def cuthill_mckee(graph):
"""Return a Cuthill-McKee ordering for the given graph.
See (for example)
Y. Saad, Iterative Methods for Sparse Linear System,
2nd edition, p. 76.
*graph* is given as an adjacency mapping, i.e. each node is
mapped to a list of its neighbors.
"""
from pytools import argmin
# this list is called "old_numbers" because it maps a
# "new number to its "old number"
old_numbers = []
visited_nodes = set()
levelset = []
all_nodes = set(graph.keys())
def levelset_cmp(node_a, node_b):
return cmp(len(graph[node_a]), len(graph[node_b]))
while len(old_numbers) < len(graph):
if not levelset:
unvisited = list(set(graph.keys()) - visited_nodes)
if not unvisited:
break
start_node = unvisited[argmin(
len(graph[node]) for node in unvisited)]
visited_nodes.add(start_node)
old_numbers.append(start_node)
levelset = [start_node]
next_levelset = set()
levelset.sort(levelset_cmp)
for node in levelset:
for neighbor in graph[node]:
if neighbor in visited_nodes:
continue
visited_nodes.add(neighbor)
next_levelset.add(neighbor)
old_numbers.append(neighbor)
levelset = list(next_levelset)
return old_numbers
def cuthill_mckee(graph):
"""Return a Cuthill-McKee ordering for the given graph.
See (for example)
Y. Saad, Iterative Methods for Sparse Linear System,
2nd edition, p. 76.
*graph* is given as an adjacency mapping, i.e. each node is
mapped to a list of its neighbors.
"""
from pytools import argmin
# this list is called "old_numbers" because it maps a
# "new number to its "old number"
old_numbers = []
visited_nodes = set()
levelset = []
all_nodes = set(graph.keys())
def levelset_cmp(node_a, node_b):
return cmp(len(graph[node_a]), len(graph[node_b]))
while len(old_numbers) < len(graph):
if not levelset:
unvisited = list(set(graph.keys()) - visited_nodes)
if not unvisited:
break
start_node = unvisited[
argmin(len(graph[node]) for node in unvisited)]
visited_nodes.add(start_node)
old_numbers.append(start_node)
levelset = [start_node]
next_levelset = set()
levelset.sort(levelset_cmp)
for node in levelset:
for neighbor in graph[node]:
if neighbor in visited_nodes:
continue
visited_nodes.add(neighbor)
next_levelset.add(neighbor)
old_numbers.append(neighbor)
levelset = list(next_levelset)
return old_numbers
def metropolis_hastings_process():
"""
Samples a bunch of algorithms (with count specified in Config), saves their
scores, and returns the best of the bunch.
"""
trainingdata = Config.LoadTrainingPairs()
print(len(trainingdata))
samples, distances = metrohast(Config.mh_samplecount, trainingdata)
best = argmin(distances)
print("Index of best player is ", best)
print("Distances under distance metric:")
print(distances)
print("Best distance: ", distances[best])
print("Best rule (along with script):")
print(samples[best].to_script())
print("------------------------------------------------------------------")
Config.SaveDistances(distances)
Config.SaveSamples([sample.to_script() for sample in samples])
return samples[best].player
def parse_superfish_format(filename, max_point_dist=0.1):
import re
def chop_comment(line):
com_start = line.find(";")
if com_start != -1:
return line[:com_start]
else:
return line
lines = [
chop_comment(line.strip().lower())
for line in file(filename, "r").readlines()
]
lines = [line for line in lines if not line.startswith("!")]
