<Text-field style="Heading 1" layout="Heading 1">Introduction</Text-field>

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Complex Nonlinear Least Squares Fitting of Immittance Data

David A. Harrington University of Victoria, Canada dharr@uvic.ca

This worksheet provides a procedure immfit that carries out complex nonlinear least squares fitting of experimental data to an arbitrary function of s = I\317\211, where I is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JkYrLUkmbXNxcnRHRiQ2Iy1GIzYmLUkjbW9HRiQ2LlEqJnVtaW51czA7RicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGPC8lKnNlcGFyYXRvckdGPC8lKXN0cmV0Y2h5R0Y8LyUqc3ltbWV0cmljR0Y8LyUobGFyZ2VvcEdGPC8lLm1vdmFibGVsaW1pdHNHRjwvJSdhY2NlbnRHRjwvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZQLUkjbW5HRiQ2JVEiMUYnRjpGPUY6Rj1GOkY9RitGOkY9 and \317\211 = 2\317\200f is the angular frequency with f the frequency in Hz. This can be used to fit impedance, admittance or other similar data, in which real and imaginary parts are measured as a function of frequency, to theoretical expressions such as expressions for the impedance of an electrical circuit. For example, in electrochemical impedance spectroscopy (EIS), measured impedance data for electrochemical reactions is modeled using electrical equivalent circuits. Alternatively, the data can be fitted to impedance functions predicted by physicochemical models, such as kinetic reaction schemes.

The procedure sets up the objective least squares function and passes it to Maple's NLPSolve routine in the Optimization package for minimization, using the nonlinearsimplex method by default. Different weighting schemes commonly used in EIS are implemented, and a variety of statistics are generated, such as standard errors. The code is in the startup code edit region, and runs before any code below.

The examples given enter the data directly in the worksheet, but the user can import data from a text data file using Maple's file reading commands (readdata, readline, fscanf etc) or from an Excel spreadsheet using the ExcelTools:-Import command. As usual in nonlinear regression, reasonable inital starting guesses for the parameters should be provided to prevent convergence to a local minimum that is different from the global minimum. It will also help if the data is scaled to be within a few orders of magnitude of unity.

<Text-field style="Heading 1" layout="Heading 1">Description of procedure immfit</Text-field>

Procedure immfit fits an arbitrary function of s = i\317\211 to complex experimental immittance data using nonlinear least squares, as implemented in Maple's NLPSolve routine in the Optimization package.

Usage: immfit(freqs,exptRe,exptIm,fn,[inivars],[svars],[weights],[errors],[samples],[printfreq],[conflevel],[options for NLPSolve])

Parameters in brackets are optional. Those after inivars may be in any order, except for the options for NLPSolve, which should be last.

freqs

Vector or list

Experimental frequencies.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJpRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y2USdub3JtYWxGJw==

exptRe

Vector or list

Experimental real parts of the immittance

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSVpLFJlRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJy1GLzYjUSFGJy9GNlEnbm9ybWFsRic=

exptIm

Vector or list

Experimental imaginary parts of the immittance. These will be negative for the usual first quadrant impedances.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSVpLEltRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJy1GLzYjUSFGJy9GNlEnbm9ybWFsRic=

