template<typename SparseMatrixType> void sparse_product(const SparseMatrixType& ref)
{
  const int rows = ref.rows();
  const int 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;

  // test matrix-matrix product
  {
    DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows);
    DenseMatrix refMat3 = DenseMatrix::Zero(rows, rows);
    DenseMatrix refMat4 = DenseMatrix::Zero(rows, rows);
    DenseMatrix dm4 = DenseMatrix::Zero(rows, rows);
    SparseMatrixType m2(rows, rows);
    SparseMatrixType m3(rows, rows);
    SparseMatrixType m4(rows, rows);
    initSparse<Scalar>(density, refMat2, m2);
    initSparse<Scalar>(density, refMat3, m3);
    initSparse<Scalar>(density, refMat4, m4);
    VERIFY_IS_APPROX(m4=m2*m3, refMat4=refMat2*refMat3);
    VERIFY_IS_APPROX(m4=m2.transpose()*m3, refMat4=refMat2.transpose()*refMat3);
    VERIFY_IS_APPROX(m4=m2.transpose()*m3.transpose(), refMat4=refMat2.transpose()*refMat3.transpose());
    VERIFY_IS_APPROX(m4=m2*m3.transpose(), refMat4=refMat2*refMat3.transpose());

    // sparse * dense
    VERIFY_IS_APPROX(dm4=m2*refMat3, refMat4=refMat2*refMat3);
    VERIFY_IS_APPROX(dm4=m2*refMat3.transpose(), refMat4=refMat2*refMat3.transpose());
    VERIFY_IS_APPROX(dm4=m2.transpose()*refMat3, refMat4=refMat2.transpose()*refMat3);
    VERIFY_IS_APPROX(dm4=m2.transpose()*refMat3.transpose(), refMat4=refMat2.transpose()*refMat3.transpose());

    // dense * sparse
    VERIFY_IS_APPROX(dm4=refMat2*m3, refMat4=refMat2*refMat3);
    VERIFY_IS_APPROX(dm4=refMat2*m3.transpose(), refMat4=refMat2*refMat3.transpose());
    VERIFY_IS_APPROX(dm4=refMat2.transpose()*m3, refMat4=refMat2.transpose()*refMat3);
    VERIFY_IS_APPROX(dm4=refMat2.transpose()*m3.transpose(), refMat4=refMat2.transpose()*refMat3.transpose());

    VERIFY_IS_APPROX(m3=m3*m3, refMat3=refMat3*refMat3);
  }

  // test matrix - diagonal product
  if(false) // it compiles, but the precision is terrible. probably doesn't matter in this branch....
  {
    DenseMatrix refM2 = DenseMatrix::Zero(rows, rows);
    DenseMatrix refM3 = DenseMatrix::Zero(rows, rows);
    DiagonalMatrix<DenseVector> d1(DenseVector::Random(rows));
    SparseMatrixType m2(rows, rows);
    SparseMatrixType m3(rows, rows);
    initSparse<Scalar>(density, refM2, m2);
    initSparse<Scalar>(density, refM3, m3);
    VERIFY_IS_APPROX(m3=m2*d1, refM3=refM2*d1);
    VERIFY_IS_APPROX(m3=m2.transpose()*d1, refM3=refM2.transpose()*d1);
    VERIFY_IS_APPROX(m3=d1*m2, refM3=d1*refM2);
    VERIFY_IS_APPROX(m3=d1*m2.transpose(), refM3=d1 * refM2.transpose());
  }

