Stream plot is basically a type of 2D plot used majorly by physicists to show fluid flow and 2D field gradients .The basic function to create a stream plot in Matplotlib is:
ax.streamplot(x_grid, y_grid, x_vec, y_vec, density=spacing)
Here x_grid and y_grid are arrays of the x and y points.The x_vec and y_vec represent the stream velocity of each point present on the grid.The attribute #density=spacing# specify that how much close the streamlines are to be drawn together.
Creating stream plot –
Let’s start by creating a simple stream plot that contains streamlines on a 10 by 10 grid.All the streamlines are parallel and pointing towards the right.The code below creates the stream plot containing horizontal parallel lines pointing to the right:
Python3
# Import librariesimport numpy as npimport matplotlib.pyplot as plt# Creating datasetx = np.arange(0, 10)y = np.arange(0, 10)# Creating gridsX, Y = np.meshgrid(x, y)# x-component to the rightu = np.ones((10, 10)) # y-component zerov = np.zeros((10, 10)) fig = plt.figure(figsize = (12, 7))# Plotting stream plotplt.streamplot(X, Y, u, v, density = 0.5)# show plotplt.show() |
Output:
Here, x and y are 1D arrays on an evenly spaced grid, u and v are 2D arrays of velocities of x and y where the number of rows should match with the length of y while the number of columns should match with x, density is a float value which controls the closeness of the stream lines.
Customization of stream plot –
With the help of streamplot() function we can create and customize a plot showing field lines based on defined 2D vector field. Many attributes are available in streamplot() function for the modification of the plots.
Python3
# Import librariesimport numpy as npimport matplotlib.pyplot as plt# Creating data setw = 3Y, X = np.mgrid[-w:w:100j, -w:w:100j]U = -1 - X**2 + YV = 1 + X - Y**2speed = np.sqrt(U**2 + V**2)# Creating plotfig = plt.figure(figsize = (12, 7))plt.streamplot(X, Y, U, V, density = 1)# show plotplt.show() |
Output:
Some of the customization of the above graph are listed below:
Varying the density of streamlines –
Python3
import numpy as npimport matplotlib.pyplot as pltimport matplotlib.gridspec as gridspec# Creating datasetw = 3Y, X = np.mgrid[-w:w:100j, -w:w:100j]U = -1 - X**2 + YV = 1 + X - Y**2speed = 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 # streamlineax = 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 plotplt.tight_layout()plt.show() |
Output:
Varying the color along a streamline –
Python3
import numpy as npimport matplotlib.pyplot as pltimport matplotlib.gridspec as gridspec# Creating datasetw = 3Y, X = np.mgrid[-w:w:100j, -w:w:100j]U = -1 - X**2 + YV = 1 + X - Y**2speed = 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 streamlineax = 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 plotplt.tight_layout()plt.show() |
Output:
Varying the line width along a streamline –
Python3
import numpy as npimport matplotlib.pyplot as pltimport matplotlib.gridspec as gridspec# Creating datasetw = 3Y, X = np.mgrid[-w:w:100j, -w:w:100j]U = -1 - X**2 + YV = 1 + X - Y**2speed = 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 streamlineax = 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 plotplt.tight_layout()plt.show() |
Output:
Controlling the starting points of streamlines –
Python3
import numpy as npimport matplotlib.pyplot as pltimport matplotlib.gridspec as gridspec# Creating datasetw = 3Y, X = np.mgrid[-w:w:100j, -w:w:100j]U = -1 - X**2 + YV = 1 + X - Y**2speed = 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 streamlinesseek_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 plotplt.tight_layout()plt.show() |
Output:
Streamlines skipping masked regions and NaN values –
Python3
# Import librariesimport numpy as npimport matplotlib.pyplot as pltimport matplotlib.gridspec as gridspec# Creating datasetw = 3Y, X = np.mgrid[-w:w:100j, -w:w:100j]U = -1 - X**2 + YV = 1 + X - Y**2speed = 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 maskmask = np.zeros(U.shape, dtype = bool)mask[40:60, 40:60] = TrueU[:20, :20] = np.nanU = 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 plotplt.tight_layout()plt.show() |
Output:
Example:
Stream plot to demonstrate the electric field due to two point charges.The electric field at any point on a surface depends upon the position and distance between the two charges:
Python3
import sysimport numpy as npimport matplotlib.pyplot as pltfrom matplotlib.patches import Circle# Function to determine electric fielddef 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 pointsnx, ny = 64, 64x = 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 chargenq = 2**1charges = []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 componentsEx, Ey = np.zeros((ny, nx)), np.zeros((ny, nx))for charge in charges: ex, ey = E(*charge, x = X, y = Y) Ex += ex Ey += eyfig = plt.figure(figsize =(18, 8))ax = fig.add_subplot(111)# Plotting the streamlines with # proper color and arrowcolor = 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# themselvescharge_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() |
Output:
