sparse_product.cpp revision 7faaa9f3f0df9d23790277834d426c3d992ac3ba 
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#include "sparse.h"
11
12template<typename SparseMatrixType, typename DenseMatrix, bool IsRowMajor=SparseMatrixType::IsRowMajor> struct test_outer;
13
14template<typename SparseMatrixType, typename DenseMatrix> struct test_outer<SparseMatrixType,DenseMatrix,false> {
15  static void run(SparseMatrixType& m2, SparseMatrixType& m4, DenseMatrix& refMat2, DenseMatrix& refMat4) {
16    typedef typename SparseMatrixType::Index Index;
17    Index c  = internal::random<Index>(0,m2.cols()-1);
18    Index c1 = internal::random<Index>(0,m2.cols()-1);
19    VERIFY_IS_APPROX(m4=m2.col(c)*refMat2.col(c1).transpose(), refMat4=refMat2.col(c)*refMat2.col(c1).transpose());
20    VERIFY_IS_APPROX(m4=refMat2.col(c1)*m2.col(c).transpose(), refMat4=refMat2.col(c1)*refMat2.col(c).transpose());
21  }
22};
23
24template<typename SparseMatrixType, typename DenseMatrix> struct test_outer<SparseMatrixType,DenseMatrix,true> {
25  static void run(SparseMatrixType& m2, SparseMatrixType& m4, DenseMatrix& refMat2, DenseMatrix& refMat4) {
26    typedef typename SparseMatrixType::Index Index;
27    Index r  = internal::random<Index>(0,m2.rows()-1);
28    Index c1 = internal::random<Index>(0,m2.cols()-1);
29    VERIFY_IS_APPROX(m4=m2.row(r).transpose()*refMat2.col(c1).transpose(), refMat4=refMat2.row(r).transpose()*refMat2.col(c1).transpose());
30    VERIFY_IS_APPROX(m4=refMat2.col(c1)*m2.row(r), refMat4=refMat2.col(c1)*refMat2.row(r));
31  }
32};
33
34// (m2,m4,refMat2,refMat4,dv1);
35//     VERIFY_IS_APPROX(m4=m2.innerVector(c)*dv1.transpose(), refMat4=refMat2.colVector(c)*dv1.transpose());
36//     VERIFY_IS_APPROX(m4=dv1*mcm.col(c).transpose(), refMat4=dv1*refMat2.col(c).transpose());
37
38template<typename SparseMatrixType> void sparse_product()
39{
40  typedef typename SparseMatrixType::Index Index;
41  Index n = 100;
42  const Index rows  = internal::random<Index>(1,n);
43  const Index cols  = internal::random<Index>(1,n);
44  const Index depth = internal::random<Index>(1,n);
45  typedef typename SparseMatrixType::Scalar Scalar;
46  enum { Flags = SparseMatrixType::Flags };
47
48  double density = (std::max)(8./(rows*cols), 0.1);
49  typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
50  typedef Matrix<Scalar,Dynamic,1> DenseVector;
51  typedef Matrix<Scalar,1,Dynamic> RowDenseVector;
52  typedef SparseVector<Scalar,0,Index> ColSpVector;
53  typedef SparseVector<Scalar,RowMajor,Index> RowSpVector;
54
55  Scalar s1 = internal::random<Scalar>();
56  Scalar s2 = internal::random<Scalar>();
57
58  // test matrix-matrix product
59  {
60    DenseMatrix refMat2  = DenseMatrix::Zero(rows, depth);
61    DenseMatrix refMat2t = DenseMatrix::Zero(depth, rows);
62    DenseMatrix refMat3  = DenseMatrix::Zero(depth, cols);
63    DenseMatrix refMat3t = DenseMatrix::Zero(cols, depth);
64    DenseMatrix refMat4  = DenseMatrix::Zero(rows, cols);
65    DenseMatrix refMat4t = DenseMatrix::Zero(cols, rows);
66    DenseMatrix refMat5  = DenseMatrix::Random(depth, cols);
67    DenseMatrix refMat6  = DenseMatrix::Random(rows, rows);
