def construct_3_step_sheaf():
global s3
s3=ps.Sheaf([ps.SheafCell(dimension=0,
compactClosure=True,
stalkDim=6,
metric=distance, # Ignores velocity
cofaces=[ps.SheafCoface(index=1,
orientation=1,
restriction=ps.LinearMorphism(np.array([[1,0,0,0,0,0],
[0,1,0,0,0,0],
[0,0,1,0,0,0],
[0,0,0,1,0,0],
[0,0,0,0,1,0]]))), # A->B
ps.SheafCoface(index=2,
orientation=1,
restriction=ps.LinearMorphism(np.array([[1,0,0,0,0,0],
[0,1,0,0,0,0],
[0,0,1,0,0,0],
[0,0,0,2,0,0],
[0,0,0,0,1,0]]))), # A->C
],
),
ps.SheafCell(dimension=1,
compactClosure=True,
stalkDim=5,
metric=distance,
cofaces=[ps.SheafCoface(index=3,
orientation=1,
restriction=ps.LinearMorphism(np.array([[1,0,0,0,0],
[0,1,0,0,0],
[0,0,1,0,0],
[0,0,0,2,0]]))), # B->D
]),
ps.SheafCell(dimension=1,
compactClosure=True,
stalkDim=5,
metric=distance, # Ignores velocity
cofaces=[ps.SheafCoface(index=3,
orientation=1,
restriction=ps.LinearMorphism(np.array([[1,0,0,0,0],
[0,1,0,0,0],
[0,0,1,0,0],
[0,0,0,1,0]]))), # C->D
]),
ps.SheafCell(dimension=2,
compactClosure=True,
stalkDim=4,
metric=distance,
cofaces=[ps.SheafCoface(index=4,
orientation=1,
restriction=ps.LinearMorphism(np.array([[1,0,0,0],
[0,1,0,0],
[0,0,1,0],
[0,0,0,1]])))]),
ps.SheafCell(dimension=3,
compactClosure=True,
stalkDim=4,
metric=distance,
cofaces=[]),
])
consistency_radii=[s1.consistencyRadius(case) for case in input_data]
return consistency_radii
#Sheaf Construction
#sheafcell=self,dimension,cofaces=[],compactClosure=True,stalkDim=None,metric=None)
#sheaf coface=(self,index,orientation,restriction)
sdim=np.ts.size #number of samples for u & v; n+m. For n or m, use sdim/2
s1=py.Sheaf([py.SheafCell(dimension=1,stalkDim=(sdim/2),cofaces=[]), \
py.SheafCell(dimension=1,stalkDim=(sdim/2),cofaces=[]), \
py.SheafCell(dimension=1,stalkDim=(sdim/2),cofaces=[]), \
py.SheafCell(dimension=1,stalkDim=(sdim/2),cofaces=[]), \
py.SheafCell \
(dimension=0,stalkDim=sdim,cofaces=[py.SheafCoface(index=0, orientation=1, restriction=py.LinearMorphism(pr1(ts))), \
py.SheafCoface(index=1, orientation=1, restriction=py.LinearMorphism(pr2(ts))), \
py.SheafCoface(index=3, orientation=1, restriction=py.SetMorphism(eqn1(ts)))]), \
py.SheafCell \
(dimension=0,stalkDim=sdim,cofaces=[py.SheafCoface(index=0, orientation=-1, restriction=py.LinearMorphism(pr1(ts))), \
py.SheafCoface(index=1, orientation=-1, restriction=py.LinearMorphism(pr2(ts))), \
py.SheafCoface(index=2, orientation=-1, restriction=py.SetMorphism(eqn2(ts)))]), \
py.SheafCell \
(dimension=0,stalkDim=(sdim/2),cofaces=[py.SheafCoface(index=0, orientation=1, restriction=py.LinearMorphism(iden(ts))), \
py.SheafCoface(index=2, orientation=1, restriction=py.LinearMorphism(ddt(ts)))]), \
py.SheafCell \
(dimension=0,stalkDim=(sdim/2),cofaces=[py.SheafCoface(index=1, orientation=1, restriction=py.LinearMorphism(iden(ts))), \
py.SheafCoface(index=3, orientation=-1, restriction=py.LinearMorphism(ddt(ts)))])])
#How to construct? Taken from search_rescue_test.py
]),
ps.SheafCell(dimension=1,
cofaces=[
ps.SheafCoface(2, -1, np.matrix(1)),
ps.SheafCoface(3, 1, np.matrix(1))
]),
