Implementation functions of Linear Algebra

linalg_funcs.py

import numpy as np


__all__ = ['get_cos_sim', 'apply_svd']


def get_cos_sim(v1:np.ndarray, v2:np.ndarray) -> np.float64:
    cos_sim = np.dot(v1, v2) / (np.linalg.norm(v1) * np.linalg.norm(v2))
    return cos_sim


def apply_svd(matrix:np.ndarray, k:int) -> tuple:
    """
    Args:
        matrix (np.ndarray): shape (m, n)
        k (int): Number of latent features
        
    Returns:
        tuple: U(m, k), Sigma(k, k), VT(k, n)
    """
    U, Sigma, VT = np.linalg.svd(matrix)  # Current shape: U(m, m), Sigma(n,), VT(n, n)
    
    U_truncated = U[:, :k]                # Shape: (m, k)
    Sigma_truncated = np.diag(Sigma[:k])  # Shape: (k, k)
    VT_truncated = VT[:k]                 # Shape: (k, n)
    
    return U_truncated, Sigma_truncated, VT_truncated