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))
print 'Dimension of local sections over three edges and a common vertex ' + str(
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)
])
sec7 = ps.Section([ps.SectionCell(1, 2), ps.SectionCell(4, 3)])
# Test transmission line sheaves
#
# 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 pysheaf as ps
import numpy as np
f = 900e6 # Operating frequency
ft2m = 12 * 0.0254 # Conversion feet to meters
wavenumber = 2 * np.pi * f / 3e8
dg = ps.DirectedGraph([(None, 1), (None, 2), (None, 3), (1, 2), (2, 3),
(3, 1)])
dg.cells[3].length = 70 * ft2m # Edge e3
dg.cells[4].length = (150 + 70) * ft2m # Edge e1
dg.cells[5].length = 150 * ft2m # Edge e2
tl = ps.TransLineSheaf(dg, wavenumber)
print tl.cohomology(0)
sec = np.sum(tl.cohomology(0), 1)
if np.allclose(
np.dot(tl.cells[6].cofaces[1].corestriction, sec[0:3]),
np.dot(tl.cells[7].cofaces[1].corestriction,
sec[3:6])) and np.allclose(
np.dot(tl.cells[6].cofaces[2].corestriction, sec[0:3]),
np.dot(tl.cells[8].cofaces[2].corestriction,
def setUp(self):
self.dg = ps.DirectedGraph([(0,1),(1,2),(1,2),(0,2)])
sh2=ps.Sheaf([ps.SheafCell(dimension=0,cofaces=[ps.SheafCoface(index=1,orientation=-1,restriction=np.matrix(1))]),
ps.SheafCell(dimension=1,cofaces=[],stalkDim=1),
ps.SheafCell(dimension=0,cofaces=[ps.SheafCoface(index=1,orientation=1,restriction=np.matrix(-1)),
ps.SheafCoface(index=3,orientation=-1,restriction=np.matrix(1))]),
ps.SheafCell(dimension=1,cofaces=[],stalkDim=1)])
sec4=ps.Assignment([ps.AssignmentCell(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.assignmentCells]
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.Assignment([ps.AssignmentCell(0,3),
ps.AssignmentCell(1,2),
ps.AssignmentCell(2,1),
ps.AssignmentCell(4,3),
ps.AssignmentCell(5,8)])
sec6=ps.Assignment([ps.AssignmentCell(0,3),
ps.AssignmentCell(1,2),
ps.AssignmentCell(2,1),
ps.AssignmentCell(4,3),
ps.AssignmentCell(5,7)])
sec7=ps.Assignment([ps.AssignmentCell(1,2),
ps.AssignmentCell(4,3)])
sec8=ps.Assignment([ps.AssignmentCell(1,2),
ps.AssignmentCell(4,3)])
print 'degree 0 induced map Collapsed->Line: ' + str(ps.inducedMap(ColLoopSheaf,LineSheaf,MorColLine,0))
print 'degree 1 induced map Collapsed->Line: ' + str(ps.inducedMap(ColLoopSheaf,LineSheaf,MorColLine,1))
print 'degree 2 induced map Collapsed->Line: ' + str(ps.inducedMap(ColLoopSheaf,LineSheaf,MorColLine,2))
PerSheaf0=ps.PersistenceSheaf([ColLoopSheaf,LineSheaf,LoopSheaf],[(0,1,MorColLine),(0,2,MorColLoop)],0)
print '0-Persistent degree 0 Betti number ' + str(PerSheaf0.betti(0))
print '0-Persistent degree 1 Betti number ' + str(PerSheaf0.betti(1))
PerSheaf1=ps.PersistenceSheaf([ColLoopSheaf,LineSheaf,LoopSheaf],[(0,1,MorColLine),(0,2,MorColLoop)],1)
print '1-Persistent degree 0 Betti number ' + str(PerSheaf1.betti(0))
print '1-Persistent degree 1 Betti number ' + str(PerSheaf1.betti(1))
fs=ps.FlowSheaf(ps.DirectedGraph([(None,1),(None,1),(1,2),(1,None),(None,2),(2,None)]))
print 'Flow sheaf degree 0 Betti number ' + str(fs.betti(0))
fs2=fs.star([6])
print 'Flow sheaf degree 0 Betti number ' + str(fs2.betti(0))
fs3=fs.star([7])
print 'Flow sheaf degree 0 Betti number ' + str(fs3.betti(0))
print 'Dimension of local sections over a single edge ' + str(fs.localSectional([0])[0].betti(0))
print 'Dimension of local sections over two edges ' + str(fs.localSectional([0,1])[0].betti(0))
print 'Dimension of local sections over three edges ' + str(fs.localSectional([0,1,2])[0].betti(0))
print 'Dimension of local sections over three edges and a common vertex ' + str(fs.localSectional([0,1,2,6])[0].betti(0))
print 'Induced map on local sections from 3 edges to 2 edges ' + str(fs.localRestriction([0,1,2],[0,1]))
print 'Induced map on local sections from 3 edges and common vertex to 3 edges ' + str(fs.localRestriction([0,1,2,6],[0,1,2]))
# Unit test for poset chain methods
#
# 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 pysheaf as ps
import numpy as np
poset = ps.Poset([
ps.Cell(0, True, [ps.Coface(1, 1), ps.Coface(2, 1)]),
ps.Cell(1, True, [ps.Coface(3, 1), ps.Coface(4, 1)]),
ps.Cell(1, True, [ps.Coface(3, 1)]),
ps.Cell(2, True, [ps.Coface(5, 1)]),
ps.Cell(2, True, []),
ps.Cell(3, True, [])
])
print poset.maximalChains(0)
dg = ps.DirectedGraph([(0, 1), (1, 2), (1, 2), (0, 2)])
print dg.maxFlow(4, 6)
# 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)