__authors__ = [
"Kyle Akira Rocha <kylerocha2024@u.northwestern.edu>",
]
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
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def func_1(x,y,z):
# Spheroid centered at [x,y]=[-1,1]
radius = 1; a = 1.2; b = 2; c = 0.8
return ( (x+1)/a )**2 + ( (y-1)/b )**2 + ( z/c )**2 - radius**2
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def func_2(x,y,z):
# Modified Rosenbrock function
a = 1; b = 3; c = abs(z) ;
rosenbrock_func = (a-x)**2 + b*(y-x**2)**2
return rosenbrock_func + c*(x-z)**2
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def func_3(x,y,z):
return np.sin( (x-0.25) ) + (y)*z
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def func_4(x,y,z):
return np.where( z < 0, abs((x)**3-(y)**3)*np.exp(-z), 0 )
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def func_5(x,y,z):
# Spheroid centered at [x,y,z]=[0.5,0.5,0.85]
radius = 0.2; a = 0.6; b = 0.2; c = 0.3;
return ((x-0.5)/a )**2+( (y-0.5)/b )**2+( (z-0.85)/c )**2 - radius**2
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def analytic_classification_3D( X, Y, Z, f_splits=[1, 2.5,-0.5, 1.8, 0.3]):
"""Unique classes 1,2,3,4,6,8 for a total of 6 classes. This nicely matches
the colormap Dark2 for plotting."""
ret_f1 = func_1(X,Y,Z)
ret_f2 = func_2(X,Y,Z)
ret_f3 = func_3(X,Y,Z)
ret_f4 = func_4(X,Y,Z)
ret_f5 = func_5(X,Y,Z)
where_above_1 = ret_f1 > f_splits[0]
where_above_2 = ret_f2 > f_splits[1]
where_above_3 = ret_f3 > f_splits[2]
where_above_4 = ret_f4 > f_splits[3]
where_above_5 = ret_f5 > f_splits[4]
# First layer - purple, yellow
base_class = np.where( where_above_3, 3, 6)
# Second layer - gray
base_class[ where_above_2 ] = 8
# Third layer - green
combined_val = np.logical_and( where_above_1, where_above_2 ) # intersect with gray
base_class[ combined_val ] = 1
# Fourth layer - pink
base_class[ where_above_4 ] = 4
# Fifth layer - orange
base_class[ np.invert(where_above_5) ] = 2
return base_class
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def analytic_regression_3D(x,y,z):
# Something simple to start with
return np.sin( np.sqrt(x**2 + y**2 + z**2) * 2*np.pi/0.75 )
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def get_raw_output_3D(X,Y,Z):
"""Get the raw output for classification and regression for
the 3D synthetic data set. Unique classes include the
following [1,2,3,4,6,8].
Returns
-------
classification_data : ndarray
Class data (unique integers) in 3d classification space.
regression_data : ndarray
Regression output frmo 3d function.
"""
if isinstance( X, (float,int) ):
X = np.array([X]); Y=np.array([Y]); Z=np.array([Z])
elif isinstance( X, list ):
X= np.array(X); Y=np.array(Y); Z=np.array(Z)
classification_data = analytic_classification_3D(X,Y,Z)
regression_data = analytic_regression_3D(X,Y,Z)
return classification_data, regression_data
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def get_output_3D(X,Y,Z):
"""Takes input points (X,Y,Z) in 3D and returns a DataFrame with the
corresponding 3D classification and regression functions.
Returns
-------
data_frame : DataFrame
Pandas dataframe including inputs, class, and outputs.
