[英]Plotting vector field for first order differential equation
我正在尝试 plot 简单速度方程的方向场。 我明白当我使用两个变量时我必须做什么。 我可以理解我必须创建的向量,但我不明白如何只为一个变量创建它。 我的程序是:
import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import odeint
def modelo2(y, t):
dydt = 32 - 0.16 * y
return dydt
t0 = 0 ; tf = 25 ; h = 0.1
t = np.arange(t0,tf+h,h)
for y0 in np.arange(0, 400, 25):
y = odeint(modelo2,y0,t )
plt.plot(t,y,'b')
x = np.arange(0, 400, 20)
z = np.arange(0, 400, 20)
X, Z = np.meshgrid(x, z)
U = modelo2(X,t)
V = modelo2 (Z, t)
plt.quiver(X, Z, U, V, scale = 70)
plt.quiver(X, Z, U, V, scale = 60)
plt.xlabel('time')
plt.ylabel('y(t)')
plt.axis([0,20,0, 500])
plt.show()
我明白了
当我期待这样的事情时
有人可以解释我做错了什么吗?
改变这个
U = modelo2(X,t)
V = modelo2 (Z, t)
对此
U = 1.0
V = modelo2(Z, None)
N = np.sqrt(U**2 + V**2)
U /= N
V /= N
如您所见,您错误地定义了U
。 将U
和V
都除以N
是标准化矢量幅度所必需的,否则它们在 plot 中的长度将根据每个点的场强而变化。 只需设置U = np.ones(Z.shape)
并且不要除以N
来查看我在说什么。
其次,您需要在plt.quiver()
中设置以下参数
plt.quiver(X, Z, U, V, angles='xy')
从文档:
angles: {'uv', 'xy'} or array-like, optional, default: 'uv' Method for determining the angle of the arrows. - 'uv': The arrow axis aspect ratio is 1 so that if *U* == *V* the orientation of the arrow on the plot is 45 degrees counter-clockwise from the horizontal axis (positive to the right). Use this if the arrows symbolize a quantity that is not based on *X*, *Y* data coordinates. - 'xy': Arrows point from (x, y) to (x+u, y+v). Use this for plotting a gradient field, for example. - Alternatively, arbitrary angles may be specified explicitly as an array of values in degrees, counter-clockwise from the horizontal axis. In this case *U*, *V* is only used to determine the length of the arrows. Note: inverting a data axis will correspondingly invert the arrows only with ``angles='xy'``.
总而言之,你的代码应该是这样的(有一些小的变量名编辑):
def modelo2(y, t):
dydt = 32 - 0.16 * y
return dydt
t0, tf, h = 0, 25, 0.1
t = np.arange(t0, tf+h, h)
ymin, ymax, ystep = 0, 400, 25
y = np.arange(ymin, ymax+ystep, ystep)
for y0 in y:
line = odeint(modelo2, y0, t)
plt.plot(t, line, 'b')
x = np.linspace(t0, tf, 20)
X, Y = np.meshgrid(x, y)
U = 1
V = modelo2(Y, None)
N = np.sqrt(U**2 + V**2)
U /= N
V /= N
plt.quiver(X, Y, U, V, angles='xy')
plt.xlabel('time')
plt.ylabel('y(t)')
plt.axis([t0, tf, ymin, ymax])
plt.show()
结果
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