# 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 (2018): 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,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# 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 TheoryLogNormal
"""
import numpy as np
from RepTate.core.Parameter import Parameter, ParameterType, OptType
from RepTate.gui.QTheory import QTheory
[docs]
class TheoryLogNormal(QTheory):
"""Log-Normal distribution: the logarithm of the molecular weight is normally distributed
* **Function**
.. math::
W(M) = W_0 \\frac{1}{\\sqrt{2\\pi\\sigma^2}} \\exp\\left[ - \\frac{\\left(\\ln{M}-(\\ln{M_0} + \\sigma^2)\\right)^2}{2\\sigma^2} \\right]
* **Parameters**
- ``logW0`` :math:`\\equiv\\log_{10}(W_0)`: Normalization constant.
- ``logM0`` :math:`\\equiv\\log_{10}(M_0)`
- ``sigma`` :math:`\\equiv\\sigma`
"""
thname = "LogNormal"
description = "LogNormal distribution"
citations = []
doi = []
html_help_file = "http://reptate.readthedocs.io/manual/Applications/MWD/Theory/theory.html#log-normal-distribution"
single_file = (
False # False if the theory can be applied to multiple files simultaneously
)
def __init__(self, name="", parent_dataset=None, axarr=None):
"""**Constructor**"""
super().__init__(name, parent_dataset, axarr)
self.function = self.LogNormal # main theory function
self.has_modes = False # True if the theory has modes
self.parameters["logW0"] = Parameter(
name="logW0",
value=5,
description="Normalization constant",
type=ParameterType.real,
opt_type=OptType.opt,
)
self.parameters["logM0"] = Parameter(
name="logM0",
value=5,
description="Log mean molecular weight",
type=ParameterType.real,
opt_type=OptType.opt,
)
self.parameters["sigma"] = Parameter(
name="sigma",
value=1,
description="Standard deviation",
type=ParameterType.real,
opt_type=OptType.opt,
min_value=0,
)
[docs]
def LogNormal(self, f=None):
"""LogNormal function"""
ft = f.data_table
tt = self.tables[f.file_name_short]
tt.num_columns = ft.num_columns
tt.num_rows = ft.num_rows
W0 = np.power(10.0, self.parameters["logW0"].value)
M0 = np.power(10.0, self.parameters["logM0"].value)
sigma = self.parameters["sigma"].value
tt.data = np.zeros((tt.num_rows, tt.num_columns))
tt.data[:, 0] = ft.data[:, 0]
# tt.data[:, 1] = (W0/ sigma/ np.sqrt(2 * np.pi)/ tt.data[:, 0]* np.exp(-((np.log(tt.data[:, 0]) - np.log(M0)) ** 2) / 2 / sigma ** 2))
tt.data[:, 1] = W0 / (sigma * np.sqrt(2 * np.pi)) * np.exp(-((np.log(tt.data[:, 0]) - (np.log(M0) + sigma**2)) ** 2) / 2 / sigma ** 2)
[docs]
def do_error(self, line):
"""Report the error of the current theory
Report the error of the current theory on all the files, taking into account the current selected xrange and yrange.
File error is calculated as the mean square of the residual, averaged over all points in the file. Total error is the mean square of the residual, averaged over all points in all files."""
super().do_error(line)
if line == "":
self.Qprint("""<h3>Characteristics of the fitted MWD</h3>""")
M0 = np.power(10.0, self.parameters["logM0"].value)
sigma = self.parameters["sigma"].value
Mn = M0 * np.exp(sigma ** 2 / 2)
Mw = M0 * np.exp(3 * sigma ** 2 / 2)
Mz = M0 * np.exp(5 * sigma ** 2 / 2)
# table='''<table border="1" width="100%">'''
# table+='''<tr><th>Mn</th><th>Mw</th><th>Mz</th><th>D</th></tr>'''
# table+='''<tr><td>%6.3gk</td><td>%6.3gk</td><td>%6.3gk</td><td>%7.3g</td></tr>'''%(Mn / 1000, Mw / 1000, Mz/1000 , Mw/Mn)
# table+='''</table><br>'''
table = [
[
"%-12s" % "Mn (kg/mol)",
"%-12s" % "Mw (kg/mol)",
"%-9s" % "Mw/Mn",
"%-9s" % "Mz/Mw",
],
]
table.append(
[
"%-12.3g" % (Mn / 1000),
"%-12.3g" % (Mw / 1000),
"%-9.3g" % (Mw / Mn),
"%-9.3g" % (Mz / Mw),
]
)
self.Qprint(table)
