Spline interpolation in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of cubic spline interpolation at given points

Given the code below using SciPy's CubicSpline, what is the output array printed?

SciPy

import numpy as np
from scipy.interpolate import CubicSpline

x = np.array([0, 1, 2, 3, 4])
y = np.array([0, 1, 0, 1, 0])
cs = CubicSpline(x, y)
print(cs([1.5, 2.5, 3.5]))

A [0.75 0.75 0.25]

B [1.0 0.0 1.0]

C [0.5 0.5 0.5]

D [0.6875 0.6875 0.3125]

💡 Hint

Think about how cubic splines smoothly connect points and evaluate at intermediate x values.

The CubicSpline fits a smooth curve through the points. Evaluating at 1.5, 2.5, and 3.5 gives values close to 0.6875, 0.6875, and 0.3125 respectively.

❓ data_output

intermediate

Number of points in spline evaluation output

Using the following code, how many points are in the output array from the spline evaluation?

SciPy

import numpy as np
from scipy.interpolate import CubicSpline

x = np.linspace(0, 10, 6)
y = np.sin(x)
cs = CubicSpline(x, y)
result = cs(np.linspace(0, 10, 50))
print(len(result))

A 6

B 60

C 50

D 10

💡 Hint

The output length matches the number of points you evaluate the spline at.

The spline is evaluated at 50 points, so the output array length is 50.

🔧 Debug

advanced

Identify the error in spline interpolation code

What error does the following code raise when run?

SciPy

import numpy as np
from scipy.interpolate import CubicSpline

x = np.array([0, 1, 2, 3])
y = np.array([1, 2])
cs = CubicSpline(x, y)

A ValueError: x and y must have the same length

B TypeError: unsupported operand type(s) for +: 'int' and 'str'

C IndexError: index out of range

D No error, code runs successfully

💡 Hint

Check if the input arrays x and y have matching lengths.

CubicSpline requires x and y to have the same length. Here y has length 2 but x has length 4, causing a ValueError.

🧠 Conceptual

advanced

Effect of boundary conditions in spline interpolation

Which boundary condition in CubicSpline ensures that the second derivative at the endpoints is zero (natural spline)?

A bc_type='not-a-knot'

B bc_type='natural'

C bc_type='clamped'

D bc_type='periodic'

💡 Hint

Natural splines have zero curvature at the ends.

The 'natural' boundary condition sets the second derivatives at the endpoints to zero, producing a natural spline.

🚀 Application

expert

Choosing spline type for periodic data

You have temperature data measured hourly over 24 hours and want to interpolate smoothly assuming the temperature at hour 0 equals hour 24. Which CubicSpline boundary condition should you use?

A bc_type='periodic'

B bc_type='natural'

C bc_type='clamped'

D bc_type='not-a-knot'

💡 Hint

Periodic data means the start and end points match in value and derivatives.

The 'periodic' boundary condition enforces that function values and derivatives match at the endpoints, ideal for cyclic data like daily temperature.