def createFractal4(reduction, N, proportion):
#parameters
M = 2*N
twoQuads = True
angles, lengths = mojette.angleSet_Symmetric(N,N,1,True,50)
perpAngle = farey.farey(1,0)
angles.append(perpAngle)
powerSpect = np.zeros((M,M))
#compute lines
centered = True
mLines = []
sLines = []
mValues = []
sValues = []
pValues = []
qValues = []
for angle in angles:
m, s, p, q, inv = farey.toFinite(angle, M)
pValues.append(p)
qValues.append(q)
if m not in mValues and m < M:
u, v = radon.getSliceCoordinates2(m, powerSpect, centered, M)
mLines.append((u,v))
mValues.append(m)
#second quadrant
if twoQuads:
if m != 0 and m != M: #dont repeat these
m = M-m
if m not in mValues and m < M:
u, v = radon.getSliceCoordinates2(m, powerSpect, centered, M)
mLines.append((u,v))
mValues.append(m)
i = (len(mValues)+len(sValues))/float(M)
if i >= 1:
break
ss = []
ss.append(M)
ss.extend(range(0, N/2))
maxLines = len(ss)
for i,s in enumerate(ss):
u, v = radon.getSliceCoordinates2(s, powerSpect, centered, M)
sLines.append((u,v))
sValues.append(s)
i = (len(mValues)+len(sValues))/float(M)
if i >= 1.5:
break
length = 0
fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(16, 8))
plt.gray()
plt.tight_layout()
maxLines = len(sLines+mLines)
i = 0
ax[0].imshow(powerSpect)
ax[1].imshow(powerSpect)
color=iter(cm.jet(np.linspace(0,1,maxLines+1)))
fareyImage = np.zeros_like(powerSpect)
fareyImage1 = np.zeros_like(powerSpect)
for i, sLine in enumerate(sLines):
u, v = sLine
ax[1].plot(u, v, '.w',markersize=1)
fareyImage[u,v] = 1
length = length + 1
i = np.count_nonzero(fareyImage)/float((M*M))
if i >= reduction*proportion:
break
maxLines = len(mLines)
for i, mLine in enumerate(mLines):
u, v = mLine
ax[0].plot(u, v, '.r', markersize=1)
ax[1].plot(u, v, '.r',markersize=1)
fareyImage[u,v] = 1
fareyImage1[u,v] = 1
length = length + 1
i = np.count_nonzero(fareyImage)/float((M*M))
if i >= reduction:
break
print("Proportion of M:", (length/float(M)))
print("Non-zero elements with holes: ", np.count_nonzero(fareyImage1)/float((M*M)) * 100)
print("Non-zero elements without holes: ", np.count_nonzero(fareyImage)/float((M*M)) * 100)
print("Absolute difference percentage extra filled in is ", (np.count_nonzero(fareyImage)- np.count_nonzero(fareyImage1))/float((M*M)) *100)
withHoles = np.count_nonzero(fareyImage1)/float((M*M)) * 100
withoutHoles = np.count_nonzero(fareyImage)/float((M*M)) * 100
percentage = (withoutHoles - withHoles)/float(withHoles) * 100
print("Percentage difference percentage extra filled in is ", percentage)
ax[0].set_title('Sampling (colour per line) for dyadic size:'+str(M))
ax[1].set_title('Sampling (same colour per line) for dyadic size:'+str(M))
imageio.imsave("farey_image_"+str(M)+"_"+".png", fareyImage)
plt.show()
lines = mLines + sLines
return fareyImage, lines
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
import numpy as np
#parameters
N = 512
M = 2*N
K = 1
twoQuads = True
print("N:", N, "M:", M)
#p = nt.nearestPrime(M)
#print("p:", p)
#pDash = nt.nearestPrime(N)
#print("p':", pDash)
#angles = mojette.angleSet_Finite(pDash, 2)
angles, lengths = mojette.angleSet_Symmetric(N,N,1,True,K) #here
#getProjectionCoordinates
perpAngle = farey.farey(1,0)
angles.append(perpAngle)
print("Number of Angles:", len(angles))
print("angles:", angles)
#powerSpect = np.zeros((p,p))
powerSpect = np.zeros((M,M))
#np.set_printoptions(threshold=np.nan)
#compute lines
print("Computing Finite lines...")
centered = True
lines = []
mValues = []
pValues = []
''' Test for the pure independent modules for number theory ''' import _libpath #add custom libs import finitetransform.numbertheory as nt import finitetransform.farey as farey x = 5 m = 641 ########## # test the multiplicative inverse mod m inv = nt.minverse(x, m) print inv identity = (inv * x) % m print identity ########## # test the Farey finite vector function vector = farey.farey(1, 2) m = farey.toFinite(vector, m) print vector, "->", m
