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Interpolating a function using SciPy's interp1d function

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by Dejaswarooba dot icon Updated: Mar 24, 2023

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A Python library called Scipy is intended for use in technical and scientific computing. It is based on the NumPy library and provides a range of mathematical tools and methods for uses in signal processing, interpolation, optimisation, and other fields. Together with Fourier transformations and image processing, Scipy also has modules for statistics and probability. Scipy is frequently used in conjunction with machine learning and data analytics in a variety of scientific fields, including physics, engineering, biology, and finance. 


The Scipy subpackage interpolate offers a number of methods for interpolating data. Mathematical interpolation is a method for estimating the value of a function between two given values. It is helpful when we need to estimate values at places where there are no data or when our data points are not evenly spaced.


Scipy's interpolate subpackage offers a number of interpolation techniques, such as:

  • interp1d: This function interpolates a one-dimensional data collection using linear and cubic spline interpolation.
  • A two-dimensional data collection can be interpolated using bilinear and bicubic spline techniques using the interp2d function.
  • griddata: This function interpolates a dispersed data collection onto an established grid.
  • These functions, splev and splrep, allow for the assessment and creation of B-splines.


The scipy.interpolate module in Python's scipy library contains the inter1d function. It is employed for a function's one-dimensional interpolation.


The inter1d function's basic syntax is as follows:

f = interp1d(x, y, kind='linear'),


where x and y are arrays containing the data points and kind indicates the interpolation method to be used. The kind parameter can be set to "linear" to perform a linear interpolation, "nearest" to perform a nearest-neighbor interpolation, "cubic" to perform a cubic interpolation, or any other interpolation method.


The interpolated function can be evaluated at any location within the range of x after the inter1d function has been defined.



Images depicting the functionality of the inter1d function.

Code

In this program, linear interpolation is carried out using the interp1d function from the scipy.interpolate package.

  • The NearestValue function uses the NumPy function argmin to determine the index of the element in the array that is closest to value.
  • The code then generates an interp1d object f by using the interp1d function with the dependent variable y and the flattened independent variable x.
  • The flatten() method is used to turn the list of lists x into a 1D array that the interp1d function requires.
  • Finally, the code displays f(0.95), which is the interpolated value of the independent variable x that corresponds to the dependent variable value of 0.95. This signifies that the code is attempting to determine the value of x at which y equals 0.95 using linear interpolation.


Using scipy.interpolate.interp1d to calculate the x value where y =0.95

Lines of Code : 31dotLicense : Strong Copyleft (CC BY-SA 4.0)

Dependent Libraries : 
import numpy as np
from scipy.interpolate import interp1d    

def NearestValue(array,value):
    #returns the index of the element of the array which is closest to value

    idx = (np.abs(array-value)).argmin()
    return idx

x =[[   0. ],[   9.9],[  19.8],[  31.5],[  41.9],[  49.1],[  59. ],[  70. ],[  80.4],[ 100. ]]

y= [ 0.011905, 0.140795, 0.600562, 0.757247, 0.874564, 0.934559, 0.961719, 0.986099,  0.990284, 0.998254]

f = interp1d(y, np.array(x).flatten())

print (f(0.95))
for i,_ in enumerate(y):
    print (_,  x[i][0], f(_))

54.728346833578776
0.011905 0.0 0.0
0.140795 9.9 9.9
0.600562 19.8 19.8
0.757247 31.5 31.5
0.874564 41.9 41.9
0.934559 49.1 49.1
0.961719 59.0 59.0
0.986099 70.0 70.0
0.990284 80.4 80.4
0.998254 100.0 100.0
  • Copy and paste the above code from kandi in your prescribed code editor.
  • Remove this part from the code.
  • The above just depicts the output received when we perform ennumeration, which is not necessary for interpolation.

Dependent Libraries

scipyby scipy

Python doticonstar image 11340 doticonVersion:v1.11.0rc1doticon
License: Permissive (BSD-3-Clause)

SciPy library main repository

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            scipyby scipy

            Python doticon star image 11340 doticonVersion:v1.11.0rc1doticon License: Permissive (BSD-3-Clause)

            SciPy library main repository
            Support
              Quality
                Security
                  License
                    Reuse

                      If you do not have SciPy that is required to run this code, you can install it by clicking on the above link and copying the pip Install command from the SciPy page in kandi.


                      You can search for any dependent library on kandi like SciPy

                      Environment tested

                      1. This code had been tested using python version 3.8.0
                      2. scipy version 1.10.1 has been used.

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