NAG Library Manual, Mark 28.6
```!   F02WGF Example Program Text
!   Mark 28.6 Release. NAG Copyright 2022.

Module f02wgfe_mod

!     F02WGF Example Program Module:
!            Parameters and User-defined Routines

!     .. Use Statements ..
Use nag_library, Only: nag_wp
!     .. Implicit None Statement ..
Implicit None
!     .. Accessibility Statements ..
Private
Public                           :: av
!     .. Parameters ..
Integer, Parameter, Public       :: nin = 5, nout = 6
Contains
!     Matrix vector subroutines

Subroutine av(iflag,m,n,x,ax,iuser,ruser)

!       Computes  w <- A*x or w <- Trans(A)*x.

!       .. Parameters ..
Real (Kind=nag_wp), Parameter  :: one = 1.0_nag_wp
Real (Kind=nag_wp), Parameter  :: zero = 0.0_nag_wp
!       .. Scalar Arguments ..
Integer, Intent (Inout)        :: iflag
Integer, Intent (In)           :: m, n
!       .. Array Arguments ..
Real (Kind=nag_wp), Intent (Inout) :: ax(*), ruser(*)
Real (Kind=nag_wp), Intent (In) :: x(*)
Integer, Intent (Inout)        :: iuser(*)
!       .. Local Scalars ..
Real (Kind=nag_wp)             :: h, k, s, t
Integer                        :: i, j
!       .. Intrinsic Procedures ..
Intrinsic                      :: min, real
!       .. Executable Statements ..
h = one/real(m+1,kind=nag_wp)
k = one/real(n+1,kind=nag_wp)
If (iflag==1) Then
ax(1:m) = zero
t = zero

Do j = 1, n
t = t + k
s = zero
Do i = 1, min(j,m)
s = s + h
ax(i) = ax(i) + k*s*(t-one)*x(j)
End Do
Do i = j + 1, m
s = s + h
ax(i) = ax(i) + k*t*(s-one)*x(j)
End Do
End Do
Else
ax(1:n) = zero
t = zero

Do j = 1, n
t = t + k
s = zero
Do i = 1, min(j,m)
s = s + h
ax(j) = ax(j) + k*s*(t-one)*x(i)
End Do
Do i = j + 1, m
s = s + h
ax(j) = ax(j) + k*t*(s-one)*x(i)
End Do
End Do
End If

Return
End Subroutine av
End Module f02wgfe_mod
Program f02wgfe

!     F02WGF Example Main Program

!     .. Use Statements ..
Use f02wgfe_mod, Only: av, nin, nout
Use nag_library, Only: f02wgf, nag_wp
!     .. Implicit None Statement ..
Implicit None
!     .. Local Scalars ..
Integer                          :: i, ifail, k, ldu, ldv, m, n, nconv,  &
ncv
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: resid(:), sigma(:), u(:,:), v(:,:)
Real (Kind=nag_wp)               :: ruser(1)
Integer                          :: iuser(1)
!     .. Executable Statements ..
Write (nout,*) 'F02WGF Example Program Results'
Write (nout,*)
!     Skip heading in data file
Read (nin,*) m, n, k, ncv
ldu = m
ldv = n
Allocate (resid(ncv),sigma(ncv),u(ldu,ncv),v(ldv,ncv))

!     ifail: behaviour on error exit
!             =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call f02wgf(m,n,k,ncv,av,nconv,sigma,u,ldu,v,ldv,resid,iuser,ruser,      &
ifail)

!     Print computed residuals
Write (nout,*) '  Singular Value    Residual'
Write (nout,99999)(sigma(i),resid(i),i=1,nconv)

99999 Format (1X,F10.5,8X,G10.2)
End Program f02wgfe
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