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Functions.py
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# -*- coding: utf-8 -*-
import math
import os
import pickle as pkl
import scipy
from scipy import signal
import scipy.signal
from scipy.optimize import curve_fit, OptimizeWarning
from scipy.signal import find_peaks
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from matplotlib.ticker import EngFormatter
from numpy import linalg as lin
from scipy import constants as cst
from scipy.optimize import curve_fit
import LoadData #for MakeIv
import pywt #for WaveletDenoising
def GetSmallMoS2PoreSize(Conductance, Sigma_Bulk=11.18):
"""
Function used to calculate pore size of small MoS2 pore:
1. Pérez M.D.B., Nicolaï A., Delarue P., Meunier V., Drndić M., Senet P. (2019). Improved model of ionic transport in 2-D MoS 2 membranes with sub-5 nm pores. Appl. Phys. Lett. 114, 023107.
doi: 10.1063/1.5061825
Parameters
----------
Conductance : float
Measured conductance.
Sigma_Bulk : float
conductivity of the buffer (bulk).
Returns
-------
scalar. Pore size in nm
"""
def SmallMoS2PoreConductance(d, sigma_bulk):
# All in nanometers
l = 0.96
phi_Cl = 0.793
phi_K = 0.832
delta_Cl = 0.41
delta_K = 0.38
epsilon_K = 1.03
epsilon_Cl = 0.97
A = sigma_bulk / 2 * 1 / ((4 * l + np.pi * d) / (np.pi * d ** 2))
B_Cl = np.exp((-4 * phi_Cl) / (np.pi * d ** 2)) * (d) / (delta_Cl + epsilon_Cl * d)
B_K = np.exp((-4 * phi_K) / (np.pi * d ** 2)) * (d) / (delta_K + epsilon_K * d)
return A * (B_Cl + B_K)
def DrndicModelRootEquation(d, G, sigma_bulk):
return SmallMoS2PoreConductance(d, sigma_bulk) - G
return scipy.optimize.fsolve(DrndicModelRootEquation, 10, (Conductance, Sigma_Bulk))
def LowPass(data, samplerate, lowPass):
"""
Function used to filter data with a digital Bessel filter of the 4th order.
Specially useful for high bandwidth recordings.
Parameters
----------
data :
Data to be filtered.
samplerate : float
Sampling frequency of the data aquisition.
lowPass : float
Cutoff frequency of the filter.
Returns
-------
dict
Dictionary output of the filtered data with in keys:
'i1' : a list of the currents filtered
'samplerate' : float of new sampling frequency corresponding to 2*Cutoff frequency (Nyquist-Shannon sampling theorem).
"""
Wn = round(2 * lowPass / samplerate, 4) # [0,1] nyquist frequency
b, a = signal.bessel(4, Wn, btype='low', analog=False) # 4-th order digital filter
z, p, k = signal.tf2zpk(b, a)
eps = 1e-9
r = np.max(np.abs(p))
approx_impulse_len = int(np.ceil(np.log(eps) / np.log(r)))
Filt_sig = (signal.filtfilt(b, a, data, method='gust', irlen=approx_impulse_len))
ds_factor = np.ceil(samplerate / (2 * lowPass))
output = {}
output['data'] = scipy.signal.resample(Filt_sig, int(len(data) / ds_factor))
output['samplerate'] = samplerate / ds_factor
return output
def WaveletDenoising(data, decompositionLevel = 5):
"""
Function used to remove noise from a signal using wavelet denoising with a bio-orthogonal wavelet implemented in the
PyWavelets package.PyWavelets is open source wavelet transform software for Python.
It uses Stationary Wavelet Transforms and a hard detail coefficients thresholding.
See Shekar, Siddharth, et al. "Wavelet denoising of high-bandwidth nanopore and Ion channel signals".
Nano letters (2019). DOI: 10.1021/acs.nanolett.8b04388
Parameters
----------
data : numpy array
Data to be filtered.
decompositionLevel : int
Maximum decomposition level for the wavelet transform.
Returns
-------
dict
Dictionary output of the filtered data with in keys:
'data' : a list of the current signal filtered
"""
#choose a wavelet basis - Here bio-orthogonal
wavelet = pywt.Wavelet('bior1.5')
N = len(data)
#choose a maximum decomposition level -> function parameter
#compute the wavelet transform for the signal x[n] to obtain detail coefficients wj,k (cD) and approximation coefficients aJ,k (cA) where j=1, ..., J and k = 1, ..., N
coeffs = pywt.swt(data, wavelet, level = decompositionLevel) #multilevel reconstruction in the paper they used 5, 7 and 8 levels
#calculate the noise threshold lambdaj for wj,k
newcoeffs=[]
j=0
while j < decompositionLevel:
sigma=np.median(abs(coeffs[j][1]-np.mean(coeffs[j][1])))/0.6745
l = sigma*np.sqrt(2*np.log(N))
#choose thresholding scheme T and threshold wj,k to obtain w'j,k = T(wj,k)
newcoeffs.append(tuple((np.array(coeffs[j][0]) , np.array(pywt.threshold(coeffs[j][1], value = l, mode='hard')))))
j=j+1
#perform the inerse wavelet transform using aj,k and w'j,k
output = {}
output['data'] = pywt.iswt(newcoeffs, wavelet) #multilevel reconstruction
return output
def GetKClConductivity(Conc, Temp):
p = pkl.load(open('KCl_ConductivityValues.p', 'rb'))
if Conc == 1.0:
Conc = np.uint(1)
return np.polyval(p[str(Conc)], Temp)
def GetTempFromKClConductivity(Conc, Cond):
p = pkl.load(open('KCl_ConductivityValues.p', 'rb'))
if Conc == 1.0:
Conc = np.uint(1)
return (Cond - p[str(Conc)][1]) / p[str(Conc)][0]
def RecursiveLowPassFast(signal, coeff, samplerate):
"""
Function used to find where roughly where event are in a noisy signal using a first order recursive
low pass filter defined as :
u[k] = au[k-1]+(1-a)i[k]
with u the mean value at sample k, i the input signal and a < 1, a parameter.
Parameters
----------
signal : numpy array of float
Input signal.
coeff: dict
Coefficients used in the recursive low pass detection of rough events.
samplerate : float
Sampling frequency of the data aquisition.
Returns
-------
numpy array of float
Array with the rough event locations in the input signal.
