text: // This file is part of Eigen, a lightweight C++ template library
  // for linear algebra.
  //
  // Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
  // Copyright (C) 2008 Daniel Gomez Ferro <dgomezferro@gmail.com>
  // Copyright (C) 2013 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
  //
  // This Source Code Form is subject to the terms of the Mozilla
  // Public License v. 2.0. If a copy of the MPL was not distributed
  // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
  
  #include "sparse.h"
  
  template<typename SparseMatrixType> void sparse_basic(const SparseMatrixType& ref)
  {
    typedef typename SparseMatrixType::Index Index;
    typedef Matrix<Index,2,1> Vector2;
    
    const Index rows = ref.rows();
    const Index cols = ref.cols();
    typedef typename SparseMatrixType::Scalar Scalar;
    enum { Flags = SparseMatrixType::Flags };
  
    double density = (std::max)(8./(rows*cols), 0.01);
    typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
    typedef Matrix<Scalar,Dynamic,1> DenseVector;
    typedef Matrix<Scalar,1,Dynamic> RowDenseVector;
    Scalar eps = 1e-6;
  
    Scalar s1 = internal::random<Scalar>();
    {
      SparseMatrixType m(rows, cols);
      DenseMatrix refMat = DenseMatrix::Zero(rows, cols);
      DenseVector vec1 = DenseVector::Random(rows);
  
      std::vector<Vector2> zeroCoords;
      std::vector<Vector2> nonzeroCoords;
      initSparse<Scalar>(density, refMat, m, 0, &zeroCoords, &nonzeroCoords);
  
      if (zeroCoords.size()==0 || nonzeroCoords.size()==0)
        return;
  
      // test coeff and coeffRef
      for (int i=0; i<(int)zeroCoords.size(); ++i)
      {
        VERIFY_IS_MUCH_SMALLER_THAN( m.coeff(zeroCoords[i].x(),zeroCoords[i].y()), eps );
        if(internal::is_same<SparseMatrixType,SparseMatrix<Scalar,Flags> >::value)
          VERIFY_RAISES_ASSERT( m.coeffRef(zeroCoords[0].x(),zeroCoords[0].y()) = 5 );
      }
      VERIFY_IS_APPROX(m, refMat);
  
      m.coeffRef(nonzeroCoords[0].x(), nonzeroCoords[0].y()) = Scalar(5);
      refMat.coeffRef(nonzeroCoords[0].x(), nonzeroCoords[0].y()) = Scalar(5);
  
      VERIFY_IS_APPROX(m, refMat);
        
        // test InnerIterators and Block expressions
        for (int t=0; t<10; ++t)
        {
          int j = internal::random<int>(0,cols-1);
          int i = internal::random<int>(0,rows-1);
          int w = internal::random<int>(1,cols-j-1);
          int h = internal::random<int>(1,rows-i-1);
  
          VERIFY_IS_APPROX(m.block(i,j,h,w), refMat.block(i,j,h,w));
          for(int c=0; c<w; c++)
          {
            VERIFY_IS_APPROX(m.block(i,j,h,w).col(c), refMat.block(i,j,h,w).col(c));
            for(int r=0; r<h; r++)
            {
              VERIFY_IS_APPROX(m.block(i,j,h,w).col(c).coeff(r), refMat.block(i,j,h,w).col(c).coeff(r));
              VERIFY_IS_APPROX(m.block(i,j,h,w).coeff(r,c), refMat.block(i,j,h,w).coeff(r,c));
            }
          }
          for(int r=0; r<h; r++)
          {
            VERIFY_IS_APPROX(m.block(i,j,h,w).row(r), refMat.block(i,j,h,w).row(r));
            for(int c=0; c<w; c++)
            {
              VERIFY_IS_APPROX(m.block(i,j,h,w).row(r).coeff(c), refMat.block(i,j,h,w).row(r).coeff(c));
              VERIFY_IS_APPROX(m.block(i,j,h,w).coeff(r,c), refMat.block(i,j,h,w).coeff(r,c));
            }
          }
          
