marchwicka/signature_function
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verbose option added

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Maria Marchwicka 2020-11-19 06:47:52 +01:00
parent 491ecc2b9c
commit bd39af1099
2 changed files with 47484 additions and 581 deletions
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142
cable_signature.sage
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@ -37,8 +37,9 @@ PLOTS_DIR = "plots"
class CableSummand(): class CableSummand():
def __init__(self, knot_as_k_values): def __init__(self, knot_as_k_values, verbose=False):
self.verbose = verbose
self.knot_as_k_values = knot_as_k_values self.knot_as_k_values = knot_as_k_values
self.knot_description = self.get_summand_descrption(knot_as_k_values) self.knot_description = self.get_summand_descrption(knot_as_k_values)
self.signature_as_function_of_theta = \ self.signature_as_function_of_theta = \
@ -198,19 +199,25 @@ class CableSummand():
for theta in range(range_limit): for theta in range(range_limit):
self.plot_summand_for_theta(theta) self.plot_summand_for_theta(theta)
def get_sigma_as_function_of_theta(self): def get_sigma_as_function_of_theta(self, verbose=None):
default_verbose = verbose or self.verbose
last_k = self.knot_as_k_values[-1] last_k = self.knot_as_k_values[-1]
last_q = 2 * abs(last_k) + 1 last_q = 2 * abs(last_k) + 1
ksi = 1/last_q ksi = 1/last_q
def sigma_as_function_of_theta(theta, print_results=False): def sigma_as_function_of_theta(theta, verbose=None, details=None):
verbose = verbose or default_verbose
details = details or verbose
# satellite part (Levine-Tristram signatures) # satellite part (Levine-Tristram signatures)
satellite_part = 0 satellite_part = 0
for i, k in enumerate(self.knot_as_k_values[:-1][::-1]): for i, k in enumerate(self.knot_as_k_values[:-1][::-1]):
# print("layer") # print("layer")
layer_num = i + 1 layer_num = i + 1
sigma_q = self.get_untwisted_signature_function(k) sigma_q = self.get_untwisted_signature_function(k)
if details:
# print(sigma_q(ksi * theta * layer_num)) # print(sigma_q(ksi * theta * layer_num))
# print(sigma_q) # print(sigma_q)
sp = 2 * sigma_q(ksi * theta * layer_num) * sign(k) sp = 2 * sigma_q(ksi * theta * layer_num) * sign(k)
@ -219,6 +226,11 @@ class CableSummand():
pp = (-last_q + 2 * theta - 2 * (theta^2/last_q)) * sign(last_k) pp = (-last_q + 2 * theta - 2 * (theta^2/last_q)) * sign(last_k)
else: else:
pp = 0 pp = 0
if verbose:
print(self.knot_description + ", theta = " + str(theta))
print("pp = " + str(pp), end=', ')
print("satellite_part = " + str(satellite_part))
return pp + satellite_part return pp + satellite_part
return sigma_as_function_of_theta return sigma_as_function_of_theta
@ -229,8 +241,9 @@ class CableSummand():
class CableSum(): class CableSum():
def __init__(self, knot_sum): def __init__(self, knot_sum, verbose=False):
self.verbose = verbose
self.knot_sum_as_k_valus = knot_sum self.knot_sum_as_k_valus = knot_sum
self.knot_description = self.get_knot_descrption(knot_sum) self.knot_description = self.get_knot_descrption(knot_sum)
self.patt_k_list = [abs(i[-1]) for i in knot_sum] self.patt_k_list = [abs(i[-1]) for i in knot_sum]
@ -243,7 +256,7 @@ class CableSum():
raise ValueError(msg) raise ValueError(msg)
self.q_order = LCM_list(self.patt_q_list) self.q_order = LCM_list(self.patt_q_list)