"""
padlen = np.uint64(samplerate)
prepadded = np.ones(padlen) * np.mean(signal[0:1000])
signaltofilter = np.concatenate((prepadded, signal))
mltemp = scipy.signal.lfilter([1 - coeff['a'], 0], [1, -coeff['a']], signaltofilter)
vltemp = scipy.signal.lfilter([1 - coeff['a'], 0], [1, -coeff['a']], np.square(signaltofilter - mltemp))
ml = np.delete(mltemp, np.arange(padlen))
vl = np.delete(vltemp, np.arange(padlen))
sl = ml - coeff['S'] * np.sqrt(vl)
Ni = len(signal)
points = np.array(np.where(signal <= sl)[0])
to_pop = np.array([])
for i in range(1, len(points)):
if points[i] - points[i - 1] == 1:
to_pop = np.append(to_pop, i)
points = np.unique(np.delete(points, to_pop))
RoughEventLocations = []
NumberOfEvents = 0
for i in points:
if NumberOfEvents is not 0:
if i >= RoughEventLocations[NumberOfEvents - 1][0] and i <= RoughEventLocations[NumberOfEvents - 1][1]:
continue
NumberOfEvents += 1
start = i
El = ml[i] + coeff['E'] * np.sqrt(vl[i])
Mm = ml[i]
Vv = vl[i]
duration = 0
endp = start
if (endp + 1) < len(signal):
while signal[endp + 1] < El and endp < (Ni - 2): # and duration < coeff['maxEventLength']*samplerate:
duration += 1
endp += 1
if duration >= coeff['maxEventLength'] * samplerate or endp > (
Ni - 10): # or duration <= coeff['minEventLength'] * samplerate:
NumberOfEvents -= 1
continue
else:
k = start
while signal[k] < Mm and k > 1:
k -= 1
start = k - 1
k2 = i + 1
# while signal[k2] > Mm:
# k2 -= 1
# endp = k2
if start < 0:
start = 0
RoughEventLocations.append((start, endp, ml[start], vl[start]))
return np.array(RoughEventLocations) # , ml, vl, sl
def RecursiveLowPassFastUp(signal, coeff, samplerate):
"""
RecursiveLowPassFast function specially written for the detection of events characterized
not by a current drop, but by a current increase.
Parameters
----------
signal : numpy array of float
Input signal.
coeff: dict
Coefficients used in the recursive low pass detection of rough events.
samplerate : float
Sampling frequency of the data aquisition.
Returns
-------
numpy array of float
Array with the rough event locations in the input signal.
"""
ml = scipy.signal.lfilter([1 - coeff['a'], 0], [1, -coeff['a']], signal)
vl = scipy.signal.lfilter([1 - coeff['a'], 0], [1, -coeff['a']], np.square(signal - ml))
sl = ml + coeff['S'] * np.sqrt(vl)
Ni = len(signal)
points = np.array(np.where(signal >= sl)[0])
to_pop = np.array([])
for i in range(1, len(points)):
if points[i] - points[i - 1] == 1:
to_pop = np.append(to_pop, i)
points = np.delete(points, to_pop)
points = np.delete(points, np.array(np.where(points == 0)[0]))
RoughEventLocations = []
NumberOfEvents = 0
for i in points:
if NumberOfEvents is not 0:
if i >= RoughEventLocations[NumberOfEvents - 1][0] and i <= RoughEventLocations[NumberOfEvents - 1][1]:
continue
NumberOfEvents += 1
start = i
El = ml[i] + coeff['E'] * np.sqrt(vl[i])
Mm = ml[i]
duration = 0
while signal[i + 1] > El and i < (Ni - 2) and duration < coeff['maxEventLength'] * samplerate:
duration += 1
i += 1
if duration >= coeff['maxEventLength'] * samplerate or i > (Ni - 10):
NumberOfEvents -= 1
else:
k = start
while signal[k] > Mm and k > 2:
k -= 1
start = k - 1
k2 = i + 1
while signal[k2] > Mm:
k2 -= 1
endp = k2
RoughEventLocations.append((start, endp, ml[start], vl[start]))
return np.array(RoughEventLocations)
def Reshape1DTo2D(inputarray, buffersize):
npieces = int(len(inputarray) / buffersize)
voltages = np.array([], dtype=np.float64)
currents = np.array([], dtype=np.float64)
for i in range(1, npieces + 1):
if i % 2 == 1:
currents = np.append(currents, inputarray[(i - 1) * buffersize:i * buffersize - 1], axis=0)
# print('Length Currents: {}'.format(len(currents)))
else:
voltages = np.append(voltages, inputarray[(i - 1) * buffersize:i * buffersize - 1], axis=0)
# print('Length Voltages: {}'.format(len(voltages)))
v1 = np.ones((len(voltages)), dtype=np.float64)
i1 = np.ones((len(currents)), dtype=np.float64)
v1[:] = voltages
i1[:] = currents
out = {'v1': v1, 'i1': i1}
#print('Currents:' + str(v1.shape))
#print('Voltages:' + str(i1.shape))
return out
#def PoreFromIVFile(file)
def MakeIVData(output, approach='exponential', delay=0.7, UseVoltageRange=0, verbose=True):
"""
Function used to build and analyse a dataset containing the applied voltages
and measured currents during a voltage sweep experiment.
Used to assess the linearity and drift of the resulting signal through a Nanopore.
MakeIVData can use 2 types of approaches to find the right current-voltage points:
approach = 'mean': the default argument, will use the Mean method. Its better to
use it for flat signals (low capacitance nanopore substrates for example).
approach = 'exponential': is to be used if there is a decay in the signal usually
due to a capacitive effet of the membrane.
Parameters
----------
output : dict
Output format of the OpenFile function of the LoadData module with the signal to use for the I-V characteristic curve points calculations.
approach : str, optional
'mean' by default. Specifies the method to extimate current-voltage data points for the I-V curve 'mean' or 'exponential'.
delay : float, optional
0.7 by default. Time delay in seconds before the first change of applied voltage.
UseVoltageRange : float, optional
0 by default.
verbose : bool, optional
False by default. If True, it will allow to print strings indicating the progress of the function in the console.
Returns
-------
dict
all the values and parameters necessary to draw an I-V characteristic plot.
