Incomplete_Cholesky_decomposition Subroutine

public subroutine Incomplete_Cholesky_decomposition(A, L)

Incomplete Cholesky decomposition of a matrix A This subroutine performs incomplete Cholesky decomposition of a given matrix A, where L is a lower triangular matrix and U is an upper triangular matrix.

Arguments

Type IntentOptional Attributes Name
real(kind=dp), intent(in), DIMENSION(:, :) :: A
real(kind=dp), intent(out), DIMENSION(SIZE(A, 1), SIZE(A, 1)) :: L

Calls

proc~~incomplete_cholesky_decomposition~~CallsGraph proc~incomplete_cholesky_decomposition Incomplete_Cholesky_decomposition proc~identity_n Identity_n proc~incomplete_cholesky_decomposition->proc~identity_n

Called by

proc~~incomplete_cholesky_decomposition~~CalledByGraph proc~incomplete_cholesky_decomposition Incomplete_Cholesky_decomposition proc~calculate_icf_preconditioner Calculate_ICF_preconditioner proc~calculate_icf_preconditioner->proc~incomplete_cholesky_decomposition

Source Code

    SUBROUTINE Incomplete_Cholesky_decomposition(A, L)

        REAL(dp), DIMENSION(:, :), INTENT(IN) :: A
        REAL(dp), DIMENSION(SIZE(A, 1), SIZE(A, 1)), INTENT(OUT) :: L
        LOGICAL, DIMENSION(SIZE(A, 1), SIZE(A, 1)) :: S
        INTEGER :: i, j, N

        N = SIZE(A, 1)

        L = Identity_n(N)
        
        S = A /= 0

        DO i = 1, N
            DO j = 1, i-1
                IF (S(i,j)) L(i,j) = (A(i,j) - DOT_PRODUCT(L(i, 1:j-1), L(j, 1:j-1))) / L(j,j)
            END DO
            IF (S(i,i)) L(i,i) = SQRT(A(i,i) - DOT_PRODUCT(L(i, 1:i-1), L(i, 1:i-1)))
        END DO

    END SUBROUTINE Incomplete_Cholesky_decomposition