1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2008-2011 Gael Guennebaud <[email protected]>
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 #if defined(_MSC_VER) && (_MSC_VER==1800)
11 // This unit test takes forever to compile in Release mode with MSVC 2013,
12 // multiple hours. So let's switch off optimization for this one.
13 #pragma optimize("",off)
14 #endif
15
16 static long int nb_temporaries;
17
on_temporary_creation()18 inline void on_temporary_creation() {
19 // here's a great place to set a breakpoint when debugging failures in this test!
20 nb_temporaries++;
21 }
22
23 #define EIGEN_SPARSE_CREATE_TEMPORARY_PLUGIN { on_temporary_creation(); }
24
25 #include "sparse.h"
26
27 #define VERIFY_EVALUATION_COUNT(XPR,N) {\
28 nb_temporaries = 0; \
29 CALL_SUBTEST( XPR ); \
30 if(nb_temporaries!=N) std::cerr << "nb_temporaries == " << nb_temporaries << "\n"; \
31 VERIFY( (#XPR) && nb_temporaries==N ); \
32 }
33
34
35
sparse_product()36 template<typename SparseMatrixType> void sparse_product()
37 {
38 typedef typename SparseMatrixType::StorageIndex StorageIndex;
39 Index n = 100;
40 const Index rows = internal::random<Index>(1,n);
41 const Index cols = internal::random<Index>(1,n);
42 const Index depth = internal::random<Index>(1,n);
43 typedef typename SparseMatrixType::Scalar Scalar;
44 enum { Flags = SparseMatrixType::Flags };
45
46 double density = (std::max)(8./(rows*cols), 0.2);
47 typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
48 typedef Matrix<Scalar,Dynamic,1> DenseVector;
49 typedef Matrix<Scalar,1,Dynamic> RowDenseVector;
50 typedef SparseVector<Scalar,0,StorageIndex> ColSpVector;
51 typedef SparseVector<Scalar,RowMajor,StorageIndex> RowSpVector;
52
53 Scalar s1 = internal::random<Scalar>();
54 Scalar s2 = internal::random<Scalar>();
55
56 // test matrix-matrix product
57 {
58 DenseMatrix refMat2 = DenseMatrix::Zero(rows, depth);
59 DenseMatrix refMat2t = DenseMatrix::Zero(depth, rows);
60 DenseMatrix refMat3 = DenseMatrix::Zero(depth, cols);
61 DenseMatrix refMat3t = DenseMatrix::Zero(cols, depth);
62 DenseMatrix refMat4 = DenseMatrix::Zero(rows, cols);
63 DenseMatrix refMat4t = DenseMatrix::Zero(cols, rows);
64 DenseMatrix refMat5 = DenseMatrix::Random(depth, cols);
65 DenseMatrix refMat6 = DenseMatrix::Random(rows, rows);
66 DenseMatrix dm4 = DenseMatrix::Zero(rows, rows);
67 // DenseVector dv1 = DenseVector::Random(rows);
68 SparseMatrixType m2 (rows, depth);
69 SparseMatrixType m2t(depth, rows);
70 SparseMatrixType m3 (depth, cols);
71 SparseMatrixType m3t(cols, depth);
72 SparseMatrixType m4 (rows, cols);
73 SparseMatrixType m4t(cols, rows);
74 SparseMatrixType m6(rows, rows);
75 initSparse(density, refMat2, m2);
76 initSparse(density, refMat2t, m2t);
77 initSparse(density, refMat3, m3);
78 initSparse(density, refMat3t, m3t);
79 initSparse(density, refMat4, m4);
80 initSparse(density, refMat4t, m4t);
81 initSparse(density, refMat6, m6);
82
83 // int c = internal::random<int>(0,depth-1);
84
85 // sparse * sparse
86 VERIFY_IS_APPROX(m4=m2*m3, refMat4=refMat2*refMat3);
87 VERIFY_IS_APPROX(m4=m2t.transpose()*m3, refMat4=refMat2t.transpose()*refMat3);