68    DenseMatrix dm4 = DenseMatrix::Zero(rows, rows);
69//     DenseVector dv1 = DenseVector::Random(rows);
70    SparseMatrixType m2 (rows, depth);
71    SparseMatrixType m2t(depth, rows);
72    SparseMatrixType m3 (depth, cols);
73    SparseMatrixType m3t(cols, depth);
74    SparseMatrixType m4 (rows, cols);
75    SparseMatrixType m4t(cols, rows);
76    SparseMatrixType m6(rows, rows);
77    initSparse(density, refMat2,  m2);
78    initSparse(density, refMat2t, m2t);
79    initSparse(density, refMat3,  m3);
80    initSparse(density, refMat3t, m3t);
81    initSparse(density, refMat4,  m4);
82    initSparse(density, refMat4t, m4t);
83    initSparse(density, refMat6, m6);
84
85//     int c = internal::random<int>(0,depth-1);
86
87    // sparse * sparse
88    VERIFY_IS_APPROX(m4=m2*m3, refMat4=refMat2*refMat3);
89    VERIFY_IS_APPROX(m4=m2t.transpose()*m3, refMat4=refMat2t.transpose()*refMat3);
90    VERIFY_IS_APPROX(m4=m2t.transpose()*m3t.transpose(), refMat4=refMat2t.transpose()*refMat3t.transpose());
91    VERIFY_IS_APPROX(m4=m2*m3t.transpose(), refMat4=refMat2*refMat3t.transpose());
92
93    VERIFY_IS_APPROX(m4 = m2*m3/s1, refMat4 = refMat2*refMat3/s1);
94    VERIFY_IS_APPROX(m4 = m2*m3*s1, refMat4 = refMat2*refMat3*s1);
95    VERIFY_IS_APPROX(m4 = s2*m2*m3*s1, refMat4 = s2*refMat2*refMat3*s1);
96
97    VERIFY_IS_APPROX(m4=(m2*m3).pruned(0), refMat4=refMat2*refMat3);
98    VERIFY_IS_APPROX(m4=(m2t.transpose()*m3).pruned(0), refMat4=refMat2t.transpose()*refMat3);
99    VERIFY_IS_APPROX(m4=(m2t.transpose()*m3t.transpose()).pruned(0), refMat4=refMat2t.transpose()*refMat3t.transpose());
100    VERIFY_IS_APPROX(m4=(m2*m3t.transpose()).pruned(0), refMat4=refMat2*refMat3t.transpose());
101
102    // test aliasing
103    m4 = m2; refMat4 = refMat2;
104    VERIFY_IS_APPROX(m4=m4*m3, refMat4=refMat4*refMat3);
105
106    // sparse * dense
107    VERIFY_IS_APPROX(dm4=m2*refMat3, refMat4=refMat2*refMat3);
108    VERIFY_IS_APPROX(dm4=m2*refMat3t.transpose(), refMat4=refMat2*refMat3t.transpose());
109    VERIFY_IS_APPROX(dm4=m2t.transpose()*refMat3, refMat4=refMat2t.transpose()*refMat3);
110    VERIFY_IS_APPROX(dm4=m2t.transpose()*refMat3t.transpose(), refMat4=refMat2t.transpose()*refMat3t.transpose());
111
112    VERIFY_IS_APPROX(dm4=m2*(refMat3+refMat3), refMat4=refMat2*(refMat3+refMat3));
113    VERIFY_IS_APPROX(dm4=m2t.transpose()*(refMat3+refMat5)*0.5, refMat4=refMat2t.transpose()*(refMat3+refMat5)*0.5);
114
115    // dense * sparse
116    VERIFY_IS_APPROX(dm4=refMat2*m3, refMat4=refMat2*refMat3);
117    VERIFY_IS_APPROX(dm4=refMat2*m3t.transpose(), refMat4=refMat2*refMat3t.transpose());
118    VERIFY_IS_APPROX(dm4=refMat2t.transpose()*m3, refMat4=refMat2t.transpose()*refMat3);
119    VERIFY_IS_APPROX(dm4=refMat2t.transpose()*m3t.transpose(), refMat4=refMat2t.transpose()*refMat3t.transpose());
120
121    // sparse * dense and dense * sparse outer product
122    test_outer<SparseMatrixType,DenseMatrix>::run(m2,m4,refMat2,refMat4);
123
124    VERIFY_IS_APPROX(m6=m6*m6, refMat6=refMat6*refMat6);
125
126    // sparse matrix * sparse vector
127    ColSpVector cv0(cols), cv1;
