Program f07fbfe

!     F07FBF Example Program Text

!     Mark 30.1 Release. NAG Copyright 2024.

!     .. Use Statements ..
      Use nag_library, Only: dposvx, nag_wp, x04caf
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
      Real (Kind=nag_wp)               :: rcond
      Integer                          :: i, ifail, info, lda, ldaf, ldb, ldx, &
                                          n, nrhs
      Character (1)                    :: equed
!     .. Local Arrays ..
      Real (Kind=nag_wp), Allocatable  :: a(:,:), af(:,:), b(:,:), berr(:),    &
                                          ferr(:), s(:), work(:), x(:,:)
      Integer, Allocatable             :: iwork(:)
!     .. Executable Statements ..
      Write (nout,*) 'F07FBF Example Program Results'
      Write (nout,*)
      Flush (nout)
!     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),s(n),    &
        work(3*n),x(ldx,nrhs),iwork(n))

!     Read the upper triangular part of A from data file

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

!     Read B from data file

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

!     Solve the equations AX = B for X
!     The NAG name equivalent of dposvx is f07fbf
      Call dposvx('Equilibration','Upper',n,nrhs,a,lda,af,ldaf,equed,s,b,ldb,  &
        x,ldx,rcond,ferr,berr,work,iwork,info)

      If ((info==0) .Or. (info==n+1)) Then

!       Print solution, error bounds, condition number and the form
!       of equilibration

!       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,*)
        Write (nout,*) 'Estimated forward error bounds (machine-dependent)'
        Write (nout,99999) ferr(1:nrhs)
        Write (nout,*)
        Write (nout,*) 'Estimate of reciprocal condition number'
        Write (nout,99999) rcond
        Write (nout,*)
        If (equed=='N') Then
          Write (nout,*) 'A has not been equilibrated'
        Else If (equed=='Y') Then
          Write (nout,*)                                                       &
            'A has been row and column scaled as diag(S)*A*diag(S)'
        End If

        If (info==n+1) Then
          Write (nout,*)
          Write (nout,*) 'The matrix A is singular to working precision'
        End If
      Else
        Write (nout,99998) 'The leading minor of order ', info,                &
          ' is not positive definite'
      End If

99999 Format ((3X,1P,7E11.1))
99998 Format (1X,A,I3,A)
    End Program f07fbfe