Python中的 Matplotlib.pyplot.streamplot()

流图基本上是物理学家主要用来显示流体流动和 2D 场梯度的一种 2D 图。在 Matplotlib 中创建流图的基本函数是：

ax.streamplot(x_grid, y_grid, x_vec, y_vec, density=spacing)

这里x_grid和y_grid是 x 和 y 点的数组。x_vec和y_vec表示网格上每个点的流速度。属性#density=spacing# 指定流线要绘制在一起的距离。

创建流图 -

让我们首先创建一个简单的流线图，其中包含 10 x 10 网格上的流线。所有流线都是平行的并指向右侧。下面的代码创建了包含指向右侧的水平平行线的流线图：

Python3

# Import libraries
import numpy as np
import matplotlib.pyplot as plt
 
# Creating dataset
x = np.arange(0, 10)
y = np.arange(0, 10)
 
# Creating grids
X, Y = np.meshgrid(x, y)
 
# x-component to the right
u = np.ones((10, 10))
 
# y-component zero
v = np.zeros((10, 10))
 
fig = plt.figure(figsize = (12, 7))
 
# Plotting stream plot
plt.streamplot(X, Y, u, v, density = 0.5)
 
# show plot
plt.show()

输出：

这里，x 和 y 是均匀间隔网格上的一维数组，u 和 v 是 x 和 y 速度的二维数组，其中行数应与 y 的长度匹配，而列数应与 x 匹配，密度为一个浮点值，它控制流线的接近程度。

流线图定制——

借助 streamplot()函数，我们可以根据定义的 2D 矢量场创建和自定义显示场线的图。 streamplot()函数中有许多属性可用于修改绘图。

Python3

# Import libraries
import numpy as np
import matplotlib.pyplot as plt
 
# Creating data set
w = 3
Y, X = np.mgrid[-w:w:100j, -w:w:100j]
U = -1 - X**2 + Y
V = 1 + X - Y**2
speed = np.sqrt(U**2 + V**2)
 
# Creating plot
fig = plt.figure(figsize = (12, 7))
plt.streamplot(X, Y, U, V, density = 1)
 
# show plot
plt.show()

输出：

下面列出了上图的一些自定义：
改变流线的密度——

Python3

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec
 
# Creating dataset
w = 3
Y, X = np.mgrid[-w:w:100j, -w:w:100j]
U = -1 - X**2 + Y
V = 1 + X - Y**2
speed = np.sqrt(U**2 + V**2)
 
fig = plt.figure(figsize =(24, 20))
gs = gridspec.GridSpec(nrows = 3, ncols = 2,
                       height_ratios =[1, 1, 2])
 
# Varying the density along a
# streamline
ax = fig.add_subplot(gs[0, 0])
ax.streamplot(X, Y, U, V,
              density =[0.4, 0.8])
 
ax.set_title('Varying the density along a streamline')
 
# show plot
plt.tight_layout()
plt.show()

输出：

沿着流线改变颜色 -

Python3

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec
 
# Creating dataset
w = 3
Y, X = np.mgrid[-w:w:100j, -w:w:100j]
U = -1 - X**2 + Y
V = 1 + X - Y**2
speed = np.sqrt(U**2 + V**2)
 
fig = plt.figure(figsize =(24, 20))
gs = gridspec.GridSpec(nrows = 3, ncols = 2,
                       height_ratios =[1, 1, 2])
 
# Varying color along a streamline
ax = fig.add_subplot(gs[0, 1])
strm = ax.streamplot(X, Y, U, V, color = U,
                     linewidth = 2, cmap ='autumn')
fig.colorbar(strm.lines)
ax.set_title('Varying the color along a streamline.')
 
# show plot
plt.tight_layout()
plt.show()   

输出：

沿流线改变线宽 -

Python3

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec
 
# Creating dataset
w = 3
Y, X = np.mgrid[-w:w:100j, -w:w:100j]
U = -1 - X**2 + Y
V = 1 + X - Y**2
speed = np.sqrt(U**2 + V**2)
 
fig = plt.figure(figsize =(24, 20))
gs = gridspec.GridSpec(nrows = 3, ncols = 2,
                       height_ratios =[1, 1, 2])
 
