NAG Library Manual, Mark 28.3
Interfaces:  FL   CL   CPP   AD 

NAG FL Interface Introduction
Example description
    Program f01gbfe

!     F01GBF Example Program Text

!     Mark 28.3 Release. NAG Copyright 2022.

!     .. Use Statements ..
      Use nag_library, Only: dgemm, f01gbf, nag_wp, x04caf
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
      Real (Kind=nag_wp)               :: t, tr
      Integer                          :: i, ifail, irevcm, lda, ldb, ldb2,    &
                                          ldx, ldy, m, n
!     .. Local Arrays ..
      Real (Kind=nag_wp), Allocatable  :: a(:,:), b(:,:), b2(:,:), comm(:),    &
                                          p(:), r(:), x(:,:), y(:,:), z(:)
      Integer, Allocatable             :: icomm(:)
!     .. Executable Statements ..
      Write (nout,*) 'F01GBF Example Program Results'
      Write (nout,*)
      Flush (nout)

!     Skip heading in data file
      Read (nin,*)
      Read (nin,*) n, m, t

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

!     Allocate required memory
      Allocate (a(lda,n))
      Allocate (b(ldb,m))
      Allocate (b2(ldb2,m))
      Allocate (comm(n*m+3*n+12))
      Allocate (x(ldx,2))
      Allocate (y(ldy,2))
      Allocate (icomm(2*n+40))
      Allocate (p(n))
      Allocate (r(n))
      Allocate (z(n))

!     Read A from data file
      Read (nin,*)(a(i,1:n),i=1,n)

!     Read B from data file
      Read (nin,*)(b(i,1:m),i=1,n)

!     Compute the trace of A
      tr = 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 f01gbf reverse communication interface
revcm: Do
        Call f01gbf(irevcm,n,m,b,ldb,t,tr,b2,ldb2,x,ldx,y,ldy,p,r,z,comm,      &
        If (irevcm==0) Then
          Exit revcm

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

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

        Else If (irevcm==3) Then
!         Compute A^T Y and store in X
          Call dgemm('T','N',n,2,n,1.0_nag_wp,a,lda,y,ldy,0.0_nag_wp,x,ldx)

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

!         Compute A^T Z and store in R
          Call dgemm('T','N',n,1,n,1.0_nag_wp,a,lda,z,n,0.0_nag_wp,r,n)
        End If

      End Do revcm

      If (ifail==0) Then
!       Print solution
        ifail = 0
        Call x04caf('G','N',n,m,b,ldb,'exp(tA)B',ifail)
      End If

    End Program f01gbfe