#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""Spectral induced polarization (SIP) spectrum class and modules."""
import sys
import codecs
from math import log10, exp, pi
import numpy as np
import pygimli as pg
from pygimli.utils import isComplex, squeezeComplex, toComplex, KramersKronig
from .importData import readTXTSpectrum, readFuchs3File, readRadicSIPFuchs
from .plotting import drawAmplitudeSpectrum, drawPhaseSpectrum, showSpectrum
from .models import DebyePhi, DebyeComplex, relaxationTerm, DoubleColeCole
from .tools import fitCCEMPhi, fitCCC
from .tools import fitCCCC, fitCCPhi, fit2CCPhi
from pygimli.frameworks import MethodManager
from pygimli.frameworks import ParameterModelling
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class SpectrumModelling(ParameterModelling):
"""Modelling framework with an array of freqencies as data space.
Attributes
----------
params: dict
function: callable
complex: bool
"""
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def __init__(self, funct=None, **kwargs):
"""Initialize.
Parameters
----------
func : function
modelling function
complex : bool
complex function
frequencies : iterable
frequency vector
"""
self._complex = kwargs.pop("complex", False)
super(SpectrumModelling, self).__init__(funct=funct, **kwargs)
self.defaultModelTrans = 'log'
self._freqs = kwargs.pop("frequencies", None)
@property
def complex(self):
"""Return if spectrum is complex."""
return self._complex
@complex.setter
def complex(self, c):
self._complex = c
@property
def freqs(self):
"""Return frequency vector."""
if self._freqs is None:
pg.critical("No frequencies defined.")
return self._freqs
@freqs.setter
def freqs(self, f):
self._freqs = f
self.dataSpace = self._freqs
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def response(self, params):
"""Model response.
Parameters
----------
params : iterable
model
Returns
-------
array_like
model response vector
"""
ret = super().response(params)
if self.complex:
return squeezeComplex(ret)
return ret
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def drawData(self, ax, data, err=None, **kwargs):
"""Draw data."""
if self.complex:
Z = toComplex(data)
showSpectrum(self.freqs, np.abs(Z), -np.angle(Z)*1000,
axs=ax, **kwargs)
else:
ax.semilogx(self.freqs, data)
ax.legend()
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class SpectrumManager(MethodManager):
"""Manager to work with spectra data."""
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def __init__(self, fop=None, **kwargs):
"""Set up spectrum manager.
Parameters
----------
fop : pg.Modelling operator, optional
Forward operator. The default is None.
**kwargs : TYPE
passed to SpectrumManager.
"""
self._funct = fop
super(SpectrumManager, self).__init__(**kwargs)
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def setFunct(self, fop, **kwargs):
"""Set forward modelling function."""
self._funct = fop
self.reinitForwardOperator(**kwargs)
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def createForwardOperator(self, **kwargs):
"""Create a Forward operator."""
if isinstance(self._funct, SpectrumModelling):
return self._funct
fop = SpectrumModelling(self._funct, **kwargs)
return fop
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def createInversionFramework(self, **kwargs):
"""Create inversion framework."""
return pg.frameworks.MarquardtInversion(**kwargs)
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def simulate(self):
"""Make a simulation."""
pass
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def setData(self, freqs=None, amp=None, phi=None, eAmp=0.03, ePhi=0.001):
"""Set data for chosen sip model.
Parameters
----------
freqs: iterable
Array-like frequencies.
amp: iterable
Array-like amplitudes to work with.
phi: iterable
Array-like phase angles to work with.
eAmp: float|iterable
Relative error for amplitudes.
ePhi: float|iterable
Absolute error for phase angles.