"""
(ChangePoints, sweepedChannel) = CutDataIntoVoltageSegments(output, verbose)
if ChangePoints is 0:
return 0
if output['graphene']:
currents = ['i1', 'i2']
else:
currents = ['i1']
Values = output[sweepedChannel][ChangePoints]
Values = np.append(Values, output[sweepedChannel][::-1][0])
delayinpoints = np.int64(delay * output['samplerate'])
if delayinpoints > ChangePoints[0]:
raise ValueError("Delay is longer than Changepoint")
# Store All Data
All = {}
for current in currents:
Item = {}
ItemExp = {}
l = len(Values)
Item['Voltage'] = np.zeros(l)
Item['StartPoint'] = np.zeros(l, dtype=np.uint64)
Item['EndPoint'] = np.zeros(l, dtype=np.uint64)
Item['Mean'] = np.zeros(l)
Item['STD'] = np.zeros(l)
Item['SE'] = np.zeros(l)
Item['SweepedChannel'] = sweepedChannel
ItemExp['SweepedChannel'] = sweepedChannel
Item['YorkFitValues'] = {}
ItemExp['YorkFitValues'] = {}
### MEAN METHOD###
# First item
Item['Voltage'][0] = Values[0]
trace = output[current][0 + delayinpoints:ChangePoints[0]]
Item['StartPoint'][0] = 0 + delayinpoints
Item['EndPoint'][0] = ChangePoints[0]
Item['Mean'][0] = np.mean(trace)
isProblematic = math.isclose(Values[0], 0, rel_tol=1e-3) or math.isclose(Values[0], np.min(Values),
rel_tol=1e-3) or math.isclose(
Values[0], np.max(Values), rel_tol=1e-3)
if sweepedChannel is 'v2' and isProblematic:
print('In Problematic If for Values: {}, index {}'.format(Values[0], 0))
Item['STD'][0] = np.std(trace[-np.int64(output['samplerate']):])
else:
Item['STD'][0] = np.std(trace)
Item['SE'][0] = Item['STD'][0] / np.sqrt(len(trace))
for i in range(1, len(Values) - 1):
trace = output[current][ChangePoints[i - 1] + delayinpoints: ChangePoints[i]]
Item['Voltage'][i] = Values[i]
Item['StartPoint'][i] = ChangePoints[i - 1] + delayinpoints
Item['EndPoint'][i] = ChangePoints[i]
if len(trace) > 0:
Item['Mean'][i] = np.mean(trace)
isProblematic = math.isclose(Values[i], 0, rel_tol=1e-3) or math.isclose(Values[i], np.min(Values),
rel_tol=1e-3) or math.isclose(
Values[i], np.max(Values), rel_tol=1e-3)
if sweepedChannel is 'v2' and isProblematic:
print('In Problematic If for Values: {}, index {}'.format(Values[i], i))
Item['STD'][i] = np.std(trace[-np.int64(output['samplerate']):])
else:
Item['STD'][i] = np.std(trace)
Item['SE'][i] = Item['STD'][i] / np.sqrt(len(trace))
if verbose:
print('{}, {},{}'.format(i, ChangePoints[i - 1] + delayinpoints, ChangePoints[i]))
else:
Item['Mean'][i] = np.NaN
Item['STD'][i] = np.NaN
# Last
if 1:
trace = output[current][ChangePoints[len(ChangePoints) - 1] + delayinpoints: len(output[current]) - 1]
Item['Voltage'][-1:] = Values[len(Values) - 1]
Item['StartPoint'][-1:] = ChangePoints[len(ChangePoints) - 1] + delayinpoints
Item['EndPoint'][-1:] = len(output[current]) - 1
if len(trace) > 0:
Item['Mean'][-1:] = np.mean(trace)
isProblematic = math.isclose(Values[-1:], 0, rel_tol=1e-3) or math.isclose(Values[-1:], np.min(Values),
rel_tol=1e-3) or math.isclose(
Values[-1:], np.max(Values), rel_tol=1e-3)
if sweepedChannel is 'v2' and isProblematic:
print('In Problematic If for Values: {}, index {}'.format(Values[-1:], i))
Item['STD'][-1:] = np.std(trace[-np.int64(output['samplerate']):])
else:
Item['STD'][-1:] = np.std(trace)
else:
Item['Mean'][-1:] = np.NaN
Item['STD'][-1:] = np.NaN
Item['SE'][-1:] = Item['STD'][-1:] / np.sqrt(len(trace))
## GET RECTIFICATION FACTOR
parts = {'pos': Item['Voltage'] > 0, 'neg': Item['Voltage'] < 0}
a = {}
b = {}
sigma_a = {}
sigma_b = {}
b_save = {}
x_values = {}
for part in parts:
(a[part], b[part], sigma_a[part], sigma_b[part], b_save[part]) = YorkFit(
Item['Voltage'][parts[part]].flatten(), Item['Mean'][parts[part]].flatten(),
1e-12 * np.ones(len(Item['Voltage'][parts[part]].flatten())),
Item['STD'][parts[part]].flatten())
factor = b['neg'] / b['pos']
Item['Rectification'] = factor
ItemExp['Rectification'] = factor
###EXPONENTIAL METHOD###
if approach is not 'mean':
l = 1000
ItemExp['StartPoint'] = np.zeros(l, dtype=np.uint64)
ItemExp['EndPoint'] = np.zeros(l, dtype=np.uint64)
baselinestd = np.std(output[current][0:np.int64(1 * output['samplerate'])])
dataset = pd.Series(output[current])
movingstd = dataset.rolling(10).std()
# Extract The Desired Parts
ind = (np.abs(movingstd - baselinestd) < 1e-9) & (np.abs(output[current]) < np.max(output[current]) / 2)
# How Many Parts?
restart = True
counter = 0
for i, value in enumerate(ind):
if value and restart:
ItemExp['StartPoint'][counter] = i
print('Start: {}\t'.format(i))
restart = False
elif not value and not restart:
if ((i - 1) - ItemExp['StartPoint'][counter]) > 1 * output['samplerate']:
ItemExp['EndPoint'][counter] = i - 1
print('End: {}'.format(i - 1))
restart = True
counter += 1
else:
restart = True
if not restart:
counter += 1
ItemExp['EndPoint'][counter] = len(ind)
ItemExp['StartPoint'] = ItemExp['StartPoint'][np.where(ItemExp['StartPoint'])]
ItemExp['EndPoint'] = ItemExp['EndPoint'][np.where(ItemExp['EndPoint'])]
NumberOfPieces = len(ItemExp['StartPoint'])
ItemExp['Voltage'] = np.zeros(NumberOfPieces)
ItemExp['ExpValues'] = np.zeros((3, NumberOfPieces))
ItemExp['STD'] = np.zeros(NumberOfPieces)
ItemExp['Mean'] = np.zeros(NumberOfPieces)
# Make It Piecewise
for i in np.arange(0, NumberOfPieces):
trace = output[current][ItemExp['StartPoint'][i]:ItemExp['EndPoint'][i]]
popt, pcov = MakeExponentialFit(np.arange(len(trace)) / output['samplerate'], trace)
ItemExp['Voltage'][i] = output[sweepedChannel][ItemExp['StartPoint'][i]]
if popt[0]:
ItemExp['ExpValues'][:, i] = popt
ItemExp['Mean'][i] = popt[2]
try:
ItemExp['STD'][i] = np.sqrt(np.diag(pcov))[2]
except RuntimeWarning:
ItemExp['STD'][i] = np.std(trace) / np.sqrt(len(trace))
print('ExpFit: STD of voltage {} failed calculating...'.format(ItemExp['Voltage'][i]))
else:
print('Exponential Fit on for ' + current + ' failed at V=' + str(ItemExp['Voltage'][0]))
ItemExp['Mean'][i] = np.mean(trace)
ItemExp['STD'][i] = np.std(trace)
## FIT THE EXP CALCULATED VALUES ###
(a, b, sigma_a, sigma_b, b_save) = YorkFit(ItemExp['Voltage'], ItemExp['Mean'],
1e-12 * np.ones(len(ItemExp['Voltage'])), ItemExp['STD'])
x_fit = np.linspace(min(Item['Voltage']), max(Item['Voltage']), 1000)
y_fit = scipy.polyval([b, a], x_fit)
ItemExp['YorkFitValues'] = {'x_fit': x_fit, 'y_fit': y_fit, 'Yintercept': a, 'Slope': b,
'Sigma_Yintercept': sigma_a,
'Sigma_Slope': sigma_b, 'Parameter': b_save}
All[current + '_Exp'] = ItemExp
##Remove NaNs
nans = np.isnan(Item['Mean'][:])
nans = np.logical_not(nans)
Item['Voltage'] = Item['Voltage'][nans]
Item['StartPoint'] = Item['StartPoint'][nans]
Item['EndPoint'] = Item['EndPoint'][nans]
Item['Mean'] = Item['Mean'][nans]
Item['STD'] = Item['STD'][nans]
Item['SE'] = Item['SE'][nans]
## Restrict to set voltage Range
if UseVoltageRange is not 0:
print('Voltages Cut')
ind = np.argwhere((Item['Voltage'] >= UseVoltageRange[0]) & (Item['Voltage'] <= UseVoltageRange[1]))
Item['Voltage'] = Item['Voltage'][ind].flatten()
Item['StartPoint'] = Item['StartPoint'][ind].flatten()
Item['EndPoint'] = Item['EndPoint'][ind].flatten()
Item['Mean'] = Item['Mean'][ind].flatten()
Item['STD'] = Item['STD'][ind].flatten()
Item['SE'] = Item['SE'][ind].flatten()
## FIT THE MEAN CALCULATED VALUES ###
# Yorkfit
(a, b, sigma_a, sigma_b, b_save) = YorkFit(Item['Voltage'].flatten(), Item['Mean'].flatten(),
1e-9 * np.ones(len(Item['Voltage'])), Item['STD'].flatten())
x_fit = np.linspace(min(Item['Voltage']), max(Item['Voltage']), 1000)
y_fit = scipy.polyval([b, a], x_fit)
Item['YorkFit'] = {'x_fit': x_fit, 'y_fit': y_fit, 'Yintercept': a, 'Slope': b, 'Sigma_Yintercept': sigma_a,
'Sigma_Slope': sigma_b, 'Parameter': b_save}
# Polyfit
p = np.polyfit(Item['Voltage'].flatten(), Item['Mean'].flatten(), 1)
x_fit2 = np.linspace(min(Item['Voltage']), max(Item['Voltage']), 1000)
y_fit2 = scipy.polyval(p, x_fit)
Item['PolyFit'] = {'x_fit': x_fit2, 'y_fit': y_fit2, 'Yintercept': p[1], 'Slope': p[0]}
All[current] = Item
All['Currents'] = currents
return All
def ExpFunc(x, a, b, c):
"""
Function used to create an exponential function used MakeIVData to fit the signal around the capacitive drift and therefore
predict the stabilised current signal at each voltage jump in the MakeIV function.
Parameters
----------
x : numpy array
Input values.
a : float
b : float
c : flaot
Returns
-------
numpy array
a*exp(-b*x)+c function.
"""
return a * np.exp(-b * x) + c
def fourier(x, a0, w, *a):
n = int(len(a) / 2)
ret = a0
for i in range(0, n):
ret += a[i] * np.cos((i + 1) * w * x)
ret += a[i + n] * np.sin((i + 1) * w * x)
return ret
def gaussian(x,b,a,mu,sigma):
ret = b - a * np.exp(-0.5 * ((x - mu) / sigma) **2)
return ret
def ImpulseFitting(trace, baseline, samplerate,verbose=False):
baseline = baseline * 1e9
trace = trace * 1e9
time = np.linspace(0, len(trace) / samplerate, num=len(trace))
# Gaussian fitting
b = baseline
a = baseline - np.min(trace) # shortEvent.currentDrop*1e9
mu = np.argmin(trace) / samplerate # len(time)/(2*samplerate)
sigma_g = (len(time) - 50) / (8 * samplerate)
p0 = [b, a, mu, sigma_g]
try:
popt, pcov = curve_fit(gaussian, time, trace, p0, method='trf')
perr = np.sqrt(np.diag(pcov))
if verbose:
print('error in fitting parameters:')
print(perr)
except RuntimeError or OptimizeWarning:
return -1
fitTrace = gaussian(time, *popt)
if verbose:
ss_res = sum((trace - fitTrace) ** 2)
ss_tot = sum((np.mean(trace) - trace) ** 2)
r2 = 1 - ss_res / ss_tot
print('RSquared of fit: {r:1.3f}'.format(r=r2))
# Calculate differential
diffTrace = np.diff(np.diff(fitTrace))
peaks, _ = find_peaks(diffTrace)
peaks = np.array([i for i in peaks if trace[i]])
maxdata = peaks[np.argsort(diffTrace[peaks])] if len(peaks) > 0 else [-3]
peaks2, _ = find_peaks(-1 * diffTrace)
# find starting and end points
pe1 = maxdata[-1] + 2
peaks2_ = [i for i in peaks2 if i < pe1]
ps1 = max(peaks2_) if len(peaks2_) > 0 else -1
peaks2_ = [i for i in peaks2 if i > pe1]
pe2 = min(peaks2_) + 2 if len(peaks2_) > 0 else -1
if ps1 > -1 and pe2 > -1 and pe1 > -1:
ss_res = sum((trace[ps1:pe2] - fitTrace[ps1:pe2])**2)
# ss_reg = sum((np.mean(trace[ps1:pe2]) - fitTrace[ps1:pe2])**2)
ss_tot = sum((np.mean(trace[ps1:pe2]) - trace[ps1:pe2])**2)
r2drop = 1 - ss_res / ss_tot
# area = baseline * (pe2-ps1) - sum(trace[ps1:pe2])
area = baseline * (pe2 - ps1) - sum(fitTrace[ps1:pe2])
Idrop = (area / (pe1 - ps1)) * 1e-9
else:
return -2
return ps1, pe1, pe2, r2drop, Idrop
def YorkFit(X, Y, sigma_X, sigma_Y, r=0):
"""
Function used to do the linear regression taking the error into account as the standard deviation.
