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plot_Cm_filtering.py
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Sun, May 12, 04:41

plot_Cm_filtering.py
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# -*- coding: utf-8 -*-
# @Author: Theo Lemaire
# @Email: theo.lemaire@epfl.ch
# @Date: 2020-07-30 15:33:22
# @Last Modified by: Theo Lemaire
# @Last Modified time: 2020-08-08 15:46:35
import logging
import numpy as np
from argparse import ArgumentParser
import matplotlib.pyplot as plt
from PySONIC.core import BilayerSonophore, AcousticDrive
from PySONIC.utils import logger
from PySONIC.postpro import filtfilt, computeTimeStep
from PySONIC.constants import NPC_DENSE
logger.setLevel(logging.INFO)
# Constants
MAX_PROFILES = 6 # max number of profiles to display simultaneously on figure
def invfiltfilt(y, *args, **kwargs):
''' Inverse signal before and after filtering. '''
return 1 / filtfilt(1 / y, *args, **kwargs)
def getCmProfiles(bls, drive, nreps):
''' Simulate mechanical model with a specific drive and return extended
time, capacitance and capacitance sinusoidal approximation profiles.
'''
data, _ = bls.simulate(drive, bls.Qm0)
logger.info('Extracting detailed capacitance profile')
Z_last = data.tail(NPC_DENSE)['Z'].values # m
Cm_last = bls.v_capacitance(Z_last) # F/m2
Cm = np.tile(Cm_last, nreps)
t = np.linspace(0, nreps / drive.f, Cm.size)
gamma = np.ptp(Cm) / (2 * bls.Cm0)
logger.info(f'Generating corresponding pure sinusoid capacitance profile (gamma = {gamma:.2f})')
Cm_approx = bls.Cm0 * (1 + gamma * np.sin(2 * np.pi * f_US * t)) # F/m2
return t, Cm, Cm_approx
def getSecondHalfAvg(x):
''' Extract the effective capacitance from the second half of a capacitance profile. '''
return np.squeeze(np.nanmean(x[x.shape[0] // 2:], axis=0))
def plotRelCmfiltsVsCutoff(rel_fcs, rel_Cm, rel_Cmfilts, condition):
''' Plot an original Cm profile and filtered variants at various cutoff frequencies. '''
rsf = int(np.ceil(rel_fcs.size / MAX_PROFILES)) # potential resampling factor
colors = plt.get_cmap('tab10').colors
fig, ax = plt.subplots(figsize=(10, 4))
ax.set_title(f'Cm profiles vs. cutoff ({condition})')
ax.set_xlabel('time (us)')
ax.set_ylabel('Cm / Cm0')
ax.plot(t * 1e6, rel_Cm, label='unfiltered', c='k')
ax.axhline(np.mean(rel_Cm), c='k', linestyle='--')
ax.axhline(1 / np.mean(1 / rel_Cm), c='k', linestyle=':')
for i, (rel_fc, rel_Cmfilt) in enumerate(zip(rel_fcs[::rsf], rel_Cmfilts[::rsf])):
ax.plot(t * 1e6, rel_Cmfilt, label=f'$f_c = {rel_fc:.2g}\\ f_{{US}}$', c=colors[i])
ax.axhline(getSecondHalfAvg(rel_Cmfilt), c=colors[i], linestyle='--')
ax.legend()
fig.tight_layout()
return fig
def plotRelCmeffVsCutoff(rel_fcs, rel_Cmavgs, rel_Cmeffs, rel_Cmfilts, condition, colors=None):
''' Plot effective capacitance as a function of cutoff frequency for various conditions. '''
fig, ax = plt.subplots()
if colors is None:
colors = plt.get_cmap('tab10').colors
ax.set_title(f'Cmeff vs. cutoff - {condition}')
ax.set_xlabel('$f_c / f_{US}$')
ax.set_ylabel('$C_{m, eff} / C_{m0}$')
ax.set_xscale('log')
for (k, Cm), c in zip(rel_Cmfilts.items(), colors):
ax.plot(rel_fcs, getSecondHalfAvg(Cm.T), label=k, c=c)
ax.axhline(rel_Cmavgs[k], linestyle='--', c=c)
ax.axhline(rel_Cmeffs[k], linestyle=':', c=c)
# if gamma is not None:
# ax.axhline(np.sqrt(1 - gamma**2), c='k', linestyle='--', label='$\\sqrt{1 - \\gamma^2}$')
ax.legend()
fig.tight_layout()
return fig
if __name__ == '__main__':
ap = ArgumentParser()
ap.add_argument('-p', '--plot', default=False, action='store_true', help='Plot profiles')
args = ap.parse_args()
# Mechanical model
a = 32e-9 # m
Cm0 = 1e-2 # resting capacitance (F/m2)
Qm0 = 0.0 # resting charge density (C/m2)
bls = BilayerSonophore(a, Cm0, Qm0)
# Acoustic parameters
freqs = np.array([20., 500., 4000.]) * 1e3 # Hz
amps = np.logspace(1, 3, 3) * 1e3 # Pa
# Define colors
colors = list(plt.get_cmap('tab20c').colors)
del colors[3::4]
amps = amps[::-1]
# Filter parameters
order = 2 # filter order
rel_fcs = np.logspace(-1, 3, 100) # relative cutoff frequencies w.r.t. US frequency
nreps = int(2 / rel_fcs.min()) # minimum number of acoustic cycles
# Plot parameters
plot_profiles = args.plot
variants = ['detailed', 'approx']
rel_Cmavgs = {k: {} for k in variants}
rel_Cmeffs = {k: {} for k in variants}
rel_Cmfilts = {k: {} for k in variants}
for f_US in freqs:
fcs = rel_fcs * f_US
for A_US in amps:
drive = AcousticDrive(f_US, A_US)
label = drive.desc
# Get original Cm signal and sinusoidal approximation
t, *Cms = getCmProfiles(bls, drive, nreps)
# Get sampling and Nyquist frequency from time signal
fs = 1 / computeTimeStep(t)
fnyq = fs / 2
# Warn if Nyquist frequency is lower than max cutoff frequency
if fcs.max() > fnyq:
logger.warning(
f'max cutoff {fcs.max() / fnyq:.2f} times higher than signal Nyquist')
# For each Cm profile variant
for k, Cm in zip(variants, Cms):
# Normalize by resting capacitance
rel_Cm = Cm / Cm0
# Compute average and effective metrics
rel_Cmavgs[k][label] = rel_Cm.mean()
rel_Cmeffs[k][label] = 1 / np.mean(1 / rel_Cm)
# Filter reciprocal at various cutoff frequencies (except those above nyquist)
rel_Cmfilts_list = []
for fc in fcs[fcs <= fnyq]:
rel_Cmfilts_list.append(invfiltfilt(rel_Cm, fs, fc, order))
for fc in fcs[fcs > fnyq]:
rel_Cmfilts_list.append(np.ones(rel_Cm.size) * np.nan)
rel_Cmfilts[k][label] = np.array(rel_Cmfilts_list)
if plot_profiles:
# Plot filtered profiles for a subset of cutoff frequencies
plotRelCmfiltsVsCutoff(rel_fcs, rel_Cm, rel_Cmfilts[k][label], label)
for k in variants:
# Plot effective capacitance as a function of cutoff frequency for various conditions
plotRelCmeffVsCutoff(
rel_fcs, rel_Cmavgs[k], rel_Cmeffs[k], rel_Cmfilts[k], k, colors=colors)
plt.show()

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