lines = [line for line in lines if line]
lines = [line for line in lines if line.startswith("&po")]
# parse the file
line_re = re.compile(r"^\&po\s+(.*)\s*\&$")
key_val_re = re.compile(r"^([0-9a-zA-Z]+)\s*\=\s*([-+0-9.a-zA-Z]+)")
proplines = []
for line in lines:
line_match = line_re.match(line)
assert line_match
line = line_match.group(1)
properties = {}
pos = 0
while pos < len(line):
if line[pos] in [" ", ","]:
pos += 1
continue
datum_match = key_val_re.match(line[pos:])
assert datum_match
properties[datum_match.group(1)] = float(datum_match.group(2))
pos += datum_match.end()
proplines.append(properties)
#for p in proplines:
#print p
# concoct x-y-points
from math import atan2, sin, cos, pi, ceil
from pytools import argmin
def add_point(pt):
points.append((pt[1], pt[0]))
points = []
for p in proplines:
shape_type = 1
if "nt" in p:
shape_type = p["nt"]
if shape_type == 1:
points.append(numpy.array((p["x"], p["y"])))
elif shape_type == 2:
# draw arc
last_point = points[-1]
if "x0" in p:
center = numpy.array((p["x0"], p["y0"]))
else:
center = numpy.zeros((2, ))
if "r" in p or "radius" in p:
if "r" in p:
r = p["r"]
assert "radius" not in p
else:
r = p["radius"]
assert "r" not in p
theta = pi / 180. * p["theta"]
tangent = numpy.array((cos(theta), sin(theta)))
upward_normal = numpy.array((-sin(theta), cos(theta)))
#print 180*theta/pi, last_point, center, tangent, upward_normal, last_point-center
if numpy.dot(last_point - center, upward_normal) < 0:
# draw ccw (positive) arc / upward
phi_start = 3 * pi / 2 + theta
phi_end = phi_start + pi / 2
else:
# draw cw (negative) arc / downward
phi_start = pi / 2 + theta
phi_end = phi_start - pi / 2
elif "x" in p:
start_pt = last_point - center
end_pt = numpy.array((p["x"], p["y"]))
r = la.norm(end_pt)
r2 = la.norm_2(start_pt)
assert abs(r - r2) / r < 1e-2
phi_start = atan2(start_pt[1], start_pt[0])
raw_phi_end = atan2(end_pt[1], end_pt[0])
phi_end_choices = [
raw_phi_end, raw_phi_end - 2 * pi, raw_phi_end + 2 * pi
]
phi_end = phi_end_choices[argmin(
abs(phi_end - phi_start) for phi_end in phi_end_choices)]
else:
raise ValueError, "arcs (nt=2) must have either r/radius or x/y specified"
steps = int(ceil((abs(phi_end - phi_start)) * r / max_point_dist))
dphi = (phi_end - phi_start) / steps
phi = phi_start + dphi
for i in range(steps):
points.append(center + r * numpy.array((cos(phi), sin(phi))))
phi += dphi
else:
raise ValueError, "unhandled shape type: nt=%s" % shape_type
# assert that last point coincides with first
assert ((points[0][0] - points[-1][0])**2 +
(points[0][1] - points[-1][1])**2) < 1e-10
# and kill it
points.pop()
# now find the on-axis line, if any, and shift it so straddles the array boundary
assert len(points) > 1
for i, (z, r) in enumerate(points):
next_i = (i + 1) % len(points)
next_r = points[next_i][1]
if r == 0 and next_r == 0:
if i < len(points):
# if the on-axis line is already the last line in the polygon,
# then that's fine--no need to change. Otherwise, shift so that
# this becomes the case.
from pytools import shift
points = shift(points, len(points) - 1 - i)
break
# assert start and end r are 0
assert points[0][1] == 0
assert points[-1][1] == 0
outf = file("gun-lines.dat", "w")
for p in points:
outf.write("%f\t%f\n" % (p[0], p[1]))
outf.close()
# turn (x,y) into (r,z)
return [(p[1], p[0]) for p in points]
def optimize_shape_bandwidth(method, state, analytic_rho, exponent):
discr = method.discretization
rec = method.depositor
adv_radius = method.mesh_data.advisable_particle_radius()
radii = [adv_radius * 2**i for i in numpy.linspace(-4, 2, 50)]
def set_radius(r):
method.depositor.set_shape_function(
state,
method.get_shape_function_class()(
r,
method.mesh_data.dimensions,
exponent,
))
tried_radii = []
l1_errors = []
debug = "shape_bw" in method.debug
visualize = set(["shape_bw", "vis_files"]) <= method.debug
if visualize:
from hedge.visualization import SiloVisualizer
vis = SiloVisualizer(discr)
import sys
if debug:
sys.stdout.write("optimizing shape bw (%d attempts): " % len(radii))
for step, radius in enumerate(radii):
if debug:
sys.stdout.write("%d." % step)
sys.stdout.flush()
try:
try:
method.set_ignore_core_warnings(True)
set_radius(radius)
except RuntimeError, re:
if "particle mass is zero" in str(re):
continue
else:
raise
finally:
method.set_ignore_core_warnings(False)
state.derived_quantity_cache.clear()
try:
try:
method.set_ignore_core_warnings(True)
rec_rho = method.deposit_rho(state)
except RuntimeError, re:
if "particle mass is zero" in str(re):
continue
else:
raise
finally:
method.set_ignore_core_warnings(False)
tried_radii.append(radius)
l1_errors.append(discr.integral(numpy.abs(rec_rho - analytic_rho)))
if visualize:
visf = vis.make_file("bwopt-%04d" % step)
method.add_to_vis(vis, visf, state, time=radius, step=step)
