问题描述
我正在尝试使用curve_fit容纳一些数据.它的效果很好，我只想使用其他参数来提高拟合度以匹配假设(例如机械效率不能大于100％等)
I am trying to use curve_fit to fit some data. it is working great, I would just like to improve the fit with additional parameters to match assumptions (such as mechanical efficiency cannot be greater than 100% etc)
y_data = [0.90 0.90 0.90 0.90 0.90 0.90 0.90 1.30 1.30 1.30 1.30 1.20 1.65 1.65 1.65 1.65 1.65 1.65 1.80 1.80 1.80 1.80 1.80 1.80 1.80 1.80 1.80 3.50 6.60 6.60 6.70 6.70 6.70 6.70 6.70 8.50 12.70] # I am aware this does not have commas
x_data = [0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.46 0.53 0.53 0.53 0.53 0.53 0.53 0.53 0.53 0.53 0.53 0.53 0.53 0.53 0.53 0.53 0.53 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02] # ditto
def poly2(x, a, b, c): return a*x**2+ b*x+c
def poly3(x,a,b,c,d): return a*x**3+b*x**2+c*b*x+d
pars = fit(poly2, x_data, y_data, bounds=bounds)
但是我想额外指定参数之间关系的界限，例如.
But I would like to additionally specify bounds to relations between parameters eg.
B**2 -4*a*c > 0 #for poly2
b**2-3*a*c=0 #for poly3
确保拟合具有水平拐点.有没有办法做到这一点?
To ensure that the fit has horizontal inflection.Is there a way to achieve this?
我发现了这一点，一旦我进行调查，可能会有所帮助:
I found this, it may help once I investigate:How do I put a constraint on SciPy curve fit?
如何按照建议使用lmfit做到这一点?
How would this be done using lmfit as suggested?
推荐答案
所以，我相信我已经基于使用lmfit的@ 9dogs注释解决了这个问题.相关文档在这里:
So I believe I have solved this, based on @9dogs comment using lmfit.relevant documentation here:
https://lmfit.github.io/lmfit-py/constraints.html
和一个有用的教程在这里:
and a helpful tutorial here:
http://blog.danallan.com/projects/2013/model/
对于我的函数poly3，此接缝可以强制执行水平或正向弯曲.
For my function poly3 this seams to work to enforce horizontal or positive inflection.
from lmfit import Parameters, Model
def poly3(x,a,b,c,d): return a*x**3+b*x**2+c*b*x+d
model = Model(poly3, independent_vars=['x'], )
params = Parameters()
为糟糕的数学道歉:三次判别式在此处给出为 https://brilliant.org/wiki/cubic-discriminant/ b**2*c**2-4*a*c**3-4*b**3*d-27*a**2*d**2+18*a*b*c*d
apologies for teh terrible maths: the cubic dicriminant is given here as https://brilliant.org/wiki/cubic-discriminant/ b**2*c**2-4*a*c**3-4*b**3*d-27*a**2*d**2+18*a*b*c*d
params = Parameters()
params..add('a', value=1, min=0, vary=True)
params.add('b', value=1, vary=True)
params.add('c', value=1, vary=True)
params.add('d', value=1, vary=True)
params.add('discr', value = 0, vary= False, expr='(b**2*c**2-4*a*c**3-4*b**3*d-27*a**2*d**2+18*a*b*c*d)')
result = model.fit(y_data, x=x_data, params=params) # do the work
pars = [] # list that will contain the optimized parameters for analysis
# create a parameters list for use in the rest of code, this is a stopgap until I refactor the rest of my code
pars.append(result.values['a'])
pars.append(result.values['b'])
pars.append(result.values['c'])
pars.append(result.values['d'])
## rest of code such as plotting
如有疑问，我将进一步扩展示例.
If there are questions I will expand the example further.
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