import numpy as np

def distance_matrix(X: np.ndarray, Y: np.ndarray):
    # compute the distance matrix between two sets of samples
    x2 = np.sum(X**2, axis=1, keepdims=True)
    y2 = np.sum(Y**2, axis=1, keepdims=True)
    xy = X.dot(Y.T)
    return np.sqrt(x2 - 2 * xy + y2.T)