作为x的函数,y可以解决该问题
问题是每个有效x有2个y值,而椭圆跨度x范围外没有(或想象)y解
下面是3.5代码,sympy 1.0应该可以打印,list comps可能不会向后兼容到2.x.
from numpy import linalg
from numpy import linspace
import numpy as np
from numpy import meshgrid
import random
import matplotlib.pyplot as plt
from scipy import optimize
from 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_list
t = 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='
')
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, f1
f0, 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()
当上述内容在Spyder中运行时：
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)
????
生成的y值函数无处不在：
f0(0.1), f1(0.1)
Out[5]: (0.12952825130864626, 0.6411040771593166)
f0(2)
Traceback (most recent call last):
File "", line 1, in
f0(2)
File "", line 1, in
ValueError: math domain error
In [7]:
域错误需要try / execpt来“感觉”有效的x范围或更多的数学
喜欢尝试/除了下面:(编辑为“关闭”绘图重新评论)
def feeloutXrange(f, midx, endx):
fxs = []
x = midx
while True:
try: f(x)
except:
break
fxs.append(x)
x += (endx - midx)/100
return fxs
midx = (min(xs) + max(xs))/2
xpos = 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 drawing
xs_ellipse = xs_ellipse + xs_ellipse[::-1] + [xs_ellipse[0]] # added x start point
plt.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 drawing
xs_ellipse = xs_ellipse + xs_ellipse[::-1] + [xs_ellipse[0]] # added x start point
