# RepTate: Rheology of Entangled Polymers: Toolkit for the Analysis of Theory and Experiments
# --------------------------------------------------------------------------------------------------------
#
# Authors:
# Jorge Ramirez, jorge.ramirez@upm.es
# Victor Boudara, victor.boudara@gmail.com
#
# Useful links:
# http://blogs.upm.es/compsoftmatter/software/reptate/
# https://github.com/jorge-ramirez-upm/RepTate
# http://reptate.readthedocs.io
#
# --------------------------------------------------------------------------------------------------------
#
# Copyright (2017-2023): Jorge Ramirez, Victor Boudara, Universidad Politécnica de Madrid, University of Leeds
#
# This file is part of RepTate.
#
# RepTate is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RepTate is distributed in the hope that it will be useful,
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# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with RepTate. If not, see <http://www.gnu.org/licenses/>.
#
# --------------------------------------------------------------------------------------------------------
"""Module TheoryHavriliakNegamiModes
Module that defines theories related to Havriliak-Negami modes, in the frequency and time domains.
"""
import numpy as np
from RepTate.core.DataTable import DataTable
from RepTate.core.Parameter import Parameter, ParameterType, OptType
from RepTate.gui.QTheory import QTheory
from PySide6.QtWidgets import QToolBar, QSpinBox
from PySide6.QtCore import QSize
from PySide6.QtGui import QIcon
from RepTate.core.DraggableArtists import DragType, DraggableModesSeries
[docs]
class TheoryHavriliakNegamiModesFrequency(QTheory):
"""Fit a generalized Havriliak-Negami model to a frequency dependent relaxation function.
* **Function**
.. math::
\\epsilon^* (\\omega) = \\epsilon_\\infty + \\frac{\\Delta\\epsilon}{\\left[ 1 + \\left( i\\omega\\tau\\right)^\\alpha\\right]^\\gamma}
* **Parameters**
- einf = :math:`\\epsilon_{\\infty}`: Unrelaxed permitivity
- :math:`n_{modes}`: number of Havriliak-Negami modes equally distributed in logarithmic scale between :math:`\\omega_{min}` and :math:`\\omega_{max}`.
- logwmin = :math:`\\log(\\omega_{min})`: decimal logarithm of the minimum frequency.
- logwmax = :math:`\\log(\\omega_{max})`: decimal logarithm of the maximum frequency.
- logDei = :math:`\\log(\\Delta\\epsilon_{i})`, where :math:`\\Delta\\epsilon_{i}=\\epsilon_{s,i}-\\epsilon_\\infty`: decimal logarithm of the relaxation strength of Debye mode :math:`i`, where :math:`\\epsilon_{s,i}` is the static permitivity of mode :math:`i`.
- :math:`\\alpha`: Asymmetry parameter
- :math:`\\gamma`: Broadness parameter
"""
thname = "Havriliak-Negami modes"
description = "Fit Havriliak-Negami modes"
citations = ["Havriliak S. and Negami S., Polymer 1967, 8, 161-210"]
doi = ["http://dx.doi.org/10.1016/0032-3861(67)90021-3"]
html_help_file = "http://reptate.readthedocs.io/manual/Applications/Dielectric/Theory/theory.html#havriliak-negami-modes"
single_file = True
def __init__(self, name="", parent_dataset=None, ax=None):
"""**Constructor**"""
super().__init__(name, parent_dataset, ax)
self.function = self.HavriliakNegamiModesFrequency
self.has_modes = False
self.MAX_MODES = 40
self.view_modes = True
wmin = self.parent_dataset.minpositivecol(0)
wmax = self.parent_dataset.maxcol(0)
nmodes = int(np.round(np.log10(wmax / wmin)))
self.parameters["einf"] = Parameter(
"einf",
0.0,
"Unrelaxed permittivity",
ParameterType.real,
opt_type=OptType.opt,
min_value=0,
)
self.parameters["alpha"] = Parameter(
"alpha",
1.0,
"Asymmetry parameter",
ParameterType.real,
opt_type=OptType.opt,
min_value=0,
)
self.parameters["gamma"] = Parameter(
"gamma",
1.0,
"Broadness parameter",
ParameterType.real,
opt_type=OptType.opt,
min_value=0,
)
self.parameters["logwmin"] = Parameter(
"logwmin",
np.log10(wmin),
"Log of frequency range minimum",
ParameterType.real,
opt_type=OptType.opt,
)
self.parameters["logwmax"] = Parameter(
"logwmax",
np.log10(wmax),
"Log of frequency range maximum",
ParameterType.real,
opt_type=OptType.opt,
)
self.parameters["nmodes"] = Parameter(
name="nmodes",
value=nmodes,
description="Number of Havriliak-Negami modes",
type=ParameterType.integer,
opt_type=OptType.const,
display_flag=False,
)
# Interpolate modes from data
w = np.logspace(np.log10(wmin), np.log10(wmax), nmodes)
eps = np.abs(
np.interp(
w,
self.parent_dataset.files[0].data_table.data[:, 0],
self.parent_dataset.files[0].data_table.data[:, 1],
)
)
for i in range(self.parameters["nmodes"].value):
self.parameters["logDe%02d" % i] = Parameter(
"logDe%02d" % i,
np.log10(eps[i]),
"Log of Mode %d amplitude" % i,
ParameterType.real,
opt_type=OptType.opt,
)
# GRAPHIC MODES
self.graphicmodes = []
self.artistmodes = []
self.setup_graphic_modes()
# add widgets specific to the theory
tb = QToolBar()
tb.setIconSize(QSize(24, 24))
self.spinbox = QSpinBox()
self.spinbox.setRange(1, self.MAX_MODES) # min and max number of modes
self.spinbox.setSuffix(" modes")
self.spinbox.setValue(self.parameters["nmodes"].value) # initial value
tb.addWidget(self.spinbox)
self.modesaction = tb.addAction(
QIcon(":/Icon8/Images/new_icons/icons8-visible.png"), "View modes"
)
self.modesaction.setCheckable(True)
self.modesaction.setChecked(True)
self.thToolsLayout.insertWidget(0, tb)
connection_id = self.spinbox.valueChanged.connect(
self.handle_spinboxValueChanged
)
connection_id = self.modesaction.triggered.connect(self.modesaction_change)
[docs]
def modesaction_change(self, checked):
"""Change visibility of modes"""
self.graphicmodes_visible(checked)
# self.view_modes = self.modesaction.isChecked()
# self.graphicmodes.set_visible(self.view_modes)
# self.do_calculate("")
[docs]
def handle_spinboxValueChanged(self, value):
"""Handle a change of the parameter 'nmode'"""
nmodesold = self.parameters["nmodes"].value
wminold = self.parameters["logwmin"].value
wmaxold = self.parameters["logwmax"].value
wold = np.logspace(wminold, wmaxold, nmodesold)
Gold = np.zeros(nmodesold)
for i in range(nmodesold):
Gold[i] = self.parameters["logDe%02d" % i].value
del self.parameters["logDe%02d" % i]
nmodesnew = value
self.set_param_value("nmodes", nmodesnew)
wnew = np.logspace(wminold, wmaxold, nmodesnew)
Gnew = np.interp(wnew, wold, Gold)
for i in range(nmodesnew):
self.parameters["logDe%02d" % i] = Parameter(
"logDe%02d" % i,
Gnew[i],
"Log of Mode %d amplitude" % i,
ParameterType.real,
opt_type=OptType.opt,
)
if self.autocalculate:
self.parent_dataset.handle_actionCalculate_Theory()
self.update_parameter_table()
[docs]
def drag_mode(self, dx, dy):
"""Drag graphical modes"""
nmodes = self.parameters["nmodes"].value
if self.parent_dataset.parent_application.current_view.log_x:
self.set_param_value("logwmin", np.log10(dx[0]))
self.set_param_value("logwmax", np.log10(dx[nmodes - 1]))
else:
self.set_param_value("logwmin", dx[0])
self.set_param_value("logwmax", dx[nmodes - 1])
if self.parent_dataset.parent_application.current_view.log_y:
for i in range(nmodes):
self.set_param_value("logDe%02d" % i, np.log10(dy[i]))
else:
for i in range(nmodes):
self.set_param_value("logDe%02d" % i, dy[i])
self.do_calculate("")
self.update_parameter_table()
