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alok/main.py Secret

Created September 14, 2017 06:01
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
import argparse
import os
import sys
import matplotlib.pyplot as plt
import numpy as np
from matplotlib import rcParams
from mpl_toolkits.mplot3d import Axes3D
parser = argparse.ArgumentParser()
parser.add_argument('--dim', '-d', type=int, default=2)
parser.add_argument('--num_points', '-p', type=int, default=1000)
parser.add_argument('--trials', '-n', type=int, default=100)
parser.add_argument('--save', '-s', action='store_true')
args = parser.parse_args()
D = args.dim
N = args.num_points
NUM_TRIALS = args.trials
def sphere(n=N, d=D):
s = np.random.normal(size=(n, d))
s /= np.linalg.norm(s, axis=1)[:, np.newaxis]
return s
def m(d=D):
'''create square matrix of specified dim `d`.'''
return np.random.random(size=(d, d))
if __name__ == '__main__':
# make points smaller
rcParams.update({'lines.markersize': 3})
for i in range(NUM_TRIALS):
f = m()
s = sphere()
eigvals, eigvecs = np.linalg.eig(f)
# Should be a non-degenerate ellipse.
image = np.array([f @ v for v in s])
fig = plt.figure()
if D == 2:
# fig.gca().set_aspect('equal', adjustable='box')
ax = fig.add_subplot(
111,
aspect='equal',
adjustable='box',
)
ax.scatter(
s[:, 0],
s[:, 1],
s=1,
)
ax.scatter(
image[:, 0],
image[:, 1],
s=3,
)
ax.axhline(0, color='black')
ax.axvline(0, color='black')
ax.quiver(
[0, 0],
[0, 0],
eigvecs[0],
eigvecs[1],
angles='xy',
scale_units='xy',
scale=1,
)
elif D == 3:
ax = fig.add_subplot(
111,
adjustable='box',
aspect='equal',
projection='3d',
)
ax.scatter(
s[:, 0],
s[:, 1],
s[:, 2],
s=1,
)
ax.scatter(
image[:, 0],
image[:, 1],
image[:, 2],
s=3,
)
ax.quiver(
[0, 0, 0],
[0, 0, 0],
[0, 0, 0],
eigvecs[0],
eigvecs[1],
eigvecs[2],
)
else:
print('Only 2D or 3D.', file=sys.stderr)
if args.save:
os.makedirs('assets/2d', exist_ok=True)
os.makedirs('assets/3d', exist_ok=True)
fig.savefig(
f'assets/{D}d/{i}.svg',
bbox_inches='tight',
dpi=100,
format='svg',
)
np.savetxt(
f'assets/{D}d/{i}.vecs.txt',
eigvecs,
)
np.savetxt(
f'assets/{D}d/{i}.vals.txt',
eigvals,
)
else:
plt.show()
plt.close('all')
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