抛物面(3D抛物线)表面贴合python

问题描述

我正在尝试拟合以下x数据:[0.4,0.165,0.165,0.585,0.585]，此y数据:[.45，.22，.63，.22，.63]和此z数据: [1，0.99，0.98,0.97,0.96]变成抛物面.我正在使用scipy的curve_fit工具.这是我的代码:

I am trying to fit this x data: [0.4,0.165,0.165,0.585,0.585], this y data: [.45, .22, .63, .22, .63], and this z data: [1, 0.99, 0.98,0.97,0.96] to a paraboloid. I am using scipy's curve_fit tool. Here is my code:

doex = [0.4,0.165,0.165,0.585,0.585]
doey = [.45, .22, .63, .22, .63]
doez = np.array([1, .99, .98,.97,.96])

def paraBolEqn(data,a,b,c,d):
    if b < .16 or b > .58  or c < .22 or c >.63:
        return 1e6
    else:
        return ((data[0,:]-b)**2/(a**2)+(data[1,:]-c)**2/(a**2))

data = np.vstack((doex,doey))
zdata = doez

opt.curve_fit(paraBolEqn,data,zdata)

我正在尝试将抛物面居中在.16和.58(x轴)之间以及.22和.63(y轴)之间.如果b或c不在此范围内，我将通过返回一个较大的值来实现此目的.

I am trying to center the paraboloid between .16 and .58 (x axis) and between .22 and .63 (y axis). I am doing this by returning a large value if b or c are outside of this range.

不幸的是，拟合度很差，我的popt值都为1，而我的pcov是inf.

Unfortunately the fit is wayyy off and my popt values are all 1, and my pcov is inf.

任何帮助都会很棒.

谢谢

推荐答案

您不必提供超出范围区域的高返回值，而需要提供一个很好的初始猜测.此外，该模式缺少偏移参数，并且抛物面符号错误.将模型更改为:

Rather than forcing high return values for out-of range regions you need to provide a good initial guess. In addition, the mode lacks an offset parameter and the paraboloid has the wrong sign. Change the model to:

def paraBolEqn(data,a,b,c,d):
    x,y = data
    return -(((x-b)/a)**2+((y-d)/c)**2)+1.0

我将偏移量固定为1.0，因为如果将其添加为拟合参数，系统将无法确定(数据点数比拟合参数少或相等).像这样的初步猜测呼叫curve_fit:

I fixed the offset to 1.0 because if it were added as fit parameter the system would be underdetermined (fewer or equal number of data points than fit parameters).Call curve_fit with an initial guess like this:

popt,pcov=opt.curve_fit(paraBolEqn,np.vstack((doex,doey)),doez,p0=[1.5,0.4,1.5,0.4])

这将产生:

[ 1.68293045  0.31074135  2.38822062  0.36205424]

与数据的很好的匹配:

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