xref: /aosp_15_r20/external/eigen/test/sparse_product.cpp (revision bf2c37156dfe67e5dfebd6d394bad8b2ab5804d4)
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