Curve fitting for loglog scale

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Navaneeth Tejasvi Mysore Nagendra
Commented: dpb on 10 May 2022
I have fitted a curve using general plot function, now if I want to fit the same data in loglog scale how can I do it.
any help is much appreciated
function [fitresult, gof] = createFit(w, AC1)
% Create a fit.
% Data for 'untitled fit 1' fit:
% X Input : w
% Y Output: AC
% Output:
% fitresult : a fit object representing the fit.
% gof : structure with goodness-of fit info.
% See also FIT, CFIT, SFIT.
% Auto-generated by MATLAB on 10-May-2022 11:38:11
%% Fit: 'untitled fit 1'.
clc;clear,close all;
opts = spreadsheetImportOptions("NumVariables", 6);
% Specify sheet and range
opts.Sheet = "Sheet1";
opts.DataRange = "A2:F202";
% Specify column names and types
opts.VariableNames = ["f1", "sigmaAcZT1", "f2", "SIGMAACZT2", "F2", "SIGMAACZT3"];
opts.VariableTypes = ["double", "double", "double", "double", "double", "double"];
% Import the data
data = readtable("C:\Users\navaneeth\Downloads\IONIC CONDUCTIVITY.xlsx", opts, "UseExcel", false);
% Convert to output type
data = table2array(data);
% Clear temporary variables
clear opts
f = data(:,1)
w = 2*pi*data(:,1);%w = 2*pi*f
AC1 = data(:,2);%AC conductivity sample 1
AC2 = data(:,4);%AC conductivity sample 2
AC3 = data(:,6);%AC conductivity sample 3
[xData1, yData1] = prepareCurveData( w, AC1 );
[xData2, yData2] = prepareCurveData( w, AC2 );
[xData3, yData3] = prepareCurveData( w, AC3 );
% Set up fittype and options.
ft = fittype( 'power2' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Algorithm = 'Levenberg-Marquardt';
opts.Display = 'Off';
opts.StartPoint = [9.32271357188677e-06 0.0429375187609614 2.50935751249309e-06];
% Fit model to data.
[fitresult1, gof1] = fit( xData1, yData1, ft, opts );
[fitresult2, gof2] = fit( xData2, yData2, ft, opts );
[fitresult3, gof3] = fit( xData3, yData3, ft, opts );
% Plot fit with data.
figure( 'Name', 'untitled fit 1' );
h = plot(fitresult1,'k',xData1,yData1,'ok');
hold on
g = plot(fitresult2,'k',xData2,yData2,'or');
hold on
f = plot(fitresult3,'k',xData3,yData3,'ob');
legend('ZT-3','fit', 'Location', 'NorthWest')
set(h, 'LineWidth',2)
set(g, 'LineWidth',2)
set(f, 'LineWidth',2)
% Label axes
xlabel( '\omega');
ylabel('\sigma_{AC} (S/cm)');
grid on
Torsten on 10 May 2022
Plotting in loglog scale is the one thing, fitting is the other. Do the first if you like, don't do the last.
dpb on 10 May 2022
I'll disagree w/ @Torsten that there's never a valid reason for log models; indeed some processes are. The error distribution is mutiplicative rather than additive in this case
As said above, you have two choices -- either
  1. log the variables, fit, evaluate y=10.^f(log10X), loglog(X,Y) (because it does the log10 internally), or
  2. use nonlinear curve fit and fit the appropriate power model directly. In this case your model will still be in original space; loglog() works as normal for both data and fitted result.

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