"""
self.fop.freqs = freqs
if phi is not None:
self.fw.dataVals = self._ensureData(toComplex(amp, phi))
if isinstance(ePhi, float):
ePhi = abs(ePhi/phi)
else:
self.fw.dataVals = self._ensureData(amp)
if isinstance(eAmp, float):
eAmp = np.ones(len(freqs)) * eAmp
if phi is not None:
err = np.asarray([*eAmp, *ePhi])
else:
err = eAmp
self.fw.errorVals = self._ensureError(err, self.fw.dataVals)
def _ensureData(self, data):
"""Check data validity."""
if isinstance(data, pg.DataContainer):
pg.critical("Implement me")
if data is None:
data = self.fw.dataVals
vals = data
if isComplex(data):
self.fop.complex = True
vals = squeezeComplex(data)
if abs(min(vals)) < 1e-12:
print(min(vals), max(vals))
pg.critical("There are zero data values.")
return vals
def _ensureError(self, err, dataVals=None):
"""Check data validity."""
if isinstance(err, pg.DataContainer):
pg.critical("Implement me")
if err is None:
err = self.fw.errorVals
vals = err
if vals is None:
return self._ensureError(0.01, dataVals)
if abs(min(vals)) < 1e-12:
print(min(vals), max(vals))
pg.critical("There are zero data values.")
return vals
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def invert(self, data=None, f=None, **kwargs):
"""Invert the spectrum."""
if f is not None:
self.fop.freqs = f
limits = kwargs.pop('limits', {})
for k, v in limits.items():
self.fop.setRegionProperties(k, limits=v)
if 'startmodel' not in kwargs:
sm = (v[1] + v[0]) / 2
if v[0] > 0:
sm = np.exp(np.log(v[0]) +
(np.log(v[1]) - np.log(v[0])) / 2.)
self.fop.setRegionProperties(k, startModel=sm)
return super(SpectrumManager, self).invert(data, **kwargs)
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def showResult(self):
"""Show resulting data."""
ax = None
if self.fop.complex:
fig, ax = pg.plt.subplots(nrows=2, ncols=1)
else:
fig, ax = pg.plt.subplots(nrows=1, ncols=1)
self.fop.drawModel(ax, self.fw.model)
self.fop.drawData(ax, self.fw.dataVals, label='data')
self.fop.drawData(ax, self.fw.response, label='response')
return ax
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class SIPSpectrum(object):
"""SIP spectrum data analysis."""
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def __init__(self, filename=None, unify=False, onlydown=True,
f=None, amp=None, phi=None, k=1, sort=True,
basename='new', **kwargs):
"""Init SIP class with either filename to read or data vectors.
Examples
--------
>>> #sip = SIPSpectrum('sipexample.txt', unify=True) # unique f values
>>> #sip = SIPSpectrum(f=f, amp=R, phi=phase, basename='new')
"""
self._verbose = False
self.basename = basename
self.fig = {}
self.k = k
self.f = None # mandatory frequencies
self.amp = None # mandatory amplitudes
self.phi = None # mandatory phases
self.epsilon0 = 8.854e-12
if filename is not None:
self.loadData(filename, **kwargs)
else:
if f is not None:
self.f = np.asarray(f)
if amp is not None:
self.amp = np.asarray(amp)
if phi is not None:
self.phi = np.asarray(phi)
if unify and self.amp is not None:
self.unifyData(onlydown)
if sort and self.amp is not None:
self.sortData()
self.ampOrg = None
self.phiOrg = None
self.phiCC = None # better make a struct of m, amp, phi (tau)
self.ampCC = None
self.mCC = None
self.phiDD = None
self.ampDD = None
self.mDD = None
self.tau = None
def __repr__(self):
"""Human readable string representation of the class."""
out = self.__class__.__name__ + " object"
if self.f is not None:
if hasattr(self.f, '__iter__'):
out += "\nnf=" + str(len(self.f)) + " min/max="
out += str(min(self.f)) + "/" + str(max(self.f))
return out
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def loadData(self, filename, **kwargs):
"""Import spectral data.
Import Data and try to assume the file format.