  // test self adjoint products
  {
    DenseMatrix b = DenseMatrix::Random(rows, rows);
    DenseMatrix x = DenseMatrix::Random(rows, rows);
    DenseMatrix refX = DenseMatrix::Random(rows, rows);
    DenseMatrix refUp = DenseMatrix::Zero(rows, rows);
    DenseMatrix refLo = DenseMatrix::Zero(rows, rows);
    DenseMatrix refS = DenseMatrix::Zero(rows, rows);
    SparseMatrixType mUp(rows, rows);
    SparseMatrixType mLo(rows, rows);
    SparseMatrixType mS(rows, rows);
    do {
      initSparse<Scalar>(density, refUp, mUp, ForceRealDiag|/*ForceNonZeroDiag|*/MakeUpperTriangular);
    } while (refUp.isZero());
    refLo = refUp.transpose().conjugate();
    mLo = mUp.transpose().conjugate();
    refS = refUp + refLo;
    refS.diagonal() *= 0.5;
    mS = mUp + mLo;
    for (int k=0; k<mS.outerSize(); ++k)
      for (typename SparseMatrixType::InnerIterator it(mS,k); it; ++it)
        if (it.index() == k)
          it.valueRef() *= 0.5;

    VERIFY_IS_APPROX(refS.adjoint(), refS);
    VERIFY_IS_APPROX(mS.transpose().conjugate(), mS);
    VERIFY_IS_APPROX(mS, refS);
    VERIFY_IS_APPROX(x=mS*b, refX=refS*b);
    VERIFY_IS_APPROX(x=mUp.template marked<UpperTriangular|SelfAdjoint>()*b, refX=refS*b);
    VERIFY_IS_APPROX(x=mLo.template marked<LowerTriangular|SelfAdjoint>()*b, refX=refS*b);
    VERIFY_IS_APPROX(x=mS.template marked<SelfAdjoint>()*b, refX=refS*b);
  }

}
Пример #2
0
template<typename SparseMatrixType> void sparse_product()
{
  typedef typename SparseMatrixType::Index Index;
  Index n = 100;
  const Index rows  = internal::random<int>(1,n);
  const Index cols  = internal::random<int>(1,n);
  const Index depth = internal::random<int>(1,n);
  typedef typename SparseMatrixType::Scalar Scalar;
  enum { Flags = SparseMatrixType::Flags };

  double density = (std::max)(8./(rows*cols), 0.1);
  typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
  typedef Matrix<Scalar,Dynamic,1> DenseVector;

  Scalar s1 = internal::random<Scalar>();
  Scalar s2 = internal::random<Scalar>();

  // test matrix-matrix product
  {
    DenseMatrix refMat2  = DenseMatrix::Zero(rows, depth);
    DenseMatrix refMat2t = DenseMatrix::Zero(depth, rows);
    DenseMatrix refMat3  = DenseMatrix::Zero(depth, cols);
    DenseMatrix refMat3t = DenseMatrix::Zero(cols, depth);
    DenseMatrix refMat4  = DenseMatrix::Zero(rows, cols);
    DenseMatrix refMat4t = DenseMatrix::Zero(cols, rows);
    DenseMatrix refMat5  = DenseMatrix::Random(depth, cols);
    DenseMatrix refMat6  = DenseMatrix::Random(rows, rows);
    DenseMatrix dm4 = DenseMatrix::Zero(rows, rows);
//     DenseVector dv1 = DenseVector::Random(rows);
    SparseMatrixType m2 (rows, depth);
    SparseMatrixType m2t(depth, rows);
    SparseMatrixType m3 (depth, cols);
    SparseMatrixType m3t(cols, depth);
    SparseMatrixType m4 (rows, cols);
    SparseMatrixType m4t(cols, rows);
    SparseMatrixType m6(rows, rows);
    initSparse(density, refMat2,  m2);
    initSparse(density, refMat2t, m2t);
    initSparse(density, refMat3,  m3);
    initSparse(density, refMat3t, m3t);
    initSparse(density, refMat4,  m4);
    initSparse(density, refMat4t, m4t);
    initSparse(density, refMat6, m6);

//     int c = internal::random<int>(0,depth-1);

    // sparse * sparse
    VERIFY_IS_APPROX(m4=m2*m3, refMat4=refMat2*refMat3);
    VERIFY_IS_APPROX(m4=m2t.transpose()*m3, refMat4=refMat2t.transpose()*refMat3);
    VERIFY_IS_APPROX(m4=m2t.transpose()*m3t.transpose(), refMat4=refMat2t.transpose()*refMat3t.transpose());
    VERIFY_IS_APPROX(m4=m2*m3t.transpose(), refMat4=refMat2*refMat3t.transpose());

