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NumPy Tutorial• 6 min read

Vectorized Universal Functions (ufuncs)

Element-wise arithmetic, trigonometry, exponentials, and logarithms

Universal functions (ufuncs) are compiled C functions that execute element-wise operations on ndarrays with zero Python overhead.

Fast Mathematical Transformations

Math ufuncs: np.add, np.subtract, np.multiply, np.divide, np.power, np.sqrt.

Exponential and Logarithmic: np.exp, np.log, np.log2, np.log10.

Trigonometric: np.sin, np.cos, np.tan, np.arctan2.

Comparison: np.greater, np.less, np.equal, np.isclose (safe floating point equality).

Vectorized Sigmoid and Math Pipeline
import numpy as np

# Vectorized raw logit scores
logits = np.array([-2.5, 0.0, 1.2, 4.5])

# Vectorized sigmoid function: 1 / (1 + exp(-x))
probabilities = 1.0 / (1.0 + np.exp(-logits))

print("Raw logits:    ", logits)
print("Probabilities: ", np.round(probabilities, 4))
np.exp executes across all 4 elements simultaneously in compiled C.
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Test Yourself With Exercise

+15 XP

Which NumPy function should you use to test if two floating-point arrays are equal within a numerical tolerance?