text: // This file is part of Eigen, a lightweight C++ template library
  // for linear algebra. Eigen itself is part of the KDE project.
  //
  // Copyright (C) 2008 Daniel Gomez Ferro <dgomezferro@gmail.com>
  //
  // Eigen is free software; you can redistribute it and/or
  // modify it under the terms of the GNU Lesser General Public
  // License as published by the Free Software Foundation; either
  // version 3 of the License, or (at your option) any later version.
  //
  // Alternatively, you can redistribute it and/or
  // modify it under the terms of the GNU General Public License as
  // published by the Free Software Foundation; either version 2 of
  // the License, or (at your option) any later version.
  //
  // Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
  // WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
  // FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
  // GNU General Public License for more details.
  //
  // You should have received a copy of the GNU Lesser General Public
  // License and a copy of the GNU General Public License along with
  // Eigen. If not, see <http://www.gnu.org/licenses/>.
  
  #include "sparse.h"
  
  template<typename Scalar> void sparse_vector(int rows, int cols)
  {
    double densityMat = std::max(8./(rows*cols), 0.01);
    double densityVec = std::max(8./float(rows), 0.1);
    typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
    typedef Matrix<Scalar,Dynamic,1> DenseVector;
    typedef SparseVector<Scalar> SparseVectorType;
    typedef SparseMatrix<Scalar> SparseMatrixType;
    Scalar eps = 1e-6;
  
    SparseMatrixType m1(rows,cols);
    SparseVectorType v1(rows), v2(rows), v3(rows);
    DenseMatrix refM1 = DenseMatrix::Zero(rows, cols);
    DenseVector refV1 = DenseVector::Random(rows),
      refV2 = DenseVector::Random(rows),
      refV3 = DenseVector::Random(rows);
  
    std::vector<int> zerocoords, nonzerocoords;
    initSparse<Scalar>(densityVec, refV1, v1, &zerocoords, &nonzerocoords);
    initSparse<Scalar>(densityMat, refM1, m1);
  
    initSparse<Scalar>(densityVec, refV2, v2);
    initSparse<Scalar>(densityVec, refV3, v3);
  
    Scalar s1 = ei_random<Scalar>();
  
    // test coeff and coeffRef
    for (unsigned int i=0; i<zerocoords.size(); ++i)
    {
      VERIFY_IS_MUCH_SMALLER_THAN( v1.coeff(zerocoords[i]), eps );
      //VERIFY_RAISES_ASSERT( v1.coeffRef(zerocoords[i]) = 5 );
    }
    {
      VERIFY(int(nonzerocoords.size()) == v1.nonZeros());
      int j=0;
      for (typename SparseVectorType::InnerIterator it(v1); it; ++it,++j)
      {
        VERIFY(nonzerocoords[j]==it.index());
        VERIFY(it.value()==v1.coeff(it.index()));
        VERIFY(it.value()==refV1.coeff(it.index()));
      }
    }
    VERIFY_IS_APPROX(v1, refV1);
  
    v1.coeffRef(nonzerocoords[0]) = Scalar(5);
    refV1.coeffRef(nonzerocoords[0]) = Scalar(5);
    VERIFY_IS_APPROX(v1, refV1);
  
    VERIFY_IS_APPROX(v1+v2, refV1+refV2);
    VERIFY_IS_APPROX(v1+v2+v3, refV1+refV2+refV3);
  
    VERIFY_IS_APPROX(v1*s1-v2, refV1*s1-refV2);
  
    VERIFY_IS_APPROX(v1*=s1, refV1*=s1);
    VERIFY_IS_APPROX(v1/=s1, refV1/=s1);
    
    VERIFY_IS_APPROX(v1+=v2, refV1+=refV2);
    VERIFY_IS_APPROX(v1-=v2, refV1-=refV2);
  
    VERIFY_IS_APPROX(v1.dot(v2), refV1.dot(refV2));
    VERIFY_IS_APPROX(v1.dot(refV2), refV1.dot(refV2));
  
  }
  
  void test_sparse_vector()
  {
    for(int i = 0; i < g_repeat; i++) {
      CALL_SUBTEST( sparse_vector<double>(8, 8) );
      CALL_SUBTEST( sparse_vector<std::complex<double> >(16, 16) );
      CALL_SUBTEST( sparse_vector<double>(299, 535) );
    }
  }
  
  