[docs]
def update_modes(self):
"""Do nothing"""
pass
[docs]
def setup_graphic_modes(self):
"""Setup graphical helpers"""
nmodes = self.parameters["nmodes"].value
w = np.logspace(
self.parameters["logwmin"].value, self.parameters["logwmax"].value, nmodes
)
eps = np.zeros(nmodes)
for i in range(nmodes):
eps[i] = np.power(10, self.parameters["logDe%02d" % i].value)
self.graphicmodes = self.ax.plot(w, eps)[0]
self.graphicmodes.set_marker("D")
self.graphicmodes.set_linestyle("")
self.graphicmodes.set_visible(self.view_modes)
self.graphicmodes.set_markerfacecolor("yellow")
self.graphicmodes.set_markeredgecolor("black")
self.graphicmodes.set_markeredgewidth(3)
self.graphicmodes.set_markersize(8)
self.graphicmodes.set_alpha(0.5)
self.artistmodes = DraggableModesSeries(
self.graphicmodes,
DragType.special,
self.parent_dataset.parent_application,
self.drag_mode,
)
self.plot_theory_stuff()
[docs]
def destructor(self):
"""Called when the theory tab is closed"""
self.graphicmodes_visible(False)
#self.ax.lines.remove(self.graphicmodes)
self.graphicmodes.remove()
[docs]
def graphicmodes_visible(self, state):
"""Change visibility of modes"""
self.view_modes = state
self.graphicmodes.set_visible(self.view_modes)
if self.view_modes:
self.artistmodes.connect()
else:
self.artistmodes.disconnect()
# self.do_calculate("")
self.parent_dataset.parent_application.update_plot()
[docs]
def get_modes(self):
"""Get the values of Maxwell Modes from this theory"""
nmodes = self.parameters["nmodes"].value
freq = np.logspace(
self.parameters["logwmin"].value, self.parameters["logwmax"].value, nmodes
)
tau = 1.0 / freq
eps = np.zeros(nmodes)
for i in range(nmodes):
eps[i] = np.power(10, self.parameters["logDe%02d" % i].value)
return tau, eps, True
[docs]
def HavriliakNegamiModesFrequency(self, f=None):
"""Calculate the theory"""
ft = f.data_table
tt = self.tables[f.file_name_short]
tt.num_columns = ft.num_columns
tt.num_rows = ft.num_rows
tt.data = np.zeros((tt.num_rows, tt.num_columns))
tt.data[:, 0] = ft.data[:, 0]
einf = self.parameters["einf"].value
alpha = self.parameters["alpha"].value
gamma = self.parameters["gamma"].value
nmodes = self.parameters["nmodes"].value
freq = np.logspace(
self.parameters["logwmin"].value, self.parameters["logwmax"].value, nmodes
)
tau = 1.0 / freq
sol = np.zeros(tt.num_rows, dtype="complex128")
sol += einf
for i in range(nmodes):
if self.stop_theory_flag:
break
eps = np.power(10, self.parameters["logDe%02d" % i].value)
sol += eps / np.power(
1.0 + np.power(1j * tt.data[:, 0] * tau[i], alpha), gamma
)
tt.data[:, 1] = np.real(sol)
tt.data[:, 2] = -np.imag(sol)
[docs]
def plot_theory_stuff(self):
"""Plot graphical helpers"""
# if not self.view_modes:
# return
data_table_tmp = DataTable(self.axarr)
data_table_tmp.num_columns = 3
nmodes = self.parameters["nmodes"].value
data_table_tmp.num_rows = nmodes
data_table_tmp.data = np.zeros((nmodes, 3))
freq = np.logspace(
self.parameters["logwmin"].value, self.parameters["logwmax"].value, nmodes
)
data_table_tmp.data[:, 0] = freq
for i in range(nmodes):
if self.stop_theory_flag:
break
data_table_tmp.data[i, 1] = data_table_tmp.data[i, 2] = np.power(
10, self.parameters["logDe%02d" % i].value
)
view = self.parent_dataset.parent_application.current_view
try:
x, y, success = view.view_proc(data_table_tmp, None)
except TypeError as e:
print(e)
return
self.graphicmodes.set_data(x, y)
for i in range(data_table_tmp.MAX_NUM_SERIES):
for nx in range(len(self.axarr)):
# self.axarr[nx].lines.remove(data_table_tmp.series[nx][i])
data_table_tmp.series[nx][i].remove()