Program f07hvfe

!     F07HVF Example Program Text

!     Mark 29.3 Release. NAG Copyright 2023.

!     .. Use Statements ..
      Use nag_library, Only: nag_wp, x04dbf, zpbrfs, zpbtrf, zpbtrs
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Complex (Kind=nag_wp), Parameter :: zero = (0.0E0_nag_wp,0.0E0_nag_wp)
      Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
      Integer                          :: i, ifail, info, j, kd, ldab, ldafb,  &
                                          ldb, ldx, n, nrhs
      Character (1)                    :: uplo
!     .. Local Arrays ..
      Complex (Kind=nag_wp), Allocatable :: ab(:,:), afb(:,:), b(:,:),         &
                                          work(:), x(:,:)
      Real (Kind=nag_wp), Allocatable  :: berr(:), ferr(:), rwork(:)
      Character (1)                    :: clabs(1), rlabs(1)
!     .. Intrinsic Procedures ..
      Intrinsic                        :: max, min
!     .. Executable Statements ..
      Write (nout,*) 'F07HVF Example Program Results'
!     Skip heading in data file
      Read (nin,*)
      Read (nin,*) n, kd, nrhs
      ldab = kd + 1
      ldafb = kd + 1
      ldb = n
      ldx = n
      Allocate (ab(ldab,n),afb(ldafb,n),b(ldb,nrhs),work(2*n),x(ldx,n),        &
        berr(nrhs),ferr(nrhs),rwork(n))

!     Set A to zero to avoid referencing uninitialized elements

      ab(1:kd+1,1:n) = zero

!     Read A and B from data file, and copy A to AFB and B to X

      Read (nin,*) uplo
      If (uplo=='U') Then
        Do i = 1, n
          Read (nin,*)(ab(kd+1+i-j,j),j=i,min(n,i+kd))
        End Do
      Else If (uplo=='L') Then
        Do i = 1, n
          Read (nin,*)(ab(1+i-j,j),j=max(1,i-kd),i)
        End Do
      End If
      Read (nin,*)(b(i,1:nrhs),i=1,n)

      afb(1:kd+1,1:n) = ab(1:kd+1,1:n)
      x(1:n,1:nrhs) = b(1:n,1:nrhs)

!     Factorize A in the array AFB

      Call zpbtrf(uplo,n,kd,afb,ldafb,info)

      Write (nout,*)
      Flush (nout)
      If (info==0) Then

!       Compute solution in the array X

        Call zpbtrs(uplo,n,kd,nrhs,afb,ldafb,x,ldx,info)

!       Improve solution, and compute backward errors and
!       estimated bounds on the forward errors

        Call zpbrfs(uplo,n,kd,nrhs,ab,ldab,afb,ldafb,b,ldb,x,ldx,ferr,berr,    &
          work,rwork,info)

!       Print solution

!       ifail: behaviour on error exit
!              =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
        ifail = 0
        Call x04dbf('General',' ',n,nrhs,x,ldx,'Bracketed','F7.4',             &
          'Solution(s)','Integer',rlabs,'Integer',clabs,80,0,ifail)

        Write (nout,*)
        Write (nout,*) 'Backward errors (machine-dependent)'
        Write (nout,99999) berr(1:nrhs)
        Write (nout,*) 'Estimated forward error bounds (machine-dependent)'
        Write (nout,99999) ferr(1:nrhs)
      Else
        Write (nout,*) 'A is not positive definite'
      End If

99999 Format ((5X,1P,4(E11.1,7X)))
    End Program f07hvfe