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.