88 VERIFY_IS_APPROX(m4=m2t.transpose()*m3t.transpose(), refMat4=refMat2t.transpose()*refMat3t.transpose());
89 VERIFY_IS_APPROX(m4=m2*m3t.transpose(), refMat4=refMat2*refMat3t.transpose());
90
91 VERIFY_IS_APPROX(m4 = m2*m3/s1, refMat4 = refMat2*refMat3/s1);
92 VERIFY_IS_APPROX(m4 = m2*m3*s1, refMat4 = refMat2*refMat3*s1);
93 VERIFY_IS_APPROX(m4 = s2*m2*m3*s1, refMat4 = s2*refMat2*refMat3*s1);
94 VERIFY_IS_APPROX(m4 = (m2+m2)*m3, refMat4 = (refMat2+refMat2)*refMat3);
95 VERIFY_IS_APPROX(m4 = m2*m3.leftCols(cols/2), refMat4 = refMat2*refMat3.leftCols(cols/2));
96 VERIFY_IS_APPROX(m4 = m2*(m3+m3).leftCols(cols/2), refMat4 = refMat2*(refMat3+refMat3).leftCols(cols/2));
97
98 VERIFY_IS_APPROX(m4=(m2*m3).pruned(0), refMat4=refMat2*refMat3);
99 VERIFY_IS_APPROX(m4=(m2t.transpose()*m3).pruned(0), refMat4=refMat2t.transpose()*refMat3);
100 VERIFY_IS_APPROX(m4=(m2t.transpose()*m3t.transpose()).pruned(0), refMat4=refMat2t.transpose()*refMat3t.transpose());
101 VERIFY_IS_APPROX(m4=(m2*m3t.transpose()).pruned(0), refMat4=refMat2*refMat3t.transpose());
102
103 #ifndef EIGEN_SPARSE_PRODUCT_IGNORE_TEMPORARY_COUNT
104 // make sure the right product implementation is called:
105 if((!SparseMatrixType::IsRowMajor) && m2.rows()<=m3.cols())
106 {
107 VERIFY_EVALUATION_COUNT(m4 = m2*m3, 2); // 2 for transposing and get a sorted result.
108 VERIFY_EVALUATION_COUNT(m4 = (m2*m3).pruned(0), 1);
109 VERIFY_EVALUATION_COUNT(m4 = (m2*m3).eval().pruned(0), 4);
110 }
111 #endif
112
113 // and that pruning is effective:
114 {
115 DenseMatrix Ad(2,2);
116 Ad << -1, 1, 1, 1;
117 SparseMatrixType As(Ad.sparseView()), B(2,2);
118 VERIFY_IS_EQUAL( (As*As.transpose()).eval().nonZeros(), 4);
119 VERIFY_IS_EQUAL( (Ad*Ad.transpose()).eval().sparseView().eval().nonZeros(), 2);
120 VERIFY_IS_EQUAL( (As*As.transpose()).pruned(1e-6).eval().nonZeros(), 2);
121 }
122
123 // dense ?= sparse * sparse
124 VERIFY_IS_APPROX(dm4 =m2*m3, refMat4 =refMat2*refMat3);
125 VERIFY_IS_APPROX(dm4+=m2*m3, refMat4+=refMat2*refMat3);
126 VERIFY_IS_APPROX(dm4-=m2*m3, refMat4-=refMat2*refMat3);
127 VERIFY_IS_APPROX(dm4 =m2t.transpose()*m3, refMat4 =refMat2t.transpose()*refMat3);
128 VERIFY_IS_APPROX(dm4+=m2t.transpose()*m3, refMat4+=refMat2t.transpose()*refMat3);
129 VERIFY_IS_APPROX(dm4-=m2t.transpose()*m3, refMat4-=refMat2t.transpose()*refMat3);
130 VERIFY_IS_APPROX(dm4 =m2t.transpose()*m3t.transpose(), refMat4 =refMat2t.transpose()*refMat3t.transpose());
131 VERIFY_IS_APPROX(dm4+=m2t.transpose()*m3t.transpose(), refMat4+=refMat2t.transpose()*refMat3t.transpose());
132 VERIFY_IS_APPROX(dm4-=m2t.transpose()*m3t.transpose(), refMat4-=refMat2t.transpose()*refMat3t.transpose());
133 VERIFY_IS_APPROX(dm4 =m2*m3t.transpose(), refMat4 =refMat2*refMat3t.transpose());
134 VERIFY_IS_APPROX(dm4+=m2*m3t.transpose(), refMat4+=refMat2*refMat3t.transpose());
135 VERIFY_IS_APPROX(dm4-=m2*m3t.transpose(), refMat4-=refMat2*refMat3t.transpose());
136 VERIFY_IS_APPROX(dm4 = m2*m3*s1, refMat4 = refMat2*refMat3*s1);
137
138 // test aliasing
139 m4 = m2; refMat4 = refMat2;
140 VERIFY_IS_APPROX(m4=m4*m3, refMat4=refMat4*refMat3);
141
142 // sparse * dense matrix
143 VERIFY_IS_APPROX(dm4=m2*refMat3, refMat4=refMat2*refMat3);
