update

1 files changed, 566 insertions, 0 deletions

diff --git a/eigen/test/sparse_basic.cpp b/eigen/test/sparse_basic.cpp
new file mode 100644
index 0000000..abe6a9d
--- /dev/null
+++ b/eigen/test/sparse_basic.cpp
@@ -0,0 +1,566 @@
+// 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)));
+
+    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))) ));
+  }
+}