          VERIFY_IS_APPROX(m.middleCols(j,w), refMat.middleCols(j,w));
          VERIFY_IS_APPROX(m.middleRows(i,h), refMat.middleRows(i,h));
          for(int r=0; r<h; r++)
          {
            VERIFY_IS_APPROX(m.middleCols(j,w).row(r), refMat.middleCols(j,w).row(r));
            VERIFY_IS_APPROX(m.middleRows(i,h).row(r), refMat.middleRows(i,h).row(r));
            for(int c=0; c<w; c++)
            {
              VERIFY_IS_APPROX(m.col(c).coeff(r), refMat.col(c).coeff(r));
              VERIFY_IS_APPROX(m.row(r).coeff(c), refMat.row(r).coeff(c));
              
              VERIFY_IS_APPROX(m.middleCols(j,w).coeff(r,c), refMat.middleCols(j,w).coeff(r,c));
              VERIFY_IS_APPROX(m.middleRows(i,h).coeff(r,c), refMat.middleRows(i,h).coeff(r,c));
              if(m.middleCols(j,w).coeff(r,c) != Scalar(0))
              {
                VERIFY_IS_APPROX(m.middleCols(j,w).coeffRef(r,c), refMat.middleCols(j,w).coeff(r,c));
              }
              if(m.middleRows(i,h).coeff(r,c) != Scalar(0))
              {
                VERIFY_IS_APPROX(m.middleRows(i,h).coeff(r,c), refMat.middleRows(i,h).coeff(r,c));
              }
            }
          }
          for(int c=0; c<w; c++)
          {
            VERIFY_IS_APPROX(m.middleCols(j,w).col(c), refMat.middleCols(j,w).col(c));
            VERIFY_IS_APPROX(m.middleRows(i,h).col(c), refMat.middleRows(i,h).col(c));
          }
        }
  
        for(int c=0; c<cols; c++)
        {
          VERIFY_IS_APPROX(m.col(c) + m.col(c), (m + m).col(c));
          VERIFY_IS_APPROX(m.col(c) + m.col(c), refMat.col(c) + refMat.col(c));
        }
  
        for(int r=0; r<rows; r++)
        {
          VERIFY_IS_APPROX(m.row(r) + m.row(r), (m + m).row(r));
          VERIFY_IS_APPROX(m.row(r) + m.row(r), refMat.row(r) + refMat.row(r));
        }
        
        
        // test assertion
        VERIFY_RAISES_ASSERT( m.coeffRef(-1,1) = 0 );
        VERIFY_RAISES_ASSERT( m.coeffRef(0,m.cols()) = 0 );
      }
  
      // test insert (inner random)
      {
        DenseMatrix m1(rows,cols);
        m1.setZero();
        SparseMatrixType m2(rows,cols);
        if(internal::random<int>()%2)
          m2.reserve(VectorXi::Constant(m2.outerSize(), 2));
        for (Index j=0; j<cols; ++j)
        {
          for (Index k=0; k<rows/2; ++k)
          {
            Index i = internal::random<Index>(0,rows-1);
            if (m1.coeff(i,j)==Scalar(0))
              m2.insert(i,j) = m1(i,j) = internal::random<Scalar>();
          }
        }
        m2.finalize();
        VERIFY_IS_APPROX(m2,m1);
      }
  
      // test insert (fully random)
      {
        DenseMatrix m1(rows,cols);
        m1.setZero();
        SparseMatrixType m2(rows,cols);
        if(internal::random<int>()%2)
          m2.reserve(VectorXi::Constant(m2.outerSize(), 2));
        for (int k=0; k<rows*cols; ++k)
        {
          Index i = internal::random<Index>(0,rows-1);
          Index j = internal::random<Index>(0,cols-1);
          if ((m1.coeff(i,j)==Scalar(0)) && (internal::random<int>()%2))
            m2.insert(i,j) = m1(i,j) = internal::random<Scalar>();
          else
          {
            Scalar v = internal::random<Scalar>();
            m2.coeffRef(i,j) += v;
            m1(i,j) += v;
          }
        }
        VERIFY_IS_APPROX(m2,m1);
      }
      