It is used in MakeIV, for the estimation of the linear regression curve of voltage versus current,
estimated by a voltage sweep experiment.
Parameters
----------
X : numpy array
Y : numpy array
sigma_X : numpy array
signma_Y : numpy array
r : float, optional
Returns
-------
tuple
coefficients a and b of the linear regression y=ax+b and their variances.
"""
N_itermax = 10 # maximum number of interations
tol = 1e-15 # relative tolerance to stop at
N = len(X)
temp = np.matrix([X, np.ones(N)])
# make initial guess at b using linear squares
tmp = np.matrix(Y) * lin.pinv(temp)
b_lse = np.array(tmp)[0][0]
# a_lse=tmp(2);
b = b_lse # initial guess
omega_X = np.true_divide(1, np.power(sigma_X, 2))
omega_Y = np.true_divide(1, np.power(sigma_Y, 2))
alpha = np.sqrt(omega_X * omega_Y)
b_save = np.zeros(N_itermax + 1) # vector to save b iterations in
b_save[0] = b
for i in np.arange(N_itermax):
W = omega_X * omega_Y / (omega_X + b * b * omega_Y - 2 * b * r * alpha)
X_bar = np.sum(W * X) / np.sum(W)
Y_bar = np.sum(W * Y) / np.sum(W)
U = X - X_bar
V = Y - Y_bar
beta = W * (U / omega_Y + b * V / omega_X - (b * U + V) * r / alpha)
b = sum(W * beta * V) / sum(W * beta * U)
b_save[i + 1] = b
if np.abs((b_save[i + 1] - b_save[i]) / b_save[i + 1]) < tol:
break
a = Y_bar - b * X_bar
x = X_bar + beta
y = Y_bar + b * beta
x_bar = sum(W * x) / sum(W)
y_bar = sum(W * y) / sum(W)
u = x - x_bar
# %v=y-y_bar
sigma_b = np.sqrt(1 / sum(W * u * u))
sigma_a = np.sqrt(1. / sum(W) + x_bar * x_bar * sigma_b * sigma_b)
return (a, b, sigma_a, sigma_b, b_save)
def DoubleExpFunc(x, Y0, percentFast, plateau, Kfast, Kslow):
SpanFast = (Y0 - plateau) * percentFast * 0.01
SpanSlow = (Y0 - plateau) * (100 - percentFast) * 0.01
return plateau + ((Y0 - plateau) * percentFast * 0.01) * np.exp(-Kfast * x) + (
(Y0 - plateau) * (100 - percentFast) * 0.01) * np.exp(-Kslow * x)
def MakeExponentialFit(xdata, ydata):
try:
popt, pcov = curve_fit(ExpFunc, xdata, ydata, method='lm', xtol=1e-20, ftol=1e-12, gtol=1e-20)
# popt, pcov = curve_fit(DoubleExpFunc, xdata, ydata, p0 = (ydata[0], 50, ydata[-1], 1 / 15, 1 / 60))
return (popt, pcov)
except RuntimeError:
popt = (0, 0, 0)
pcov = 0
return (popt, pcov)
def CutDataIntoVoltageSegments(output, verbose=False):
"""
Function used to make the I-V curve (in MakeIVData). It cuts the data in segments
where a constant voltage was applied.
Parameters
----------
output : dict
Output format of the OpenFile function of the LoadData module with the signal to use for the I-V characteristic curve points calculations.
verbose : bool, optional
False by default. If True, it will allow to print strings indicating the progress of the function in the console.
Returns
-------
tuple
ChangePoints: ndarray with data points where the voltage applied changed
sweepedChannel: string with the key giving acess to the stored the voltage values applied.
"""
sweepedChannel = ''
if output['type'] == 'ChimeraNotRaw' or (output['type'] == 'Axopatch' and not output['graphene']):
ChangePoints = np.where(np.diff(output['v1']))[0]
sweepedChannel = 'v1'
if len(ChangePoints) is 0:
print('No voltage sweeps in this file:\n{}'.format(output['filename']))
return (0, 0)
elif (output['type'] == 'Axopatch' and output['graphene']):
ChangePoints = np.where(np.diff(output['v1']))[0]
sweepedChannel = 'v1'
if len(ChangePoints) is 0:
ChangePoints = np.where(np.diff(output['v2']))[0]
if len(ChangePoints) is 0:
print('No voltage sweeps in this file')
return (0, 0)
else:
sweepedChannel = 'v2'
if verbose:
print('Cutting into Segments...\n{} change points detected in channel {}...'.format(len(ChangePoints),
sweepedChannel))
return (ChangePoints, sweepedChannel)
def CalculatePoreSize(G, L, s):
# https://doi.org/10.1088/0957-4484/22/31/315101
return (G + np.sqrt(G * (G + 16 * L * s / np.pi))) / (2 * s)
def CalculateCapillarySize(G, D=0.3e-3, t=3.3e-3, s=10.5):
# DOI: 10.1021/nn405029j
# s=conductance (10.5 S/m at 1M KCl)
# t=taper length (3.3 mm)
# D=diameter nanocapillary at the shaft (0.3 mm)
return G * (4 * t / np.pi + 0.5 * D) / (s * D - 0.5 * G)
def CalculateShrunkenCapillarySize(G, D=0.3e-3, t=3.3e-3, s=10.5, ts=500e-9, Ds=500e-9):
# DOI: 10.1021/nn405029j
# s=conductance (10.5 S/m at 1M KCl)
# t=taper length (3.3 mm)
# D=diameter nanocapillary at the shaft (0.3 mm)
# ts=taper length of the shrunken part (543nm fit)
# Ds=diameter nanocapillary at the shrunken part (514nm fit)
return G * D * (8 * ts / np.pi + Ds) / ((2 * s * D * Ds) - (G * (8 * t / np.pi + Ds)))
def CalculateConductance(L, s, d):
return s * 1 / (4 * L / (np.pi * d ** 2) + 1 / d)
def GetSurfaceChargeFromLeeEquation(s, c, D, G, L, A, B, version=1):
lDu = 1 / (8 * np.pi * B * D * s) * (
