Matplotlib 中的 Quiver 绘图箭头太大得离谱
Quiver plot arrows in Matplotlib are ridiculously too large
我正在努力创建一个可以模拟电场线的 python 脚本，但是箭袋图的箭头太大了。我试过更改单位和比例，但 matplotlib 上的文档对我来说也毫无意义......这似乎只是一个主要问题，当系统中只有一次收费时，但箭头仍然略微过大任意数量的费用。箭头往往在所有情况下都过大，但只有一个粒子时最明显。
import matplotlib.pyplot as plt
import numpy as np
import sympy as sym
import astropy as astro
k = 9 * 10 ** 9
def get_inputs():
inputs_loop = False
while inputs_loop is False:
""""
get inputs
"""
inputs_loop = True
particles_loop = False
while particles_loop is False:
try:
particles_loop = True
"""
get n particles with n charges.
"""
num_particles = int(raw_input('How many particles are in the system? '))
parts = []
for i in range(num_particles):
parts.append([float(raw_input("What is the charge of particle %s in Coulombs? " % (str(i + 1)))),
[float(raw_input("What is the x position of particle %s? " % (str(i + 1)))),
float(raw_input('What is the y position of particle %s? ' % (str(i + 1))))]])
except ValueError:
print 'Could not convert input to proper data type. Please try again.'
particles_loop = False
return parts
def vec_addition(vectors):
x_sum = 0
y_sum = 0
for b in range(len(vectors)):
x_sum += vectors[b][0]
y_sum += vectors[b][1]
return [x_sum,y_sum]
def electric_field(particle, point):
if particle[0] > 0:
"""
Electric field exitation is outwards
If the x position of the particle is > the point, then a different calculation must be made than in not.
"""
field_vector_x = k * (
particle[0] / np.sqrt((particle[1][0] - point[0]) ** 2 + (particle[1][1] - point[1]) ** 2) ** 2) * \
(np.cos(np.arctan2((point[1] - particle[1][1]), (point[0] - particle[1][0]))))
field_vector_y = k * (
particle[0] / np.sqrt((particle[1][0] - point[0]) ** 2 + (particle[1][1] - point[1]) ** 2) ** 2) * \
(np.sin(np.arctan2((point[1] - particle[1][1]), (point[0] - particle[1][0]))))
"""
Defining the direction of the components
"""
if point[1] < particle[1][1] and field_vector_y > 0:
print field_vector_y
field_vector_y *= -1
elif point[1] > particle[1][1] and field_vector_y < 0:
print field_vector_y
field_vector_y *= -1
else:
pass
if point[0] < particle[1][0] and field_vector_x > 0:
print field_vector_x
field_vector_x *= -1
elif point[0] > particle[1][0] and field_vector_x < 0:
print field_vector_x
field_vector_x *= -1
else:
pass
"""
If the charge is negative
"""
elif particle[0] < 0:
field_vector_x = k * (
particle[0] / np.sqrt((particle[1][0] - point[0]) ** 2 + (particle[1][1] - point[1]) ** 2) ** 2) * (
np.cos(np.arctan2((point[1] - particle[1][1]), (point[0] - particle[1][0]))))
field_vector_y = k * (
particle[0] / np.sqrt((particle[1][0] - point[0]) ** 2 + (particle[1][1] - point[1]) ** 2) ** 2) * (
np.sin(np.arctan2((point[1] - particle[1][1]), (point[0] - particle[1][0]))))
"""
Defining the direction of the components
"""
if point[1] > particle[1][1] and field_vector_y > 0:
print field_vector_y
field_vector_y *= -1
elif point[1] < particle[1][1] and field_vector_y < 0:
print field_vector_y
field_vector_y *= -1
else:
pass
if point[0] > particle[1][0] and field_vector_x > 0:
print field_vector_x
field_vector_x *= -1
elif point[0] < particle[1][0] and field_vector_x < 0:
print field_vector_x
field_vector_x *= -1
else:
pass
return [field_vector_x, field_vector_y]
def main(particles):
"""
Graphs the electrical field lines.
:param particles:
:return:
"""
"""
plot particle positions
"""
particle_x = 0
particle_y = 0
for i in range(len(particles)):
if particles[i][0]<0:
particle_x = particles[i][1][0]
particle_y = particles[i][1][1]
plt.plot(particle_x,particle_y,'r+',linewidth=1.5)
else:
particle_x = particles[i][1][0]
particle_y = particles[i][1][1]
plt.plot(particle_x,particle_y,'r_',linewidth=1.5)
"""
Plotting out the quiver plot.
