def angleSet_Finite(p, quadrants=1, finiteList=False):
'''
Generate the minimal L1 angle set for the MT that has finite coverage.
If quadrants is more than 1, two quadrants will be used.
'''
fareyVectors = farey.Farey()
octants = 2
if quadrants > 1:
octants = 4
if quadrants > 2:
octants = 8
fareyVectors.compactOn()
fareyVectors.generate(p / 2, octants)
vectors = fareyVectors.vectors
sortedVectors = sorted(
vectors, key=lambda x: x.real**2 + x.imag**2) #sort by L2 magnitude
#compute corresponding m values
finiteAngles = []
for vector in sortedVectors:
if vector.real == 0:
m = 0
elif vector.imag == 0:
m = p
else:
m, inv = toFinite(vector, p)
finiteAngles.append(m)
# print("m:", m, "vector:", vector)
# print("sortedVectors:", sortedVectors)
#print(finiteAngles)
#ensure coverage
count = 0
filled = [0] * (p + 1) #list of zeros
finalVectors = []
finalFiniteAngles = []
for vector, m in zip(sortedVectors, finiteAngles):
if filled[m] == 0:
count += 1
filled[m] = 1
finalVectors.append(vector)
finalFiniteAngles.append(m)
if count == p + 1:
break
if finiteList:
return finalVectors, finalFiniteAngles
return finalVectors
def angleSubSets_Symmetric(s, mode, P, Q, octant=0, binLengths=False, K=1):
'''
Generate the minimal L1 angle set for the MT for s subsets.
Parameter K controls the redundancy, K = 1 is minimal.
If octant is non-zero, full quadrant will be used. Octant schemes are as follows:
If octant = -1, the opposing octant is also used.
If octant = 0,1 (default), only use one octant.
If octant = 2, octant will be mirrored from diagonal to form a quadrant.
If octant = 4, 2 quadrants.
If octant = 8, all quadrants.
Function can also return bin lengths for each bin.
'''
angles = []
subsetAngles = []
for i in range(s):
subsetAngles.append([])
fareyVectors = farey.Farey()
maxPQ = max(P, Q)
fareyVectors.compactOff()
fareyVectors.generate(maxPQ - 1, 1)
vectors = fareyVectors.vectors
sortedVectors = sorted(
vectors, key=lambda x: x.real**2 + x.imag**2) #sort by L2 magnitude
index = 0
subsetIndex = 0
binLengthList = []
angles.append(sortedVectors[index])
subsetAngles[subsetIndex].append(sortedVectors[index])
binLengthList.append(projectionLength(sortedVectors[index], P, Q))
while not isKatzCriterion(P, Q, angles,
K) and index < len(sortedVectors): # check Katz
index += 1
angles.append(sortedVectors[index])
subsetAngles[subsetIndex].append(sortedVectors[index])
p, q = farey.get_pq(sortedVectors[index]) # p = imag, q = real
binLengthList.append(projectionLength(sortedVectors[index], P, Q))
# if isKatzCriterion(P, Q, angles):
# break
if octant == 0:
continue
#add octants
if octant == -1:
nextOctantAngle = farey.farey(p, -q) #mirror from axis
angles.append(nextOctantAngle)
subsetAngles[subsetIndex].append(nextOctantAngle)
binLengthList.append(projectionLength(nextOctantAngle, P, Q))
if mode == 1:
subsetIndex += 1
subsetIndex %= s
if octant > 0 and p != q:
nextOctantAngle = farey.farey(q, p) #swap to mirror from diagonal
angles.append(nextOctantAngle)
subsetAngles[subsetIndex].append(nextOctantAngle)
binLengthList.append(projectionLength(nextOctantAngle, P, Q))
if mode == 1:
subsetIndex += 1
subsetIndex %= s
if octant > 1:
nextOctantAngle = farey.farey(p, -q) #mirror from axis
angles.append(nextOctantAngle)
subsetAngles[subsetIndex].append(nextOctantAngle)
binLengthList.append(projectionLength(nextOctantAngle, P, Q))
if mode == 1:
subsetIndex += 1
subsetIndex %= s
if p != q: #dont replicate
nextOctantAngle = farey.farey(
q, -p) #mirror from axis and swap to mirror from diagonal
angles.append(nextOctantAngle)
subsetAngles[subsetIndex].append(nextOctantAngle)
binLengthList.append(projectionLength(nextOctantAngle, P, Q))
if mode == 1:
subsetIndex += 1
subsetIndex %= s
if mode == 0:
subsetIndex += 1
subsetIndex %= s
if octant > 1: #add the diagonal and column projections when symmetric (all quadrant are wanted)
nextOctantAngle = farey.farey(1, 0) #mirror from axis
angles.append(nextOctantAngle)
subsetAngles[0].append(nextOctantAngle)
binLengthList.append(projectionLength(nextOctantAngle, P, Q))
if binLengths:
return angles, subsetAngles, binLengthList
return angles, subsetAngles
# -*- coding: utf-8 -*-
"""
Created on Fri Dec 18 14:30:21 2015
@author: shakes
"""
import _libpath #add custom libs
import numpy as np
import finitetransform.farey as farey
n = 32
#Farey vectors
fareyVectors = farey.Farey()
#~ fareyVectors.compactOn()
fareyVectors.generate(n - 1, 8)
#fareyVectors.generate2(n, 8)
vectors = fareyVectors.vectors
print vectors
countX = 0
countY = 0
vectorImage = np.zeros((2 * n + 1, 2 * n + 1))
vectorImage[n, n] += 1
for vector in vectors:
x = abs(vector.real)
y = abs(vector.imag)
vectorImage[int(vector.real + n), int(vector.imag + n)] += 1
countX += x
countY += y