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betan.py
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betan.py
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import matplotlib as mpl
import matplotlib.pyplot as plt
from matplotlib import ticker
import pandas as pd
import os
import numpy as np
import scipy
import statsmodels.formula.api as smf
import scipy.stats as ss
"""
Created on Mon Apr 9 11:29:12 2018
@author: architdatar
Integrated for use with the SESAMI website by Gianmarco Terrones.
"""
mpl.use("agg")
mpl.rcParams["mathtext.default"] = "regular" # preventing italics in axis labels
pd.set_option("display.max_rows", 500)
class BETAn:
def __init__(
self, selected_gas, selected_temperature, minlinelength, plotting_information
):
self.R = 8.314 # J/mol/K
self.N_A = 6.023e23 # molecules/mol
self.T = selected_temperature
if selected_gas == "Argon":
self.selected_gas_cs = 0.142e-18 # m²/molecule; Ref: 10.1039/D1TA08021K
elif selected_gas == "Nitrogen":
self.selected_gas_cs = 0.162e-18 # m²/molecule; Ref: 10.1039/D1TA08021K
# elif selected_gas == "Carbon dioxide":
# self.selected_gas_cs = 0.142e-18 # m²/molecule; Ref: 10.1039/D1TA08021K
# elif selected_gas == "Krypton":
# self.selected_gas_cs = 0.210e-18 # m²/molecule; Ref: 10.1039/D1TA08021K
elif selected_gas == "Custom":
# Multiply by 1e-20 to convert to m²/molecule, from Ų/molecule
self.selected_gas_cs = float(plotting_information['custom cross section']) * 1e-20
self.loadunits = "mol/kg"
# self.weight_of_box = 1e-20 #gm
self.minlinelength = (
minlinelength # min number of points for it to be called a line.
)
self.R2cutoff = plotting_information[
"R2 cutoff"
] # Website default is 0.9995
# This is the minimum R2 value required for a region to be considered a line.
self.R2min = plotting_information[
"R2 min"
] # Website default is 0.998
# Setting these variables to None initially.
self.eswminima = None
self.con1limit = None
def prepdata(
self, data, loading_col="Loading", conv_to_molperkg=1, p0=1e5, full=True
):
"""
This function prepares data for BET analysis. We create the columns P_rel, BETy, BET_y2 and phi. Needs arguments data and weight of box to calculate the required columns.
Parameters
----------
data : pandas.core.frame.DataFrame
Represents an isotherm. Columns are "Pressure" and "Loading".
loading_col : str
The name of the column in data that contains the loading data.
conv_to_molperkg : int
Specify the conversion to convert from the current units to mol/kg. For SESAMI 1.0 integrated with the SESAMI website, this is taken care of before betan.py.
p0 : float
Saturation pressure. We assume that we want to plot from 0 to this pressure.
full : bool
Indicates whether or not to calculate Consistency 1 maximum and ESW minimum.
Returns
-------
data: pandas.core.frame.DataFrame
The augmented data representing an isotherm. Columns are "Pressure", "Loading", "P_rel", "BETy", "BET_y2", and "phi".
"""
# Next, we will prepare the data for analysis by assigning the appropriate column numbers and names.
data = data.copy(deep=True)
# First, we will sort the incoming data.
data["P_rel"] = data["Pressure"] / p0
data.sort_values("P_rel", inplace=True)
data["Loading"] = data[loading_col] * conv_to_molperkg
# data['VolLoad'] = vol_loading
data["BETy"] = data["P_rel"] / (data["Loading"] * (1 - data["P_rel"]))
data["BET_y2"] = data["Loading"] * (1 - data["P_rel"]) # Used for first Rouquerol consistency criterion. See SESAMI 1 paper.
data["phi"] = (
data["Loading"] / 1000 * self.R * self.T * scipy.log(data["P_rel"])
) # J/g ; equation 1 of https://doi.org/10.1021/acs.jpcc.9b02116. Factor of 1000 to convert from 1/kg to 1/g
# We will also add a line here that calculates the consistency 1 limit. This will ensure that the we need to compute the upper limit of consistency1 only once.
if (
full
): # In some applications, we don't want the ESW limits and stuff, we only want the values.
# In those cases, we can simply change this parameter to something else.
# The first Rouquerol consistency criterion is as follows:
# The linear region should only be a range of p/p0 in which the value of q(1-p/p0) monotonically increases with p/p0
# Where q is loading and p/p0 is P_rel. So, the setting of con1limit below is the largest P_rel data point in the isotherm in the first region where q(1-p/p0) is monotonically increasing with p/p0
self.con1limit = self.getlocalextremum(
data, column="BET_y2", x="P_rel", how="Maxima", which=0, points=3
)[0]
self.eswminima = self.getlocalextremum(
data, column="phi", x="P_rel", how="Minima", which=0, points=3
)[0]
return data
def getlocalextremum(self, data, column=None, x=None, how="Minima", which=0, points=3):
"""
This function will get the optimum value and the corresponding index from a given set of finite number of data points.