144 VERIFY_IS_APPROX(dm4=m2*refMat3t.transpose(), refMat4=refMat2*refMat3t.transpose());
145 VERIFY_IS_APPROX(dm4=m2t.transpose()*refMat3, refMat4=refMat2t.transpose()*refMat3);
146 VERIFY_IS_APPROX(dm4=m2t.transpose()*refMat3t.transpose(), refMat4=refMat2t.transpose()*refMat3t.transpose());
147
148 VERIFY_IS_APPROX(dm4=m2*refMat3, refMat4=refMat2*refMat3);
149 VERIFY_IS_APPROX(dm4=dm4+m2*refMat3, refMat4=refMat4+refMat2*refMat3);
150 VERIFY_IS_APPROX(dm4+=m2*refMat3, refMat4+=refMat2*refMat3);
151 VERIFY_IS_APPROX(dm4-=m2*refMat3, refMat4-=refMat2*refMat3);
152 VERIFY_IS_APPROX(dm4.noalias()+=m2*refMat3, refMat4+=refMat2*refMat3);
153 VERIFY_IS_APPROX(dm4.noalias()-=m2*refMat3, refMat4-=refMat2*refMat3);
154 VERIFY_IS_APPROX(dm4=m2*(refMat3+refMat3), refMat4=refMat2*(refMat3+refMat3));
155 VERIFY_IS_APPROX(dm4=m2t.transpose()*(refMat3+refMat5)*0.5, refMat4=refMat2t.transpose()*(refMat3+refMat5)*0.5);
156
157 // sparse * dense vector
158 VERIFY_IS_APPROX(dm4.col(0)=m2*refMat3.col(0), refMat4.col(0)=refMat2*refMat3.col(0));
159 VERIFY_IS_APPROX(dm4.col(0)=m2*refMat3t.transpose().col(0), refMat4.col(0)=refMat2*refMat3t.transpose().col(0));
160 VERIFY_IS_APPROX(dm4.col(0)=m2t.transpose()*refMat3.col(0), refMat4.col(0)=refMat2t.transpose()*refMat3.col(0));
161 VERIFY_IS_APPROX(dm4.col(0)=m2t.transpose()*refMat3t.transpose().col(0), refMat4.col(0)=refMat2t.transpose()*refMat3t.transpose().col(0));
162
163 // dense * sparse
164 VERIFY_IS_APPROX(dm4=refMat2*m3, refMat4=refMat2*refMat3);
165 VERIFY_IS_APPROX(dm4=dm4+refMat2*m3, refMat4=refMat4+refMat2*refMat3);
166 VERIFY_IS_APPROX(dm4+=refMat2*m3, refMat4+=refMat2*refMat3);
167 VERIFY_IS_APPROX(dm4-=refMat2*m3, refMat4-=refMat2*refMat3);
168 VERIFY_IS_APPROX(dm4.noalias()+=refMat2*m3, refMat4+=refMat2*refMat3);
169 VERIFY_IS_APPROX(dm4.noalias()-=refMat2*m3, refMat4-=refMat2*refMat3);
170 VERIFY_IS_APPROX(dm4=refMat2*m3t.transpose(), refMat4=refMat2*refMat3t.transpose());
171 VERIFY_IS_APPROX(dm4=refMat2t.transpose()*m3, refMat4=refMat2t.transpose()*refMat3);
172 VERIFY_IS_APPROX(dm4=refMat2t.transpose()*m3t.transpose(), refMat4=refMat2t.transpose()*refMat3t.transpose());
173
174 // sparse * dense and dense * sparse outer product
175 {
176 Index c = internal::random<Index>(0,depth-1);
177 Index r = internal::random<Index>(0,rows-1);
178 Index c1 = internal::random<Index>(0,cols-1);
179 Index r1 = internal::random<Index>(0,depth-1);
180 DenseMatrix dm5 = DenseMatrix::Random(depth, cols);
181
182 VERIFY_IS_APPROX( m4=m2.col(c)*dm5.col(c1).transpose(), refMat4=refMat2.col(c)*dm5.col(c1).transpose());
183 VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
184 VERIFY_IS_APPROX( m4=m2.middleCols(c,1)*dm5.col(c1).transpose(), refMat4=refMat2.col(c)*dm5.col(c1).transpose());
185 VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
186 VERIFY_IS_APPROX(dm4=m2.col(c)*dm5.col(c1).transpose(), refMat4=refMat2.col(c)*dm5.col(c1).transpose());
187
188 VERIFY_IS_APPROX(m4=dm5.col(c1)*m2.col(c).transpose(), refMat4=dm5.col(c1)*refMat2.col(c).transpose());
189 VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
