绘制方向字段

Question

有没有办法在python中绘制方向字段？

我的尝试是修改http://www.compdigitec.com/labs/files/slopefields.py给出

#!/usr/bin/python

import math
from subprocess import CalledProcessError, call, check_call

def dy_dx(x, y):
    try:
        # declare your dy/dx here:
        return x**2-x-2
    except ZeroDivisionError:
        return 1000.0

# Adjust window parameters
XMIN = -5.0
XMAX = 5.0
YMIN = -10.0
YMAX = 10.0
XSCL = 0.5
YSCL = 0.5

DISTANCE = 0.1

def main():
    fileobj = open("data.txt", "w")
    for x1 in xrange(int(XMIN / XSCL), int(XMAX / XSCL)):
        for y1 in xrange(int(YMIN / YSCL), int(YMAX / YSCL)):
            x= float(x1 * XSCL)
            y= float(y1 * YSCL)
            slope = dy_dx(x,y)
            dx = math.sqrt( DISTANCE/( 1+math.pow(slope,2) ) )
            dy = slope*dx
            fileobj.write(str(x) + " " + str(y) + " " + str(dx) + " " + str(dy) + "\n")
    fileobj.close()


    try:
        check_call(["gnuplot","-e","set terminal png size 800,600 enhanced font \"Arial,12\"; set xrange [" + str(XMIN) + ":" + str(XMAX) + "]; set yrange [" + str(YMIN) + ":" + str(YMAX) + "]; set output 'output.png'; plot 'data.txt' using 1:2:3:4 with vectors"])
    except (CalledProcessError, OSError):
        print "Error: gnuplot not found on system!"
        exit(1)
    print "Saved image to output.png"
    call(["xdg-open","output.png"])
    return 0

if __name__ == '__main__':
    main()

然而,我从中获得的最佳图像是. 如何获得看起来更像第一张图像的输出？另外,如何添加三条实线？

Answer 1

您可以使用此matplotlib代码作为基础.根据您的需要进行修改.我已更新代码以显示相同长度的箭头.

也可以将轴形式"框"改为"箭头".如果您需要更改,请告诉我,我可以添加它.

import matplotlib.pyplot as plt
from scipy import *
from scipy import integrate
from scipy.integrate import ode
import numpy as np

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

## Vector field function
def vf(t,x):
  dx=np.zeros(2)
  dx[0]=1
  dx[1]=x[0]**2-x[0]-2
  return dx

#Solution curves
t0=0; tEnd=10; dt=0.01;
r = ode(vf).set_integrator('vode', method='bdf',max_step=dt)
ic=[[-3.5,-10], [-3,-10], [-2.5,-10]]
color=['r','b','g']
for k in range(len(ic)):
    Y=[];T=[];S=[];
    r.set_initial_value(ic[k], t0).set_f_params()
    while r.successful() and r.t +dt < tEnd:
        r.integrate(r.t+dt)
        Y.append(r.y)

    S=np.array(np.real(Y))
    ax.plot(S[:,0],S[:,1], color = color[k], lw = 1.25)

#Vector field
X,Y = np.meshgrid( np.linspace(-5,5,20),np.linspace(-10,10,20) )
U = 1
V = X**2-X-2
#Normalize arrows
N = np.sqrt(U**2+V**2)  
U2, V2 = U/N, V/N
ax.quiver( X,Y,U2, V2)


plt.xlim([-5,5])
plt.ylim([-10,10])
plt.xlabel(r"$x$")
plt.ylabel(r"$y$")
plt.show()