! E02DHF Example Program Text
! Mark 30.0 Release. NAG Copyright 2024.
Module e02dhfe_mod
! E02DHF 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 :: print_spline
! .. Parameters ..
Integer, Parameter, Public :: nin = 5, nout = 6
Contains
Subroutine print_spline(ngx,gridx,ngy,gridy,z,zder)
! Print spline function and spline derivative evaluation
! .. Use Statements ..
Use nag_library, Only: x04cbf
! .. Parameters ..
Integer, Parameter :: indent = 0, ncols = 80
Character (1), Parameter :: chlabel = 'C', diag = 'N', &
matrix = 'G'
Character (4), Parameter :: form = 'F8.3'
! .. Scalar Arguments ..
Integer, Intent (In) :: ngx, ngy
! .. Array Arguments ..
Real (Kind=nag_wp), Intent (In) :: gridx(ngx), gridy(ngy), z(ngx*ngy), &
zder(ngx*ngy)
! .. Local Scalars ..
Integer :: i, ifail
Character (48) :: title
! .. Local Arrays ..
Character (10), Allocatable :: clabs(:), rlabs(:)
! .. Executable Statements ..
! Allocate for row and column label
Allocate (clabs(ngx),rlabs(ngy))
! Generate column and row labels to print the results with.
Do i = 1, ngx
Write (clabs(i),99999) gridx(i)
End Do
Do i = 1, ngy
Write (rlabs(i),99999) gridy(i)
End Do
! Print the spline evaluations.
title = 'Spline evaluated on X-Y grid (X across, Y down):'
Write (nout,*)
Flush (nout)
ifail = 0
Call x04cbf(matrix,diag,ngy,ngx,z,ngy,form,title,chlabel,rlabs, &
chlabel,clabs,ncols,indent,ifail)
! Print the spline derivative evaluations.
title = 'Spline derivative evaluated on X-Y grid:'
Write (nout,*)
Flush (nout)
ifail = 0
Call x04cbf(matrix,diag,ngy,ngx,zder,ngy,form,title(1:40),chlabel, &
rlabs,chlabel,clabs,ncols,indent,ifail)
Deallocate (clabs,rlabs)
99999 Format (F5.2)
End Subroutine print_spline
End Module e02dhfe_mod
Program e02dhfe
! E02DHF Example Main Program
! .. Use Statements ..
Use e02dhfe_mod, Only: nin, nout, print_spline
Use nag_library, Only: e02dcf, e02dhf, nag_wp
! .. Implicit None Statement ..
Implicit None
! .. Local Scalars ..
Real (Kind=nag_wp) :: delta, fp, s, xhi, xlo, yhi, ylo
Integer :: i, ifail, liwrk, lwrk, mx, my, nc, &
ngx, ngy, nux, nuy, nx, nxest, ny, &
nyest
Character (1) :: start
! .. Local Arrays ..
Real (Kind=nag_wp), Allocatable :: c(:), f(:), gridx(:), gridy(:), &
lamda(:), mu(:), wrk(:), x(:), y(:), &
z(:), zder(:)
Integer, Allocatable :: iwrk(:)
! .. Intrinsic Procedures ..
Intrinsic :: max, real
! .. Executable Statements ..
Write (nout,*) 'E02DHF Example Program Results'
! Skip heading in data file
Read (nin,*)
! Input the number of X, Y co-ordinates MX, MY.
Read (nin,*) mx, my
nxest = mx + 4
nyest = my + 4
nc = (nxest-4)*(nyest-4)
! Allocations for spline fit
Allocate (lamda(nxest),mu(nyest),c(nc))
! Allocations for e02dcf only
lwrk = 4*(mx+my) + 11*(nxest+nyest) + nxest*my + max(my,nxest) + 54
liwrk = 3 + mx + my + nxest + nyest
Allocate (x(mx),y(my),f(mx*my),wrk(lwrk),iwrk(liwrk))
Read (nin,*) x(1:mx)
Read (nin,*) y(1:my)
! Input the MX*MY function values F at grid points and smoothing factor.
Read (nin,*) f(1:mx*my)
Read (nin,*) s
! Determine the spline approximation.
start = 'C'
ifail = 0
Call e02dcf(start,mx,x,my,y,f,s,nxest,nyest,nx,lamda,ny,mu,c,fp,wrk, &
lwrk,iwrk,liwrk,ifail)
Deallocate (x,y,f,wrk,iwrk)
Write (nout,*)
Write (nout,99999) 'Spline fit used smoothing factor S =', s, '.'
Write (nout,99998) 'Number of knots in each direction =', nx, ny
Write (nout,*)
Write (nout,99999) 'Sum of squared residuals =', fp, '.'
! Spline and its derivative to be evaluated on rectangular grid with
! ngx*ngy points on the domain [xlo,xhi]x[ylo,yhi].
Read (nin,*) ngx, xlo, xhi
Read (nin,*) ngy, ylo, yhi
! Allocations for e02dhf (spline evaluation).
Allocate (gridx(ngx),gridy(ngy),z(ngx*ngy),zder(ngx*ngy))
delta = (xhi-xlo)/real(ngx-1,kind=nag_wp)
gridx(1) = xlo
Do i = 2, ngx - 1
gridx(i) = gridx(i-1) + delta
End Do
gridx(ngx) = xhi
delta = (yhi-ylo)/real(ngy-1,kind=nag_wp)
gridy(1) = ylo
Do i = 2, ngy - 1
gridy(i) = gridy(i-1) + delta
End Do
gridy(ngy) = yhi
! Evaluate spline (nux=nuy=0)
nux = 0
nuy = 0
ifail = 0
Call e02dhf(ngx,ngy,nx,ny,gridx,gridy,lamda,mu,c,nux,nuy,z,ifail)
! Evaluate spline partial derivative of order (nux,nuy)
Read (nin,*) nux, nuy
Write (nout,*)
Write (nout,99998) 'Derivative of spline has order nux, nuy =', nux, nuy
ifail = 0
Call e02dhf(ngx,ngy,nx,ny,gridx,gridy,lamda,mu,c,nux,nuy,zder,ifail)
! Print tabulated spline and derivative evaluations.
Call print_spline(ngx,gridx,ngy,gridy,z,zder)
99999 Format (1X,A,1P,E13.4,A)
99998 Format (1X,A,I5,',',I5,'.')
End Program e02dhfe