# Distribution of unaltered copies permitted for noncommercial use only
# All other uses require express permission of the author
# This software comes with no warrantees express or implied
import numpy as np
import pysheaf as ps
if __name__ == '__main__':
targ1=ps.DirectedGraph([(None,1),(1,2),(2,None),(None,3),(3,4),(4,None)])
fs1=ps.FlowSheaf(targ1)
targ2=ps.DirectedGraph([(None,1),(None,1),(1,2),(2,None),(2,None)])
targ3=ps.DirectedGraph([(None,1),(None,1),(1,2),(2,None)])
map1=[(0,0),(1,2),(2,3),(3,1),(4,2),(5,4),(6,5),(7,6),(8,5),(9,6)]
map2=[(0,0),(1,1),(2,2),(3,3),(4,3),(5,4)]
print 'Ready to compute!'
pf1,pf1m=fs1.pushForward(targ2,map1)
print 'pushforward FS 1 induced map ' + str(ps.inducedMap(pf1,fs1,pf1m,0))
fs2,fsm2=pf1.flowCollapse()
print 'collapse 1 induced map ' + str(ps.inducedMap(pf1,fs2,fsm2,0))
pf2,pf2m=fs2.pushForward(targ3,map2)
print 'pushforward FS 2 induced map ' + str(ps.inducedMap(pf2,fs2,pf2m,0))
fs3,fsm3=pf2.flowCollapse()
print 'collapse 2 induced map ' + str(ps.inducedMap(pf2,fs3,fsm3,0))
persh=ps.PersistenceSheaf([fs1,pf1,fs2,pf2,fs3],[(1,0,pf1m),(1,2,fsm2),(3,2,pf2m),(3,4,fsm3)],0)
print 'Persistence Betti 0=' + str(persh.betti(0))
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
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=[
# Distribution of unaltered copies permitted for noncommercial use only
# All other uses require express permission of the author
# This software comes with no warrantees express or implied
import numpy as np
import pysheaf as ps
if __name__ == '__main__':
targ1=ps.DirectedGraph([(None,1),(1,2),(2,None),(None,3),(3,4),(4,None)])
fs1=ps.FlowSheaf(targ1)
targ2=ps.DirectedGraph([(None,1),(None,1),(1,2),(2,None),(2,None)])
targ3=ps.DirectedGraph([(None,1),(None,1),(1,2),(2,None)])
map1=[(0,0),(1,2),(2,3),(3,1),(4,2),(5,4),(6,5),(7,6),(8,5),(9,6)]
map2=[(0,0),(1,1),(2,2),(3,3),(4,3),(5,4)]
print 'Ready to compute!'
pf1,pf1m=fs1.pushForward(targ2,map1)
print 'pushforward FS 1 induced map ' + str(ps.inducedMap(pf1,fs1,pf1m,0))
fs2,fsm2=pf1.flowCollapse()
print 'collapse 1 induced map ' + str(ps.inducedMap(pf1,fs2,fsm2,0))
pf2,pf2m=fs2.pushForward(targ3,map2)
print 'pushforward FS 2 induced map ' + str(ps.inducedMap(pf2,fs2,pf2m,0))
fs3,fsm3=pf2.flowCollapse()
print 'collapse 2 induced map ' + str(ps.inducedMap(pf2,fs3,fsm3,0))
persh=ps.PersistenceSheaf([fs1,pf1,fs2,pf2,fs3],[(1,0,pf1m),(1,2,fsm2),(3,2,pf2m),(3,4,fsm3)],0)
print 'Persistence Sheaf Betti 0=' + str(persh.cobetti(0))
# 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]))]),
ps.SheafCell(dimension=1,stalkDim=1),
ps.SheafCell(dimension=1,stalkDim=1),
ps.SheafCell(dimension=1,compactClosure=False,stalkDim=1),
# 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.SheafMorphismCell(destinations=[0,1,2],maps=[np.matrix(1),np.matrix(1),np.matrix(1)]),
ps.SheafMorphismCell(destinations=[3],maps=[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]))]),
ps.SheafCell(dimension=1,stalkDim=1),
ps.SheafCell(dimension=1,stalkDim=1),
ps.SheafCell(dimension=1,compactClosure=False,stalkDim=1),