"""
if isinstance( X, (float,int) ):
X = np.array([X]); Y=np.array([Y]); Z=np.array([Z])
elif isinstance( X, list ):
X= np.array(X); Y=np.array(Y); Z=np.array(Z)
classification_data, regression_data = get_raw_output_3D(X,Y,Z)
if X.ndim > 1 or Y.ndim > 1 or Z.ndim > 1:
classification_data = classification_data.flatten()
regression_data = regression_data.flatten()
X=X.flatten(); Y=Y.flatten(); Z=Z.flatten()
data_frame = pd.DataFrame()
data_frame["input_1"] = X
data_frame["input_2"] = Y
data_frame["input_3"] = Z
data_frame["class"] = classification_data.flatten()
data_frame["output_1"] = regression_data.flatten()
return data_frame
# EXAMPLE
# x_vals = np.linspace(-1,1,15)
# X, Y, Z = np.meshgrid( x_vals, x_vals+0.01, x_vals-0.02, indexing='ij')
# pd_data = get_output_3D( X,Y,Z )
# print( pd_data )
# -----------------------------------------------------------------------------
###########################
## PLOTTING ##
###########################
if (__name__ == "main"):
# SLICE PLOTS
all_Z_vals = [-1, -0.5, 0, 0.5, 1]
fig, (subs_xy, subs_xz) = plt.subplots(nrows = 2, ncols = len(all_Z_vals),
figsize=( 4*len(all_Z_vals), 7.5), dpi=50 )
for ct, zed_val in enumerate(all_Z_vals):
N = 90
# X-Y slice
X, Y = np.meshgrid( np.linspace(-1,1,N), np.linspace(-1,1,N) )
Z = np.ones( X.shape ) * zed_val
f_out = analytic_classification_3D( X, Y, Z )
image = subs_xy[ct].pcolor( X, Y, f_out,
cmap="Dark2", vmin=0.5, vmax=8.5 )
subs_xy[ct].set_title("z = {:.2f}".format(zed_val), fontsize=14 )
# X-Z slice
X, Z = np.meshgrid( np.linspace(-1,1,N), np.linspace(-1,1,N) )
Y = np.ones( X.shape ) * zed_val
f_out_2 = analytic_classification_3D( X, Y, Z )
image = subs_xz[ct].pcolor( X, Z, f_out_2,
cmap="Dark2", vmin=0.5, vmax=8.5 )
subs_xz[ct].set_title("y = {:.2f}".format(zed_val), fontsize=14 )
# horizontal lines
subs_xy[ct].hlines( all_Z_vals, xmin=-1, xmax=1, color="w", linestyle='--', alpha =0.35 )
# split subplot into two exes and change one to cbar
from mpl_toolkits.axes_grid1 import make_axes_locatable
for sub_plot_ax in [subs_xy[ct], subs_xz[ct]]:
divider = make_axes_locatable( sub_plot_ax )
cax2 = divider.append_axes("right", size="5%", pad=0.1)
fig.colorbar(image, cax=cax2)
subs_xy[0].set_ylabel("Y", fontsize=15, rotation=0)
subs_xz[0].set_ylabel("Z", fontsize=15, rotation=0)
for i in range(len(all_Z_vals)):
subs_xy[i].set_xlabel("X", fontsize=15);
subs_xz[i].set_xlabel("X", fontsize=15);
#fig.colorbar(image, ax=subs_xy[ct])
plt.subplots_adjust(hspace=0.35)
plt.show()
# 3D Plots
from matplotlib.cm import get_cmap
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
n = 45
x_vals = np.linspace(-1,1,n)
y_vals = np.linspace(-1.01,1,n)
z_vals = np.linspace(-1,1.01,n)
X, Y, Z = np.meshgrid( x_vals, y_vals, z_vals, indexing='ij')
test_f_out = analytic_classification_3D( X, Y, Z )
# Plotting all points for a given class
# 4, 1, 8, 3, 6, 2
for ct, number in enumerate( [4,6,2] ):
cmap = get_cmap('Dark2')
rgba = cmap( number/8.5 )
where_good_pts = np.where( test_f_out == number )
ax.scatter( X[where_good_pts], Y[where_good_pts], Z[where_good_pts],
color=rgba, alpha=0.55, s=10 )
# Plotting all points in a z slice
slice_zed_val = 0
slice_val = np.argmin( abs(slice_zed_val-z_vals) ) # which zed val
# for ct, number in enumerate( np.unique(test_f_out) ):
# cmap = get_cmap('Dark2')
# rgba = cmap( number/8.5 )
# where_good_pts = np.where( test_f_out[:,:,slice_val] == number )
# ax.scatter( X[:,:,slice_val][where_good_pts],
# Y[:,:,slice_val][where_good_pts],
# Z[:,:,slice_val][where_good_pts],
# color=rgba, alpha=0.85, s=10 )
ax.set_xlim3d(1,-1); ax.set_ylim3d(1,-1); ax.set_zlim3d(-1,1)
ax.set_xlabel('X', fontsize=15); ax.set_ylabel('Y', fontsize=15); ax.set_zlabel('Z', fontsize=15)
ax.view_init(elev=89.5, azim=90)
plt.show()
# Regression
x_vals = np.linspace(-1,1,15)
X, Y, Z = np.meshgrid( x_vals, x_vals+0.01, x_vals-0.02, indexing='ij')
pd_data = get_output_3D( X,Y,Z )
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
scatter_plot = ax.scatter( X, Y, Z, c=pd_data["output_1"].values, alpha=1, s=10 )
ax.set_xlim3d(1,-1); ax.set_ylim3d(1,-1); ax.set_zlim3d(-1,1)
ax.set_xlabel('X', fontsize=15); ax.set_ylabel('Y', fontsize=15); ax.set_zlabel('Z', fontsize=15)
ax.view_init(elev=89.5, azim=90)
fig.colorbar(scatter_plot)
plt.show()