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chapter xvii, example 3. bivariate spline interpolation
c followed by conversion to pp-repr and evaluation
c from * a practical guide to splines * by c. de boor
calls spli2d(bsplvb,banfac/slv),interv,bspp2d(bsplvb*),ppvalu(interv*)
c parameter nx=7,kx=3,ny=6,ky=4
c integer i,iflag,j,jj,lefty,lx,ly,mflag
c real bcoef(nx,ny),breakx(6),breaky(4),coef(kx,5,ky,3),taux(nx)
c * ,tauy(ny),tx(10),ty(10)
c * ,work1(nx,ny),work2(nx),work3(42)
c * ,work4(kx,kx,ny),work5(ny,kx,5),work6(ky,ky,21)
integer i,iflag,j,jj,kp1,kx,ky,lefty,lx,ly,mflag,nx,ny
real bcoef(7,6),breakx(6),breaky(4),coef(3,5,4,3),taux(7)
* ,tauy(6),tx(10),ty(10)
* ,work1(7,6),work2(7),work3(42)
* ,work4(3,3,6),work5(6,3,5),work6(4,4,21)
real ppvalu,g,x,y
data nx,kx,ny,ky / 7,3,6,4 /
c note that , with the above parameters, lx=5, ly = 3
equivalence (work4,work6)
g(x,y) = amax1(x-3.5,0.)**2 + amax1(y-3.,0.)**3
c *** set up data points and knots
c in x, interpolate between knots by parabolic splines, using
c not-a-knot end condition
do 10 i=1,nx
10 taux(i) = float(i)
do 11 i=1,kx
tx(i) = taux(1)
11 tx(nx+i) = taux(nx)
kp1 = kx+1
do 12 i=kp1,nx
12 tx(i) = (taux(i-kx+1) + taux(i-kx+2))/2.
c in y, interpolate at knots by cubic splines, using not-a-knot
c end condition
do 20 i=1,ny
20 tauy(i) = float(i)
do 21 i=1,ky
ty(i) = tauy(1)
21 ty(ny+i) = tauy(ny)
kp1 = ky+1
do 22 i=kp1,ny
22 ty(i) = tauy(i-ky+2)
c *** generate and print out function values
print 620,(tauy(i),i=1,ny)
620 format(11h given data//6f12.1)
do 32 i=1,nx
do 31 j=1,ny
31 bcoef(i,j) = g(taux(i),tauy(j))
32 print 632,taux(i),(bcoef(i,j),j=1,ny)
632 format(f5.1,6e12.5)
c
c *** construct b-coefficients of interpolant
c
call spli2d(taux,bcoef,tx,nx,kx,ny,work2,work3,work1,iflag)
call spli2d(tauy,work1,ty,ny,ky,nx,work2,work3,bcoef,iflag)
c
c *** convert to pp-representation
c
call bspp2d(tx,bcoef,nx,kx,ny,work4,breakx,work5,lx)
call bspp2d(ty,work5,ny,ky,lx*kx,work6,breaky,coef,ly)
c
c *** evaluate interpolation error at mesh points and print out
print 640,(tauy(j),j=1,ny)
640 format(//20h interpolation error//6f12.1)
do 45 j=1,ny
call interv(breaky,ly,tauy(j),lefty,mflag)
do 45 i=1,nx
do 41 jj=1,ky
41 work2(jj)=ppvalu(breakx,coef(1,1,jj,lefty),lx,kx,taux(i),0)
45 work1(i,j) = g(taux(i),tauy(j)) -
* ppvalu(breaky(lefty),work2,1,ky,tauy(j),0)
do 46 i=1,nx
46 print 632,taux(i),(work1(i,j),j=1,ny)
stop
end
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