"""
verbose = kwargs.pop('verbose', self._verbose)
with codecs.open(filename, 'r', encoding='iso-8859-15',
errors='replace') as f:
firstLine = f.readline()
fnLow = filename.lower()
self.basename = filename[:-4]
if 'SIP Fuchs III' in firstLine:
if verbose:
pg.info("Reading SIP Fuchs III file")
self.f, self.amp, self.phi, self.header = readFuchs3File(
filename, verbose=verbose, **kwargs)
self.phi *= -np.pi/180.
elif 'SIP-Quad' in firstLine:
if verbose:
pg.info("Reading SIP Quad file")
self.f, self.amp, self.phi, self.header = readFuchs3File(
filename, nfr=9, namp=10, nphi=11, nk=7,
verbose=verbose, **kwargs)
self.phi *= -np.pi/180.
elif 'SIP-Fuchs' in firstLine:
if verbose:
pg.info("Reading SIP Fuchs file")
self.f, self.amp, self.phi, drhoa, dphi = readRadicSIPFuchs(
filename, verbose=verbose, quad='SIP-Quad' in firstLine,
**kwargs)
self.phi *= -np.pi/180.
elif fnLow.endswith('.txt') or fnLow.endswith('.csv'):
self.f, self.amp, self.phi = readTXTSpectrum(filename, **kwargs)
else:
try:
out = np.genfromtxt(filename, names=True)
self.f = out["FreqHz"]
self.amp = out["AppResOhmm"]
self.phi = -out["Phasedeg"] * np.pi / 180
except BaseException:
raise Exception("Don't know how to read data.")
self.amp *= self.k
return self.f, self.amp, self.phi
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def unifyData(self, onlydown=False):
"""Unify data (only one value per frequency) by mean or selection."""
if self.f is None:
return
fu = np.unique(self.f)
if len(fu) < len(self.f) or onlydown:
if onlydown:
nonzero = np.nonzero(np.diff(self.f) > 0)[0]
if len(nonzero) > 0:
wende = min(nonzero)
if wende > 0:
self.f = self.f[wende::-1]
self.amp = self.amp[wende::-1]
self.phi = self.phi[wende::-1]
else:
amp = np.zeros(fu.shape)
phi = np.zeros(fu.shape)
for i in range(len(fu)):
ind = np.nonzero(self.f == fu[i])[0]
amp[i] = np.mean(self.amp[ind])
phi[i] = np.mean(self.phi[ind])
self.f = fu
self.amp = amp
self.phi = phi
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def sortData(self):
"""Sort data along increasing frequency (e.g. useful for KK)."""
if self.f is None:
return
ind = np.argsort(self.f)
self.amp = self.amp[ind]
self.phi = self.phi[ind]
self.f = self.f[ind]
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def cutF(self, fcut=1e99, down=False):
"""Cut (delete) frequencies above a certain value fcut."""
if down:
ind = self.f >= fcut
else:
ind = self.f <= fcut
self.amp = self.amp[ind]
self.phi = self.phi[ind]
if np.any(self.phiOrg):
self.phiOrg = self.phiOrg[ind]
if np.any(self.ampOrg):
self.ampOrg = self.ampOrg[ind]
self.f = self.f[ind]
# self.amp = self.amp[self.f <= fcut]
# self.phi = self.phi[self.f <= fcut]
# if np.any(self.phiOrg):
# self.phiOrg = self.phiOrg[self.f <= fcut]
# # finally cut f
# self.f = self.f[self.f <= fcut]
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def omega(self):
"""Angular frequency."""
return self.f * 2 * np.pi
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def realimag(self, cond=False):
"""Real and imaginary part of resistivity/conductivity (cond=True)."""
if cond:
amp = 1. / self.amp
else:
amp = self.amp
return amp * np.cos(self.phi), amp * np.sin(self.phi)
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def zNorm(self):
"""Normalized real (difference) and imag. z :cite:`NordsiekWel2008`."""
re, im = self.realimag()
R0 = max(self.amp)
zNormRe = 1. - re / R0
zNormIm = im / R0
return zNormRe, zNormIm
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def showPhase(self, ax=None, **kwargs):
"""Plot phase spectrum (-phi over frequency)."""
if ax is None:
fig, ax = pg.plt.subplots()
self.fig['phase'] = fig
drawPhaseSpectrum(ax, self.f, self.phi*1000, **kwargs)
return ax
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def showData(self, reim=False, znorm=False, cond=False, nrows=2, ax=None,
**kwargs):
"""Show amplitude and phase spectrum in two subplots.