    VERIFY_IS_APPROX(m4 = m2*m3/s1, refMat4 = refMat2*refMat3/s1);
    VERIFY_IS_APPROX(m4 = m2*m3*s1, refMat4 = refMat2*refMat3*s1);
    VERIFY_IS_APPROX(m4 = s2*m2*m3*s1, refMat4 = s2*refMat2*refMat3*s1);

    VERIFY_IS_APPROX(m4=(m2*m3).pruned(0), refMat4=refMat2*refMat3);
    VERIFY_IS_APPROX(m4=(m2t.transpose()*m3).pruned(0), refMat4=refMat2t.transpose()*refMat3);
    VERIFY_IS_APPROX(m4=(m2t.transpose()*m3t.transpose()).pruned(0), refMat4=refMat2t.transpose()*refMat3t.transpose());
    VERIFY_IS_APPROX(m4=(m2*m3t.transpose()).pruned(0), refMat4=refMat2*refMat3t.transpose());

    // test aliasing
    m4 = m2; refMat4 = refMat2;
    VERIFY_IS_APPROX(m4=m4*m3, refMat4=refMat4*refMat3);

    // sparse * dense
    VERIFY_IS_APPROX(dm4=m2*refMat3, refMat4=refMat2*refMat3);
    VERIFY_IS_APPROX(dm4=m2*refMat3t.transpose(), refMat4=refMat2*refMat3t.transpose());
    VERIFY_IS_APPROX(dm4=m2t.transpose()*refMat3, refMat4=refMat2t.transpose()*refMat3);
    VERIFY_IS_APPROX(dm4=m2t.transpose()*refMat3t.transpose(), refMat4=refMat2t.transpose()*refMat3t.transpose());

    VERIFY_IS_APPROX(dm4=m2*(refMat3+refMat3), refMat4=refMat2*(refMat3+refMat3));
    VERIFY_IS_APPROX(dm4=m2t.transpose()*(refMat3+refMat5)*0.5, refMat4=refMat2t.transpose()*(refMat3+refMat5)*0.5);

    // dense * sparse
    VERIFY_IS_APPROX(dm4=refMat2*m3, refMat4=refMat2*refMat3);
    VERIFY_IS_APPROX(dm4=refMat2*m3t.transpose(), refMat4=refMat2*refMat3t.transpose());
    VERIFY_IS_APPROX(dm4=refMat2t.transpose()*m3, refMat4=refMat2t.transpose()*refMat3);
    VERIFY_IS_APPROX(dm4=refMat2t.transpose()*m3t.transpose(), refMat4=refMat2t.transpose()*refMat3t.transpose());

    // sparse * dense and dense * sparse outer product
    test_outer<SparseMatrixType,DenseMatrix>::run(m2,m4,refMat2,refMat4);

    VERIFY_IS_APPROX(m6=m6*m6, refMat6=refMat6*refMat6);
  }

  // test matrix - diagonal product
  {
    DenseMatrix refM2 = DenseMatrix::Zero(rows, cols);
    DenseMatrix refM3 = DenseMatrix::Zero(rows, cols);
    DenseMatrix d3 = DenseMatrix::Zero(rows, cols);
    DiagonalMatrix<Scalar,Dynamic> d1(DenseVector::Random(cols));
    DiagonalMatrix<Scalar,Dynamic> d2(DenseVector::Random(rows));
    SparseMatrixType m2(rows, cols);
    SparseMatrixType m3(rows, cols);
    initSparse<Scalar>(density, refM2, m2);
    initSparse<Scalar>(density, refM3, m3);
    VERIFY_IS_APPROX(m3=m2*d1, refM3=refM2*d1);
    VERIFY_IS_APPROX(m3=m2.transpose()*d2, refM3=refM2.transpose()*d2);
    VERIFY_IS_APPROX(m3=d2*m2, refM3=d2*refM2);
    VERIFY_IS_APPROX(m3=d1*m2.transpose(), refM3=d1*refM2.transpose());
    
