Refact. Add SignatureFunction.plot_title var. Plot many sf at once - function plot_many
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@ -1,13 +1,15 @@
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#!/usr/bin/python
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#!/usr/bin/env sage -python
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import numpy as np
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import itertools as it
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import matplotlib.pyplot as plt
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import warnings
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import re
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import inspect
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from typing import Iterable
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from collections import Counter
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from sage.arith.functions import LCM_list
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import warnings
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import re
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import matplotlib.pyplot as plt
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import inspect
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# 9.11 (9.8)
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# 9.15 (9.9)
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@ -22,7 +24,6 @@ class CableSummand():
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self.signature_as_function_of_theta = \
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self.get_summand_signature_as_theta_function()
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@staticmethod
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def get_summand_descrption(knot_as_k_values):
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description = ""
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@ -33,7 +34,6 @@ class CableSummand():
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description += "2, " + str(2 * abs(k) + 1) + "; "
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return description[:-2] + ")"
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@classmethod
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def get_blanchfield_for_pattern(cls, k_n, theta=0):
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@ -45,17 +45,13 @@ class CableSummand():
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k = abs(k_n)
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assert theta <= k, msg
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results = []
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results = []
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ksi = 1/(2 * k + 1)
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counter = Counter()
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# print("lambda_odd, i.e. (theta + e) % 2 != 0")
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for e in range(1, k + 1):
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if (theta + e) % 2 != 0:
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counter[e * ksi] = 1 * sgn(k_n)
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counter[1 - e * ksi] = -1 * sgn(k_n)
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results.append((e * ksi, 1 * sgn(k_n)))
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results.append((1 - e * ksi, -1 * sgn(k_n)))
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@ -139,7 +135,18 @@ class CableSummand():
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pattern_part = self.get_blanchfield_for_pattern(patt_k, theta)
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satellite_part = self.get_satellite_part(*knot_as_k_values,
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theta=theta)
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return pattern_part, satellite_part
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sf = satellite_part + pattern_part
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satellite_part.plot_title = self.knot_description + \
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", theta = " + str(theta) + \
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", satellite part."
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pattern_part.plot_title = self.knot_description + \
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", theta = " + str(theta) + \
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", pattern part."
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sf.plot_title = self.knot_description +\
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", theta = " + str(theta)
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return pattern_part, satellite_part, sf
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get_summand_signture_function.__doc__ = \
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get_summand_signture_function_docsting
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@ -156,7 +163,7 @@ class CableSummand():
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return name
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def plot_summand_for_theta(self, theta, save_path=None):
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pp, sp = self.signature_as_function_of_theta(theta)
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pp, sp, sf = self.signature_as_function_of_theta(theta)
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title = self.knot_description + ", theta = " + str(theta)
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if save_path is not None:
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file_name = self.get_file_name_for_summand_plot(theta)
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@ -221,7 +228,7 @@ class CableSum():
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for i, knot in enumerate(self.knot_summands):
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knot.plot_summand_for_theta(thetas[i], save_path=save_path)
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pp, sp = self.signature_as_function_of_theta(*thetas)
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pp, sp, sf = self.signature_as_function_of_theta(*thetas)
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title = self.knot_description + ", thetas = " + str(thetas)
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if save_path is not None:
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file_name = re.sub(r', ', '_', str(thetas))
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@ -232,9 +239,18 @@ class CableSum():
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if save_path is not None:
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file_path = os.path.join(save_path, "all_" + file_name)
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sf_list = [knot.signature_as_function_of_theta(thetas[i])
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sf_list = [knot.signature_as_function_of_theta(thetas[i])[2]
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for i, knot in enumerate(self.knot_summands)]
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# pp, sp = knot.signature_as_function_of_theta(thetas[i])
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sf_list.append(sf_list[-1])
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sf_list.append(sf_list[-1])
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sf_list.append(sf_list[-1])
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sf_list.append(sf_list[-1])
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sf_list.append(sf_list[-1])
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sf_list.append(sf_list[-1])
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# sf_list.append(sf_list[-1])
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SignatureFunction.plot_many(*sf_list)
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# pp, sp, sf = knot.signature_as_function_of_theta(thetas[i])
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# (pp + sp) = sp.plot
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#
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# pp.plot_sum_with_other(sp, title=title, save_path=file_path)
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@ -249,7 +265,6 @@ class CableSum():
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for knot in self.knot_summands:
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knot.plot_summand()
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def parse_thetas(self, *thetas):
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summands_num = len(self.knot_sum_as_k_valus)
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if not thetas:
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@ -302,7 +317,7 @@ class CableSum():
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# for each cable knot (summand) in cable sum apply theta
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for i, knot in enumerate(self.knot_summands):
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sfth = knot.signature_as_function_of_theta
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pp, sp = sfth(thetas[i])
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pp, sp, _ = sfth(thetas[i])
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pattern_part += pp
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satellite_part += sp
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sf = pattern_part + satellite_part
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@ -312,7 +327,7 @@ class CableSum():
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print(str(thetas))
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print(sf)
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assert sf.total_sign_jump() == 0
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return pattern_part, satellite_part
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return pattern_part, satellite_part, sf
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signature_as_function_of_theta.__doc__ =\
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signature_as_function_of_theta_docstring
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@ -340,8 +355,7 @@ class CableSum():
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# has a large signature.
