```
Program f07abfe
! F07ABF Example Program Text
! Mark 27.0 Release. NAG Copyright 2019.
! .. Use Statements ..
Use nag_library, Only: dgesvx, 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(:), &
c(:), ferr(:), r(:), work(:), x(:,:)
Integer, Allocatable :: ipiv(:), iwork(:)
! .. Executable Statements ..
Write (nout,*) 'F07ABF 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),c(n),ferr(nrhs), &
r(n),work(4*n),x(ldx,nrhs),ipiv(n),iwork(n))
! Read A and B from data file
Read (nin,*)(a(i,1: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 dgesvx is f07abf
Call dgesvx('Equilibration','No transpose',n,nrhs,a,lda,af,ldaf,ipiv, &
equed,r,c,b,ldb,x,ldx,rcond,ferr,berr,work,iwork,info)
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 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,*)
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,*) 'Reciprocal condition number estimate of scaled matrix'
Write (nout,99999) rcond
Write (nout,*)
Write (nout,*) 'Estimate of reciprocal pivot growth factor'
Write (nout,99999) work(1)
If (info==n+1) Then
Write (nout,*)
Write (nout,*) 'The matrix A is singular to working precision'
End If
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 f07abfe
```