Program f07chfe

!     F07CHF Example Program Text

!     Mark 27.3 Release. NAG Copyright 2021.

!     .. Use Statements ..
      Use nag_library, Only: dgtrfs, dgttrf, dgttrs, nag_wp, x04caf
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
      Integer                          :: i, ifail, info, ldb, ldx, n, nrhs
!     .. Local Arrays ..
      Real (Kind=nag_wp), Allocatable  :: b(:,:), berr(:), d(:), df(:), dl(:), &
                                          dlf(:), du(:), du2(:), duf(:),       &
                                          ferr(:), work(:), x(:,:)
      Integer, Allocatable             :: ipiv(:), iwork(:)
!     .. Executable Statements ..
      Write (nout,*) 'F07CHF Example Program Results'
      Write (nout,*)
      Flush (nout)
!     Skip heading in data file
      Read (nin,*)
      Read (nin,*) n, nrhs
      ldb = n
      ldx = n
      Allocate (b(ldb,nrhs),berr(nrhs),d(n),df(n),dl(n-1),dlf(n-1),du(n-1),    &
        du2(n-2),duf(n-1),ferr(nrhs),work(3*n),x(ldx,nrhs),ipiv(n),iwork(n))

!     Read the tridiagonal matrix A from data file

      Read (nin,*) du(1:n-1)
      Read (nin,*) d(1:n)
      Read (nin,*) dl(1:n-1)

!     Read the right hand matrix B

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

!     Copy A into DUF, DF and DLF, and copy B into X

      duf(1:n-1) = du(1:n-1)
      df(1:n) = d(1:n)
      dlf(1:n-1) = dl(1:n-1)
      x(1:n,1:nrhs) = b(1:n,1:nrhs)

!     Factorize the copy of the tridiagonal matrix A
!     The NAG name equivalent of dgttrf is f07cdf
      Call dgttrf(n,dlf,df,duf,du2,ipiv,info)

      If (info==0) Then

!       Solve the equations AX = B
!       The NAG name equivalent of dgttrs is f07cef
        Call dgttrs('No transpose',n,nrhs,dlf,df,duf,du2,ipiv,x,ldx,info)

!       Improve the solution and compute error estimates
!       The NAG name equivalent of dgtrfs is f07chf
        Call dgtrfs('No transpose',n,nrhs,dl,d,du,dlf,df,duf,du2,ipiv,b,ldb,x, &
          ldx,ferr,berr,work,iwork,info)

!       Print the solution and the forward and backward error
!       estimates

!       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)
      Else
        Write (nout,99998) 'The (', info, ',', info, ')',                      &
          ' element of the factor U is zero'
      End If

99999 Format ((3X,1P,7E11.1))
99998 Format (1X,A,I3,A,I3,A,A)
    End Program f07chfe