restriction=np.matrix(1))
]),
ps.SheafCell(dimension=1, cofaces=[], stalkDim=1)
])
sec4 = ps.Section([ps.SectionCell(0, 1)])
# Extending along a line
if sec4.extend(sh2, 1) and sec4.extend(sh2, 2) and sec4.extend(sh2, 3):
print[s.value for s in sec4.sectionCells]
print "Test 2 passed"
else:
print "Test 2 failed"
# Mayer-Vietoris example from tspbook
sh3 = ps.FlowSheaf(
ps.DirectedGraph([(None, 0), (None, 0), (0, None), (0, 1), (None, 1),
(1, None)]))
sec5 = ps.Section([
ps.SectionCell(0, 3),
ps.SectionCell(1, 2),
ps.SectionCell(2, 1),
ps.SectionCell(4, 3),
ps.SectionCell(5, 8)
])
sec6 = ps.Section([
ps.SectionCell(0, 3),
ps.SectionCell(1, 2),
ps.SectionCell(2, 1),
ps.SectionCell(4, 3),
ps.SectionCell(5, 7)
])
print '0-Persistent degree 0 Sheaf Betti number ' + str(
PerSheaf0.cobetti(0))
print '0-Persistent degree 1 Sheaf Betti number ' + str(
PerSheaf0.cobetti(1))
PerSheaf1 = ps.PersistenceSheaf([ColLoopSheaf, LineSheaf, LoopSheaf],
[(0, 1, MorColLine),
(0, 2, MorColLoop)], 1)
print '1-Persistent degree 0 Sheaf Betti number ' + str(
PerSheaf1.cobetti(0))
print '1-Persistent degree 1 Sheaf Betti number ' + str(
PerSheaf1.cobetti(1))
fs = ps.FlowSheaf(
ps.DirectedGraph([(None, 1), (None, 1), (1, 2), (1, None), (None, 2),
(2, None)]))
print 'Flow sheaf degree 0 Sheaf Betti number ' + str(fs.cobetti(0))
fs2 = fs.star([6])
print 'Flow sheaf degree 0 Sheaf Betti number ' + str(fs2.cobetti(0))
fs3 = fs.star([7])
print 'Flow sheaf degree 0 Sheaf Betti number ' + str(fs3.cobetti(0))
print 'Dimension of local sections over a single edge ' + str(
fs.localSectional([0])[0].cobetti(0))
print 'Dimension of local sections over two edges ' + str(
fs.localSectional([0, 1])[0].cobetti(0))
print 'Dimension of local sections over three edges ' + str(
fs.localSectional([0, 1, 2])[0].cobetti(0))
# Sample persistence sheaf calculation
#
# Copyright (c) 2013-2014, Michael Robinson
# 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)