version * np.sqrt(
(4 * np.pi * A * D ** 2 * s + np.pi * B * D ** 2 * s - 4 * B * G * L - 8 * np.pi * D * G) ** 2
- 16 * np.pi * B * D * s * (np.pi * A * D ** 3 * s - 4 * A * D * G * L - 2 * np.pi * D ** 2 * G))
- 4 * np.pi * A * D ** 2 * s - np.pi * B * D ** 2 * s + 4 * B * G * L + 8 * np.pi * D * G
)
e = cst.elementary_charge
Na = cst.Avogadro
return lDu * (2 * c * Na * 1e3 * e)
def ConductivityFromConductanceModel(L, d, G):
return G * (4 * L / (np.pi * d ** 2) + 1 / d)
def RefinedEventDetection(out, AnalysisResults, signals, limit):
for sig in signals:
# Choose correct reference
if sig is 'i1_Up':
sig1 = 'i1'
elif sig is 'i2_Up':
sig1 = 'i2'
else:
sig1 = sig
if sig is 'i1' or 'i1_Up':
volt = 'v1'
elif sig is 'i2' or 'i2_Up':
volt = 'v2'
if len(AnalysisResults[sig]['RoughEventLocations']) > 1:
startpoints = np.uint64(AnalysisResults[sig]['RoughEventLocations'][:, 0])
endpoints = np.uint64(AnalysisResults[sig]['RoughEventLocations'][:, 1])
localBaseline = AnalysisResults[sig]['RoughEventLocations'][:, 2]
localVariance = AnalysisResults[sig]['RoughEventLocations'][:, 3]
CusumBaseline = 500
numberofevents = len(startpoints)
AnalysisResults[sig]['StartPoints'] = startpoints
AnalysisResults[sig]['EndPoints'] = endpoints
AnalysisResults[sig]['LocalBaseline'] = localBaseline
AnalysisResults[sig]['LocalVariance'] = localVariance
AnalysisResults[sig]['NumberOfEvents'] = len(startpoints)
deli = np.zeros(numberofevents)
dwell = np.zeros(numberofevents)
fitvalue = np.zeros(numberofevents)
AllEvents = []
#####FIX THE UP AND DOWN STORY!! ALL THE PROBLEMS ARE IN HERE...
for i in range(numberofevents):
length = endpoints[i] - startpoints[i]
if out[sig1][startpoints[i]] < 0 and (sig == 'i1_Up' or sig == 'i2_Up'):
if length <= limit and length > 3:
# Impulsion Fit to minimal value
fitvalue[i] = np.max(out[sig1][startpoints[i] + np.uint(1):endpoints[i] - np.uint(1)])
elif length > limit:
fitvalue[i] = np.mean(out[sig1][startpoints[i] + np.uint(5):endpoints[i] - np.uint(5)])
else:
fitvalue[i] = np.max(out[sig1][startpoints[i]:endpoints[i]])
deli[i] = -(localBaseline[i] - fitvalue[i])
elif out[sig1][startpoints[i]] < 0 and (sig == 'i1' or sig == 'i2'):
if length <= limit and length > 3:
# Impulsion Fit to minimal value
fitvalue[i] = np.min(out[sig1][startpoints[i] + np.uint(1):endpoints[i] - np.uint(1)])
elif length > limit:
fitvalue[i] = np.mean(out[sig1][startpoints[i] + np.uint(5):endpoints[i] - np.uint(5)])
else:
fitvalue[i] = np.min(out[sig1][startpoints[i]:endpoints[i]])
deli[i] = -(localBaseline[i] - fitvalue[i])
elif out[sig1][startpoints[i]] > 0 and (sig == 'i1_Up' or sig == 'i2_Up'):
if length <= limit and length > 3:
# Impulsion Fit to minimal value
fitvalue[i] = np.max(out[sig1][startpoints[i] + np.uint(1):endpoints[i] - np.uint(1)])
elif length > limit:
fitvalue[i] = np.mean(out[sig1][startpoints[i] + np.uint(5):endpoints[i] - np.uint(5)])
else:
fitvalue[i] = np.max(out[sig1][startpoints[i]:endpoints[i]])
deli[i] = (localBaseline[i] - fitvalue[i])
elif out[sig1][startpoints[i]] > 0 and (sig == 'i1' or sig == 'i2'):
if length <= limit and length > 3:
# Impulsion Fit to minimal value
fitvalue[i] = np.min(out[sig1][startpoints[i] + np.uint(1):endpoints[i] - np.uint(1)])
elif length > limit:
fitvalue[i] = np.mean(out[sig1][startpoints[i] + np.uint(5):endpoints[i] - np.uint(5)])
else:
fitvalue[i] = np.min(out[sig1][startpoints[i]:endpoints[i]])
deli[i] = (localBaseline[i] - fitvalue[i])
else:
print(
'Strange event that has to come from a neighboring universe...Computer will self-destruct in 3s!')
dwell[i] = (endpoints[i] - startpoints[i]) / out['samplerate']
AllEvents.append(out[sig1][startpoints[i]:endpoints[i]])
frac = deli / localBaseline
dt = np.array(0)
dt = np.append(dt, np.diff(startpoints) / out['samplerate'])
numberofevents = len(dt)
# AnalysisResults[sig]['CusumFits'] = AllFits
AnalysisResults[sig]['FractionalCurrentDrop'] = frac
AnalysisResults[sig]['DeltaI'] = deli
AnalysisResults[sig]['DwellTime'] = dwell
AnalysisResults[sig]['Frequency'] = dt
AnalysisResults[sig]['LocalVoltage'] = out[volt][startpoints]
AnalysisResults[sig]['AllEvents'] = AllEvents
AnalysisResults[sig]['FitLevel'] = fitvalue
else:
AnalysisResults[sig]['NumberOfEvents'] = 0
return AnalysisResults
def MakeIV(filenames, directory, conductance=10, title=''):
"""
Function used to make IV plots for a voltage sweep.
To do so, it calls the MakeIVData function seen earlier and plots its output.
Parameters
----------
filenames : list of strings
Full paths to data files.
directory : string
Full path to directory used to save I-V curve images.
conductance : list of float, optional
title : str, optional
Plot title.
