cart-elc

Source code for CART-ELC
git clone git://git.laack.co/cart-elc.git
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sparse_product.cpp (25557B)


      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 #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 
     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 
     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
    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>
    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>
    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 
    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 }