def f(fself, question = ("Question:", HtmlBox(self._question)),
attempt = ('Answer:',self._answer[1]),
submit = UpdateButton('Submit'),
feedback = HtmlBox('')):
if 'attempt' in fself._changed and attempt != '':
attempts.append(attempt)
if self._start_time == 0:
self._start_time = walltime()
self._number_of_attempts += 1
correct, fself.feedback = self._check_attempt(attempt)
if correct:
cb({'attempts':attempts, 'time':walltime()-self._start_time})
def f(fself,
question=("Question:", HtmlBox(self._question)),
attempt=('Answer:', self._answer[1]),
submit=UpdateButton('Submit'),
feedback=HtmlBox('')):
if 'attempt' in fself._changed and attempt != '':
attempts.append(attempt)
if self._start_time == 0:
self._start_time = walltime()
self._number_of_attempts += 1
correct, fself.feedback = self._check_attempt(attempt)
if correct:
cb({
'attempts': attempts,
'time': walltime() - self._start_time
})
def _check_attempt(self, attempt):
from sage.misc.all import walltime
response = "<div class='well'>"
correct = False
try:
r = self._check(attempt)
if isinstance(r, tuple) and len(r) == 2:
correct = r[0]
comment = r[1]
else:
correct = bool(r)
comment = ''
except TypeError as msg:
response += "<h3 style='color:darkgreen'>Huh? -- %s (attempt=%s)</h3>" % (
msg, attempt)
else:
if correct:
response += "<h1 style='color:blue'>RIGHT!</h1>"
if self._start_time:
response += "<h2 class='lighten'>Time: %.1f seconds</h2>" % (
walltime() - self._start_time, )
if self._number_of_attempts == 1:
response += "<h3 class='lighten'>You got it first try!</h3>"
else:
response += "<h3 class='lighten'>It took you %s attempts.</h3>" % (
self._number_of_attempts, )
else:
response += "<h3 style='color:darkgreen'>Not correct yet...</h3>"
if self._number_of_attempts == 1:
response += "<h4 style='lighten'>(first attempt)</h4>"
else:
response += "<h4 style='lighten'>(%s attempts)</h4>" % self._number_of_attempts
if self._number_of_attempts > len(self._hints):
hint = self._hints[-1]
else:
hint = self._hints[self._number_of_attempts - 1]
if hint:
response += "<span class='lighten'>(HINT: %s)</span>" % (
hint, )
if comment:
response += '<h4>%s</h4>' % comment
response += "</div>"
#interact.feedback = response#HtmlBox(response,label='')
return correct, response
def _check_attempt(self, attempt):
from sage.misc.all import walltime
response = "<div class='well'>"
correct=False
try:
r = self._check(attempt)
if isinstance(r, tuple) and len(r)==2:
correct = r[0]
comment = r[1]
else:
correct = bool(r)
comment = ''
except TypeError as msg:
response += "<h3 style='color:darkgreen'>Huh? -- %s (attempt=%s)</h3>"%(msg, attempt)
else:
if correct:
response += "<h1 style='color:blue'>RIGHT!</h1>"
if self._start_time:
response += "<h2 class='lighten'>Time: %.1f seconds</h2>"%(walltime()-self._start_time,)
if self._number_of_attempts == 1:
response += "<h3 class='lighten'>You got it first try!</h3>"
else:
response += "<h3 class='lighten'>It took you %s attempts.</h3>"%(self._number_of_attempts,)
else:
response += "<h3 style='color:darkgreen'>Not correct yet...</h3>"
if self._number_of_attempts == 1:
response += "<h4 style='lighten'>(first attempt)</h4>"
else:
response += "<h4 style='lighten'>(%s attempts)</h4>"%self._number_of_attempts
if self._number_of_attempts > len(self._hints):
hint = self._hints[-1]
else:
hint = self._hints[self._number_of_attempts-1]
if hint:
response += "<span class='lighten'>(HINT: %s)</span>"%(hint,)
if comment:
response += '<h4>%s</h4>'%comment
response += "</div>"
#interact.feedback = response#HtmlBox(response,label='')
return correct, response
def ask(self, cb):
from sage.misc.all import walltime
self._start_time = walltime()
self._number_of_attempts = 0
attempts = []
@interact(layout=[[('question',12)],[('attempt',12)], [('submit',12)],[('feedback',12)]])
def f(fself, question = ("Question:", HtmlBox(self._question)),
attempt = ('Answer:',self._answer[1]),
submit = UpdateButton('Submit'),
feedback = HtmlBox('')):