    // evaluate to a dense matrix to check the .row() and .col() iterator functions
    VERIFY_IS_APPROX(d3=m2*d1, refM3=refM2*d1);
    VERIFY_IS_APPROX(d3=m2.transpose()*d2, refM3=refM2.transpose()*d2);
    VERIFY_IS_APPROX(d3=d2*m2, refM3=d2*refM2);
    VERIFY_IS_APPROX(d3=d1*m2.transpose(), refM3=d1*refM2.transpose());
  }

  // test self adjoint products
  {
    DenseMatrix b = DenseMatrix::Random(rows, rows);
    DenseMatrix x = DenseMatrix::Random(rows, rows);
    DenseMatrix refX = DenseMatrix::Random(rows, rows);
    DenseMatrix refUp = DenseMatrix::Zero(rows, rows);
    DenseMatrix refLo = DenseMatrix::Zero(rows, rows);
    DenseMatrix refS = DenseMatrix::Zero(rows, rows);
    SparseMatrixType mUp(rows, rows);
    SparseMatrixType mLo(rows, rows);
    SparseMatrixType mS(rows, rows);
    do {
      initSparse<Scalar>(density, refUp, mUp, ForceRealDiag|/*ForceNonZeroDiag|*/MakeUpperTriangular);
    } while (refUp.isZero());
    refLo = refUp.adjoint();
    mLo = mUp.adjoint();
    refS = refUp + refLo;
    refS.diagonal() *= 0.5;
    mS = mUp + mLo;
    // TODO be able to address the diagonal....
    for (int k=0; k<mS.outerSize(); ++k)
      for (typename SparseMatrixType::InnerIterator it(mS,k); it; ++it)
        if (it.index() == k)
          it.valueRef() *= 0.5;

    VERIFY_IS_APPROX(refS.adjoint(), refS);
    VERIFY_IS_APPROX(mS.adjoint(), mS);
    VERIFY_IS_APPROX(mS, refS);
    VERIFY_IS_APPROX(x=mS*b, refX=refS*b);

    VERIFY_IS_APPROX(x=mUp.template selfadjointView<Upper>()*b, refX=refS*b);
    VERIFY_IS_APPROX(x=mLo.template selfadjointView<Lower>()*b, refX=refS*b);
    VERIFY_IS_APPROX(x=mS.template selfadjointView<Upper|Lower>()*b, refX=refS*b);
  }
}
Пример #3
0
template<typename Scalar> void sparse_llt(int rows, int cols)
{
  double density = std::max(8./(rows*cols), 0.01);
  typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
  typedef Matrix<Scalar,Dynamic,1> DenseVector;

    // TODO fix the issue with complex (see SparseLLT::solveInPlace)
    SparseMatrix<Scalar> m2(rows, cols);
    DenseMatrix refMat2(rows, cols);

    DenseVector b = DenseVector::Random(cols);
    DenseVector ref_x(cols), x(cols);
    DenseMatrix B = DenseMatrix::Random(rows,cols);
    DenseMatrix ref_X(rows,cols), X(rows,cols);

    initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, 0, 0);

    for(int i=0; i<rows; ++i)
      m2.coeffRef(i,i) = refMat2(i,i) = internal::abs(internal::real(refMat2(i,i)));

    ref_x = refMat2.template selfadjointView<Lower>().llt().solve(b);
    if (!NumTraits<Scalar>::IsComplex)
    {
      x = b;
      SparseLLT<SparseMatrix<Scalar> > (m2).solveInPlace(x);
      VERIFY(ref_x.isApprox(x,test_precision<Scalar>()) && "LLT: default");
    }
        
