marchwicka/signature_function
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Dictionary is replaced by counter everywhere. Tests to each rpelacement.

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This commit is contained in:
Maria Marchwicka 2020-08-05 18:23:49 +02:00
parent 9b68822357
commit 949344193c
1 changed files with 66 additions and 33 deletions
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99
my_signature.sage
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@ -43,7 +43,7 @@ class Config(object):
# is the ratio restriction for values in k_vector taken into account # is the ratio restriction for values in k_vector taken into account
# False flag is usefull to make quick script tests # False flag is usefull to make quick script tests
self.only_slice_candidates = True self.only_slice_candidates = True
# self.only_slice_candidates = False self.only_slice_candidates = False
self.stop_after_firts_large_signature = True self.stop_after_firts_large_signature = True
self.stop_after_firts_large_signature = False self.stop_after_firts_large_signature = False
@ -60,22 +60,24 @@ class SignatureFunction(object):
and value encodes the value of the jump. Remember that we treat and value encodes the value of the jump. Remember that we treat
signature functions as defined on the interval [0,1). signature functions as defined on the interval [0,1).
""" """
def __init__(self, values=[], counter=collections.Counter()): def __init__(self, values=None, counter=None):
# set values of signature jumps # set values of signature jumps
self.signature_jumps = collections.defaultdict(int, counter) if counter is None:
self.cnt_signature_jumps = counter counter = collections.Counter()
if not counter: if values is None:
values = []
for jump_arg, jump in values: for jump_arg, jump in values:
assert 0 <= jump_arg < 1, \ assert 0 <= jump_arg < 1, \
"Signature function is defined on the interval [0, 1)." "Signature function is defined on the interval [0, 1)."
self.signature_jumps[jump_arg] = jump counter[jump_arg] = jump
self.cnt_signature_jumps = collections.Counter(self.signature_jumps) self.cnt_signature_jumps = counter
self.signature_jumps = collections.defaultdict(int, counter)
def sum_of_absolute_values(self): def sum_of_absolute_values(self):
result = sum([abs(i) for i in self.signature_jumps.values()]) result = sum([abs(i) for i in self.signature_jumps.values()])
test = sum([abs(i) for i in self.cnt_signature_jumps.values()]) test = sum([abs(i) for i in self.cnt_signature_jumps.values()])
assert test == result assert test == result
return result return sum([abs(i) for i in self.cnt_signature_jumps.values()])
def is_zero_everywhere(self): def is_zero_everywhere(self):
result = not any(self.signature_jumps.values()) result = not any(self.signature_jumps.values())
@ -98,8 +100,8 @@ class SignatureFunction(object):
t_data.append((jump_arg/2, jump)) t_data.append((jump_arg/2, jump))
t_data.append((1/2 + jump_arg/2, jump)) t_data.append((1/2 + jump_arg/2, jump))
sf = SignatureFunction(t_data) sf = SignatureFunction(values=t_data)
a = SignatureFunction(new_data) a = SignatureFunction(values=new_data)
assert a == sf assert a == sf
return sf return sf
@ -115,24 +117,34 @@ class SignatureFunction(object):
if jump_arg < 1/2: if jump_arg < 1/2:
t_data.append((2 * jump_arg, jump)) t_data.append((2 * jump_arg, jump))
sf = SignatureFunction(t_data) sf = SignatureFunction(values=t_data)
a = SignatureFunction(new_data) a = SignatureFunction(values=new_data)
assert a == sf assert a == sf
return sf return sf