if 'attempt' in fself._changed and attempt != '':
attempts.append(attempt)
if self._start_time == 0:
self._start_time = walltime()
self._number_of_attempts += 1
correct, fself.feedback = self._check_attempt(attempt)
if correct:
cb({'attempts':attempts, 'time':walltime()-self._start_time})
def ask(self, cb):
from sage.misc.all import walltime
self._start_time = walltime()
self._number_of_attempts = 0
attempts = []
@interact(layout=[[('question', 12)], [('attempt', 12)],
[('submit', 12)], [('feedback', 12)]])
def f(fself,
question=("Question:", HtmlBox(self._question)),
attempt=('Answer:', self._answer[1]),
submit=UpdateButton('Submit'),
feedback=HtmlBox('')):
if 'attempt' in fself._changed and attempt != '':
attempts.append(attempt)
if self._start_time == 0:
self._start_time = walltime()
self._number_of_attempts += 1
correct, fself.feedback = self._check_attempt(attempt)
if correct:
cb({
'attempts': attempts,
'time': walltime() - self._start_time
})
correct=False
try:
r = self._check(attempt)
if isinstance(r, tuple) and len(r)==2:
correct = r[0]
comment = r[1]
else:
correct = bool(r)
comment = ''
except TypeError, msg:
response += "<h3 style='color:darkgreen'>Huh? -- %s (attempt=%s)</h3>"%(msg, attempt)
else:
if correct:
response += "<h1 style='color:blue'>RIGHT!</h1>"
if self._start_time:
response += "<h2 class='lighten'>Time: %.1f seconds</h2>"%(walltime()-self._start_time,)
if self._number_of_attempts == 1:
response += "<h3 class='lighten'>You got it first try!</h3>"
else:
response += "<h3 class='lighten'>It took you %s attempts.</h3>"%(self._number_of_attempts,)
else:
response += "<h3 style='color:darkgreen'>Not correct yet...</h3>"
if self._number_of_attempts == 1:
response += "<h4 style='lighten'>(first attempt)</h4>"
else:
response += "<h4 style='lighten'>(%s attempts)</h4>"%self._number_of_attempts
if self._number_of_attempts > len(self._hints):
hint = self._hints[-1]
else:
hint = self._hints[self._number_of_attempts-1]
def __call__(self, f, inputs):
"""
Parallel iterator using ``fork()``.
INPUT:
- ``f`` -- a Python function that need not be pickleable or anything else!
- ``inputs`` -- a list of pickleable pairs ``(args, kwds)``, where
``args`` is a tuple and ``kwds`` is a dictionary.
OUTPUT:
EXAMPLES::
sage: F = sage.parallel.use_fork.p_iter_fork(2,3)
sage: sorted(list( F( (lambda x: x^2), [([10],{}), ([20],{})])))
[(([10], {}), 100), (([20], {}), 400)]
sage: sorted(list( F( (lambda x, y: x^2+y), [([10],{'y':1}), ([20],{'y':2})])))
[(([10], {'y': 1}), 101), (([20], {'y': 2}), 402)]
TESTS:
The output of functions decorated with :func:parallel is read
as a pickle by the parent process. We intentionally break the
unpickling and demonstrate that this failure is handled
gracefully (an exception is displayed and an empty list is
returned)::
sage: Polygen = parallel(polygen)
sage: list(Polygen([QQ]))
[(((Rational Field,), {}), x)]
sage: from sage.structure.sage_object import unpickle_override, register_unpickle_override
sage: register_unpickle_override('sage.rings.polynomial.polynomial_rational_flint', 'Polynomial_rational_flint', Integer)
sage: L = list(Polygen([QQ]))
('__init__() takes at most 2 positional arguments (4 given)', <type 'sage.rings.integer.Integer'>, (Univariate Polynomial Ring in x over Rational Field, [0, 1], False, True))
sage: L
[]
Fix the unpickling::
sage: del unpickle_override[('sage.rings.polynomial.polynomial_rational_flint', 'Polynomial_rational_flint')]
sage: list(Polygen([QQ,QQ]))
[(((Rational Field,), {}), x), (((Rational Field,), {}), x)]
"""
n = self.ncpus
v = list(inputs)
import os, sys, signal
from sage.structure.sage_object import load
from sage.misc.all import tmp_dir, walltime
dir = tmp_dir()
timeout = self.timeout
workers = {}
try:
while len(v) > 0 or len(workers) > 0:
# Spawn up to n subprocesses
while len(v) > 0 and len(workers) < n:
# Subprocesses shouldn't inherit unflushed buffers (cf. #11778):
sys.stdout.flush()
sys.stderr.flush()
pid = os.fork()
