dbnslv Subroutine

private subroutine dbnslv(w, nroww, nrow, nbandl, nbandu, b)

Companion routine to dbnfac. it returns the solution x of the linear system a*x = b in place of b, given the lu-factorization for a in the work array w from dbnfac.

(with , as stored in w), the unit lower triangular system is solved for , and y stored in b. then the upper triangular system is solved for x. the calculations are so arranged that the innermost loops stay within columns.

History

  • banslv written by carl de boor [5]
  • dbnslv from SLATEC library [1]
  • Jacob Williams, 5/10/2015 : converted to free-form Fortran.

Arguments

Type IntentOptional Attributes Name
real(kind=wp), intent(in), dimension(nroww,nrow) :: w

describes the lu-factorization of a banded matrix a of order nrow as constructed in dbnfac.
integer, intent(in) :: nroww

describes the lu-factorization of a banded matrix a of order nrow as constructed in dbnfac.
integer, intent(in) :: nrow

describes the lu-factorization of a banded matrix a of order nrow as constructed in dbnfac.
integer, intent(in) :: nbandl

describes the lu-factorization of a banded matrix a of order nrow as constructed in dbnfac.
integer, intent(in) :: nbandu

describes the lu-factorization of a banded matrix a of order nrow as constructed in dbnfac.
real(kind=wp), intent(inout), dimension(nrow) :: b

in: right side of the system to be solved out: the solution x, of order nrow

Called by

proc~~dbnslv~~CalledByGraph proc~dbnslv dbnslv proc~dbintk dbintk proc~dbintk->proc~dbnslv proc~dbtpcf dbtpcf proc~dbtpcf->proc~dbnslv proc~dbtpcf->proc~dbintk proc~db1ink db1ink proc~db1ink->proc~dbtpcf proc~db2ink db2ink proc~db2ink->proc~dbtpcf proc~interp_surf interp_surf proc~interp_surf->proc~db2ink program~test_bspline test_bspline program~test_bspline->proc~interp_surf

Source Code

    subroutine dbnslv(w,nroww,nrow,nbandl,nbandu,b)

    integer,intent(in) :: nroww   !! describes the lu-factorization of a banded matrix a of order nrow as constructed in [[dbnfac]].
    integer,intent(in) :: nrow    !! describes the lu-factorization of a banded matrix a of order nrow as constructed in [[dbnfac]].
    integer,intent(in) :: nbandl  !! describes the lu-factorization of a banded matrix a of order nrow as constructed in [[dbnfac]].
    integer,intent(in) :: nbandu  !! describes the lu-factorization of a banded matrix a of order nrow as constructed in [[dbnfac]].
    real(wp),dimension(nroww,nrow),intent(in) :: w    !! describes the lu-factorization of a banded matrix a of order nrow as constructed in [[dbnfac]].
    real(wp),dimension(nrow),intent(inout) :: b  !! **in**: right side of the system to be solved
                                                 !! **out**: the solution x, of order nrow

    integer :: i, j, jmax, middle, nrowm1

    middle = nbandu + 1
    if (nrow/=1) then

        nrowm1 = nrow - 1
        if (nbandl/=0) then

            ! forward pass
            ! for i=1,2,...,nrow-1, subtract right side(i)*(i-th column of l)
            !                       from right side (below i-th row).
            do i=1,nrowm1
                jmax = min(nbandl,nrow-i)
                do j=1,jmax
                    b(i+j) = b(i+j) - b(i)*w(middle+j,i)
                enddo
            enddo

        endif

        ! backward pass
        ! for i=nrow,nrow-1,...,1, divide right side(i) by i-th diagonal
        !                          entry of u, then subtract right side(i)*(i-th column
        !                          of u) from right side (above i-th row).
        if (nbandu<=0) then
            ! a is lower triangular.
            do i=1,nrow
                b(i) = b(i)/w(1,i)
            enddo
            return
        endif

        i = nrow
        do
            b(i) = b(i)/w(middle,i)
            jmax = min(nbandu,i-1)
            do j=1,jmax
                b(i-j) = b(i-j) - b(i)*w(middle-j,i)
            enddo
            i = i - 1
            if (i<=1) exit
        enddo

    endif

    b(1) = b(1)/w(middle,1)

    endsubroutine dbnslv