"""
parts_x = [particles[i][1][0] for i in range(len(particles))]
graph_x_min = min(parts_x)
graph_x_max = max(parts_x)
x,y = np.meshgrid(np.arange(graph_x_min-(graph_x_max-graph_x_min),graph_x_max+(graph_x_max-graph_x_min)),
np.arange(graph_x_min-(graph_x_max-graph_x_min),graph_x_max+(graph_x_max-graph_x_min)))
if len(particles)<2:
for x_pos in range(int(particles[0][1][0]-10),int(particles[0][1][0]+10)):
for y_pos in range(int(particles[0][1][0]-10),int(particles[0][1][0]+10)):
vecs = []
for particle_n in particles:
vecs.append(electric_field(particle_n, [x_pos, y_pos]))
final_vector = vec_addition(vecs)
distance = np.sqrt((final_vector[0] - x_pos) ** 2 + (final_vector[1] - y_pos) ** 2)
plt.quiver(x_pos, y_pos, final_vector[0], final_vector[1], distance, angles='xy', scale_units='xy',
scale=1, width=0.05)
plt.axis([particles[0][1][0]-10,particles[0][1][0]+10,
particles[0][1][0] - 10, particles[0][1][0] + 10])
else:
for x_pos in range(int(graph_x_min-(graph_x_max-graph_x_min)),int(graph_x_max+(graph_x_max-graph_x_min))):
for y_pos in range(int(graph_x_min-(graph_x_max-graph_x_min)),int(graph_x_max+(graph_x_max-graph_x_min))):
vecs = []
for particle_n in particles:
vecs.append(electric_field(particle_n,[x_pos,y_pos]))
final_vector = vec_addition(vecs)
distance = np.sqrt((final_vector[0]-x_pos)**2+(final_vector[1]-y_pos)**2)
plt.quiver(x_pos,y_pos,final_vector[0],final_vector[1],distance,angles='xy',units='xy')
plt.axis([graph_x_min-(graph_x_max-graph_x_min),graph_x_max+(graph_x_max-graph_x_min),graph_x_min-(graph_x_max-graph_x_min),graph_x_max+(graph_x_max-graph_x_min)])
plt.grid()
plt.show()
g = get_inputs()
main(g)}
您可以设置比例，使其大致对应于 u 和 v 向量。
plt.quiver(x_pos, y_pos, final_vector[0], final_vector[1], scale=1e9, units="xy")
这将导致如下结果：
如果我解释正确，您想绘制点电荷的场矢量。环顾四周其他人是如何做到这一点的，人们发现例如this blog entry 克里斯蒂安·希尔。他使用 streamplot 而不是 quiver 但我们可能会采用计算字段的代码并替换绘图。
无论如何，我们不想要也不需要 100 个不同的箭袋图，就像问题的代码中那样，而只需要一个绘制整个字段的箭袋图。如果我们想让场矢量的长度表示场强，我们当然会 运行 遇到一个问题，因为幅度与粒子距离的 3 次方成正比。一个解决方案可能是缩放场在绘图之前以对数方式计算，这样箭头长度仍然以某种方式可见，即使在距离粒子一定距离处也是如此。 quiver 图的比例参数然后可用于调整箭头的长度，以便它们以某种方式适合其他图参数。
""" Original code by Christian Hill
http://scipython.com/blog/visualizing-a-vector-field-with-matplotlib/
Changes made to display the field as a quiver plot instead of streamlines
"""
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.patches import Circle
def E(q, r0, x, y):
"""Return the electric field vector E=(Ex,Ey) due to charge q at r0."""
den = ((x-r0[0])**2 + (y-r0[1])**2)**1.5
return q * (x - r0[0]) / den, q * (y - r0[1]) / den
# Grid of x, y points
nx, ny = 32, 32
x = np.linspace(-2, 2, nx)
y = np.linspace(-2, 2, ny)
X, Y = np.meshgrid(x, y)
charges = [[5.,[-1,0]],[-5.,[+1,0]]]
# Electric field vector, E=(Ex, Ey), as separate components
Ex, Ey = np.zeros((ny, nx)), np.zeros((ny, nx))
for charge in charges:
ex, ey = E(*charge, x=X, y=Y)
Ex += ex
Ey += ey
fig = plt.figure()
ax = fig.add_subplot(111)
f = lambda x:np.sign(x)*np.log10(1+np.abs(x))
ax.quiver(x, y, f(Ex), f(Ey), scale=33)
# Add filled circles for the charges themselves
charge_colors = {True: 'red', False: 'blue'}
for q, pos in charges:
ax.add_artist(Circle(pos, 0.05, color=charge_colors[q>0]))
ax.set_xlabel('$x$')
ax.set_ylabel('$y$')
ax.set_xlim(-2,2)
ax.set_ylim(-2,2)
ax.set_aspect('equal')
plt.show()
（请注意，此处的字段未以任何方式归一化，这对于可视化而言根本无关紧要。）
另一种选择是查看例如this code 也从点电荷绘制场线。
我正在努力创建一个可以模拟电场线的 python 脚本，但是箭袋图的箭头太大了。我试过更改单位和比例，但 matplotlib 上的文档对我来说也毫无意义......这似乎只是一个主要问题，当系统中只有一次收费时，但箭头仍然略微过大任意数量的费用。箭头往往在所有情况下都过大，但只有一个粒子时最明显。
import matplotlib.pyplot as plt
import numpy as np
import sympy as sym
import astropy as astro
k = 9 * 10 ** 9
def get_inputs():
inputs_loop = False
while inputs_loop is False:
""""
get inputs
"""
inputs_loop = True
particles_loop = False
while particles_loop is False:
try:
particles_loop = True
"""
get n particles with n charges.
