可以解决y作为x的函数的问题
问题是每个有效x都有y的2个值，并且在椭圆跨度x的范围之外没有（或虚数）y个解
下面是3.5代码，sympy 1.0应该可以，但是可以打印，列表组合可能无法向后兼容2.x
from numpy import linalgfrom numpy import linspaceimport numpy as npfrom numpy import meshgridimport randomimport matplotlib.pyplot as pltfrom scipy import optimizefrom sympy import *xs = [1.02, 0.95, 0.87, 0.77, 0.67, 0.56, 0.44, 0.30, 0.16, 0.01]ys = [0.39, 0.32, 0.27, 0.22, 0.18, 0.15, 0.13, 0.12, 0.12, 0.15]b = [i ** 2 for i in xs] # That is the list that contains the results that are given as x^2 from the equation.def fxn(x, y): # That is the function that solves the given equation to find each parameter. my_list = [] #It is the main list. for z in range(len(x)): w = [0] * 5 w[0] = y[z] ** 2 w[1] = x[z] * y[z] w[2] = x[z] w[3] = y[z] w[4] = 1 my_list.append(w) return my_listt = linalg.lstsq(fxn(xs, ys), b)def ysolv(coeffs): x,y,a,b,c,d,e = symbols('x y a b c d e') ellipse = a*y**2 + b*x*y + c*x + d*y + e - x**2 y_sols = solve(ellipse, y) print(*y_sols, sep='n') num_coefs = [(a, f) for a, f in (zip([a,b,c,d,e], coeffs))] y_solsf0 = y_sols[0].subs(num_coefs) y_solsf1 = y_sols[1].subs(num_coefs) f0 = lambdify([x], y_solsf0) f1 = lambdify([x], y_solsf1) return f0, f1f0, f1 = ysolv(t[0])y0 = [f0(x) for x in xs]y1 = [f1(x) for x in xs]plt.scatter(xs, ys)plt.scatter(xs, y0, s=100, color = 'red', marker='+')plt.scatter(xs, y1, s=100, color = 'green', marker='+')plt.show()在Spyder中运行以上命令时：
runfile('C:/Users/john/mypy/mySE_answers/ellipse.py', wdir='C:/Users/john/mypy/mySE_answers')(-b*x - d + sqrt(-4*a*c*x - 4*a*e + 4*a*x**2 + b**2*x**2 + 2*b*d*x + d**2))/(2*a)-(b*x + d + sqrt(-4*a*c*x - 4*a*e + 4*a*x**2 + b**2*x**2 + 2*b*d*x + d**2))/(2*a)
为y值生成的函数并非在所有地方都有效：
f0(0.1), f1(0.1)Out[5]: (0.12952825130864626, 0.6411040771593166)f0(2)Traceback (most recent call last): File "<ipython-input-6-9ce260237dcd>", line 1, in <module> f0(2) File "<string>", line 1, in <lambda>ValueError: math domain errorIn [7]:
域错误将需要尝试/执行才能“感觉”到有效的x范围或更多数学运算
像下面的try / except一样：（编辑为“关闭”图纸，重新注释）
def feeloutXrange(f, midx, endx): fxs = [] x = midx while True: try: f(x) except: break fxs.append(x) x += (endx - midx)/100 return fxsmidx = (min(xs) + max(xs))/2xpos = feeloutXrange(f0, midx, max(xs))xnegs = feeloutXrange(f0, midx, min(xs))xs_ellipse = xnegs[::-1] + xpos[1:]y0s = [f0(x) for x in xs_ellipse]y1s = [f1(x) for x in xs_ellipse]ys_ellipse = y0s + y1s[::-1] + [y0s[0]] # add y start point to end to close drawingxs_ellipse = xs_ellipse + xs_ellipse[::-1] + [xs_ellipse[0]] # added x start pointplt.scatter(xs, ys)plt.scatter(xs, y0, s=100, color = 'red', marker='+')plt.scatter(xs, y1, s=100, color = 'green', marker='+')plt.plot(xs_ellipse, ys_ellipse)plt.show()
编辑：将重复的起点添加到椭圆点列表的末尾以关闭绘图
ys_ellipse = y0s + y1s[::-1] + [y0s[0]] # add y start point to end to close drawingxs_ellipse = xs_ellipse + xs_ellipse[::-1] + [xs_ellipse[0]] # added x start point
