NAG Library Manual, Mark 28.5
Interfaces:  FL   CL   CPP   AD 

NAG FL Interface Introduction
Example description
    Program f07bpfe

!     F07BPF Example Program Text

!     Mark 28.5 Release. NAG Copyright 2022.

!     .. Use Statements ..
      Use nag_library, Only: nag_wp, x04dbf, zgbsvx
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
      Real (Kind=nag_wp)               :: rcond
      Integer                          :: i, ifail, info, j, k, kl, ku, ldab,  &
                                          ldafb, ldb, ldx, n, nrhs
      Character (1)                    :: equed
!     .. Local Arrays ..
      Complex (Kind=nag_wp), Allocatable :: ab(:,:), afb(:,:), b(:,:),         &
                                          work(:), x(:,:)
      Real (Kind=nag_wp), Allocatable  :: berr(:), c(:), ferr(:), r(:),        &
      Integer, Allocatable             :: ipiv(:)
      Character (1)                    :: clabs(1), rlabs(1)
!     .. Intrinsic Procedures ..
      Intrinsic                        :: max, min
!     .. Executable Statements ..
      Write (nout,*) 'F07BPF Example Program Results'
      Write (nout,*)
      Flush (nout)
!     Skip heading in data file
      Read (nin,*)
      Read (nin,*) n, nrhs, kl, ku
      ldb = n
      ldx = n
      ldab = kl + ku + 1
      ldafb = ldab + kl
      Allocate (ab(ldab,n),afb(ldafb,n),b(ldb,nrhs),work(2*n),x(ldx,nrhs),     &

!     Read the band matrix A and B from data file

      k = ku + 1
      Read (nin,*)((ab(k+i-j,j),j=max(i-kl,1),min(i+ku,n)),i=1,n)
      Read (nin,*)(b(i,1:nrhs),i=1,n)

!     Solve the equations AX = B for X

!     The NAG name equivalent of zgbsvx is f07bpf
      Call zgbsvx('Equilibration','No transpose',n,kl,ku,nrhs,ab,ldab,afb,     &

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

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

!       ifail: behaviour on error exit
!              =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
        ifail = 0
        Call x04dbf('General',' ',n,nrhs,x,ldx,'Bracketed','F7.4',             &

        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=='R') Then
          Write (nout,*) 'A has been row scaled as diag(R)*A'
        Else If (equed=='C') Then
          Write (nout,*) 'A has been column scaled as A*diag(C)'
        Else If (equed=='B') Then
          Write (nout,*)                                                       &
            'A has been row and column scaled as diag(R)*A*diag(C)'
        End If
        Write (nout,*)
        Write (nout,*) 'Estimate of reciprocal pivot growth factor'
        Write (nout,99999) rwork(1)

        If (info==n+1) Then
          Write (nout,*)
          Write (nout,*) 'The matrix A is singular to working precision'
        End If
        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 f07bpfe