Extrapolate with LinearNDInterpolator

Question

I\'ve got a 3D dataset that I want to interpolate AND extrapolate linearly. The interpolation can be done easily with scipy.interpolate.LinearNDInterpolator. The module can

Answer 1

I propose a method, the code is awful but I hope it will help you. The idea is, if you know by advance the bounds in which you will have to extrapolate, you can add extra columns/rows at the edge of your arrays with linearly extrapolated values, and then interpolate on the new array. Here is an example with some data that will be extrapolated until x=+-50 and y=+-40:

import numpy as np
x,y=np.meshgrid(np.linspace(0,6,7),np.linspace(0,8,9)) # create x,y grid
z=x**2*y # and z values
# create larger versions with two more columns/rows
xlarge=np.zeros((x.shape[0]+2,x.shape[1]+2))
ylarge=np.zeros((x.shape[0]+2,x.shape[1]+2))
zlarge=np.zeros((x.shape[0]+2,x.shape[1]+2))
xlarge[1:-1,1:-1]=x # copy data on centre
ylarge[1:-1,1:-1]=y
zlarge[1:-1,1:-1]=z
# fill extra columns/rows
xmin,xmax=-50,50
ymin,ymax=-40,40
xlarge[:,0]=xmin;xlarge[:,-1]=xmax # fill first/last column
xlarge[0,:]=xlarge[1,:];xlarge[-1,:]=xlarge[-2,:] # copy first/last row
ylarge[0,:]=ymin;ylarge[-1,:]=ymax
ylarge[:,0]=ylarge[:,1];ylarge[:,-1]=ylarge[:,-2]
# for speed gain: store factor of first/last column/row
first_column_factor=(xlarge[:,0]-xlarge[:,1])/(xlarge[:,1]-xlarge[:,2]) 
last_column_factor=(xlarge[:,-1]-xlarge[:,-2])/(xlarge[:,-2]-xlarge[:,-3])
first_row_factor=(ylarge[0,:]-ylarge[1,:])/(ylarge[1,:]-ylarge[2,:])
last_row_factor=(ylarge[-1,:]-ylarge[-2,:])/(ylarge[-2,:]-ylarge[-3,:])
# extrapolate z; this operation only needs to be repeated when zlarge[1:-1,1:-1] is updated
zlarge[:,0]=zlarge[:,1]+first_column_factor*(zlarge[:,1]-zlarge[:,2]) # extrapolate first column
zlarge[:,-1]=zlarge[:,-2]+last_column_factor*(zlarge[:,-2]-zlarge[:,-3]) # extrapolate last column
zlarge[0,:]=zlarge[1,:]+first_row_factor*(zlarge[1,:]-zlarge[2,:]) # extrapolate first row
zlarge[-1,:]=zlarge[-2,:]+last_row_factor*(zlarge[-2,:]-zlarge[-3,:]) #extrapolate last row

Then you can interpolate on (xlarge,ylarge,zlarge). Since all operations are numpy slices operations, I hope it will be fast enough for you. When z data are updated, copy them in zlarge[1:-1,1:-1] and re-execute the 4 last lines.