如另一个答案中所建议，您可以将lmfit用于此类问题。因此，我还添加了一个有关如何使用它的示例，以防有人对此主题感兴趣。
假设您有一个数据集，如下所示：
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])
并且您想要使模型适合数据，如下所示：
model = n1 + (n2 * x + n3) * 1./ (1. + np.exp(n4 * (n5 - x)))
受到限制
0.2 < n1 < 0.8-0.3 < n2 < 0
lmfit然后使用（版本0.8.3）获得以下输出：
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)
如您所见，拟合非常好地再现了数据，并且参数在请求的范围内。
这是完整的代码，它重现了该图并带有一些其他注释：
from lmfit import minimize, Parameters, Parameter, report_fitimport numpy as npxdata = 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 boundariesparams = 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 modelresult = minimize(fit_fc, params, args=(xdata, ydata))# write error reportreport_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 resultstry: import pylab pylab.plot(xdata, ydata, 'k+') pylab.plot(xplot, yplot, 'r') pylab.show()except: pass编辑：
如果您使用的是0.9.x版，则需要相应地调整代码。在此处检查从0.8.3到0.9.x进行了哪些更改。