Such a function is not easily available elsewhere. The rationale is that we compute the slope at every point by fitting
a line through 'points' number of points before and after the chosen point. We then compute the minimum where the slope changes
sign. In order to ensure that we are not selecting a point due to the noise, we compute the mean value of 'points' number of points
before and after the chosen point and ensure that it is greater than the value at the chosen point (suggested by Li-Chiang).
This code may not be very efficient since it involves a lot of regression, but it works for a small quantum of data.
Parameters
----------
data : pandas.core.frame.DataFrame
Represents an isotherm. Columns are "Pressure", "Loading", "P_rel", "BETy", "BET_y2", and "phi".
column : str
The name of the feature for which to get the optimum.
x : str
The name of the dependent variable. Always "P_rel" for this script.
how : str
"Minima" or "Maxima", depending if it is desired to minimize or maximize the feature in `column`.
which : int
Which of the good minimas (good meaning that it is not just a minima due to noise) to choose from.
points : int
How many points before and after a point to use in computing slope. Also used in computing the mean of the points before and after a point.
Returns
-------
minima : numpy.int64
Index of minima of the feature represented by `column`.
targetvalue : numpy.float64
Minima of the feature represented by `column`.
data[["x", "target", "slopes"]] : pandas.core.frame.DataFrame
Contains information of interest for the independent and dependent variable, as well as the slopes at each data point for target vs x.
"""
data = data.copy(deep=True)
start = data.index.values[0]
end = data.index.values[-1]
# Target is the name of the column that we will choose
if column is None:
target = data.columns[0]
if type(column) == int:
target = data.columns[column]
if type(column) == str:
target = column
data["target"] = data[target]
if how == "Maxima":
data["target"] = -data["target"]
if x is None:
data["x"] = data.index
elif type(x) == int:
data["x"] = data[data.columns[x]]
elif type(x) == str:
data["x"] = data[x]
else:
raise ValueError
data["slopes"] = 0.0
points = int(points) # Number of points before and after a chosen point.
for i in np.arange(start + points, end - points + 1, 1):
regdata = data[i - points : i + points + 1][["target", "x"]]
res = smf.ols("target ~ x", regdata).fit()
slope = res.params[1]
data.at[i, "slopes"] = slope
minimas = data.index[
(data["slopes"].shift(1).fillna(0) < 0)
& (data["slopes"].shift(-1).fillna(0) > 0)
].values
# We thus have a list of potential minimas. But now, we need to discard the ones that are there because of the noise.
goodminimas = []
if minimas.shape[0] != 0:
for minimap in minimas:
if (
data[minimap - points : minimap]["target"].mean()
> data[data.index == minimap]["target"].values[0]
and data[minimap + 1 : minimap + points + 1]["target"].mean()
> data[data.index == minimap]["target"].values[0]
):
# This means that this is really a minimum and not just due to the noise.
# The data points before the candidate minimum are greater on average than the candidate, and those after the candidate are greater on average.
goodminimas.append(minimap)
if goodminimas != []:
# Now, we need to get the minima that we are really looking for.
if type(which) == int:
minima = goodminimas[which]
targetvalue = data[data.index == minima]["target"].values[0]
if type(which) == list:
minima = [goodminimas[minima] for minima in which]
targetvalue = [
data[data.index == minima]["target"].values[0]
for minima in minima
]
else:
minima = None
targetvalue = None
else:
minima = None
targetvalue = None
return minima, targetvalue, data[["x", "target", "slopes"]]
def th_loading(self, x, params):
"""
Calculates the BET loading given relative pressures and BET parameters.
See equation 3 of Fagerlund, G. (1973). Determination of specific surface by the BET method.
Parameters
----------
x : numpy.ndarray
Array of p/p0 values. p is vapor pressure, and p0 is saturation vapor pressure.
params : tuple
The variables needed for the BET equations. A molar version of Xm (qm) and C, from Fagerlund, G. (1973). Determination of specific surface by the BET method.
Returns
-------
bet_loading: numpy.ndarray
The mass adsorbed at each relative vapor pressure in x.
"""
[qm, C] = params
bet_y = (C - 1) / (qm * C) * x + 1 / (qm * C)
bet_loading = x / (bet_y * (1 - x)) # See equation 3 of the original BET paper.
return bet_loading
def gen_phi(self, load, p_rel, T=87.0):
"""
This function will generate phi values given the x points.