#ifdef EIGEN_CHOLMOD_SUPPORT
    // legacy API
    {
      // Cholmod, as configured in CholmodSupport.h, only supports self-adjoint matrices
      SparseMatrix<Scalar> m3 = m2.adjoint()*m2;
      DenseMatrix refMat3 = refMat2.adjoint()*refMat2;
      
      ref_x = refMat3.template selfadjointView<Lower>().llt().solve(b);
      
      x = b;
      SparseLLT<SparseMatrix<Scalar>, Cholmod>(m3).solveInPlace(x);
      VERIFY((m3*x).isApprox(b,test_precision<Scalar>()) && "LLT legacy: cholmod solveInPlace");
      
      x = SparseLLT<SparseMatrix<Scalar>, Cholmod>(m3).solve(b);
      VERIFY(ref_x.isApprox(x,test_precision<Scalar>()) && "LLT legacy: cholmod solve");
    }
    
    // new API
    {
      // Cholmod, as configured in CholmodSupport.h, only supports self-adjoint matrices
      SparseMatrix<Scalar> m3 = m2 * m2.adjoint(), m3_lo(rows,rows), m3_up(rows,rows);
      DenseMatrix refMat3 = refMat2 * refMat2.adjoint();
      
      m3_lo.template selfadjointView<Lower>().rankUpdate(m2,0);
      m3_up.template selfadjointView<Upper>().rankUpdate(m2,0);
      
      // with a single vector as the rhs
      ref_x = refMat3.template selfadjointView<Lower>().llt().solve(b);

      x = CholmodDecomposition<SparseMatrix<Scalar>, Lower>(m3).solve(b);
      VERIFY(ref_x.isApprox(x,test_precision<Scalar>()) && "LLT: cholmod solve, single dense rhs");
      
      x = CholmodDecomposition<SparseMatrix<Scalar>, Upper>(m3).solve(b);
      VERIFY(ref_x.isApprox(x,test_precision<Scalar>()) && "LLT: cholmod solve, single dense rhs");
      
      x = CholmodDecomposition<SparseMatrix<Scalar>, Lower>(m3_lo).solve(b);
      VERIFY(ref_x.isApprox(x,test_precision<Scalar>()) && "LLT: cholmod solve, single dense rhs");
      
      x = CholmodDecomposition<SparseMatrix<Scalar>, Upper>(m3_up).solve(b);
      VERIFY(ref_x.isApprox(x,test_precision<Scalar>()) && "LLT: cholmod solve, single dense rhs");
      
      
      // with multiple rhs
      ref_X = refMat3.template selfadjointView<Lower>().llt().solve(B);

      #ifndef EIGEN_DEFAULT_TO_ROW_MAJOR
      // TODO make sure the API is properly documented about this fact
      X = CholmodDecomposition<SparseMatrix<Scalar>, Lower>(m3).solve(B);
      VERIFY(ref_X.isApprox(X,test_precision<Scalar>()) && "LLT: cholmod solve, multiple dense rhs");
      
      X = CholmodDecomposition<SparseMatrix<Scalar>, Upper>(m3).solve(B);
      VERIFY(ref_X.isApprox(X,test_precision<Scalar>()) && "LLT: cholmod solve, multiple dense rhs");
      #endif
      
      
      // with a sparse rhs
      SparseMatrix<Scalar> spB(rows,cols), spX(rows,cols);
      B.diagonal().array() += 1;
      spB = B.sparseView(0.5,1);
      
      ref_X = refMat3.template selfadjointView<Lower>().llt().solve(DenseMatrix(spB));

      spX = CholmodDecomposition<SparseMatrix<Scalar>, Lower>(m3).solve(spB);
      VERIFY(ref_X.isApprox(spX.toDense(),test_precision<Scalar>()) && "LLT: cholmod solve, multiple sparse rhs");
      
      spX = CholmodDecomposition<SparseMatrix<Scalar>, Upper>(m3).solve(spB);
      VERIFY(ref_X.isApprox(spX.toDense(),test_precision<Scalar>()) && "LLT: cholmod solve, multiple sparse rhs");
    }
#endif

}