def compute_boundary_operators(self):
"""Compute and return matrix form of boundary operators.
Return list of sparse `SimpleMatrix` instances.
Matrix form of boundary operators operates on column vectors:
the `i`-th differential `D[i]` is `dim C[i-1]` rows (range) by
`dim C[i]` columns (domain).
"""
D = DifferentialComplex()
D.append(NullMatrix, 0, self.module[0].dimension)
for i in xrange(1, self.length):
d = SimpleMatrix(self.module[i-1].dimension,
self.module[i].dimension)
for j in xrange(self.module[i].dimension):
for (k, c) in self.module[i-1].coordinates(
self.differential[i](
self.module[i].base[j])).iteritems():
d.addToEntry(k, j, c)
D.append(d, self.module[i-1].dimension, self.module[i].dimension)
logging.info(" Computed %dx%d matrix D[%d]",
len(self.module[i-1].base),
len(self.module[i].base),
i)
return D
def compute_boundary_operators(self):
#: Matrix form of boundary operators; the `i`-th differential
#: `D[i]` is `dim C[i-1]` rows (range) by `dim C[i]` columns
#: (domain).
m = self.module # micro-optimization
D = DifferentialComplex()
D.append(NullMatrix, 0, len(m[0]))
for i in xrange(1, len(self)):
timing.start("D[%d]" % i)
p = len(m[i - 1]) # == dim C[i-1]
q = len(m[i]) # == dim C[i]
try:
checkpoint = os.path.join(runtime.options.checkpoint_dir,
('M%d,%d-D%d.sms' %
(runtime.g, runtime.n, i)))
except AttributeError:
checkpoint = None
# maybe load `D[i]` from persistent storage
if checkpoint and p > 0 and q > 0 and runtime.options.restart:
d = SimpleMatrix(p, q)
if d.load(checkpoint):
D.append(d, p, q)
logging.info(" Loaded %dx%d matrix D[%d] from file '%s'",
p, q, i, checkpoint)
continue # with next `i`
# compute `D[i]`
d = SimpleMatrix(p, q)
j0 = 0
for pool1 in m[i].iterblocks():
k0 = 0
for pool2 in m[i - 1].iterblocks():
for edgeno in xrange(pool1.graph.num_edges):
if pool1.graph.is_loop(edgeno):
continue # with next `edgeno`
for (j, k, s) in NumberedFatgraphPool.facets(
pool1, edgeno, pool2):
assert k < len(pool2)
assert j < len(pool1)
assert k + k0 < p
assert j + j0 < q
d.addToEntry(k + k0, j + j0, s)
k0 += len(pool2)
# # `pool2` will never be used again, so clear it from the cache.
# # XXX: using implementation detail!
# pool2.graph._cache_isomorphisms.clear()
j0 += len(pool1)
# `pool1` will never be used again, so clear it from the cache.
# XXX: using implementation detail!
pool1.graph._cache_isomorphisms.clear()
timing.stop("D[%d]" % i)
if checkpoint:
d.save(checkpoint)
D.append(d, p, q)
logging.info(" Computed %dx%d matrix D[%d] (elapsed: %.3fs)", p,
q, i, timing.get("D[%d]" % i))
return D
def compute_boundary_operators(self):
#: Matrix form of boundary operators; the `i`-th differential
#: `D[i]` is `dim C[i-1]` rows (range) by `dim C[i]` columns
#: (domain).