vis.add_data(
visf,
[
("rho", rec_rho),
#("j", method.deposit_j(state)),
("rho_analytic", analytic_rho),
],
expressions=[("rho_diff", "rho-rho_analytic")],
time=radius,
step=step)
try:
rec.visualize_grid_quantities
except AttributeError:
pass
else:
rec.visualize_grid_quantities(visf, [
("rho_grid", rec.deposit_grid_rho(state)),
("j_grid",
rec.deposit_grid_j(state, method.velocities(state))),
("rho_resid",
rec.remap_residual(rec.deposit_grid_rho(state))),
])
visf.close()
if debug:
sys.stdout.write("\n")
sys.stdout.flush()
if visualize:
vis.close()
from pytools import argmin
min_idx = argmin(l1_errors)
min_rad = tried_radii[min_idx]
min_l1_error = l1_errors[min_idx]
rel_l1_error = abs(min_l1_error / discr.integral(analytic_rho))
if rel_l1_error > 0.1:
from warnings import warn
warn("Charge density is very poorly resolved (rel L1 error=%g)" %
rel_l1_error)
def is_local_minimum(list, i):
if i == 0:
return False
elif i == len(list) - 1:
return False
else:
return list[i] < list[i - 1] and list[i] < list[i + 1]
local_minima = [
idx for idx in range(len(tried_radii))
if is_local_minimum(l1_errors, idx)
]
chosen_idx = max(local_minima)
chosen_rad = tried_radii[chosen_idx]
if "shape_bw" in method.debug:
chosen_l1_error = l1_errors[chosen_idx]
print "radius: guessed optimum=%g, found optimum=%g, chosen=%g" % (
adv_radius, min_rad, chosen_rad)
print "radius: optimum l1 error=%g, chosen l1 error=%g" % (
min_l1_error, chosen_l1_error)
set_radius(chosen_rad)
state.derived_quantity_cache.clear()
if set(["interactive", "shape_bw"]) < method.debug:
from pylab import semilogx, show
semilogx(tried_radii, l1_errors)
show()
def parse_superfish_format(filename, max_point_dist=0.1):
import re
def chop_comment(line):
com_start = line.find(";")
if com_start != -1:
return line[:com_start]
else:
return line
lines = [chop_comment(line.strip().lower()) for line in file(filename, "r").readlines()]
lines = [line for line in lines if not line.startswith("!")]
lines = [line for line in lines if line]
lines = [line for line in lines if line.startswith("&po")]
# parse the file
line_re = re.compile(r"^\&po\s+(.*)\s*\&$")
key_val_re = re.compile(r"^([0-9a-zA-Z]+)\s*\=\s*([-+0-9.a-zA-Z]+)")
proplines = []
for line in lines:
line_match = line_re.match(line)
assert line_match
line = line_match.group(1)
properties = {}
pos = 0
while pos < len(line):
if line[pos] in [" ", ","]:
pos += 1
continue
datum_match = key_val_re.match(line[pos:])
assert datum_match
properties[datum_match.group(1)] = float(datum_match.group(2))
pos += datum_match.end()
proplines.append(properties)
#for p in proplines:
#print p
# concoct x-y-points
from math import atan2, sin, cos, pi, ceil
from pytools import argmin
def add_point(pt):
points.append((pt[1], pt[0]))
points = []
for p in proplines:
shape_type = 1
if "nt" in p:
shape_type = p["nt"]
if shape_type == 1:
points.append(numpy.array((p["x"], p["y"])))
elif shape_type == 2:
# draw arc
last_point = points[-1]
if "x0" in p:
center = numpy.array((p["x0"], p["y0"]))
else:
center = numpy.zeros((2,))
if "r" in p or "radius" in p:
if "r" in p:
r = p["r"]
assert "radius" not in p
else:
r = p["radius"]
assert "r" not in p
theta = pi/180.*p["theta"]
tangent = numpy.array((cos(theta), sin(theta)))
upward_normal = numpy.array((-sin(theta), cos(theta)))
#print 180*theta/pi, last_point, center, tangent, upward_normal, last_point-center
if numpy.dot(last_point - center, upward_normal) < 0:
# draw ccw (positive) arc / upward
phi_start = 3*pi/2 + theta
phi_end = phi_start + pi/2
else:
# draw cw (negative) arc / downward
phi_start = pi/2 + theta
phi_end = phi_start - pi/2
elif "x" in p:
start_pt = last_point - center
end_pt = numpy.array((p["x"], p["y"]))
r = la.norm(end_pt)
r2 = la.norm_2(start_pt)
assert abs(r-r2)/r < 1e-2
phi_start = atan2(start_pt[1], start_pt[0])
raw_phi_end = atan2(end_pt[1], end_pt[0])
phi_end_choices = [
raw_phi_end,
raw_phi_end-2*pi,
raw_phi_end+2*pi]
phi_end = phi_end_choices[argmin(
abs(phi_end-phi_start) for phi_end in phi_end_choices)]
else:
raise ValueError, "arcs (nt=2) must have either r/radius or x/y specified"
steps = int(ceil((abs(phi_end-phi_start))*r/max_point_dist))
dphi = (phi_end-phi_start) / steps
phi = phi_start+dphi
for i in range(steps):
points.append(center + r*numpy.array((cos(phi), sin(phi))))
phi += dphi
else:
raise ValueError, "unhandled shape type: nt=%s" % shape_type
# assert that last point coincides with first
assert ((points[0][0]-points[-1][0])**2 + (points[0][1]-points[-1][1])**2) < 1e-10
# and kill it
points.pop()
# now find the on-axis line, if any, and shift it so straddles the array boundary
assert len(points) > 1
for i, (z, r) in enumerate(points):
next_i = (i+1)%len(points)
next_r = points[next_i][1]
if r == 0 and next_r == 0:
if i < len(points):