Parameters
----------
load : numpy.ndarray
The adsorption loadings of the isotherm data.
p_rel : numpy.ndarray
The relative pressures of the isotherm data.
T : float
The temperature.
Returns
-------
phi: numpy.ndarray
Excess sorption work.
"""
# See equation 1 of 10.1021/acs.jpcc.9b02116. The SESAMI 1 paper.
phi = load / 1000 * 8.314 * T * scipy.log(p_rel)
return phi
def makeisothermplot(
self,
plotting_information,
ax,
data,
yerr=None,
maketitle="Yes",
tryminorticks="Yes",
xscale="log",
with_fit="No",
fit_data=None,
):
"""
This function takes an axis as an input and makes an isotherm plot on it.
Parameters
----------
plotting_information : dict
Lots of plotting and calculation settings from the front end (i.e. the SESAMI webpage). The keys are 'dpi', 'font size', 'font type', 'legend', 'R2 cutoff', 'R2 min', 'gas', 'scope', 'ML', 'custom adsorbate', 'custom cross section', 'custom temperature', and 'custom saturation pressure'.
ax : matplotlib.axes._subplots.AxesSubplot
The axes on which to plot.
data : pandas.core.frame.DataFrame
Represents an isotherm. Columns are "Pressure", "Loading", "P_rel", "BETy", "BET_y2", and "phi".
yerr : float or array-like
The errorbar sizes.
maketitle : str
If set to "Yes", the plot will be titled; otherwise, not.
tryminorticks : str
If xscale='log' and tryminorticks='Yes', the xscale will be from 0 to 1. The user has no control over it.
xscale : str
Either 'log' or 'linear'. Affects the x-axis. If xscale='log' and tryminorticks='Yes', the xscale will be from 0 to 1. The user has no control over it.
with_fit : str
If set to "Yes", the plot will include the BET fit, the BET+ESW fit, the BET region, and the BET+ESW region; otherwise, not.
fit_data : list
Information for BET and BET+ESW. In particular (for BET and for BET+ESW), the indices of the data points that start and end the chosen linear region (rbet), as well as a molar version of Xm (called qm here) and C. These last two are referred to as params in the code.
Returns
-------
None
"""
scope = plotting_information['scope']
# ax.errorbar essentially is ax.plot with the settings used below. Makes a scatter. Benefit is that it shows up last in the legend.
ax.errorbar(
data["P_rel"],
data["Loading"],
yerr=yerr,
fmt="o",
capsize=3,
label="Isotherm data points",
)
ax.xaxis.label.set_text("$p/p_0$")
ax.yaxis.label.set_text("$q$" + " / " + "$%s$" % self.loadunits)
if xscale == "log":
ax.set_xscale("log")
if tryminorticks == "Yes":
locmaj = mpl.ticker.LogLocator(base=10.0, numticks=10)
ax.xaxis.set_major_locator(locmaj)
locmin = mpl.ticker.LogLocator(
base=10.0,
subs=(0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9),
numticks=10,
)
ax.xaxis.set_minor_locator(locmin)
ax.xaxis.set_minor_formatter(mpl.ticker.NullFormatter())
# We will try to set the ticks for y axis.
if xscale == "linear":
ax.set_xlim((0, 1))
ax.set_xticks(np.arange(0, 1.1, 0.1))
ax.set_ylim((0, ax.get_ylim()[1]))
if scope == 'BET and BET+ESW': # In this case, run the BET+ESW code and the BET code.
if with_fit == "Yes":
[bet_info, betesw_info] = fit_data
[rbet, bet_params] = bet_info
[rbetesw, betesw_params] = betesw_info
if rbet != (None, None):
ax.axvspan(
data.at[rbet[0], "P_rel"],
data.at[rbet[1], "P_rel"],
facecolor=plt.cm.PuOr(70),
edgecolor="none",
alpha=0.6,
label="BET region",
)
ax.plot(
data["P_rel"].values,
self.th_loading(data["P_rel"].values, bet_params),
color=plt.cm.PuOr(20),
label="BET fit",
)
if rbetesw != (None, None):
ax.axvspan(
data.at[rbetesw[0], "P_rel"],
data.at[rbetesw[1], "P_rel"],
facecolor=plt.cm.Greens(70),
edgecolor="none",
alpha=0.6,
label="BET+ESW region",
)
ax.plot(
data["P_rel"].values,
self.th_loading(data["P_rel"].values, betesw_params),
color=plt.cm.Greens(200),
label="BET+ESW fit",
)
# Setting the y-axis limits to include more of the fit
# Only consider BET values that correspond to x values within our plotting range
bet_values = [
data["Loading"].values[i]
for i, value in enumerate(data["P_rel"].values)
if ax.get_xlim()[0] <= value <= ax.get_xlim()[1]
]
y_max = max(bet_values) + 10
ax.set_ylim(top=y_max)
if self.eswminima is not None:
ax.vlines(
data.at[self.eswminima, "P_rel"],
ax.get_ylim()[0],
ax.get_ylim()[1],
colors=plt.cm.Greens(200),
linestyles="dashed",
label="First ESW minimum",
)
if self.con1limit is not None:
ax.vlines(
data.at[self.con1limit, "P_rel"],
ax.get_ylim()[0],
ax.get_ylim()[1],
linestyles="dashed",
color=plt.cm.Purples(230),
label="Consistency 1 maximum",
)
if maketitle == "Yes":
titletext = "Isotherm Data"
ax.set_title(titletext)
if plotting_information["legend"] == "Yes": # Add a legend in this case.
