Python绘制高斯分布图像

文章目录

• ​​Python绘制高斯分布图像​​

• ​​一、需求介绍​​
• ​​二、第一个任务​​
• ​​三、第二个任务​​
• ​​四、readme文件​​

一、需求介绍

我们这里旨在使用Python来绘制图像，其他的操作一概先不管，绘制高斯分布的图像。

二、第一个任务

代码

import matplotlib.pyplot as plt
import numpy as np
from scipy.stats import beta
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
import math
import random


def x_gauss(mu=0, sigma=1):
    """
    x_gauss(you can change this method to make it can be input.)
    :param mu: mu_x
    :param sigma: sigma_x
    :return: mu, sigma
    """
    return mu, sigma
    # multiple variables.


def y_gauss(mu=0, sigma=1):
    """
    y_gauss(you can change this method to make it can be input.)
    :param mu: mu_y
    :param sigma: sigma_y
    :return: mu, sigma
    """
    return mu, sigma
    # multiple variables.


def z_beta(alpha0=1, p0=1):
    """
    z_beta(you can change this method to make it can be input.)
    :param alpha0: alpha0
    :param p0: p0
    :return: alpha0, p0
    """
    return alpha0, p0
    # p is a multiple variable, but alpha is not.


if __name__ == '__main__':
    mu_x, sigma_x = x_gauss()
    mu_y, sigma_y = y_gauss()
    # get the mu and sigma parameter of the gauss.

    X = np.arange(mu_x - 5 * sigma_x, mu_x + 5 * sigma_x, 10 * sigma_x / 100)
    # range is related with sigma_x.
    Y = np.arange(mu_y - 5 * sigma_y, mu_y + 5 * sigma_y, 10 * sigma_y / 100)
    # range is related with sigma_y.
    # X and Y are arrays, ranging from mu - 5 * sigma to mu + 5 * sigma.

    X, Y = np.meshgrid(X, Y)
    # make meshgrided.

    alpha, p = z_beta()
    eta = beta.pdf(Y, alpha, p)  # Beta.
    # the equation of the eta.(eta ~ B(1, p))
    # however, as i need a range, so i use the range of Y.

    Z = \
        (1 / (pow(2 * math.pi, 1 / 2))) \
        * np.exp(- ((X - mu_x) ** 2) / (2 * (sigma_x ** 2))) \
        + eta * \
        (1 / (pow(2 * math.pi, 1 / 2))) \
        * np.exp(- ((Y - mu_y) ** 2) / (2 * (sigma_y ** 2)))
    # Z = X + eta * Y.

    list_z = []
    # hist list.
    for line in Z:  # 100 lines.
        appending = random.choices(line, k=10)
        # 100 lines, 10 choices => 100 * 10 = 1000.

        for data in appending:
            list_z.append(data)

    """
    two pictures => two windows.
    one is hist,
    the other is 3D.
    """

    # print(list_z, len(list_z))
    # 1000 points.
    plt.title('N~Z')
    # title.
    plt.xlabel('Z=X+η*Y')
    plt.ylabel('N')
    # labels.
    plt.hist(list_z)
    # draw the hist.

    fig = plt.figure()
    ax = Axes3D(fig)
    ax.plot_surface(X, Y, Z, rstride=1, cstride=1, alpha=0.5, cmap=cm.coolwarm)
    # draw the 3D function.
    plt.show()
    # show.      

效果：

以及：

三、第二个任务

代码

import matplotlib.pyplot as plt
import numpy as np
from scipy.stats import beta
import math
import random


def x_gauss(mu=0, sigma=1):
    """
    x_gauss(you can change this method to make it can be input.)
    :param mu: mu_x
    :param sigma: sigma_x
    :return: mu, sigma
    """
    return mu, sigma
    # multiple variables.


def y_gauss(mu=0, sigma=1):
    """
    y_gauss(you can change this method to make it can be input.)
    :param mu: mu_y
    :param sigma: sigma_y
    :return: mu, sigma
    """
    return mu, sigma
    # multiple variables.


def z_beta(alpha0=1, p0=1):
    """
    z_beta(you can change this method to make it can be input.)
    :param alpha0: alpha0
    :param p0: p0
    :return: alpha0, p0
    """
    return alpha0, p0
    # p is a multiple variable, but alpha is not.


if __name__ == '__main__':
    """
    n is a multiple variable.
    """
    n = 100
    # multiple variable.

    mu_x, sigma_x = x_gauss()
    mu_y, sigma_y = y_gauss()
    # get the mu and sigma parameter of the gauss.

    X = np.arange(mu_x - 5 * sigma_x, mu_x + 5 * sigma_x, 10 * sigma_x / 5000)
    # range is related with sigma_x.
    Y = np.arange(mu_y - 5 * sigma_y, mu_y + 5 * sigma_y, 10 * sigma_y / 5000)
    # range is related with sigma_y.
    # X and Y are arrays, ranging from mu - 5 * sigma to mu + 5 * sigma.

    X, Y = np.meshgrid(X, Y)
    # make meshgrided.

    alpha, p = z_beta()
    eta = beta.pdf(Y, alpha, p)  # Beta.
    # the equation of the eta.(eta ~ B(1, p))
    # however, as i need a range, so i use the range of Y.

    Z = \
        (1 / (pow(2 * math.pi, 1 / 2))) \
        * np.exp(- ((X - mu_x) ** 2) / (2 * (sigma_x ** 2))) \
        + eta * \
        (1 / (pow(2 * math.pi, 1 / 2))) \
        * np.exp(- ((Y - mu_y) ** 2) / (2 * (sigma_y ** 2)))
    # Z = X + eta * Y.

    u = []
    # calculate the u.(1000)
    for i in range(1000):  # 1000.
        z_i = random.choices(Z[i], k=n)  # k = n.
        # n z.

        # calculate the u.

        u.append((1 / pow(n * np.var(z_i), 1 / 2)) * (sum(z_i) - n * np.mean(z_i)))
        # Ui = (1 / pow(n * np.var(z_i), 1 / 2)) * (sum(z_i) - n * np.mean(z_i))
        # 1000 u.

    plt.title('N~Ui')
    # title.
    plt.xlabel('Ui')
    plt.ylabel('N')
    # labels.
    plt.hist(u)
    # show the u.
    plt.show()
    # show      

效果：

四、readme文件

This is the homework, there are two packages,
homework1 and homework2, homework1 is related
to work 1, and homework2 is related to work 2.

There may be some modules that you do not have
in your environment, so maybe you should install
those modules first, such as, numpy, scipy,
matplotlib, mpl_toolkits and so on.

After adding all the modules, you can change the
parameters like mu, sigma, p and so on, well,
you can also keep the parameters as you want,
and then,you can run the project and get the
results.

In fact, homework2 is related to homework1,
but, in order to make the question more clear,
i divide the whole question into two small
questions, all in all, they are the same.