Universal functions (ufuncs) in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of numpy ufunc with broadcasting

What is the output of this code snippet using numpy universal functions and broadcasting?

NumPy

import numpy as np
arr1 = np.array([1, 2, 3])
arr2 = np.array([[1], [2], [3]])
result = np.add(arr1, arr2)
print(result)

A

[[2 3 4]
 [3 4 5]
 [4 5 6]]

B

[[2 3 4]
 [3 4 5]
 [4 5 5]]

C

[[2 3 4]
 [3 4 5]
 [4 5 7]]

D

[[2 3 4]
 [3 5 6]
 [4 6 7]]

💡 Hint

Remember numpy broadcasts arrays to compatible shapes before applying ufuncs.

The array arr1 has shape (3,) and arr2 has shape (3,1). Broadcasting expands arr1 to (3,3) by repeating its row, and arr2 to (3,3) by repeating its column. Adding element-wise results in [[1+1,2+1,3+1],[1+2,2+2,3+2],[1+3,2+3,3+3]] = [[2,3,4],[3,4,5],[4,5,6]].

❓ data_output

intermediate

Result of numpy sqrt ufunc on negative values

What is the output array when applying numpy.sqrt to this array containing negative values?

NumPy

import numpy as np
arr = np.array([4, 9, -1, 16])
result = np.sqrt(arr)
print(result)

A [2. 3. -1. 4.]

B [2. 3. 1. 4.]

C [2. 3. nan 4.]

D [2. 3. 0. 4.]

💡 Hint

Square root of negative numbers is not defined in real numbers, numpy returns nan with a warning.

Numpy sqrt returns nan for negative inputs and issues a runtime warning. So sqrt(-1) is nan, while sqrt(4), sqrt(9), sqrt(16) are 2, 3, 4 respectively.

❓ visualization

advanced

Visualizing numpy ufunc output with vectorize

Which plot correctly shows the output of applying a numpy ufunc to a range of values using np.vectorize?

NumPy

import numpy as np
import matplotlib.pyplot as plt

def custom_func(x):
    return np.sin(x) if x >= 0 else 0

vec_func = np.vectorize(custom_func)
x = np.linspace(-np.pi, np.pi, 100)
y = vec_func(x)
plt.plot(x, y)
plt.title('Custom function output')
plt.show()

A A sine wave mirrored about y-axis

B A full sine wave from -pi to pi

C A flat line at zero

D A plot showing sine wave only for x >= 0 and zero for x < 0

💡 Hint

The function returns sine only for non-negative x, zero otherwise.

The vectorized function applies the condition element-wise. For negative x values, output is zero, for non-negative x, output is sine(x). The plot shows half sine wave starting at zero and zero on the negative side.

🧠 Conceptual

advanced

Understanding numpy ufunc reduce method

What is the output of this code using numpy's ufunc reduce method?

NumPy

import numpy as np
arr = np.array([1, 2, 3, 4])
result = np.add.reduce(arr)
print(result)

A [1 3 6 10]

B 10

C 24

D [1 2 3 4]

💡 Hint

ufunc reduce applies the operation cumulatively to the array elements.

np.add.reduce sums all elements of the array: 1+2+3+4 = 10.

🔧 Debug

expert

Identify the error in this numpy ufunc usage

What error does this code raise when applying numpy's power ufunc with incompatible shapes?

NumPy

import numpy as np
base = np.array([1, 2, 3])
exponent = np.array([[1, 2], [3, 4]])
result = np.power(base, exponent)
print(result)

A ValueError: operands could not be broadcast together with shapes (3,) (2,2)

B No error, outputs a 2x3 array

C IndexError: index out of bounds

D TypeError: unsupported operand type(s) for ** or pow()

💡 Hint

Check if the shapes of base and exponent arrays can be broadcast together.

The base array has shape (3,) and exponent has shape (2,2). These shapes are not compatible for broadcasting, so numpy raises a ValueError about broadcasting.

Practice

1. What is the main purpose of NumPy universal functions (ufuncs)?

easy

A. To convert arrays into lists

B. To perform element-wise operations on arrays efficiently

C. To sort arrays in ascending order

D. To create new arrays from scratch

Solution

1. Step 1: Understand what ufuncs do

   Ufuncs apply mathematical operations element-wise on arrays, making calculations fast and simple.

