<reponame>arifmudi/Applying-Math-with-Python<filename>Chapter 09/using-gradient-descent-methods.py

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D



def descend(func, x0, grad, bounds, tol=1e-8, max_iter=100):
    xn = x0
    xnm1 = np.inf
    grad_xn = grad(x0)

    for i in range(max_iter):
        
        if np.linalg.norm(xn - xnm1) < tol:
            break

        direction = -grad_xn
        
        xnm1 = xn
        xn = xn + 0.2*direction
        grad_xn = grad(xn)
        yield i, xn, func(xn), grad_xn


def func(x):
    return ((x[0] - 0.5)**2 + (x[1] + 0.5)**2)*np.cos(0.5*x[0]*x[1])


x_r = np.linspace(-1, 1)
y_r = np.linspace(-2, 2)

x, y = np.meshgrid(x_r, y_r)

z = func([x, y])


surf_fig = plt.figure(tight_layout=True)
surf_ax = surf_fig.add_subplot(projection="3d")
surf_ax.tick_params(axis="both", which="major", labelsize=9)
surf_ax.set(xlabel="x", ylabel="y", zlabel="z")
surf_ax.set_title("Objective function")

surf_ax.plot_surface(x, y, z, alpha=0.7)


x0 = np.array([-0.8, 1.3])
surf_ax.plot([x0[0]], [x0[1]], func(x0), "r*")


def grad(x):
    c1 = x[0]**2 - x[0] + x[1]**2 + x[1] + 0.5
    cos_t = np.cos(0.5*x[0]*x[1])
    sin_t = np.sin(0.5*x[0]*x[1])
    return np.array([
        (2*x[0]-1)*cos_t - 0.5*x[1]*c1*sin_t,
        (2*x[1]+1)*cos_t - 0.5*x[0]*c1*sin_t
    ])


cont_fig, cont_ax = plt.subplots()
cont_ax.set(xlabel="x", ylabel="y")
cont_ax.set_title("Contour plot with iterates")
cont_ax.contour(x, y, z, levels=30)

bounds = ((-1, 1), (-2, 2))

xnm1 = x0
for i, xn, fxn, grad_xn in descend(func, x0, grad, bounds):
    cont_ax.plot([xnm1[0], xn[0]], [xnm1[1], xn[1]], "k*--")
    xnm1, grad_xnm1 = xn, grad_xn

print(f"iterations={i}")
print(f"min val at {xn}")
print(f"min func value = {fxn}")


plt.show()
09/using-gradient-descent-methods.py

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D



def descend(func, x0, grad, bounds, tol=1e-8, max_iter=100):
    xn = x0
    xnm1 = np.inf
    grad_xn = grad(x0)

    for i in range(max_iter):
        
        if np.linalg.norm(xn - xnm1) < tol:
            break

        direction = -grad_xn
        
        xnm1 = xn
        xn = xn + 0.2*direction
        grad_xn = grad(xn)
        yield i, xn, func(xn), grad_xn


def func(x):
    return ((x[0] - 0.5)**2 + (x[1] + 0.5)**2)*np.cos(0.5*x[0]*x[1])


x_r = np.linspace(-1, 1)
y_r = np.linspace(-2, 2)

x, y = np.meshgrid(x_r, y_r)

z = func([x, y])


surf_fig = plt.figure(tight_layout=True)
surf_ax = surf_fig.add_subplot(projection="3d")
surf_ax.tick_params(axis="both", which="major", labelsize=9)
surf_ax.set(xlabel="x", ylabel="y", zlabel="z")
surf_ax.set_title("Objective function")

surf_ax.plot_surface(x, y, z, alpha=0.7)


x0 = np.array([-0.8, 1.3])
surf_ax.plot([x0[0]], [x0[1]], func(x0), "r*")


def grad(x):
    c1 = x[0]**2 - x[0] + x[1]**2 + x[1] + 0.5
    cos_t = np.cos(0.5*x[0]*x[1])
    sin_t = np.sin(0.5*x[0]*x[1])
    return np.array([
        (2*x[0]-1)*cos_t - 0.5*x[1]*c1*sin_t,
        (2*x[1]+1)*cos_t - 0.5*x[0]*c1*sin_t
    ])


cont_fig, cont_ax = plt.subplots()
cont_ax.set(xlabel="x", ylabel="y")
cont_ax.set_title("Contour plot with iterates")
cont_ax.contour(x, y, z, levels=30)

bounds = ((-1, 1), (-2, 2))

xnm1 = x0
for i, xn, fxn, grad_xn in descend(func, x0, grad, bounds):
    cont_ax.plot([xnm1[0], xn[0]], [xnm1[1], xn[1]], "k*--")
    xnm1, grad_xnm1 = xn, grad_xn

print(f"iterations={i}")
print(f"min val at {xn}")
print(f"min func value = {fxn}")


plt.show()