Initial commit
authorDmitriy Morozov <dmitriy@mrzv.org>
Tue, 12 Jun 2012 22:22:00 -0700
changeset 0 337c84a13184
child 1 a0e045bf9248
Initial commit
01-setup.py
02-simplex.py
03-complex.py
04-alpha-shapes.py
05-rips.py
06-flat-torus.py
07-ls-filtration.py
08-extended-persistence.py
10-circular.py
circular.py
data/annulus.pts
data/cgal/elephant.off
data/circle.pts
data/double-torus.pts
data/torus.pts
data/trefoil.pts
data/two-annuli.pts
read-obj.py
readers.py
tutorial.py
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/01-setup.py	Tue Jun 12 22:22:00 2012 -0700
@@ -0,0 +1,5 @@
+# Setup
+from dionysus import *
+from dionysus.viewer import *
+
+from readers import *               # readers for the demo
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/02-simplex.py	Tue Jun 12 22:22:00 2012 -0700
@@ -0,0 +1,13 @@
+s = Simplex([1,2,3])
+print "Simplex:", s
+print "Dimension:", s.dimension()
+
+print "Vertices:"
+for v in s.vertices:
+    print v
+
+print "Boundary:"
+for sb in s.boundary:
+    print sb
+
+s.data = 5
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/03-complex.py	Tue Jun 12 22:22:00 2012 -0700
@@ -0,0 +1,21 @@
+## Complexes
+# Square
+#square = [[0], [1], [2], [3], [0,1], [0,3], [1,2], [2,3]]
+#square = [Simplex(vertices) for vertices in square]
+
+#square_points = [[0,0], [0,1], [1,1], [1,0]]
+#show_complex(square_points, square)
+
+# 8-sphere
+simplex_9 = Simplex(range(10))          # 9-simplex
+sphere_8 = closure([simplex_9], 8)      # 8-skeleton of the 9_simplex
+print "Number of simplices:", len(sphere_8)
+
+f = Filtration(sphere_8, dim_cmp)
+p = StaticPersistence(f)
+p.pair_simplices()
+
+dgms = init_diagrams(p, f, lambda s: 0)
+for i, dgm in enumerate(dgms):
+    print "Dimension:", i
+    print dgm
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/04-alpha-shapes.py	Tue Jun 12 22:22:00 2012 -0700
@@ -0,0 +1,17 @@
+# Alpha shapes
+points = read_points('data/trefoil.pts')
+f = Filtration()
+fill_alpha_complex(points, f)
+for s in f:
+    print s, s.data
+
+from math import sqrt
+show_complex(points, [s for s in f if sqrt(s.data[0]) < .5])
+show_complex(points, [s for s in f if sqrt(s.data[0]) < .8])
+
+f.sort(dim_data_cmp)
+p = StaticPersistence(f)
+p.pair_simplices()
+
+dgms = init_diagrams(p, f, lambda s: s.data[0])
+show_diagram(dgms)
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/05-rips.py	Tue Jun 12 22:22:00 2012 -0700
@@ -0,0 +1,19 @@
+# Rips
+points = read_points('data/trefoil.pts')
+distances = PairwiseDistances(points)
+rips = Rips(distances)
+
+f = Filtration()
+rips.generate(2, 1.7, f.append)
+print "Number of simplices:", len(f)
+
+show_complex(points, f)
+show_complex(points, [s for s in f if rips.eval(s) < 1.6])
+
+f.sort(rips.cmp)
+
+p = StaticPersistence(f)
+p.pair_simplices()
+
+dgms = init_diagrams(p, f, rips.eval)
+show_diagram(dgms[:2])
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/06-flat-torus.py	Tue Jun 12 22:22:00 2012 -0700
@@ -0,0 +1,33 @@
+# Flat torus
+from    random      import uniform
+from    math        import sqrt
+
+class TorusDistances:
+    def __init__(self, count):
+        self.points = []
+        for i in xrange(count):
+            self.points.append((uniform(0,1), uniform(0,1)))
+
+    def __len__(self):