Parameters
----------
reim : bool
show real/imaginary part instead of amplitude/phase
znorm : bool (true forces reim)
use normalized real/imag parts after Nordsiek&Weller (2008)
nrows - use nrows subplots (default=2)
Returns
-------
fig, ax : mpl.figure, mpl.axes array
"""
if reim or znorm or cond:
addstr = ''
if znorm:
re, im = self.zNorm()
addstr = ' (norm)'
else:
re, im = self.realimag(cond=cond)
fig, ax = showSpectrum(self.f, re, im, ylog=cond, nrows=nrows,
axs=ax, **kwargs)
self.fig['data'] = fig
ax[0].set_ylabel('real part'+addstr)
ax[1].set_ylabel('imaginary part'+addstr)
else:
fig, ax = showSpectrum(self.f, self.amp, self.phi*1000,
axs=ax, **kwargs)
self.fig['data'] = fig
ax[0].set_title(kwargs.pop("title", self.basename))
return fig, ax
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def getKK(self, use0=False):
"""Compute Kramers-Kronig impedance values (re->im and im->re)."""
re, im = self.realimag()
if False:
ind = np.argsort(self.f)
reKK, imKK = KramersKronig(self.f[ind], re[ind], im[ind],
usezero=use0)
else:
fsort, ind = np.unique(self.f, return_index=True)
reKK, imKK = KramersKronig(fsort, re[ind], im[ind], usezero=use0)
re[ind] = reKK # sort back
im[ind] = imKK
return re, im
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def getPhiKK(self, use0=False):
"""Compute phase from Kramers-Kronig quantities."""
_, imKK = self.getKK(use0)
re, _ = self.realimag()
return np.arctan2(imKK, re)
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def showDataKK(self, use0=False):
"""Show data as real/imag subplots along with Kramers-Kronig curves."""
fig, ax = self.showData(reim=True)
reKK, imKK = self.getKK(use0)
ax[0].semilogx(self.f, reKK, label='KK')
ax[1].semilogx(self.f, imKK, label='KK')
for a in ax:
a.set_yscale('linear')
a.legend()
self.fig['dataKK'] = fig
return fig, ax
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def checkCRKK(self, useEps=False, use0=False, ax=None):
"""Check coupling removal (CR) by Kramers-Kronig (KK) relation."""
if ax is None:
fig, ax = pg.plt.subplots()
self.fig['dataCRKK'] = fig
ax.semilogx(self.f, self.phi*1000, "+-", label='org')
ax.semilogx(self.f, self.getPhiKK(use0)*1000, "x-", label='orgKK')
if useEps:
self.removeEpsilonEffect()
else:
self.fitCCEM()
ax.semilogx(self.f, self.phi*1000, "+--", label='corr')
ax.semilogx(self.f, self.getPhiKK(use0)*1000, "+--", label='corrKK')
ax.grid(True)
ax.legend(loc='best')
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def showPolarPlot(self, cond=False):
"""Show data in a polar plot (imaginary vs. real parts)."""
re, im = self.realimag(cond=cond)
fig, ax = pg.plt.subplots()
self.fig['polar'] = fig
ax.plot(re, im, 'b.')
ax.set_aspect(1)
ax.grid(True)
for i in range(0, len(re), 5):
fi = self.f[i]
mul = 10**np.floor(np.log10(fi) - 2) # 3 counting digits
ax.text(re[i], im[i], str(int(fi / mul) * mul))
return fig, ax
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def epsilonR(self):
"""Calculate relative permittivity from imaginary conductivity."""
_, sigmaI = self.realimag(cond=True)
return sigmaI / (self.f * 2 * pi * self.epsilon0)
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def determineEpsilon(self, mode=0, sigmaR=None, sigmaI=None):
"""Retrieve frequency-independent epsilon for f->Inf.
