指數曲線擬合與python

Question

我想轉換一些Matlab代碼，我有曲線擬合我的數據到Python代碼，但我有麻煩得到類似的答案。這些數據是：

x = array([ 0. , 12.5 , 24.5 , 37.75, 54. , 70.25, 87.5 , 
    108.5 , 129.5 , 150.5 , 171.5 , 193.75, 233.75, 273.75]) 
y = array([-8.79182857, -5.56347794, -5.45683824, -4.30737662, -1.4394612 , 
    -1.58047016, -0.93225927, -0.6719836 , -0.45977157, -0.37622436, 
    -0.56115757, -0.3038559 , -0.26594558, -0.26496367]) 

的Matlab代碼是：

function [estimates, model] = curvefit(xdata, ydata) 
% fits data to the curve y(x)=A-B*e(-lambda*x) 

start_point = rand(1,3); 

model =@efun; 
options = optimset('Display','off','TolFun',1e-16,'TolX',1e-16); 
estimates = fminsearch(model, start_point,options); 
% expfun accepts curve parameters as inputs, and outputs sse, 
% the sum of squares error for A -B* exp(-lambda * xdata) - ydata, 
% and the FittedCurve. 
    function [sse,FittedCurve] = efun(v) 
     A=v(1); 
     B=v(2); 
     lambda=v(3); 
     FittedCurve =A - B*exp(-lambda*xdata); 
     ErrorVector=FittedCurve-ydata; 
     sse = sum(ErrorVector .^2); 
    end 
end 
err = Inf; 
numattempts = 100; 
for k=1:numattempts 
[intermed,model]=curvefit(x, y)); 
[thiserr,thismodel]=model(intermed); 
if thiserr<err 
    err = thiserr; 
    coeffs = intermed; 
    ymodel = thismodel; 
end 

，並在Python到目前爲止，我：

import numpy as np 
from pandas import Series, DataFrame 
import pandas as pd 
import matplotlib.pyplot as plt 
from scipy import stats 
from scipy.optimize import curve_fit 
import pickle 

def fitFunc(A, B, k, t): 
    return A - B*np.exp(-k*t) 
init_vals = np.random.rand(1,3) 
fitParams, fitCovariances = curve_fit(fitFunc, y, x], p0=init_vals) 

我想我必須做一些事情上運行的100次嘗試p0，但曲線只會收斂大約1/10倍，並且會收斂到一條直線，與我在Matlab中獲得的值相反。還有關於曲線擬合的大多數問題，我已經看到使用B np.exp（-k t）+ A，但是我有上面的指數公式是我必須使用的數據。有什麼想法嗎？感謝您的時間！

Answer 1

curve_fit(fitFunc, y, x], p0=init_vals)應該是curve_fit(fitFunc, x,y, p0=init_vals)即，x在y之前。 fitFunc(A, B, k, t)應該是fitFunc(t,A, B, k)。自變量先行。看到下面的代碼：

import numpy as np 
import matplotlib.pyplot as plt 
from scipy.optimize import curve_fit 

x = np.array([ 0. , 12.5 , 24.5 , 37.75, 54. , 70.25, 87.5 , 
    108.5 , 129.5 , 150.5 , 171.5 , 193.75, 233.75, 273.75]) 
y = np.array([-8.79182857, -5.56347794, -5.45683824, -4.30737662, -1.4394612 , 
    -1.58047016, -0.93225927, -0.6719836 , -0.45977157, -0.37622436, 
    -0.56115757, -0.3038559 , -0.26594558, -0.26496367]) 

def fitFunc(t, A, B, k): 
    return A - B*np.exp(-k*t) 
init_vals = np.random.rand(1,3) 

fitParams, fitCovariances = curve_fit(fitFunc, x, y, p0=init_vals) 
print fitParams 
plt.plot(x,y) 
plt.plot(x,fitFunc(x,*fitParams)) 
plt.show()