在python中使用lmfit将数据拟合到2D函数

Question

I wish to fitting data with a 2D function in order to extract parameter (a) and (b) using lmfit package. Basically as a 1D function fitting, I am trying to fit every data point to the 2D function at the same coordinates (x,y). This is mean that every data point has its initial guess value which different from another data point since each data has different coordinate(x,y). This is my code:

    #!/usr/bin/ python
    import pyfits
    import numpy as np
    import math
    from lmfit import minimize, Parameters, Parameter, report_errors,report_fit,     
         conf_interval, printfuncs


    xn =np.linspace(0,3,4)    # x-component
    yn =np.linspace(0,3,4)    # y-component

    data= [0.0, 0.16, 0.33, 0.5, 0.2, 0.26, 0.38, 0.53, 0.4, 0.43, 0.52, 0.64, 0.6, 0.62,   
    0.67, 0.78]   # (x1,y1) generate (data[0]), (x1,y2) generate (data[1]) and so on


    params = Parameters()
    params.add('a', value=3)
    params.add('b', value=5)                     


    def residual(params,x,y,data=None):
        a = params['a'].value             # parameter
        b = params['b'].value             # parameter
        model=(x**2/a**2+y**2/b**2)**0.5      # 2D function            
        if data is None:
           return data
        return model - data


    out=minimize(residual,params,args=(x,y,data,))        # lmfit minimizer
    final=data+out.residual
    report_fit(params)
    ci = conf_interval(out, sigmas=[0.68,0.95])           # confidence interval
    printfuncs.report_ci(ci)

However, I got this error message:

    ValueError: operands could not be broadcast together with shapes (4) (16)  

Obviously, dimension of x and y is not the same of data, but I don't know how to make data[0] takes (x1,y1), data[1] takes (x1,y2)..., data[5] takes (x2,y1) and so on. Please could anyone help me to fix this problem or make any suggestion, thank you in advance.

Answer 1

Do you need to zip your data?

x = [x1, x2, ...]
y = [y1, y2, ...]
data = zip(x, y) # [(x1, y1), (x2, y2), ... ]