algebraic expression

Function of s to be fitted. Here s means LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21uR0YkNiRRLSZJbWFnaW5hcnlJO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RMSZJbnZpc2libGVUaW1lcztGJ0Y1LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y+LyUpc3RyZXRjaHlHRj4vJSpzeW1tZXRyaWNHRj4vJShsYXJnZW9wR0Y+LyUubW92YWJsZWxpbWl0c0dGPi8lJ2FjY2VudEdGPi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRk0tRiw2JVEoJm9tZWdhO0YnLyUnaXRhbGljR0Y+RjVGNUYrLyUrZXhlY3V0YWJsZUdGPkY1 or 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, were LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC8lK2V4ZWN1dGFibGVHRj1GOQ==is frequency and I is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbXNxcnRHRiQ2Iy1GIzYlLUkjbW9HRiQ2LVEoJm1pbnVzO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOS8lKXN0cmV0Y2h5R0Y5LyUqc3ltbWV0cmljR0Y5LyUobGFyZ2VvcEdGOS8lLm1vdmFibGVsaW1pdHNHRjkvJSdhY2NlbnRHRjkvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZILUkjbW5HRiQ2JFEiMUYnRjRGNC8lK2V4ZWN1dGFibGVHRjlGNA==. It is possible to use a different variable for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21uR0YkNiRRLSZJbWFnaW5hcnlJO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RMSZJbnZpc2libGVUaW1lcztGJ0Y1LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y+LyUpc3RyZXRjaHlHRj4vJSpzeW1tZXRyaWNHRj4vJShsYXJnZW9wR0Y+LyUubW92YWJsZWxpbWl0c0dGPi8lJ2FjY2VudEdGPi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRk0tRiw2JVEoJm9tZWdhO0YnLyUnaXRhbGljR0Y+RjVGNUYrLyUrZXhlY3V0YWJsZUdGPkY1 by using the svar parameter. The function should be a real function of s ; a warning is given if LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbXNxcnRHRiQ2Iy1GIzYlLUkjbW9HRiQ2LVEoJm1pbnVzO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOS8lKXN0cmV0Y2h5R0Y5LyUqc3ltbWV0cmljR0Y5LyUobGFyZ2VvcEdGOS8lLm1vdmFibGVsaW1pdHNHRjkvJSdhY2NlbnRHRjkvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZILUkjbW5HRiQ2JFEiMUYnRjRGNC8lK2V4ZWN1dGFibGVHRjlGNA== appears explicitly (i.e., apart from implicitly in s). Another symbol being used for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbXNxcnRHRiQ2Iy1GIzYlLUkjbW9HRiQ2LVEoJm1pbnVzO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOS8lKXN0cmV0Y2h5R0Y5LyUqc3ltbWV0cmljR0Y5LyUobGFyZ2VvcEdGOS8lLm1vdmFibGVsaW1pdHNHRjkvJSdhY2NlbnRHRjkvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZILUkjbW5HRiQ2JFEiMUYnRjRGNC8lK2V4ZWN1dGFibGVHRjlGNA== as specified in interface(imaginaryunit) is accepted.

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

inivars

{name1=value1, name2=value2,...}

Initial (starting) values for the parameters to be fitted. Omitted parameters are given an initial value of 1. Additional parameters and values generate a warning but are ignored. The minimum found can be sensitive to the starting values, so it is recommended that they are supplied. A list or set may be supplied, with a list enforcing the output order.

svar

svar=value

Alternative name for s in the function to be fitted, e.g., svar=p

weights

weights=unit

unit weighting scheme, i.e., unweighted.

weights=magexp

weights for both the real and imaginary parts are inversely proportional to the squared magnitude of the experimental point. Computationally efficient but if data is accidentally very small can lead to numerical problems. This is the default.

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

weights=magtheory

as for magexp except the value of the fitted function at that point is used. This is computationally more intensive than magexp, but not subject to experimental fluctuations and is generally a good choice.

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

weights=propexp

"Proportional" weighting. Here the weights for the real and imaginary parts are different, inversely proportional to the squared magnitude of the real (or imaginary) experimental parts. Can be superior if real and imaginary values are very different in magnitude, but often makes the solution more sensitive to the initial values.

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

weights=proptheory

Proportional weighting using the fitted value of the real (imaginary) parts at that frequency. Computionally the most intensive option.

