interpolate linear array to non linear array using python numpy or scipy

Question

i have to arrays:

a linear one;

x = array([ 0. ,  0.1,  0.2,  0.3,  0.4,  0.5,  0.6,  0.7,  0.8,  0.9,  1. , 1.1,  1.2,  1.3,  1.4])

And a corresponding result which is a non-linear one;

y = array([ 13.07,  13.7 ,  14.35,  14.92,  15.5 ,  16.05,  16.56,  17.12,
        17.62,  18.08,  18.55,  19.02,  19.45,  19.88,  20.25])

Now: I want to convert y to a linearly spaced array and find the corresponding interpolated values of x.

i.e. find x when

y = array([ 13. ,  13.5,  14. ,  14.5,  15. ,  15.5,  16. ,  16.5,  17. , 17.5,  18. ,  18.5,  19. ,  19.5,  20. ])

Thanks in advance.

I use the following method using the interp function in numpy:

ynew = np.linspace(np.min(y), np.max(y), len(y))
xnew = np.interp(ynew, y, x)

i.e. exchanging x and y in the np.interp function.

Is this always correct ? or will it break down for some condition.

How do you want to get from y1 to y2? What's the logic there? — jedwards
– jedwards, Commented Mar 17, 2015 at 5:53

Curt F. · Accepted Answer · 2015-03-17 05:54:26Z

4

Unless I'm missing something, this case calls for a simple invocation of numpy.interp. You want to predict x from y which is the reverse of how people usually do their variable definitions, but other than that wrinkle, all you need is:

import numpy as np
x = np.array([ 0. ,  0.1,  0.2,  0.3,  0.4,  0.5,  0.6,  0.7,  0.8,  0.9,  1. , 1.1,  1.2,  1.3,  1.4])
y = np.array([ 13.07,  13.7 ,  14.35,  14.92,  15.5 ,  16.05,  16.56,  17.12,
        17.62,  18.08,  18.55,  19.02,  19.45,  19.88,  20.25])
ynew = np.array([ 13. ,  13.5,  14. ,  14.5,  15. ,  15.5,  16. ,  16.5,  17. , 17.5,  18. ,  18.5,  19. ,  19.5,  20. ])
xnew = np.interp(ynew, y, x)
print xnew

Which gives as ouput:

[ 0.          0.06825397  0.14615385  0.22631579  0.3137931   0.4
  0.49090909  0.58823529  0.67857143  0.776       0.8826087   0.9893617
  1.09574468  1.21162791  1.33243243]

answered Mar 17, 2015 at 5:54

Curt F.

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4 Comments

JBuch Over a year ago

i just found that answer myself. so i have modified my question to find wheather this method is valid for all cases.

Curt F. Over a year ago

Sorry I missed your edit superbuch -- it looks like it came in after my answer? Either way, I hope the answer was still useful to you. I think the np.interp function is generally useful, but without knowing exactly what you mean by "all" cases, I would hesitate to use that word.

JBuch Over a year ago

thanks for answer. By all cases i mean when either x or y or both are negative or when one or the other or both are decreasing or one is increasing and the other is decreasing.

Curt F. Over a year ago

You could try a few quick variations: np.interp(ynew, y[::-1], x[::-1]), np.interp(ynew, -y[::-1], -x[::-1]), np.interp(-ynew[::-1], -y[::-1], -x[::-1]), etc., and see which ones work and which ones run into problems. At least a few of those will give results that are not useful. It took a moment or two but eventually for each one I realized what the problem was.

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