Book3_Elements-of-Mathematics/Book3_Ch13_Python_Codes/Bk3_Ch13_01.py at main · lxh754/Book3_Elements-of-Mathematics · GitHub

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###############
# Authored by Weisheng Jiang
# Book 3  |  From Basic Arithmetic to Machine Learning
# Published and copyrighted by Tsinghua University Press
# Beijing, China, 2022
###############

# Bk3_Ch13_01

import math
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import cm

def mesh_square(x1_0,x2_0,r,num):

    # generate mesh

    rr = np.linspace(-r,r,num)
    xx1,xx2 = np.meshgrid(rr,rr);

    xx1 = xx1 + x1_0;
    xx2 = xx2 + x2_0;

    return xx1, xx2

def plot_surf(xx1,xx2,ff,caption):

    norm_plt = plt.Normalize(ff.min(), ff.max())
    colors = cm.coolwarm(norm_plt(ff))

    fig = plt.figure()
    ax = fig.gca(projection='3d')
    surf = ax.plot_surface(xx1,xx2,ff,
    facecolors=colors, shade=False)
    surf.set_facecolor((0,0,0,0))
    # z_lim = [ff.min(),ff.max()]
    # ax.plot3D([0,0],[0,0],z_lim,'k')
    plt.show()

    plt.tight_layout()
    ax.set_xlabel('$\it{x_1}$')
    ax.set_ylabel('$\it{x_2}$')
    ax.set_zlabel('$\it{f}$($\it{x_1}$,$\it{x_2}$)')
    ax.set_title(caption)


    ax.xaxis._axinfo["grid"].update({"linewidth":0.25, "linestyle" : ":"})
    ax.yaxis._axinfo["grid"].update({"linewidth":0.25, "linestyle" : ":"})
    ax.zaxis._axinfo["grid"].update({"linewidth":0.25, "linestyle" : ":"})

    plt.rcParams["font.family"] = "Times New Roman"
    plt.rcParams["font.size"] = "10"

def plot_contourf(xx1,xx2,ff,caption):

    fig, ax = plt.subplots()

    cntr2 = ax.contourf(xx1,xx2,ff, levels = 15, cmap="RdBu_r")

    fig.colorbar(cntr2, ax=ax)
    plt.show()

    ax.set_xlabel('$\it{x_1}$')
    ax.set_ylabel('$\it{x_2}$')

    ax.set_title(caption)
    ax.grid(linestyle='--', linewidth=0.25, color=[0.5,0.5,0.5])

#%% initialization

x1_0  = 0;  # center of the mesh
x2_0  = 0;  # center of the mesh
r     = 2;  # radius of the mesh
num   = 30; # number of mesh grids
xx1,xx2 = mesh_square(x1_0,x2_0,r,num); # generate mesh

#%% Visualizations

plt.close('all')

# f(x1,x2) = -x1

ff = -xx1;
caption = '$\it{f} = -\it{x_1}$';
plot_surf (xx1,xx2,ff,caption)
plot_contourf (xx1,xx2,ff,caption)


#%% f(x1,x2) = x2

ff = xx2;
caption = '$\it{f} = \it{x_2}$';
plot_surf (xx1,xx2,ff,caption)
plot_contourf (xx1,xx2,ff,caption)

#%% f(x1,x2) = x1 + x2

ff = xx1 + xx2;
caption = '$\it{f} = \it{x_1} + \it{x_2}$';
plot_surf (xx1,xx2,ff,caption)
plot_contourf (xx1,xx2,ff,caption)

#%% f(x1,x2) = -x1 + x2

ff = -xx1 + xx2;
caption = '$\it{f} = -\it{x_1} + \it{x_2}$';
plot_surf (xx1,xx2,ff,caption)
plot_contourf (xx1,xx2,ff,caption)