def design_matrix(x_train, M):
    '''
    :param x_train: ciag treningowy Nx1
    :param M: stopien wielomianu 0,1,2,...
    :return: funkcja wylicza Design Matrix Nx(M+1) dla wielomianu rzedu M
    matrix = np.ones(shape=(x_train.shape[0], M+1))
    for col in range(M + 1):
        for row in range(matrix.shape[0]):
            matrix[row][col] = pow(x_train[row][0], col)
    '''
    return np.array([[pow(x_train[row][0], col) for col in range(M+1)] for row in range(x_train.shape[0])])