code_challenge_2d_gradient_ascent.py

 # %% 
import numpy as np
import matplotlib.pyplot as plt
import sympy as sym # sympy to compute partial derivatives

from IPython import display
display.set_matplotlib_formats('svg')
# %%
# Gradient ascent in 2D

# the "peaks" function

def peaks(x,y):
    # expand to a 2D mesh
    x,y = np.meshgrid(x,y)

    z = 3*(1-x)**2 * np.exp(-(x**2) - (y+1)**2) \
    - 10*(x/5 - x**3 - y**5) * np.exp(-x**2-y**2) \
    - 1/3*np.exp(-(x+1)**2 - y**2)

    return z


# %%
# create the landscape
x = np.linspace(-3,3,201)
y = np.linspace(-3,3,201)

Z = peaks(x,y)

# let's have a look!
plt.imshow(Z,extent=[x[0],x[-1],y[0],y[-1]], vmin=-5, vmax=5, origin='lower')
plt.show()
# %%
# create derivative functions using sympy
sx, sy = sym.symbols('sx sy')

sZ = 3*(1-sx)**2 * sym.exp(-(sx**2) - (sy+1)**2) \
    -10*(sx/5 - sx**3 - sy**5) * sym.exp(-sx**2-sy**2) \
    - 1/3*sym.exp(-(sx+1)**2 - sy**2)

# create functions from the sympy-computed derivatives
df_x = sym.lambdify((sx,sy),sym.diff(sZ,sx),'sympy')
df_y = sym.lambdify((sx,sy),sym.diff(sZ,sy),'sympy')

df_x(1,1).evalf()


# %%
# random starting point (uniform between -2 and +2)
localmax = np.random.rand(2)*4-2 # also try specifying coordinates
startpnt = localmax[:] # make a copy, not re-assign

# learning parameters
learning_rate = 0.01
training_epochs = 1000

# run through training
trajectory = np.zeros((training_epochs,2))
for i in range(training_epochs):
    # compute the gradient at the current point
    grad = np.array([df_x(localmax[0],localmax[1]).evalf(),df_y(localmin[0],localmin[1]).evalf()])
    
    # take a step
    localmax = localmax + learning_rate*grad
    
    # store the current point
    trajectory[i,:] = localmax

print(localmax)
print(startpnt)
# %%
# let's have a look!
plt.imshow(Z,extent=[x[0],x[-1],y[0],y[-1]], vmin=-5, vmax=5, origin='lower')
plt.plot(startpnt[0],startpnt[1],'bs')
plt.plot(localmax[0],localmax[1],'ro')
plt.plot(trajectory[:,0],trajectory[:,1],'r')
plt.legend(['rnd start','local max'])
plt.colorbar()
plt.show()
# %%