2D interpolation (interp2d, griddata) in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of 2D interpolation using interp2d

What is the output of the following code snippet that uses interp2d for interpolation?

SciPy

import numpy as np
from scipy.interpolate import interp2d

x = np.array([0, 1, 2])
y = np.array([0, 1, 2])
z = np.array([[0, 1, 4], [1, 2, 5], [4, 5, 8]])

f = interp2d(x, y, z, kind='linear')
result = f(1.5, 1.5)
print(result[0])

A 6.0

B 5.0

C 5.5

D Error: interp2d deprecated

💡 Hint

Recall that interp2d returns an array even for single points; check the interpolation formula for linear kind.

The interp2d function performs bilinear interpolation. At point (1.5, 1.5), the interpolated value is 5.0. The function returns an array, so we print the first element.

❓ data_output

intermediate

Number of points interpolated with griddata

Given scattered points and values, how many points will be interpolated by the following code using griddata?

SciPy

import numpy as np
from scipy.interpolate import griddata

points = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])
values = np.array([0, 1, 1, 0])
xi = np.array([[0.5, 0.5], [0.2, 0.8], [1.5, 1.5]])

zi = griddata(points, values, xi, method='linear')
print(len(zi))

A 1

B 2

C 3

D Error: xi shape mismatch

💡 Hint

Count how many points are in xi and how griddata handles points outside convex hull.

The input xi has 3 points, so griddata returns 3 interpolated values. Points outside the convex hull get NaN but are still counted.

🔧 Debug

advanced

Identify the error in griddata usage

What error does the following code raise when using griddata?

SciPy

import numpy as np
from scipy.interpolate import griddata

points = np.array([[0, 0], [1, 1]])
values = np.array([1, 2])
xi = np.array([0.5, 0.5])

zi = griddata(points, values, xi, method='nearest')
print(zi)

A TypeError: xi must be 2D array with shape (n, 2)

B ValueError: points and values length mismatch

C IndexError: index out of range

D No error, output: [1. 1.]

💡 Hint

Check the shape of xi; griddata expects a 2D array with each row as a point.

The xi array is 1D with shape (2,), but griddata expects a 2D array with shape (n, 2). This causes a TypeError.

❓ visualization

advanced

Visualizing interpolation results with griddata

Which option correctly describes the plot generated by this code using griddata with cubic interpolation?

SciPy

import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import griddata

points = np.random.rand(10, 2)
values = np.sin(points[:,0]*10) + np.cos(points[:,1]*10)

grid_x, grid_y = np.mgrid[0:1:100j, 0:1:100j]

grid_z = griddata(points, values, (grid_x, grid_y), method='cubic')

plt.imshow(grid_z.T, extent=(0,1,0,1), origin='lower')
plt.scatter(points[:,0], points[:,1], c='red')
plt.title('Cubic interpolation of scattered data')
plt.colorbar()
plt.show()

A A grid of flat colors with sharp edges and no smooth transitions

B A scatter plot of points only, no color gradient

C An error due to incompatible shapes in griddata

D A smooth color gradient surface with red dots marking original points

💡 Hint

Cubic interpolation creates smooth surfaces; red dots show original data points.

The plot shows a smooth color gradient from cubic interpolation with red dots marking the scattered points. This visualizes how interpolation fills the gaps.

🧠 Conceptual

expert

Choosing interpolation method for irregular data

You have irregularly spaced 2D data points with noisy measurements. Which interpolation method is best to estimate values on a regular grid while minimizing oscillations?

A Use <code>griddata</code> with 'linear' method to balance smoothness and noise

B Use <code>interp2d</code> with 'cubic' method for smooth results

C Use <code>griddata</code> with 'nearest' method for smoothness

D Use <code>interp2d</code> with 'nearest' method to avoid oscillations

💡 Hint

Consider how each method handles noise and irregular spacing.

For irregular noisy data, 'linear' method in griddata balances smoothness and noise without introducing oscillations that cubic might cause. Nearest can be too rough.