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Interpolating a function in two dimensions using SciPy's interp2d function

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by sneha@openweaver.com dot icon Updated: Apr 5, 2023

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Interpolating a function in two dimensions is approximating a function based on data points in two-dimensional space. It involves finding a function that passes through the given data points and estimating the values of the function between these points. 



Scipy is a Python library used for scientific computing. It provides modules for optimization, integration, linear algebra, interpolation, FFT, special functions, ODE solvers, signal and image processing, and other tasks common in science and engineering. 


SciPy's interp2d function is a two-dimensional interpolation function that can be used to find the value of a function at a given point in a two-dimensional grid. 

  • It is useful for plotting data points that are not evenly distributed across the grid. 
  • It can also be used to interpolate between two surfaces or to fill in missing values in a data set. 


Interpolating a function in two dimensions using SciPy's interp2d function is a technique that enables a user to fill in the missing data points in a 2D array by estimating the values of the missing points based on the values of the existing points. The interp2d function uses various interpolation algorithms to generate the missing data points, such as linear, cubic, and higher-order polynomial methods. 



Here is an example of Interpolating a function in two dimensions using SciPy's interp2d function. 



Fig1: Preview of Code



Fig2: Preview of the Output

Code


In this solution, we will use SciPy's interp2d function

2D linear interpolation: data and interpolated points

PythondotLines of Code : 30dotLicense : Strong Copyleft (CC BY-SA 4.0)

Dependent Libraries : 
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import numpy as np
from scipy.interpolate import interp2d

# Your original function
x = y = np.arange(0, 5, 0.1)
xx, yy = np.meshgrid(x, y)
zz = 2 * (xx ** 2) - (xx ** 3) - (yy ** 2)

# Your scattered points
x = y = np.arange(0, 5)
z = [0, 0, -4, -18, -48]

# Your interpolation
Z_inter = interp2d(x, y, z)
x_mesh = y_mesh = np.linspace(1.0, 4, num=10)
Z_interpolated = Z_inter(x_mesh, y_mesh)

fig = plt.figure()
ax = fig.gca(projection='3d')
# Plot your original function
ax.plot_surface(xx, yy, zz, color='b', alpha=0.5)
# Plot your initial scattered points
ax.scatter(x, y, z, color='r', marker='o')
# Plot your interpolation data
X_real_mesh, Y_real_mesh = np.meshgrid(x_mesh, y_mesh)
ax.scatter(X_real_mesh, Y_real_mesh, Z_interpolated, color='g', marker='^')
plt.show()

Instructions


  1. Install Jupyter Notebook on your computer.
  2. Open terminal and install the required libraries with following commands.
  3. Install Scipy- pip install scipy
  4. Install Numpy - pip install numpy
  5. Install matplotlib - pip install matplotlib
  6. Copy the snippet using the 'copy' button and paste it into that file.
  7. Run the file using run button.


I hope you found this useful. I have added the link to dependent libraries, version information in the following sections.


I found this code snippet by searching for "Interpolating in two dimensions using interp2d" in kandi. You can try any such use case!

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
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                  License
                    Reuse

                      numpyby numpy

                      Python doticonstar image 23755 doticonVersion:v1.25.0rc1doticon
                      License: Permissive (BSD-3-Clause)

                      The fundamental package for scientific computing with Python.

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                                numpyby numpy

                                Python doticon star image 23755 doticonVersion:v1.25.0rc1doticon License: Permissive (BSD-3-Clause)

                                The fundamental package for scientific computing with Python.
                                Support
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                                    Security
                                      License
                                        Reuse

                                          matplotlibby matplotlib

                                          Python doticonstar image 17559 doticonVersion:v3.7.1doticon
                                          no licences License: No License (null)

                                          matplotlib: plotting with Python

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                                                    matplotlibby matplotlib

                                                    Python doticon star image 17559 doticonVersion:v3.7.1doticonno licences License: No License

                                                    matplotlib: plotting with Python
                                                    Support
                                                      Quality
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                                                              If you do not have SciPy or numpy 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 numpy page in kandi.


                                                              You can search for any dependent library on kandi like numpy/SciPy /matplotlib.

                                                              Environment Tested


                                                              I tested this solution in the following versions. Be mindful of changes when working with other versions.

                                                              1. The solution is created in Python3.9.6
                                                              2. The solution is tested on SciPy-Python 1.9.1 version.


                                                              Using this solution, we are able to Interpolate a function in two dimensions using SciPy's interp2d function.


                                                              This process also facilities an easy to use, hassle free method to create a hands-on working version of code which would help us to interpolate a function in two dimensions using SciPy's interp2d function.

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