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

errors

errors=value

Error estimates for the fitted parameters: errors=linear (default) estimates using the linear approximation method from derivatives at the minimum; errors=MC estimates using the Monte Carlo method (computationally very expensive).

samples

samples=value

Number of samples to use for the sampling methods (Monte Carlo or bootstrap) (default = 500)

printfreq

printfreq=value

Number of iterations to print progress information for sampling methods (Monte Carlo or bootstrap) (default=100). Use printfreq=0 to suppress printing.

conflevel

conflevel=value

Confidence level to use for statistical tests, e.g., 0.99 means 99% (default=0.95)

options

These are optional and are passed to the NLPSolve routine. Defaults for method and evaluationlimit are nonlinearsimplex and 2000; other defaults are as used by the NLPSolve routine. Bounds should be given before keyword options.

sequence of name=range

Bounds on the fitting parameters, e.g., R1 = 0..100, R2=0..3. Only available for the modifiednewton method.

method=methodname

Method used. Default is nonlinearsimplex, other possibilities are pcg and modifiednewton

evaluationlimit=positive integer

Maximum number of evaluations of the objective function. Default is 2000.

keyword=value

Other options accepted by NLPSolve, e.g., assume=nonnegative (use of these options has not been tested)

The output is a Maple table containing containing items that describe the input problem, methods used, the fitted values and other various statistical quantities, e.g,

fitted["weightedresidualmeansquare"] gives 0.173961692232186618e-1

fitted["parametervalues"] gives [a = 0.376627005255112e-3, t__d = .517171735093426, t__theta = 0.193295076010340e-1]

eval(fitted) shows the table with all the possible outputs; indices(fitted) gives all names of all possible outputs.

The names of the outputs are similar to those of the Statistics:-Fit output module, but prefixed with "weighted" as appropriate. Specifically:

Results

"parametervalues"

list of equations of fitted parameter values. The order is as specified in inivars if that was given as a list.

"fittedvaluesRe"

Vector of real parts of fitted values

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

"fittedvaluesIm"

Vector of imaginary parts of fitted values

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

"residualsRe"

Vector of residuals of real parts

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"residualsIm"

Vector of residuals of imaginary parts

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

"weightsRe"

Vector of weights for the real parts (at the minimum for theory weights)

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEid0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSVpLFJlRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJy1GLzYjUSFGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y2USdub3JtYWxGJw==

"weightsIm"

Vector of weights for the imaginary parts (at the minimum for theory weights)

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEid0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSVpLEltRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJy1GLzYjUSFGJy9GNlEnbm9ybWFsRic=

"leastsquaresfunction"

the fitted function, with numerical values of the parameters inserted

"weightedresidualsumofsquares"

value of the objective function at the minimum; weighted residual sum of squares

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

"weightedresidualmeansquare"

the weighted sum of the residuals divided by the number of degrees of freedom.

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

"weightedresidualstandarddeviation"

square root of "weightedresidualmeansquare"

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

"standarderrors"

list of standard errors of the parameters

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"confidenceintervals"

list of confidence intervals of the parameters at confidence level conflevel

"tvalue"

list of t ratios, (parameter value)/(standard error); used with tprobability to test if parameter is different from zero.

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

"tprobability"

list of the probabilities that the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEnJmJldGE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GLzYlUSJqRicvRjNRJXRydWVGJy9GNlEnaXRhbGljRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnLUYvNiNRIUYnRjU= would be found to be this large if they really were zero. Two-tailed t-tests on the above t ratios.

"weightedresidualmeansquare(MC)"

weighted residual mean square from Monte Carlo to compare with "weightedresidualmeansquare". Agreement gives confidence in the MC results, and disagreement may occur if the errors in the parameters are too large compared to the mean.

JSFH

"AIC"

Akaike's Information Criterion, 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, where LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw== is the likelihood. This quantity enables comparison of different models; the one with the minimum (most negative) AIC is the best model. The criterion trades off better fit vs number of parameters.

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"AICc"

Akaike's Information Criterion, with bias correction for small samples. This is required for cases when (number of frequencies)/(number of parameters) < 20, but can be used routinely.

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"BIC"

Bayesian Information Criterion. Similar to AIC, but based on Bayesian statistical ideas.

