Matplotlib module¶
Matplotlib is a plotting library. This section gives a brief introduction to the matplotlib.pyplot module, which provides a plotting system similar to that of MATLAB.
To use the matplotlib.pyplot module, you first need to import it, with the optional as plt (or whatever name you'd like to call by) that declare the alias.
import matplotlib.pyplot as plt
Importing numpy is not necessary for importing matplotlib, but you will usually do, because your data will be expressed in the array format.
import numpy as np
Plot¶
The most frequently used function in matplotlib should be plot, which allows you to plot 2D data.
t = np.arange(0,10,0.01) # points from 0 to 10 spaced by 0.01
x1 = np.exp(-t)*np.sin(3*t)
plt.figure()
plt.plot(t,x1)
plt.show()
Other useful functions and expressions you will use follow below.
t = np.linspace(0,10,1000) # equally spaced 1000 points from 0 to 10
x1 = np.exp(-t)*np.sin(3*t)
x2 = np.exp(-t)*np.sin(3*t+1)
x3 = np.exp(-2*t)*np.cos(3*t+1)
plt.figure(figsize=(8,6))
plt.plot(t,x1, label=r'$x_1=e^{-t}\sin(3t)$')
plt.plot(t,x2, label=r'$x_2=e^{-t}\sin(3t+1)$')
plt.plot(t,x3, label=r'$x_3=e^{-2t}\sin(3t+1)$')
plt.xlabel(r'$t$')
plt.ylabel('Response')
plt.xlim(0,6)
plt.ylim(-0.4,1)
plt.grid()
plt.legend()
plt.savefig('responses.png')
plt.show()
You will have to draw log-scale plots at some points in your career as an electrical engineer.
The following draws the Bode plots of $$ G(s) = \frac{s+3}{s^2+s+3} $$
w = np.logspace(-2,2,1000) # log-spaced 1000 points from 0.01 to 100
s = w*1j # s = jw
g = (s+3)/(s*s+s+3) # G(s)=(s+3)/(s^2+s+3)
plt.figure(figsize=(8,6))
plt.subplot(211)
plt.semilogx(w,20*np.log(abs(g)))
plt.ylabel('Magnitude (dB)')
plt.grid(True)
plt.title('Bode diagram')
plt.subplot(212)
plt.semilogx(w,180/np.pi*np.angle(g))
plt.ylabel('Phase (deg)')
plt.xlabel('Frequency (rad/s)')
plt.grid()
plt.savefig('bodeplot.png')
plt.show()
And the Nyquist diagram of the above?
plt.figure(figsize=(8,6))
plt.plot(np.real(g),np.imag(g),'--')
plt.plot(np.real(g),-np.imag(g),'-.')
plt.plot(-1,0,'r*')
plt.title('Nyquist diagram')
plt.xlabel('Re')
plt.ylabel('Im')
plt.axis('equal')
plt.xlim(-1.5,1.5)
plt.grid()
plt.savefig('nyquistplot.png')
plt.show()
Scatter plots. You will get to know, at some point in this class, how you can have your computer to automatically cluster those data points for you.
np.random.seed(0)
x1 = np.random.randn(2,100)
x2 = 5*np.random.rand(2,50)
x3 = np.random.randn(2,150)
A1 = np.array([[1,-0.5],[-0.5,4]])
A2 = np.array([[1,0.5],[0.5,4]])
A3 = np.array([[2,0],[0,2]])
b1 = np.array([-1,3]).reshape(2,1)
b2 = np.array([0,0]).reshape(2,1)
b3 = np.array([5,-5]).reshape(2,1)
y1 = np.dot(A1,x1) + b1
y2 = np.dot(A2,x2) + b2
y3 = np.dot(A3,x3) + b3
plt.figure(figsize=(8,6))
#plt.plot(y1[0,:], y1[1,:], 'ro', alpha=0.5)
#plt.plot(y2[0,:], y2[1,:], 'bv', alpha=0.5)
#plt.plot(y3[0,:], y3[1,:], 'k^', alpha=1.0)
plt.plot(y1[0,:], y1[1,:], "ro")
plt.plot(y2[0,:], y2[1,:], "ro")
plt.plot(y3[0,:], y3[1,:], "ro")
#plt.legend(['A','B','C'])
plt.grid()
plt.show()
Histograms.
x = np.random.randn(100000,5)
plt.figure(figsize=(8,6))
plt.hist(x[:,0], 50, density=1)
plt.title('Standard normal distribution')
plt.grid()
plt.xlabel(r'$x$')
plt.ylabel('Probability density function')
plt.xlim(-4,4)
plt.grid(True)
plt.show()
xsq = x*x
x2 = np.sum(xsq[:,0:2], axis=1)
x3 = np.sum(xsq[:,0:3], axis=1)
x4 = np.sum(xsq[:,0:4], axis=1)
x5 = np.sum(xsq[:,0:5], axis=1)
plt.figure(figsize=(8,6))
plt.hist(x2, 200, density=1, alpha=1.0)
plt.hist(x3, 200, density=1, alpha=0.8)
plt.hist(x4, 200, density=1, alpha=0.6)
plt.hist(x5, 200, density=1, alpha=0.4)
plt.title('Chi squared distribution')
plt.grid()
plt.xlabel(r'$x$')
plt.ylabel('Probability density function')
plt.xlim(0,10)
plt.legend([r'$\chi^2_2$',r'$\chi^2_3$',r'$\chi^2_4$',r'$\chi^2_5$'])
plt.grid(True)
plt.show()
