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example_grid_coarsen.py
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example_grid_coarsen.py
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"""
Plot uniformly sampled random connected subgraphs of n*n grid.
"""
import numpy
from connection import order_vertices, order_edges, make_frontiers, \
make_connectedness_tree, reduce_beads
from bdd import bdd_count_solutions, bdd_generate_random_solution
def make_grid_graph(n):
"""
makes graph (V, E) of n^2 grid
"""
vertices = set()
edges = {}
for i in xrange(n):
for j in xrange(n):
vertices.add((i, j))
for (i, j) in vertices:
for (i2, j2) in ((i, j-1), (i, j+1), (i-1, j), (i+1, j)):
if (i2, j2) in vertices:
edges[(i, j)] = edges.get((i, j), []) + [(i2, j2)]
return (vertices, edges)
def make_bmp_graph(bmp):
assert len(bmp.shape) == 2
n, m = bmp.shape
vertices = set()
edges = {}
for i in xrange(n):
for j in xrange(m):
if bmp[i, j]:
vertices.add((i, j))
for (i, j) in vertices:
for (i2, j2) in ((i, j-1), (i, j+1), (i-1, j), (i+1, j)):
if (i2, j2) in vertices:
edges[(i, j)] = edges.get((i, j), []) + [(i2, j2)]
return (vertices, edges)
def gen_random_solutions(beads, how_many):
bdd_beads = {
's' : len(beads),
'dag' : beads,
}
c = {}
n_solns = bdd_count_solutions(bdd_beads, c)
print 'number of solutions : %d' % n_solns
print 'here are a few random ones:'
for _ in xrange(how_many):
yield bdd_generate_random_solution(
bdd_beads,
c,
rand = numpy.random.rand
)
def make_bdd(vertices, edges, root):
vertex_order = order_vertices(vertices, edges, root)
edge_order = order_edges(vertices, edges, vertex_order)
frontiers = make_frontiers(vertex_order, edge_order)
print 'begin horrific connectedness tree construction procedure'
beads = make_connectedness_tree(
vertex_order,
edge_order,
frontiers,
verbose = True,
)
print '\noutput (unreduced) contains %d beads\n' % len(beads)
beads = reduce_beads(beads)
print '\noutput (reduced) contains %d beads\n' % len(beads)
return beads, edge_order, vertex_order
def make_bmp(n, edge_order, vertex_order, soln):
bmp = numpy.zeros((2 * n + 1, ) * 2, dtype = numpy.int)
def carve_edge(bmp, edge_i):
(u_i, v_i) = edge_order[edge_i]
(u_x, u_y) = vertex_order[u_i]
(v_x, v_y) = vertex_order[v_i]
bmp[2 * u_x + 1, 2 * u_y + 1] = 1
bmp[2 * v_x + 1, 2 * v_y + 1] = 1
if u_x == v_x and u_y == v_y + 1:
bmp[2 * u_x + 1, 2 * v_y + 2] = 1
elif u_x == v_x and u_y + 1 == v_y:
bmp[2 * u_x + 1, 2 * u_y + 2] = 1
elif u_x == v_x + 1 and u_y == v_y:
bmp[2 * v_x + 2, 2 * u_y + 1] = 1
elif u_x + 1 == v_x and u_y == v_y:
bmp[2 * u_x + 2, 2 * u_y + 1] = 1
for i, edge in enumerate(soln):
if edge:
carve_edge(bmp, i)
return bmp
def coarsen_bmp(bmp, coarse_factor):
coarse_shape = tuple(coarse_factor * n for n in bmp.shape)
coarse_bmp = numpy.zeros(coarse_shape)
for i in xrange(coarse_factor):
for j in xrange(coarse_factor):
coarse_bmp[i::coarse_factor, j::coarse_factor] = bmp
return coarse_bmp
def print_bmp(bmp):
for line in bmp:
print ''.join(['#' if x else ' ' for x in line])
def main():
# trying anything above n = 5 may prove a bit foolish
n = 2
print 'making a %d by %d grid' % (n, n)
vertices, edges = make_grid_graph(n)
# using a corner vertex as root works much better
# than a central one in terms of reducing the
# size of the connectedness tree
beads, edge_order, vertex_order = make_bdd(vertices, edges, root = (0, 0))
subplot_width = 2 * n + 1
subplot_height = 2 * n + 1
(soln, ) = list(gen_random_solutions(beads, how_many = 1))
bmp = make_bmp(n, edge_order, vertex_order, soln)
print_bmp(bmp)
coarse_bmp = coarsen_bmp(bmp, coarse_factor = 2)
print_bmp(coarse_bmp)
c_vertices, c_edges = make_bmp_graph(coarse_bmp)
print 'n vertices: %d; n edges: %d' % (len(c_vertices), len(c_edges))
c_root = min(c_vertices)
beads, edge_order, vertex_order = make_bdd(c_vertices, c_edges, c_root)
for soln in gen_random_solutions(beads, how_many = 25):
bmp = make_bmp(coarse_bmp.shape[0], edge_order, vertex_order, soln)
print_bmp(bmp)
if __name__ == '__main__':
main()