190 VERIFY_IS_APPROX(m4=dm5.col(c1)*m2.middleCols(c,1).transpose(), refMat4=dm5.col(c1)*refMat2.col(c).transpose());
191 VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
192 VERIFY_IS_APPROX(dm4=dm5.col(c1)*m2.col(c).transpose(), refMat4=dm5.col(c1)*refMat2.col(c).transpose());
193
194 VERIFY_IS_APPROX( m4=dm5.row(r1).transpose()*m2.col(c).transpose(), refMat4=dm5.row(r1).transpose()*refMat2.col(c).transpose());
195 VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
196 VERIFY_IS_APPROX(dm4=dm5.row(r1).transpose()*m2.col(c).transpose(), refMat4=dm5.row(r1).transpose()*refMat2.col(c).transpose());
197
198 VERIFY_IS_APPROX( m4=m2.row(r).transpose()*dm5.col(c1).transpose(), refMat4=refMat2.row(r).transpose()*dm5.col(c1).transpose());
199 VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
200 VERIFY_IS_APPROX( m4=m2.middleRows(r,1).transpose()*dm5.col(c1).transpose(), refMat4=refMat2.row(r).transpose()*dm5.col(c1).transpose());
201 VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
202 VERIFY_IS_APPROX(dm4=m2.row(r).transpose()*dm5.col(c1).transpose(), refMat4=refMat2.row(r).transpose()*dm5.col(c1).transpose());
203
204 VERIFY_IS_APPROX( m4=dm5.col(c1)*m2.row(r), refMat4=dm5.col(c1)*refMat2.row(r));
205 VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
206 VERIFY_IS_APPROX( m4=dm5.col(c1)*m2.middleRows(r,1), refMat4=dm5.col(c1)*refMat2.row(r));
207 VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
208 VERIFY_IS_APPROX(dm4=dm5.col(c1)*m2.row(r), refMat4=dm5.col(c1)*refMat2.row(r));
209
210 VERIFY_IS_APPROX( m4=dm5.row(r1).transpose()*m2.row(r), refMat4=dm5.row(r1).transpose()*refMat2.row(r));
211 VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
212 VERIFY_IS_APPROX(dm4=dm5.row(r1).transpose()*m2.row(r), refMat4=dm5.row(r1).transpose()*refMat2.row(r));
213 }
214
215 VERIFY_IS_APPROX(m6=m6*m6, refMat6=refMat6*refMat6);
216
217 // sparse matrix * sparse vector
218 ColSpVector cv0(cols), cv1;
219 DenseVector dcv0(cols), dcv1;
220 initSparse(2*density,dcv0, cv0);
221
222 RowSpVector rv0(depth), rv1;
223 RowDenseVector drv0(depth), drv1(rv1);
224 initSparse(2*density,drv0, rv0);
225
226 VERIFY_IS_APPROX(cv1=m3*cv0, dcv1=refMat3*dcv0);
227 VERIFY_IS_APPROX(rv1=rv0*m3, drv1=drv0*refMat3);
228 VERIFY_IS_APPROX(cv1=m3t.adjoint()*cv0, dcv1=refMat3t.adjoint()*dcv0);
229 VERIFY_IS_APPROX(cv1=rv0*m3, dcv1=drv0*refMat3);
230 VERIFY_IS_APPROX(rv1=m3*cv0, drv1=refMat3*dcv0);
231 }
232
233 // test matrix - diagonal product
234 {
235 DenseMatrix refM2 = DenseMatrix::Zero(rows, cols);
236 DenseMatrix refM3 = DenseMatrix::Zero(rows, cols);
237 DenseMatrix d3 = DenseMatrix::Zero(rows, cols);
238 DiagonalMatrix<Scalar,Dynamic> d1(DenseVector::Random(cols));
239 DiagonalMatrix<Scalar,Dynamic> d2(DenseVector::Random(rows));
240 SparseMatrixType m2(rows, cols);
241 SparseMatrixType m3(rows, cols);
242 initSparse<Scalar>(density, refM2, m2);
243 initSparse<Scalar>(density, refM3, m3);
244 VERIFY_IS_APPROX(m3=m2*d1, refM3=refM2*d1);
245 VERIFY_IS_APPROX(m3=m2.transpose()*d2, refM3=refM2.transpose()*d2);
246 VERIFY_IS_APPROX(m3=d2*m2, refM3=d2*refM2);
247 VERIFY_IS_APPROX(m3=d1*m2.transpose(), refM3=d1*refM2.transpose());
248
