63 lines
2.1 KiB
Fortran
63 lines
2.1 KiB
Fortran
recursive function splint(t,n,c,nc,k,a,b,wrk) result(splint_res)
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implicit none
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real*8 :: splint_res
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c function splint calculates the integral of a spline function s(x)
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c of degree k, which is given in its normalized b-spline representation
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c
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c calling sequence:
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c aint = splint(t,n,c,k,a,b,wrk)
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c
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c input parameters:
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c t : array,length n,which contains the position of the knots
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c of s(x).
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c n : integer, giving the total number of knots of s(x).
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c c : array,length nc, containing the b-spline coefficients.
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c the length of the array, nc >= n - k -1.
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c further coefficients are ignored.
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c k : integer, giving the degree of s(x).
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c a,b : real values, containing the end points of the integration
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c interval. s(x) is considered to be identically zero outside
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c the interval (t(k+1),t(n-k)).
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c
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c output parameter:
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c aint : real, containing the integral of s(x) between a and b.
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c wrk : real array, length n. used as working space
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c on output, wrk will contain the integrals of the normalized
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c b-splines defined on the set of knots.
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c
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c other subroutines required: fpintb.
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c
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c references :
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c gaffney p.w. : the calculation of indefinite integrals of b-splines
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c j. inst. maths applics 17 (1976) 37-41.
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c dierckx p. : curve and surface fitting with splines, monographs on
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c numerical analysis, oxford university press, 1993.
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c
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c author :
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c p.dierckx
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c dept. computer science, k.u.leuven
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c celestijnenlaan 200a, b-3001 heverlee, belgium.
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c e-mail : Paul.Dierckx@cs.kuleuven.ac.be
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c
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c latest update : march 1987
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c
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c ..scalar arguments..
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real*8 a,b
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integer n,k, nc
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c ..array arguments..
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real*8 t(n),c(nc),wrk(n)
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c ..local scalars..
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integer i,nk1
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c ..
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nk1 = n-k-1
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c calculate the integrals wrk(i) of the normalized b-splines
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c ni,k+1(x), i=1,2,...nk1.
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call fpintb(t,n,wrk,nk1,a,b)
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c calculate the integral of s(x).
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splint_res = 0.0d0
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do 10 i=1,nk1
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splint_res = splint_res+c(i)*wrk(i)
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10 continue
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return
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end
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