"""
if len(conductance) is 1:
conductance = np.ones(len(filenames)) * conductance
for idx, filename in enumerate(filenames):
print(filename)
# Make Dir to save images
output = LoadData.OpenFile(filename)
if not os.path.exists(directory):
os.makedirs(directory)
AllData = MakeIVData(output, delay=2)
if AllData == 0:
print('!!!! No Sweep in: ' + filename)
continue
# Plot Considered Part
# figExtracteParts = plt.figure(1)
# ax1 = figExtracteParts.add_subplot(211)
# ax2 = figExtracteParts.add_subplot(212, sharex=ax1)
# (ax1, ax2) = uf.PlotExtractedPart(output, AllData, current = 'i1', unit=1e9, axis = ax1, axis2=ax2)
# plt.show()
# figExtracteParts.savefig(directory + os.sep + 'PlotExtracted_' + str(os.path.split(filename)[1])[:-4] + '.eps')
# figExtracteParts.savefig(directory + os.sep + 'PlotExtracted_' + str(os.path.split(filename)[1])[:-4] + '.png', dpi=150)
# Plot IV
if output['graphene']:
figIV2 = plt.figure(3)
ax2IV = figIV2.add_subplot(111)
ax2IV = PlotIV(output, AllData, current='i2', unit=1e9, axis=ax2IV, WithFit=1, title=title[idx])
figIV2.tight_layout()
figIV2.savefig(directory + os.sep + str(os.path.split(filename)[1]) + '_IV_i2.png', dpi=300)
figIV2.savefig(directory + os.sep + str(os.path.split(filename)[1]) + '_IV_i2.eps')
figIV2.clear()
figIV = plt.figure(2)
ax1IV = figIV.add_subplot(111)
ax1IV = PlotIV(output, AllData, current='i1', unit=1e9, axis=ax1IV, WithFit=1,
PoreSize=[conductance[idx], 20e-9], title=title[idx])
figIV.tight_layout()
# Save Figures
figIV.savefig(directory + os.sep + str(os.path.split(filename)[1]) + 'IV_i1.png', dpi=300)
figIV.savefig(directory + os.sep + str(os.path.split(filename)[1]) + 'IV_i1.eps')
figIV.clear()
def TwoChannelAnalysis(filenames, outdir, UpwardsOn=0):
"""
Function used to analyse two channel recordings with in one channel the current and voltage values across the nanopore and
in the other of the transverse current and voltage values just before the nanopore.
Calls the RecursiveLowPassFast function to detect the events (and if needed the RecursiveLowPassFastUp for the argument UpwardsOn = 1)
to detect the events. Then calls RefinedEventDetection to get more precise informations on the events.
It correlates the 2 channels to seek the common and uncommon events.
Finally the TranslocationEvents detection will be plotted.
Parameters
----------
filenames : list of strings
Full paths to data files.
outdir :
Full path to output directory.
UpwardsOn : bool, optional
False by default. If True, we will run a RecursiveLowPassFastUp to detect events with current increases instead of current drops.
"""
for filename in filenames:
print(filename)
inp = LoadData.OpenFile(filename)
file = os.sep + str(os.path.split(filename)[1][:-4])
if not os.path.exists(outdir):
os.makedirs(outdir)
# Low Pass Event Detection
AnalysisResults = {}
if inp['graphene']:
chan = ['i1', 'i2'] # For looping over the channels
else:
chan = ['i1']
for sig in chan:
AnalysisResults[sig] = {}
AnalysisResults[sig]['RoughEventLocations'] = RecursiveLowPassFast(inp[sig], pm.coefficients[sig],
inp['samplerate'])
if UpwardsOn: # Upwards detection can be turned on or off
AnalysisResults[sig + '_Up'] = {}
AnalysisResults[sig + '_Up']['RoughEventLocations'] = RecursiveLowPassFastUp(inp[sig],
pm.coefficients[sig],
inp['samplerate'])
# f.PlotRecursiveLPResults(AnalysisResults['i2'], inp, directory, 1e-3, channel='i2')
# f.PlotRecursiveLPResults(AnalysisResults['i2_Up'], inp, directory+'UP_', 1e-3, channel='i2')
# Refine the Rough Event Detection done by the LP filter and Add event infos
AnalysisResults = RefinedEventDetection(inp, AnalysisResults, signals=chan,
limit=pm.MinimalFittingLimit * inp['samplerate'])
# Correlate the two channels
if inp['graphene']:
(CommonIndexes, OnlyIndexes) = f.CorrelateTheTwoChannels(AnalysisResults, 10e-3 * inp['samplerate'])
print('\n\nAnalysis Done...\nThere are {} common events\n{} Events on i1 only\n{} Events on i2 only'.format(
len(CommonIndexes['i1']), len(OnlyIndexes['i1']), len(OnlyIndexes['i2'])))
# Plot The Events
f.SaveAllPlots(CommonIndexes, OnlyIndexes, AnalysisResults, directory, inp, pm.PlotBuffer)
else:
# Plot The Events
f.SaveAllAxopatchEvents(AnalysisResults, directory, inp, pm.PlotBuffer)
def PlotExtractedPart(output, AllData, current='i1', unit=1e9, axis='', axis2=''):
time = np.arange(0, len(output[current])) / output['samplerate']
axis.plot(time, output[current] * unit, 'b', label=str(os.path.split(output['filename'])[1])[:-4])
axis.set_ylabel('Current ' + current + ' [nA]')
axis.set_title('Time Trace')
for i in range(0, len(AllData[current]['StartPoint'])):
axis.plot(time[AllData[current]['StartPoint'][i]:AllData[current]['EndPoint'][i]],
output[current][AllData[current]['StartPoint'][i]:AllData[current]['EndPoint'][i]] * unit, 'r')
axis2.plot(time, output[AllData[current]['SweepedChannel']], 'b',
label=str(os.path.split(output['filename'])[1])[:-4])
axis2.set_ylabel('Voltage ' + AllData[current]['SweepedChannel'] + ' [V]')
axis2.set_xlabel('Time')
return (axis, axis2)
def xcorr(x, y, k, normalize=True):
n = x.shape[0]
# initialize the output array
out = np.empty((2 * k) + 1, dtype=np.double)
lags = np.arange(-k, k + 1)
# pre-compute E(x), E(y)
mu_x = x.mean()
mu_y = y.mean()
# loop over lags
for ii, lag in enumerate(lags):
# use slice indexing to get 'shifted' views of the two input signals
if lag < 0:
xi = x[:lag]
yi = y[-lag:]
elif lag > 0:
xi = x[:-lag]
yi = y[lag:]
else:
xi = x
yi = y
# x - mu_x; y - mu_y
xdiff = xi - mu_x
ydiff = yi - mu_y
# E[(x - mu_x) * (y - mu_y)]
out[ii] = xdiff.dot(ydiff) / n
# NB: xdiff.dot(ydiff) == (xdiff * ydiff).sum()
if normalize:
# E[(x - mu_x) * (y - mu_y)] / (sigma_x * sigma_y)
out /= np.std(x) * np.std(y)
return lags, out
def CUSUM(input, delta, h,verbose=False):
"""
Function used in the detection of abrupt changes in mean current; optimal for Gaussian signals.
