Program f08kp_t1w_fe
! F08KP_T1W_F Example Program Text
! Mark 30.1 Release. NAG Copyright 2024.
! .. Use Statements ..
Use iso_c_binding, Only: c_ptr
Use nagad_library, Only: f08kp_t1w_f, nagad_t1w_set_derivative, &
nagad_t1w_w_ctype, nagad_t1w_w_rtype, &
x10aa_t1w_f, x10ab_t1w_f, Assignment (=)
Use nag_library, Only: nag_wp, x04daf
! .. Implicit None Statement ..
Implicit None
! .. Parameters ..
Integer, Parameter :: nb = 64, nin = 5, nout = 6
! .. Local Scalars ..
Type (c_ptr) :: ad_handle
Integer :: i, ifail, j, lda, ldu, ldvt, lwork, &
m, n
! .. Local Arrays ..
Type (nagad_t1w_w_ctype), Allocatable :: a(:,:), ax(:,:), u(:,:), &
vt(:,:), work(:)
Type (nagad_t1w_w_ctype) :: dummy(1)
Type (nagad_t1w_w_rtype), Allocatable :: rwork(:), s(:)
Complex (Kind=nag_wp), Allocatable :: ac(:,:), dsda(:,:), uc(:,:), &
vc(:,:)
! .. Intrinsic Procedures ..
Intrinsic :: cmplx, max, nint
! .. Executable Statements ..
Write (nout,*) 'F08KP_T1W_F Example Program Results'
! Skip heading in data file
Read (nin,*)
Read (nin,*) m, n
lda = m
ldu = m
ldvt = n
Allocate (a(lda,n),s(m),u(ldu,m),vt(ldvt,n),rwork(5*n))
Allocate (ac(m,n),ax(lda,n),uc(ldu,m),vc(ldvt,n),dsda(n,m))
! Create AD configuration data object
ifail = 0
Call x10aa_t1w_f(ad_handle,ifail)
! Use routine workspace query to get optimal workspace.
lwork = -1
ifail = 0
Call f08kp_t1w_f(ad_handle,'A','A',m,n,a,lda,s,u,ldu,vt,ldvt,dummy, &
lwork,rwork,ifail)
! Make sure that there is enough workspace for block size nb.
lwork = max(m+3*n+nb*(m+n),nint(dummy(1)%vreal%value))
Allocate (work(lwork))
! Read the m by n matrix A from data file
Read (nin,*)(ac(i,1:n),i=1,m)
a = ac
Do i = 1, 2*m
If (i<=m) Then
Call nagad_t1w_set_derivative(a(i,1)%vreal,1.0_nag_wp)
Else
Call nagad_t1w_set_derivative(a(i-m,1)%vimag,1.0_nag_wp)
End If
ax = a
! Compute the singular values and left and right singular vectors
! of A (A = U*S*(V**T), m.le.n)
ifail = 0
Call f08kp_t1w_f(ad_handle,'A','A',m,n,ax,lda,s,u,ldu,vt,ldvt,work, &
lwork,rwork,ifail)
If (i<=m) Then
a(i,1)%vreal%tangent = 0.0_nag_wp
Do j = 1, n
dsda(j,i) = s(j)%tangent
End Do
Else
a(i-m,1)%vimag%tangent = 0.0_nag_wp
Do j = 1, n
dsda(j,i-m) = dsda(j,i-m) + cmplx(0.0_nag_wp,s(j)%tangent,kind= &
nag_wp)
End Do
End If
End Do
! Print solution
Write (nout,*)
Write (nout,*) 'Singular values'
Write (nout,99999) s(1:n)%value
99999 Format (3X,(8F8.4))
Flush (nout)
Do i = 1, m
Do j = 1, m
uc(i,j) = cmplx(u(i,j)%vreal%value,u(i,j)%vimag%value,kind=nag_wp)
End Do
End Do
Do i = 1, n
Do j = 1, n
vc(i,j) = cmplx(vt(i,j)%vreal%value,vt(i,j)%vimag%value,kind=nag_wp)
End Do
End Do
! ifail: behaviour on error exit
! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call x04daf('General',' ',m,m,uc,m,'Left singular vectors',ifail)
Write (nout,*)
Flush (nout)
Call x04daf('General',' ',n,n,vc,n,'Right singular vectors by row', &
ifail)
Write (nout,*)
Write (nout,*) ' Derivatives calculated: First order tangents'
Write (nout,*) ' Computational mode : algorithmic'
Write (nout,*)
Write (nout,*) ' Derivatives of S w.r.t. first column of A:'
Call x04daf('General',' ',n,m,dsda,n,'',ifail)
! Remove computational data object
Call x10ab_t1w_f(ad_handle,ifail)
End Program f08kp_t1w_fe