249 // also check with a SparseWrapper:
250 DenseVector v1 = DenseVector::Random(cols);
251 DenseVector v2 = DenseVector::Random(rows);
252 DenseVector v3 = DenseVector::Random(rows);
253 VERIFY_IS_APPROX(m3=m2*v1.asDiagonal(), refM3=refM2*v1.asDiagonal());
254 VERIFY_IS_APPROX(m3=m2.transpose()*v2.asDiagonal(), refM3=refM2.transpose()*v2.asDiagonal());
255 VERIFY_IS_APPROX(m3=v2.asDiagonal()*m2, refM3=v2.asDiagonal()*refM2);
256 VERIFY_IS_APPROX(m3=v1.asDiagonal()*m2.transpose(), refM3=v1.asDiagonal()*refM2.transpose());
257
258 VERIFY_IS_APPROX(m3=v2.asDiagonal()*m2*v1.asDiagonal(), refM3=v2.asDiagonal()*refM2*v1.asDiagonal());
259
260 VERIFY_IS_APPROX(v2=m2*v1.asDiagonal()*v1, refM2*v1.asDiagonal()*v1);
261 VERIFY_IS_APPROX(v3=v2.asDiagonal()*m2*v1, v2.asDiagonal()*refM2*v1);
262
263 // evaluate to a dense matrix to check the .row() and .col() iterator functions
264 VERIFY_IS_APPROX(d3=m2*d1, refM3=refM2*d1);
265 VERIFY_IS_APPROX(d3=m2.transpose()*d2, refM3=refM2.transpose()*d2);
266 VERIFY_IS_APPROX(d3=d2*m2, refM3=d2*refM2);
267 VERIFY_IS_APPROX(d3=d1*m2.transpose(), refM3=d1*refM2.transpose());
268 }
269
270 // test self-adjoint and triangular-view products
271 {
272 DenseMatrix b = DenseMatrix::Random(rows, rows);
273 DenseMatrix x = DenseMatrix::Random(rows, rows);
274 DenseMatrix refX = DenseMatrix::Random(rows, rows);
275 DenseMatrix refUp = DenseMatrix::Zero(rows, rows);
276 DenseMatrix refLo = DenseMatrix::Zero(rows, rows);
277 DenseMatrix refS = DenseMatrix::Zero(rows, rows);
278 DenseMatrix refA = DenseMatrix::Zero(rows, rows);
279 SparseMatrixType mUp(rows, rows);
280 SparseMatrixType mLo(rows, rows);
281 SparseMatrixType mS(rows, rows);
282 SparseMatrixType mA(rows, rows);
283 initSparse<Scalar>(density, refA, mA);
284 do {
285 initSparse<Scalar>(density, refUp, mUp, ForceRealDiag|/*ForceNonZeroDiag|*/MakeUpperTriangular);
286 } while (refUp.isZero());
287 refLo = refUp.adjoint();
288 mLo = mUp.adjoint();
289 refS = refUp + refLo;
290 refS.diagonal() *= 0.5;
291 mS = mUp + mLo;
292 // TODO be able to address the diagonal....
293 for (int k=0; k<mS.outerSize(); ++k)
294 for (typename SparseMatrixType::InnerIterator it(mS,k); it; ++it)
295 if (it.index() == k)
296 it.valueRef() *= Scalar(0.5);
297
298 VERIFY_IS_APPROX(refS.adjoint(), refS);
299 VERIFY_IS_APPROX(mS.adjoint(), mS);
300 VERIFY_IS_APPROX(mS, refS);
301 VERIFY_IS_APPROX(x=mS*b, refX=refS*b);
302
303 // sparse selfadjointView with dense matrices
304 VERIFY_IS_APPROX(x=mUp.template selfadjointView<Upper>()*b, refX=refS*b);
305 VERIFY_IS_APPROX(x=mLo.template selfadjointView<Lower>()*b, refX=refS*b);
306 VERIFY_IS_APPROX(x=mS.template selfadjointView<Upper|Lower>()*b, refX=refS*b);
307
308 VERIFY_IS_APPROX(x=b * mUp.template selfadjointView<Upper>(), refX=b*refS);
309 VERIFY_IS_APPROX(x=b * mLo.template selfadjointView<Lower>(), refX=b*refS);
310 VERIFY_IS_APPROX(x=b * mS.template selfadjointView<Upper|Lower>(), refX=b*refS);
311
312 VERIFY_IS_APPROX(x.noalias()+=mUp.template selfadjointView<Upper>()*b, refX+=refS*b);
313 VERIFY_IS_APPROX(x.noalias()-=mLo.template selfadjointView<Lower>()*b, refX-=refS*b);
