How to use the scipy.interpolate.griddata() method

Overview

Scipy is a Python library useful for scientific computing. It contains numerous modules, including the interpolate module, which is helpful when it comes to interpolating data points in different dimensions whether one-dimension as in a line or two-dimension as in a grid.

The scipy.interpolate.griddata() method is used to interpolate on a 2-Dimension grid.

Syntax

The syntax is as below:

scipy.interpolate.griddata(points, values, xi, method='linear', 
 fill_value=nan, rescale=False)

Parameters

  • points means the randomly generated data points.

  • values are data points generated using a function.

  • xi are the grid data points to be used when interpolating.

  • method means the method of interpolation. It can be cubic, linear or nearest.

  • The fill_value, which defaults to nan if the specified points are out of range. However, for nearest, it has no effect.

  • rescale is useful when some points generated might be extremely large. In that case, it is set to True.

Return value

The function returns an array of interpolated values in a grid.

Code

import numpy as np
import matplotlib.pyplot as plt
import scipy
from scipy.interpolate import griddata
#define a function
def func(x,y):
    return (x**2+y**2+(x*y)**2)**2
#generate grid data using mgrid
grid_x,grid_y = np.mgrid[0:1:1000j, 0:1:2000j]
#generate random points
rng = np.random.default_rng()
points = rng.random((1000, 2))
#generate values from the points generated above
values = func(points[:,0], points[:,1])
#generate grid data using the points and values above
grid_a = griddata(points, values, (grid_x, grid_y), method='cubic')
grid_b = griddata(points, values, (grid_x, grid_y), method='linear')
grid_c = griddata(points, values, (grid_x, grid_y), method='nearest')
#visualizations
fig, axs = plt.subplots(2, 2)
axs[0, 0].plot(func(grid_x,grid_y))
axs[0, 0].set_title("main")
axs[1, 0].plot(grid_a)
axs[1, 0].set_title("cubic")
axs[0, 1].plot(grid_b)
axs[0, 1].set_title("linear")
axs[1, 1].plot(grid_c)
axs[1, 1].set_title("nearest")
fig.tight_layout()
plt.savefig('output/graph.png')

Explanation

Here is a line-by-line explanation of the code above:

  • Lines 1–4: We import the necessary modules.
  • Lines 8 and 9: We define a function that will be used to generate values later in line 19.
  • Line 12: We generate grid data and return a 2-D grid.
  • Line 15: We initialize a generator object for generating random numbers.
  • Line 16: We use the generator object in line 15 to generate 1000, 2-D arrays.
  • Line 20: We generate values using the points in line 16 and the function defined in lines 8-9.
  • Lines 23–27: We generate grid points using the griddata method, over different grids, specifying different method parameters.
  • Lines 31–42: We plot the different griddata visualizations.

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