# The way fork works is that pid returns the
# nonzero pid of the subprocess for the master
# process and returns 0 for the subprocess.
if pid:
# This is the parent master process.
workers[pid] = [v[0], walltime(), '']
del v[0]
else:
# This is the subprocess.
self._subprocess(f, dir, v[0])
if len(workers) > 0:
# Now wait for one subprocess to finish and report the result.
# However, wait at most the time since the oldest process started.
if timeout:
oldest = min([X[1] for X in workers.values()])
alarm(max(timeout - (walltime() - oldest), 0.1))
try:
pid = os.wait()[0]
cancel_alarm()
w = workers.pop(pid)
except AlarmInterrupt:
cancel_alarm()
# Kill workers that are too old
for pid, X in workers.iteritems():
if walltime() - X[1] > timeout:
if self.verbose:
print(
"Killing subprocess %s with input %s which took too long"
% (pid, X[0]))
os.kill(pid, signal.SIGKILL)
X[-1] = ' (timed out)'
except KeyError:
# Some other process exited, not our problem...
pass
else:
# collect data from process that successfully terminated
sobj = os.path.join(dir, '%s.sobj' % pid)
if not os.path.exists(sobj):
X = "NO DATA" + w[-1] # the message field
else:
X = load(sobj, compress=False)
os.unlink(sobj)
out = os.path.join(dir, '%s.out' % pid)
if not os.path.exists(out):
output = "NO OUTPUT"
else:
output = open(out).read()
os.unlink(out)
if output.strip():
print output,
yield (w[0], X)
except Exception as msg:
print msg
finally:
# Clean up all temporary files.
try:
for X in os.listdir(dir):
os.unlink(os.path.join(dir, X))
os.rmdir(dir)
except OSError as msg:
if self.verbose:
print msg
# Send "kill -9" signal to workers that are left.
if len(workers) > 0:
if self.verbose:
print "Killing any remaining workers..."
sys.stdout.flush()
for pid in workers.keys():
try:
os.kill(pid, signal.SIGKILL)
os.waitpid(pid, 0)
except OSError as msg:
if self.verbose:
print msg
r = self._check(attempt)
if isinstance(r, tuple) and len(r) == 2:
correct = r[0]
comment = r[1]
else:
correct = bool(r)
comment = ''
except TypeError, msg:
response += "<h3 style='color:darkgreen'>Huh? -- %s (attempt=%s)</h3>" % (
msg, attempt)
else:
if correct:
response += "<h1 style='color:blue'>RIGHT!</h1>"
if self._start_time:
response += "<h2 class='lighten'>Time: %.1f seconds</h2>" % (
walltime() - self._start_time, )
if self._number_of_attempts == 1:
response += "<h3 class='lighten'>You got it first try!</h3>"
else:
response += "<h3 class='lighten'>It took you %s attempts.</h3>" % (
self._number_of_attempts, )
else:
response += "<h3 style='color:darkgreen'>Not correct yet...</h3>"
if self._number_of_attempts == 1:
response += "<h4 style='lighten'>(first attempt)</h4>"
else:
response += "<h4 style='lighten'>(%s attempts)</h4>" % self._number_of_attempts
if self._number_of_attempts > len(self._hints):
hint = self._hints[-1]
else:
def __call__(self, f, inputs):
"""
Parallel iterator using ``fork()``.