ps.SheafCell(dimension=2, stalkDim=1),
ps.SheafCell(dimension=2, stalkDim=1)
])
print 'S^2 Sheaf Betti numbers: ' + str(
(SphSheaf.cobetti(0), SphSheaf.cobetti(1), SphSheaf.cobetti(2)))
MorCirDisk = ps.SheafMorphism([
ps.SheafMorphismCell(destinations=[0, 1, 2],
maps=[
ps.LinearMorphism(np.matrix(1)),
ps.LinearMorphism(np.matrix(1)),
ps.LinearMorphism(np.matrix(1))
]),
ps.SheafMorphismCell(destinations=[3],
maps=[ps.LinearMorphism(np.matrix(1))]),
ps.SheafMorphismCell(destinations=[], maps=[])
])
print 'degree 0 induced map S^1->D^2: ' + str(
ps.inducedMap(DiskSheaf, CircSheaf, MorCirDisk, 0))
print 'degree 1 induced map S^1->D^2:' + str(
ps.inducedMap(DiskSheaf, CircSheaf, MorCirDisk, 1))
print 'degree 2 induced map S^1->D^2:' + str(
ps.inducedMap(DiskSheaf, CircSheaf, MorCirDisk, 2))
# Sheaf over a graph with an undirected loop
# 6: V1 = S1 (theta1)
# 7: V2 = S1 (theta2)
# 8: V3 = R (t)
s1 = ps.Sheaf([
ps.SheafCell(
dimension=0,
compactClosure=True,
stalkDim=6,
metric=distance_alt, # Ignores velocity
cofaces=[
ps.SheafCoface(index=2,
orientation=1,
restriction=ps.LinearMorphism(
np.array([[1, 0, 0, 0, 0,
0], [0, 1, 0, 0, 0, 0],
[0, 0, 1, 0, 0,
0], [0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 1, 0]]))), # X->U2
ps.SheafCoface(index=3,
orientation=1,
restriction=ps.SetMorphism(A)), # X->U3
ps.SheafCoface(index=4,
orientation=1,
restriction=ps.SetMorphism(B)), # X->U4
ps.SheafCoface(index=5,
orientation=1,
restriction=ps.SetMorphism(E))
]), # X->U5
ps.SheafCell(dimension=2,
compactClosure=True,
stalkDim=3,
def construct_sheaf():
global s1
s1 = ps.Sheaf([
ps.SheafCell(
dimension=0,
compactClosure=True,
stalkDim=6,
metric=distance_alt, # Ignores velocity
cofaces=[
ps.SheafCoface(index=2,
orientation=1,
restriction=ps.LinearMorphism(
np.array([[1, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0],
[0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 1, 0]]))), # X->U2
ps.SheafCoface(index=3,
orientation=1,
restriction=ps.SetMorphism(A)), # X->U3
ps.SheafCoface(index=4,
orientation=1,
restriction=ps.SetMorphism(B)), # X->U4
ps.SheafCoface(index=5,
orientation=1,
restriction=ps.SetMorphism(E))
], # X->U5
bounds=scene_bounds_0),
ps.SheafCell(dimension=2,
compactClosure=True,
stalkDim=3,
metric=distance_alt,
cofaces=[]), # U1
ps.SheafCell(
dimension=1,
compactClosure=True,
stalkDim=5,
metric=distance_alt, # Ignores velocity
cofaces=[
ps.SheafCoface(index=1,
orientation=1,
restriction=ps.LinearMorphism(
np.array([[1, 0, 0, 0, 0], [0, 1, 0, 0, 0],
[0, 0, 1, 0, 0]])))
]), # U2->U1
ps.SheafCell(
dimension=1,
compactClosure=True,
stalkDim=2,
metric=lambda x, y: min(anglemetric(x[0], y[0]), abs(x[1] - y[1])),
cofaces=[
ps.SheafCoface(index=6,
orientation=1,
restriction=ps.LinearMorphism(np.array(
[[1, 0]]))), # U3->V1
ps.SheafCoface(index=8,
orientation=1,
restriction=ps.LinearMorphism(np.array([[0,
1]])))
], # U3->V3
bounds=[(70, 80), (-pi, pi)]), # U3->V3
ps.SheafCell(
dimension=1,
compactClosure=True,
stalkDim=2,
metric=lambda x, y: min(anglemetric(x[0], y[0]), abs(x[1] - y[1])),
cofaces=[
