Spline interpolation in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the spline interpolation function from scipy.

SciPy

from scipy.interpolate import [1]

Drag options to blanks, or click blank then click option'

AUnivariateSpline

Bspline

Cinterp1d

Dgriddata

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'interp1d' which is for linear or other simple interpolations, not splines.

Using 'spline' which is deprecated in scipy.

Using 'griddata' which is for scattered data interpolation.

The UnivariateSpline function from scipy.interpolate is used for spline interpolation of 1D data.

2fill in blank

medium

Complete the code to create a spline interpolation object for given x and y data.

SciPy

spline = UnivariateSpline(x, [1])

Drag options to blanks, or click blank then click option'

Az

Bw

Ct

Dy

Attempts:

3 left

💡 Hint

Common Mistakes

Passing unrelated variables instead of y data.

Confusing x and y variables.

The UnivariateSpline function takes the x and y data points to create the spline.

3fill in blank

hard

Fix the error in the code to evaluate the spline at new points.

SciPy

y_new = spline([1])

Drag options to blanks, or click blank then click option'

Ax

Bx_new

Cy_new

Dnew_x

Attempts:

3 left

💡 Hint

Common Mistakes

Passing the original x or y data instead of new points.

Using undefined variables.

To evaluate the spline, pass the new x-values where you want predictions, usually stored in x_new.

4fill in blank

hard

Fill both blanks to create a dictionary of squared errors for points where y is greater than 0.

SciPy

errors = {x: (y - spline(x))[1]2 for x, y in zip(x_vals, y_vals) if y [2] 0}

Drag options to blanks, or click blank then click option'

A**

B>

C<

D*

Attempts:

3 left

💡 Hint

Common Mistakes

Using multiplication instead of power for squaring.

Using wrong comparison operators.

The squared error is calculated using the power operator **. The condition filters points where y is greater than zero using >.

5fill in blank

hard

Fill all three blanks to create a dictionary of absolute errors for points where y is less than 5.

SciPy

abs_errors = [1]: abs([2] - spline([1])) for [1] , [2] in zip(x_vals, y_vals) if [2] [3] 5}

Drag options to blanks, or click blank then click option'

Ax

By

C<

D>

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing up x and y in the dictionary comprehension.

Using wrong comparison operators.

The dictionary keys are the x values. The absolute error is the absolute difference between y and the spline evaluated at x. The condition filters points where y is less than 5 using <.

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