2. Step 2: Compare with other options

   Creating arrays, sorting, or converting to lists are not the main roles of ufuncs.

3. Final Answer:

   To perform element-wise operations on arrays efficiently -> Option B

4. Quick Check:

   Ufuncs = element-wise fast operations [OK]

Hint: Remember: ufuncs work element-wise on arrays fast [OK]

Common Mistakes:

• Confusing ufuncs with array creation functions
• Thinking ufuncs sort arrays
• Assuming ufuncs convert arrays to lists

2. Which of the following is the correct syntax to use the NumPy universal function for square root on array arr?

easy

A. np.sqrt(arr)

B. np.square(arr)

C. np.root(arr)

D. np.sqrt_of(arr)

Solution

1. Step 1: Identify the correct ufunc for square root

   The NumPy function for square root is np.sqrt().

2. Step 2: Check the syntax with the array

   Calling np.sqrt(arr) applies square root element-wise on arr.

3. Final Answer:

   np.sqrt(arr) -> Option A

4. Quick Check:

   Square root ufunc = np.sqrt() [OK]

Hint: Square root ufunc is always np.sqrt(array) [OK]

Common Mistakes:

• Using np.square instead of np.sqrt
• Trying non-existent functions like np.root
• Adding extra words in function name

3. What is the output of the following code?

import numpy as np
arr = np.array([1, 4, 9, 16])
result = np.sqrt(arr)
print(result)

medium

A. [1. 2. 3. 4.]

B. [1 2 3 4]

C. [1. 4. 9. 16.]

D. [0. 2. 3. 4.]

Solution

1. Step 1: Understand np.sqrt on array elements

   Applying np.sqrt on each element: sqrt(1)=1.0, sqrt(4)=2.0, sqrt(9)=3.0, sqrt(16)=4.0.

2. Step 2: Check output format

   NumPy returns floats for sqrt, so output is [1. 2. 3. 4.].

3. Final Answer:

   [1. 2. 3. 4.] -> Option A

4. Quick Check:

   np.sqrt([1,4,9,16]) = [1. 2. 3. 4.] [OK]

Hint: Square root returns floats, watch decimal points [OK]

Common Mistakes:

• Expecting integer output instead of float
• Confusing np.sqrt with np.square
• Misreading array output format

4. The following code throws an error. What is the problem?

import numpy as np
arr = np.array([1, 2, 3])
result = np.add(arr, 5, 10)
print(result)

medium

A. np.add cannot add a scalar to an array

B. The array must be of float type for np.add

C. np.add takes only two arguments, but three were given

D. The print statement is incorrect

Solution

1. Step 1: Check np.add function signature

   np.add takes exactly two arguments: two arrays or an array and a scalar.

2. Step 2: Identify the error in arguments

   Here, three arguments are passed: arr, 5, and 10, which is invalid.

3. Final Answer:

   np.add takes only two arguments, but three were given -> Option C

4. Quick Check:

   np.add = 2 args only [OK]

Hint: np.add needs exactly two inputs, no extras [OK]

Common Mistakes:

• Passing more than two arguments to np.add
• Thinking np.add requires float arrays
• Blaming print instead of function call

5. You have two arrays:

a = np.array([1, 2, 3])
b = np.array([4, 5, 6])

Which code correctly computes the element-wise product and then applies the square root to each product?

hard

A. np.multiply(a, b) + np.sqrt(a)

B. np.multiply(np.sqrt(a), np.sqrt(b))

C. np.sqrt(a) * np.sqrt(b)

D. np.sqrt(np.multiply(a, b))

Solution

1. Step 1: Understand element-wise product and sqrt

   First multiply elements of a and b, then apply square root on the result.

2. Step 2: Check each option

   np.sqrt(np.multiply(a, b)) does np.multiply(a, b) then np.sqrt(), which is correct. Options B and C apply sqrt before multiply, which is different. np.multiply(a, b) + np.sqrt(a) adds sqrt(a), which is incorrect.

3. Final Answer:

   np.sqrt(np.multiply(a, b)) -> Option D

4. Quick Check:

   Multiply then sqrt = np.sqrt(np.multiply(a,b)) [OK]

Hint: Multiply first, then sqrt for correct order [OK]

Common Mistakes:

• Applying sqrt before multiplication
• Adding instead of multiplying
• Mixing order of operations