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Settings

"svariable"

value of svar argument passed to immfit

"nfrequencies"

number of frequencies

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiTkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==

"nparameters"

number of parameters in fitting function

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==

"degreesoffreedom"

number of degrees of freedom

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

"initialpoint"

set or list of equations of parameter values used as the initial values for the fitting

"fitfunction"

function that was fitted; the fn passed to immfit

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

"parameternames"

list of parameter names, same order as "parametervalues"

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"weighting"

value of the weights argument passed to immfit, e.g., magexp

"fitmethod"

method used in fitting, e.g., nonlinearsimplex

"fitoptions"

list of the arguments passed to NLPSolve, other than the objective function

"errormethod"

value of errors argument, e.g., MC or linear

"confidencelevel"

value of confidence level; default of 0.95 or as set by conflevel

"samples(MC)"

number of samples used in the MC statistics estimation.

Data

"frequencies"

Vector of experimental frequencies passed to immfit

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"exptRe"

Vector of experimental immittance real parts passed to immfit

"exptIm"

Vector of experimental immittance imaginary parts passed to immfit

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSVpLEltRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJy1GLzYjUSFGJy9GNlEnbm9ybWFsRic=

Examples:

fitted:=immfit(freqs,Y2Reexpt,Y2Imexpt,-a/cosh(sqrt(s*t__d))/(1+s*t__theta),{a= 0.0003, t__d = 0.4,t__theta = 0.03}, weights=magtheory,AIC);

fits -a/cosh(sqrt(s*t__d))/(1+s*t__theta)to the data in the lists freqs,Y2Reexpt,Y2Imexpt using the nonlinearsimplex method with a maximum of 2000 objective evaluations and the magnitude theory weighting scheme. Statistical error analysis is by the default linear method, with the default confidence level of 95%. AIC results will be output. The output is assigned to a table called fitted , which may be used as in the description of the output given above.

fitted:=immfit(freqs,Y2Reexpt,Y2Imexpt,-a/cosh(sqrt(p*t__d))/(1+p*t__theta),svar=p,errors=MC,samples=2000,conflevel=0.99);

As above, but with the i*omega variable now called p, with all initial values 1, and with the default magexp weighting scheme. The Monte Carlo method is used for the statistical analysis with 2000 samples, printing out progress at the default frequency (every 100 iterations), and produces 99% confidence intervals for the parameters.

<Text-field style="Heading 1" layout="Heading 1">Examples</Text-field>

Example 1

An equivalent circuit with a constant phase element, capacitor and three resistors. Give the impedance to be fitted as a function of s = i\317\211

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

LCZJJVJfX3NHNiIiIiIqJCwmKiYpSSJzR0YkSSZhbHBoYUdGJEYlSSZZX19kbEdGJEYlRiUqJCwmSSZSX19jdEdGJEYlKiQsJiomRipGJUkiQ0dGJEYlRiUqJEkiUkdGJCEiIkYlRjZGJUY2RiVGNkYl

Read in or generate some data (lists or Vectors). Frequencies in Hz

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

IiNh

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

NygvSSVSX19zRzYiXTQwMTUxMjAyMzhENjVDQjQvSSZZX19kbEdGJV0zRURGM0M1ODZBRTZDQ0RCL0kmYWxwaGFHRiVdM0ZFQTdBNTdBOTdGNUM1NC9JJlJfX2N0R0YlXTQwMzNFNUVCRTA2NEMzOUQvSSJDR0YlXTNGNkJFODA5QzRFMTBDNTEvSSJSR0YlXTQwMzVGMDU3QURBRTEyNDQ=

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Plot experimental data with fitted function. Use conjugate in complexplot, and negative the experimental imaginary parts in pointplot to get the plot the conventional way up.

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Example 2 Function to fit

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

KihJJXlfXzBHNiIiIiItSSVjb3NoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMqJCkqJkkic0dGJEYlSSV0X19kR0YkRiUjRiUiIiNGJSEiIiwmKiZGL0YlSSt0X18mdGhldGE7R0YkRiVGJUYlRiVGMw==

Generate some data.

