使 erf 函数适合数据 [英] Fit erf function to data

问题描述

所以我有磁滞回线.我想使用 erf 函数来拟合我的数据.

我的循环的一部分在下图中以黑色显示.

我正在尝试使用 参数[0] = 1.83289895，参数

<小时>

这是重现上述图的代码

将 numpy 导入为 np从 scipy.special 导入 erf从 scipy.optimize 导入 curve_fit导入 matplotlib.pyplot 作为 pltdef erfunc(x, mFL, a, b):返回 mFL*erf((x-a)/(b*np.sqrt(2)))x_data = np.linspace(-3000, 3000, 100)mFL, a, b = 0.0003, 500, 100y_data = erfunc(x_data, mFL, a, b)y_noise = np.random.rand(y_data.size)/1e4y_noisy_data = y_data + y_noiseparams, extras = curve_fit(erfunc, x_data, y_noisy_data)# 通过 p0 arg 为 curve_fit 提供初始猜测上级参数，额外的 = 曲线拟合(erfunc，x_data，y_noisy_data，p0=[0.001, 100, 100])fig = plt.figure()ax1 = fig.add_subplot(121)ax2 = fig.add_subplot(122)ax1.plot(x_data, erfunc(x_data, *params))ax1.plot(x_data, y_noisy_data, 'k')ax1.set_title('猜之前')ax2.plot(x_data, erfunc(x_data, *superior_params))ax2.plot(x_data, y_noisy_data, 'k')ax2.set_title('猜后')

So I have hysteresis loop. I want to use the erf function to fit it with my data.

A portion of my loop is shown in black on the lower graph.

I am trying to use the scipy.optimize.curve_fit and scipy.special.erf function to fit the data with the following code:

import scipy.special
import scipy.optimize

def erfunc(x,a,b):
    return mFL*scipy.special.erf((x-a)/(b*np.sqrt(2)))

params,extras = scipy.optimize.curve_fit(erfunc,x_data,y_data)

x_erf = list(range(-3000,3000,1))
y_erf = erfunc(x_erf,params[0],params[1])

mFL is a constant, a controls the position of the erf curve and b the slope of the curve. (To my knowledge)

However, when I plot the obtained x_erf and y_erf data (in blue). I get the following fitting, which is not ideal to say the least:

Is there a way i can get a proper fit?

Edit: Link to data file: https://www.dropbox.com/s/o0uoieg3jkliun7/xydata.csv?dl=0 Params[0] = 1.83289895, Params1 = 0.27837306

解决方案

I suspect two things are needed for a good fit here. First, I believe you need to add mFL to your erfunc function, and second, as suggested by Glostas, you need to specify some initial guesses for your fitting parameters. I created some artificial data in an attempt to replicate your data. The plot on the left is before giving curve_fit some initial parameters and the plot on the right is after.

---

Here is the code to reproduce the above plots

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


def erfunc(x, mFL, a, b):
    return mFL*erf((x-a)/(b*np.sqrt(2)))

x_data  = np.linspace(-3000, 3000, 100)

mFL, a, b = 0.0003, 500, 100

y_data  = erfunc(x_data, mFL, a, b)
y_noise = np.random.rand(y_data.size) / 1e4
y_noisy_data = y_data + y_noise

params, extras = curve_fit(erfunc, x_data, y_noisy_data)
# supply initial guesses to curve_fit through p0 arg
superior_params, extras = curve_fit(erfunc, x_data, y_noisy_data,
                                    p0=[0.001, 100, 100])

fig = plt.figure()
ax1 = fig.add_subplot(121)
ax2 = fig.add_subplot(122)

ax1.plot(x_data, erfunc(x_data, *params))
ax1.plot(x_data, y_noisy_data, 'k')
ax1.set_title('Before Guesses')

ax2.plot(x_data, erfunc(x_data, *superior_params))
ax2.plot(x_data, y_noisy_data, 'k')
ax2.set_title('After Guesses')

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