QR_Gram_Schmidt_Classical_decomposition Subroutine

public subroutine QR_Gram_Schmidt_Classical_decomposition(A, Q, R)

QR decomposition using Classical Gram-Schmidt method

Arguments

Type IntentOptional Attributes Name
real(kind=dp), intent(in), DIMENSION(:, :) :: A
real(kind=dp), intent(out), DIMENSION(SIZE(A, 1) ,SIZE(A, 2)) :: Q
real(kind=dp), intent(out), DIMENSION(SIZE(A, 1) ,SIZE(A, 2)) :: R

Called by

proc~~qr_gram_schmidt_classical_decomposition~~CalledByGraph proc~qr_gram_schmidt_classical_decomposition QR_Gram_Schmidt_Classical_decomposition proc~qr_decomposition QR_decomposition proc~qr_decomposition->proc~qr_gram_schmidt_classical_decomposition proc~eigen Eigen proc~eigen->proc~qr_decomposition proc~is_spd is_SPD proc~is_spd->proc~eigen

Source Code

    SUBROUTINE QR_Gram_Schmidt_Classical_decomposition(A, Q, R)
        REAL(dp), DIMENSION(:, :), INTENT(IN) :: A
        REAL(dp), DIMENSION(SIZE(A, 1) ,SIZE(A, 2)), INTENT(OUT) :: Q, R
        REAL(dp), DIMENSION(SIZE(A, 1)) :: u
        INTEGER :: N, i, j

        N= SIZE(A, 1)
        Q = 0.d0
        R = 0.d0

        DO j = 1, N
            u = A(:, j)
            DO i = 1, j-1
                R(i, j) = DOT_PRODUCT(Q(:, i),A(:, j))
                u = u - (R(i, j) * Q(:, i))
            END DO
            R(j, j) = NORM2(u)
            Q(:, j) = u / R(j, j)
        END DO

    END SUBROUTINE QR_Gram_Schmidt_Classical_decomposition