NAG Library Manual, Mark 28.3
```    Program f01hbfe

!     F01HBF Example Program Text

!     Mark 28.3 Release. NAG Copyright 2022.

!     .. Use Statements ..
Use nag_library, Only: f01hbf, nag_wp, x04daf, zgemm
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
Complex (Kind=nag_wp)            :: t, tr
Integer                          :: i, ifail, irevcm, lda, ldb, ldb2,    &
ldx, ldy, m, n
!     .. Local Arrays ..
Complex (Kind=nag_wp), Allocatable :: a(:,:), b(:,:), b2(:,:), ccomm(:), &
p(:), r(:), x(:,:), y(:,:), z(:)
Real (Kind=nag_wp), Allocatable  :: comm(:)
Integer, Allocatable             :: icomm(:)
!     .. Executable Statements ..
Write (nout,*) 'F01HBF Example Program Results'
Write (nout,*)
Flush (nout)

!     Skip heading in data file

lda = n
ldb = n
ldb2 = n
ldx = n
ldy = n

!     Allocate required space
Allocate (a(lda,n))
Allocate (b(ldb,m))
Allocate (b2(ldb2,m))
Allocate (ccomm(n*(m+2)))
Allocate (x(ldx,2))
Allocate (y(ldy,2))
Allocate (icomm(2*n+40))
Allocate (comm(14+3*n))
Allocate (p(n))
Allocate (r(n))
Allocate (z(n))

!     Read A from data file

!     Read B from data file

!     Compute the trace of A
tr = (0.0_nag_wp,0.0_nag_wp)
Do i = 1, n
tr = tr + a(i,i)
End Do

!     Find exp(tA)B

irevcm = 0
ifail = 0

!      Initial call to reverse communication interface f01hbf
revcm: Do
Call f01hbf(irevcm,n,m,b,ldb,t,tr,b2,ldb2,x,ldx,y,ldy,p,r,z,ccomm,     &
comm,icomm,ifail)
If (irevcm==0) Then
Exit revcm

Else If (irevcm==1) Then
!         Compute AB and store in B2
Call zgemm('N','N',n,m,n,(1.0_nag_wp,0.0_nag_wp),a,lda,b,ldb,        &
(0.0_nag_wp,0.0_nag_wp),b2,ldb2)

Else If (irevcm==2) Then
!         Compute AX and store in Y
Call zgemm('N','N',n,2,n,(1.0_nag_wp,0.0_nag_wp),a,lda,x,ldx,        &
(0.0_nag_wp,0.0_nag_wp),y,ldy)

Else If (irevcm==3) Then
!         Compute A^H Y and store in X
Call zgemm('C','N',n,2,n,(1.0_nag_wp,0.0_nag_wp),a,lda,y,ldy,        &
(0.0_nag_wp,0.0_nag_wp),x,ldx)

Else If (irevcm==4) Then
!         Compute Az and store in p
Call zgemm('N','N',n,1,n,(1.0_nag_wp,0.0_nag_wp),a,lda,z,n,          &
(0.0_nag_wp,0.0_nag_wp),p,n)

Else If (irevcm==5) Then
!         Compute A^H z and store in r
Call zgemm('C','N',n,1,n,(1.0_nag_wp,0.0_nag_wp),a,lda,z,n,          &
(0.0_nag_wp,0.0_nag_wp),r,n)
End If