      // test insert (un-compressed)
      for(int mode=0;mode<4;++mode)
      {
        DenseMatrix m1(rows,cols);
        m1.setZero();
        SparseMatrixType m2(rows,cols);
        VectorXi r(VectorXi::Constant(m2.outerSize(), ((mode%2)==0) ? m2.innerSize() : std::max<int>(1,m2.innerSize()/8)));
        m2.reserve(r);
        for (int k=0; k<rows*cols; ++k)
        {
          Index i = internal::random<Index>(0,rows-1);
          Index j = internal::random<Index>(0,cols-1);
          if (m1.coeff(i,j)==Scalar(0))
            m2.insert(i,j) = m1(i,j) = internal::random<Scalar>();
          if(mode==3)
            m2.reserve(r);
        }
        if(internal::random<int>()%2)
          m2.makeCompressed();
        VERIFY_IS_APPROX(m2,m1);
      }
  
    // test innerVector()
    {
      DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows);
      SparseMatrixType m2(rows, rows);
      initSparse<Scalar>(density, refMat2, m2);
      Index j0 = internal::random<Index>(0,rows-1);
      Index j1 = internal::random<Index>(0,rows-1);
      if(SparseMatrixType::IsRowMajor)
        VERIFY_IS_APPROX(m2.innerVector(j0), refMat2.row(j0));
      else
        VERIFY_IS_APPROX(m2.innerVector(j0), refMat2.col(j0));
  
      if(SparseMatrixType::IsRowMajor)
        VERIFY_IS_APPROX(m2.innerVector(j0)+m2.innerVector(j1), refMat2.row(j0)+refMat2.row(j1));
      else
        VERIFY_IS_APPROX(m2.innerVector(j0)+m2.innerVector(j1), refMat2.col(j0)+refMat2.col(j1));
  
      SparseMatrixType m3(rows,rows);
      m3.reserve(VectorXi::Constant(rows,rows/2));
      for(Index j=0; j<rows; ++j)
        for(Index k=0; k<j; ++k)
          m3.insertByOuterInner(j,k) = k+1;
      for(Index j=0; j<rows; ++j)
      {
        VERIFY(j==numext::real(m3.innerVector(j).nonZeros()));
        if(j>0)
          VERIFY(j==numext::real(m3.innerVector(j).lastCoeff()));
      }
      m3.makeCompressed();
      for(Index j=0; j<rows; ++j)
      {
        VERIFY(j==numext::real(m3.innerVector(j).nonZeros()));
        if(j>0)
          VERIFY(j==numext::real(m3.innerVector(j).lastCoeff()));
      }
  
      //m2.innerVector(j0) = 2*m2.innerVector(j1);
      //refMat2.col(j0) = 2*refMat2.col(j1);
      //VERIFY_IS_APPROX(m2, refMat2);
    }
  
    // test innerVectors()
    {
      DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows);
      SparseMatrixType m2(rows, rows);
      initSparse<Scalar>(density, refMat2, m2);
      if(internal::random<float>(0,1)>0.5) m2.makeCompressed();
      
