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real*8 function dblint(tx,nx,ty,ny,c,kx,ky,xb,xe,yb,ye,wrk)
c function dblint calculates the double integral
c / xe / ye
c | | s(x,y) dx dy
c xb / yb /
c with s(x,y) a bivariate spline of degrees kx and ky, given in the
c b-spline representation.
c
c calling sequence:
c aint = dblint(tx,nx,ty,ny,c,kx,ky,xb,xe,yb,ye,wrk)
c
c input parameters:
c tx : real array, length nx, which contains the position of the
c knots in the x-direction.
c nx : integer, giving the total number of knots in the x-direction
c ty : real array, length ny, which contains the position of the
c knots in the y-direction.
c ny : integer, giving the total number of knots in the y-direction
c c : real array, length (nx-kx-1)*(ny-ky-1), which contains the
c b-spline coefficients.
c kx,ky : integer values, giving the degrees of the spline.
c xb,xe : real values, containing the boundaries of the integration
c yb,ye domain. s(x,y) is considered to be identically zero out-
c side the rectangle (tx(kx+1),tx(nx-kx))*(ty(ky+1),ty(ny-ky))
c
c output parameters:
c aint : real , containing the double integral of s(x,y).
c wrk : real array of dimension at least (nx+ny-kx-ky-2).
c used as working space.
c on exit, wrk(i) will contain the integral
c / xe
c | ni,kx+1(x) dx , i=1,2,...,nx-kx-1
c xb /
c with ni,kx+1(x) the normalized b-spline defined on
c the knots tx(i),...,tx(i+kx+1)
c wrk(j+nx-kx-1) will contain the integral
c / ye
c | nj,ky+1(y) dy , j=1,2,...,ny-ky-1
c yb /
c with nj,ky+1(y) the normalized b-spline defined on
c the knots ty(j),...,ty(j+ky+1)
c
c other subroutines required: fpintb
c
c references :
c gaffney p.w. : the calculation of indefinite integrals of b-splines
c j. inst. maths applics 17 (1976) 37-41.
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 1989
c
c ..scalar arguments..
integer nx,ny,kx,ky
real*8 xb,xe,yb,ye
c ..array arguments..
real*8 tx(nx),ty(ny),c((nx-kx-1)*(ny-ky-1)),wrk(nx+ny-kx-ky-2)
c ..local scalars..
integer i,j,l,m,nkx1,nky1
real*8 res
c ..
nkx1 = nx-kx-1
nky1 = ny-ky-1
c we calculate the integrals of the normalized b-splines ni,kx+1(x)
call fpintb(tx,nx,wrk,nkx1,xb,xe)
c we calculate the integrals of the normalized b-splines nj,ky+1(y)
call fpintb(ty,ny,wrk(nkx1+1),nky1,yb,ye)
c calculate the integral of s(x,y)
dblint = 0.
do 200 i=1,nkx1
res = wrk(i)
if(res.eq.0.) go to 200
m = (i-1)*nky1
l = nkx1
do 100 j=1,nky1
m = m+1
l = l+1
dblint = dblint+res*wrk(l)*c(m)
100 continue
200 continue
return
end
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