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