[SciPy-User] Problems with 2D interpolation of data on polar grid

josef.pktd@gmai... josef.pktd@gmai...
Fri Aug 20 11:58:05 CDT 2010


On Fri, Aug 20, 2010 at 11:52 AM, Kyle Parfrey <kparfrey@gmail.com> wrote:
> Hi all,
>
> I've been having some trouble doing 2D interpolation with both
> interp2d and bisplrep/bisplev. My data is on a spherical polar (r,
> theta) grid, and I'm trying to interpolate functions similar to the
> vector components of a dipole field. The output looks very wrong, and
> I keep getting warnings like (from interp2d):
>
> Warning:     No more knots can be added because the number of B-spline
> coefficients
>    already exceeds the number of data points m. Probably causes: either
>    s or m too small. (fp>s)
>        kx,ky=1,1 nx,ny=16,9 m=90 fp=0.000000 s=0.000000
>
> or, from bisplrep:
>
> /usr/lib/python2.6/dist-packages/scipy/interpolate/fitpack.py:763:
> DeprecationWarning: integer argument expected, got float
>  tx,ty,nxest,nyest,wrk,lwrk1,lwrk2)
>
> One thing: I'm not trying to regrid---I'll need to be able to
> interpolate to any arbitrary point, since I'll be using this to
> calculate field lines. I've pasted some code below that should give
> some idea of the problem. I hope I haven't done something obviously
> stupid!
>
> Thanks in advance,
> Kyle
>
> ----------------------------------------------------
>
> import numpy as np
> from scipy import interpolate
> from math import *
> import matplotlib.pyplot as plt
>
> ### Make polar grid ###
> rvec = np.arange(1.0, 11.0, 1.0)
> tvec = np.arange(pi/10.0, pi, pi/10.0)
> Nr = len(rvec)
> Nt = len(tvec)
> X = np.empty([Nr,Nt])
> Y = np.empty([Nr,Nt])
> Z = np.empty([Nr,Nt])
>
> for i in range(Nr):
>  for j in range(Nt):
>    r = rvec[i]
>    t = tvec[j]
>    X[i,j] = r*sin(t)
>    Y[i,j] = r*cos(t)
>    Z[i,j] = cos(t)/pow(r,3) # cos(theta)/r^3: Br of dipole
>
>
> ### Do the interpolation ###
> #interp_poly = interpolate.interp2d(X,Y,Z, kind='linear')
> tck = interpolate.bisplrep(X,Y,Z, kx=3, ky=3)
>
>
> ### interpolate onto new grid ###
> rnew = np.arange(1.0, 10.1, 0.1)
> tnew = np.arange(pi/100.0, pi, pi/100.0)
> Nr2 = len(rnew)
> Nt2 = len(tnew)
> X2 = np.empty([Nr2,Nt2])
> Y2 = np.empty([Nr2,Nt2])
> Z2 = np.empty([Nr2,Nt2])
> for i in range(Nr2):
>  for j in range(Nt2):
>    r = rnew[i]
>    t = tnew[j]
>    X2[i,j] = r*sin(t)
>    Y2[i,j] = r*cos(t)
>    #Z2[i,j] = interp_poly(X2[i,j], Y2[i,j])
>    Z2[i,j] = interpolate.bisplev(X2[i,j], Y2[i,j], tck)
>
>
> ### Pseudocolour plot ###
> fig = plt.figure()
> fig.add_subplot(111, aspect='equal')
> plt.pcolor(X2,Y2,Z2)
> plt.colorbar()
> plt.show()


I'm not a graphical person, but if I reduce the radius

### interpolate onto new grid ###
rnew = np.arange(1.0, 10.1, 0.1)[:20]

the plot seems to look reasonable.

plotting the original X,Y,Z also has color variation only close to the
origin. contour plot also shows "action" only around the origin.
looks like most of the area is flat close to zero.

I don't see a problem with the spline interpolation itself.

Josef

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