preconditioner_ic.h

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#ifndef MUI_PRECONDITIONER_IC_H_
#define MUI_PRECONDITIONER_IC_H_
 
#include <math.h>
#include <limits>
 
namespace mui {
namespace linalg {
 
// Constructor
template<typename ITYPE, typename VTYPE>
incomplete_cholesky_preconditioner<ITYPE,VTYPE>::incomplete_cholesky_preconditioner(const sparse_matrix<ITYPE,VTYPE>& A) {
    // Initialise the lower triangular matrix
    L_.resize(A.get_rows(), A.get_cols());
    // Construct the lower triangular matrix
    for (ITYPE i = 0; i < A.get_rows(); ++i) {
        for (ITYPE j = 0; j <= i; ++j) {
            if (i == j) {
                VTYPE sum = 0;
                for (ITYPE k = 0; k < j; ++k) {
                 sum += std::pow(L_.get_value(j, k), 2);
                }
                L_.set_value(j, j, (std::sqrt(A.get_value(j, j) - sum)));
            } else {
                VTYPE sum = 0;
                for (ITYPE k = 0; k < j; ++k) {
                 sum += L_.get_value(i, k) * L_.get_value(j, k);
                }
                assert(std::abs(L_.get_value(j, j)) >= std::numeric_limits<VTYPE>::min() &&
                        "MUI Error [preconditioner_ic.h]: Divide by zero assert for L_.get_value(j, j)");
                L_.set_value(i, j, ((A.get_value(i, j) - sum) / L_.get_value(j, j)));
            }
        }
    }
 }
 
// Destructor
template<typename ITYPE, typename VTYPE>
incomplete_cholesky_preconditioner<ITYPE,VTYPE>::~incomplete_cholesky_preconditioner() {
    // Deallocate the memory for the lower triangular matrix
    L_.set_zero();
}
 
// Member function on preconditioner apply
template<typename ITYPE, typename VTYPE>
sparse_matrix<ITYPE,VTYPE> incomplete_cholesky_preconditioner<ITYPE,VTYPE>::apply(const sparse_matrix<ITYPE,VTYPE>& x) {
    assert((x.get_cols()==1) &&
        "MUI Error [preconditioner_ic.h]: apply only works for column vectors");
    sparse_matrix<ITYPE,VTYPE> y(x.get_rows(), x.get_cols());
    sparse_matrix<ITYPE,VTYPE> z(x.get_rows(), x.get_cols());
 
    // Forward substitution
    for (ITYPE i = 0; i < x.get_rows(); ++i) {
        VTYPE sum = 0;
        for (ITYPE j = 0; j < i; ++j) {
            sum += L_.get_value(i, j) * y.get_value(j,0);
        }
        assert(std::abs(L_.get_value(i, i)) >= std::numeric_limits<VTYPE>::min() &&
                "MUI Error [preconditioner_ic.h]: Divide by zero assert for L_.get_value(i, i)");
        y.set_value(i, 0, ((x.get_value(i, 0) - sum) / L_.get_value(i, i)));
    }
 
    // Backward substitution
    for (ITYPE i = x.get_rows() - 1; i >= 0; --i) {
        VTYPE sum = 0;
        for (ITYPE j = i + 1; j < x.get_rows(); ++j) {
            sum += L_.get_value(j, i) * z.get_value(j,0);
        }
        assert(std::abs(L_.get_value(i, i)) >= std::numeric_limits<VTYPE>::min() &&
          "MUI Error [preconditioner_ic.h]: Divide by zero assert for L_.get_value(i, i)");
        z.set_value(i, 0, ((y.get_value(i, 0) - sum) / L_.get_value(i, i)));
    }
    return z;
}
 
} // linalg
} // mui
 
#endif /* MUI_PRECONDITIONER_IC_H_ */