Timur A. Fatkhullin
5279d1c41a
start developing of FITPACK C++ bindings mount_server.cpp: fix compilation error with GCC15
92 lines
3.2 KiB
Fortran
92 lines
3.2 KiB
Fortran
recursive function dblint(tx,nx,ty,ny,c,kx,ky,xb,xe,yb,
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* ye,wrk) result(dblint_res)
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implicit none
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real*8 :: dblint_res
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c function dblint calculates the double integral
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c / xe / ye
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c | | s(x,y) dx dy
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c xb / yb /
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c with s(x,y) a bivariate spline of degrees kx and ky, given in the
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c b-spline representation.
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c
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c calling sequence:
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c aint = dblint(tx,nx,ty,ny,c,kx,ky,xb,xe,yb,ye,wrk)
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c
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c input parameters:
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c tx : real array, length nx, which contains the position of the
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c knots in the x-direction.
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c nx : integer, giving the total number of knots in the x-direction
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c ty : real array, length ny, which contains the position of the
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c knots in the y-direction.
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c ny : integer, giving the total number of knots in the y-direction
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c c : real array, length (nx-kx-1)*(ny-ky-1), which contains the
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c b-spline coefficients.
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c kx,ky : integer values, giving the degrees of the spline.
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c xb,xe : real values, containing the boundaries of the integration
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c yb,ye domain. s(x,y) is considered to be identically zero out-
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c side the rectangle (tx(kx+1),tx(nx-kx))*(ty(ky+1),ty(ny-ky))
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c
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c output parameters:
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c aint : real , containing the double integral of s(x,y).
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c wrk : real array of dimension at least (nx+ny-kx-ky-2).
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c used as working space.
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c on exit, wrk(i) will contain the integral
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c / xe
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c | ni,kx+1(x) dx , i=1,2,...,nx-kx-1
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c xb /
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c with ni,kx+1(x) the normalized b-spline defined on
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c the knots tx(i),...,tx(i+kx+1)
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c wrk(j+nx-kx-1) will contain the integral
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c / ye
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c | nj,ky+1(y) dy , j=1,2,...,ny-ky-1
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c yb /
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c with nj,ky+1(y) the normalized b-spline defined on
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c the knots ty(j),...,ty(j+ky+1)
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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 1989
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c
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c ..scalar arguments..
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integer nx,ny,kx,ky
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real*8 xb,xe,yb,ye
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c ..array arguments..
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real*8 tx(nx),ty(ny),c((nx-kx-1)*(ny-ky-1)),wrk(nx+ny-kx-ky-2)
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c ..local scalars..
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integer i,j,l,m,nkx1,nky1
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real*8 res
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c ..
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nkx1 = nx-kx-1
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nky1 = ny-ky-1
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c we calculate the integrals of the normalized b-splines ni,kx+1(x)
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call fpintb(tx,nx,wrk,nkx1,xb,xe)
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c we calculate the integrals of the normalized b-splines nj,ky+1(y)
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call fpintb(ty,ny,wrk(nkx1+1),nky1,yb,ye)
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c calculate the integral of s(x,y)
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dblint_res = 0.
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do 200 i=1,nkx1
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res = wrk(i)
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if(res.eq.0.) go to 200
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m = (i-1)*nky1
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l = nkx1
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do 100 j=1,nky1
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m = m+1
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l = l+1
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dblint_res = dblint_res + res*wrk(l)*c(m)
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100 continue
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200 continue
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return
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end
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