import numpy as np

def least_square_estimator(X, Y, method = None):
    """
    Compute beta (minimum cost computation)
    --------------------------
    (((X^T)X)^-1)((X^T)Y)
    --------------------------
    X : ndarray, shape(m_number, n_features)

    Y : ndarray, shape(m_number, )
    """
    if method is 'QR':
        """
        ((R^-1)((Q^T)Y)
        """
        R = np.linalg.qr(X)[1]
        return np.dot(np.linalg.inv(R), np.dot(Q.T, Y))

    elif method is 'Cholesky':
        """
        ((L(L^T))^-1)((X^T)Y)
        """
        L = np.linalg.cholesky(np.dot(X.T, X))
        return np.dot(np.linalg.inv(np.dot(L, L.T)), np.dot(X.T, Y))

    elif method is 'SVD':
        """
        (V(D^-1))((U^T)Y)
        """
        u, s, vh = np.linalg.svd(X, full_matrices = True)
        d = np.diag(s)
        u = u[:, :d.shape[0]]
        return np.dot(np.dot(np.dot(vh.T, np.linalg.inv(d)), u.T), Y)
    return np.dot(np.linalg.inv(np.dot(X.T, X)), np.dot(X.T, Y))