ax.legend(loc="upper left")
else: # This indicates the scope is 'BET'. Only run the BET related code. No BET+ESW region nor BET+ESW fit nor ESW minimum vertical line.
if with_fit == "Yes":
[bet_info, betesw_info] = fit_data
[rbet, bet_params] = bet_info
if rbet != (None, None):
ax.axvspan(
data.at[rbet[0], "P_rel"],
data.at[rbet[1], "P_rel"],
facecolor=plt.cm.PuOr(70),
edgecolor="none",
alpha=0.6,
label="BET region",
)
ax.plot(
data["P_rel"].values,
self.th_loading(data["P_rel"].values, bet_params),
color=plt.cm.PuOr(20),
label="BET fit",
)
# Setting the y-axis limits to include more of the fit
# Only consider BET values that correspond to x values within our plotting range
bet_values = [
data["Loading"].values[i]
for i, value in enumerate(data["P_rel"].values)
if ax.get_xlim()[0] <= value <= ax.get_xlim()[1]
]
y_max = max(bet_values) + 10
ax.set_ylim(top=y_max)
if self.con1limit is not None:
ax.vlines(
data.at[self.con1limit, "P_rel"],
ax.get_ylim()[0],
ax.get_ylim()[1],
linestyles="dashed",
color=plt.cm.Purples(230),
label="Consistency 1 maximum",
)
if maketitle == "Yes":
titletext = "Isotherm Data"
ax.set_title(titletext)
if plotting_information["legend"] == "Yes": # Add a legend in this case.
ax.legend(loc="upper left")
def makeconsistencyplot(
self, plotting_information, ax3, data, maketitle="Yes", tryminorticks="Yes"
):
"""
This function takes an axis as an input and makes the plot to see the limits of the region
to be chosen to satisfy the first consistency criterion.
Parameters
----------
plotting_information : dict
Lots of plotting and calculation settings from the front end (i.e. the SESAMI webpage). The keys are 'dpi', 'font size', 'font type', 'legend', 'R2 cutoff', 'R2 min', 'gas', 'scope', 'ML', 'custom adsorbate', 'custom cross section', 'custom temperature', and 'custom saturation pressure'.
ax3 : matplotlib.axes._subplots.AxesSubplot
The axes on which to plot.
data : pandas.core.frame.DataFrame
Represents an isotherm. Columns are "Pressure", "Loading", "P_rel", "BETy", "BET_y2", and "phi".
maketitle : str
If set to "Yes", the plot will be titled; otherwise, not.
tryminorticks : str
If tryminorticks='Yes', the xscale will be from 0 to 1. The user has no control over it.
Returns
-------
None
"""
ax3.xaxis.label.set_text("$p/p_0$")
ax3.yaxis.label.set_text("$q(1-p/p_{0})$" + " / " + "$%s$" % self.loadunits)
ax3.set_xscale("log")
if maketitle == "Yes":
titletext = "BET Consistency Plot"
ax3.set_title(titletext)
ax3.errorbar(data["P_rel"], data["BET_y2"], fmt="o", label="Isotherm data points")
ax3.set_ylim(ax3.get_ylim())
if tryminorticks == "Yes":
locmaj = mpl.ticker.LogLocator(base=10.0, numticks=10)
ax3.xaxis.set_major_locator(locmaj)
locmin = mpl.ticker.LogLocator(
base=10.0,
subs=(0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9),
numticks=10,
)
ax3.xaxis.set_minor_locator(locmin)
ax3.xaxis.set_minor_formatter(mpl.ticker.NullFormatter())
# We will use our code to determine x_max
ind_max = self.con1limit
if ind_max is not None:
x_max = data[data.index == ind_max]["P_rel"].values[0]
ax3.vlines(
x_max,
ax3.get_ylim()[0],
ax3.get_ylim()[1],
colors=plt.cm.Purples(230),
linestyles="dashed",
label="Consistency 1 maximum",
)
else:
x_max = data["P_rel"][data["BET_y2"].idxmax()]
# bbox_props = dict(boxstyle='square', ec= 'k', fc='w', lw = 1.0)
# ax3.annotate('$p/p_0$'+'=%.2e'%(x_max), xy=(x_max,0 ),xytext =(-150, 15),
# textcoords='offset points',arrowprops=dict(facecolor='black',width=0.5, shrink=0.05, headwidth=5), bbox=bbox_props)
if self.eswminima is not None:
ax3.vlines(
data.at[self.eswminima, "P_rel"],
ax3.get_ylim()[0],
ax3.get_ylim()[1],
colors=plt.cm.Greens(200),
linestyles="dashed",
label="First ESW minimum",
)
ax3.set_xlim(right=1.000)
if plotting_information["legend"] == "Yes": # Add a legend in this case.
