NAG Library Manual, Mark 28.5
```!   F11DTF Example Program Text
!   Mark 28.5 Release. NAG Copyright 2022.

Program f11dtfe

!     .. Use Statements ..
Use nag_library, Only: f11dtf, nag_wp
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: dtolg
Integer                          :: i, ifail, k, la, lfillg, lindb,      &
liwork, mb, n, nb, nnz, nnzc, nover
Character (1)                    :: milug, pstrag
!     .. Local Arrays ..
Complex (Kind=nag_wp), Allocatable :: a(:), b(:)
Real (Kind=nag_wp), Allocatable  :: dtol(:)
Integer, Allocatable             :: icol(:), idiag(:), indb(:),          &
ipivp(:), ipivq(:), irow(:),         &
istb(:), istr(:), iwork(:),          &
lfill(:), npivm(:)
Character (1), Allocatable       :: milu(:), pstrat(:)
!     .. Intrinsic Procedures ..
Intrinsic                        :: maxval, minval
!     .. Executable Statements ..

Write (nout,*) 'F11DTF Example Program Results'
Write (nout,*)

!     Skip heading in data file

!     Get the square matrix size

!     Allocate arrays with lengths based on mesh.
liwork = 9*n + 3
Allocate (b(n),iwork(liwork))

!     Get the number of non zero (nnz) matrix entries
la = 20*nnz
Allocate (a(la),irow(la),icol(la))

lindb = 3*n
Allocate (idiag(lindb),indb(lindb),ipivp(lindb),ipivq(lindb),            &
istr(lindb+1))

!     Allocate arrays with length based on number of blocks.
Allocate (dtol(nb),istb(nb+1),lfill(nb),npivm(nb),milu(nb),pstrat(nb))

!     Define diagonal block indices.
!     In this example use blocks of MB consecutive rows and initialize
!     assuming no overlap.
mb = (n+nb-1)/nb
Do k = 1, nb
istb(k) = (k-1)*mb + 1
End Do
istb(nb+1) = n + 1
Do i = 1, n
indb(i) = i
End Do

!     Modify INDB and ISTB to account for overlap.
Call f11dtfe_overlap(n,nnz,la,irow,icol,nb,istb,indb,lindb,nover,iwork)
If (iwork(1)==-999) Then
Write (nout,*) '** LINDB too small, LINDB = ', lindb, '.'
Go To 100
End If

!     Output matrix and blocking details
Write (nout,*) ' Original Matrix'
Write (nout,99998) ' N     =', n
Write (nout,99998) ' NNZ   =', nnz
Write (nout,99998) ' NB    =', nb
Do k = 1, nb
Write (nout,99994) ' Block ', k, ': order = ', istb(k+1) - istb(k),    &
', start row = ', minval(indb(istb(k):istb(k+1)-1))
End Do

!     Set algorithmic parameters for each block from global values
lfill(1:nb) = lfillg
dtol(1:nb) = dtolg
pstrat(1:nb) = pstrag
milu(1:nb) = milug

!     Calculate factorization
ifail = 0
Call f11dtf(n,nnz,a,la,irow,icol,nb,istb,indb,lindb,lfill,dtol,pstrat,   &
milu,ipivp,ipivq,istr,idiag,nnzc,npivm,iwork,liwork,ifail)

!     Output details of the factorization
Write (nout,99997) ' Factorization'
Write (nout,99998) '  NNZC  =', nnzc

Write (nout,99997) ' Elements of factorization'
Write (nout,99997)                                                       &
'      I   J              C(I,J)                Index'
Do k = 1, nb
Write (nout,99995) ' C_', k,                                           &
' -----------------------------------------------'
!       Elements of the k-th block
Do i = istr(istb(k)), istr(istb(k+1)) - 1
Write (nout,99993) irow(i), icol(i), a(i), i
End Do
End Do

Write (nout,99997) ' Details of factorized blocks'
If (maxval(npivm(1:nb))>0) Then
!       Including pivoting details.
