"""
This module contains some utility functions for math operations.
"""
import numpy as np

def get_mean(values:list):
    """
    Get the mean of the values.
    """
    return np.mean(values)

def get_standard_deviation(values:list):
    """
    Get the standard deviation of the values.

    :param values: values
    :return: standard deviation of the values
    """
    return np.std(values)

def get_x_y_z_mean(discrete_values:list):
    """
    Get the mean of the x and y coordinates in the discrete range.

    :param x: x coordinates
    :param y: y coordinates
    :return: mean of x and y coordinates in the discrete range
    """
    x = [vertex[0] for vertex in discrete_values]
    y = [vertex[1] for vertex in discrete_values]
    z = [vertex[2] for vertex in discrete_values]
    return get_mean(x), get_mean(y), get_mean(z)

def get_radius_from_x_y(xi:float, yi:float, x_mean:float, y_mean:float):
    """
    Get the radius from the x and y coordinates.

    :param xi: x coordinate
    :param yi: y coordinate
    :param x_mean: mean of x coordinates in the discrete range
    :param y_mean: mean of y coordinates in the discrete range
    :return: radius for this point
    """
    return np.sqrt((xi - x_mean) ** 2 + (yi - y_mean) ** 2)

def get_mean_radius(discrete_values:list):
    """
    Get the mean of the radius in the discrete range.

    :param discrete_values: discrete values
    :return: mean of the radius in the discrete range
    """
    x_mean, y_mean, z_mean = get_x_y_z_mean(discrete_values)
    radius = []
    for x,y,z in discrete_values:
        radius.append(get_radius_from_x_y(x,y,x_mean,y_mean))
    return get_mean(radius)

def get_radius_std(discrete_values:list):
    """
    Get the standard deviation of the radius in the discrete range.

    :param discrete_values: discrete values
    :return: standard deviation of the radius in the discrete range
    """
    x_mean, y_mean, z_mean = get_x_y_z_mean(discrete_values)
    radius = []
    for x,y,z in discrete_values:
        radius.append(get_radius_from_x_y(x,y,x_mean,y_mean))
    return get_standard_deviation(radius)

def get_mean_teta(discrete_values:list):
    """
    Get the mean of the teta in the discrete range.

    :param discrete_values: discrete values
    :return: mean of the teta in the discrete range
    """
    x_mean, y_mean, z_mean = get_x_y_z_mean(discrete_values)
    teta = []
    for x,y,z in discrete_values:
        teta.append(get_teta_from_x_y(x,y,x_mean,y_mean))
    return get_mean(teta)

def get_teta_from_x_y(xi:float, yi:float, x_mean:float, y_mean:float):
    """
    Get the teta from the x and y coordinates.

    :param xi: x coordinate
    :param yi: y coordinate
    :param x_mean: mean of x coordinates in the discrete range
    :param y_mean: mean of y coordinates in the discrete range
    :return: teta for this point
    """
    return np.arctan2((xi - x_mean),(yi - y_mean))