m = self.module # micro-optimization
D = DifferentialComplex()
D.append(NullMatrix, 0, len(m[0]))
for i in xrange(1, len(self)):
timing.start("D[%d]" % i)
p = len(m[i-1]) # == dim C[i-1]
q = len(m[i]) # == dim C[i]
try:
checkpoint = os.path.join(runtime.options.checkpoint_dir,
('M%d,%d-D%d.sms' % (runtime.g, runtime.n, i)))
except AttributeError:
checkpoint = None
# maybe load `D[i]` from persistent storage
if checkpoint and p>0 and q>0 and runtime.options.restart:
d = SimpleMatrix(p, q)
if d.load(checkpoint):
D.append(d, p, q)
logging.info(" Loaded %dx%d matrix D[%d] from file '%s'",
p, q, i, checkpoint)
continue # with next `i`
# compute `D[i]`
d = SimpleMatrix(p, q)
j0 = 0
for pool1 in m[i].iterblocks():
k0 = 0
for pool2 in m[i-1].iterblocks():
for edgeno in xrange(pool1.graph.num_edges):
if pool1.graph.is_loop(edgeno):
continue # with next `edgeno`
for (j, k, s) in NumberedFatgraphPool.facets(pool1, edgeno, pool2):
assert k < len(pool2)
assert j < len(pool1)
assert k+k0 < p
assert j+j0 < q
d.addToEntry(k+k0, j+j0, s)
k0 += len(pool2)
# # `pool2` will never be used again, so clear it from the cache.
# # XXX: using implementation detail!
# pool2.graph._cache_isomorphisms.clear()
j0 += len(pool1)
# `pool1` will never be used again, so clear it from the cache.
# XXX: using implementation detail!
pool1.graph._cache_isomorphisms.clear()
timing.stop("D[%d]" % i)
if checkpoint:
d.save(checkpoint)
D.append(d, p, q)
logging.info(" Computed %dx%d matrix D[%d] (elapsed: %.3fs)",
p, q, i, timing.get("D[%d]" % i))
return D
def compute_boundary_operators(self):
"""Compute and return matrix form of boundary operators.
Return list of sparse `SimpleMatrix` instances.
Matrix form of boundary operators operates on column vectors:
the `i`-th differential `D[i]` is `dim C[i-1]` rows (range) by
`dim C[i]` columns (domain).
"""
D = DifferentialComplex()
D.append(NullMatrix, 0, self.module[0].dimension)
for i in xrange(1, self.length):
d = SimpleMatrix(self.module[i - 1].dimension,
self.module[i].dimension)
for j in xrange(self.module[i].dimension):
for (k,
c) in self.module[i - 1].coordinates(self.differential[i](
self.module[i].base[j])).iteritems():
d.addToEntry(k, j, c)
D.append(d, self.module[i - 1].dimension, self.module[i].dimension)
logging.info(" Computed %dx%d matrix D[%d]",
len(self.module[i - 1].base),
len(self.module[i].base), i)
return D
from collections import defaultdict
import logging
import os.path
import numbers
## application-local imports
from fatghol.loadsave import load, save
from fatghol.runtime import runtime
from fatghol.simplematrix import SimpleMatrix, is_null_product
import fatghol.timing as timing
## main
NullMatrix = SimpleMatrix(0, 0)
#@cython.cclass
class VectorSpace(object):
"""Represent the vector space generated by the given `base` vectors.
After construction, you can retrieve the base vectors set and the
dimension from instance attributes `base` and `dimension`.
The `base` elements are assumed to be *linearly independent*, so
the `dimension` of the generated vector space equals the number of
elements in the base set.
"""
def __init__(self, base):
"""Constructor, taking list of base vectors.
return (0, 0)
i0 = 0
while thresholds[i0] < i:
i0 += 1
i0 -= 1
return (i0, i-i0)
def labelfn(D, i):
i0, i1 = matrix_index_to_G(i)
return ("G_{%d,%d}^{(%d)}" % (num_edges-1, i0, i))
p = len(all_graphs[num_edges-1]) if (num_edges-1 in all_graphs) else 0
q = len(all_graphs[num_edges]) if (num_edges in all_graphs) else 0
r = num_edges - min_num_edges + 1
matrix_file = os.path.join(dir, ("M%d,%d-D%d.sms" % (g,n,r)))
if os.path.exists(matrix_file):
d = SimpleMatrix(p, q)
d.load(matrix_file)
k0 = 0
for j, G in enumerate(graphs):
pool = pools[j]
name = ("G_{%d,%d}" % (num_edges, j))
orientable = G.is_oriented()
outfile.start_graph(name, G, pool)
# print automorphisms
Aut = list(G.automorphisms())
if len(Aut) > 1:
outfile.add_automorphisms(Aut)
if pool[0].is_oriented():
# print markings
if n > 1: