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*) integer i,iflag,j,jj,kx,ky,lefty,lx,ly,mflag,nx,ny parameter (nx=7,kx=3,ny=6,ky=4, lx=nx+1-kx, ly=ny+1-ky) real bcoef(nx,ny),taux(nx),tauy(ny),tx(nx+kx),ty(ny+ky) * ,work1(nx,ny),work2(nx),work3(nx*ny) * ,breakx(lx+1),breaky(ly+1),coef(kx,lx,ky,ly) * ,work4(kx,kx,ny),work5(ny,kx,lx),work6(ky,ky,nx*kx) C integer i,iflag,j,jj,kp1,kx,ky,lefty,lx,ly,mflag,nx,ny C data nx,kx,ny,ky / 7,3,6,4 / C real bcoef(7,6),breakx(6),breaky(4),coef(3,5,4,3),taux(7) C * ,tauy(6),tx(10),ty(10) C * ,work1(7,6),work2(7),work3(42) C * ,work4(3,3,6),work5(6,3,5),work6(4,4,21) 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) call bspp2d(ty,work5,ny,ky,lx*kx,work6,breaky,coef) c c *** evaluate interpolation error at mesh points and print out print 640,(tauy(j),j=1,ny) 640 format(//' 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