Timur A. Fatkhullin
5279d1c41a
start developing of FITPACK C++ bindings mount_server.cpp: fix compilation error with GCC15
158 lines
4.6 KiB
Fortran
158 lines
4.6 KiB
Fortran
recursive subroutine pardtc(tx,nx,ty,ny,c,kx,ky,nux,nuy,
|
|
* newc,ier)
|
|
implicit none
|
|
c subroutine pardtc takes the knots and coefficients of a bivariate
|
|
c spline, and returns the coefficients for a new bivariate spline that
|
|
c evaluates the partial derivative (order nux, nuy) of the original
|
|
c spline.
|
|
c
|
|
c calling sequence:
|
|
c call pardtc(tx,nx,ty,ny,c,kx,ky,nux,nuy,newc,ier)
|
|
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 (hidden)
|
|
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 (hidden)
|
|
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 nux : integer values, specifying the order of the partial
|
|
c nuy derivative. 0<=nux<kx, 0<=nuy<ky.
|
|
c
|
|
c output parameters:
|
|
c newc : real array containing the coefficients of the derivative.
|
|
c the dimension is (nx-nux-kx-1)*(ny-nuy-ky-1).
|
|
c ier : integer error flag
|
|
c ier=0 : normal return
|
|
c ier=10: invalid input data (see restrictions)
|
|
c
|
|
c restrictions:
|
|
c 0 <= nux < kx, 0 <= nuy < kyc
|
|
c
|
|
c other subroutines required:
|
|
c none
|
|
c
|
|
c references :
|
|
c de boor c : on calculating with b-splines, j. approximation theory
|
|
c 6 (1972) 50-62.
|
|
c dierckx p. : curve and surface fitting with splines, monographs on
|
|
c numerical analysis, oxford university press, 1993.
|
|
c
|
|
c based on the subroutine "parder" by Paul Dierckx.
|
|
c
|
|
c author :
|
|
c Cong Ma
|
|
c Department of Mathematics and Applied Mathematics, U. of Cape Town
|
|
c Cross Campus Road, Rondebosch 7700, Cape Town, South Africa.
|
|
c e-mail : cong.ma@uct.ac.za
|
|
c
|
|
c latest update : may 2019
|
|
c
|
|
c ..scalar arguments..
|
|
integer nx,ny,kx,ky,nux,nuy,ier, nc
|
|
c ..array arguments..
|
|
real*8 tx(nx),ty(ny),c((nx-kx-1)*(ny-ky-1)),
|
|
* newc((nx-kx-1)*(ny-ky-1))
|
|
c ..local scalars..
|
|
integer i,j,kx1,ky1,lx,ly,l1,l2,m,m0,m1,
|
|
* nkx1,nky1,nxx,nyy,newkx,newky
|
|
real*8 ak,fac
|
|
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
|
|
if(nux.lt.0 .or. nux.ge.kx) go to 400
|
|
if(nuy.lt.0 .or. nuy.ge.ky) go to 400
|
|
kx1 = kx+1
|
|
ky1 = ky+1
|
|
nkx1 = nx-kx1
|
|
nky1 = ny-ky1
|
|
nc = nkx1*nky1
|
|
ier = 0
|
|
nxx = nkx1
|
|
nyy = nky1
|
|
newkx = kx
|
|
newky = ky
|
|
c the partial derivative of order (nux,nuy) of a bivariate spline of
|
|
c degrees kx,ky is a bivariate spline of degrees kx-nux,ky-nuy.
|
|
c we calculate the b-spline coefficients of this spline
|
|
c that is to say newkx = kx - nux, newky = ky - nuy
|
|
do 70 i=1,nc
|
|
newc(i) = c(i)
|
|
70 continue
|
|
if(nux.eq.0) go to 200
|
|
lx = 1
|
|
do 100 j=1,nux
|
|
ak = newkx
|
|
nxx = nxx-1
|
|
l1 = lx
|
|
m0 = 1
|
|
do 90 i=1,nxx
|
|
l1 = l1+1
|
|
l2 = l1+newkx
|
|
fac = tx(l2)-tx(l1)
|
|
if(fac.le.0.) go to 90
|
|
do 80 m=1,nyy
|
|
m1 = m0+nyy
|
|
newc(m0) = (newc(m1)-newc(m0))*ak/fac
|
|
m0 = m0+1
|
|
80 continue
|
|
90 continue
|
|
lx = lx+1
|
|
newkx = newkx-1
|
|
100 continue
|
|
200 if(nuy.eq.0) go to 400
|
|
c orig: if(nuy.eq.0) go to 300
|
|
ly = 1
|
|
do 230 j=1,nuy
|
|
ak = newky
|
|
nyy = nyy-1
|
|
l1 = ly
|
|
do 220 i=1,nyy
|
|
l1 = l1+1
|
|
l2 = l1+newky
|
|
fac = ty(l2)-ty(l1)
|
|
if(fac.le.0.) go to 220
|
|
m0 = i
|
|
do 210 m=1,nxx
|
|
m1 = m0+1
|
|
newc(m0) = (newc(m1)-newc(m0))*ak/fac
|
|
m0 = m0+nky1
|
|
210 continue
|
|
220 continue
|
|
ly = ly+1
|
|
newky = newky-1
|
|
230 continue
|
|
m0 = nyy
|
|
m1 = nky1
|
|
do 250 m=2,nxx
|
|
do 240 i=1,nyy
|
|
m0 = m0+1
|
|
m1 = m1+1
|
|
newc(m0) = newc(m1)
|
|
240 continue
|
|
m1 = m1+nuy
|
|
250 continue
|
|
c300 iwx = 1+nxx*nyy
|
|
c iwy = iwx+mx*(kx1-nux)
|
|
c
|
|
c from parder.f:
|
|
c call fpbisp(tx(nux+1),nx-2*nux,ty(nuy+1),ny-2*nuy,newc,newkx,newky,
|
|
c * x,mx,y,my,z,newc(iwx),newc(iwy),iwrk(1),iwrk(mx+1))
|
|
c
|
|
c from bispev.f:
|
|
c call fpbisp(tx, nx, ty, ny, c, kx, ky,
|
|
c * x,mx,y,my,z,wrk(1), wrk(iw), iwrk(1),iwrk(mx+1))
|
|
c
|
|
c from fpbisp.f:
|
|
c fpbisp(tx, nx, ty, ny, c, kx, ky,
|
|
c * x,mx,y,my,z,wx, wy, lx, ly)
|
|
400 return
|
|
end
|
|
|