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for shift in range(1, self.q_order):
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shifted_thetas = [shift * th for th in thetas]
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pp, sp = self.signature_as_function_of_theta(*shifted_thetas)
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sf = pp + sp
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pp, sp, sf= self.signature_as_function_of_theta(*shifted_thetas)
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limit = 5 + np.count_nonzero(shifted_thetas)
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extremum = abs(sf.extremum(limit=limit))
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if shift > 1:
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@ -378,6 +392,7 @@ class CableSum():
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print("\nOK")
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return True
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class CableTemplate():
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def __init__(self, knot_formula, q_vector=None, k_vector=None,
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@ -421,7 +436,6 @@ class CableTemplate():
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self.knot_sum_as_k_valus = eval(self.knot_formula)
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self._cable = CableSum(self.knot_sum_as_k_valus)
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self._q_vector = [2 * k_val + 1 for k_val in k]
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@property
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@ -467,7 +481,6 @@ class CableTemplate():
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other.knot_formula)
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return self + CableTemplate(o_formula)
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def __add__(self, other):
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knot_formula = self.knot_formula[:-1] + ",\n" + other.knot_formula[1:]
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return CableTemplate(knot_formula)
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26
main.sage
26
main.sage
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#!/usr/bin/python
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#!/usr/bin/env sage -python
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# TBD: read about Factory Method, variable in docstring, sage documentation,
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# print calc. to output file
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@ -15,13 +15,22 @@ import numpy as np
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attach("signature.sage")
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attach("cable_signature.sage")
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# if not os.path.isfile('signature.py'):
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# os.system('sage --preparse cable_signature.sage')
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# os.system('mv cable_signature.sage.py cable_signature.py')
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# from signature import SignatureFunction
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class Config(object):
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def __init__(self):
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self.f_results = os.path.join(os.getcwd(), "results.out")
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self.verbose = True
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# self.verbose = False
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# knot_formula is a schema for knots which signature function
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# will be calculated
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self.knot_formula = "[[k[0], k[1], k[3]], " + \
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@ -42,10 +51,7 @@ class Config(object):
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# [-k[0], -k[3], -k[4]], [-k[1], -k[2]]]"
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# self.knot_formula = "[[k[0], k[1], k[2]], [k[3]],\
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# [-k[0], -k[1], -k[3]], [-k[2]]]"
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self.limit = 3
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self.verbose = True
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# self.verbose = False
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@ -68,7 +74,7 @@ def main(arg=None):
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# knot_formula = config.knot_formula
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# q_vector = (3, 5, 7, 13)
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# q_vector = (3, 5, 7, 11)
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return
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formula_1 = "[[k[0], k[5], k[3]], " + \
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"[-k[1], -k[3]], " + \
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"[k[2], k[3]], " + \
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@ -85,11 +91,11 @@ def main(arg=None):
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cable_template_1 = CableTemplate(knot_formula=formula_1)
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cable_template_2 = CableTemplate(knot_formula=formula_2)
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cable_template = cable_template_1 + cable_template_2
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cable_with_shift = cable_template_1.add_with_shift(cable_template_2)
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# cable_with_shift = cable_template_1.add_with_shift(cable_template_2)
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print(cable_with_shift.knot_formula)
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cable_template.fill_q_vector()
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print(cable_template.q_vector)
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print(cable_template.knot_formula)
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# cable_template.fill_q_vector()
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# print(cable_template.q_vector)
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# print(cable_template.knot_formula)
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cable = cable_template.cable
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sf = cable(4,4,4,4,0,0,0,0)
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@ -104,7 +110,7 @@ def main(arg=None):
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cable_template_2 = CableTemplate(knot_formula=formula_2)
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cable_template = cable_template_1 + cable_template_2
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# cable_template.cable.is_signature_big_for_all_metabolizers()
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# sf = cable_template.cable.signature_as_function_of_theta(4,4,4,4,0,0,0,0)
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sf = cable_template.cable.signature_as_function_of_theta(4,4,4,4,0,0,0,0)
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@ -1,4 +1,4 @@
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#!/usr/bin/python
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#!/usr/bin/env sage -python
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import numpy as np
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import itertools as it
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from typing import Iterable
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@ -16,13 +16,12 @@ from pathlib import Path
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class SignatureFunction():
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def __init__(self, values=None, counter=None):
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def __init__(self, values=None, counter=None, plot_title=''):
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# counter of signature jumps
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if counter is None:
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counter = Counter()
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if values is None:
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values = []
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values = values or []
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for k, v in values:
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counter[k] += v
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@ -34,6 +33,7 @@ class SignatureFunction():
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counter[0] += 0
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counter[1] += 0
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self.jumps_counter = counter
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self.plot_title = plot_title
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def __rshift__(self, shift):
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# A shift of the signature functions corresponds to the rotation.
