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chapter ix. example comparing the b-representation of a cubic f with
c its values at knot averages.
c from * a practical guide to splines * by c. de boor
c
integer i,id,j,jj,n,nm4
real bcoef(23),d(4),d0(4),dtip1,dtip2,f(23),t(27),tave(23),x
c the taylor coefficients at 0 for the polynomial f are
data d0 /-162.,99.,-18.,1./
c
c set up knot sequence in the array t .
n = 13
do 5 i=1,4
t(i) = 0.
5 t(n+i) = 10.
nm4 = n-4
do 6 i=1,nm4
6 t(i+4) = float(i)
c
do 50 i=1,n
c use nested multiplication to get taylor coefficients d at
c t(i+2) from those at 0 .
do 20 j=1,4
20 d(j) = d0(j)
do 21 j=1,3
id = 4
do 21 jj=j,3
id = id-1
21 d(id) = d(id) + d(id+1)*t(i+2)
c
c compute b-spline coefficients by formula (9).
dtip1 = t(i+2) - t(i+1)
dtip2 = t(i+3) - t(i+2)
bcoef(i) = d(1) + (d(2)*(dtip2-dtip1)-d(3)*dtip1*dtip2)/3.
c
c evaluate f at corresp. knot average.
tave(i) = (t(i+1) + t(i+2) + t(i+3))/3.
x = tave(i)
50 f(i) = d0(1) + x*(d0(2) + x*(d0(3) + x*d0(4)))
c
print 650, (i,tave(i), f(i), bcoef(i),i=1,n)
650 format(45h i tave(i) f at tave(i) bcoef(i)//
* (i3,f10.5,2f16.5))
stop
end
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