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authorJoe Hunkeler <jhunkeler@gmail.com>2015-08-11 16:51:37 -0400
committerJoe Hunkeler <jhunkeler@gmail.com>2015-08-11 16:51:37 -0400
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tree4464880c571602d54f6ae114729bf62a89518057 /math/deboor/progs/prog21.f
downloadiraf-osx-40e5a5811c6ffce9b0974e93cdd927cbcf60c157.tar.gz
Repatch (from linux) of OSX IRAF
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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