python - 在二维数据上拟合抛物线——已编辑

Question

我已经搜索了使用抛物线和/或双曲线进行二维数据拟合的示例代码，但没有成功运行任何代码。

我使用了scipy.optimize.leastsq来进行拟合练习:

NEW修改代码如下:

def hyprsinc_errors(pararr, t,x,datarr):
    x=np.array(x)
    pararr[4] = np.abs(pararr[4])
    outarr = np.zeros((np.size(t),np.size(x)),float)
    for ix in x:
        it = int(np.sqrt(pararr[0]*(ix-pararr[1])**2)+pararr[2])
        if it < max(t)-int(pararr[4])-1:
            for iit in range(-int(pararr[4])+it,it+int(pararr[4])+1,1):
                outarr[iit,ix] =(-1)**int(pararr[4])*pararr[0]/pararr[3]
           #end for it
            outarr[it,ix]=pararr[3]
   #end for ix
    output =  ((outarr-datarr).ravel()).sum()
    print(type(output),output)
    return np.float(output)
#
import numpy as np
import matplotlib as plt
from scipy.optimize import curve_fit
#
datarr = np.array([[ 4,  0,  1,  0,  2,  3,  1,  5,  2,  0],\
                  [ 2,  0,  0,  2,  1,  0,  5,  5,  3,  5],\
                  [ 4,  2,  0,  2,  0,  1,  5,  4,  3,  4],\
                  [ 2,  0,  1,  3,  5,  2,  3,  5,  3,  3],\
                  [ 5,  3,  3,  4, 12, 12,  5,  0,  2,  3],\
                  [ 2,  0,  5, 12, 12, 11, 13,  0,  4,  3],\
                  [ 5,  3, 12, 11,  2,  2, 10, 15,  2,  3],\
                  [ 1, 15, 11,  3,  4,  0,  0, 11, 10,  3],\
                  [14, 12,  1,  1,  2,  5,  3,  2, 12, 14],\
                  [10,  3,  4,  4,  1,  4,  0,  5,  4, 10]])
#
T = np.linspace(0, 9, 10)
X = np.linspace(0, 9, 10)


hyprsinc_errors((T,X),datarr, 1,4,4,10,0)
optimized_result = leastsq(hyprsinc_errors,x0=np.array([1.,5,5,10,0]),args=(T,X,datarr))
print("opt_result = ", optimized_result[0])

我收到新错误:

在[92]中:p1,success = lesssq(hyprsinc_errors,x0=np.array([1.,5,5,10,0]),args=(T,X,datarr))

(, -388.0) <-- 在错误函数的最后一行打印!

> - TypeError                                 Traceback (most recent call last)
> /nfs/rvl/sip/gs/nobackup3/holland/interferometry16/multiples/python_build/intel/python/<ipython-input-92-5f7acb18d23f>
> in <module>()
> ----> 1 p1,success = leastsq(hyprsinc_errors,x0=np.array([1.,5,5,10,0]),args=(T,X,datarr))
> 
> /apps/sss/epd/7.2.2/lib/python2.7/site-packages/scipy/optimize/minpack.py
> in leastsq(func, x0, args, Dfun, full_output, col_deriv, ftol, xtol,
> gtol, maxfev, epsfcn, factor, diag)
>     276     m = _check_func('leastsq', 'func', func, x0, args, n)[0]
>     277     if n > m:
> --> 278         raise TypeError('Improper input: N=%s must not exceed M=%s' % (n,m))
>     279     if Dfun is None:
>     280         if (maxfev == 0):
> 
> TypeError: Improper input: N=5 must not exceed M=1

<小时/>

Answer 1

curve_fit更适合拟合二维函数。您看到的错误是因为您将二维数组作为 ydata 参数传递，这意味着是一个 m 长度的数组(即一维)。大多数时候，沿着函数的单个切片拟合参数会产生不正确的结果。

我建议你使用least_squares而不是curve_fit。请记住，它的级别有点低:它要求您手动计算错误并提供对参数的猜测:

from scipy.optimize import least_squares
XX,YY = np.meshgrid(X,Y)
prbola_errors = lambda args: (prbola(XX,YY, *args) - dataarr).ravel()
optimize_result = least_squares(prbola_errors, (0., 1., 0., 1.))

这是一个演示:https://gist.github.com/FranciscoDA/378b2223957d2b0e201350b0e66aec84

编辑:关于更新的问题，需要修复一些问题:

• leastsq() 期望传递的函数返回一个包含计算误差的一维数组
• 作为leastsq() 的x0 参数传递的参数数量与函数期望的参数数量不匹配(这里我添加了一个初始化为0 的虚拟变量)
• 该函数尝试使用非 int 标量对数组进行索引。在这里，我在需要的地方将它们转换为 int

更新的代码:

import numpy as np
import matplotlib as plt
from scipy.optimize import curve_fit, leastsq

def hyprsinc_errors(pararr, t,x,datarr):
    x=np.array(x)
    pararr[4] = np.abs(pararr[4])
    outarr = np.zeros((np.size(t),np.size(x)),float)
    for ix in x:
        it = int(np.sqrt(pararr[0]*(ix-pararr[1])**2)+pararr[2])
        if it < max(t)-int(pararr[4])-1:
            for iit in range(-int(pararr[4])+it,it+int(pararr[4])+1,1):
                outarr[int(iit),int(ix)] =(-1)**int(pararr[4])*pararr[0]/pararr[3]
            outarr[int(it),int(ix)]=pararr[3]
    output = (outarr-datarr).ravel()
    return output
#

#
datarr = np.array([[ 4,  0,  1,  0,  2,  3,  1,  5,  2,  0],\
                  [ 2,  0,  0,  2,  1,  0,  5,  5,  3,  5],\
                  [ 4,  2,  0,  2,  0,  1,  5,  4,  3,  4],\
                  [ 2,  0,  1,  3,  5,  2,  3,  5,  3,  3],\
                  [ 5,  3,  3,  4, 12, 12,  5,  0,  2,  3],\
                  [ 2,  0,  5, 12, 12, 11, 13,  0,  4,  3],\
                  [ 5,  3, 12, 11,  2,  2, 10, 15,  2,  3],\
                  [ 1, 15, 11,  3,  4,  0,  0, 11, 10,  3],\
                  [14, 12,  1,  1,  2,  5,  3,  2, 12, 14],\
                  [10,  3,  4,  4,  1,  4,  0,  5,  4, 10]])
#
T = np.linspace(0, 9, 10)
X = np.linspace(0, 9, 10)

optimized_result = leastsq(hyprsinc_errors,x0=np.array([1.,5,5,10,0,0]),args=(T,X,datarr))
print("opt_result = ", optimized_result[0])

示例输出:opt_result = [ 1.5.00000006 5.10.42857143 0.0.]