# Varying line width along a streamline
ax = fig.add_subplot(gs[1, 0])
lw = 5 * speed / speed.max()
ax.streamplot(X, Y, U, V, density = 0.6,
              color ='k', linewidth = lw)
 
ax.set_title('Varying line width along a streamline')
 
# show plot
plt.tight_layout()
plt.show()

输出：

控制流线的起点——

Python3

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec
 
# Creating dataset
w = 3
Y, X = np.mgrid[-w:w:100j, -w:w:100j]
U = -1 - X**2 + Y
V = 1 + X - Y**2
speed = np.sqrt(U**2 + V**2)
 
fig = plt.figure(figsize =(24, 20))
gs = gridspec.GridSpec(nrows = 3, ncols = 2,
                       height_ratios =[1, 1, 2])
 
# Controlling the starting points
# of the streamlines
seek_points = np.array([[-2, -1, 0, 1, 2, -1],
                        [-2, -1,  0, 1, 2, 2]])
 
ax = fig.add_subplot(gs[1, 1])
strm = ax.streamplot(X, Y, U, V, color = U,
                     linewidth = 2,
                     cmap ='autumn',
                     start_points = seek_points.T)
 
fig.colorbar(strm.lines)
ax.set_title('Controlling the starting\
points of the streamlines')
 
# Displaying the starting points
# with blue symbols.
ax.plot(seek_points[0], seek_points[1], 'bo')
ax.set(xlim =(-w, w), ylim =(-w, w))
 
# show plot
plt.tight_layout()
plt.show()

输出：

流线型跳过遮罩区域和 NaN 值 –

Python3

# Import libraries
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec
 
# Creating dataset
w = 3
Y, X = np.mgrid[-w:w:100j, -w:w:100j]
U = -1 - X**2 + Y
V = 1 + X - Y**2
speed = np.sqrt(U**2 + V**2)
 
fig = plt.figure(figsize =(20, 16))
gs = gridspec.GridSpec(nrows = 3, ncols = 2, height_ratios =[1, 1, 2])
 
# Create a mask
mask = np.zeros(U.shape, dtype = bool)
mask[40:60, 40:60] = True
U[:20, :20] = np.nan
U = np.ma.array(U, mask = mask)
 
ax = fig.add_subplot(gs[2:, :])
ax.streamplot(X, Y, U, V, color ='r')
ax.set_title('Streamplot with Masking')
 
ax.imshow(~mask, extent =(-w, w, -w, w), alpha = 0.5,
          interpolation ='nearest', cmap ='gray', aspect ='auto')
ax.set_aspect('equal')
 
# show plot
plt.tight_layout()
plt.show()

输出：

例子：
流线图演示由两个点电荷引起的电场。表面上任意点的电场取决于两个电荷之间的位置和距离：

Python3

import sys
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.patches import Circle
 
# Function to determine electric field
def E(q, r0, x, y):
    den = np.hypot(x-r0[0], y-r0[1])**3
    return q * (x - r0[0]) / den, q * (y - r0[1]) / den
 
# Grid of x, y points
nx, ny = 64, 64
x = np.linspace(-2, 2, nx)
y = np.linspace(-2, 2, ny)
X, Y = np.meshgrid(x, y)
 
# Create a multipole with nq charges of
# alternating sign, equally spaced
# on the unit circle.
 
# Increase the power with increase in charge
nq = 2**1
charges = []
for i in range(nq):
    q = i % 2 * 2 - 1
    charges.append((q, (np.cos(2 * np.pi * i / nq),
                        np.sin(2 * np.pi * i / nq))))
 
# 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(figsize =(18, 8))
ax = fig.add_subplot(111)
 
# Plotting the streamlines with
# proper color and arrow
color = 2 * np.log(np.hypot(Ex, Ey))
ax.streamplot(x, y, Ex, Ey, color = color,
              linewidth = 1, cmap = plt.cm.inferno,
              density = 2, arrowstyle ='->',
              arrowsize = 1.5)
 
# Add filled circles for the charges
# themselves
charge_colors = {True: '#AA0000',
                 False: '#0000AA'}
 
for q, pos in charges:
    ax.add_artist(Circle(pos, 0.05,
                         color = charge_colors[q>0]))
 
ax.set_xlabel('X-axis')
ax.set_ylabel('X-axis')
ax.set_xlim(-2, 2)
ax.set_ylim(-2, 2)
ax.set_aspect('equal')
 
plt.show()

输出：