314 VERIFY_IS_APPROX(x.noalias()+=mS.template selfadjointView<Upper|Lower>()*b, refX+=refS*b);
315
316 // sparse selfadjointView with sparse matrices
317 SparseMatrixType mSres(rows,rows);
318 VERIFY_IS_APPROX(mSres = mLo.template selfadjointView<Lower>()*mS,
319 refX = refLo.template selfadjointView<Lower>()*refS);
320 VERIFY_IS_APPROX(mSres = mS * mLo.template selfadjointView<Lower>(),
321 refX = refS * refLo.template selfadjointView<Lower>());
322
323 // sparse triangularView with dense matrices
324 VERIFY_IS_APPROX(x=mA.template triangularView<Upper>()*b, refX=refA.template triangularView<Upper>()*b);
325 VERIFY_IS_APPROX(x=mA.template triangularView<Lower>()*b, refX=refA.template triangularView<Lower>()*b);
326 VERIFY_IS_APPROX(x=b*mA.template triangularView<Upper>(), refX=b*refA.template triangularView<Upper>());
327 VERIFY_IS_APPROX(x=b*mA.template triangularView<Lower>(), refX=b*refA.template triangularView<Lower>());
328
329 // sparse triangularView with sparse matrices
330 VERIFY_IS_APPROX(mSres = mA.template triangularView<Lower>()*mS, refX = refA.template triangularView<Lower>()*refS);
331 VERIFY_IS_APPROX(mSres = mS * mA.template triangularView<Lower>(), refX = refS * refA.template triangularView<Lower>());
332 VERIFY_IS_APPROX(mSres = mA.template triangularView<Upper>()*mS, refX = refA.template triangularView<Upper>()*refS);
333 VERIFY_IS_APPROX(mSres = mS * mA.template triangularView<Upper>(), refX = refS * refA.template triangularView<Upper>());
334 }
335 }
336
337 // New test for Bug in SparseTimeDenseProduct
sparse_product_regression_test()338 template<typename SparseMatrixType, typename DenseMatrixType> void sparse_product_regression_test()
339 {
340 // This code does not compile with afflicted versions of the bug
341 SparseMatrixType sm1(3,2);
342 DenseMatrixType m2(2,2);
343 sm1.setZero();
344 m2.setZero();
345
346 DenseMatrixType m3 = sm1*m2;
347
348
349 // This code produces a segfault with afflicted versions of another SparseTimeDenseProduct
350 // bug
351
352 SparseMatrixType sm2(20000,2);
353 sm2.setZero();
354 DenseMatrixType m4(sm2*m2);
355
356 VERIFY_IS_APPROX( m4(0,0), 0.0 );
357 }
358
359 template<typename Scalar>
bug_942()360 void bug_942()
361 {
362 typedef Matrix<Scalar, Dynamic, 1> Vector;
363 typedef SparseMatrix<Scalar, ColMajor> ColSpMat;
364 typedef SparseMatrix<Scalar, RowMajor> RowSpMat;
365 ColSpMat cmA(1,1);
366 cmA.insert(0,0) = 1;
367
368 RowSpMat rmA(1,1);
369 rmA.insert(0,0) = 1;
370
371 Vector d(1);
372 d[0] = 2;
373
374 double res = 2;
375
376 VERIFY_IS_APPROX( ( cmA*d.asDiagonal() ).eval().coeff(0,0), res );
377 VERIFY_IS_APPROX( ( d.asDiagonal()*rmA ).eval().coeff(0,0), res );
378 VERIFY_IS_APPROX( ( rmA*d.asDiagonal() ).eval().coeff(0,0), res );
379 VERIFY_IS_APPROX( ( d.asDiagonal()*cmA ).eval().coeff(0,0), res );
380 }
381
382 template<typename Real>
test_mixing_types()383 void test_mixing_types()
384 {
385 typedef std::complex<Real> Cplx;
386 typedef SparseMatrix<Real> SpMatReal;
387 typedef SparseMatrix<Cplx> SpMatCplx;
388 typedef SparseMatrix<Cplx,RowMajor> SpRowMatCplx;
389 typedef Matrix<Real,Dynamic,Dynamic> DenseMatReal;
390 typedef Matrix<Cplx,Dynamic,Dynamic> DenseMatCplx;
