Scipy的最佳曲线拟合极限 [英] Scipy's Optimize Curve Fit Limits
问题描述
有什么办法可以为Scipy的优化曲线拟合提供限制吗？
我的示例：
def Optimized_formula（x，m_1，m_2，y_1，y_2，ratio_2）：
return（log（x [0]）* m_1 + m_2）*（（1-x [1] / max_age）*（1-ratio_2））+（（log（x [x [1]）* y_1 + y_2）*（x [1] / max_age）* ratio_2）
popt， pcov = optimize.curve_fit（optimized_formula，usage_and_age，价格）
x [0]是age，max_age是一个常数。考虑到这一点，当x [0]接近最大值时，x [1] / max_age接近1。
是否有可能提供一个约束/限制，从而x [1 ] / max_age> 0.3且x [1] / max_age< 0.7和其他约束条件，例如m_1< 0，m_2> 0，依此类推。
根据另一个答案的建议，您可以使用
如您所见，拟合度很好地再现了数据，并且该参数位于请求的范围内。
以下是重绘该图的整个代码，并带有一些其他注释：
来自lmfit导入最小化，参数，参数，report_fit
导入numpy为np
xdata = np.array（[177.，180。 ，183.，187.，189.，190.，19 6.，197.，201.，202.，203.，204.，206.，218.，225.，231.，234。，
252.，262.，266.，267.268 。，277.，286.，303。]）
ydata = np.array（[0.81,0.74,0.78,0.75,0.77,0.81,0.73,0.76,0.71,0.74,0.81,0.71 ，0.74,0.71，
0.72,0.69,0.75,0.59,0.61,0.63,0.64,0.63,0.35,0.27,0.26]）
def fit_fc（params，x，data）：
n1 = params ['n1']。value
n2 = params ['n2']。value
n3 = params ['n3']。value
n4 = params ['n4']。value
n5 = params ['n5']。value
model = n1 +（n2 * x + n3）* 1. /（1。 + np.exp（n4 *（n5-x）））
返回模型-数据＃这就是您要最小化的功能
＃创建一组参数
＃'value'是初始条件
＃'min'和'max'定义边界
params = Parameters（）
params.add（'n1'，value = 0.2，min = 0.2，max = 0.8）
params.add（'n2'，value = -0.005，min = -0.3，max = 10 **（-10））
params.add（'n3' ，value = 1.0766，min = -1000。，max = 1000。）
params.add（'n4'，value = -0.36379，min = -1000。，max = 1000。）
params。 add（'n5'，value = 274.0，min = 0。，max = 1000。）
＃可以拟合，这里使用最小二乘模型
结果=最小化（fit_fc，params，args = （xdata，ydata））
＃写入错误报告
report_fit（params）
xplot = np.linspace（min（xdata），max（xdata）， 1000）
yplot = result.values ['n1'] +（result.values ['n2'] * xplot + result.values ['n3']）* \
1. /（1 。+ np.exp（result.values ['n4'] *（result.values ['n5']-xplot）））
#plot结果
尝试：
impo rt pylab
pylab.plot（xdata，ydata，'k +'）
pylab.plot（xplot，yplot，'r'）
pylab.show（）
除外：
通过
编辑：
如果您使用的是0.9.x版，则需要相应地调整代码。在此处进行检查。从0.8开始进行了更改。 3至0.9.x。
Is there any way I can provide limits for the Scipy's Optimize Curve Fit?
My example:
def optimized_formula(x, m_1, m_2, y_1, y_2, ratio_2):
return (log(x[0]) * m_1 + m_2)*((1 - x[1]/max_age)*(1-ratio_2)) + ((log(x[1]) * y_1 + y_2)*(x[1]/max_age)*ratio_2)
popt, pcov = optimize.curve_fit(optimized_formula, usage_and_age, prices)
x[0] is age and max_age is a constant. With that in mind, as x[0] approaches maximum, x[1]/max_age approaches 1.
Is it possible to provide a constraint/limit whereby x[1]/max_age > 0.3 and x[1]/max_age < 0.7 and other constraints such as m_1 < 0, m_2 > 0, and so on.
As suggested in another answer, you could use lmfit for these kind of problems. Therefore, I add an example on how to use it in case someone is interested in this topic, too.
Let's say you have a dataset as follows:
xdata = np.array([177.,180.,183.,187.,189.,190.,196.,197.,201.,202.,203.,204.,206.,218.,225.,231.,234.,
252.,262.,266.,267.,268.,277.,286.,303.])
ydata = np.array([0.81,0.74,0.78,0.75,0.77,0.81,0.73,0.76,0.71,0.74,0.81,0.71,0.74,0.71,
0.72,0.69,0.75,0.59,0.61,0.63,0.64,0.63,0.35,0.27,0.26])
and you want to fit a model to the data which looks like this:
model = n1 + (n2 * x + n3) * 1./ (1. + np.exp(n4 * (n5 - x)))
with the constraints that
0.2 < n1 < 0.8
-0.3 < n2 < 0
Using lmfit (version 0.8.3) you then obtain the following output:
n1: 0.26564921 +/- 0.024765 (9.32%) (init= 0.2)
n2: -0.00195398 +/- 0.000311 (15.93%) (init=-0.005)
n3: 0.87261892 +/- 0.068601 (7.86%) (init= 1.0766)
n4: -1.43507072 +/- 1.223086 (85.23%) (init=-0.36379)
n5: 277.684530 +/- 3.768676 (1.36%) (init= 274)
As you can see, the fit reproduces the data very well and the parameters are in the requested ranges.
Here is the entire code that reproduces the plot with a few additional comments:
from lmfit import minimize, Parameters, Parameter, report_fit
import numpy as np
xdata = np.array([177.,180.,183.,187.,189.,190.,196.,197.,201.,202.,203.,204.,206.,218.,225.,231.,234.,
252.,262.,266.,267.,268.,277.,286.,303.])
ydata = np.array([0.81,0.74,0.78,0.75,0.77,0.81,0.73,0.76,0.71,0.74,0.81,0.71,0.74,0.71,
0.72,0.69,0.75,0.59,0.61,0.63,0.64,0.63,0.35,0.27,0.26])
def fit_fc(params, x, data):
n1 = params['n1'].value
n2 = params['n2'].value
n3 = params['n3'].value
n4 = params['n4'].value
n5 = params['n5'].value
model = n1 + (n2 * x + n3) * 1./ (1. + np.exp(n4 * (n5 - x)))
return model - data #that's what you want to minimize
# create a set of Parameters
# 'value' is the initial condition
# 'min' and 'max' define your boundaries
params = Parameters()
params.add('n1', value= 0.2, min=0.2, max=0.8)
params.add('n2', value= -0.005, min=-0.3, max=10**(-10))
params.add('n3', value= 1.0766, min=-1000., max=1000.)
params.add('n4', value= -0.36379, min=-1000., max=1000.)
params.add('n5', value= 274.0, min=0., max=1000.)
# do fit, here with leastsq model
result = minimize(fit_fc, params, args=(xdata, ydata))
# write error report
report_fit(params)
xplot = np.linspace(min(xdata), max(xdata), 1000)
yplot = result.values['n1'] + (result.values['n2'] * xplot + result.values['n3']) * \
1./ (1. + np.exp(result.values['n4'] * (result.values['n5'] - xplot)))
#plot results
try:
import pylab
pylab.plot(xdata, ydata, 'k+')
pylab.plot(xplot, yplot, 'r')
pylab.show()
except:
pass
EDIT:
If you use version 0.9.x you need to adjust the code accordingly; check here which changes have been made from 0.8.3 to 0.9.x.
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