#黃金分割法python求解PPT上第一個例題
#因為函數(shù)要求解最大值而這個方法一般求解最小值所以把函數(shù)取負(fù)

import numpy as np
import matplotlib.pyplot as plt

rate = 0.618034

def f(x):
    #求解體積函數(shù)公式，乘1.0將結(jié)果變?yōu)楦↑c數(shù)
    return -1.0*x*(350-2*x)*(260-2*x)  

def tarceback(f,a0,b0,accuracy):
    a = a0
    b = b0
    x2 = a+rate*(b-a)
    x1 = b-rate*(b-a)
    f1 = f(x1)
    f2 = f(x2)
    print(x1,x2)
    arr = search(f,a,b,x1,x2,f1,f2,accuracy)
    printFunc(f,a,b,arr[0],arr[1])
    
def search(f,a,b,x1,x2,f1,f2,accuracy):
    if f1<=f2:
        if x2-a<accuracy:
            print(x1,f1)
            return (x1,f1)
        else:
            b = x2
            x2 = x1
            f2 = f1
            x1 = a+b-x2
            f1 = f(x1)
            print(x1,x2)
            return search(f,a,b,x1,x2,f1,f2,accuracy)
    else:
        if b-x1<accuracy:
            print(x2,f2)
            return (x2,f2)
        else:
            a = x1
            x1 = x2
            f1 = f2
            x2 = a+b-x1
            f2 = f(x2)
            print(x1,x2)
            return search(f,a,b,x1,x2,f1,f2,accuracy)

def printFunc(f,a,b,x,y):
    t = np.arange(a,b,0.01)
    s = f(t)
    plt.plot(t,s)
    plt.plot([x],[y],'ro')
    plt.plot([x,x],[y,0],'k--')
    plt.plot([0,x],[y,y],'k--')
#     plt.annotate(r'$(x,y)$',xy=(x,y))
    plt.show()

tarceback(f,0,130,0.05)