1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
|
subroutine spalde(t,n,c,k1,x,d,ier)
c subroutine spalde evaluates at a point x all the derivatives
c (j-1)
c d(j) = s (x) , j=1,2,...,k1
c of a spline s(x) of order k1 (degree k=k1-1), given in its b-spline
c representation.
c
c calling sequence:
c call spalde(t,n,c,k1,x,d,ier)
c
c input parameters:
c t : array,length n, which contains the position of the knots.
c n : integer, giving the total number of knots of s(x).
c c : array,length n, which contains the b-spline coefficients.
c k1 : integer, giving the order of s(x) (order=degree+1)
c x : real, which contains the point where the derivatives must
c be evaluated.
c
c output parameters:
c d : array,length k1, containing the derivative values of s(x).
c ier : error flag
c ier = 0 : normal return
c ier =10 : invalid input data (see restrictions)
c
c restrictions:
c t(k1) <= x <= t(n-k1+1)
c
c further comments:
c if x coincides with a knot, right derivatives are computed
c ( left derivatives if x = t(n-k1+1) ).
c
c other subroutines required: fpader.
c
c references :
c de boor c : on calculating with b-splines, j. approximation theory
c 6 (1972) 50-62.
c cox m.g. : the numerical evaluation of b-splines, j. inst. maths
c applics 10 (1972) 134-149.
c dierckx p. : curve and surface fitting with splines, monographs on
c numerical analysis, oxford university press, 1993.
c
c author :
c p.dierckx
c dept. computer science, k.u.leuven
c celestijnenlaan 200a, b-3001 heverlee, belgium.
c e-mail : Paul.Dierckx@cs.kuleuven.ac.be
c
c latest update : march 1987
c
c ..scalar arguments..
integer n,k1,ier
real*8 x
c ..array arguments..
real*8 t(n),c(n),d(k1)
c ..local scalars..
integer l,nk1
c ..
c before starting computations a data check is made. if the input data
c are invalid control is immediately repassed to the calling program.
ier = 10
nk1 = n-k1
if(x.lt.t(k1) .or. x.gt.t(nk1+1)) go to 300
c search for knot interval t(l) <= x < t(l+1)
l = k1
100 if(x.lt.t(l+1) .or. l.eq.nk1) go to 200
l = l+1
go to 100
200 if(t(l).ge.t(l+1)) go to 300
ier = 0
c calculate the derivatives.
call fpader(t,n,c,k1,x,l,d)
300 return
end
|
