Python lmfit：拟合2D模型 [英] Python lmfit: Fitting a 2D Model

问题描述

我正在尝试将2D高斯拟合到某些由2D数组给出的灰度图像数据上。
lmfit库实现了一个易于使用的Model类，应该能够做到这一点。
不幸的是，文档（ http://lmfit.github.io/lmfit-py /model.html ）仅提供一维拟合的示例。对于我来说，我只是用2个独立变量构造lmfit模型。

I'm trying to fit a 2D-Gaussian to some greyscale image data, which is given by one 2D array. The lmfit library implements a easy-to-use Model class, that should be capable of doing this. Unfortunately the documentation (http://lmfit.github.io/lmfit-py/model.html) does only provide examples for 1D fitting. For my case I simply construct the lmfit Model with 2 independent variables.

以下代码对我来说似乎是有效的，但会导致scipy抛出 minpack.error：函数调用不是正确的float数组。

The following code seems valid for me, but causes scipy to throw a "minpack.error: Result from function call is not a proper array of floats."

Tom总结：如何将2D（x1，x2）->（y）数据输入到lmfit。？

Tom sum it up: How to input 2D (x1,x2)->(y) data to a Model of lmfit.?

这是我的方法：
一切都包装在GaussianFit2D类中，但这是重要的部分：
这就是高斯函数。文档中介绍了有关用户定义函数的信息

Here is my approach: Everything is packed in a GaussianFit2D class, but here are the important parts: That's the Gaussian function. The documentation says about user defined functions

当然，模型函数必须返回一个与数据大小相同的数组被模仿。通常，这也可以通过指定一个或多个自变量来处理。

Of course, the model function will have to return an array that will be the same size as the data being modeled. Generally this is handled by also specifying one or more independent variables.

我真的不明白这是什么意思，因为值x1，x2唯一合理的结果是标量值。

I don't really get what this should mean, since for given values x1,x2 the only reasonable result is a scalar value.

def _function(self, x1, x2, amp, wid, cen1, cen2):
    val = (amp/(np.sqrt(2*np.pi)*wid)) * np.exp(-((x1-cen1)**2+(x2-cen2)**2)/(2*wid**2))
    return val

此处生成模型：

def _buildModel(self, **kwargs):
    model = lmfit.Model(self._function, independent_vars=["x1", "x2"],
                        param_names=["amp", "wid", "cen1", "cen2"])
    return model

这是获取数据，构建模型和参数并调用lmfit fit（）的函数：

That's the function that takes the data, builds the model and params and calls lmfit fit():

def fit(self, data, freeX, **kwargs):
    freeX = np.asarray(freeX, float)
    model = self._buildModel(**kwargs)
    params = self._generateModelParams(model, **kwargs)

    model.fit(data, x1=freeX[0], x2=freeX[1], params=params)

Anf最后在这里将此拟合函数称为：

Anf finally here this fit function gets called:

    data = np.asarray(img, float)
    gaussFit = GaussianFit2D()
    x1 = np.arange(len(img[0, :]))
    x2 = np.arange(len(img[:, 0]))
    fit = gaussFit.fit(data, [x1, x2])

推荐答案

好，与开发人员写信并得到了他们的答案（感谢Matt在这里）。

Ok, wrote with the devs and got the answer from them (thanks to Matt here).

基本思想是将所有输入平整为一维数据，对lmfit而言隐藏> 1维输入。
这是您的操作方式。
修改函数：

The basic idea is to flatten all the input to 1D data, hiding from lmfit the >1 dimensional input. Here's how you do it. Modify your function:

 def function(self, x1, x2):
       return (x1+x2).flatten()

展平您要适合的2D输入数组：

Flatten your 2D input array you want to fit to:

...
data = data.flatten()
...

修改两个1D x变量，使其具有它们的任意组合：

Modify the two 1D x-variables such that you have any combination of them:

...
x1n = []
x2n = []
    for i in x1:
         for j in x2:
              x1n.append(i)
              x2n.append(j)
x1n = np.asarray(x1n)
x2n = np.asarray(x2n)
...

然后将任何东西扔进钳工中：

And throw anything into the fitter:

model.fit(data, x1=x1n, x2=x2n, params=params)

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