def minus_square_root(self): def minus_square_root(self):
# to read values for t^(1/2) # to read values for t^(1/2)
counter = collections.Counter()
new_data = [] new_data = []
for jump_arg, jump in self.cnt_signature_jumps.items(): for jump_arg, jump in self.cnt_signature_jumps.items():
if jump_arg >= 1/2: if jump_arg >= 1/2:
counter[mod_one(2 * jump_arg)] = jump
new_data.append((mod_one(2 * jump_arg), jump)) new_data.append((mod_one(2 * jump_arg), jump))
t_data = [] t_data = []
for jump_arg, jump in self.signature_jumps.items(): for jump_arg, jump in self.signature_jumps.items():
if jump_arg >= 1/2: if jump_arg >= 1/2:
t_data.append((mod_one(2 * jump_arg), jump)) t_data.append((mod_one(2 * jump_arg), jump))
a = SignatureFunction(t_data) print(t_data)
sf = SignatureFunction(new_data) a = SignatureFunction(values=t_data)
sf = SignatureFunction(values=new_data)
sf2 = SignatureFunction(counter=counter)
print(new_data)
print(counter.items())
assert a == sf assert a == sf
print("repr")
print(repr(sf2))
print(repr(a))
assert a == sf2
return sf return sf
def __lshift__(self, shift): def __lshift__(self, shift):
@ -146,16 +158,20 @@ class SignatureFunction(object):
new_data = [] new_data = []
for jump_arg, jump in self.cnt_signature_jumps.items(): for jump_arg, jump in self.cnt_signature_jumps.items():
new_data.append((mod_one(jump_arg + shift), jump)) new_data.append((mod_one(jump_arg + shift), jump))
sf = SignatureFunction(new_data) sf = SignatureFunction(values=new_data)
a = SignatureFunction(t_data) a = SignatureFunction(values=t_data)
assert a == sf assert a == sf
return sf return sf
def __neg__(self): def __neg__(self):
new_data = [] new_data = []
print("neg")
print("start values sign and cnt")
print(self.signature_jumps.items())
print(self.cnt_signature_jumps.items())
for jump_arg, jump in self.signature_jumps.items(): for jump_arg, jump in self.signature_jumps.items():
new_data.append((jump_arg, -jump)) new_data.append((jump_arg, -jump))
a = SignatureFunction(new_data) a = SignatureFunction(values=new_data)
counter = collections.Counter() counter = collections.Counter()
counter.subtract(self.cnt_signature_jumps) counter.subtract(self.cnt_signature_jumps)
sf = SignatureFunction(counter=counter) sf = SignatureFunction(counter=counter)
@ -188,33 +204,44 @@ class SignatureFunction(object):
return sf return sf
def __str__(self): def __str__(self):
return ''.join([str(jump_arg) + ": " + str(jump) + "\n" result2 = ''.join([str(jump_arg) + ": " + str(jump) + "\n"
for jump_arg, jump in sorted(self.signature_jumps.items())]) for jump_arg, jump in sorted(self.signature_jumps.items())])
result = ''.join([str(jump_arg) + ": " + str(jump) + "\n"
for jump_arg, jump in sorted(self.cnt_signature_jumps.items())])
assert result == result2
return result
def __repr__(self): def __repr__(self):
result = ''.join([str(jump_arg) + ": " + str(jump) + ", " result2 = ''.join([str(jump_arg) + ": " + str(jump) + ", "
for jump_arg, jump in sorted(self.signature_jumps.items())]) for jump_arg, jump in sorted(self.signature_jumps.items())])
result = ''.join([str(jump_arg) + ": " + str(jump) + ", "
for jump_arg, jump in sorted(self.cnt_signature_jumps.items())])
assert result == result2
return result[:-2] + "." return result[:-2] + "."
def __call__(self, arg): def __call__(self, arg):
# Compute the value of the signature function at the point arg. # Compute the value of the signature function at the point arg.
# This requires summing all signature jumps that occur before arg. # This requires summing all signature jumps that occur before arg.
