Implement Cosine Similarity

Linear Algebra

Easy

Compute the cosine similarity between two vectors:

\operatorname{cosine}(a,b) = \frac{a \cdot b}{\lVert a \rVert_2 \, \lVert b \rVert_2}

Here, $a \cdot b$ is the dot product and $\lVert a \rVert_2$ and $\lVert b \rVert_2$ are Euclidean norms. For this problem, return 0.0 when either vector has zero norm. Otherwise, return the similarity as a Python float.

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Examples

Input: a = [1, 2, 3], b = [2, 4, 6]

Output: 1.0

Explanation: One vector is a positive multiple of the other, so they point in the same direction.

Input: a = [1, 0], b = [0, 1]

Output: 0.0

Hint 1

Use np.dot(a, b) for the numerator.

Hint 2

Use np.linalg.norm() on both vectors before dividing.

Requirements

Compute the dot product and both Euclidean norms with NumPy
Return 0.0 when either vector has zero norm
Return a Python float

Constraints

a and b are equal-length, nonempty one-dimensional numeric lists
Each vector contains at most $10^6$ values
Use NumPy only

Try Similar Problems

Dot Product Euclidean Distance Manhattan Distance Jaccard Similarity Cosine Embedding Loss

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