IiNK

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

NyUvSSV0X19kRzYiXTNGRDJDMTE0M0ZEOUU5RjgvSSV5X18wR0YlXUJGRDJENTk3NzBBNkExQzYvSSt0X18mdGhldGE7R0YlXTNGODYzRTVBMDkwQTc2QTA=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEmcGxvdHNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSM6LUYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZMLUYsNiVRKGRpc3BsYXlGJ0YvRjItSShtZmVuY2VkR0YkNiQtRiM2LUYrRjUtRiw2JVEqcG9pbnRwbG90RidGL0YyLUZTNiQtRiM2Ky1GLDYjUSFGJy1GIzYnLUYsNiVRJ1ZlY3RvckYnRi9GMi1GNjYtUTAmQXBwbHlGdW5jdGlvbjtGJ0Y5RjtGPkZARkJGREZGRkhGSkZNLUZTNiQtRiM2JS1GLDYlUSlZMlJlZXhwdEYnRi9GMi8lK2V4ZWN1dGFibGVHRj1GOUY5RmpvRjktRjY2LVEiLEYnRjlGOy9GP0YxRkBGQkZERkZGSEZKL0ZOUSwwLjMzMzMzMzNlbUYnLUYjNidGXW9GYG8tRlM2JC1GIzYlLUYsNiVRKVkySW1leHB0RidGL0YyRmpvRjlGOUZqb0Y5RlxwLUYjNictRiw2JVEoc2NhbGluZ0YnRi9GMi1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjI3Nzc3NzhlbUYnL0ZORmRxLUYsNiVRLGNvbnN0cmFpbmVkRidGL0YyRmpvRjlGaG5Gam9GOUY5RlxwRitGNS1GLDYlUSxjb21wbGV4cGxvdEYnRi9GMi1GUzYkLUYjNjEtRiw2JVElZXZhbEYnRi9GMi1GUzYkLUYjNjEtRiw2JVEnZml0dGVkRidGL0YyLUZTNiYtRiM2J0Zobi1JI21zR0YkNiNRNWxlYXN0c3F1YXJlc2Z1bmN0aW9uRidGaG5Gam9GOUY5LyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRlxwLUY2Ni1RIn5GJ0Y5RjtGPkZARkJGREZGRkhGSkZNLUYsNiVRInNGJy9GMEY9RjlGYHEtSSNtbkdGJDYkUSIyRidGOUZocy1GLDYlUScmIzk2MDtGJ0ZedEY5RmhzLUYsNiVRIklGJ0ZedEY5RmhzLUklbXN1cEdGJDYlLUZgdDYkUSMxMEYnRjktRiM2JS1GLDYlUSVsb2dmRidGL0YyRi9GMi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGam9GOUY5RlxwRmF1RmBxLUY2Ni1RKiZ1bWludXMwO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZbdi1GYHQ2JFEiM0YnRjktRjY2LVEjLi5GJ0Y5RjtGPkZARkJGREZGRkhGanVGTUZfdEZccC1GLDYlUSdjb2xvdXJGJ0YvRjJGYHEtRiw2JVEkcmVkRidGL0YyRmpvRjlGOUZqb0Y5RjlGam9GOQ==

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Look at all the possible outputs.

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

JSFH

<Text-field style="Heading 1" layout="Heading 1">References</Text-field>

The use of complex nonlinear least squares fitting in electrochemical impedance spectroscopy is introduced in several of the books on the subject, e.g.,

A. Lasia, Electrochemical Impedance Spectroscopy and its Applications, Spinger, New York, 2014 doi: 10.1007/978-1-4614-8933-7

The method for calculating AIC for weighted data is described in M. Ingdal, R. Johnsen, D.A. Harrington, The Akaike information criterion in weighted regression of immittance data, Electrochimica Acta, 317 (2019) 648-653. doi: 10.1016/j.electacta.2019.06.030

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