CODEWITHSUNDEEP
pythonarraysnumpydictionaryinterpolation
flotr
flotr

Reputation: 165

Interpolate values in a 2D Python numerical dictionary

I have Python dictionaries that look like this:

a = {0.0 : {0.0: 343, 0.5: 23, 1.0: 34, 1.5: 9454, ...}, 0.5 : {0.0: 359, 0.5: -304, ...}, ...}

So they are 2D dictionaries that resemble 2D grids of m * n elements.

The values are evenly distributed, but the dictionaries may have different "resolutions". For instance, in the above example the values are separated by 0.5. Another dictionary has the separation of 1.0. Further, the range of the values is also variable, for example:

I need to create a function that takes a 2D value (e.g. 3.49, 20.31) and returns the interpolated value in the grid.

How to do that?

I guess it'd help to first convert this form to a Numpy array, but I don't know how to do it.

Edit:

Upvotes: 2

Views: 2340

Answers (1)

hpaulj
hpaulj

Reputation: 231605

With a sample dictionary, I constructed the required numpy arrays, x, y, and 2d z. And then used a scipy interpolator to do the rest.

import numpy as np

a = {0.0 : {0.0: 0, 0.5: 3, 1.0: 6, 1.5: 9},
 0.5 : {0.0: 1, 0.5: 5, 1.0: 9, 1.5: 13},
 1.0 : {0.0: 2, 0.5: 7, 1.0: 12, 1.5: 17},
 1.5 : {0.0: 3, 0.5: 9, 1.0: 15, 1.5: 21},
 2.0 : {0.0: 4, 0.5: 11, 1.0: 18, 1.5: 25},
    }
print a
x = np.array(sorted(a.keys()))   # dictionary keys might not be sorted
print x
y = np.array(sorted(a[x[0]].keys()))
print y
z = np.zeros((len(x),len(y)))
for i,m in enumerate(x):
    for j,n in enumerate(y):   # assumes nested keys are all the same
        z[i,j] = a[m][n]
print z

Note that these arrays look a lot like lists, or lists of lists. 

from scipy import interpolate
f = interpolate.interp2d(y,x,z,kind='linear') #  columns, rows, data
print f([0,.25,.5,.75],[0,.25,.5,.75])

producing:

{0.0: {0.0: 0, 0.5: 3, 1.5: 9, 1.0: 6}...}}  # dict

[ 0.   0.5  1.   1.5  2. ]   # x
[ 0.   0.5  1.   1.5]    # y
[[  0.   3.   6.   9.]   # z
 [  1.   5.   9.  13.]
 [  2.   7.  12.  17.]
 [  3.   9.  15.  21.]
 [  4.  11.  18.  25.]]

[[  0.     1.5    3.     4.5    6.  ]
 [  0.5    2.25   4.     5.75   7.5 ]
 [  1.     3.     5.     7.     9.  ]
 [  1.5    3.75   6.     8.25  10.5 ]
 [  2.     4.5    7.     9.5   12.  ]]

http://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.interpolate.interp2d.html

Upvotes: 2

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