Program f07mhfe

!     F07MHF Example Program Text

!     Mark 29.1 Release. NAG Copyright 2023.

!     .. Use Statements ..
      Use nag_library, Only: dsyrfs, dsytrf, dsytrs, nag_wp, x04caf
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
      Integer                          :: i, ifail, info, lda, ldaf, ldb, ldx, &
                                          lwork, n, nrhs
      Character (1)                    :: uplo
!     .. Local Arrays ..
      Real (Kind=nag_wp), Allocatable  :: a(:,:), af(:,:), b(:,:), berr(:),    &
                                          ferr(:), work(:), x(:,:)
      Integer, Allocatable             :: ipiv(:), iwork(:)
!     .. Executable Statements ..
      Write (nout,*) 'F07MHF Example Program Results'
!     Skip heading in data file
      Read (nin,*)
      Read (nin,*) n, nrhs
      lda = n
      ldaf = n
      ldb = n
      ldx = n
      lwork = 64*n
      Allocate (a(lda,n),af(ldaf,n),b(ldb,nrhs),berr(nrhs),ferr(nrhs),         &
        work(lwork),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,*) uplo
      If (uplo=='U') Then
        Do i = 1, n
          Read (nin,*) a(i,i:n)
          af(i,i:n) = a(i,i:n)
        End Do
      Else If (uplo=='L') Then
        Do i = 1, n
          Read (nin,*) a(i,1:i)
          af(i,1:i) = a(i,1:i)
        End Do
      End If
      Read (nin,*)(b(i,1:nrhs),i=1,n)

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

!     Factorize A in the array AF
!     The NAG name equivalent of dsytrf is f07mdf
      Call dsytrf(uplo,n,af,ldaf,ipiv,work,lwork,info)

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

!       Compute solution in the array X
!       The NAG name equivalent of dsytrs is f07mef
        Call dsytrs(uplo,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 dsyrfs is f07mhf
        Call dsyrfs(uplo,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 D is singular'
      End If

99999 Format ((3X,1P,7E11.1))
    End Program f07mhfe