Python多变量非线性回归计算

Question

i was trying to make a curve fit of data and want to find nonlinear regression equation.

thats what my plot looks like i got x,y data which will be my reference data, then i got x0 and y0 which will be my second point, dx and dy will be difference between them when i show this as vector it showed form of

when i convert dx,dy to R and theta it showed x^2+y^2 form, is it possible to find those equation with it? here's my current code

import matplotlib.pyplot as plt
import numpy as np
import math
import seaborn as sns
from statsmodels.formula.api import ols
from mpl_toolkits.mplot3d import Axes3D
from scipy.interpolate import griddata
"""setting dpi for graph shown in editor"""
import matplotlib as mpl
mpl.rcParams['figure.dpi'] = 300

import pandas as pd
"""reading data from excel sheet 1"""
df = pd.read_excel(r'C:\Users\JRKIM\Desktop\data\2513data.xlsx')

"""variable selection"""

tx_0 = df.loc[:,'TRUE_x_0']
ty_0 = df.loc[:,'TRUE_y_0']

v_x_0 = df.loc[:,'vx']
v_y_0 = df.loc[:,'vy']

dx0_0 = tx_0-v_x_0
dy0_0 = ty_0-v_y_0

dr0_0 = df.loc[:,'dr']




fig1, ax0 = plt.subplots()
ax0.set_title("delta0 in vector")

qk = ax0.quiver(tx_0,ty_0,dx0_0,dy0_0)
ax0.scatter(tx_0, ty_0, color='r', s=1)

"""3d graph with vector and position """

fig4 = plt.figure()
ax4 = fig4.add_subplot(111, projection='3d')

ax4.scatter(tx_0, ty_0, dr0_0, marker='*',linewidth = 0.01, cmap="jet")

ax4.set_xlabel('X Label')
ax4.set_ylabel('Y Label')
ax4.set_zlabel('dr Label')

Answer 1

you can use scipy.optimize.curve_fit as follows.

from scipy.optimize import curve_fit

def quadratic_function(x, a, b):
    return a * x[0]**2 + b * x[1]**2 # + c * x[0]*x[1] if you want to satisfy quadratic form

xdata = np.vstack([np.array(dx0_0).flatten(),np.array(dy0_0).flatten()])
ydata = np.array(dr0_0).flatten()
popt, pcov = curve_fit(quadratic_function,xdata,ydata)
print(popt) # values for a and b

this should get you the coefficients for a and b for the least squares fitting of a*x**2 + b*y**2 = r , you have to further calculate the error and see if the error is low enough for your liking.

Edit: corrected the dimensions of inputs