[python] How to plot vectors in python using matplotlib

I am taking a course on linear algebra and I want to visualize the vectors in action, such as vector addition, normal vector, so on.

For instance:

V = np.array([[1,1],[-2,2],[4,-7]])

In this case I want to plot 3 vectors V1 = (1,1), M2 = (-2,2), M3 = (4,-7).

Then I should be able to add V1,V2 to plot a new vector V12(all together in one figure).

when I use the following code, the plot is not as intended

import numpy as np
import matplotlib.pyplot as plt
M = np.array([[1,1],[-2,2],[4,-7]])

print("vector:1")
print(M[0,:])
# print("vector:2")
# print(M[1,:])
rows,cols = M.T.shape
print(cols)

for i,l in enumerate(range(0,cols)):
    print("Iteration: {}-{}".format(i,l))
    print("vector:{}".format(i))
    print(M[i,:])
    v1 = [0,0],[M[i,0],M[i,1]]
    # v1 = [M[i,0]],[M[i,1]]
    print(v1)
    plt.figure(i)
    plt.plot(v1)
    plt.show()

This question is related to python python-2.7 numpy matplotlib vector

The answer is


Thanks to everyone, each of your posts helped me a lot. rbierman code was pretty straight for my question, I have modified a bit and created a function to plot vectors from given arrays. I'd love to see any suggestions to improve it further.

import numpy as np
import matplotlib.pyplot as plt
def plotv(M):
    rows,cols = M.T.shape
    print(rows,cols)

    #Get absolute maxes for axis ranges to center origin
    #This is optional
    maxes = 1.1*np.amax(abs(M), axis = 0)
    colors = ['b','r','k']
    fig = plt.figure()
    fig.suptitle('Vectors', fontsize=10, fontweight='bold')

    ax = fig.add_subplot(111)
    fig.subplots_adjust(top=0.85)
    ax.set_title('Vector operations')

    ax.set_xlabel('x')
    ax.set_ylabel('y')

    for i,l in enumerate(range(0,cols)):
        # print(i)
        plt.axes().arrow(0,0,M[i,0],M[i,1],head_width=0.2,head_length=0.1,zorder=3)

        ax.text(M[i,0],M[i,1], str(M[i]), style='italic',
            bbox={'facecolor':'red', 'alpha':0.5, 'pad':0.5})

    plt.plot(0,0,'ok') #<-- plot a black point at the origin
    # plt.axis('equal')  #<-- set the axes to the same scale
    plt.xlim([-maxes[0],maxes[0]]) #<-- set the x axis limits
    plt.ylim([-maxes[1],maxes[1]]) #<-- set the y axis limits

    plt.grid(b=True, which='major') #<-- plot grid lines
    plt.show()

r = np.random.randint(4,size=[2,2])
print(r[0,:])
print(r[1,:])
r12 = np.add(r[0,:],r[1,:])
print(r12)
plotv(np.vstack((r,r12)))

Vector addition performed on random vectors


This may also be achieved using matplotlib.pyplot.quiver, as noted in the linked answer;

plt.quiver([0, 0, 0], [0, 0, 0], [1, -2, 4], [1, 2, -7], angles='xy', scale_units='xy', scale=1)
plt.xlim(-10, 10)
plt.ylim(-10, 10)
plt.show()

mpl output


In order to match the vector lenght and angle with the x,y coordinates of the plot, you can use to following options to plt.quiver:

plt.figure(figsize=(5,2), dpi=100)
plt.quiver(0,0,250,100, angles='xy', scale_units='xy', scale=1)
plt.xlim(0,250)
plt.ylim(0,100)

Your main problem is you create new figures in your loop, so each vector gets drawn on a different figure. Here's what I came up with, let me know if it's still not what you expect:

CODE:

import numpy as np
import matplotlib.pyplot as plt
M = np.array([[1,1],[-2,2],[4,-7]])

rows,cols = M.T.shape

#Get absolute maxes for axis ranges to center origin
#This is optional
maxes = 1.1*np.amax(abs(M), axis = 0)

for i,l in enumerate(range(0,cols)):
    xs = [0,M[i,0]]
    ys = [0,M[i,1]]
    plt.plot(xs,ys)

plt.plot(0,0,'ok') #<-- plot a black point at the origin
plt.axis('equal')  #<-- set the axes to the same scale
plt.xlim([-maxes[0],maxes[0]]) #<-- set the x axis limits
plt.ylim([-maxes[1],maxes[1]]) #<-- set the y axis limits
plt.legend(['V'+str(i+1) for i in range(cols)]) #<-- give a legend
plt.grid(b=True, which='major') #<-- plot grid lines
plt.show()

OUTPUT:

enter image description here

EDIT CODE:

import numpy as np
import matplotlib.pyplot as plt
M = np.array([[1,1],[-2,2],[4,-7]])

rows,cols = M.T.shape

#Get absolute maxes for axis ranges to center origin
#This is optional
maxes = 1.1*np.amax(abs(M), axis = 0)
colors = ['b','r','k']


for i,l in enumerate(range(0,cols)):
    plt.axes().arrow(0,0,M[i,0],M[i,1],head_width=0.05,head_length=0.1,color = colors[i])

plt.plot(0,0,'ok') #<-- plot a black point at the origin
plt.axis('equal')  #<-- set the axes to the same scale
plt.xlim([-maxes[0],maxes[0]]) #<-- set the x axis limits
plt.ylim([-maxes[1],maxes[1]]) #<-- set the y axis limits
plt.grid(b=True, which='major') #<-- plot grid lines
plt.show()

EDIT OUTPUT: enter image description here


What did you expect the following to do?

v1 = [0,0],[M[i,0],M[i,1]]
v1 = [M[i,0]],[M[i,1]]

This is making two different tuples, and you overwrite what you did the first time... Anyway, matplotlib does not understand what a "vector" is in the sense you are using. You have to be explicit, and plot "arrows":

In [5]: ax = plt.axes()

In [6]: ax.arrow(0, 0, *v1, head_width=0.05, head_length=0.1)
Out[6]: <matplotlib.patches.FancyArrow at 0x114fc8358>

In [7]: ax.arrow(0, 0, *v2, head_width=0.05, head_length=0.1)
Out[7]: <matplotlib.patches.FancyArrow at 0x115bb1470>

In [8]: plt.ylim(-5,5)
Out[8]: (-5, 5)

In [9]: plt.xlim(-5,5)
Out[9]: (-5, 5)

In [10]: plt.show()

Result:

enter image description here


How about something like

import numpy as np
import matplotlib.pyplot as plt

V = np.array([[1,1], [-2,2], [4,-7]])
origin = np.array([[0, 0, 0],[0, 0, 0]]) # origin point

plt.quiver(*origin, V[:,0], V[:,1], color=['r','b','g'], scale=21)
plt.show()

enter image description here

Then to add up any two vectors and plot them to the same figure, do so before you call plt.show(). Something like:

plt.quiver(*origin, V[:,0], V[:,1], color=['r','b','g'], scale=21)
v12 = V[0] + V[1] # adding up the 1st (red) and 2nd (blue) vectors
plt.quiver(*origin, v12[0], v12[1])
plt.show()

enter image description here

NOTE: in Python2 use origin[0], origin[1] instead of *origin


All nice solutions, borrowing and improvising for special case -> If you want to add a label near the arrowhead:


    arr = [2,3]
    txt = “Vector X”
    ax.annotate(txt, arr)
    ax.arrow(0, 0, *arr, head_width=0.05, head_length=0.1)


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