128    DenseVector dcv0(cols), dcv1;
129    initSparse(2*density,dcv0, cv0);
130
131    RowSpVector rv0(depth), rv1;
132    RowDenseVector drv0(depth), drv1(rv1);
133    initSparse(2*density,drv0, rv0);
134
135    VERIFY_IS_APPROX(cv1=rv0*m3, dcv1=drv0*refMat3);
136    VERIFY_IS_APPROX(rv1=rv0*m3, drv1=drv0*refMat3);
137    VERIFY_IS_APPROX(cv1=m3*cv0, dcv1=refMat3*dcv0);
138    VERIFY_IS_APPROX(cv1=m3t.adjoint()*cv0, dcv1=refMat3t.adjoint()*dcv0);
139    VERIFY_IS_APPROX(rv1=m3*cv0, drv1=refMat3*dcv0);
140  }
141
142  // test matrix - diagonal product
143  {
144    DenseMatrix refM2 = DenseMatrix::Zero(rows, cols);
145    DenseMatrix refM3 = DenseMatrix::Zero(rows, cols);
146    DenseMatrix d3 = DenseMatrix::Zero(rows, cols);
147    DiagonalMatrix<Scalar,Dynamic> d1(DenseVector::Random(cols));
148    DiagonalMatrix<Scalar,Dynamic> d2(DenseVector::Random(rows));
149    SparseMatrixType m2(rows, cols);
150    SparseMatrixType m3(rows, cols);
151    initSparse<Scalar>(density, refM2, m2);
152    initSparse<Scalar>(density, refM3, m3);
153    VERIFY_IS_APPROX(m3=m2*d1, refM3=refM2*d1);
154    VERIFY_IS_APPROX(m3=m2.transpose()*d2, refM3=refM2.transpose()*d2);
155    VERIFY_IS_APPROX(m3=d2*m2, refM3=d2*refM2);
156    VERIFY_IS_APPROX(m3=d1*m2.transpose(), refM3=d1*refM2.transpose());
157
158    // also check with a SparseWrapper:
159    DenseVector v1 = DenseVector::Random(cols);
160    DenseVector v2 = DenseVector::Random(rows);
161    VERIFY_IS_APPROX(m3=m2*v1.asDiagonal(), refM3=refM2*v1.asDiagonal());
162    VERIFY_IS_APPROX(m3=m2.transpose()*v2.asDiagonal(), refM3=refM2.transpose()*v2.asDiagonal());
163    VERIFY_IS_APPROX(m3=v2.asDiagonal()*m2, refM3=v2.asDiagonal()*refM2);
164    VERIFY_IS_APPROX(m3=v1.asDiagonal()*m2.transpose(), refM3=v1.asDiagonal()*refM2.transpose());
165
166    VERIFY_IS_APPROX(m3=v2.asDiagonal()*m2*v1.asDiagonal(), refM3=v2.asDiagonal()*refM2*v1.asDiagonal());
167
168    // evaluate to a dense matrix to check the .row() and .col() iterator functions
169    VERIFY_IS_APPROX(d3=m2*d1, refM3=refM2*d1);
170    VERIFY_IS_APPROX(d3=m2.transpose()*d2, refM3=refM2.transpose()*d2);
171    VERIFY_IS_APPROX(d3=d2*m2, refM3=d2*refM2);
172    VERIFY_IS_APPROX(d3=d1*m2.transpose(), refM3=d1*refM2.transpose());
173  }
174
175  // test self adjoint products
176  {
177    DenseMatrix b = DenseMatrix::Random(rows, rows);
178    DenseMatrix x = DenseMatrix::Random(rows, rows);
179    DenseMatrix refX = DenseMatrix::Random(rows, rows);
180    DenseMatrix refUp = DenseMatrix::Zero(rows, rows);
181    DenseMatrix refLo = DenseMatrix::Zero(rows, rows);
182    DenseMatrix refS = DenseMatrix::Zero(rows, rows);
183    SparseMatrixType mUp(rows, rows);
184    SparseMatrixType mLo(rows, rows);
185    SparseMatrixType mS(rows, rows);
186    do {
187      initSparse<Scalar>(density, refUp, mUp, ForceRealDiag|/*ForceNonZeroDiag|*/MakeUpperTriangular);
188    } while (refUp.isZero());
189    refLo = refUp.adjoint();
190    mLo = mUp.adjoint();
191    refS = refUp + refLo;
192    refS.diagonal() *= 0.5;
193    mS = mUp + mLo;
194    // TODO be able to address the diagonal....
