使用 lmfit.Model 或 scipy.optimize.curve_fit 优化函数的卷积

Question

使用 lmfit.Model 或 scipy.optimize.curve_fit 我必须优化一个函数，其输出需要与一些实验数据进行卷积，然后才能适合其他一些实验数据。总而言之，工作流程是这样的：

(1)定义了函数A（例如高斯函数）。 (2) 函数 A 的输出与称为数据 B 的实验信号进行卷积。 (3) 函数A的参数针对(2)中提到的卷积进行了优化，以完美匹配其他一些称为数据C的实验数据。

我正在使用傅立叶变换将函数 A 的输出与数据 B 进行卷积，如下所示：

from scipy.fftpack import fft, ifft

    def convolve(data_B, function_A):
        convolved = ifft(fft(IRF) * fft(model)).real
        return convolved

如何使用 lmfit.Model 或 scipy.optimize.curve_fit 将“卷积”拟合到数据 C？

编辑：作为对提交答案的回应，我已将我的卷积步骤合并到用于拟合的方程中，方式如下：

#1 component exponential distribution:
def ExpDecay_1(x, ampl1, tau1, y0, x0, args=(new_y_irf)): # new_y_irf is a list. 
    h = np.zeros(x.size) 
    lengthVec = len(new_y_decay)
    
    shift_1 = np.remainder(np.remainder(x-np.floor(x0)-1, lengthVec) + lengthVec, lengthVec)
    shift_Incr1 = (1 - x0 + np.floor(x0))*new_y_irf[shift_1.astype(int)]
    
    shift_2 = np.remainder(np.remainder(x-np.ceil(x0)-1, lengthVec) + lengthVec, lengthVec)
    shift_Incr2 = (x0 - np.floor(x0))*new_y_irf[shift_2.astype(int)]
    
    irf_shifted = (shift_Incr1 + shift_Incr2)
    irf_norm = irf_shifted/sum(irf_shifted)
    h = ampl1*np.exp(-(x)/tau1)
    conv = ifft(fft(h) * fft(irf_norm)).real # This is the convolution step.
    return conv

然而，当我尝试这样做时：

gmodel = Model(ExpDecay_1)

我明白了：

gmodel = Model(ExpDecay_1) Traceback (most recent call last):

File "", line 1, in gmodel = Model(ExpDecay_1)

File "C:\Users\lopez\Anaconda3\lib\site-packages\lmfit\model.py", line 273, in init self._parse_params()

File "C:\Users\lopez\Anaconda3\lib\site-packages\lmfit\model.py", line 477, in _parse_params if fpar.default == fpar.empty:

ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()

编辑 2：我设法使其工作如下：

import pandas as pd
import matplotlib.pyplot as plt
from scipy.interpolate import interp1d
import numpy as np
from lmfit import Model
from scipy.fftpack import fft, ifft

def Test_fit2(x, arg=new_y_irf, data=new_y_decay, num_decay=1):
    IRF = arg
    DATA = data
    def Exp(x, ampl1=1.0, tau1=3.0): # This generates an exponential model.
        res = ampl1*np.exp(-x/tau1)
        return res
    def Conv(IRF,decay): # This convolves a model with the data (data = Instrument Response Function, IRF).
        conv = ifft(fft(decay) * fft(IRF)).real
        return conv
    if num_decay == 1: # If the user chooses to use a model equation with one exponential term.
        def fitting(x, ampl1=1.0, tau1=3.0): 
            exponential = Exp(x,ampl1,tau1)
            convolved = Conv(IRF,exponential)
            return convolved
        modelling = Model(fitting)
        res = modelling.fit(DATA,x=new_x_decay,ampl1=1.0,tau1=2.0)
    if num_decay == 2: # If the user chooses to use a model equation with two exponential terms.
        def fitting(x, ampl1=1.0, tau1=3.0, ampl2=1.0, tau2=1.0): 
            exponential = Exp(x,ampl1,tau1)+Exp(x,ampl2,tau2)
            convolved = Conv(IRF,exponential)
            return convolved
        modelling = Model(fitting)
        res = modelling.fit(DATA,x=new_x_decay,ampl1=1.0,tau1=2.0)
    if num_decay == 3: # If the user chooses to use a model equation with three exponential terms.
        def fitting(x, ampl1=1.0, tau1=3.0, ampl2=2.0, tau2=1.0, ampl3=3.0, tau3=5.0): 
            exponential = Exp(x,ampl1,tau1)+Exp(x,ampl2,tau2)+Exp(x,ampl3,tau3)
            convolved = Conv(IRF,exponential)
            return convolved
        modelling = Model(fitting)
        res = modelling.fit(DATA,x=new_x_decay,ampl1=1.0,tau1=2.0)
    if num_decay == 4: # If the user chooses to use a model equation with four exponential terms.
        def fitting(x, ampl1=1.0, tau1=0.1, ampl2=2.0, tau2=1.0, ampl3=3.0, tau3=5.0, ampl4=1.0, tau4=10.0): 
            exponential = Exp(x,ampl1,tau1)+Exp(x,ampl2,tau2)+Exp(x,ampl3,tau3)+Exp(x,ampl4,tau4)
            convolved = Conv(IRF,exponential)
            return convolved
        modelling = Model(fitting)
        res = modelling.fit(DATA,x=new_x_decay,ampl1=1.0,tau1=2.0)
    return res

Answer 1

它总是有助于 post 一个完整的、最小的例子来说明您正在尝试做的事情。没有完整的例子，只能给出模糊的答案。

您可以简单地在 lmfit.Model 包装的模型函数中进行卷积，传入内核数组以在卷积中使用。或者您可以创建卷积核和函数，并将卷积作为建模过程的一部分，如 https://lmfit.github.io/lmfit-py/examples/documentation/model_composite.html

中所述

我想如果内核实际上并不打算在拟合期间更改，那么第一种方法会更容易，但如果没有更多细节，很难确定这一点。

使用 lmfit.Model 或 scipy.optimize.curve_fit 优化函数的卷积

Optimizing the convolution of a function with lmfit.Model or scipy.optimize.curve_fit

scipy

lmfit