NumPy with SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of SciPy's integration with NumPy arrays

What is the output of the following code that uses SciPy to integrate a NumPy function over a range?

NumPy

import numpy as np
from scipy.integrate import quad

f = lambda x: np.sin(x)
result, error = quad(f, 0, np.pi)
print(round(result, 5))

A 2.0

B 3.14159

C 0.0

D 1.99999

💡 Hint

Recall the integral of sin(x) from 0 to pi is 2.

The integral of sin(x) from 0 to pi is exactly 2. The quad function returns 2.0, which rounds to 2.0.

❓ data_output

intermediate

Shape of output from SciPy's hierarchical clustering

Given the following code using SciPy's hierarchical clustering on a NumPy array, what is the shape of the linkage matrix returned?

NumPy

import numpy as np
from scipy.cluster.hierarchy import linkage

X = np.array([[1, 2], [3, 4], [5, 6], [7, 8]])
Z = linkage(X, method='single')
print(Z.shape)

A (4, 3)

B (3, 3)

C (4, 4)

D (3, 4)

💡 Hint

The linkage matrix has n-1 rows and 4 columns for n samples.

For n samples, the linkage matrix has n-1 rows and 4 columns. Here n=4, so shape is (3,4).

❓ visualization

advanced

Correct dendrogram plot from hierarchical clustering

Which option shows the correct code to plot a dendrogram from a linkage matrix Z using SciPy and Matplotlib?

NumPy

import numpy as np
from scipy.cluster.hierarchy import linkage, dendrogram
import matplotlib.pyplot as plt

X = np.random.rand(5, 2)
Z = linkage(X, 'ward')

A

plt.dendrogram(Z)
plt.show()

B

plt.plot(dendrogram(Z))
plt.show()

C

dendrogram(Z)
plt.show()

D

dendrogram(X)
plt.show()

💡 Hint

The dendrogram function is from scipy.cluster.hierarchy, not matplotlib.

The dendrogram function is imported from scipy.cluster.hierarchy and called with the linkage matrix Z. Then plt.show() displays the plot.

🧠 Conceptual

advanced

Understanding output of SciPy's fftpack with NumPy arrays

What does the output array represent when applying SciPy's fftpack.fft function to a NumPy array of real numbers?

A The sorted input array in ascending order

B The frequency components of the input signal as complex numbers

C The cumulative sum of the input array elements

D The inverse Fourier transform of the input array

💡 Hint

FFT transforms a signal from time domain to frequency domain.

The fft function computes the discrete Fourier transform, returning complex numbers representing amplitude and phase of frequency components.

🔧 Debug

expert

Identify the error in SciPy optimization with NumPy function

What error will the following code raise when trying to minimize a function using SciPy's optimize.minimize with a NumPy array input?

NumPy

import numpy as np
from scipy.optimize import minimize

def f(x):
    return np.sum(x**2)

x0 = np.array([1, 2, 3])
res = minimize(f, x0, method='BFGS', jac=True)
print(res.fun)

A TypeError: The 'jac' parameter is True but the function does not return a gradient

B ValueError: jacobian function must return array_like

C TypeError: 'bool' object is not callable

D TypeError: f() missing 1 required positional argument

💡 Hint

The jac parameter expects a function or False, not True, unless the function returns gradient.

Setting jac=True tells minimize that the function returns both value and gradient, but f returns only value, causing a TypeError.

Practice

1. What is the main benefit of using SciPy together with NumPy?

easy

A. SciPy replaces NumPy for basic array operations.

B. SciPy provides extra math functions that NumPy does not have.

C. SciPy is used only for plotting graphs.

D. SciPy is a database for storing NumPy arrays.

Solution

1. Step 1: Understand NumPy's role

   NumPy is mainly for fast array operations and basic math.

2. Step 2: Understand SciPy's role

   SciPy adds many advanced math and scientific functions on top of NumPy.