195    for (int k=0; k<mS.outerSize(); ++k)
196      for (typename SparseMatrixType::InnerIterator it(mS,k); it; ++it)
197        if (it.index() == k)
198          it.valueRef() *= 0.5;
199
200    VERIFY_IS_APPROX(refS.adjoint(), refS);
201    VERIFY_IS_APPROX(mS.adjoint(), mS);
202    VERIFY_IS_APPROX(mS, refS);
203    VERIFY_IS_APPROX(x=mS*b, refX=refS*b);
204
205    VERIFY_IS_APPROX(x=mUp.template selfadjointView<Upper>()*b, refX=refS*b);
206    VERIFY_IS_APPROX(x=mLo.template selfadjointView<Lower>()*b, refX=refS*b);
207    VERIFY_IS_APPROX(x=mS.template selfadjointView<Upper|Lower>()*b, refX=refS*b);
208
209    // sparse selfadjointView * sparse
210    SparseMatrixType mSres(rows,rows);
211    VERIFY_IS_APPROX(mSres = mLo.template selfadjointView<Lower>()*mS,
212                     refX = refLo.template selfadjointView<Lower>()*refS);
213    // sparse * sparse selfadjointview
214    VERIFY_IS_APPROX(mSres = mS * mLo.template selfadjointView<Lower>(),
215                     refX = refS * refLo.template selfadjointView<Lower>());
216  }
217
218}
219
220// New test for Bug in SparseTimeDenseProduct
221template<typename SparseMatrixType, typename DenseMatrixType> void sparse_product_regression_test()
222{
223  // This code does not compile with afflicted versions of the bug
224  SparseMatrixType sm1(3,2);
225  DenseMatrixType m2(2,2);
226  sm1.setZero();
227  m2.setZero();
228
229  DenseMatrixType m3 = sm1*m2;
230
231
232  // This code produces a segfault with afflicted versions of another SparseTimeDenseProduct
233  // bug
234
235  SparseMatrixType sm2(20000,2);
236  sm2.setZero();
237  DenseMatrixType m4(sm2*m2);
238
239  VERIFY_IS_APPROX( m4(0,0), 0.0 );
240}
241
242void test_sparse_product()
243{
244  for(int i = 0; i < g_repeat; i++) {
245    CALL_SUBTEST_1( (sparse_product<SparseMatrix<double,ColMajor> >()) );
246    CALL_SUBTEST_1( (sparse_product<SparseMatrix<double,RowMajor> >()) );
247    CALL_SUBTEST_2( (sparse_product<SparseMatrix<std::complex<double>, ColMajor > >()) );
248    CALL_SUBTEST_2( (sparse_product<SparseMatrix<std::complex<double>, RowMajor > >()) );
249    CALL_SUBTEST_3( (sparse_product<SparseMatrix<float,ColMajor,long int> >()) );
250    CALL_SUBTEST_4( (sparse_product_regression_test<SparseMatrix<double,RowMajor>, Matrix<double, Dynamic, Dynamic, RowMajor> >()) );
251  }
252}
253