      Index j0 = internal::random<Index>(0,rows-2);
      Index j1 = internal::random<Index>(0,rows-2);
      Index n0 = internal::random<Index>(1,rows-(std::max)(j0,j1));
      if(SparseMatrixType::IsRowMajor)
        VERIFY_IS_APPROX(m2.innerVectors(j0,n0), refMat2.block(j0,0,n0,cols));
      else
        VERIFY_IS_APPROX(m2.innerVectors(j0,n0), refMat2.block(0,j0,rows,n0));
      if(SparseMatrixType::IsRowMajor)
        VERIFY_IS_APPROX(m2.innerVectors(j0,n0)+m2.innerVectors(j1,n0),
                         refMat2.middleRows(j0,n0)+refMat2.middleRows(j1,n0));
      else
        VERIFY_IS_APPROX(m2.innerVectors(j0,n0)+m2.innerVectors(j1,n0),
                        refMat2.block(0,j0,rows,n0)+refMat2.block(0,j1,rows,n0));
      
      VERIFY_IS_APPROX(m2, refMat2);
      
      m2.innerVectors(j0,n0) = m2.innerVectors(j0,n0) + m2.innerVectors(j1,n0);
      if(SparseMatrixType::IsRowMajor)
        refMat2.middleRows(j0,n0) = (refMat2.middleRows(j0,n0) + refMat2.middleRows(j1,n0)).eval();
      else
        refMat2.middleCols(j0,n0) = (refMat2.middleCols(j0,n0) + refMat2.middleCols(j1,n0)).eval();
      
      VERIFY_IS_APPROX(m2, refMat2);
      
    }
    
    // test basic computations
    {
      DenseMatrix refM1 = DenseMatrix::Zero(rows, rows);
      DenseMatrix refM2 = DenseMatrix::Zero(rows, rows);
      DenseMatrix refM3 = DenseMatrix::Zero(rows, rows);
      DenseMatrix refM4 = DenseMatrix::Zero(rows, rows);
      SparseMatrixType m1(rows, rows);
      SparseMatrixType m2(rows, rows);
      SparseMatrixType m3(rows, rows);
      SparseMatrixType m4(rows, rows);
      initSparse<Scalar>(density, refM1, m1);
      initSparse<Scalar>(density, refM2, m2);
      initSparse<Scalar>(density, refM3, m3);
      initSparse<Scalar>(density, refM4, m4);
  
      VERIFY_IS_APPROX(m1+m2, refM1+refM2);
      VERIFY_IS_APPROX(m1+m2+m3, refM1+refM2+refM3);
      VERIFY_IS_APPROX(m3.cwiseProduct(m1+m2), refM3.cwiseProduct(refM1+refM2));
      VERIFY_IS_APPROX(m1*s1-m2, refM1*s1-refM2);
  
      VERIFY_IS_APPROX(m1*=s1, refM1*=s1);
      VERIFY_IS_APPROX(m1/=s1, refM1/=s1);
  
      VERIFY_IS_APPROX(m1+=m2, refM1+=refM2);
      VERIFY_IS_APPROX(m1-=m2, refM1-=refM2);
  
      if(SparseMatrixType::IsRowMajor)
        VERIFY_IS_APPROX(m1.innerVector(0).dot(refM2.row(0)), refM1.row(0).dot(refM2.row(0)));
      else
        VERIFY_IS_APPROX(m1.innerVector(0).dot(refM2.row(0)), refM1.col(0).dot(refM2.row(0)));
      
      DenseVector rv = DenseVector::Random(m1.cols());
      DenseVector cv = DenseVector::Random(m1.rows());
      Index r = internal::random<Index>(0,m1.rows()-2);
      Index c = internal::random<Index>(0,m1.cols()-1);
      VERIFY_IS_APPROX(( m1.template block<1,Dynamic>(r,0,1,m1.cols()).dot(rv)) , refM1.row(r).dot(rv));
      VERIFY_IS_APPROX(m1.row(r).dot(rv), refM1.row(r).dot(rv));
      VERIFY_IS_APPROX(m1.col(c).dot(cv), refM1.col(c).dot(cv));
  
