元组函数的最小值

Question

我有一个数据集：

2.699994   -2541.184861   
2.749996   -2541.189717   
2.779995   -2541.190735   
2.789996   -2541.190777   
2.799993   -2541.190668   
2.829992   -2541.189523   
2.858996   -2541.187427   

我知道这适合多项式，例如：f(x)=a+b*x+c*x^3

我需要获得该函数的最小值。

我用Google搜索，看起来像scipy.optimize是我正在寻找的，但无法理解如何提供数据。 请帮助

Answer 1

所以有两个步骤：首先通过拟合函数找到参数。我使用了curve_fit。然后最小化功能。我使用最小化，但这也可以通过分析完成。

import scipy as sp
import scipy.optimize
import matplotlib.pyplot as plt
%matplotlib inline

# data
xdata = sp.array([2.699994, 2.749996, 2.779995, 2.789996, 2.799993, 2.829992, 2.858996])
ydata = sp.array([-2541.184861, -2541.189717, -2541.190735, -2541.190777, -2541.190668, -2541.189523, -2541.187427])

# function to fit
def f(x, a, b, c):
return a + b*x + c*x**3

# fit the parameters a, b, c
popt, pcov = sp.optimize.curve_fit(f, xdata, ydata)
print('Parameters a, b, c are: {0}'.format(popt))

# minimize the function (could also be done analytically)
res = sp.optimize.minimize(lambda x: f(x, *popt), 2.8)
print('Function is minimized for {0}.'.format(float(res['x'])))

# plot data, fitted function and minimum

# function
x = sp.linspace(2.65, 2.9, 100)
y = f(x, *popt)
plt.plot(x, y)

# data
plt.scatter(xdata, ydata)

# minimum
plt.scatter(res['x'], f(res['x'], *popt), color = 'red', s = 80)
plt.show()