plots in python

import matplotlib.pyplot as plt
import numpy as np

A simple plot:

x = np.linspace(0,2*np.pi,361)
fx = np.sin(x)
plt.plot(x,fx)
plt.show()

rng = np.random.default_rng() # make a RNG

u = rng.random(50) * 2 * np.pi
v = np.sin(u) + rng.normal(0,1/4,50)

plt.plot(x,fx,label= "true underlying function")
plt.plot(u,v,'o',label = "noisy observations")
plt.xlabel('x')
plt.legend()
plt.show()

Another way to set up a figure and a set of axes and build a plot and then show it.

fig, ax = plt.subplots( figsize = (10,4))

ax.plot(x,fx, label = "True function")
ax.plot(u,v,'o', label = "observations")
ax.set_title("A cool plot")
ax.legend()

ax2 = ax.twinx()
ax2.hist(u,color= (0.545,0,0,.2))
ax2.set_ylabel('Frequency of observations')
plt.show()

fig, axs = plt.subplot_mosaic([['A','B'],['Bottom','Bottom']], figsize=(10,8) )

axs['A'].plot(u,v,'o')
axs['B'].plot(x,fx)
axs['Bottom'].hist(u)

fig.suptitle('An example of subplot mosaic', fontsize = 18, y = .95)

plt.show()

Defining functions in Python

def f(x): return( x * np.sin(x))

f(1)

0.8414709848078965

A function with more than one line:

Say we want to get the hypotenuse from two sides of a right triangle.

def hyp(a,b):

    csq = a**2 + b**2
    c = np.sqrt(csq)
    return c

print(hyp(3,4))
print(hyp(5,10))
    

5.0
11.180339887498949

What if we want a function to return more than one output??

Example: A function which gives Euclidean coordinates from polar.

def eucl(r,th):

    x = r * np.cos(th)
    y = r * np.sin(th)
    return x, y

print(eucl(r=1,th=np.pi/2))
print(eucl(r=1,th=np.pi/3))

(6.123233995736766e-17, 1.0)
(0.5000000000000001, 0.8660254037844386)

A function which takes some values by default:

def logistic(x,a=0,b=1):

    l = a + b * x
    val = np.exp(l) / (1 + np.exp(l))
    return val
  

x = np.linspace(-4,4,201)
fx1 = logistic(x)
fx2 = logistic(x,a = 2,b=2)

plt.rcParams['text.usetex'] # this allows you to use LaTex code in your plot labels

fig, ax = plt.subplots(figsize = (10,5))

ax.plot(x,fx1, label = '$a = 0$, $b = 1$')
ax.plot(x,fx2, label = '$a = 2$, $b = 2$')

ax.text(-3, .6, "$f(x) = \\frac{e^{a + b x}}{1 + e^{a + bx} }$")

ax.legend()
plt.show()

Conditional programming

Make a function which rolls two dice and prints different phrases depending on the outcome.

np.random.choice(np.arange(1,7),1)  # roll a six-sided die

array([3])

def rolldice():

    # roll two six-sided dice
    r1 = np.random.choice(np.arange(1,7),1)
    r2 = np.random.choice(np.arange(1,7),1)

    print("You rolled a " + str(r1) + " and a " + str(r2) + ".")

    if(r1 == r2):

        print("Doubles!!!!!")

    elif( (r1 + r2) > 10):

        print("No doubles, but pretty nice.")

    else:

        print("Not bad.")


    

rolldice()

You rolled a [3] and a [5].
Not bad.

Can take advantage of coercion of booleans to numbers when we do conditional programming:

def softthresh(x,lam):

    return (x < -lam)*(x + lam) + (x > lam)*(x - lam)

A cool 3d plot

def bivn(x,y,rho=0):

    r = 1 - rho**2
    z = x**2 + y**2 - 2*rho*x*y
    f = 1/(2 * np.pi) * 1/np.sqrt(r) * np.exp( - z / (2 * r))
    return f

bivn(1,1/2,-1/4)

0.07385823208730814

gs = 101 # this is the "grid size"
grid = np.linspace(-3,3,gs)
X, Y = np.meshgrid(grid,grid)
F = bivn(X,Y,rho=1/2)

fig = plt.figure(figsize = (8,8))
ax = fig.add_subplot(projection='3d')
ax.plot_surface(X,Y,F, cmap = plt.cm.YlGnBu_r)

plt.show()