コード例 #1
0
ファイル: persistence_test.py プロジェクト: TimPut/pysheaf
# 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))
コード例 #2
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    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=[
コード例 #3
0
ファイル: persistence_test.py プロジェクト: ndcroos/pysheaf
# 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))
コード例 #4
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    # 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),
コード例 #5
0
ファイル: pysheaf_test.py プロジェクト: TimPut/pysheaf
    # 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),