带有symfit的全局拟合示例 [英] Global fitting example with symfit

问题描述

我正在尝试使用 symfit 包进行全局拟合。 ：//symfit.readthedocs.io/zh-CN/latest/fitting_types.html#global-fitting rel = nofollow noreferrer>符号文档。

I am trying to perform global fitting with symfit package, following symfit documentation.

import numpy as np
import symfit as sf
import matplotlib.pyplot as plt
%matplotlib inline # for ipynb

# Generate example data
t = np.arange(0.0, 600.1, 30)
k = 0.005
C1_0, C2_0 = 1.0, 2.0
C1 = C1_0 * np.exp(-k*t)
C2 = C2_0 * np.exp(-k*t)

# Construct model
x_1, x_2, y_1, y_2 = sf.variables('x_1, x_2, y_1, y_2')
kg = sf.Parameter(value=0.01, min=0.0, max=0.1)
a_1, a_2 = sf.parameters('a_1, a_2')
globalmodel = sf.Model({
    y_1: a_1 * np.e**(- kg * x_1),
    y_2: a_2 * np.e**(- kg * x_2),
})

# Do fit
globalfit = sf.Fit(globalmodel, x_1=t, x_2=t, y_1=C1, y_2=C2)
globalfit_result = globalfit.execute()
print(globalfit_result)

### EDITED START
while globalfit_result.r_squared < 0.99:
    kg = sf.Parameter(value=globalfit_result.params['kg'])
    a_1 = sf.Parameter(value=globalfit_result.params['a_1'])
    a_2 = sf.Parameter(value=globalfit_result.params['a_2'])
    globalmodel = sf.Model({
        y_1: a_1 * np.e**(- kg * x_1),
        y_2: a_2 * np.e**(- kg * x_2),
    })
    globalfit = sf.Fit(globalmodel, x_1=t, x_2=t, y_1=C1, y_2=C2)
    globalfit_result = globalfit.execute()
### EDITED END

y_r = globalmodel(x_1=t, x_2=t, **globalfit_result.params)

# Plot fit
plt.plot(t,C1,'ro')
plt.plot(t,C2,'b+')
plt.plot(t,y_r[0],'r-')
plt.plot(t,y_r[1],'b-')
plt.show()

在此示例中，我希望将 globalmodel中的 kg参数优化为0.005。但是， kg的值约为9.6e-3，太接近初始值（10.0e-3）。我认为我做一些愚蠢的事情，但我无法弄清楚。

In this example, I expect the "kg" parameter in the "globalmodel" is optimized to 0.005. However, the value of "kg" is about 9.6e-3, which is too near to the initial value (10.0e-3). I think I do something stupid, but I cannot figure it out.

欢迎任何评论和建议！

已编辑

我添加了（非常难看）while循环以获取最佳拟合。我不确定为什么应该这样做，但是它似乎可以正常工作。

I added (a very ugly) while loop to get the best fit. I am not sure why it should be, but it seems to work.

推荐答案

看来边界正在引起问题。 。我在测试中将其删除，然后一切正常。在 symfit 0.3.3 中，这是一个已知的问题，其中， ̶[1]̶BRANCH ON̶G̶i̶t̶h̶u̶b̶.̶̶̶我上传新的开发人员版你可以立即安装使用̶ PIP安装̶s̶y̶m̶f̶i̶t̶=̶=̶0̶.̶3̶.̶3̶.̶d̶e̶v̶1̶5̶5̶̶-̶升级̶，̶直到我正式发布0.3.4̶（这将是相同的，但具有扩展文档）̶，目前已被固定在较新版本。

It would appear that the bounds are causing the problem. I removed them in my test and then everything works fine. This is a known problem in symfit 0.3.3, a̶n̶d̶ ̶o̶n̶e̶ ̶I̶ ̶a̶l̶r̶e̶a̶d̶y̶ ̶f̶i̶x̶e̶d̶ ̶i̶n̶ ̶t̶h̶e̶ ̶[̶̶m̶a̶s̶t̶e̶r̶̶]̶[̶1̶]̶ ̶b̶r̶a̶n̶c̶h̶ ̶o̶n̶ ̶G̶i̶t̶h̶u̶b̶.̶ ̶ ̶ ̶I̶ ̶u̶p̶l̶o̶a̶d̶e̶d̶ ̶a̶ ̶n̶e̶w̶ ̶d̶e̶v̶ ̶v̶e̶r̶s̶i̶o̶n̶ ̶y̶o̶u̶ ̶c̶o̶u̶l̶d̶ ̶n̶o̶w̶ ̶i̶n̶s̶t̶a̶l̶l̶ ̶u̶s̶i̶n̶g̶ ̶̶p̶i̶p̶ ̶i̶n̶s̶t̶a̶l̶l̶ ̶s̶y̶m̶f̶i̶t̶=̶=̶0̶.̶3̶.̶3̶.̶d̶e̶v̶1̶5̶5̶ ̶-̶-̶u̶p̶g̶r̶a̶d̶e̶̶,̶ ̶u̶n̶t̶i̶l̶ ̶I̶ ̶o̶f̶f̶i̶c̶i̶a̶l̶l̶y̶ ̶r̶e̶l̶e̶a̶s̶e̶ ̶0̶.̶3̶.̶4̶ ̶(̶w̶h̶i̶c̶h̶ ̶w̶i̶l̶l̶ ̶b̶e̶ ̶i̶d̶e̶n̶t̶i̶c̶a̶l̶ ̶b̶u̶t̶ ̶w̶i̶t̶h̶ ̶e̶x̶t̶e̶n̶d̶e̶d̶ ̶d̶o̶c̶u̶m̶e̶n̶t̶a̶t̶i̶o̶n̶)̶, which has now been fixed in newer versions.

请注意，我将您的 np.e 更改为 sf.exp ，因为这是象征性的。我的工作代码如下，与您的工作代码相同，除了提到的更改并在 0.3.3.dev155 中运行。

Please note, I changed your np.e to sf.exp because that is symbolic. My working code is below, identical to yours except for the change mentioned and running in 0.3.3.dev155.

import numpy as np
import symfit as sf
import matplotlib.pyplot as plt

# Generate example data
t = np.arange(0.0, 600.1, 30)
k = 0.005
C1_0, C2_0 = 1.0, 2.0
C1 = C1_0 * np.exp(-k*t)
C2 = C2_0 * np.exp(-k*t)

# Construct model
x_1, x_2, y_1, y_2 = sf.variables('x_1, x_2, y_1, y_2')
kg = sf.Parameter(value=0.01, min=0.0, max=0.1)
a_1, a_2 = sf.parameters('a_1, a_2')
globalmodel = sf.Model({
    y_1: a_1 * sf.exp(- kg * x_1),
    y_2: a_2 * sf.exp(- kg * x_2),
})

# Do fit
globalfit = sf.Fit(globalmodel, x_1=t, x_2=t, y_1=C1, y_2=C2)
globalfit_result = globalfit.execute()
print(globalfit_result)

y_r = globalmodel(x_1=t, x_2=t, **globalfit_result.params)

# Plot fit
plt.plot(t,C1,'ro')
plt.plot(t,C2,'b+')
plt.plot(t,y_r[0],'r-')
plt.plot(t,y_r[1],'b-')
plt.show()

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