公式

代码

衰减

#coding:utf-8
import matplotlib.pyplot as plt
import matplotlib
import numpy as np
import pandas as pd
%matplotlib inline

# https://blog.csdn.net/zhufenghao/article/details/80879260
import numpy as np
def exponential_decay(t, init=0.8, m=30, finish=0.2):
    alpha = np.log(init / finish) / m
    l = - np.log(init) / alpha
    decay = np.exp(-alpha * (t + l))
    return decay

# 剔除init
def exponential_decay_v2(t, init=0.8, m=30, finish=0.2):
    alpha = np.log(init / finish) / m
    l = 0
    decay = np.exp(-alpha * (t + l))
    return decay
    
# get alpha 衰减
def get_alpha(init=0.8, m=30, finish=0.2):
    alpha = np.log(init / finish) / m
    print("alpha:" + str(alpha))
    return alpha

# 
def calculate(t, init= 1, alpha = 1):
    decay = init *np.exp(-alpha * (t)) #init !!
    return decay


max_para = 2
init = max_para
m = 6
finish = 1
alpha = get_alpha(init, m, finish)


# plot
x  = []
y = []
for a in range(0,7):
    x.append(a)
    y.append(calculate(a, init,alpha))
print(x)
print(y)
# 绘制第一条折线
plt.plot(x,y,label="decay")
plt.xlabel("hour")
plt.ylabel("ratio")
plt.scatter(x,y,label="decay")
# 设置数字标签
for a, b in zip(x, y):
    plt.text(a, b, round(b,2), ha='center', va='bottom', fontsize=10)

image.png

指数提升

求解alpha的公式改为

alpha = -np.log(init / finish) / m

# get alpha 提升
def get_alpha(init=0.8, m=30, finish=0.2):
    alpha = -np.log(init / finish) / m
    print("alpha:" + str(alpha))
    return alpha

# 
def calculate(t, init= 1, alpha = 1):
    decay = init *np.exp(alpha * (t)) #init !!
    return decay

max_para = 0.5
init = max_para
m = 6
finish = 1
alpha = get_alpha(init, m, finish)


# plot
x  = []
y = []
for a in range(0,7):
    x.append(a)
    y.append(calculate(a, init,alpha))
print(x)
print(y)
# 绘制第一条折线
plt.xlabel("hour")
plt.ylabel("ratio")
plt.plot(x,y,label="decay")
plt.scatter(x,y,label="decay")
# 设置数字标签
for a, b in zip(x, y):
    plt.text(a, b, round(b,2), ha='center', va='bottom', fontsize=10)

image.png

reference

https://blog.csdn.net/zhufenghao/article/details/80879260