b, dA, b);
308 }
309 }
310
311 // First, get the folder
312 #ifdef TEST_REAL_CASES
313 if (internal::is_same<Scalar, float>::value
314 || internal::is_same<Scalar, std::complex<float> >::value)
315 return ;
316
317 std::string mat_folder = get_matrixfolder<Scalar>();
318 MatrixMarketIterator<Scalar> it(mat_folder);
319 for (; it; ++it)
320 {
321 std::cout<< " ==== SOLVING WITH MATRIX " << it.matname() << " ==== \n";
322 check_sparse_solving_real_cases(solver, it.matrix(), it.rhs(), it.refX());
323 }
324 #endif
325
326 }
327
check_sparse_square_determinant(Solver & solver)328 template<typename Solver> void check_sparse_square_determinant(Solver& solver)
329 {
330 typedef typename Solver::MatrixType Mat;
331 typedef typename Mat::Scalar Scalar;
332 typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
333
334 // generate the problem
335 Mat A;
336 DenseMatrix dA;
337 generate_sparse_square_problem(solver, A, dA, 30);
338 A.makeCompressed();
339 for (int i = 0; i < g_repeat; i++) {
340 check_sparse_determinant(solver, A, dA);
341 }
342 }
343
check_sparse_square_abs_determinant(Solver & solver)344 template<typename Solver> void check_sparse_square_abs_determinant(Solver& solver)
345 {
346 typedef typename Solver::MatrixType Mat;
347 typedef typename Mat::Scalar Scalar;
348 typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
349
350 // generate the problem
351 Mat A;
352 DenseMatrix dA;
353 generate_sparse_square_problem(solver, A, dA, 30);
354 A.makeCompressed();
355 for (int i = 0; i < g_repeat; i++) {
356 check_sparse_abs_determinant(solver, A, dA);
357 }
358 }
359
360