391
392 Index n = internal::random<Index>(1,100);
393 double density = (std::max)(8./(n*n), 0.2);
394
395 SpMatReal sR1(n,n);
396 SpMatCplx sC1(n,n), sC2(n,n), sC3(n,n);
397 SpRowMatCplx sCR(n,n);
398 DenseMatReal dR1(n,n);
399 DenseMatCplx dC1(n,n), dC2(n,n), dC3(n,n);
400
401 initSparse<Real>(density, dR1, sR1);
402 initSparse<Cplx>(density, dC1, sC1);
403 initSparse<Cplx>(density, dC2, sC2);
404
405 VERIFY_IS_APPROX( sC2 = (sR1 * sC1), dC3 = dR1.template cast<Cplx>() * dC1 );
406 VERIFY_IS_APPROX( sC2 = (sC1 * sR1), dC3 = dC1 * dR1.template cast<Cplx>() );
407 VERIFY_IS_APPROX( sC2 = (sR1.transpose() * sC1), dC3 = dR1.template cast<Cplx>().transpose() * dC1 );
408 VERIFY_IS_APPROX( sC2 = (sC1.transpose() * sR1), dC3 = dC1.transpose() * dR1.template cast<Cplx>() );
409 VERIFY_IS_APPROX( sC2 = (sR1 * sC1.transpose()), dC3 = dR1.template cast<Cplx>() * dC1.transpose() );
410 VERIFY_IS_APPROX( sC2 = (sC1 * sR1.transpose()), dC3 = dC1 * dR1.template cast<Cplx>().transpose() );
411 VERIFY_IS_APPROX( sC2 = (sR1.transpose() * sC1.transpose()), dC3 = dR1.template cast<Cplx>().transpose() * dC1.transpose() );
412 VERIFY_IS_APPROX( sC2 = (sC1.transpose() * sR1.transpose()), dC3 = dC1.transpose() * dR1.template cast<Cplx>().transpose() );
413
414 VERIFY_IS_APPROX( sCR = (sR1 * sC1), dC3 = dR1.template cast<Cplx>() * dC1 );
415 VERIFY_IS_APPROX( sCR = (sC1 * sR1), dC3 = dC1 * dR1.template cast<Cplx>() );
416 VERIFY_IS_APPROX( sCR = (sR1.transpose() * sC1), dC3 = dR1.template cast<Cplx>().transpose() * dC1 );
417 VERIFY_IS_APPROX( sCR = (sC1.transpose() * sR1), dC3 = dC1.transpose() * dR1.template cast<Cplx>() );
418 VERIFY_IS_APPROX( sCR = (sR1 * sC1.transpose()), dC3 = dR1.template cast<Cplx>() * dC1.transpose() );
419 VERIFY_IS_APPROX( sCR = (sC1 * sR1.transpose()), dC3 = dC1 * dR1.template cast<Cplx>().transpose() );
420 VERIFY_IS_APPROX( sCR = (sR1.transpose() * sC1.transpose()), dC3 = dR1.template cast<Cplx>().transpose() * dC1.transpose() );
421 VERIFY_IS_APPROX( sCR = (sC1.transpose() * sR1.transpose()), dC3 = dC1.transpose() * dR1.template cast<Cplx>().transpose() );
422
423
424 VERIFY_IS_APPROX( sC2 = (sR1 * sC1).pruned(), dC3 = dR1.template cast<Cplx>() * dC1 );
425 VERIFY_IS_APPROX( sC2 = (sC1 * sR1).pruned(), dC3 = dC1 * dR1.template cast<Cplx>() );
426 VERIFY_IS_APPROX( sC2 = (sR1.transpose() * sC1).pruned(), dC3 = dR1.template cast<Cplx>().transpose() * dC1 );
427 VERIFY_IS_APPROX( sC2 = (sC1.transpose() * sR1).pruned(), dC3 = dC1.transpose() * dR1.template cast<Cplx>() );
428 VERIFY_IS_APPROX( sC2 = (sR1 * sC1.transpose()).pruned(), dC3 = dR1.template cast<Cplx>() * dC1.transpose() );
429 VERIFY_IS_APPROX( sC2 = (sC1 * sR1.transpose()).pruned(), dC3 = dC1 * dR1.template cast<Cplx>().transpose() );
430 VERIFY_IS_APPROX( sC2 = (sR1.transpose() * sC1.transpose()).pruned(), dC3 = dR1.template cast<Cplx>().transpose() * dC1.transpose() );
431 VERIFY_IS_APPROX( sC2 = (sC1.transpose() * sR1.transpose()).pruned(), dC3 = dC1.transpose() * dR1.template cast<Cplx>().transpose() );
432
433 VERIFY_IS_APPROX( sCR = (sR1 * sC1).pruned(), dC3 = dR1.template cast<Cplx>() * dC1 );
