是否可以使用Matplotlib繪製隱式方程？

Question

我想繪製Matplotlib中的隱式方程（形式爲f（x，y）= g（x，y），例如X^y = y^x）。這可能嗎？

Answer 1

我不相信有這很好的支持，但你可以嘗試像

import matplotlib.pyplot 
from numpy import arange 
from numpy import meshgrid 

delta = 0.025 
xrange = arange(-5.0, 20.0, delta) 
yrange = arange(-5.0, 20.0, delta) 
X, Y = meshgrid(xrange,yrange) 

# F is one side of the equation, G is the other 
F = Y**X 
G = X**Y 

matplotlib.pyplot.contour(X, Y, (F - G), [0]) 
matplotlib.pyplot.show() 

見API docs爲contour：如果第四個參數是那麼一個序列它指定了等高線繪製。但情節只會與你的範圍的分辨率一樣好，並且有些特徵可能永遠不會正確，通常在自我交叉點。

Answer 2

matplotlib不繪製方程;它繪製了系列的點。您可以使用類似scipy​.optimize這樣的工具從數值上計算隱式方程的x值（反之亦然），或根據需要任意數量的其他工具來計算y點。

---

例如，這裏是我繪製隱含方程x ** 2 + x * y + y ** 2 = 10在一定區域內的例子。

from functools import partial 

import numpy 
import scipy.optimize 
import matplotlib.pyplot as pp 

def z(x, y): 
    return x ** 2 + x * y + y ** 2 - 10 

x_window = 0, 5 
y_window = 0, 5 

xs = [] 
ys = [] 
for x in numpy.linspace(*x_window, num=200): 
    try: 
     # A more efficient technique would use the last-found-y-value as a 
     # starting point 
     y = scipy.optimize.brentq(partial(z, x), *y_window) 
    except ValueError: 
     # Should we not be able to find a solution in this window. 
     pass 
    else: 
     xs.append(x) 
     ys.append(y) 

pp.plot(xs, ys) 
pp.xlim(*x_window) 
pp.ylim(*y_window) 
pp.show() 

Answer 3

如果你願意用比matplotlib以外的東西（但仍蟒蛇），有聖人：

一個例子：http://sagenb.org/home/pub/1806

Documentation for implicit_plot

The Sage Homepage

Answer 4

許多謝謝Steve，Mike，Alex。我已經與史蒂夫的解決方案一起（請參閱下面的代碼）。我唯一剩下的問題是等高線圖出現在我的網格線後面，而不是一個規則的情節，我可以用zorder強迫它到前面。任何更多halp非常讚賞。

乾杯， 格迪斯

import matplotlib.pyplot as plt 
from matplotlib.ticker import MultipleLocator, FormatStrFormatter 
import numpy as np 

fig = plt.figure(1) 
ax = fig.add_subplot(111) 

# set up axis 
ax.spines['left'].set_position('zero') 
ax.spines['right'].set_color('none') 
ax.spines['bottom'].set_position('zero') 
ax.spines['top'].set_color('none') 
ax.xaxis.set_ticks_position('bottom') 
ax.yaxis.set_ticks_position('left') 

# setup x and y ranges and precision 
x = np.arange(-0.5,5.5,0.01) 
y = np.arange(-0.5,5.5,0.01) 

# draw a curve 
line, = ax.plot(x, x**2,zorder=100) 

# draw a contour 
X,Y=np.meshgrid(x,y) 
F=X**Y 
G=Y**X 
ax.contour(X,Y,(F-G),[0],zorder=100) 

#set bounds 
ax.set_xbound(-1,7) 
ax.set_ybound(-1,7) 

#produce gridlines of different colors/widths 
ax.xaxis.set_minor_locator(MultipleLocator(0.2)) 
ax.yaxis.set_minor_locator(MultipleLocator(0.2)) 
ax.xaxis.grid(True,'minor',linestyle='-') 
ax.yaxis.grid(True,'minor',linestyle='-') 

minor_grid_lines = [tick.gridline for tick in ax.xaxis.get_minor_ticks()] 
for idx,loc in enumerate(ax.xaxis.get_minorticklocs()): 
    if loc % 2.0 == 0: 
     minor_grid_lines[idx].set_color('0.3') 
     minor_grid_lines[idx].set_linewidth(2) 
    elif loc % 1.0 == 0: 
     minor_grid_lines[idx].set_c('0.5') 
     minor_grid_lines[idx].set_linewidth(1) 
    else: 
     minor_grid_lines[idx].set_c('0.7') 
     minor_grid_lines[idx].set_linewidth(1) 

minor_grid_lines = [tick.gridline for tick in ax.yaxis.get_minor_ticks()] 
for idx,loc in enumerate(ax.yaxis.get_minorticklocs()): 
    if loc % 2.0 == 0: 
     minor_grid_lines[idx].set_color('0.3') 
     minor_grid_lines[idx].set_linewidth(2) 
    elif loc % 1.0 == 0: 
     minor_grid_lines[idx].set_c('0.5') 
     minor_grid_lines[idx].set_linewidth(1) 
    else: 
     minor_grid_lines[idx].set_c('0.7') 
     minor_grid_lines[idx].set_linewidth(1) 

plt.show() 

Answer 5

既然你已經標記爲sympy這個問題，我會給這樣一個例子。

從文檔：http://docs.sympy.org/modules/plotting.html。

from sympy import var, Plot 
var('x y') 
Plot(x*y**3 - y*x**3) 

Answer 6

sympy中有一個隱式方程（和不等式）繪圖儀。它是作爲GSoC的一部分創建的，它將圖形生成爲matplotlib圖形實例。在http://docs.sympy.org/latest/modules/plotting.html#sympy.plotting.plot_implicit.plot_implicit

文檔由於sympy版本0.7.2可用的是：

>>> from sympy.plotting import plot_implicit 
>>> p = plot_implicit(x < sin(x)) # also creates a window with the plot 
>>> the_matplotlib_axes_instance = p._backend._ax