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@ -52,7 +52,11 @@ class SignatureFunction():
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def __add__(self, other):
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counter = copy(self.jumps_counter)
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counter.update(other.jumps_counter)
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return SignatureFunction(counter=counter)
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if self.plot_title and other.plot_title:
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title = self.plot_title + " + " + other.plot_title
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else:
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title = self.plot_title or other.plot_title
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return SignatureFunction(counter=counter, plot_title=title)
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def __sub__(self, other):
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counter = copy(self.jumps_counter)
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@ -79,9 +83,6 @@ class SignatureFunction():
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result = [jump for jump_arg, jump in items if jump_arg < mod_one(arg)]
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return 2 * sum(result) + self.jumps_counter[arg]
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def is_zero_everywhere(self):
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return not any(self.jumps_counter.values())
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def double_cover(self):
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# to read values for t^2
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items = self.jumps_counter.items()
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@ -103,6 +104,11 @@ class SignatureFunction():
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counter = Counter({mod_one(2 * k) : v for k, v in items if k >= 1/2})
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return SignatureFunction(counter=counter)
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def is_zero_everywhere(self):
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return not any(self.jumps_counter.values())
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def extremum(self, limit=None):
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max = 0
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current = 0
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@ -121,13 +127,36 @@ class SignatureFunction():
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# Total signature jump is the sum of all jumps.
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return sum([j[1] for j in sorted(self.jumps_counter.items())])
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def plot_four(self, sf1, sf2, sf3, save_path=None, title=''):
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fig, axes_matrix = plt.subplots(2, 2, sharey=True,
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figsize=(10,5))
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sf0 = self
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@staticmethod
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def plot_many(*sf_list, save_path=None, title='',):
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axes_num = len(sf_list)
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if axes_num > 36:
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sf_list = sf_list[36]
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axes_num = 36
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# print war, set val in conf
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rows = ceil(sqrt(axes_num))
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cols = ceil(axes_num/rows)
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fig, axes_matrix = plt.subplots(rows, cols,
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sharey=True,
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sharex=True,)
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for i, sf in enumerate(sf_list):
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col = i % cols
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row = (i - col)/cols
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sf.plot(subplot=True,
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ax=axes_matrix[0][1])
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ax=axes_matrix[row][col],
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title=sf.plot_title)
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plt.tight_layout()
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save_path = save_path or os.path.join(os.getcwd(),"tmp.png")
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save_path = Path(save_path).with_suffix('.png')
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plt.savefig(save_path)
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plt.close()
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image = Image.open(save_path)
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image.show()
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return
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sf1.plot(subplot=True,
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ax=axes_matrix[1][0],
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@ -146,18 +175,13 @@ class SignatureFunction():
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plt.tight_layout()
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save_path = save_path or os.path.join(os.getcwd(),"tmp.png")
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save_path = Path(save_path)
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save_path = save_path.with_suffix('.png')
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save_path = Path(save_path).with_suffix('.png')
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plt.savefig(save_path)
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plt.close()
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image = Image.open(save_path)
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image.show()
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pass
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def plot_sum_with_other(self, other,
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save_path=None, title=''):
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tp = self
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@ -209,10 +233,6 @@ class SignatureFunction():
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image = Image.open(save_path)
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image.show()
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pass
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def plot(self, subplot=False, ax=None, save_as='sf',
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title="",
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alpha=1,
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@ -241,8 +261,6 @@ class SignatureFunction():
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image = Image.open(save_as)
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image.show()
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def step_function_data(self):
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# Transform the signature jump data to a format understandable
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# by the plot function.
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