bispev.f

Go to the documentation of this file.

      subroutine bispev(tx,nx,ty,ny,c,kx,ky,x,mx,y,my,z,wrk,lwrk,
     * iwrk,kwrk,ier)
      implicit none
c  subroutine bispev evaluates on a grid (x(i),y(j)),i=1,...,mx; j=1,...
c  ,my a bivariate spline s(x,y) of degrees kx and ky, given in the
c  b-spline representation.
c
c  calling sequence:
c     call bispev(tx,nx,ty,ny,c,kx,ky,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   x     : real array of dimension (mx).
c           before entry x(i) must be set to the x co-ordinate of the
c           i-th grid point along the x-axis.
c           tx(kx+1)<=x(i-1)<=x(i)<=tx(nx-kx), i=2,...,mx.
c   mx    : on entry mx must specify the number of grid points along
c           the x-axis. mx >=1.
c   y     : real array of dimension (my).
c           before entry y(j) must be set to the y co-ordinate of the
c           j-th grid point along the y-axis.
c           ty(ky+1)<=y(j-1)<=y(j)<=ty(ny-ky), j=2,...,my.
c   my    : on entry my must specify the number of grid points along
c           the y-axis. my >=1.
c   wrk   : real array of dimension lwrk. used as workspace.
c   lwrk  : integer, specifying the dimension of wrk.
c           lwrk >= mx*(kx+1)+my*(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 (mx*my).
c           on succesful exit z(my*(i-1)+j) contains the value of s(x,y)
c           at the point (x(i),y(j)),i=1,...,mx;j=1,...,my.
c   ier   : integer error flag
c    ier=0 : normal return
c    ier=10: invalid input data (see restrictions)
c
c  restrictions:
c   mx >=1, my >=1, lwrk>=mx*(kx+1)+my*(ky+1), kwrk>=mx+my
c   tx(kx+1) <= x(i-1) <= x(i) <= tx(nx-kx), i=2,...,mx
c   ty(ky+1) <= y(j-1) <= y(j) <= ty(ny-ky), j=2,...,my
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    cox m.g.  : the numerical evaluation of b-splines, j. inst. maths
c                applics 10 (1972) 134-149.
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 1987
c
c  ..scalar arguments..
      integer nx,ny,kx,ky,mx,my,lwrk,kwrk,ier
c  ..array arguments..
      integer iwrk(kwrk)
      real*8 tx(nx),ty(ny),c((nx-kx-1)*(ny-ky-1)),x(mx),y(my),z(mx*my),
     * wrk(lwrk)
c  ..local scalars..
      integer i,iw,lwest
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.
C      write(6,*) "x, nx = ", x(1),mx, " y, ny = ", y(1), my
      ier = 10
      lwest = (kx+1)*mx+(ky+1)*my
      if(lwrk.lt.lwest) go to 100
      if(kwrk.lt.(mx+my)) go to 100
      if(mx-1) 100,30,10
  10  do 20 i=2,mx
        if(x(i).lt.x(i-1)) go to 100
  20  continue
  30  if(my-1) 100,60,40
  40  do 50 i=2,my
        if(y(i).lt.y(i-1)) go to 100
  50  continue
  60  ier = 0
      iw = mx*(kx+1)+1
C      write(6,*) tx, nx, ty, ny, c, kx, ky, x, mx, y, my
C      write(6,*) "WRK = ", wrk(1), wrk(iw)
      call fpbisp(tx,nx,ty,ny,c,kx,ky,x,mx,y,my,z,wrk(1),wrk(iw),
     * iwrk(1),iwrk(mx+1))
C      write(6,*) "x,y = ", x(1), y(1)
C      write(6,*) "flux = ",z(1)
 100  return
      end