ax3.legend(loc="upper left")
def makelinregplot(
self, plotting_information, ax2, p, q, data, maketitle="Yes", mode="BET"
):
"""
This function takes an axis as an input to make a plot summarizing information about a
chosen linear region.
Parameters
----------
plotting_information : dict
Lots of plotting and calculation settings from the front end (i.e. the SESAMI webpage). The keys are 'dpi', 'font size', 'font type', 'legend', 'R2 cutoff', 'R2 min', 'gas', 'scope', 'ML', 'custom adsorbate', 'custom cross section', 'custom temperature', and 'custom saturation pressure'.
ax2 : matplotlib.axes._subplots.AxesSubplot
The axes on which to plot.
p : numpy.int64
The index of the data point that is chosen as the start of the linear region.
q : numpy.int64
The index of the data point that is chosen as the end of the linear region.
data : pandas.core.frame.DataFrame
Represents an isotherm. Columns are "Pressure", "Loading", "P_rel", "BETy", "BET_y2", and "phi".
maketitle : str
If set to "Yes", the plot will be titled; otherwise, not.
mode : str
Either "BET" or "BET+ESW". This affects the title of the plot if one is made.
Returns
-------
my_dict: dict
Contains SESAMI 1.0 intermediate calculation results, and the predicted area A_BET. The keys are "C", "qm", "A_BET", "con3", "con4", "length_linear_region", "R2_linear_region", "low_P_linear_region", and "high_P_linear_region".
"""
bbox_props = dict(boxstyle="square", ec="k", fc="w", lw=1.0)
if (p, q) == (None, None):
ax2.text(
0.97,
0.22,
"No suitable linear region found.",
horizontalalignment="right",
verticalalignment="center",
bbox=bbox_props,
transform=ax2.transAxes,
)
else:
[
linear,
stats,
C,
qm,
x_max,
x_BET3,
x_BET4,
con1,
con2,
con3,
con4,
A_BET,
] = self.linregauto(p, q, data)
[ftest, ttest, outlierdata, shaptest, r2, r2adj, results] = stats
intercept, slope = results.params
low_p = data.iloc[p]["Pressure"]
high_p = data.iloc[q]["Pressure"]
ax2.xaxis.label.set_text("$p/p_0$")
ax2.yaxis.label.set_text(r"$\frac{p/p_0}{q(1-p/p_0)}$" + " / " + "kg/mol")
if maketitle == "Yes":
if mode == "BET":
titletext = "BET Linear Region Plot"
elif mode == "BET+ESW":
titletext = "BET+ESW Linear Region Plot"
ax2.set_title(titletext)
ax2.errorbar(
linear["P_rel"], linear["BETy"], fmt="o", label="BET data points"
)
ax2.plot(
linear["P_rel"],
slope * linear["P_rel"] + intercept,
"k",
alpha=0.5,
label="Fitted Linear Region",
)
# ax2.text(linear['P_rel'].values[4], linear['BETy'].values[1], "R2=%.6f, C= %.4g,\nqm=%.2fmlSTP/gm, \nBETSA=%.2f m2/g"%(results.rsquared, C, qm,A_BET))
# Change: I comment out the properties, since they will be displayed separately on the website.
# ax2.text(0.97, 0.22,'C= %.4g\n'%C+'$q_m$'+'=%.2f mol/kg \nBETSA=%.3f'%(qm,A_BET)+ '$m^{2}/g$'+'\nConsistency 3: %s\n Consistency 4: %s\n'%(con3, con4)+'Length of region: %d\n'%(q-p)+'$R^{2}$'+'=%.6f'%(results.rsquared),horizontalalignment='right', verticalalignment='center', bbox = bbox_props,transform= ax2.transAxes)
ax2.xaxis.set_major_formatter(ticker.FormatStrFormatter("%.1e"))
ax2.yaxis.set_major_formatter(ticker.FormatStrFormatter("%.1e"))
plt.setp(ax2.xaxis.get_majorticklabels(), rotation=30)
plt.setp(ax2.yaxis.get_majorticklabels(), rotation=30)
# fig2.subplots_adjust(left =-0.1)
if plotting_information["legend"] == "Yes": # Add a legend in this case.