"""
num_particles = int(raw_input('How many particles are in the system? '))
parts = []
for i in range(num_particles):
parts.append([float(raw_input("What is the charge of particle %s in Coulombs? " % (str(i + 1)))),
[float(raw_input("What is the x position of particle %s? " % (str(i + 1)))),
float(raw_input('What is the y position of particle %s? ' % (str(i + 1))))]])
except ValueError:
print 'Could not convert input to proper data type. Please try again.'
particles_loop = False
return parts
def vec_addition(vectors):
x_sum = 0
y_sum = 0
for b in range(len(vectors)):
x_sum += vectors[b][0]
y_sum += vectors[b][1]
return [x_sum,y_sum]
def electric_field(particle, point):
if particle[0] > 0:
"""
Electric field exitation is outwards
If the x position of the particle is > the point, then a different calculation must be made than in not.
"""
field_vector_x = k * (
particle[0] / np.sqrt((particle[1][0] - point[0]) ** 2 + (particle[1][1] - point[1]) ** 2) ** 2) * \
(np.cos(np.arctan2((point[1] - particle[1][1]), (point[0] - particle[1][0]))))
field_vector_y = k * (
particle[0] / np.sqrt((particle[1][0] - point[0]) ** 2 + (particle[1][1] - point[1]) ** 2) ** 2) * \
(np.sin(np.arctan2((point[1] - particle[1][1]), (point[0] - particle[1][0]))))
"""
Defining the direction of the components
"""
if point[1] < particle[1][1] and field_vector_y > 0:
print field_vector_y
field_vector_y *= -1
elif point[1] > particle[1][1] and field_vector_y < 0:
print field_vector_y
field_vector_y *= -1
else:
pass
if point[0] < particle[1][0] and field_vector_x > 0:
print field_vector_x
field_vector_x *= -1
elif point[0] > particle[1][0] and field_vector_x < 0:
print field_vector_x
field_vector_x *= -1
else:
pass
"""
If the charge is negative
"""
elif particle[0] < 0:
field_vector_x = k * (
particle[0] / np.sqrt((particle[1][0] - point[0]) ** 2 + (particle[1][1] - point[1]) ** 2) ** 2) * (
np.cos(np.arctan2((point[1] - particle[1][1]), (point[0] - particle[1][0]))))
field_vector_y = k * (
particle[0] / np.sqrt((particle[1][0] - point[0]) ** 2 + (particle[1][1] - point[1]) ** 2) ** 2) * (
np.sin(np.arctan2((point[1] - particle[1][1]), (point[0] - particle[1][0]))))
"""
Defining the direction of the components
"""
if point[1] > particle[1][1] and field_vector_y > 0:
print field_vector_y
field_vector_y *= -1
elif point[1] < particle[1][1] and field_vector_y < 0:
print field_vector_y
field_vector_y *= -1
else:
pass
if point[0] > particle[1][0] and field_vector_x > 0:
print field_vector_x
field_vector_x *= -1
elif point[0] < particle[1][0] and field_vector_x < 0:
print field_vector_x
field_vector_x *= -1
else:
pass
return [field_vector_x, field_vector_y]
def main(particles):
"""
Graphs the electrical field lines.
:param particles:
:return:
"""
"""
plot particle positions
"""
particle_x = 0
particle_y = 0
for i in range(len(particles)):
if particles[i][0]<0:
particle_x = particles[i][1][0]
particle_y = particles[i][1][1]
plt.plot(particle_x,particle_y,'r+',linewidth=1.5)
else:
particle_x = particles[i][1][0]
particle_y = particles[i][1][1]
plt.plot(particle_x,particle_y,'r_',linewidth=1.5)
"""
Plotting out the quiver plot.
