Simplex_Construction.ipynb

Kernel: Python 3

Summary of the Code

In this code, we use matplotlib to visualise the construction of simplices from ReLU functions

import matplotlib.pyplot as plt
import numpy as np
import matplotlib as mpl
from matplotlib import cm
from matplotlib.colors import LinearSegmentedColormap, ListedColormap
from matplotlib.ticker import LinearLocator

#customising colormap
YlGn_r_big = mpl.colormaps['YlGn_r']
newcmp = ListedColormap(YlGn_r_big(np.linspace(0.05, 0.75, 256)))


ax = plt.figure(figsize=(10,10)).add_subplot(projection='3d')

# Make data.
X = np.arange(-1, 1, 0.025)
xlen = len(X)
Y = np.arange(-1, 1, 0.025)
ylen = len(Y)
X, Y = np.meshgrid(X, Y)
r= np.zeros(xlen)
R = np.fmax(r,X)


#plotting
ax.plot_surface(X,Y,R, alpha = 1, cmap=newcmp)
plt.xlabel('x')
plt.ylabel('y')
ax.set_zlabel('z')
ax.set_zlim(-1, 1)
ax.zaxis.set_major_locator(LinearLocator(6))
ax.set_facecolor("#93c280")
ax.view_init(30, 250)
plt.show()

import matplotlib.pyplot as plt
import numpy as np
import matplotlib as mpl
from matplotlib import cm
from matplotlib.colors import LinearSegmentedColormap, ListedColormap
from matplotlib.ticker import LinearLocator

#customising colormap
YlGn_r_big = mpl.colormaps['YlGn_r']
newcmp = ListedColormap(YlGn_r_big(np.linspace(0.05, 0.75, 256)))


ax = plt.figure(figsize=(10,10)).add_subplot(projection='3d')

# Make data.
X = np.arange(-5, 5, 0.025)
xlen = len(X)
Y = np.arange(-5, 5, 0.025)
ylen = len(Y)
X, Y = np.meshgrid(X, Y)
r= np.zeros(xlen)
Z = np.fmax(r,(1-np.fmax(r,0.3*X)-np.fmax(r,-0.3*X)-np.fmax(r,-0.3*Y)-np.fmax(r,0.3*Y)))


#plotting
ax.plot_surface(X,Y,Z, alpha = 1, cmap=newcmp)
plt.xlabel('x')
plt.ylabel('y')
ax.set_zlabel('z')
ax.set_zlim(-1, 1)
ax.zaxis.set_major_locator(LinearLocator(6))
ax.set_facecolor("#93c280")
ax.view_init(30, 250)
plt.show()

import matplotlib.pyplot as plt
import numpy as np
import matplotlib as mpl
from matplotlib import cm
from matplotlib.colors import LinearSegmentedColormap, ListedColormap
from matplotlib.ticker import LinearLocator

#colormap customisation
YlGn_r_big = mpl.colormaps['YlGn_r']
newcmp = ListedColormap(YlGn_r_big(np.linspace(0.05, 0.75, 256)))

ax = plt.figure(figsize=(10,10)).add_subplot(projection='3d')

def a(n,x,y):
  return np.fmax(r,(1-np.fmax(r,n*(x))-np.fmax(r,-n*(x))-np.fmax(r,-n*(y))-np.fmax(r,n*(y))))
# Make data.
X = np.arange(-3.5, 3.5, 0.005)
xlen = len(X)
Y = np.arange(-3.5, 3.5, 0.005)
ylen = len(Y)
X, Y = np.meshgrid(X, Y)
r= np.zeros(xlen)
R = np.fmax(r,X) #relu
Z= a(0.3,X,Y) #pyramid
D= 0.35*(a(0.5,1.5+X,Y)+a(0.5,1.5 -X,Y)+a(0.5,X,1.5-Y)+a(0.5,X,1.5+Y))+0.35*(a(0.5,1-X,1-Y)+a(0.5,1+X,1+Y)+a(0.5,1-X,1+Y)+a(0.5,1+X,1-Y)) #random function

#plotting
ax.plot_surface(X,Y,D, alpha = 1, cmap=newcmp)
plt.xlabel('x')
plt.ylabel('y')
ax.set_zlabel('z')
ax.set_zlim(-1,1)
ax.set_ylim(-3.5, 3.5)
ax.set_xlim(-3.5, 3.5)
ax.zaxis.set_major_locator(LinearLocator(6))
ax.set_facecolor("#93c280")
ax.view_init(30, 60)
plt.show()