Cosine Similarity
~15 mincode completion
Implement cosine_similarity(u, v) that returns the cosine similarity between two 1D vectors.
Examples
Identical vectors: similarity = 1.0
- Input
- cosine_similarity([1, 0], [1, 0])
- Output
- 1
Orthogonal vectors: similarity = 0.0
- Input
- cosine_similarity([1, 0], [0, 1])
- Output
- 0
Parallel vectors (not unit): similarity = 1.0
- Input
- cosine_similarity([1, 1], [3, 3])
- Output
- 1
Hints
Hint 1
gives the magnitude in one call; pick the axis deliberately.
Hint 2
Do not forget to divide by norms. That step is easy to skip.
Requirements
u: 1D NumPy arrayv: 1D NumPy array of the same lengthReturn Scalar cosine similarity in [-1, 1].
Constraints
Allowed library: NumPy only
Time limit: 200 ms, Memory: 64 MB
Where this shows up
~15 min
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Python
import numpy as np
def cosine_similarity(u: np.ndarray, v: np.ndarray) -> float:
"""
Compute cosine similarity between vectors u and v.
Args:
u: 1D NumPy array
v: 1D NumPy array of the same length
Returns:
Scalar cosine similarity in [-1, 1].
"""
# YOUR CODE HERE
pass