ax2.legend()
# Returning stats to display in the website.
my_dict = {
"C": C,
"qm": qm,
"A_BET": A_BET,
"con3": con3,
"con4": con4,
"length_linear_region": q - p,
"R2_linear_region": results.rsquared,
"low_P_linear_region": low_p,
"high_P_linear_region": high_p
} # This will be BET_dict or BET_ESW_dict
return my_dict
def eswdata(self, data, eswpoints=3):
"""
This function computes the ESW area and ESW minima.
Inputs:
data: The DataFrame containing columns 'Pressure' in Pa and 'Loading' in mol/kg framework. Also contains 'P_rel'
eswpoints (optional): int. Helps calculate the slope at a point. The number of points around the point at which slope is to be
computed.
Outputs:
data['Loading']: Pandas Series object containing 'Loading' data in mol/kg framework
data['phi']: Pandas series object containing 'phi' values in J/g
phi: qxNaxAcs where q: Loading in mol/kg=framework, Na: Avogadro number, Acs: Cross-sectional area of Ar atom.
minima: numpy.int64. The index of 'Loading' value corresponding to a minima of 'phi' values.
eswarea: numpy.float64. The surface area in m²/g corresponding to the 'Loading' at which 'phi' is minimum.
"""
data = data.copy(deep=True)
data["phi"] = (
data["Loading"] / 1000 * self.R * self.T * scipy.log(data["P_rel"])
) # J/g ; equation 1 of https://doi.org/10.1021/acs.jpcc.9b02116. Factor of 1000 to convert from 1/kg to 1/g
# Now, we will use our function to get minima.
if self.eswminima is None:
minima = self.getlocalextremum(
data, column="phi", x="P_rel", how="Minima", which=0, points=eswpoints
)[0]
else:
minima = self.eswminima
if minima is not None:
eswarea = (
data[data.index == minima]["Loading"].values[0]
/ 1000
* self.N_A
* self.selected_gas_cs
) # m²/g
else:
eswarea = None
return [data["Loading"], data["phi"], minima, eswarea]
def makeeswplot(
self,
plotting_information,
ax,
data,
eswpoints=3,
maketitle="Yes",
with_fit="No",
fit_data=None,
):
"""
This function modifies the axes parsed as input to make an ESW figure.
Inputs:
ax: Axes to be modified to make a figure upon
data: The DataFrame from which the graph is to be constructed.
Parameters
----------
plotting_information : dict
Lots of plotting and calculation settings from the front end (i.e. the SESAMI webpage). The keys are 'dpi', 'font size', 'font type', 'legend', 'R2 cutoff', 'R2 min', 'gas', 'scope', 'ML', 'custom adsorbate', 'custom cross section', 'custom temperature', and 'custom saturation pressure'.
ax : matplotlib.axes._subplots.AxesSubplot
The axes on which to plot.
data : pandas.core.frame.DataFrame
Represents an isotherm. Columns are "Pressure", "Loading", "P_rel", "BETy", "BET_y2", and "phi".
eswpoints : int
Helps calculate the slope at a point. The number of points around the point at which slope is to be computed.
maketitle : str
If set to "Yes", the plot will be titled; otherwise, not.
with_fit : str
If set to "Yes", the plot will include the BET fit, the BET+ESW fit, the BET region, and the BET+ESW region; otherwise, not.
fit_data : list
Information for BET and BET+ESW. In particular (for BET and for BET+ESW), the indices of the data points that start and end the chosen linear region (rbet), as well as a molar version of Xm (called qm here) and C. These last two are referred to as params in the code.
