# -*- coding: utf-8 -*-

'''

二次插值法python實現

f(x)=x^4 - 4x^3 - 6x^2 -16x +4極值

區間[-1,6] e=0.05

'''

import numpy as np

import matplotlib.pyplot as plt

'''

函數表達式

'''

def f(x):

return 1.0 * (pow(x, 4) - 4 * pow(x, 3) - 6 * pow(x, 2) - 16 * x + 4)

'''

繪制函數圖像

'''

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.show()

'''

e為精度

'''

def search(f, x1, x2, x3, e):

if f(x2) > f(x1) or f(x2) > f(x3):

print "不滿足兩頭大中間小的性質"

return

#系數矩陣

A = [[pow(x1, 2), x1, 1], [pow(x2, 2), x2, 1], [pow(x3, 2), x3, 1]]

b = [f(x1), f(x2), f(x3)]

X= np.linalg.solve(A, b)

a0 = X[0]

a1 = X[1]

a2 = X[2]

x = (-1)*a1/(2 * a0)

print x

if abs(x - x2) < e:

if f(x) < f(x2):

y = f(x)

print x

return (x, y)

else:

y = f(x2)

print x2

return (x2, y)

arr = [x1, x2, x3, x]

arr.sort()

if f(x2)> f(x):

index = arr.index(x)

x2 = x

x1 = arr[index - 1]

x3 = arr[index + 1]

else:

index = arr.index(x2)

x1 = arr[index - 1]

x3 = arr[index + 1]

return search(f, x1, x2, x3, e)

def regre(f, a, b, e):

x1 = a

x3 = b

x2 = (a + b)/2.0

p = search(f, x1, x2, x3, e)

printFunc(f, a, b, p[0], p[1])

a = -1.0

b = 6.0

e = 0.05

regre(f, a, b, e)

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