Program f11jbfe

!     F11JBF Example Program Text

!     Mark 28.6 Release. NAG Copyright 2022.

!     .. Use Statements ..
      Use nag_library, Only: f11jaf, f11jbf, nag_wp
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
      Real (Kind=nag_wp)               :: dscale, dtol
      Integer                          :: i, ifail, la, lfill, liwork, n, nnz, &
                                          nnzc, npivm
      Character (1)                    :: check, mic, pstrat
!     .. Local Arrays ..
      Real (Kind=nag_wp), Allocatable  :: a(:), x(:), y(:)
      Integer, Allocatable             :: icol(:), ipiv(:), irow(:), istr(:),  &
                                          iwork(:), perm_fwd(:), perm_inv(:)
!     .. Executable Statements ..
      Write (nout,*) 'F11JBF Example Program Results'
!     Skip heading in data file
      Read (nin,*)

!     Read order of matrix and number of nonzero entries

      Read (nin,*) n
      Read (nin,*) nnz

      la = 3*nnz
      liwork = 2*la + 7*n + 1

      Allocate (a(la),x(n),y(n),icol(la),ipiv(n),irow(la),istr(n+1),           &
        iwork(liwork),perm_fwd(n),perm_inv(n))

!     Read the matrix A

      Do i = 1, nnz
        Read (nin,*) a(i), irow(i), icol(i)
      End Do

!     Read the vector y

      Read (nin,*) y(1:n)

!     Calculate Cholesky factorization

      lfill = -1
      dtol = 0.0E0_nag_wp
      mic = 'N'
      dscale = 0.0E0_nag_wp
      pstrat = 'M'

!     ifail: behaviour on error exit
!             =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
      ifail = 0
      Call f11jaf(n,nnz,a,la,irow,icol,lfill,dtol,mic,dscale,pstrat,ipiv,istr, &
        nnzc,npivm,iwork,liwork,ifail)

!     Check the output value of NPIVM
      If (npivm/=0) Then
        Write (nout,99998) 'Factorization is not complete', npivm
      Else
!       Solve P L D L^T P^T x = y
        check = 'C'
        ifail = 0
        Call f11jbf(n,a,la,irow,icol,ipiv,istr,check,y,x,ifail)
!       Output results
        Write (nout,*) ' Solution of linear system'
        Write (nout,99999) x(1:n)
      End If

!     Compute reverse Cuthill-McKee permutation for bandwidth reduction
      Call do_rcm(irow,icol,a,y,istr,perm_fwd,perm_inv,iwork)

      ifail = 0
      Call f11jaf(n,nnz,a,la,irow,icol,lfill,dtol,mic,dscale,pstrat,ipiv,istr, &
        nnzc,npivm,iwork,liwork,ifail)

!     Check the output value of NPIVM
      If (npivm/=0) Then
        Write (nout,99998) 'Factorization is not complete', npivm
      Else
!       Solve P L D L^T P^T x = y
        ifail = 0
        Call f11jbf(n,a,la,irow,icol,ipiv,istr,check,y,x,ifail)
!       Output results
        Write (nout,*) ' Solution of linear system with Reverse Cuthill-McKee'
        Write (nout,99999)(x(perm_inv(i)),i=1,n)
      End If

99999 Format (1X,E16.4)
99998 Format (1X,A,I20)
    Contains
      Subroutine do_rcm(irow,icol,a,y,istr,perm_fwd,perm_inv,iwork)

!       .. Use Statements ..
        Use nag_library, Only: f11yef, f11zaf, f11zbf
!       .. Parameters ..
        Logical, Parameter             :: lopts(5) = (/.False.,.False.,.True., &
                                          .True.,.True./)
!       .. Array Arguments ..
        Real (Kind=nag_wp), Intent (Inout) :: a(la), y(n)
        Integer, Intent (Inout)        :: icol(la), irow(la), istr(n+1),       &
                                          iwork(*)
        Integer, Intent (Out)          :: perm_fwd(n), perm_inv(n)
!       .. Local Scalars ..
        Integer                        :: i, ifail, j, nnz_cs, nnz_scs
!       .. Local Arrays ..
        Real (Kind=nag_wp), Allocatable :: rwork(:)
        Integer                        :: info(4), mask(1)
!       .. Intrinsic Procedures ..
        Intrinsic                      :: size
!       .. Executable Statements ..

!       SCS to CS, must add the upper triangle entries.
        j = nnz + 1
        Do i = 1, nnz
          If (irow(i)>icol(i)) Then
!           strictly lower triangle, add the transposed
            a(j) = a(i)
            irow(j) = icol(i)
            icol(j) = irow(i)
            j = j + 1
          End If
        End Do
        nnz_cs = j - 1

!       Reorder, CS to CCS, icolzp in istr
        ifail = 0
        Call f11zaf(n,nnz_cs,a,icol,irow,'F','F',istr,iwork,ifail)

!       Calculate reverse Cuthill-McKee
        ifail = 0
        Call f11yef(n,nnz_cs,istr,irow,lopts,mask,perm_fwd,info,ifail)

!       compute inverse perm, in perm_inv(1:n)
        Do i = 1, n
          perm_inv(perm_fwd(i)) = i
        End Do

!       Apply permutation on column/row indices
        icol(1:nnz_cs) = perm_inv(icol(1:nnz_cs))
        irow(1:nnz_cs) = perm_inv(irow(1:nnz_cs))

!       restrict to lower triangle, SCS format
!       copying entries upwards
        j = 1
        Do i = 1, nnz_cs
          If (irow(i)>=icol(i)) Then
!           non-upper triangle, bubble up
            a(j) = a(i)
            icol(j) = icol(i)
            irow(j) = irow(i)
            j = j + 1
          End If
        End Do
        nnz_scs = j - 1

!       sort
        ifail = 0
        Call f11zbf(n,nnz_scs,a,irow,icol,'S','K',istr,iwork,ifail)

!       permute rhs vector
        Allocate (rwork(size(perm_fwd)))
        rwork(:) = y(perm_fwd(:))
        y(:) = rwork(:)
        Deallocate (rwork)
      End Subroutine do_rcm
    End Program f11jbfe