Parameters
----------
mode : int
Operation mode:
=0 - extrapolate using two highest frequencies (default)
<0 - take last -n frequencies
>0 - take n-th frequency
sigmaR/sigmaI : float
real and imaginary conductivity (if not given take data)
Returns
-------
er : float
relative permittivity (epsilon) value (dimensionless)
"""
if sigmaR is None or sigmaI is None:
sigmaR, sigmaI = self.realimag(cond=True)
epsr = sigmaI / self.omega() / self.epsilon0
nmax = np.argmax(self.f)
if mode == 0:
f1 = self.f * 1
a = f1[nmax] * 1.
f1[nmax] = 0
nmax1 = np.argmax(f1)
a = a / f1[nmax1]
er = (a*epsr[nmax] - epsr[nmax1]) / (a-1)
elif mode < 0:
er = np.median(epsr[mode:])
else:
er = epsr[nmax]
return er
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def removeEpsilonEffect(self, er=None, mode=0):
"""Remove effect of (constant high-frequency) epsilon from sigma.
Parameters
----------
er : float
relative epsilon to correct for (else automatically determined)
mode : int
automatic epsilon determination mode (see determineEpsilon)
Returns
-------
er : float
determined permittivity (see determineEpsilon)
"""
sigR, sigI = self.realimag(cond=True)
if er is None: #
er = self.determineEpsilon(mode=mode, sigmaR=sigR, sigmaI=sigI)
print("detected epsilon of ", er)
sigI -= er * self.omega() * self.epsilon0
self.phiOrg = self.phi
self.phi = np.arctan(sigI/sigR)
self.ampOrg = self.amp
self.amp = 1. / np.sqrt(sigR**2 + sigI**2)
return er
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def fitCCPhi(self, ePhi=0.001, lam=1000., mpar=(0, 0, 1),
taupar=(0, 1e-5, 100), cpar=(0.3, 0, 1), verbose=False):
"""Fit a Cole-Cole term (to phase only).
Parameters
----------
ePhi : float
absolute error of phase angle
lam : float
regularization parameter
mpar, taupar, cpar : list[3]
inversion parameters (starting value, lower bound, upper bound)
for Cole-Cole parameters (m, tau, c) and EM relaxation time (em)
"""
if taupar[0] == 0:
taupar = (1.0 / self.f[np.argmax(self.phi)] / 2.0 / pi,
taupar[1], taupar[2])
# taupar[0] = 1.0 / self.f[np.argmax(self.phi)] / 2.0 / pi
print("taupar", taupar)
if mpar[0] == 0:
mpar = (1. - min(self.amp)/max(self.amp), mpar[1], mpar[2])
# mpar[0] = 1. - min(self.amp)/max(self.amp)
print("mpar", mpar)
self.mCC, self.phiCC, self.chi2 = fitCCPhi(
self.f, self.phi, ePhi, lam, mpar=mpar, taupar=taupar, cpar=cpar)
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def fit2CCPhi(self, ePhi=0.001, lam=1000., mpar=(0, 0, 1),
taupar1=(0, 1e-5, 1), taupar2=(0, 1e-1, 1000),
cpar=(0.5, 0, 1), verbose=False):
"""Fit two Cole-Cole terms (to phase only).
Parameters
----------
ePhi : float
absolute error of phase angle
lam : float
regularization parameter
mpar : list[3]
starting value, lower bound, upper bound for chargeability
taupar1 / taupar2 : list[3]
starting value, lower bound, upper bound for 2 time constants
cpar1 / cpar2 : list[3]
starting value, lower bound, upper bound for 2 relaxation exponents
"""
if taupar1[0] == 0:
taupar1 = (np.sqrt(taupar1[1]*taupar1[2]), taupar1[1], taupar1[2])
print("taupar1", taupar1)
if taupar2[0] == 0:
taupar2 = (np.sqrt(taupar2[1]*taupar2[2]), taupar2[1], taupar2[2])
print("taupar2", taupar2)
# taupar1[0] = 1.0 / self.f[np.argmax(self.phi)] / 2.0 / pi
if mpar[0] == 0:
mpar = (1. - min(self.amp)/max(self.amp), mpar[1], mpar[2]) # *2
print("mpar", mpar)
self.mCC, self.phiCC = fit2CCPhi(self.f, self.phi, ePhi, lam,
mpar1=mpar, mpar2=mpar,
cpar1=cpar, cpar2=cpar,
taupar1=taupar1, taupar2=taupar2)
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def fitCCEM(self, ePhi=0.001, lam=1000., remove=True,
mpar=(0.2, 0, 1), taupar=(1e-2, 1e-5, 100),
cpar=(0.25, 0, 1), empar=(1e-7, 1e-9, 1e-5), verbose=False):
"""Fit a Cole-Cole term with additional EM term to phase.
