incomplete_cholesky.cpp File Reference

#include "sparse_solver.h"
#include <Eigen/IterativeLinearSolvers>

Functions
template<typename T , typename I_ >
void	test_incomplete_cholesky_T ()
template<int >
void	bug1150 ()
void	test_non_spd ()
	EIGEN_DECLARE_TEST (incomplete_cholesky)

Function Documentation

bug1150()

template<int >

void bug1150

(

)

               {
  // regression for bug 1150
  for (int N = 1; N < 20; ++N) {
    Eigen::MatrixXd b(N, N);
    b.setOnes();
 
    Eigen::SparseMatrix<double> m(N, N);
    m.reserve(Eigen::VectorXi::Constant(N, 4));
    for (int i = 0; i < N; ++i) {
      m.insert(i, i) = 1;
      m.coeffRef(i, i / 2) = 2;
      m.coeffRef(i, i / 3) = 2;
      m.coeffRef(i, i / 4) = 2;
    }
 
    Eigen::SparseMatrix<double> A;
    A = m * m.transpose();
 
    Eigen::ConjugateGradient<Eigen::SparseMatrix<double>, Eigen::Lower | Eigen::Upper,
                             Eigen::IncompleteCholesky<double> >
        solver(A);
    VERIFY(solver.preconditioner().info() == Eigen::Success);
    VERIFY(solver.info() == Eigen::Success);
  }
}

References b, i, Eigen::Lower, m, N, solver, Eigen::Success, Eigen::Upper, and VERIFY.

EIGEN_DECLARE_TEST()

EIGEN_DECLARE_TEST

(

incomplete_cholesky

)

                                        {
  CALL_SUBTEST_1((test_incomplete_cholesky_T<double, int>()));
  CALL_SUBTEST_2((test_incomplete_cholesky_T<std::complex<double>, int>()));
  CALL_SUBTEST_3((test_incomplete_cholesky_T<double, long int>()));
 
  CALL_SUBTEST_4((bug1150<0>()));
  CALL_SUBTEST_4(test_non_spd());
}

References CALL_SUBTEST_1, CALL_SUBTEST_2, CALL_SUBTEST_3, CALL_SUBTEST_4, test_incomplete_cholesky_T(), and test_non_spd().

test_incomplete_cholesky_T()

template<typename T , typename I_ >

void test_incomplete_cholesky_T

(

)

                                  {
  typedef SparseMatrix<T, 0, I_> SparseMatrixType;
  ConjugateGradient<SparseMatrixType, Lower, IncompleteCholesky<T, Lower, AMDOrdering<I_> > > cg_illt_lower_amd;
  ConjugateGradient<SparseMatrixType, Lower, IncompleteCholesky<T, Lower, NaturalOrdering<I_> > > cg_illt_lower_nat;
  ConjugateGradient<SparseMatrixType, Upper, IncompleteCholesky<T, Upper, AMDOrdering<I_> > > cg_illt_upper_amd;
  ConjugateGradient<SparseMatrixType, Upper, IncompleteCholesky<T, Upper, NaturalOrdering<I_> > > cg_illt_upper_nat;
  ConjugateGradient<SparseMatrixType, Upper | Lower, IncompleteCholesky<T, Lower, AMDOrdering<I_> > > cg_illt_uplo_amd;
 
  CALL_SUBTEST(check_sparse_spd_solving(cg_illt_lower_amd));
  CALL_SUBTEST(check_sparse_spd_solving(cg_illt_lower_nat));
  CALL_SUBTEST(check_sparse_spd_solving(cg_illt_upper_amd));
  CALL_SUBTEST(check_sparse_spd_solving(cg_illt_upper_nat));
  CALL_SUBTEST(check_sparse_spd_solving(cg_illt_uplo_amd));
}

References CALL_SUBTEST, and check_sparse_spd_solving().

Referenced by EIGEN_DECLARE_TEST().

test_non_spd()

void test_non_spd

(

)

                    {
  Eigen::SparseMatrix<double> A(2, 2);
  A.insert(0, 0) = 0;
  A.insert(1, 1) = 3;
 
  Eigen::IncompleteCholesky<double> solver(A);
 
  // Recover original matrix.
  Eigen::MatrixXd M = solver.permutationP().transpose() *
                      (solver.scalingS().asDiagonal().inverse() *
                       (solver.matrixL() * solver.matrixL().transpose() -
                        solver.shift() * Eigen::MatrixXd::Identity(A.rows(), A.cols())) *
                       solver.scalingS().asDiagonal().inverse()) *
                      solver.permutationP();
  VERIFY_IS_APPROX(A.toDense(), M);
}

References Eigen::PlainObjectBase< Derived >::cols(), Eigen::PlainObjectBase< Derived >::rows(), solver, and VERIFY_IS_APPROX.

Referenced by EIGEN_DECLARE_TEST().