INPUT:
- ``f`` -- a Python function that need not be pickleable or anything else!
- ``inputs`` -- a list of pickleable pairs ``(args, kwds)``, where
``args`` is a tuple and ``kwds`` is a dictionary.
OUTPUT:
EXAMPLES::
sage: F = sage.parallel.use_fork.p_iter_fork(2,3)
sage: sorted(list( F( (lambda x: x^2), [([10],{}), ([20],{})])))
[(([10], {}), 100), (([20], {}), 400)]
sage: sorted(list( F( (lambda x, y: x^2+y), [([10],{'y':1}), ([20],{'y':2})])))
[(([10], {'y': 1}), 101), (([20], {'y': 2}), 402)]
TESTS:
The output of functions decorated with :func:parallel is read
as a pickle by the parent process. We intentionally break the
unpickling and demonstrate that this failure is handled
gracefully (an exception is displayed and an empty list is
returned)::
sage: Polygen = parallel(polygen)
sage: list(Polygen([QQ]))
[(((Rational Field,), {}), x)]
sage: from sage.structure.sage_object import unpickle_override, register_unpickle_override
sage: register_unpickle_override('sage.rings.polynomial.polynomial_rational_flint', 'Polynomial_rational_flint', Integer)
sage: L = list(Polygen([QQ]))
('__init__() takes at most 2 positional arguments (4 given)', <type 'sage.rings.integer.Integer'>, (Univariate Polynomial Ring in x over Rational Field, [0, 1], False, True))
sage: L
[]
Fix the unpickling::
sage: del unpickle_override[('sage.rings.polynomial.polynomial_rational_flint', 'Polynomial_rational_flint')]
sage: list(Polygen([QQ,QQ]))
[(((Rational Field,), {}), x), (((Rational Field,), {}), x)]
"""
n = self.ncpus
v = list(inputs)
import os, sys, signal
from sage.structure.sage_object import load
from sage.misc.all import tmp_dir, walltime
dir = tmp_dir()
timeout = self.timeout
workers = {}
try:
while len(v) > 0 or len(workers) > 0:
# Spawn up to n subprocesses
while len(v) > 0 and len(workers) < n:
# Subprocesses shouldn't inherit unflushed buffers (cf. #11778):
sys.stdout.flush()
sys.stderr.flush()
pid = os.fork()
# The way fork works is that pid returns the
# nonzero pid of the subprocess for the master
# process and returns 0 for the subprocess.
if pid:
# This is the parent master process.
workers[pid] = [v[0], walltime(), '']
del v[0]
else:
# This is the subprocess.
self._subprocess(f, dir, v[0])
if len(workers) > 0:
# Now wait for one subprocess to finish and report the result.
# However, wait at most the time since the oldest process started.
if timeout:
oldest = min([X[1] for X in workers.values()])
alarm(max(timeout - (walltime()-oldest), 0.1))
try:
pid = os.wait()[0]
cancel_alarm()
w = workers.pop(pid)
except AlarmInterrupt:
cancel_alarm()
# Kill workers that are too old
for pid, X in workers.iteritems():
if walltime() - X[1] > timeout:
if self.verbose:
print(
"Killing subprocess %s with input %s which took too long"
% (pid, X[0]) )
os.kill(pid, signal.SIGKILL)
X[-1] = ' (timed out)'
except KeyError:
# Some other process exited, not our problem...
pass
else:
# collect data from process that successfully terminated
sobj = os.path.join(dir, '%s.sobj'%pid)
if not os.path.exists(sobj):
X = "NO DATA" + w[-1] # the message field
else:
X = load(sobj, compress=False)
os.unlink(sobj)
out = os.path.join(dir, '%s.out'%pid)
if not os.path.exists(out):
output = "NO OUTPUT"
else:
output = open(out).read()
os.unlink(out)
if output.strip():
print output,
yield (w[0], X)
except Exception as msg:
print msg
finally:
# Clean up all temporary files.
try:
for X in os.listdir(dir):
os.unlink(os.path.join(dir, X))
os.rmdir(dir)
except OSError as msg:
if self.verbose:
print msg
# Send "kill -9" signal to workers that are left.
if len(workers) > 0:
if self.verbose:
print "Killing any remaining workers..."