self.knot_summands = [CableSummand(k) for k in knot_sum] self.knot_summands = [CableSummand(k, verbose) for k in knot_sum]
self.signature_as_function_of_theta = \ self.signature_as_function_of_theta = \
self.get_signature_as_function_of_theta() self.get_signature_as_function_of_theta()
self.sigma_as_function_of_theta = \ self.sigma_as_function_of_theta = \
@ -286,20 +299,20 @@ class CableSum():
for i, knot in enumerate(self.knot_summands): for i, knot in enumerate(self.knot_summands):
knot.plot_summand_for_theta(thetas[i], save_path=save_path) knot.plot_summand_for_theta(thetas[i], save_path=save_path)
pp, sp, sf = self.signature_as_function_of_theta(*thetas) # pp, sp, sf = self.signature_as_function_of_theta(*thetas)
title = self.knot_description + ", thetas = " + str(thetas) # title = self.knot_description + ", thetas = " + str(thetas)
if save_path is not None: # if save_path is not None:
file_name = re.sub(r', ', '_', str(thetas)) # file_name = re.sub(r', ', '_', str(thetas))
file_name = re.sub(r'[\[\]]', '', str(file_name)) # file_name = re.sub(r'[\[\]]', '', str(file_name))
file_path = os.path.join(save_path, file_name) # file_path = os.path.join(save_path, file_name)
sig.SignaturePloter.plot_sum_of_two(pp, sp, title=title, # sig.SignaturePloter.plot_sum_of_two(pp, sp, title=title,
save_path=file_path) # save_path=file_path)
#
if save_path is not None: # if save_path is not None:
file_path = os.path.join(save_path, "all_" + file_name) # file_path = os.path.join(save_path, "all_" + file_name)
sf_list = [knot.signature_as_function_of_theta(thetas[i])[2] # sf_list = [knot.signature_as_function_of_theta(thetas[i])[2]
for i, knot in enumerate(self.knot_summands)] # for i, knot in enumerate(self.knot_summands)]
sig.SignaturePloter.plot_many(*sf_list, cols=2) # sig.SignaturePloter.plot_many(*sf_list, cols=2)
# pp, sp, sf = knot.signature_as_function_of_theta(thetas[i]) # pp, sp, sf = knot.signature_as_function_of_theta(thetas[i])
# (pp + sp) = sp.plot # (pp + sp) = sp.plot
# #
@ -390,6 +403,10 @@ class CableSum():
signature_as_function_of_theta_docstring signature_as_function_of_theta_docstring
return signature_as_function_of_theta return signature_as_function_of_theta
def get_sign_ext_for_theta(self, thetas, limit):
_, _, sf = self.signature_as_function_of_theta(*thetas)
return sf.extremum(limit=limit)[1]
def is_metabolizer(self, theta): def is_metabolizer(self, theta):
# Check if square alternating difference # Check if square alternating difference
# divided by last q value is integer. # divided by last q value is integer.
@ -399,7 +416,13 @@ class CableSum():
# old_sum += (el^2 / self.patt_q_list[idx] * (-1)^idx) # old_sum += (el^2 / self.patt_q_list[idx] * (-1)^idx)
return result.is_integer() return result.is_integer()
def is_signature_big_in_ranges(self, ranges_list): def is_function_big_in_ranges(self, ranges_list, invariant=SIGMA,
verbose=None):
verbose = verbose or self.verbose
if invariant == SIGNATURE:
get_invariant = self.get_sign_ext_for_theta
else:
get_invariant = self.sigma_as_function_of_theta
for thetas in it.product(*ranges_list): for thetas in it.product(*ranges_list):
@ -407,31 +430,34 @@ class CableSum():
if not self.is_metabolizer(thetas) or not any(thetas): if not self.is_metabolizer(thetas) or not any(thetas):