"""
parts_x = [particles[i][1][0] for i in range(len(particles))]
graph_x_min = min(parts_x)
graph_x_max = max(parts_x)
x,y = np.meshgrid(np.arange(graph_x_min-(graph_x_max-graph_x_min),graph_x_max+(graph_x_max-graph_x_min)),
np.arange(graph_x_min-(graph_x_max-graph_x_min),graph_x_max+(graph_x_max-graph_x_min)))
if len(particles)<2:
for x_pos in range(int(particles[0][1][0]-10),int(particles[0][1][0]+10)):
for y_pos in range(int(particles[0][1][0]-10),int(particles[0][1][0]+10)):
vecs = []
for particle_n in particles:
vecs.append(electric_field(particle_n, [x_pos, y_pos]))
final_vector = vec_addition(vecs)
distance = np.sqrt((final_vector[0] - x_pos) ** 2 + (final_vector[1] - y_pos) ** 2)
plt.quiver(x_pos, y_pos, final_vector[0], final_vector[1], distance, angles='xy', scale_units='xy',
scale=1, width=0.05)
plt.axis([particles[0][1][0]-10,particles[0][1][0]+10,
particles[0][1][0] - 10, particles[0][1][0] + 10])
else:
for x_pos in range(int(graph_x_min-(graph_x_max-graph_x_min)),int(graph_x_max+(graph_x_max-graph_x_min))):
for y_pos in range(int(graph_x_min-(graph_x_max-graph_x_min)),int(graph_x_max+(graph_x_max-graph_x_min))):
vecs = []
for particle_n in particles:
vecs.append(electric_field(particle_n,[x_pos,y_pos]))
final_vector = vec_addition(vecs)
distance = np.sqrt((final_vector[0]-x_pos)**2+(final_vector[1]-y_pos)**2)
plt.quiver(x_pos,y_pos,final_vector[0],final_vector[1],distance,angles='xy',units='xy')
plt.axis([graph_x_min-(graph_x_max-graph_x_min),graph_x_max+(graph_x_max-graph_x_min),graph_x_min-(graph_x_max-graph_x_min),graph_x_max+(graph_x_max-graph_x_min)])
plt.grid()
plt.show()
g = get_inputs()
main(g)}
您可以设置比例，使其大致对应于 u 和 v 向量。
plt.quiver(x_pos, y_pos, final_vector[0], final_vector[1], scale=1e9, units="xy")
这将导致如下结果：
如果我解释正确，您想绘制点电荷的场矢量。环顾四周其他人是如何做到这一点的，人们发现例如this blog entry 克里斯蒂安·希尔。他使用 streamplot 而不是 quiver 但我们可能会采用计算字段的代码并替换绘图。
无论如何，我们不想要也不需要 100 个不同的箭袋图，就像问题的代码中那样，而只需要一个绘制整个字段的箭袋图。如果我们想让场矢量的长度表示场强，我们当然会 运行 遇到一个问题，因为幅度与粒子距离的 3 次方成正比。一个解决方案可能是缩放场在绘图之前以对数方式计算，这样箭头长度仍然以某种方式可见，即使在距离粒子一定距离处也是如此。 quiver 图的比例参数然后可用于调整箭头的长度，以便它们以某种方式适合其他图参数。
""" Original code by Christian Hill
http://scipython.com/blog/visualizing-a-vector-field-with-matplotlib/
Changes made to display the field as a quiver plot instead of streamlines
"""
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.patches import Circle
def E(q, r0, x, y):
"""Return the electric field vector E=(Ex,Ey) due to charge q at r0."""
den = ((x-r0[0])**2 + (y-r0[1])**2)**1.5
return q * (x - r0[0]) / den, q * (y - r0[1]) / den
# Grid of x, y points
nx, ny = 32, 32
x = np.linspace(-2, 2, nx)
y = np.linspace(-2, 2, ny)
X, Y = np.meshgrid(x, y)
charges = [[5.,[-1,0]],[-5.,[+1,0]]]
# Electric field vector, E=(Ex, Ey), as separate components
Ex, Ey = np.zeros((ny, nx)), np.zeros((ny, nx))
for charge in charges:
ex, ey = E(*charge, x=X, y=Y)
Ex += ex
Ey += ey
fig = plt.figure()
ax = fig.add_subplot(111)
f = lambda x:np.sign(x)*np.log10(1+np.abs(x))
ax.quiver(x, y, f(Ex), f(Ey), scale=33)
# Add filled circles for the charges themselves
charge_colors = {True: 'red', False: 'blue'}
for q, pos in charges:
ax.add_artist(Circle(pos, 0.05, color=charge_colors[q>0]))
ax.set_xlabel('$x$')
ax.set_ylabel('$y$')
ax.set_xlim(-2,2)
ax.set_ylim(-2,2)
ax.set_aspect('equal')
plt.show()
（请注意，此处的字段未以任何方式归一化，这对于可视化而言根本无关紧要。）
另一种选择是查看例如this code 也从点电荷绘制场线。