Issues with 2D-Interpolation in Scipy

In my application, the data data is sampled on a distorted grid, and I would like to resample it to a nondistorted grid. In order to test this, I wrote this program with examplary distortions and a simple function as data:

from __future__ import division

import numpy as np
import scipy.interpolate as intp
import pylab as plt

# Defining some variables:

quadratic = -3/128
linear = 1/16
pn = np.poly1d([quadratic, linear,0])

pixels_x = 50
pixels_y = 30
frame = np.zeros((pixels_x,pixels_y))

x_width= np.concatenate((np.linspace(8,7.8,57) , np.linspace(7.8,8,pixels_y-57)))

def data(x,y):
    z = y*(np.exp(-(x-5)**2/3) + np.exp(-(x)**2/5) + np.exp(-(x+5)**2))
    return(z)

# Generating grid coordinates

yt = np.arange(380,380+pixels_y*4,4)
xt = np.linspace(-7.8,7.8,pixels_x)
X, Y = np.meshgrid(xt,yt)
Y=Y.T
X=X.T

Y_m = np.zeros((pixels_x,pixels_y))
X_m = np.zeros((pixels_x,pixels_y))

# generating distorted grid coordinates:    

for i in range(pixels_y):
    Y_m[:,i] = Y[:,i] - pn(xt)
    X_m[:,i] = np.linspace(-x_width[i],x_width[i],pixels_x)


# Sample data:
for i in range(pixels_y):
    for j in range(pixels_x):
        frame[j,i] = data(X_m[j,i],Y_m[j,i])


Y_m = Y_m.flatten()
X_m = X_m.flatten()
frame = frame.flatten()
##
Y = Y.flatten()
X = X.flatten()
ipf = intp.interp2d(X_m,Y_m,frame)
interpolated_frame = ipf(xt,yt)

At this point, I have to questions:

1. The code works, but I get the the following warning:

   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=54,31 m=1500 fp=0.000006 s=0.000000

Also, some interpolation artifacts appear, and I assume that they are related to the warning - Do you guys know what I am doing wrong?

1. For my actual applications, the frames nee开发者_开发知识库d to be around 500*100, but when doing this, I get a MemoryError - Is there something I can do to help that, apart from splitting the frame into several parts?

Thanks!

This problem is most likely related to the usage of bisplrep and bisplev within interp2d. The docs mention that they use a smooting factor of s=0.0 and that bisplrep and bisplev should be used directly if more control over s is needed. The related docs mention that s should be found between (m-sqrt(2*m),m+sqrt(2*m)) where m is the number of points used to construct the splines. I had a similar problem and found it solved when using bisplrep and bisplev directly, where s is only optional.

For 2d interpolation, griddata is solid, local, fast. Take a look at problem-with-2d-interpolation-in-scipy-non-rectangular-grid on SO.

You might want to look at the following interp method in basemap:

mpl_toolkits.basemap.interp http://matplotlib.sourceforge.net/basemap/doc/html/api/basemap_api.html

unless you really need spline-based interpolation.