Write (nout,99997)                                                     &
'  K   I      ISTR(I)  IDIAG(I)   INDB(I)  IPIVP(I)  IPIVQ(I)'
Do k = 1, nb
i = istb(k)
Write (nout,99996) k, i, istr(i), idiag(i), indb(i), ipivp(i),       &
ipivq(i)
Do i = istb(k) + 1, istb(k+1) - 1
Write (nout,99999) i, istr(i), idiag(i), indb(i), ipivp(i),        &
ipivq(i)
End Do
Write (nout,*)                                                       &
' -----------------------------------------------------'
End Do
Else
!       No pivoting on any block.
Write (nout,99997) '  K   I      ISTR(I)  IDIAG(I)   INDB(I)'
Do k = 1, nb
i = istb(k)
Write (nout,99996) k, i, istr(i), idiag(i), indb(i)
Do i = istb(k) + 1, istb(k+1) - 1
Write (nout,99999) i, istr(i), idiag(i), indb(i)
End Do
Write (nout,*) ' ------------------------------------'
End Do
End If

100   Continue

99999 Format (1X,I7,5(I10))
99998 Format (1X,A,I4)
99997 Format (1X,/,1X,A)
99996 Format (1X,I3,1X,I3,5(I10))
99995 Format (1X,A3,I1,A)
99994 Format (1X,A,I3,A,I3,A,I3)
99993 Format (4X,2I4,4X,'(',E13.5,',',E13.5,')',I8)

Contains
Subroutine f11dtfe_overlap(n,nnz,la,irow,icol,nb,istb,indb,lindb,nover,  &
iwork)

!       Purpose
!       =======
!       This routine takes a set of row indices INDB defining the diagonal
!       blocks to be used in F11DTF to define a block Jacobi or additive
!       Schwarz preconditioner, and expands them to allow for NOVER levels of
!       overlap.
!       The pointer array ISTB is also updated accordingly, so that the
!       returned values of ISTB and INDB can be passed to F11DTF to define
!       overlapping diagonal blocks.
!       ----------------------------------------------------------------------

!       .. Implicit None Statement ..
Implicit None
!       .. Scalar Arguments ..
Integer, Intent (In)           :: la, lindb, n, nb, nnz, nover
!       .. Array Arguments ..
Integer, Intent (In)           :: icol(la), irow(la)
Integer, Intent (Inout)        :: indb(lindb), istb(nb+1)
Integer, Intent (Out)          :: iwork(3*n+1)
!       .. Local Scalars ..
Integer                        :: i, ik, ind, iover, k, l, n21, nadd,  &
row
!       .. Executable Statements ..

!       Find the number of nonzero elements in each row of the matrix A, and
!       and start address of each row. Store the start addresses in
!       IWORK(N+1,...,2*N+1).

iwork(1:n) = 0
Do k = 1, nnz
iwork(irow(k)) = iwork(irow(k)) + 1
End Do
iwork(n+1) = 1
Do i = 1, n
iwork(n+i+1) = iwork(n+i) + iwork(i)
End Do

!       Loop over blocks.
blocks: Do k = 1, nb

!         Initialize marker array.
iwork(1:n) = 0

!         Mark the rows already in block K in the workspace array.
Do l = istb(k), istb(k+1) - 1
iwork(indb(l)) = 1
End Do

!         Loop over levels of overlap.
Do iover = 1, nover

!           Initialize counter of new row indices to be added.
ind = 0

!           Loop over the rows currently in the diagonal block.
Do l = istb(k), istb(k+1) - 1
row = indb(l)

!             Loop over nonzero elements in row ROW.
Do i = iwork(n+row), iwork(n+row+1) - 1

!               If the column index of the nonzero element is not in the
!               existing set for this block, store it to be added later, and
!               mark it in the marker array.
If (iwork(icol(i))==0) Then
iwork(icol(i)) = 1
ind = ind + 1
iwork(2*n+1+ind) = icol(i)
End If
End Do
End Do

!           Shift the indices in INDB and add the new entries for block K.
!           Change ISTB accordingly.
iwork(1) = -999
Exit blocks
End If

Do i = istb(nb+1) - 1, istb(k+1), -1