```
Program f04bcfe
! F04BCF Example Program Text
! Mark 26.1 Release. NAG Copyright 2017.
! .. Use Statements ..
Use nag_library, Only: f04bcf, nag_wp, x04caf
! .. Implicit None Statement ..
Implicit None
! .. Parameters ..
Integer, Parameter :: nin = 5, nout = 6
! .. Local Scalars ..
Real (Kind=nag_wp) :: errbnd, rcond
Integer :: i, ierr, ifail, ldb, n, nrhs
! .. Local Arrays ..
Real (Kind=nag_wp), Allocatable :: b(:,:), d(:), dl(:), du(:), du2(:)
Integer, Allocatable :: ipiv(:)
! .. Executable Statements ..
Write (nout,*) 'F04BCF Example Program Results'
Write (nout,*)
Flush (nout)
! Skip heading in data file
Read (nin,*)
Read (nin,*) n, nrhs
ldb = n
Allocate (b(ldb,nrhs),d(n),dl(n-1),du(n-1),du2(n-2),ipiv(n))
! Read A and B from data file
Read (nin,*) du(1:n-1)
Read (nin,*) d(1:n)
Read (nin,*) dl(1:n-1)
Read (nin,*)(b(i,1:nrhs),i=1,n)
! Solve the equations AX = B for X
! ifail: behaviour on error exit
! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 1
Call f04bcf(n,nrhs,dl,d,du,du2,ipiv,b,ldb,rcond,errbnd,ifail)
If (ifail==0) Then
! Print solution, estimate of condition number and approximate
! error bound
ierr = 0
Call x04caf('General',' ',n,nrhs,b,ldb,'Solution',ierr)
Write (nout,*)
Write (nout,*) 'Estimate of condition number'
Write (nout,99999) 1.0E0_nag_wp/rcond
Write (nout,*)
Write (nout,*) 'Estimate of error bound for computed solutions'
Write (nout,99999) errbnd
Else If (ifail==n+1) Then
! Matrix A is numerically singular. Print estimate of
! reciprocal of condition number and solution
Write (nout,*)
Write (nout,*) 'Estimate of reciprocal of condition number'
Write (nout,99999) rcond
Write (nout,*)
Flush (nout)
ierr = 0
Call x04caf('General',' ',n,nrhs,b,ldb,'Solution',ierr)
Else If (ifail>0 .And. ifail<=n) Then
! The upper triangular matrix U is exactly singular. Print
! details of factorization
Write (nout,*) 'Details of factorization'
Write (nout,*)
Write (nout,*) ' Second superdiagonal of U'
Write (nout,99998) du2(1:n-2)
Write (nout,*)
Write (nout,*) ' First superdiagonal of U'
Write (nout,99998) du(1:n-1)
Write (nout,*)
Write (nout,*) ' Main diagonal of U'
Write (nout,99998) d(1:n)
Write (nout,*)
Write (nout,*) ' Multipliers'
Write (nout,99998) dl(1:n-1)
Write (nout,*)
Write (nout,*) ' Vector of interchanges'
Write (nout,99997) ipiv(1:n)
Else
Write (nout,99996) ifail
End If
99999 Format (6X,1P,E9.1)
99998 Format (1X,8F9.4)
99997 Format (1X,8I9)
99996 Format (1X,' ** F04BCF returned with IFAIL = ',I5)
End Program f04bcfe
```