+        return len(self.points)
+
+    def __call__(self, i, j):
+        x1,y1 = self.points[i]
+        x2,y2 = self.points[j]
+
+        sq_dist = ((x1 - x2) % 1)**2 + ((y1 - y2) % 1)**2
+        return sqrt(sq_dist)
+
+rips = Rips(TorusDistances(200))
+f = Filtration()
+rips.generate(2, .5, f.append)
+print "Number of simplices:", len(f)
+
+f.sort(rips.cmp)
+
+p = StaticPersistence(f)
+p.pair_simplices()
+
+dgm = init_diagrams(p, f, rips.eval)
+show_diagram(dgm[:2])
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/07-ls-filtration.py	Tue Jun 12 22:22:00 2012 -0700
@@ -0,0 +1,49 @@
+# Lower-star filtration
+elephant_points, elephant_complex = read_off('data/cgal/elephant.off')
+show_complex(elephant_points, elephant_complex)
+
+elephant_complex = closure(elephant_complex, 2)
+show_complex(elephant_points, elephant_complex)
+
+def axis(points, axis = 1):
+    def value(v):
+        return points[v][1]
+
+    return value
+
+value = axis(elephant_points, 1)
+
+
+def max_vertex_compare(points):
+    def max_vertex(s):
+        return max(value(v) for v in s.vertices)
+
+    def compare(s1, s2):
+        return cmp(s1.dimension(), s2.dimension()) or cmp(max_vertex(s1), max_vertex(s2))
+
+    return compare
+
+f = Filtration(elephant_complex, max_vertex_compare(elephant_points))
+
+##persistence = StaticPersistence(f)
+persistence = DynamicPersistenceChains(f)
+persistence.pair_simplices()
+
+dgms = init_diagrams(persistence, f, lambda s: max(value(v) for v in s.vertices), lambda i: i)
+
+print "Betti numbers:"
+for i,dgm in enumerate(dgms):
+    print len([p for p in dgm if p[1] == float('inf')])
+
+while True:
+    pt = show_diagram(dgms)
+    if not pt: break
+    print pt
+    i = pt[2]
+    smap = persistence.make_simplex_map(f)
+    chain = [smap[ii] for ii in i.chain]
+    pair_cycle = [smap[ii] for ii in i.pair().cycle]
+    pair_chain = [smap[ii] for ii in i.pair().chain]
+    show_complex(elephant_points, subcomplex = chain)
+    show_complex(elephant_points, subcomplex = pair_cycle + pair_chain)
+    #show_complex(elephant_points, [s for s in f if s.dimension() != 1], subcomplex = cycle)
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/08-extended-persistence.py	Tue Jun 12 22:22:00 2012 -0700
@@ -0,0 +1,44 @@
+# Extended persistence (FIXME)
+cone = [Simplex([-1] + [v for v in s.vertices]) for s in elephant_complex]
+cone.append(Simplex([-1]))
+
+def ep_compare(points):
+    def max_vertex(s):
+        return max(points[v][2] for v in s.vertices if v != -1)
+
+    def min_vertex(s):
+        return max(points[v][2] for v in s.vertices if v != -1)
+
+    def compare(s1, s2):
+        if s1.dimension() != s2.dimension():
+            return cmp(s1.dimension(), s2.dimension())
+
+        if (-1 in s1.vertices) ^ (-1 in s2.vertices):
+            return -1 if -1 in s1.vertices else 1
+        elif -1 in s1.vertices:
+            return cmp(min_vertex(s1), min_vertex(s2))
+        else:
+            return cmp(max_vertex(s1), max_vertex(s2))
+
+    return compare
+
+f = Filtration(elephant_complex + cone)
+f.sort(ep_compare(elephant_points))
+
+persistence = StaticPersistence(f)
+persistence.pair_simplices()
+
+def eval_ep(points):
+    def eval(s):
+        if -1 in s.vertices:
+            return min(elephant_points[v][2] for v in s.vertices)
+        else:
+            return max(elephant_points[v][2] for v in s.vertices)
+
+    return eval
+
+dgms = init_diagrams(persistence, f, eval_ep(elephant_points), lambda i: i)
+
+#show_diagram(dgms)
+print dgms
+print len(dgms)
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/10-circular.py	Tue Jun 12 22:22:00 2012 -0700
@@ -0,0 +1,24 @@
+from    math        import sqrt
+
+f = Filtration()
+fill_alpha_complex(points, f)
+f.sort(dim_data_cmp)
+
+p = StaticCohomologyPersistence(f, prime = 11)
+p.pair_simplices()
+
+dgms = init_diagrams(p,f, lambda s: sqrt(s.data[0]), lambda n: n.cocycle)
+
+pt = show_diagram(dgms)
+
+if pt:
+    #rf = Filtration((s for s in f if sqrt(s.data[0]) <= pt[0]))
+    #rf = Filtration((s for s in f if sqrt(s.data[0]) < pt[1]))
+    rf = Filtration((s for s in f if sqrt(s.data[0]) <= (pt[0] + pt[1])/2))
+    #rf = Filtration((s for s in f if sqrt(s.data[0]) < min(pt1[1], pt2[1], pt3[1])))
+    values = circular.smooth(rf, pt[2])
+    cocycle = [rf[i] for (c,i) in pt[2] if i < len(rf)]
+    #print cocycle
+    show_complex(points, subcomplex = cocycle)
+    show_complex(points, values = values)
+    #show_complex(points, rf, values = values, subcomplex = cocycle)
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/circular.py	Tue Jun 12 22:22:00 2012 -0700
@@ -0,0 +1,50 @@
+from    dionysus    import *
+from    dionysus    import viewer as v
+
+import  sys
+from    math        import sqrt
+
+
+if len(sys.argv) < 2:
+    print "Usage: %s POINTS" % sys.argv[0]
+
+points = read_points(sys.argv[1])
+f = Filtration()
+fill_alpha_complex(points, f)
+#f = Filtration((s for s in f if s.data[0] < 1))
+f.sort(dim_data_cmp)
+
+p = StaticCohomologyPersistence(f, prime = 11)
+p.pair_simplices()
+
+dgms = init_diagrams(p,f, lambda s: sqrt(s.data[0]), lambda n: n.cocycle)
+
+#v.show_diagram(dgms[0])
+#pt = v.show_diagram(dgms[1])
+pt = v.show_diagram(dgms)
+#pt1 = v.show_diagram(dgms[1])
+#pt2 = v.show_diagram(dgms[1])
+#pt3 = v.show_diagram(dgms[1])
+#print pt
+
+if pt:
+#if pt1 and pt2 and pt3:
+    #rf = Filtration((s for s in f if sqrt(s.data[0]) <= pt[0]))
+    #rf = Filtration((s for s in f if sqrt(s.data[0]) < pt[1]))
+    rf = Filtration((s for s in f if sqrt(s.data[0]) <= (pt[0] + pt[1])/2))
+    #rf = Filtration((s for s in f if sqrt(s.data[0]) < min(pt1[1], pt2[1], pt3[1])))
+    values = circular.smooth(rf, pt[2])
+    #values1 = circular.smooth(rf, pt1[2])
+    #values2 = circular.smooth(rf, pt2[2])
+    #values3 = circular.smooth(rf, pt3[2])
+    #print pt[2]
+    cocycle = [rf[i] for (c,i) in pt[2] if i < len(rf)]
+    #print cocycle
+    v.show_complex(points, values = values)
+    v.show_complex(points, subcomplex = cocycle)
+    v.show_complex(points, rf, values = values, subcomplex = cocycle)
+    #vals = [values1[i] + values2[i] + values3[i] for i in xrange(len(values1))]
+    #v.show_complex(points, values = vals)
+    #v.show_complex(points, rf, values)
+    #v.show_complex(points, rf, values, point_size = 6.)
+    #v.show_complex(points, rf, vals, point_size = 6.)
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/data/annulus.pts	Tue Jun 12 22:22:00 2012 -0700
@@ -0,0 +1,1000 @@
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