#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
input_data=[py.Section([py.SectionCell(support=0,value=np.array(ts[:(sdim/2)])), # U
py.SectionCell(support=1,value=np.array(ts[(sdim/2):]))])] # V
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
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,
metric=distance_alt,
cofaces=[]), # U1
ps.SheafCell(
dimension=1,
compactClosure=True,
ts, alpha, beta, sigma, rho, gamma = parseddata_quarterly
sdim = ts.size #number of samples for u & v; n+m. For n or m, use sdim/2
print "size of time series is " + str(ts.shape)
tsu = ts[:sdim / 2]
tsv = ts[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(lambda x: eqn1(x,alpha,beta,sigma)))]), \
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(lambda x:eqn2(x,alpha,gamma,rho)))]), \
py.SheafCell \
(dimension=0,stalkDim=(sdim/2),cofaces=[py.SheafCoface(index=0, orientation=1, restriction=py.LinearMorphism(iden(tsu))), \
py.SheafCoface(index=2, orientation=1, restriction=py.LinearMorphism(ddt(tsu)))]), \
py.SheafCell \
(dimension=0,stalkDim=(sdim/2),cofaces=[py.SheafCoface(index=1, orientation=1, restriction=py.LinearMorphism(iden(tsv))), \
py.SheafCoface(index=3, orientation=-1, restriction=py.LinearMorphism(ddt(tsv)))])])
input_data = [
py.Section([
py.SectionCell(support=0, value=tsu), # U
py.SectionCell(support=1, value=tsv), #V