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How to plot a Quiver plot in Python?

In this tutorial, we’ll try to understand how to plot a quiver plot in Python with the help of some examples.

What is a Quiver plot?

A quiver plot is basically a type of 2D plot which shows vector lines as arrows. These types of plots are used by Electrical engineers to visualize electrical potential and show stress gradients in Mechanical engineering.

We can plot a quiver plot in Python using axes.quiver method in matplotlib.

Quiver Plot using matpltolib.Axes.quiver() method

We can plot a Quiver plot in Python using the Axes.quiver method within the matplotlib module. The following is the syntax –

Basic Syntax:

axes.quiver([x, y], u, v, [c], **kwargs)

Parameters:

  • x: 1D or 2D array, sequence. The x coordinates of the arrow locations
  • y: 1D or 2D array, sequence. The y coordinates of the arrow locations
  • u: 1D or 2D array, sequence. The x components of the arrow vectors
  • v: 1D or 2D array, sequence. The y components of the arrow vectors
  • c: 1D or 2D array, sequence. The arrow colors

For more details, about the parameters, refer this.

Now let us try to understand the above method using some examples.

Example 1 – Quiver plot with a single arrow

import matplotlib.pyplot as plt
import numpy as np

#generating the figure and axes
fig, ax = plt.subplots()

#defining the parameters
x = 0
y = 0
u = 1
v = 1

#plotting the Quiver plot
ax.quiver(x,y,u,v)
plt.show()

Output:

quiver plot with single array

The steps followed in the above examples are:

  • Import the modules
  • create a figure and axes using pyplot.subplots (refer this).
  • Define the parameters
  • Plot the Quiver plot using axes.quiver method (refer this).

Example 2 – Quiver plot with two arrows

import matplotlib.pyplot as plt
import numpy as np

#generating the figure and axes
fig, ax = plt.subplots()

#defining the parameters
x = [0, -0.5]
y = [0, 0.5]
u = [1, 0]
v = [1, -1]

#plotting the Quiver plot
ax.quiver(x,y,u,v)
plt.show()

Output:

quiver plot with two arrows

The steps followed in the above examples are:

  • Import the modules
  • create a figure and axes using pyplot.subplots (refer this).
  • Define the parameters
  • Plot the Quiver plot using axes.quiver method (refer this).

Example 3 – Quiver plot using a meshgrid

import matplotlib.pyplot as plt
import numpy as np

#generating the figure and axes
fig, ax = plt.subplots()

#defining the parameters
X = np.arange(0,2.2,0.2)
Y = np.arange(0,2.2,0.2)

x, y = np.meshgrid(X, Y)
u = np.cos(x)*y
v = np.sin(y)*y

#plotting the Quiver plot
ax.quiver(x,y,u,v)
plt.show()

Output:

quiver plot using meshgrid

The steps followed in the above examples are:

  • Import the modules
  • create a figure and axes using pyplot.subplots
  • Define the parameters
    • generate X,Y values using numpy.arange (refer this)generate a meshgrid using numpy.meshgrid (refer this).Then create the respective u and v values
  • Plot the Quiver plot using axes.quiver method.

Example 4 – Quiver plot along with gradient

import matplotlib.pyplot as plt
import numpy as np

#generating the figure and axes
fig, ax = plt.subplots()

#defining the parameters

x = np.arange(-2,2.2,0.2)
y = np.arange(-2,2.2,0.2)

X, Y = np.meshgrid(x, y)
z = X*np.exp(-X**2 -Y**2)
dx, dy = np.gradient(z)

#plotting the Quiver plot
ax.quiver(x,y,dx,dy)
plt.show()

Output:

quiver plot with a gradient

The steps followed in the above examples are:

  • Import the modules
  • create a figure and axes using pyplot.subplots
  • Define the parameters
    • generate X,Y values using numpy.arangegenerate a meshgrid using numpy.meshgridThen create the respective dx and dy values using numpy.gradient (refer this)
  • Plot the Quiver plot using axes.quiver method

Example 5 – Quiver plot along with four vortices

import matplotlib.pyplot as plt
import numpy as np

#generating the figure and axes
fig, ax = plt.subplots()

#defining the parameters

x = np.arange(0,2*np.pi+2*np.pi/20,2*np.pi/20)
y = np.arange(0,2*np.pi+2*np.pi/20,2*np.pi/20)

X,Y = np.meshgrid(x,y)

u = np.sin(X)*np.cos(Y)
v = -np.cos(X)*np.sin(Y)

#plotting the Quiver plot
ax.quiver(x,y,u,v)
plt.show()

Output:

quiver plot with four vortices

The steps followed in the above examples are:

  • Import the modules
  • create a figure and axes using pyplot.subplots
  • Define the parameters
    • generate X,Y values using numpy.arangegenerate a meshgrid using numpy.meshgridThen create the respective u and v values.
  • Plot the Quiver plot using axes.quiver method

Example 5 – Quiver plot with colour

import matplotlib.pyplot as plt
import numpy as np

#generating the figure and axes
fig, ax = plt.subplots()

#defining the parameters
x = np.arange(0,2.2,0.2)
y = np.arange(0,2.2,0.2)

X, Y = np.meshgrid(x, y)
u = np.cos(X)*Y
v = np.sin(y)*Y

n = -2
color_array = np.sqrt(((v-n)/2)**2 + ((u-n)/2)**2)

#plotting the Quiver plot
ax.quiver(x,y,u,v, color_array, alpha=0.8)
plt.show()

Output:

quiver plot with color

The steps followed in the above examples are:

  • Import the modules
  • create a figure and axes using pyplot.subplots
  • Define the parameters
    • generate X,Y values using numpy.arange generate a meshgrid using numpy.meshgridThen create the respective u and v values
  • Plot the Quiver plot using axes.quiver method by adding a color array for colours.

Example 7 – Quiver plot in 3D

import matplotlib.pyplot as plt
import numpy as np

#generating the figure and axes
ax = plt.figure().add_subplot(projection='3d')

#defining the parameters
X = np.arange(-0.8, 1, 0.2)
Y = np.arange(-0.8, 1, 0.2)
Z = np.arange(-0.8, 1, 0.8)
x, y, z = np.meshgrid(X,Y,Z)

u = np.sin(np.pi * x) * np.cos(np.pi * y) * np.cos(np.pi * z)
v = -np.cos(np.pi * x) * np.sin(np.pi * y) * np.cos(np.pi * z)
w = (np.sqrt(2.0 / 3.0) * np.cos(np.pi * x) * np.cos(np.pi * y) *
     np.sin(np.pi * z))

#plotting the Quiver plot
ax.quiver(x, y, z, u, v, w, length=0.1, normalize=True)
plt.show()

Output:

quiver plot in 3d

The steps followed in the above examples are:

  • Import the modules
  • Create an axes using pyplot.figure.add_subplot(projection='3d') for the 3D plot.
  • Define the parameters
    • generate X,Y,Z values using numpy.arange generate a meshgrid using numpy.meshgridThen create the respective u,v and w values.
  • Plot the Quiver plot using axes.quiver method

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Author

  • Chaitanya Betha

    I'm an undergrad student at IIT Madras interested in exploring new technologies. I have worked on various projects related to Data science, Machine learning & Neural Networks, including image classification using Convolutional Neural Networks, Stock prediction using Recurrent Neural Networks, and many more machine learning model training. I write blog articles in which I would try to provide a complete guide on a particular topic and try to cover as many different examples as possible with all the edge cases to understand the topic better and have a complete glance over the topic.

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