How to transform a plot to use a logarithmic scale?

[Leonid92]

I wrote the following code in MATLAB:

t = [0:0.001:0.1];
noise = randn(1,size(t,2));
a = 15*10^9;
b = 15*10^(-3);
c = 7*10^8;
y = a*exp(-t/b)+c+noise*100000000;
fun = @(p,t)p(1)*exp(-t/p(2))+p(3);
p0 = [15.5*10^9, 14*10^(-3), 6*10^8];
p = lsqcurvefit(fun, p0, t, y);
t_fit = [0:0.0001:0.1];
y_fit = fun(p,t_fit);
fig = figure('Visible','on');
plot(t,y,'.');
hold on;
grid on;
plot(t_fit,y_fit,'r','linewidth',2);
disp(sprintf('a=%d; b=%.4f; c=%d',p(1),p(2),p(3)))

Thus I generated data whose behavior is described by equation y = a*exp(-t/b)+c, with adding some noise. Then I fit mentioned function to these data and found values of parameters:

a=1.550000e+10; b=0.0149; c=6.000000e+08

The plot of simulated data and fit is below:

One person told me that it would be good to consider this problem in logarithmic scale. Could you please tell me, what is usually implied when talking about transforming ordinary plot to logarithmic scale? How should I implement this procedure? Should I first convert my simulated y-values into log-scale and after that perform fit with another function? What formulas should I use? Is it reasonable to use logarithm with base 10 or logarithm with base 'e'?
I will be very appreciate for any help or advice.
P.S. Unfortunately, I don't have opportunity to ask that person in more detail regarding this question.

 

[jedishrfu]

Check this out

https://www.maths.unsw.edu.au/sites...lfPaced/lesson10/MatlabLesson10_LogScale.html

 

[Leonid92]

Check this out

https://www.maths.unsw.edu.au/sites...lfPaced/lesson10/MatlabLesson10_LogScale.html

Thank you for reply! I know about semilogy, semilogx and loglog functions, but I'd like to understand how to perform conversion from linear scale to logarithmic scale manually, i.e. without embedded MATLAB functions.

 

[Dr Transport]

solve for $t$, it took me two lines, it is easily found.

 

[Leonid92]

solve for $t$, it took me two lines, it is easily found.

You mean

b*ln( (y-c)/a ) = -t

?
I don't understand. I have simulated data and need to convert y-values to log-scale. Should I just take logarithm(y) ?

 

[jedishrfu]

Have you tried substituting log(y_fun) for y_fun in the plot() line?

 

[Leonid92]

Have you tried substituting log(y_fun) for y_fun in the plot() line?

In my code, I changed two lines:

plot(t,log(y),'.');
plot(t_fit,log(y_fit),'r','linewidth',2);

And the plot is:

But I have doubt, is it right? I mean, is this what I need? What is the sense in this operation? I thought that firstly I should convert simulated y-values to log-scale, and then perform fitting with new, logarithmic function - fit logarithmic function to transformed y-values, is it right?

 

[Leonid92]

I tried the following:

t = [0:0.001:0.1];
noise = randn(1,size(t,2));
a = 15*10^9;
b = 15*10^(-3);
c = 7*10^8;
y = a*exp(-t/b)+c+noise*100000000;
y = log(y); % here is the change!
fun = @(p,t)log(p(1)*exp(-t/p(2))+p(3)); % here is the change!
p0 = [15.5*10^9, 14*10^(-3), 6*10^8];
p = lsqcurvefit(fun, p0, t, y);
t_fit = [0:0.0001:0.1];
y_fit = fun(p,t_fit);
fig = figure('Visible','on');
plot(t,y,'.');
hold on;
grid on;
plot(t_fit,y_fit,'r','linewidth',2);
disp(sprintf('a=%d; b=%.4f; c=%d',p(1),p(2),p(3)))

The plot is:

I.e. firstly I converted simulated y-values to ln(y), and then performed fitting with function log( a*exp(-t/b)+c ), and it is seen that fit is not good.
Found parameters in this case are the following:

a=1.550000e+10; b=0.0156; c=6.000001e+08

So for me, transition to log-scale doesn't make sense.

 

[BvU]

Problem being the constant present, and the weights of the individual points. In the normal fit the points values had equal weights. In the fit of the log the low values get disproportional weights.

 

[kreil]

You can change the axis scaling to logarithmic with the XScale/YScale properties of the axes object in the figure:

ax = gca;
ax.YScale = 'log';

If you do this you wouldn't need to calculate any logs beforehand, the axes will transform to a log scale.

More info: https://www.mathworks.com/help/matl...xes-properties.html#budumk7_sep_shared-XScale