NAG Library Manual, Mark 29.3
Interfaces:  FL   CL   CPP   AD 

NAG FL Interface Introduction
Example description
    Program f07jhfe

!     F07JHF Example Program Text

!     Mark 29.3 Release. NAG Copyright 2023.

!     .. Use Statements ..
      Use nag_library, Only: dptrfs, dpttrf, dpttrs, 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(:), e(:),  &
                                          ef(:), ferr(:), work(:), x(:,:)
!     .. Executable Statements ..
      Write (nout,*) 'F07JHF 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),e(n-1),ef(n-1),ferr(nrhs),   &

!     Read the lower bidiagonal part of the tridiagonal matrix A from
!     data file

      Read (nin,*) d(1:n)
      Read (nin,*) e(1:n-1)

!     Read the right hand matrix B

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

!     Copy A into DF and EF, and copy B into X

      df(1:n) = d(1:n)
      ef(1:n-1) = e(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 dpttrf is f07jdf
      Call dpttrf(n,df,ef,info)

      If (info==0) Then

!       Solve the equations AX = B
!       The NAG name equivalent of dpttrs is f07jef
        Call dpttrs(n,nrhs,df,ef,x,ldx,info)

!       Improve the solution and compute error estimates
!       The NAG name equivalent of dptrfs is f07jhf
        Call dptrfs(n,nrhs,d,e,df,ef,b,ldb,x,ldx,ferr,berr,work,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)
        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 f07jhfe