Returns
-------
None
"""
[loading, phi, minima, eswarea] = self.eswdata(data, eswpoints)
# ax.errorbar essentially is ax.plot with the settings used below. Makes a scatter. Benefit is that it shows up last in the legend.
ax.errorbar(
loading,
phi,
yerr=None,
fmt="o",
capsize=3,
label="Isotherm data points",
)
ax.set_ylim(ax.get_ylim())
ax.xaxis.label.set_text("q / mol/kg")
ax.yaxis.label.set_text("$\Phi$" + " / J/g")
if maketitle == "Yes":
ax.set_title("ESW Plot")
ax.set_xlim((0, ax.get_xlim()[1]))
bbox_props = dict(boxstyle="square", ec="k", fc="w", lw=1.0)
if with_fit == "Yes":
[bet_info, betesw_info] = fit_data
[rbet, bet_params] = bet_info
[rbetesw, betesw_params] = betesw_info
if rbet != (None, None):
ax.axvspan(
data.at[rbet[0], "Loading"],
data.at[rbet[1], "Loading"],
facecolor=plt.cm.PuOr(70),
edgecolor="none",
alpha=0.6,
label="BET region",
)
load_bet = self.th_loading(data["P_rel"].values, bet_params)
ax.plot(
load_bet,
self.gen_phi(load_bet, data["P_rel"].values),
color=plt.cm.PuOr(20),
label="BET fit",
)
if rbetesw != (None, None):
ax.axvspan(
data.at[rbetesw[0], "Loading"],
data.at[rbetesw[1], "Loading"],
facecolor=plt.cm.Greens(70),
edgecolor="none",
alpha=0.6,
label="BET+ESW region",
)
load_betesw = self.th_loading(data["P_rel"].values, betesw_params)
ax.plot(
load_betesw,
self.gen_phi(load_betesw, data["P_rel"].values),
color=plt.cm.Greens(200),
label="BET+ESW fit",
)
# Setting the y-axis limits to include more of the fit
# Only consider phi values that correspond to x values within our plotting range
phi_values = [
phi[i]
for i, value in enumerate(loading)
if ax.get_xlim()[0] <= value <= ax.get_xlim()[1]
]
y_min = min(phi_values) - 10
y_max = max(phi_values) + 10
ax.set_ylim(bottom=y_min, top=y_max)
if minima is not None:
ax.vlines(
data.at[minima, "Loading"],
ax.get_ylim()[0],
ax.get_ylim()[1],
colors=plt.cm.Greens(200),
linestyles="dashed",
label="First ESW minimum",
)
else:
ax.text(
0.03,
0.90,
"Minima not found",
horizontalalignment="left",
verticalalignment="center",
transform=ax.transAxes,
bbox=bbox_props,
)
if self.con1limit is not None:
ax.vlines(
data.at[self.con1limit, "Loading"],
ax.get_ylim()[0],
ax.get_ylim()[1],
colors=plt.cm.Purples(230),
linestyles="dashed",
label="Consistency 1 maximum",
)
if plotting_information["legend"] == "Yes": # Add a legend in this case.
ax.legend(loc="upper center")
# include ANOVA, t-tests, shapiro wilk test, outliers, generate graphs of residuals.
def linregauto(self, p, q, data):
"""
This function computes all the statistical parameters associated with the fitting of a line.
It also checks which consistency criteria the linear region satisfies and which ones it does not.
Parameters
----------
p : numpy.int64
The index of the data point that is chosen as the start of the linear region.
q : numpy.int64
The index of the data point that is chosen as the end of the linear region.
data : pandas.core.frame.DataFrame
Represents an isotherm. Columns are "Pressure", "Loading", "P_rel", "BETy", "BET_y2", and "phi".
Returns
-------
linear : pandas.core.frame.DataFrame
The initial data, but only the rows of the linear region.
stats : list
The results of various statistical tests.
C : float
See equation 6 of Fagerlund, G. (1973). Determination of specific surface by the BET method. Heat of adsorption in the first layer.
qm : float
See equation 5 of Fagerlund, G. (1973). Determination of specific surface by the BET method. Mass of adsorbate forming a monolayer on unit mass of adsorbent.
x_max : numpy.float64
The relative pressure at which BET_y2 is maximized. BET_y2 is defined in prepdata.
x_BET3 : numpy.float64
Value of relative pressure that corresponds to monolayer loading capacity.
x_BET4 : numpy.float64
Value used in the evaluation of the fourth Rouquerol consistency criterion.
con1 : str
"Yes" or "No", depending on whether the first consistency criterion is satisfied.
con2 : str
"Yes" or "No", depending on whether the second consistency criterion is satisfied.
con3 : str
"Yes" or "No", depending on whether the third consistency criterion is satisfied.
con4 : str
"Yes" or "No", depending on whether the fourth consistency criterion is satisfied.
A_BET : float
The predicted BET surface area.