Parameters
----------
ePhi : float
absolute error of phase angle
lam : float
regularization parameter
remove: bool
remove EM term from data
mpar, taupar, cpar, empar : list[3]
inversion parameters (starting value, lower bound, upper bound)
for Cole-Cole parameters (m, tau, c) and EM relaxation time (em)
"""
self.mCC, self.phiCC = fitCCEMPhi(self.f, self.phi, ePhi, lam, mpar,
taupar, cpar, empar, verbose=verbose)
# correct EM term from data
if remove:
self.phiOrg = self.phi
self.phi = self.phi + \
np.angle(relaxationTerm(self.f, self.mCC[3]))
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def fitColeCole(self, useCond=False, **kwargs):
"""Fit a Cole-Cole model to the phase data.
Parameters
----------
useCond : bool
use conductivity form of Cole-Cole model instead of resistivity
error : float [0.01]
absolute phase error
lam : float [1000]
initial regularization parameter
mpar : tuple/list (0, 0, 1)
inversion parameters for chargeability: start, lower, upper bound
taupar : tuple/list (1e-2, 1e-5, 100)
inversion parameters for time constant: start, lower, upper bound
cpar : tuple/list (0.25, 0, 1)
inversion parameters for Cole exponent: start, lower, upper bound
"""
if useCond: # use conductivity formulation instead of resistivity
self.mCC, self.ampCC, self.phiCC, self.chi2 = fitCCCC(
self.f, self.amp, self.phi, **kwargs)
self.mCC[0] = 1. / self.mCC[0]
else:
self.mCC, self.ampCC, self.phiCC, self.chi2 = fitCCC(
self.f, self.amp, self.phi, **kwargs)
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def fitDoubleColeCole(self, ePhi=0.001, eAmp=0.01, lam=1000., robust=False,
verbose=True, useRho=True, useMult=False, aphi=True,
mpar1=(0.2, 0, 1), mpar2=(0.2, 0, 1), tauRho=True,
taupar1=(1e-2, 1e-5, 100), taupar2=(1e-4, 1e-5, 100),
cpar1=(0.5, 0, 1), cpar2=(0.5, 0, 1)):
"""Fit double Cole-Cole term to complex resistivity or phase.
Parameters
----------
ePhi : float [0.001]
absolute error of phase angle in rad
eAmp : float [0.01 = 1%]
absolute error of phase angle
lam : float
regularization parameter
robust : bool [False]
use robustData (L1 norm on data side)
useRho : bool [True]
Cole-Cole defined for impedance/resistivity, otherwise conductivity
useMult : bool [False]
the two terms are combined as product (otherwise sum)
tauRho : bool [False]
in case of useRho=False the time constant is defined like for rho
mpar1/2, taupar1/2, cpar1/2 : list[3]
inversion parameters (starting value, lower bound, upper bound)
for Cole-Cole parameters (m, tau, c)
"""
f2CC = DoubleColeCole(self.f, rho=useRho, aphi=aphi, tauRho=False,
mult=useMult)
if useRho:
rhoStart = min(self.amp)
f2CC.region(0).setParameters(rhoStart, 0., rhoStart*10)
else:
sigStart = 1./max(self.amp)
f2CC.region(0).setParameters(sigStart, 0., sigStart*10)
f2CC.region(1).setParameters(*mpar1) # m (start,lower,upper)
f2CC.region(2).setParameters(*taupar1) # tau
f2CC.region(3).setParameters(*cpar1) # c
f2CC.region(4).setParameters(*mpar2) # m (start,lower,upper)
f2CC.region(5).setParameters(*taupar2) # tau
f2CC.region(6).setParameters(*cpar2) # c
if aphi:
amp = self.amp if useRho else 1./self.amp
data = np.hstack((amp, self.phi))
