Simpson's rule (simpson) in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the Simpson's rule function from scipy.integrate.

SciPy

from scipy.integrate import [1]

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

Asimpson

Bquad

Cromb

Dtrapz

Attempts:

3 left

💡 Hint

Common Mistakes

Importing trapz instead of simpson.

Using quad which is for adaptive quadrature, not Simpson's rule.

The simpson function is imported from scipy.integrate to perform numerical integration using Simpson's rule.

2fill in blank

medium

Complete the code to calculate the integral of y over x using Simpson's rule.

SciPy

result = simpson(y, [1])

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

Arange

Bdx

Caxis

Dx

Attempts:

3 left

💡 Hint

Common Mistakes

Passing dx instead of x array.

Using axis which is a keyword argument, not positional here.

The second argument to simpson is the x values over which y is sampled.

3fill in blank

hard

Fix the error in the code to correctly compute the integral with simpson when y is a 2D array along axis 0.

SciPy

integral = simpson(y, x, axis=[1])

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

A1

B-1

C0

D2

Attempts:

3 left

💡 Hint

Common Mistakes

Using axis=1 which integrates along columns instead.

Using axis=-1 which is last axis, not axis 0.

When y is 2D and integration is along axis 0, axis=0 must be specified.

4fill in blank

hard

Fill both blanks to create a dictionary comprehension that maps each word to its length only if the length is greater than 3.

SciPy

lengths = {word: [1] for word in words if [2]

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

Alen(word)

Blen(word) > 3

Cword

Dword > 3

Attempts:

3 left

💡 Hint

Common Mistakes

Using word instead of len(word) for the value.

Using word > 3 which compares string to int.

The dictionary comprehension maps word to its length (len(word)) and filters words with length > 3.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps uppercase words to their values only if the value is positive.

SciPy

result = [1]: [2] for [3] in data.items() if [2] > 0}

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

Ak.upper()

Bv

Ck, v

Ditem

Attempts:

3 left

💡 Hint

Common Mistakes

Using item instead of k, v in the loop.

Not converting keys to uppercase.

The comprehension maps uppercase keys (k.upper()) to values (v) for key-value pairs (k, v) where value is positive.

Practice

1. What is the main purpose of Simpson's rule in data science?

easy

A. To find the maximum value in a dataset

B. To estimate the area under a curve using parabolas

C. To sort data points in ascending order

D. To calculate the mean of a list of numbers

Solution

1. Step 1: Understand the goal of Simpson's rule

   Simpson's rule is a numerical method used to estimate the area under a curve by approximating the curve with parabolas between points.

2. Step 2: Compare options with this goal

   Only To estimate the area under a curve using parabolas describes this purpose correctly. Other options describe unrelated tasks.

3. Final Answer:

   To estimate the area under a curve using parabolas -> Option B

4. Quick Check:

   Simpson's rule = area estimation [OK]

Hint: Simpson's rule estimates area under curves using parabolas [OK]

Common Mistakes:

• Confusing Simpson's rule with sorting or averaging
• Thinking it finds max or min values
• Assuming it requires a formula for the curve

2. Which of the following is the correct way to import the Simpson's rule function from scipy for numerical integration?

easy

A. from scipy.integrate import simpson

B. import scipy.simpson

C. from scipy import simpson

D. import simpson from scipy.integrate

Solution

1. Step 1: Recall the correct import syntax for functions in scipy

   Functions like simpson are in the integrate module, so the correct import is from scipy.integrate import simpson.

2. Step 2: Check each option

   from scipy.integrate import simpson matches the correct syntax. Options A, B, and D are incorrect. import simpson from scipy.integrate uses wrong import order.

3. Final Answer:

   from scipy.integrate import simpson -> Option A

4. Quick Check:

   Correct import = from scipy.integrate import simpson [OK]

Hint: Import simpson from scipy.integrate module [OK]

Common Mistakes:

• Trying to import simpson directly from scipy
• Using wrong import syntax order
• Assuming simpson is a standalone package

3. What is the output of the following code?

from scipy.integrate import simpson
import numpy as np
x = np.array([0, 1, 2, 3, 4])
y = np.array([0, 1, 4, 9, 16])
result = simpson(y, x)
print(round(result, 2))

medium

A. 22.67

B. 18.00

C. 20.00

D. 21.33

Solution

1. Step 1: Understand the data points and function

   x values are [0,1,2,3,4], y values are squares of x: [0,1,4,9,16]. Simpson's rule estimates the integral of y with respect to x.

2. Step 2: Calculate the integral using simpson

   Using scipy's simpson function on these points gives exactly 21.3333. Rounded to two decimals, it is 21.33.

3. Final Answer:

   21.33 -> Option D

4. Quick Check:

   Simpson integral ≈ 21.33 [OK]

Hint: Use simpson(y, x) and round result for quick check [OK]

Common Mistakes:

• Forgetting to provide x values to simpson
• Rounding incorrectly or too early
• Confusing simpson with trapezoidal rule

4. Identify the error in this code snippet using Simpson's rule:

from scipy.integrate import simpson
import numpy as np
x = np.array([0, 1, 2, 3])
y = np.array([1, 4, 9])
result = simpson(y, x)
print(result)

medium

A. x and y arrays have different lengths

B. simpson function is not imported correctly

C. x array must be sorted in descending order

D. y array contains non-numeric values

Solution

1. Step 1: Check array lengths

   x has 4 elements, y has 3 elements. Simpson's rule requires x and y to have the same length.

2. Step 2: Verify other options

   Import is correct, x order is fine, y contains numeric values. So only length mismatch is the error.

3. Final Answer:

   x and y arrays have different lengths -> Option A

4. Quick Check:

   Length mismatch error = x and y arrays have different lengths [OK]

Hint: Check x and y array lengths match before integration [OK]

Common Mistakes:

• Ignoring length mismatch causing runtime error
• Assuming simpson auto-corrects array sizes
• Thinking x must be descending

5. You have noisy sensor data sampled unevenly over time:

time = [0, 0.5, 1.5, 2.2, 3.8]
values = [2, 3, 5, 4, 6]

How can you use Simpson's rule to estimate the total area under the sensor curve? Choose the best approach.

hard

A. Interpolate values to evenly spaced points, then use simpson without x

B. Use simpson(values) without x, ignoring time points

C. Use simpson(values, time) directly to integrate over uneven intervals

D. Sum values and multiply by average time interval

Solution

1. Step 1: Understand uneven sampling

   Time points are unevenly spaced, so integration must consider x values explicitly.

2. Step 2: Apply simpson with x values

   Passing values and time arrays to simpson allows correct numerical integration over uneven intervals.

3. Step 3: Evaluate other options

   Interpolating or ignoring x loses accuracy; summing values times average interval is a rough estimate, not Simpson's rule.

4. Final Answer:

   Use simpson(values, time) directly to integrate over uneven intervals -> Option C

5. Quick Check:

   Simpson with x for uneven data = Use simpson(values, time) directly to integrate over uneven intervals [OK]

Hint: Always provide x for unevenly spaced data in simpson [OK]

Common Mistakes:

• Ignoring uneven spacing and skipping x parameter
• Using interpolation unnecessarily
• Using simple sum times average interval instead of integration