# if the on-axis line is already the last line in the polygon,
# then that's fine--no need to change. Otherwise, shift so that
# this becomes the case.
from pytools import shift
points = shift(points, len(points)-1-i)
break
# assert start and end r are 0
assert points[0][1] == 0
assert points[-1][1] == 0
outf = file("gun-lines.dat", "w")
for p in points:
outf.write("%f\t%f\n" % (p[0], p[1]))
outf.close()
# turn (x,y) into (r,z)
return [(p[1], p[0]) for p in points]
def optimize_shape_bandwidth(method, state, analytic_rho, exponent):
discr = method.discretization
rec = method.depositor
adv_radius = method.mesh_data.advisable_particle_radius()
radii = [adv_radius*2**i
for i in numpy.linspace(-4, 2, 50)]
def set_radius(r):
method.depositor.set_shape_function(
state,
method.get_shape_function_class()
(r, method.mesh_data.dimensions, exponent,))
tried_radii = []
l1_errors = []
debug = "shape_bw" in method.debug
visualize = set(["shape_bw", "vis_files"]) <= method.debug
if visualize:
from hedge.visualization import SiloVisualizer
vis = SiloVisualizer(discr)
import sys
if debug:
sys.stdout.write("optimizing shape bw (%d attempts): " % len(radii))
for step, radius in enumerate(radii):
if debug:
sys.stdout.write("%d." % step)
sys.stdout.flush()
try:
try:
method.set_ignore_core_warnings(True)
set_radius(radius)
except RuntimeError, re:
if "particle mass is zero" in str(re):
continue
else:
raise
finally:
method.set_ignore_core_warnings(False)
state.derived_quantity_cache.clear()
try:
try:
method.set_ignore_core_warnings(True)
rec_rho = method.deposit_rho(state)
except RuntimeError, re:
if "particle mass is zero" in str(re):
continue
else:
raise
finally:
method.set_ignore_core_warnings(False)
tried_radii.append(radius)
l1_errors.append(discr.integral(numpy.abs(rec_rho-analytic_rho)))
if visualize:
visf = vis.make_file("bwopt-%04d" % step)
method.add_to_vis(vis, visf, state, time=radius, step=step)
vis.add_data(visf, [
("rho", rec_rho),
#("j", method.deposit_j(state)),
("rho_analytic", analytic_rho),
],
expressions=[("rho_diff", "rho-rho_analytic")],
time=radius, step=step)
try:
rec.visualize_grid_quantities
except AttributeError:
pass
else:
rec.visualize_grid_quantities(visf, [
("rho_grid", rec.deposit_grid_rho(state)),
("j_grid", rec.deposit_grid_j(state, method.velocities(state))),
("rho_resid", rec.remap_residual(rec.deposit_grid_rho(state))),
])
visf.close()
if debug:
sys.stdout.write("\n")
sys.stdout.flush()
if visualize:
vis.close()
from pytools import argmin
min_idx = argmin(l1_errors)
min_rad = tried_radii[min_idx]
min_l1_error = l1_errors[min_idx]
rel_l1_error = abs(min_l1_error / discr.integral(analytic_rho))
if rel_l1_error > 0.1:
from warnings import warn
warn("Charge density is very poorly resolved (rel L1 error=%g)" % rel_l1_error)
def is_local_minimum(list, i):
if i == 0:
return False
elif i == len(list)-1:
return False
else:
return list[i] < list[i-1] and list[i] < list[i+1]
local_minima = [idx for idx in range(len(tried_radii))
if is_local_minimum(l1_errors, idx)]
chosen_idx = max(local_minima)
chosen_rad = tried_radii[chosen_idx]
if "shape_bw" in method.debug:
chosen_l1_error = l1_errors[chosen_idx]
print "radius: guessed optimum=%g, found optimum=%g, chosen=%g" % (
adv_radius, min_rad, chosen_rad)
print "radius: optimum l1 error=%g, chosen l1 error=%g" % (
min_l1_error, chosen_l1_error)
set_radius(chosen_rad)
state.derived_quantity_cache.clear()
if set(["interactive", "shape_bw"]) < method.debug:
from pylab import semilogx, show
semilogx(tried_radii, l1_errors)
show()