      VERIFY_IS_APPROX(m1.conjugate(), refM1.conjugate());
      VERIFY_IS_APPROX(m1.real(), refM1.real());
  
      refM4.setRandom();
      // sparse cwise* dense
      VERIFY_IS_APPROX(m3.cwiseProduct(refM4), refM3.cwiseProduct(refM4));
      // dense cwise* sparse
      VERIFY_IS_APPROX(refM4.cwiseProduct(m3), refM4.cwiseProduct(refM3));
  //     VERIFY_IS_APPROX(m3.cwise()/refM4, refM3.cwise()/refM4);
  
      // test aliasing
      VERIFY_IS_APPROX((m1 = -m1), (refM1 = -refM1));
      VERIFY_IS_APPROX((m1 = m1.transpose()), (refM1 = refM1.transpose().eval()));
      VERIFY_IS_APPROX((m1 = -m1.transpose()), (refM1 = -refM1.transpose().eval()));
      VERIFY_IS_APPROX((m1 += -m1), (refM1 += -refM1));
    }
  
    // test transpose
    {
      DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows);
      SparseMatrixType m2(rows, rows);
      initSparse<Scalar>(density, refMat2, m2);
      VERIFY_IS_APPROX(m2.transpose().eval(), refMat2.transpose().eval());
      VERIFY_IS_APPROX(m2.transpose(), refMat2.transpose());
  
      VERIFY_IS_APPROX(SparseMatrixType(m2.adjoint()), refMat2.adjoint());
    }
  
    
    
    // test generic blocks
    {
      DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows);
      SparseMatrixType m2(rows, rows);
      initSparse<Scalar>(density, refMat2, m2);
      Index j0 = internal::random<Index>(0,rows-2);
      Index j1 = internal::random<Index>(0,rows-2);
      Index n0 = internal::random<Index>(1,rows-(std::max)(j0,j1));
      if(SparseMatrixType::IsRowMajor)
        VERIFY_IS_APPROX(m2.block(j0,0,n0,cols), refMat2.block(j0,0,n0,cols));
      else
        VERIFY_IS_APPROX(m2.block(0,j0,rows,n0), refMat2.block(0,j0,rows,n0));
      
      if(SparseMatrixType::IsRowMajor)
        VERIFY_IS_APPROX(m2.block(j0,0,n0,cols)+m2.block(j1,0,n0,cols),
                        refMat2.block(j0,0,n0,cols)+refMat2.block(j1,0,n0,cols));
      else
        VERIFY_IS_APPROX(m2.block(0,j0,rows,n0)+m2.block(0,j1,rows,n0),
                        refMat2.block(0,j0,rows,n0)+refMat2.block(0,j1,rows,n0));
        
      Index i = internal::random<Index>(0,m2.outerSize()-1);
      if(SparseMatrixType::IsRowMajor) {
        m2.innerVector(i) = m2.innerVector(i) * s1;
        refMat2.row(i) = refMat2.row(i) * s1;
        VERIFY_IS_APPROX(m2,refMat2);
      } else {
        m2.innerVector(i) = m2.innerVector(i) * s1;
        refMat2.col(i) = refMat2.col(i) * s1;
        VERIFY_IS_APPROX(m2,refMat2);
      }
      
      VERIFY_IS_APPROX(DenseVector(m2.col(j0)), refMat2.col(j0));
      VERIFY_IS_APPROX(m2.col(j0), refMat2.col(j0));
      
      VERIFY_IS_APPROX(RowDenseVector(m2.row(j0)), refMat2.row(j0));
      VERIFY_IS_APPROX(m2.row(j0), refMat2.row(j0));
      
      VERIFY_IS_APPROX(m2.block(j0,j1,n0,n0), refMat2.block(j0,j1,n0,n0));
      VERIFY_IS_APPROX((2*m2).block(j0,j1,n0,n0), (2*refMat2).block(j0,j1,n0,n0));
    }
  
    // test prune
    {
      SparseMatrixType m2(rows, rows);
      DenseMatrix refM2(rows, rows);
      refM2.setZero();
      int countFalseNonZero = 0;
      int countTrueNonZero = 0;
      for (Index j=0; j<m2.outerSize(); ++j)
      {
        m2.startVec(j);
        for (Index i=0; i<m2.innerSize(); ++i)
        {
          float x = internal::random<float>(0,1);
          if (x<0.1)
          {
            // do nothing
          }
          else if (x<0.5)
          {
            countFalseNonZero++;
            m2.insertBackByOuterInner(j,i) = Scalar(0);
          }
          else
          {
            countTrueNonZero++;
            m2.insertBackByOuterInner(j,i) = Scalar(1);
            if(SparseMatrixType::IsRowMajor)
              refM2(j,i) = Scalar(1);
            else
              refM2(i,j) = Scalar(1);
          }
        }
      }
      m2.finalize();
      VERIFY(countFalseNonZero+countTrueNonZero == m2.nonZeros());
      VERIFY_IS_APPROX(m2, refM2);
      m2.prune(Scalar(1));
      VERIFY(countTrueNonZero==m2.nonZeros());
      VERIFY_IS_APPROX(m2, refM2);
    }
  
    // test setFromTriplets
    {
      typedef Triplet<Scalar,Index> TripletType;
      std::vector<TripletType> triplets;
      int ntriplets = rows*cols;
      triplets.reserve(ntriplets);
      DenseMatrix refMat(rows,cols);
      refMat.setZero();
      for(int i=0;i<ntriplets;++i)
      {
        Index r = internal::random<Index>(0,rows-1);
        Index c = internal::random<Index>(0,cols-1);
        Scalar v = internal::random<Scalar>();
        triplets.push_back(TripletType(r,c,v));
        refMat(r,c) += v;
      }
      SparseMatrixType m(rows,cols);
      m.setFromTriplets(triplets.begin(), triplets.end());
      VERIFY_IS_APPROX(m, refMat);
    }
  
    // test triangularView
    {
      DenseMatrix refMat2(rows, rows), refMat3(rows, rows);
      SparseMatrixType m2(rows, rows), m3(rows, rows);
      initSparse<Scalar>(density, refMat2, m2);
      refMat3 = refMat2.template triangularView<Lower>();
      m3 = m2.template triangularView<Lower>();
      VERIFY_IS_APPROX(m3, refMat3);
  
      refMat3 = refMat2.template triangularView<Upper>();
      m3 = m2.template triangularView<Upper>();
      VERIFY_IS_APPROX(m3, refMat3);
  
      refMat3 = refMat2.template triangularView<UnitUpper>();
      m3 = m2.template triangularView<UnitUpper>();
      VERIFY_IS_APPROX(m3, refMat3);
  
      refMat3 = refMat2.template triangularView<UnitLower>();
      m3 = m2.template triangularView<UnitLower>();
      VERIFY_IS_APPROX(m3, refMat3);
  
      refMat3 = refMat2.template triangularView<StrictlyUpper>();
      m3 = m2.template triangularView<StrictlyUpper>();
      VERIFY_IS_APPROX(m3, refMat3);
  
      refMat3 = refMat2.template triangularView<StrictlyLower>();
      m3 = m2.template triangularView<StrictlyLower>();
      VERIFY_IS_APPROX(m3, refMat3);
    }
    
    // test selfadjointView
    if(!SparseMatrixType::IsRowMajor)
    {
      DenseMatrix refMat2(rows, rows), refMat3(rows, rows);
      SparseMatrixType m2(rows, rows), m3(rows, rows);
      initSparse<Scalar>(density, refMat2, m2);
      refMat3 = refMat2.template selfadjointView<Lower>();
      m3 = m2.template selfadjointView<Lower>();
      VERIFY_IS_APPROX(m3, refMat3);
    }
    
    // test sparseView
    {
      DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows);
      SparseMatrixType m2(rows, rows);
      initSparse<Scalar>(density, refMat2, m2);
      VERIFY_IS_APPROX(m2.eval(), refMat2.sparseView().eval());
    }
  
    // test diagonal
    {
      DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows);
      SparseMatrixType m2(rows, rows);
      initSparse<Scalar>(density, refMat2, m2);
      VERIFY_IS_APPROX(m2.diagonal(), refMat2.diagonal().eval());
    }
    
    // test conservative resize
    {
        std::vector< std::pair<Index,Index> > inc;
        inc.push_back(std::pair<Index,Index>(-3,-2));
        inc.push_back(std::pair<Index,Index>(0,0));
        inc.push_back(std::pair<Index,Index>(3,2));
        inc.push_back(std::pair<Index,Index>(3,0));
        inc.push_back(std::pair<Index,Index>(0,3));
        
        for(size_t i = 0; i< inc.size(); i++) {
          Index incRows = inc[i].first;
          Index incCols = inc[i].second;
          SparseMatrixType m1(rows, cols);
          DenseMatrix refMat1 = DenseMatrix::Zero(rows, cols);
          initSparse<Scalar>(density, refMat1, m1);
          
          m1.conservativeResize(rows+incRows, cols+incCols);
          refMat1.conservativeResize(rows+incRows, cols+incCols);
          if (incRows > 0) refMat1.bottomRows(incRows).setZero();
          if (incCols > 0) refMat1.rightCols(incCols).setZero();
          
          VERIFY_IS_APPROX(m1, refMat1);
          
          // Insert new values
          if (incRows > 0) 
            m1.insert(m1.rows()-1, 0) = refMat1(refMat1.rows()-1, 0) = 1;
          if (incCols > 0) 
            m1.insert(0, m1.cols()-1) = refMat1(0, refMat1.cols()-1) = 1;
            
          VERIFY_IS_APPROX(m1, refMat1);
            
            
        }
    }
  
    // test Identity matrix
    {
      DenseMatrix refMat1 = DenseMatrix::Identity(rows, rows);
      SparseMatrixType m1(rows, rows);
      m1.setIdentity();
      VERIFY_IS_APPROX(m1, refMat1);
      for(int k=0; k<rows*rows/4; ++k)
      {
        Index i = internal::random<Index>(0,rows-1);
        Index j = internal::random<Index>(0,rows-1);
        Scalar v = internal::random<Scalar>();
        m1.coeffRef(i,j) = v;
        refMat1.coeffRef(i,j) = v;
        VERIFY_IS_APPROX(m1, refMat1);
        if(internal::random<Index>(0,10)<2)
          m1.makeCompressed();
      }
      m1.setIdentity();
      refMat1.setIdentity();
      VERIFY_IS_APPROX(m1, refMat1);
    }
  }
  
  void test_sparse_basic()
  {
    for(int i = 0; i < g_repeat; i++) {
      int s = Eigen::internal::random<int>(1,50);
      EIGEN_UNUSED_VARIABLE(s);
      CALL_SUBTEST_1(( sparse_basic(SparseMatrix<double>(8, 8)) ));
      CALL_SUBTEST_2(( sparse_basic(SparseMatrix<std::complex<double>, ColMajor>(s, s)) ));
      CALL_SUBTEST_2(( sparse_basic(SparseMatrix<std::complex<double>, RowMajor>(s, s)) ));
      CALL_SUBTEST_1(( sparse_basic(SparseMatrix<double>(s, s)) ));
      CALL_SUBTEST_1(( sparse_basic(SparseMatrix<double,ColMajor,long int>(s, s)) ));
      CALL_SUBTEST_1(( sparse_basic(SparseMatrix<double,RowMajor,long int>(s, s)) ));
      
      CALL_SUBTEST_1(( sparse_basic(SparseMatrix<double,ColMajor,short int>(short(s), short(s))) ));
      CALL_SUBTEST_1(( sparse_basic(SparseMatrix<double,RowMajor,short int>(short(s), short(s))) ));
    }
  }
  