"""
data = data.copy(deep=True)
linear = data[p:q] # Grab the rows of the DataFrame that correspond to the data points in the chosen linear region
results = smf.ols("BETy ~ P_rel", linear).fit()
intercept, slope = results.params
# We will perform all the statistical tests here.
# First, the whole model ANOVA test.
ftest = (results.fvalue, results.f_pvalue)
# Then, we will do the parameter tests. We won't really do the effect test, since there is
# only one variable.
Ttest = results.t_test(np.array([[1, 0], [0, 1]]))
ttest = (Ttest.tvalue, Ttest.pvalue)
influence = results.get_influence()
# We are using externally studentized residuals.
resid_stud = influence.get_resid_studentized_external()
# If any studentized residual is above 3, we will flag this as an outlier. Different softwares have
# different ways of flagging outliers, but we will use 3.0 (https://tinyurl.com/ycomecvg)
prel = linear["P_rel"].values
bety = linear["BETy"].values
isoutlier = "No"
preloutlier = False
betyoutlier = False
if np.absolute(resid_stud).max() > 3.0:
isoutlier = "Yes"
arrindexoutlier = np.where(resid_stud > 3.0)[0]
preloutlier = prel[arrindexoutlier]
betyoutlier = bety[arrindexoutlier]
outlierdata = [isoutlier, preloutlier, betyoutlier]
# Ultimately, we would like to highlight the outlier points on the graph.
# Now, we want to perform the Shapiro Wilk test on the residuals. We will perform it on normalized residuals.
norm_res = (resid_stud - resid_stud.mean()) / resid_stud.std()
shaptest = ss.shapiro(norm_res)
# Model adequacy
r2 = results.rsquared
r2adj = results.rsquared_adj
# Now, we want to pack the results of all these tests into a single list.
stats = [ftest, ttest, outlierdata, shaptest, r2, r2adj, results]
if intercept == 0.0:
intercept += 1e23
C = slope / intercept + 1
qm = 1 / (slope + intercept) # 1/(mol/kg framework)
# To check for 1st consistency criterion
# See https://doi.org/10.1021/acs.jpcc.9b02116 (3rd paragraph in introduction) for the consistency criteria
ind_max = self.con1limit
if ind_max is not None:
x_max = data[data.index == ind_max]["P_rel"].values[0]
else:
x_max = data["P_rel"][data["BET_y2"].idxmax()]
if linear["P_rel"].max() <= x_max:
con1 = "Yes"
else:
con1 = "No"
# Checking for second consistency criterion
if C > 0:
con2 = "Yes"
else:
con2 = "No"
# Checking if third consistency criterion is satisfied
lower_limit_y = data["Loading"][data["Loading"] <= qm].max()
upper_limit_y = data["Loading"][data["Loading"] > qm].min()
lower_limit_x = data["P_rel"][data["Loading"] <= qm].max()
upper_limit_x = data["P_rel"][data["Loading"] > qm].min()
# Now I will do a linear interpolation to figure out x
m = (upper_limit_y - lower_limit_y) / (upper_limit_x - lower_limit_x) # slope
x_BET3 = upper_limit_x - (upper_limit_y - qm) / m
if linear["P_rel"].min() <= x_BET3 <= linear["P_rel"].max():
con3 = "Yes"
else:
con3 = "No"
# Checking for fourth consistency criterion
x_BET4 = 1 / (scipy.sqrt(C) + 1)
if np.abs((x_BET4 - x_BET3) / x_BET3) < 0.2: # 20% tolerance
con4 = "Yes"
else:
con4 = "No"
# This is related to equation 1 of Fagerlund, G. (1973). Determination of specific surface by the BET method.
# qm[=]mmol/g[=]mol/kg
# self.N_A[=]atoms/mol
# self.selected_gas_cs[=]m²/atom
# Factor of 1000 to convert from mmol to mol.
# A_BET[=]m²/g
A_BET = qm * self.N_A * self.selected_gas_cs / 1000 # m²/g
return [
linear,
stats,
C,
qm,
x_max,
x_BET3,
x_BET4,
con1,
con2,
con3,
con4,
A_BET,
]
def picklen(self, data, method="BET+ESW"):
"""
The objective of this function is to choose a linear region.
-------------------------------------------------------------------------------------------------------------------------------------
HOWEVER, WE MUST EMPHASIZE THAT THE PROCESS OF CHOOSING A LINEAR REGION IS HIGHLY DEPENDENT ON THE QUALITY OF THE DATA. DO NOT TAKE
THE RESULT OF THIS FUNCTION AS FINAL. HUMAN INTERFERENCE IS HIGHLY RECOMMENDED FOR THIS STEP.
-------------------------------------------------------------------------------------------------------------------------------------
We are trying to make this process objective. The way we will go about this is that we will start choosing linear regions from the largest
to the smallest. We will assign priority in the following order:
1. No. of consistency criteria fulfilled (among the 3rd and 4th)
2. Length of the region.
3. R2 value (we will keep that as a lower limit)