sys.stdout.flush()
for pid in workers.keys():
try:
os.kill(pid, signal.SIGKILL)
os.waitpid(pid, 0)
except OSError as msg:
if self.verbose:
print msg
def __init__(self,base,p,discriminant,abtuple = None,level = 1,grouptype = None,seed = None,outfile = None,magma = None,timeout = 0, use_shapiro = True, character = None, nscartan = None, matrix_group = False):
self.seed = seed
self.magma = magma
self._use_shapiro = use_shapiro
self._matrix_group = matrix_group
if seed is not None:
verbose('Setting Magma seed to %s'%seed)
self.magma.eval('SetSeed(%s)'%seed)
self.F = base
if self.F != QQ:
Fideal = self.F.maximal_order().ideal
self.ideal_p = Fideal(p)
self.norm_p = ZZ(p.norm())
self.discriminant = Fideal(discriminant)
self.level = Fideal(level)
else:
self.ideal_p = ZZ(p)
self.norm_p = ZZ(p)
self.discriminant = ZZ(discriminant)
self.level = ZZ(level)
if nscartan is not None:
self.level *= nscartan
self.p = self.norm_p.prime_divisors()[0]
if not self.ideal_p.is_prime():
raise ValueError('p (=%s) must be prime'%self.p)
if self._use_shapiro:
covol = covolume(self.F,self.discriminant,self.level)
else:
covol = covolume(self.F,self.discriminant,self.ideal_p * self.level)
verbose('Estimated Covolume = %s'%covol)
difficulty = covol**2
verbose('Estimated Difficulty = %s'%difficulty)
verbose('Initializing arithmetic group G(pn)...')
t = walltime()
lev = self.ideal_p * self.level
if character is not None:
lev = [lev, character]
self.Gpn = ArithGroup(self.F,self.discriminant,abtuple,lev,grouptype = grouptype,magma = magma, compute_presentation = not self._use_shapiro, timeout = timeout,nscartan=nscartan)
self.Gpn.get_embedding = self.get_embedding
self.Gpn.embed = self.embed
self.Gpn.embed_matrix = self.embed_matrix
verbose('Initializing arithmetic group G(n)...')
lev = self.level
if character is not None:
lev = [lev, character]
self.Gn = ArithGroup(self.F,self.discriminant,abtuple,lev,info_magma = self.Gpn,grouptype = grouptype,magma = magma, compute_presentation = True, timeout = timeout,nscartan=nscartan)
self.Gn.embed_matrix = self.embed_matrix
t = walltime(t)
verbose('Time for calculation T = %s'%t)
verbose('T = %s x difficulty'%RealField(25)(t/difficulty))
self.Gn.get_embedding = self.get_embedding
self.Gn.embed = self.embed
if hasattr(self.Gn.B,'is_division_algebra'):
fwrite('# B = F<i,j,k>, with i^2 = %s and j^2 = %s'%(self.Gn.B.gens()[0]**2,self.Gn.B.gens()[1]**2),outfile)
else:
fwrite('# B = M_2(F)',outfile)
try:
basis_data_1 = list(self.Gn.Obasis)
if not self.use_shapiro():
basis_data_p = list(self.Gpn.Obasis)
except AttributeError:
try:
basis_data_1 = self.Gn.basis_invmat.inverse().columns()
if not self.use_shapiro():
basis_data_p = self.Gpn.basis_invmat.inverse().columns()
except AttributeError:
basis_data_1 = '?'
basis_data_p = '?'
