ground/gcs/src/libs/eigen/test/sparse_product.cpp

   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
  12 template<typename SparseMatrixType, typename DenseMatrix, bool IsRowMajor=SparseMatrixType::IsRowMajor> struct test_outer;
  13
  14 template<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
  24 template<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
  38 template<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
 221 template<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
 242 void 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 }