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I'm fairly new to programming and thought I'd try writing a piecewise linear interpolation function. (perhaps which is done with numpy.interp or scipy.interpolate.interp1d)

Say I am given data as follows: x= [1, 2.5, 3.4, 5.8, 6] y=[2, 4, 5.8, 4.3, 4]

I want to design a piecewise interpolation function that will give the coefficents of all the Linear polynomial pieces between 1 and 2.5, 2.5 to 3.4 and so on using Python. of course matlab has the interp1 function which do this but im using python and i want to do exactly the same job as matlab but python only gives the valuse but not linear polynomials coefficient ! (in matlab we could get this with pp.coefs) . but how to get pp.coefs in python numpy.interp ?

Nima Geran
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2 Answers2

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You can use polyfit from numpy, which gives you the list of coefficient, from the highest degree (here there are two coefficient on your degree 1 polynom) for a given fitting. The below will thus give you the list of coefficient for each segment [1, 2.5], [2.5, 3.4], etc

import numpy as np

x = np.array(x)
y = np.array(y)

[np.polyfit(x[i:(i+2)], y[i:(i+2)],1) for i in range(len(x)-1)]
#[array([ 1.33333333,  0.66666667]), array([ 2., -1.]), array([-0.625,  7.925]), array([ -1.5,  13. ])]
Colonel Beauvel
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  • thanks for your answer sir . . . but i really dont want to have just one polynomial and i prefer for some reasons to attach the points with line segments and then i have to find the intersection point of the resulting curve to another line . . . – Nima Geran Mar 24 '17 at 13:28
  • @Nima, there is not only one polynomial there, the coefficients above are the one for each line segments! – Colonel Beauvel Mar 24 '17 at 13:32
  • Thanks so much . i got my answer . . . do you know how could i find the intersection point between the two graphs now ? – Nima Geran Mar 25 '17 at 11:11
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If you're doing linear interpolation you can just use the formula that the line from point (x0, y0) to (x1, y1) the line that interpolates them is given by y - y0 = ((y0 - y1)/(x0 - x1)) * (x - x0). You can take 2 element slices of your list using the slice syntax; for example to get [2.5, 3.4] you would use x[1:3].

Using the slice syntax you can then implement the linear interpolation formula to calculate the coefficients of the linear polynomial interpolations.

Jake Conkerton-Darby
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  • thanx for your answer . . . but my primary question is to finding the intersecting point between two curves, one is a line for example y = 2*x and another is the set of points (for example : x= [1, 2.5, 3.4, 5.8, 6] y=[2, 4, 5.8, 4.3, 4]) that forms a piecewise curve which i prefer to use piecewise linear . . . i firstly should form this piecewise linear curve and then finding the intersection point with the ((solve)) . . . of course infact i dont have a line. . . – Nima Geran Mar 24 '17 at 13:24
  • I'm afraid I don't understand this comment. The method I detailed will allow you to calculate the coefficients. From this you will be able to generate the linear interpolation of the provided points as you requested. – Jake Conkerton-Darby Mar 24 '17 at 14:40