3. Final Answer:

   SciPy provides extra math functions that NumPy does not have. -> Option B

4. Quick Check:

   Extra math tools = SciPy [OK]

Hint: SciPy adds advanced math tools beyond NumPy basics [OK]

Common Mistakes:

• Thinking SciPy replaces NumPy
• Confusing SciPy with plotting libraries
• Believing SciPy stores data like a database

2. Which of the following is the correct way to import the SciPy stats module alongside NumPy?

easy

A. import numpy as np; import scipy.stats as stats

B. import numpy; import scipy.stats

C. from numpy import stats; import scipy

D. import numpy.stats; import scipy as sp

Solution

1. Step 1: Check standard import conventions

   NumPy is usually imported as np, SciPy submodules like stats as stats or sp.stats.

2. Step 2: Validate each option

   import numpy as np; import scipy.stats as stats uses correct aliases and imports the stats submodule properly.

3. Final Answer:

   import numpy as np; import scipy.stats as stats -> Option A

4. Quick Check:

   Standard imports = import numpy as np; import scipy.stats as stats [OK]

Hint: Use 'import numpy as np' and 'import scipy.stats as stats' [OK]

Common Mistakes:

• Importing non-existent numpy.stats
• Using wrong aliases or missing 'as'
• Importing whole scipy without submodule

3. What is the output of this code?

import numpy as np
from scipy import stats
arr = np.array([1, 2, 2, 3, 4])
mode_result = stats.mode(arr)
print(mode_result.mode[0])

medium

A. 1

B. 4

C. 3

D. 2

Solution

1. Step 1: Understand the array values

   The array is [1, 2, 2, 3, 4], where 2 appears twice, others once.

2. Step 2: Understand stats.mode function

   stats.mode returns the most frequent value; here it is 2.

3. Final Answer:

   2 -> Option D

4. Quick Check:

   Most frequent value = 2 [OK]

Hint: Mode is the most frequent number in the array [OK]

Common Mistakes:

• Confusing mode with mean or median
• Not accessing mode_result.mode[0]
• Assuming first element is mode

4. Find the error in this code snippet:

import numpy as np
from scipy import stats
arr = np.array([1, 2, 3, 4])
mode_result = stats.mode(arr)
print(mode_result[0])

medium

A. mode_result is an object; correct access is mode_result.mode, not mode_result[0].

B. stats.mode returns a tuple, so indexing with [0] is correct.

C. The array must be a list, not a NumPy array.

D. Missing import for numpy as np.

Solution

1. Step 1: Check stats.mode return type

   stats.mode returns an object with attributes like mode and count, not a tuple.

2. Step 2: Identify correct attribute access

   Access the mode value with mode_result.mode, not by indexing mode_result[0].

3. Final Answer:

   mode_result is an object; correct access is mode_result.mode, not mode_result[0]. -> Option A

4. Quick Check:

   Use .mode attribute, not [0] index [OK]

Hint: Use .mode attribute to get mode, not indexing [OK]

Common Mistakes:

• Using indexing instead of attribute access
• Confusing return type as tuple
• Thinking array must be list

5. You have two NumPy arrays:

import numpy as np
from scipy import stats
arr1 = np.array([1, 2, 2, 3])
arr2 = np.array([2, 2, 3, 4])

How can you find the combined mode of all elements from both arrays using SciPy?

hard

A. Use stats.mode(arr1 + arr2)

B. Use stats.mode(arr1 * arr2)

C. Use stats.mode(np.concatenate((arr1, arr2)))

D. Use stats.mode(arr1) and stats.mode(arr2) separately and pick the higher

Solution

1. Step 1: Combine both arrays

   Use np.concatenate to join arr1 and arr2 into one array.

2. Step 2: Apply stats.mode on combined array

   Passing the combined array to stats.mode finds the overall mode.

3. Final Answer:

   Use stats.mode(np.concatenate((arr1, arr2))) -> Option C

4. Quick Check:

   Combine arrays first, then mode [OK]

Hint: Join arrays with concatenate before finding mode [OK]

Common Mistakes:

• Adding or multiplying arrays instead of concatenating
• Finding modes separately and comparing manually
• Not combining arrays before mode