Cosine Similarity

Cosine similarity compares the direction of two vectors and ignores their length. Semantic search uses it to find texts with similar embeddings:

cos(a, b) = (a · b) / (|a| × |b|), where |a| = √(a₁² + a₂² + … + aₙ²)

The result is 1 for the same direction, 0 for perpendicular vectors and -1 for opposite directions. If either vector is all zeros, return 0.

Implement cosine_similarity(a, b).

Input

a, b: Two lists of numbers with the same length.

Output

Return the cosine similarity as a decimal number.

सीमाएँ

1 ≤ length ≤ 1,000

-1,000 ≤ each value ≤ 1,000

उदाहरण

इनपुट:
a = [1.0, 0.0]
b = [0.0, 1.0]

अपेक्षित आउटपुट:
expected = 0.0

इनपुट:
std::vector<double> a = {1.0, 0.0};
std::vector<double> b = {0.0, 1.0};

अपेक्षित आउटपुट:
double expected = 0.0;

इनपुट:
double[] a = new double[] {1.0, 0.0};
double[] b = new double[] {0.0, 1.0};

अपेक्षित आउटपुट:
double expected = 0.0;

इनपुट:
a = [1.0, 2.0, 3.0]
b = [2.0, 4.0, 6.0]

अपेक्षित आउटपुट:
expected = 1.0

इनपुट:
std::vector<double> a = {1.0, 2.0, 3.0};
std::vector<double> b = {2.0, 4.0, 6.0};

अपेक्षित आउटपुट:
double expected = 1.0;

इनपुट:
double[] a = new double[] {1.0, 2.0, 3.0};
double[] b = new double[] {2.0, 4.0, 6.0};

अपेक्षित आउटपुट:
double expected = 1.0;

संदर्भ

यह चुनौती CodeUtility के लिए अनुकूलित की गई है। ऊपर दिए गए स्टेटमेंट और सीमाओं का पालन करें।

• scikit-learn, Cosine similarity
• Goodfellow, Bengio and Courville, Deep Learning