self._prec = -1
self.get_embedding(200)
fwrite('# R with basis %s'%basis_data_1,outfile)
self.Gn.get_Up_reps = self.get_Up_reps
if not self.use_shapiro():
fwrite('# R(p) with basis %s'%basis_data_p,outfile)
self.Gpn.get_Up_reps = self.get_Up_reps
self.Gn.wp = self.wp
self.Gpn.wp = self.wp
verbose('Done initializing arithmetic groups')
verbose('Done initialization of BigArithmeticGroup')
def __init__(self,
base,
p,
discriminant,
abtuple=None,
level=1,
outfile=None,
magma=None,
character=None,
**kwargs):
seed = kwargs.get('seed', None)
self.seed = seed
self.magma = magma
self._use_shapiro = kwargs.get('use_shapiro', True)
hardcode_matrices = kwargs.get('hardcode_matrices', None)
if hardcode_matrices is None:
self._hardcode_matrices = ((abtuple is None and discriminant == 1)
or abtuple == (1, 1))
nscartan = kwargs.get('nscartan', None)
if seed is not None:
verbose('Setting Magma seed to %s' % seed)
self.magma.eval('SetSeed(%s)' % seed)
self.F = base
if self.F != QQ:
Fideal = self.F.maximal_order().ideal
self.ideal_p = Fideal(p)
self.norm_p = ZZ(p.norm())
self.discriminant = Fideal(discriminant)
self.level = Fideal(level)
else:
self.ideal_p = ZZ(p)
self.norm_p = ZZ(p)
self.discriminant = ZZ(discriminant)
self.level = ZZ(level)
if nscartan is not None:
self.level *= nscartan
if self._hardcode_matrices:
assert abtuple is None and self.discriminant == 1 or abtuple == (1,
1)
self.p = self.norm_p.prime_divisors()[0]
if not self.ideal_p.is_prime():
raise ValueError('p (=%s) must be prime' % self.p)
if self._use_shapiro:
covol = covolume(self.F, self.discriminant, self.level)
else:
covol = covolume(self.F, self.discriminant,
self.ideal_p * self.level)
verbose('Estimated Covolume = %s' % covol)
difficulty = covol**2
verbose('Estimated Difficulty = %s' % difficulty)
verbose('Initializing arithmetic group G(pn)...')
t = walltime()
lev = self.ideal_p * self.level
if character is not None:
lev = [lev, character]
self.Gpn = ArithGroup(self.F,
self.discriminant,
abtuple,
lev,
magma=magma,
compute_presentation=not self._use_shapiro,
**kwargs)
self.Gpn.get_embedding = self.get_embedding
self.Gpn.embed = self.embed
verbose('Initializing arithmetic group G(n)...')
lev = self.level
if character is not None:
lev = [lev, character]
self.Gn = ArithGroup(self.F,
self.discriminant,
abtuple,
lev,
info_magma=self.Gpn,
magma=magma,
compute_presentation=True,
**kwargs)
t = walltime(t)
verbose('Time for calculation T = %s' % t)
verbose('T = %s x difficulty' % RealField(25)(t / difficulty))
self.Gn.get_embedding = self.get_embedding
self.Gn.embed = self.embed
if hasattr(self.Gpn.B, 'is_division_algebra'):
fwrite(
'# B = F<i,j,k>, with i^2 = %s and j^2 = %s' %
(self.Gpn.B.gens()[0]**2, self.Gpn.B.gens()[1]**2), outfile)
else:
fwrite('# B = M_2(F)', outfile)
try:
basis_data_1 = list(self.Gn.Obasis)
if not self.use_shapiro():
basis_data_p = list(self.Gpn.Obasis)
except AttributeError:
try:
basis_data_1 = self.Gn._get_basis_invmat().inverse().columns()
if not self.use_shapiro():
basis_data_p = self.Gpn._get_basis_invmat().inverse(
).columns()
except AttributeError:
basis_data_1 = '?'
basis_data_p = '?'
self._prec = -1
self.get_embedding(200)
fwrite('# R with basis %s' % basis_data_1, outfile)
self.Gn.get_Up_reps = self.get_Up_reps
if not self.use_shapiro():
fwrite('# R(p) with basis %s' % basis_data_p, outfile)
self.Gpn.get_Up_reps = self.get_Up_reps
self.Gn.wp = self.wp
self.Gpn.wp = self.wp
self.Gn._F_to_local = self._F_to_local
self.Gpn._F_to_local = self._F_to_local
verbose('Done initializing arithmetic groups')
verbose('Done initialization of BigArithmeticGroup')