ps.SheafCoface(index=8,
orientation=-1,
restriction=ps.LinearMorphism(np.array(
[[0, 1]]))), # U4->V3
ps.SheafCoface(index=7,
orientation=1,
restriction=ps.LinearMorphism(np.array([[1,
0]])))
], # U4->V2
bounds=[(60, 70), (-pi, pi)]), # U4->V2
ps.SheafCell(
dimension=1,
compactClosure=True,
stalkDim=2,
metric=distance,
cofaces=[
ps.SheafCoface(index=6,
orientation=-1,
restriction=ps.SetMorphism(C)), # U5->V1
ps.SheafCoface(index=7,
orientation=-1,
restriction=ps.SetMorphism(D))
], # U5->V2
bounds=[(-55, -75), (40, 50)]),
ps.SheafCell(dimension=2,
compactClosure=True,
stalkDim=1,
metric=anglemetric,
cofaces=[]), # V1
ps.SheafCell(dimension=2,
compactClosure=True,
stalkDim=1,
metric=anglemetric,
cofaces=[]), # V2
ps.SheafCell(dimension=2, compactClosure=True, stalkDim=1, cofaces=[])
]) # V3
ps.SheafCell(dimension=1,cofaces=[ps.SheafCoface(2,1,np.matrix(1))]),
ps.SheafCell(dimension=2,stalkDim=1)])
print 'Disk Betti numbers: ' + str((DiskSheaf.betti(0),DiskSheaf.betti(1),DiskSheaf.betti(2)))
# A 2-sphere
SphSheaf=ps.Sheaf([ps.SheafCell(dimension=0,cofaces=[
ps.SheafCoface(1,-1,np.matrix(1)),
ps.SheafCoface(1,1,np.matrix(1))]),
ps.SheafCell(dimension=1,cofaces=[
ps.SheafCoface(2,-1,np.matrix(1)),
ps.SheafCoface(3,1,np.matrix(1))]),
ps.SheafCell(dimension=2,stalkDim=1),
ps.SheafCell(dimension=2,stalkDim=1)])
print 'S^2 Betti numbers: ' + str((SphSheaf.betti(0),SphSheaf.betti(1),SphSheaf.betti(2)))
MorCirDisk=ps.SheafMorphism([ps.SheafMorphismCell(destinations=[0,1,2],maps=[ps.LinearMorphism(np.matrix(1)),ps.LinearMorphism(np.matrix(1)),ps.LinearMorphism(np.matrix(1))]),
ps.SheafMorphismCell(destinations=[3],maps=[ps.LinearMorphism(np.matrix(1))]),
ps.SheafMorphismCell(destinations=[],maps=[])])
print 'degree 0 induced map S^1->D^2: ' + str(ps.inducedMap(DiskSheaf,CircSheaf,MorCirDisk,0))
print 'degree 1 induced map S^1->D^2:' + str(ps.inducedMap(DiskSheaf,CircSheaf,MorCirDisk,1))
print 'degree 2 induced map S^1->D^2:' + str(ps.inducedMap(DiskSheaf,CircSheaf,MorCirDisk,2))
# Sheaf over a graph with an undirected loop
LoopSheaf=ps.Sheaf([ps.SheafCell(dimension=0,cofaces=[
ps.SheafCoface(2,1,np.matrix([1,0])),
ps.SheafCoface(3,1,np.matrix([0,0])),
ps.SheafCoface(4,-1,np.matrix([1,1]))]),
ps.SheafCell(dimension=0,cofaces=[
ps.SheafCoface(2,-1,np.matrix([1,0])),
ps.SheafCoface(3,-1,np.matrix([0,1])),
ps.SheafCoface(5,1,np.matrix([1,1]))]),
#U2=PxF
#U3=WxF
#U4=WxP
#V1=P
#V2=F
#V3=W
#difference between LINEAR morphism and SET morphism
s1 = ps.Sheaf([
ps.SheafCell(
dimension=0,
compactClosure=True,
stalkDim=2, #THIS IS THE NUMBER OF COLUMNS ?!?!
cofaces=[
ps.SheafCoface(index=4,
orientation=1,
restriction=ps.LinearMorphism(
np.array([[1.0, 0], [0, 1.0]]))), #X>U3 ?!?!?!
ps.SheafCoface(index=5,
orientation=-1,
restriction=ps.LinearMorphism(
np.array([[0, 0], [1.0, 0], [0, 1.0], [0, 0]])))
]), #X>U4
ps.SheafCell(
dimension=0,
compactClosure=True,
stalkDim=
4, #WHICH INDEX OF COLUMNS IS THIS REFERRING TO, THE SEED OR THE FINALS
cofaces=[
ps.SheafCoface(index=4,
orientation=1,
restriction=ps.LinearMorphism(
np.array([[1.0, 1.0, 0, 0],