Interpolation for smoothing data in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of linear interpolation on noisy data

What is the output of the following code snippet that uses linear interpolation to smooth noisy data points?

SciPy

import numpy as np
from scipy.interpolate import interp1d

x = np.array([0, 1, 2, 3, 4])
y = np.array([0, 2, 1, 3, 7])  # noisy data
f = interp1d(x, y, kind='linear')
x_new = np.array([0.5, 1.5, 2.5, 3.5])
y_new = f(x_new)
print(np.round(y_new, 2))

A [1.0 1.5 2.0 5.0]

B [1.0 1.5 2.0 4.0]

C [1.0 1.5 2.0 3.0]

D [0.5 1.5 2.5 3.5]

💡 Hint

Linear interpolation finds values on the straight line between known points.

The function interp1d with kind='linear' calculates values between points by connecting them with straight lines. For example, between x=3 (y=3) and x=4 (y=7), at x=3.5 the value is halfway: (3+7)/2=5.

❓ data_output

intermediate

Number of points after cubic interpolation

Given the code below that uses cubic interpolation to smooth data, how many points are in the resulting interpolated array?

SciPy

import numpy as np
from scipy.interpolate import interp1d

x = np.linspace(0, 10, 6)
y = np.sin(x)
f = interp1d(x, y, kind='cubic')
x_new = np.linspace(0, 10, 50)
y_new = f(x_new)
print(len(y_new))

A 6

B 60

C 44

D 50

💡 Hint

The length of the output matches the length of the new x values.

The interpolated y values correspond to the new x array, which has 50 points, so the output length is 50.

🔧 Debug

advanced

Error type from extrapolation attempt

What error does the following code raise when trying to interpolate a value outside the original data range?

SciPy

import numpy as np
from scipy.interpolate import interp1d

x = np.array([1, 2, 3, 4])
y = np.array([10, 20, 30, 40])
f = interp1d(x, y)
print(f(0))

A IndexError

B KeyError

C ValueError

D TypeError

💡 Hint

By default, interp1d does not allow values outside the input range.

Calling the interpolation function with a value outside the original x range raises a ValueError about extrapolation not being allowed.

🚀 Application

advanced

Choosing interpolation method for smooth curve

You have temperature data recorded hourly and want a smooth curve to estimate temperatures every 10 minutes. Which interpolation method from scipy.interpolate is best for smoothness?

A interp1d with kind='nearest'

B interp1d with kind='cubic'

C interp1d with kind='linear'

D interp1d with kind='zero'

💡 Hint

Smooth curves require higher order interpolation than linear.

Cubic interpolation creates smooth curves by fitting cubic polynomials between points, better for estimating values between hourly data.

🧠 Conceptual

expert

Effect of smoothing spline parameter on data fit

In smoothing spline interpolation using scipy's UnivariateSpline, what is the effect of increasing the smoothing factor 's' on the fitted curve?

A The curve becomes smoother and may deviate more from data points.

B The curve fits the data points exactly with no smoothing.

C The curve becomes more jagged and follows noise closely.

D The curve ignores all data points and becomes a flat line.

💡 Hint

Higher smoothing factor reduces overfitting to noise.

Increasing 's' allows the spline to smooth more, reducing sensitivity to noise but possibly deviating from exact data points.