Spline interpolation in SciPy - Mini Project: Build & Apply

Spline interpolation

📖 Scenario: You have some data points from a sensor measuring temperature at different times. The data is not smooth, and you want to estimate the temperature at times between the measurements smoothly.

🎯 Goal: You will create a spline interpolation to estimate temperature values at new time points smoothly using scipy.

📋 What You'll Learn

Create a dictionary with exact time and temperature data points

Create a variable for new time points to estimate temperature

Use scipy.interpolate.make_interp_spline to create a spline interpolation

Calculate interpolated temperature values at new time points

Print the interpolated temperature values

💡 Why This Matters

🌍 Real World

Spline interpolation is used in sensor data smoothing, animation paths, and estimating missing data points in many fields like weather forecasting and engineering.

💼 Career

Data scientists and engineers use spline interpolation to create smooth models from discrete data, improving predictions and visualizations.

1

Create the original data points

Create a dictionary called data_points with these exact entries: 1: 15.0, 2: 18.5, 3: 21.0, 4: 19.5, 5: 22.0 representing time in hours and temperature in Celsius.

SciPy

# Create the dictionary data_points with exact time and temperature values
# Your code here

Hint

Use curly braces to create a dictionary with keys as time and values as temperature.

2

Create new time points for interpolation

Create a list called new_times with these exact values: [1.5, 2.5, 3.5, 4.5] representing the times where you want to estimate temperature.

SciPy

data_points = {1: 15.0, 2: 18.5, 3: 21.0, 4: 19.5, 5: 22.0}
# Create the list new_times with exact values
# Your code here

Hint

Use square brackets to create a list with the exact values.

3

Create spline interpolation and calculate new values

Import make_interp_spline from scipy.interpolate. Create variables times and temps from data_points keys and values. Use make_interp_spline(times, temps) to create a spline called spline. Calculate interpolated temperatures at new_times and store in interpolated_temps.

SciPy

data_points = {1: 15.0, 2: 18.5, 3: 21.0, 4: 19.5, 5: 22.0}
new_times = [1.5, 2.5, 3.5, 4.5]
# Import make_interp_spline and create spline interpolation
# Your code here

Hint

Use list() to get keys and values from the dictionary. Then create spline and call it with new times.

4

Print the interpolated temperature values

Write a print statement to display the variable interpolated_temps.

SciPy

from scipy.interpolate import make_interp_spline

data_points = {1: 15.0, 2: 18.5, 3: 21.0, 4: 19.5, 5: 22.0}
new_times = [1.5, 2.5, 3.5, 4.5]

times = list(data_points.keys())
temps = list(data_points.values())

spline = make_interp_spline(times, temps)
interpolated_temps = spline(new_times)
# Print the interpolated_temps variable
# Your code here

Hint

Use print(interpolated_temps) to show the result.

Practice

1. What is the main purpose of spline interpolation in data science?

easy

A. To calculate the mean of data points

B. To sort data points in ascending order

C. To create a smooth curve that passes through given data points

D. To remove outliers from data

Solution

1. Step 1: Understand spline interpolation

   Spline interpolation fits a smooth curve through known data points to estimate values between them.

2. Step 2: Compare options with definition

   Only To create a smooth curve that passes through given data points describes creating a smooth curve through data points, which matches spline interpolation.

3. Final Answer:

   To create a smooth curve that passes through given data points -> Option C

4. Quick Check:

   Spline interpolation = smooth curve through points [OK]

Hint: Spline interpolation = smooth curve fitting through points [OK]

Common Mistakes:

• Confusing interpolation with sorting
• Thinking it removes outliers
• Mixing interpolation with averaging

2. Which of the following is the correct way to import the spline interpolation function from scipy?

easy

A. import scipy.spline as make_interp_spline

B. from scipy.interpolate import make_interp_spline

C. from scipy import spline_interpolation

D. import make_interp_spline from scipy.interpolate

Solution

1. Step 1: Recall correct import syntax

   The function make_interp_spline is in scipy.interpolate and imported using 'from scipy.interpolate import make_interp_spline'.

