Program f07ahfe

!     F07AHF Example Program Text

!     Mark 29.0 Release. NAG Copyright 2023.

!     .. Use Statements ..
      Use nag_library, Only: dgerfs, dgetrf, dgetrs, nag_wp, x04caf
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Integer, Parameter               :: nin = 5, nout = 6
      Character (1), Parameter         :: trans = 'N'
!     .. Local Scalars ..
      Integer                          :: i, ifail, info, lda, ldaf, ldb, ldx, &
                                          n, nrhs
!     .. Local Arrays ..
      Real (Kind=nag_wp), Allocatable  :: a(:,:), af(:,:), b(:,:), berr(:),    &
                                          ferr(:), work(:), x(:,:)
      Integer, Allocatable             :: ipiv(:), iwork(:)
!     .. Executable Statements ..
      Write (nout,*) 'F07AHF Example Program Results'
!     Skip heading in data file
      Read (nin,*)
      Read (nin,*) n, nrhs
      lda = n
      ldaf = n
      ldb = n
      ldx = n
      Allocate (a(lda,n),af(ldaf,n),b(ldb,nrhs),berr(nrhs),ferr(nrhs),         &
        work(3*n),x(ldx,n),ipiv(n),iwork(n))

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

      Read (nin,*)(a(i,1:n),i=1,n)
      Read (nin,*)(b(i,1:nrhs),i=1,n)

      af(1:n,1:n) = a(1:n,1:n)
      x(1:n,1:nrhs) = b(1:n,1:nrhs)

!     Factorize A in the array AF

!     The NAG name equivalent of dgetrf is f07adf
      Call dgetrf(n,n,af,ldaf,ipiv,info)

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

!       Compute solution in the array X

!       The NAG name equivalent of dgetrs is f07aef
        Call dgetrs(trans,n,nrhs,af,ldaf,ipiv,x,ldx,info)

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

!       The NAG name equivalent of dgerfs is f07ahf
        Call dgerfs(trans,n,nrhs,a,lda,af,ldaf,ipiv,b,ldb,x,ldx,ferr,berr,     &
          work,iwork,info)

!       Print solution

!       ifail: behaviour on error exit
!              =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
        ifail = 0

        Call x04caf('General',' ',n,nrhs,x,ldx,'Solution(s)',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,*) 'The factor U is singular'
      End If

99999 Format ((3X,1P,7E11.1))
    End Program f07ahfe