arg = mod_one(arg) arg = mod_one(arg)
cnt = self.cnt_signature_jumps
before_arg = [jump for jump_arg, jump in cnt.items() if jump_arg < arg]
result = 2 * sum(before_arg) + cnt[arg]
# TBD to delete
val = 0 val = 0
for jump_arg, jump in self.signature_jumps.items(): for jump_arg, jump in self.signature_jumps.items():
if jump_arg < arg: if jump_arg < arg:
val += 2 * jump val += 2 * jump
elif jump_arg == arg: elif jump_arg == arg:
val += jump val += jump
result = 0 assert result == val
for jump_arg, jump in self.cnt_signature_jumps.items(): # end of to delete
if jump_arg < arg:
result += 2 * jump
elif jump_arg == arg:
result += jump
assert val == result return result
return val
def main(arg): def main(arg):
@ -243,7 +270,7 @@ def search_for_large_signature_value(knot_formula=None,
limit = max(limit, k_vector_size) limit = max(limit, k_vector_size)
combinations = it.combinations(range(1, limit + 1), k_vector_size) combinations = it.combinations(range(1, limit + 1), k_vector_size)
P = Primes() P = Primes()
good_knots = []
# with open(config.f_results, 'w') as f_results: # with open(config.f_results, 'w') as f_results:
for c in combinations: for c in combinations:
k = [(P.unrank(i) - 1)/2 for i in c] k = [(P.unrank(i) - 1)/2 for i in c]
@ -257,6 +284,8 @@ def search_for_large_signature_value(knot_formula=None,
result = eval_cable_for_large_signature(k_vector=k, result = eval_cable_for_large_signature(k_vector=k,
knot_formula=knot_formula, knot_formula=knot_formula,
print_results=False) print_results=False)
good_knots.append(result)
return good_knots
@ -274,6 +303,9 @@ def eval_cable_for_large_signature(k_vector=None,
if q_vector is None: if q_vector is None:
# TBD docstring # TBD docstring
print("Please give a list of k (k_vector) or q values (q_vector).") print("Please give a list of k (k_vector) or q values (q_vector).")
return None
else:
k_vector = [(i - 1)/2 for i in q_vector]
k = k_vector k = k_vector
knot_sum = eval(knot_formula) knot_sum = eval(knot_formula)
@ -370,7 +402,7 @@ def eval_cable_for_large_signature(k_vector=None,
print("*" * 100 + "\n" * 5) print("*" * 100 + "\n" * 5)
else: else:
print(knot_description + "\t" + str(v_theta) +\ print(knot_description + "\t" + str(v_theta) +\
"\t" + str(sigma_v)) "\t" + str(sigma_v) + "\t" + str(2 * sigma_q_1(2 * ksi * a_4)))
if config.stop_after_firts_large_signature: if config.stop_after_firts_large_signature:
break break
else: else:
@ -384,7 +416,8 @@ def eval_cable_for_large_signature(k_vector=None,
print("*" * 100 + "\n" * 5) print("*" * 100 + "\n" * 5)
else: else:
print(knot_description + "\t" + str(v_theta) +\ print(knot_description + "\t" + str(v_theta) +\
"\t" + str(sigma_v)) "\t" + str(sigma_v) + "\t" + str(2 * sigma_q_1(2 * ksi * a_4)))
large_sigma_for_all_v_comninations = False large_sigma_for_all_v_comninations = False
print("ojojojoj") print("ojojojoj")
@ -634,7 +667,7 @@ def get_blanchfield_for_pattern(k_n, theta):
continue continue
results.append((e * ksi, -1 * sgn(k_n))) results.append((e * ksi, -1 * sgn(k_n)))
results.append((1 - e * ksi, 1 * sgn(k_n))) results.append((1 - e * ksi, 1 * sgn(k_n)))
return SignatureFunction(results) return SignatureFunction(values=results)
def get_signature_summand_as_theta_function(*arg): def get_signature_summand_as_theta_function(*arg):
def get_signture_function(theta): def get_signture_function(theta):
@ -675,7 +708,7 @@ def get_untwisted_signature_function(j):
w = ([((2 * a + 1)/(4 * k + 2), -1 * sgn(j)) for a in range(k)] + w = ([((2 * a + 1)/(4 * k + 2), -1 * sgn(j)) for a in range(k)] +
[((2 * a + 1)/(4 * k + 2), 1 * sgn(j)) [((2 * a + 1)/(4 * k + 2), 1 * sgn(j))
for a in range(k + 1, 2 * k + 1)]) for a in range(k + 1, 2 * k + 1)])
return SignatureFunction(w) return SignatureFunction(values=w)
def get_signature_as_theta_function(*arg, **key_args): def get_signature_as_theta_function(*arg, **key_args):
@ -699,7 +732,7 @@ def get_signature_as_theta_function(*arg, **key_args):
" arguments or no argument at all (" + str(lt) + " given)." " arguments or no argument at all (" + str(lt) + " given)."
raise TypeError(msg) raise TypeError(msg)
sf = SignatureFunction([(0, 0)]) sf = SignatureFunction()
# for each cable in cable sum apply theta # for each cable in cable sum apply theta
for i, knot in enumerate(arg): for i, knot in enumerate(arg):