error = np.hstack((np.ones_like(amp)*eAmp,
ePhi / np.abs(self.phi)))
else:
re, im = self.realimag(not useRho)
data = np.hstack((re, im))
error = np.ones(len(self.f)*2) * eAmp
ICC = pg.core.Inversion(data, f2CC, False) # set up inversion class
ICC.setRelativeError(error) # 1 mrad
ICC.setLambda(lam) # start with large damping and cool later
ICC.setMarquardtScheme(0.8) # lower lambda by 20%/it., no stop chi=1
ICC.setRobustData(robust)
ICC.setDeltaPhiAbortPercent(1)
# ICC.setMaxIter(0)
self.mCC = ICC.run() # run inversion
self.chi2 = ICC.chi2()
if verbose:
ICC.echoStatus()
one, two = np.split(ICC.response(), 2)
if aphi:
self.ampCC = one
self.phiCC = two
[docs]
def fitDebyeModel(self, ePhi=0.001, lam=1e3, lamFactor=0.8,
tau=None, mint=None, maxt=None, nt=None, useComplex=True,
showFit=False, verbose=False, **kwargs):
"""Fit a (smooth) continuous Debye model (Debye decomposition).
Parameters
----------
ePhi : float
absolute error of phase angle
lam : float
regularization parameter
lamFactor : float
regularization factor for subsequent iterations
mint/maxt : float
minimum/maximum tau values to use (else automatically from f)
nt : int
number of tau values (default number of frequencies * 2)
new : bool
new implementation (experimental)
showFit : bool
show fit
cType : int
constraint type (1/2=smoothness 1st/2nd order, 0=minimum norm)
phi : iterable
use phi instead of self.phi
"""
nf = len(self.f)
if tau is None:
if mint is None:
mint = .1 / max(self.f)
if maxt is None:
maxt = .5 / min(self.f)
if nt is None:
nt = nf*2
self.tau = np.logspace(log10(mint), log10(maxt), nt)
else:
self.tau = tau
# discretize tau, setup DD and perform DD inversion
startModel = pg.Vector(len(self.tau), 0.01)
new = kwargs.pop("new", useComplex) # renamed kwargs
if new:
reNorm, imNorm = self.zNorm()
fDD = DebyeComplex(self.f, self.tau)
Znorm = pg.cat(reNorm, imNorm)
IDD = pg.Inversion(fop=fDD)
absErr = max(Znorm)*0.003+ePhi
self.mDD = IDD.run(Znorm, absoluteError=absErr,
startModel=startModel,
lam=lam, lambdaFactor=lamFactor,
**kwargs)
IDD.echoStatus()
else:
fDD = DebyePhi(self.f, self.tau)
IDD = pg.Inversion(fop=fDD)
phi = kwargs.pop("phi", self.phi)
self.mDD = IDD.run(phi, absoluteError=ePhi, startModel=startModel,
lam=lam, lambdaFactor=lamFactor, **kwargs)
self.invDD = IDD
if new:
print("ARMS=", IDD.absrms(), "RRMS=", IDD.absrms()/max(Znorm)*100)
resp = np.array(IDD.response)
respRe = resp[:nf]
respIm = resp[nf:]
respC = ((1 - respRe) + respIm * 1j) * max(self.amp)
self.phiDD = np.angle(respC)
self.ampDD = np.abs(respC)
if showFit:
fig, ax = self.showData(znorm=True, nrows=3)
self.fig['DebyeFit'] = fig
ax[0].plot(self.f, respRe, 'r-')
ax[1].plot(self.f, respIm, 'r-')
ax[2].semilogx(self.tau, self.mDD, 'r-')
ax[2].set_xlim(max(self.tau), min(self.tau))
ax[2].set_ylim(0., max(self.mDD))
ax[2].grid(True)
ax[2].set_xlabel(r'$\tau$ (s)')
ax[2].set_ylabel('$m$ (-)')
else:
self.phiDD = IDD.response
if showFit:
fig, ax = self.showData(nrows=3)
self.fig['DebyeSpectrum'] = fig
ax[2].semilogx(self.tau, self.mDD, 'r-')
[docs]
def totalChargeability(self):
"""Total chargeability (sum) from Debye curve."""