continue continue
signature_is_small = True function_is_small = True
# Check if any element generated by thetas vector # Check if any element generated by thetas vector
# has a large signature. # has a large signature.
for shift in range(1, self.q_order): for shift in range(1, self.q_order):
shifted_thetas = [shift * th for th in thetas] shifted_thetas = [shift * th for th in thetas]
pp, sp, sf= self.signature_as_function_of_theta(*shifted_thetas)
limit = 5 + np.count_nonzero(shifted_thetas) limit = 5 + np.count_nonzero(shifted_thetas)
ext = sf.extremum(limit=limit)[1]
extremum = abs(ext) # pp, sp, sf= self.signature_as_function_of_theta(*shifted_thetas)
inv_value = get_invariant(shifted_thetas, limit=limit)
# print(ext)
abs_value = abs(inv_value)
if shift > 1: if shift > 1:
print(shifted_thetas, end=" ") print(shifted_thetas, end=" ")
print(extremum) print(inv_value)
if extremum > limit: elif shift == 1 and verbose:
signature_is_small = False
break
elif shift == 1:
print("*" * 10) print("*" * 10)
print(shifted_thetas, end=" ") print(shifted_thetas, end=" ")
print(ext) print(inv_value)
if signature_is_small:
if abs_value > limit:
function_is_small = False
break
if function_is_small:
print("\n" * 10 + "!" * 1000) print("\n" * 10 + "!" * 1000)
return False return False
return True return True
def is_function_big_for_all_metabolizers(self, function_type=SIGMA): def is_function_big_for_all_metabolizers(self, invariant=SIGMA):
num_of_summands = len(self.knot_sum_as_k_valus) num_of_summands = len(self.knot_sum_as_k_valus)
if num_of_summands % 4: if num_of_summands % 4:
f_name = self.is_signature_big_for_all_metabolizers.__name__ f_name = self.is_signature_big_for_all_metabolizers.__name__
@ -444,61 +470,19 @@ class CableSum():
ranges_list[shift : shift + 3] = \ ranges_list[shift : shift + 3] = \
[range(0, i + 1) for i in self.patt_k_list[shift: shift + 3]] [range(0, i + 1) for i in self.patt_k_list[shift: shift + 3]]
ranges_list[shift + 3] = range(0, 2) ranges_list[shift + 3] = range(0, 2)
if function_type == SIGNATURE: if not self.is_function_big_in_ranges(ranges_list, invariant):
if not self.is_signature_big_in_ranges(ranges_list): return False
return False
else:
if not self.is_sigma_big_in_ranges(ranges_list):
return False
print("\nOK") print("\nOK")
return True return True
def is_sigma_big_in_ranges(self, ranges_list):
for thetas in it.product(*ranges_list):
# Check only non-zero metabolizers.
if not self.is_metabolizer(thetas) or not any(thetas):
continue
signature_is_small = True
# Check if any element generated by thetas vector
# has a large signature.
for shift in range(1, self.q_order):
shifted_thetas = [shift * th for th in thetas]
# pp, sp, sf= self.signature_as_function_of_theta(*shifted_thetas)
limit = 5 + np.count_nonzero(shifted_thetas)
ext = self.sigma_as_function_of_theta(shifted_thetas)
# print(ext)
extremum = abs(ext)
if shift > 1:
print(shifted_thetas, end=" ")
print(extremum)
if extremum > limit:
signature_is_small = False
break
elif shift == 1:
print("*" * 10)
print(shifted_thetas, end=" ")
print(ext)
if signature_is_small:
print("\n" * 10 + "!" * 1000)
return False
return True
class CableTemplate(): class CableTemplate():
def __init__(self, knot_formula, q_vector=None, k_vector=None, def __init__(self, knot_formula, q_vector=None, k_vector=None,
generate_q_vector=True, slice=True): generate_q_vector=True, slice=True, verbose=False):
self.verbose = verbose
self._knot_formula = knot_formula self._knot_formula = knot_formula
# q_i = 2 * k_i + 1 # q_i = 2 * k_i + 1
if k_vector is not None: if k_vector is not None:
@ -537,7 +521,7 @@ class CableTemplate():
raise IndexError(msg) raise IndexError(msg)
self.knot_sum_as_k_valus = eval(self.knot_formula) self.knot_sum_as_k_valus = eval(self.knot_formula)
self._cable = CableSum(self.knot_sum_as_k_valus) self._cable = CableSum(self.knot_sum_as_k_valus, verbose=self.verbose)
self._q_vector = [2 * k_val + 1 for k_val in k] self._q_vector = [2 * k_val + 1 for k_val in k]
@property @property

47923
main.ipynb
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