434 VERIFY_IS_APPROX( sCR = (sC1 * sR1).pruned(), dC3 = dC1 * dR1.template cast<Cplx>() );
435 VERIFY_IS_APPROX( sCR = (sR1.transpose() * sC1).pruned(), dC3 = dR1.template cast<Cplx>().transpose() * dC1 );
436 VERIFY_IS_APPROX( sCR = (sC1.transpose() * sR1).pruned(), dC3 = dC1.transpose() * dR1.template cast<Cplx>() );
437 VERIFY_IS_APPROX( sCR = (sR1 * sC1.transpose()).pruned(), dC3 = dR1.template cast<Cplx>() * dC1.transpose() );
438 VERIFY_IS_APPROX( sCR = (sC1 * sR1.transpose()).pruned(), dC3 = dC1 * dR1.template cast<Cplx>().transpose() );
439 VERIFY_IS_APPROX( sCR = (sR1.transpose() * sC1.transpose()).pruned(), dC3 = dR1.template cast<Cplx>().transpose() * dC1.transpose() );
440 VERIFY_IS_APPROX( sCR = (sC1.transpose() * sR1.transpose()).pruned(), dC3 = dC1.transpose() * dR1.template cast<Cplx>().transpose() );
441
442
443 VERIFY_IS_APPROX( dC2 = (sR1 * sC1), dC3 = dR1.template cast<Cplx>() * dC1 );
444 VERIFY_IS_APPROX( dC2 = (sC1 * sR1), dC3 = dC1 * dR1.template cast<Cplx>() );
445 VERIFY_IS_APPROX( dC2 = (sR1.transpose() * sC1), dC3 = dR1.template cast<Cplx>().transpose() * dC1 );
446 VERIFY_IS_APPROX( dC2 = (sC1.transpose() * sR1), dC3 = dC1.transpose() * dR1.template cast<Cplx>() );
447 VERIFY_IS_APPROX( dC2 = (sR1 * sC1.transpose()), dC3 = dR1.template cast<Cplx>() * dC1.transpose() );
448 VERIFY_IS_APPROX( dC2 = (sC1 * sR1.transpose()), dC3 = dC1 * dR1.template cast<Cplx>().transpose() );
449 VERIFY_IS_APPROX( dC2 = (sR1.transpose() * sC1.transpose()), dC3 = dR1.template cast<Cplx>().transpose() * dC1.transpose() );
450 VERIFY_IS_APPROX( dC2 = (sC1.transpose() * sR1.transpose()), dC3 = dC1.transpose() * dR1.template cast<Cplx>().transpose() );
451
452
453 VERIFY_IS_APPROX( dC2 = dR1 * sC1, dC3 = dR1.template cast<Cplx>() * sC1 );
454 VERIFY_IS_APPROX( dC2 = sR1 * dC1, dC3 = sR1.template cast<Cplx>() * dC1 );
455 VERIFY_IS_APPROX( dC2 = dC1 * sR1, dC3 = dC1 * sR1.template cast<Cplx>() );
456 VERIFY_IS_APPROX( dC2 = sC1 * dR1, dC3 = sC1 * dR1.template cast<Cplx>() );
457
458 VERIFY_IS_APPROX( dC2 = dR1.row(0) * sC1, dC3 = dR1.template cast<Cplx>().row(0) * sC1 );
459 VERIFY_IS_APPROX( dC2 = sR1 * dC1.col(0), dC3 = sR1.template cast<Cplx>() * dC1.col(0) );
460 VERIFY_IS_APPROX( dC2 = dC1.row(0) * sR1, dC3 = dC1.row(0) * sR1.template cast<Cplx>() );
461 VERIFY_IS_APPROX( dC2 = sC1 * dR1.col(0), dC3 = sC1 * dR1.template cast<Cplx>().col(0) );
462 }
463
EIGEN_DECLARE_TEST(sparse_product)464 EIGEN_DECLARE_TEST(sparse_product)
465 {
466 for(int i = 0; i < g_repeat; i++) {
467 CALL_SUBTEST_1( (sparse_product<SparseMatrix<double,ColMajor> >()) );
468 CALL_SUBTEST_1( (sparse_product<SparseMatrix<double,RowMajor> >()) );
469 CALL_SUBTEST_1( (bug_942<double>()) );
470 CALL_SUBTEST_2( (sparse_product<SparseMatrix<std::complex<double>, ColMajor > >()) );
471 CALL_SUBTEST_2( (sparse_product<SparseMatrix<std::complex<double>, RowMajor > >()) );
472 CALL_SUBTEST_3( (sparse_product<SparseMatrix<float,ColMajor,long int> >()) );
473 CALL_SUBTEST_4( (sparse_product_regression_test<SparseMatrix<double,RowMajor>, Matrix<double, Dynamic, Dynamic, RowMajor> >()) );
474
475 CALL_SUBTEST_5( (test_mixing_types<float>()) );
476 }
477 }
478