subroutine pardeu(tx,nx,ty,ny,c,kx,ky,nux,nuy,x,y,z,m, * wrk,lwrk,iwrk,kwrk,ier) c subroutine pardeu evaluates on a set of points (x(i),y(i)),i=1,...,m c the partial derivative ( order nux,nuy) of a bivariate spline c s(x,y) of degrees kx and ky, given in the b-spline representation. c c calling sequence: c call parder(tx,nx,ty,ny,c,kx,ky,nux,nuy,x,mx,y,my,z,wrk,lwrk, c * iwrk,kwrk,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 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 nux : integer values, specifying the order of the partial c nuy derivative. 0<=nux= 1. c wrk : real array of dimension lwrk. used as workspace. c lwrk : integer, specifying the dimension of wrk. c lwrk >= mx*(kx+1-nux)+my*(ky+1-nuy)+(nx-kx-1)*(ny-ky-1) c iwrk : integer array of dimension kwrk. used as workspace. c kwrk : integer, specifying the dimension of iwrk. kwrk >= mx+my. c c output parameters: c z : real array of dimension (m). c on succesful exit z(i) contains the value of the c specified partial derivative of s(x,y) at the point c (x(i),y(i)),i=1,...,m. c ier : integer error flag c ier=0 : normal return c ier=10: invalid input data (see restrictions) c c restrictions: c lwrk>=m*(kx+1-nux)+m*(ky+1-nuy)+(nx-kx-1)*(ny-ky-1), c c other subroutines required: c fpbisp,fpbspl 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 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,m,lwrk,kwrk,ier,nux,nuy c ..array arguments.. integer iwrk(kwrk) real*8 tx(nx),ty(ny),c((nx-kx-1)*(ny-ky-1)),x(m),y(m),z(m), * wrk(lwrk) c ..local scalars.. integer i,iwx,iwy,j,kkx,kky,kx1,ky1,lx,ly,lwest,l1,l2,mm,m0,m1, * nc,nkx1,nky1,nxx,nyy 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 kx1 = kx+1 ky1 = ky+1 nkx1 = nx-kx1 nky1 = ny-ky1 nc = nkx1*nky1 if(nux.lt.0 .or. nux.ge.kx) go to 400 if(nuy.lt.0 .or. nuy.ge.ky) go to 400 lwest = nc +(kx1-nux)*m+(ky1-nuy)*m if(lwrk.lt.lwest) go to 400 if(kwrk.lt.(m+m)) go to 400 if (m.lt.1) go to 400 ier = 0 nxx = nkx1 nyy = nky1 kkx = kx kky = 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 do 70 i=1,nc wrk(i) = c(i) 70 continue if(nux.eq.0) go to 200 lx = 1 do 100 j=1,nux ak = kkx nxx = nxx-1 l1 = lx m0 = 1 do 90 i=1,nxx l1 = l1+1 l2 = l1+kkx fac = tx(l2)-tx(l1) if(fac.le.0.) go to 90 do 80 mm=1,nyy m1 = m0+nyy wrk(m0) = (wrk(m1)-wrk(m0))*ak/fac m0 = m0+1 80 continue 90 continue lx = lx+1 kkx = kkx-1 100 continue 200 if(nuy.eq.0) go to 300 ly = 1 do 230 j=1,nuy ak = kky nyy = nyy-1 l1 = ly do 220 i=1,nyy l1 = l1+1 l2 = l1+kky fac = ty(l2)-ty(l1) if(fac.le.0.) go to 220 m0 = i do 210 mm=1,nxx m1 = m0+1 wrk(m0) = (wrk(m1)-wrk(m0))*ak/fac m0 = m0+nky1 210 continue 220 continue ly = ly+1 kky = kky-1 230 continue m0 = nyy m1 = nky1 do 250 mm=2,nxx do 240 i=1,nyy m0 = m0+1 m1 = m1+1 wrk(m0) = wrk(m1) 240 continue m1 = m1+nuy 250 continue c we partition the working space and evaluate the partial derivative 300 iwx = 1+nxx*nyy iwy = iwx+m*(kx1-nux) do 390 i=1,m call fpbisp(tx(nux+1),nx-2*nux,ty(nuy+1),ny-2*nuy,wrk,kkx,kky, * x(i),1,y(i),1,z(i),wrk(iwx),wrk(iwy),iwrk(1),iwrk(2)) 390 continue 400 return end