import numpy as np


def construct_gram_matrix(distance_matrix):
    # M_ij = (D_1j^2 + D_i1^2 - D_ij^2) / 2
    row, col = distance_matrix.shape
    gram = np.zeros([row, col])
    for i in range(row):
        for j in range(col):
            gram[i][j] = 0.5 * (
                    (distance_matrix[0][j]) ** 2 + (distance_matrix[i][0]) ** 2 - (distance_matrix[i][j]) ** 2)
    return gram


def get_coordinates_by_distance(distance_matrix):
    eps = 1e-5

    gram_matrix = construct_gram_matrix(distance_matrix)
    # get eigenvalue and eigenvectors
    feature_values, feature_vectors = np.linalg.eig(gram_matrix)
    select_feature_values = []

    # if eigenvalue == 0, delete it and its eigenvector
    for i in range(len(feature_values) - 1, -1, -1):
        if feature_values[i] > eps:
            select_feature_values.append(feature_values[i])
        else:
            feature_vectors = np.delete(feature_vectors, i, axis=1)
    eye_matrix = np.eye(len(select_feature_values))
    select_feature_values.reverse()
    # sqrt(eigenvalues) * eigenvectors
    for i in range(len(select_feature_values)):
        eye_matrix[i, i] = select_feature_values[i]
    return np.dot(feature_vectors, eye_matrix ** 0.5)


def from_dist_get_coord(dist_matrix):
    dist_array = np.array(dist_matrix)
    coordinates_array = get_coordinates_by_distance(dist_array)
    coordinates = coordinates_array.tolist()
    return coordinates


def cross_judge(l1p1, l1p2, l2p1, l2p2):
    if min(l1p1[0], l1p2[0]) <= max(l2p1[0], l2p2[0]) \
            and min(l2p1[1], l2p2[1]) <= max(l1p1[1], l1p2[1]) \
            and min(l2p1[0], l2p2[0]) <= max(l1p1[0], l1p2[0]) \
            and min(l1p1[1], l1p2[1]) <= max(l2p1[1], l2p2[1]):
        return True
    else:
        return False


if __name__ == "__main__":
    dist_matrix = [
        [0, 1, 1],
        [1, 0, 1],
        [1, 1, 0]
    ]
    coordinates = from_dist_get_coord(dist_matrix)
    print(coordinates)
    a = [1, 1]
    b = [2, 2]
    c = [1, 2]
    d = [4, 1]
    a = cross_judge(a, b, c, d)
    print(a)