2. Step 2: Check each option

   'from scipy.interpolate import make_interp_spline' matches the correct syntax. The other options use invalid import statements.

3. Final Answer:

   from scipy.interpolate import make_interp_spline -> Option B

4. Quick Check:

   Correct import syntax = from scipy.interpolate import make_interp_spline [OK]

Hint: Use 'from scipy.interpolate import make_interp_spline' [OK]

Common Mistakes:

• Using incorrect import keywords
• Trying to import non-existent modules
• Wrong order of import statement

3. What will be the output of the following code snippet?

import numpy as np
from scipy.interpolate import make_interp_spline

x = np.array([0, 1, 2, 3])
y = np.array([0, 1, 4, 9])
spline = make_interp_spline(x, y)
x_new = np.array([1.5, 2.5])
y_new = spline(x_new)
print(np.round(y_new, 2))

medium

A. [2.25 6.25]

B. [1.5 2.5]

C. [3.0 5.0]

D. [1.75 3.75]

Solution

1. Step 1: Understand the input data and spline creation

   x and y define points (0,0), (1,1), (2,4), (3,9). The spline fits a smooth curve through these points.

2. Step 2: Calculate spline values at x_new points

   At x=1.5, y is close to 2.25 (between 1 and 4). At x=2.5, y is close to 6.25 (between 4 and 9). Rounded values are [2.25, 6.25].

3. Final Answer:

   [2.25 6.25] -> Option A

4. Quick Check:

   Spline interpolation at 1.5 and 2.5 = [2.25 6.25] [OK]

Hint: Spline smooths between points; expect values between neighbors [OK]

Common Mistakes:

• Assuming linear interpolation instead of spline
• Not rounding output
• Confusing input and output arrays

4. Identify the error in the following code snippet for spline interpolation:

import numpy as np
from scipy.interpolate import make_interp_spline

x = np.array([0, 1, 2])
y = np.array([0, 1, 4, 9])
spline = make_interp_spline(x, y)
print(spline(1.5))

medium

A. x and y arrays have different lengths

B. make_interp_spline is not imported correctly

C. x array contains non-numeric values

D. spline function cannot take float inputs

Solution

1. Step 1: Check array lengths

   x has length 3, y has length 4. For spline interpolation, x and y must have the same length.

2. Step 2: Verify other parts

   Import is correct, x contains numeric values, and spline accepts float inputs. So, only length mismatch is error.

3. Final Answer:

   x and y arrays have different lengths -> Option A

4. Quick Check:

   Array length mismatch = x and y arrays have different lengths [OK]

Hint: Check x and y lengths match before spline creation [OK]

Common Mistakes:

• Ignoring length mismatch error
• Assuming spline can't take floats
• Misreading import statements

5. You have noisy temperature data recorded hourly: x = [0, 1, 2, 3, 4] and y = [15, 14, 16, 15, 17]. You want a smooth curve to estimate temperature every 0.5 hour. Which approach using scipy spline interpolation is best?

hard

A. Use make_interp_spline but only evaluate at original points

B. Use linear interpolation instead of spline for smoothness

C. Use spline interpolation but with reversed x and y arrays

D. Use make_interp_spline with x and y, then evaluate at new points with 0.5 increments

Solution

1. Step 1: Understand the goal

   We want a smooth curve estimating temperature every 0.5 hour, so we need interpolation at finer points.

2. Step 2: Choose correct method

   make_interp_spline fits a smooth curve through given points. Evaluating it at 0.5 increments gives smooth estimates. Linear interpolation is less smooth. Evaluating only at original points gives no new info. Reversing arrays is incorrect.

3. Final Answer:

   Use make_interp_spline with x and y, then evaluate at new points with 0.5 increments -> Option D

4. Quick Check:

   Spline + finer evaluation points = smooth estimates [OK]

Hint: Fit spline on data, evaluate at desired finer points [OK]

Common Mistakes:

• Using linear interpolation for smoothness
• Not evaluating spline at new points
• Reversing data arrays unnecessarily