CUSUM is based on the cummulative sum algorithm.
This function will define new start and end points more precisely than just
the RecursiveLowPassFast and will fit levels inside the TransolocationEvent objects.
Parameters
----------
input : numpy array
Input signal.
delat : float
Most likely jump to be detected in the signal.
h : float
Threshold for the detection test.
Returns
-------
mc : the piecewise constant segmented signal
kd : a list of float detection times (in samples)
krmv : a list of float estimated change times (in samples).
"""
# initialization
Nd = k0 = 0
kd = []
krmv = []
k = 1
l = len(input)
m = np.zeros(l)
m[k0] = input[k0]
v = np.zeros(l)
sp = np.zeros(l)
Sp = np.zeros(l)
gp = np.zeros(l)
sn = np.zeros(l)
Sn = np.zeros(l)
gn = np.zeros(l)
while k < l:
m[k] = np.mean(input[k0:k + 1])
v[k] = np.var(input[k0:k + 1])
sp[k] = delta / v[k] * (input[k] - m[k] - delta / 2)
sn[k] = -delta / v[k] * (input[k] - m[k] + delta / 2)
Sp[k] = Sp[k - 1] + sp[k]
Sn[k] = Sn[k - 1] + sn[k]
gp[k] = np.max([gp[k - 1] + sp[k], 0])
gn[k] = np.max([gn[k - 1] + sn[k], 0])
if gp[k] > h or gn[k] > h:
kd.append(k)
if gp[k] > h:
kmin = np.argmin(Sp[k0:k + 1])
krmv.append(kmin + k0)
else:
kmin = np.argmin(Sn[k0:k + 1])
krmv.append(kmin + k0)
# Re-initialize
k0 = k
m[k0] = input[k0]
v[k0] = sp[k0] = Sp[k0] = gp[k0] = sn[k0] = Sn[k0] = gn[k0] = 0
Nd = Nd + 1
k += 1
if verbose:
print('delta:' + str(delta))
print('h:' + str(h))
print('Nd: '+ str(Nd))
print('krmv: ' + str(krmv))
if Nd == 0:
mc = np.mean(input) * np.ones(k)
elif Nd == 1:
mc = np.append(m[krmv[0]] * np.ones(krmv[0]), m[k - 1] * np.ones(k - krmv[0]))
else:
mc = m[krmv[0]] * np.ones(krmv[0])
for ii in range(1, Nd):
mc = np.append(mc, m[krmv[ii]] * np.ones(krmv[ii] - krmv[ii - 1]))
mc = np.append(mc, m[k - 1] * np.ones(k - krmv[Nd - 1]))
return (mc, kd, krmv)
def GetPSD(input):
Fulltrace = input['i1']
samplerate = input['samplerate']
f, Pxx_den = sig.welch(Fulltrace, samplerate, nperseg=2**18)
return f, Pxx_den
def CondPoreSizeTick(x, pos):
formCond = EngFormatter(unit='S')
formPoreSize = EngFormatter(unit='m')
outstring = '{}, {}'.format(formCond.format_eng(x), formPoreSize.format_eng(CalculatePoreSize(x, 1e-9, 10)))
return outstring
def DebyeHuckelParam(c, T=20):
## Valid Only for same valency and c1 = c2
epsilon_r = 87.740 - 0.40008 * T + 9.398e-4 * T ** 2 - 1.410e-6 * T ** 3
print('Dielectric of Water is {}'.format(epsilon_r))
n = c * 1e3 * cst.Avogadro
formCond = EngFormatter(unit='m')
k = np.sqrt((cst.e ** 2 * 2 * n) / (cst.k * (T + 273.15) * cst.epsilon_0 * epsilon_r))
return [k, 1 / k] # , '{}'.format(formCond.format_eng(1/k))]
def ElectrostaticPotential(T, sigma, Tau=5e18, pK=7.9, pH=11):
return cst.k * T / cst.e * (np.log(-sigma / (cst.e * Tau + sigma)) + (pK - pH) * np.log(10))
def GetTempRedoxPotential(Cdiff=1e-3 / 1e-1, T=293.15):
return cst.R * T / cst.physical_constants['Faraday constant'][0] * np.log(Cdiff)
def GetRedoxError(cmax, cmin, ErrorPercent=0.1, T=293.15):
cmaxErr = cmax * ErrorPercent
cminErr = cmin * ErrorPercent
return cst.R * T / cst.physical_constants['Faraday constant'][0] * np.sqrt(
(1 / cmax ** 2 * cmaxErr ** 2 + 1 / cmin ** 2 * cminErr ** 2))
##Result: Negative ion divided by positive ion
# Goldman–Hodgkin–Katz voltage equation
def GetIonSelectivityWithoutPotential(c_trans, c_cis, Erev, T):
n_trans = c_trans # *1e3#*cst.Avogadro
n_cis = c_cis # *1e3#*cst.Avogadro
A = Erev * cst.physical_constants['Faraday constant'][0] / (cst.R * T)
return -(n_trans - n_cis * np.exp(-A)) * (1 - np.exp(A)) / ((n_trans - n_cis * np.exp(A)) * (1 - np.exp(-A)))
def GetIonSelectivityWithPotential(c_trans, c_cis, Erev, T, phi):
sel1 = GetIonSelectivityWithoutPotential(c_trans, c_cis, Erev, T)
return sel1 * np.exp((-2 * phi * cst.physical_constants['Faraday constant'][0]) / (cst.R * T))
def Selectivity(ConcGradient, V):
return V * cst.physical_constants['Faraday constant'][0] / ((cst.R * 293.15) * np.log(ConcGradient))
def GetRedox(cmax, cmin, T=295.15):
return cst.R * T / cst.physical_constants['Faraday constant'][0] * np.log(cmax / cmin)

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