return sum(self.mDD)
[docs]
def logMeanTau(self):
"""Mean logarithmic relaxation time (50% cumulative log curve)."""
return exp(np.sum(np.log(self.tau) * self.mDD) / sum(self.mDD))
[docs]
def showAll(self, save=False, ax=None):
"""Plot spectrum, Cole-Cole fit and Debye distribution."""
if np.any(self.mCC): # generate title strings
mCC = self.mCC
rstr = r'$\rho$={:.4f} '
cstr = r'CC: m={:.3f} $\tau$={:.1e}s c={:.2f} '
if len(mCC) == 7: # double Cole-Cole
tstr = rstr + cstr + cstr
elif len(mCC) == 6: # double Cole-Cole only Phi
tstr = cstr + cstr
elif len(mCC) == 4:
tstr = rstr + cstr
else:
tstr = cstr
tCC = tstr.format(*mCC)
if ax is None:
fig, ax = pg.plt.subplots(nrows=2+(self.mDD is not None),
figsize=(12, 12))
else:
fig = ax[0].figure
self.fig['all'] = fig
fig.subplots_adjust(hspace=0.25)
# amplitude
drawAmplitudeSpectrum(ax[0], self.f, self.amp,
label='data', ylog=0)
if np.any(self.ampDD):
ax[0].plot(self.f, self.ampDD, 'm-', label='DD response')
if np.any(self.ampCC):
ax[0].semilogx(self.f, self.ampCC, 'r-', label='CC model')
ax[0].legend(loc='best')
# phase
if np.any(self.ampOrg):
ax[0].semilogx(self.f, self.ampOrg, 'cx-', label='org. data')
ax[0].legend(loc='best')
if np.any(self.phiOrg):
ax[1].semilogx(self.f, self.phiOrg * 1e3, 'cx-', label='org. data')
ax[1].semilogx(self.f, self.phi * 1e3, 'b+-', label='data')
if np.any(self.phiCC):
ax[1].semilogx(self.f, self.phiCC * 1e3, 'r-', label='CC model')
if np.any(self.phiDD):
ax[1].semilogx(self.f, self.phiDD * 1e3, 'm-', label='DD model')
ax[1].grid(True)
ax[1].legend(loc='best')
ax[1].set_xlabel('f (Hz)')
ax[1].set_ylabel('-phi (mrad)')
if np.any(self.mCC):
ax[1].set_title(tCC, loc='left')
if np.any(self.mDD):
mtot = self.totalChargeability()
lmtau = self.logMeanTau()
tDD = r'DD: m={:.3f} $\tau$={:.1e}s'.format(mtot, lmtau)
ax[2].semilogx(self.tau, self.mDD * 1e3)
ax[2].set_xlim(ax[2].get_xlim()[::-1])
ax[2].grid(True)
ax[2].set_xlabel(r'$\tau$ (s)')
ax[2].set_ylabel('m (mV/V)')
ax[2].set_title(tDD, loc='left')
if save:
if isinstance(save, str):
savename = save
else:
savename = self.basename + '.pdf'
fig.savefig(savename, bbox_inches='tight')
pg.plt.show(block=False)
return fig, ax
def run_SIPSPectrum(myfile):
"""Run typical SIP spectrum workflow for a given file."""
sip = SIPSpectrum(myfile)
# sip.showData(znorm=True)
if True: # Pelton
sip.fitCCEM()
else:
sip.removeEpsilonEffect()
sip.fitColeCole(useCond=False)
sip.fitDebyeModel() # , showFit=True)
# create titles and plot data, fit and model
sip.showAll(save=True)
if __name__ == "__main__":
if len(sys.argv) < 2:
print("No filename given, falling back to test case")
run_SIPSPectrum('sipexample.txt')
else:
run_SIPSPectrum(sys.argv[1])
