## Monday, April 12, 2010

### Full width at half maximum

Hi everyone, I have a new reader and we talked about Full Width at Half Maximum - FWHM here (in the comments).

We developed a code for finding the FWHM of a given peak in a function, and now the code will be posted in this post.

function [fwhm_positions, fwhm_values] = fwhm(x, positions)
tp = positions; //assign the peak position into tp

t_aux = 1;
while x(tp) < 2*x(tp + t_aux),
t_aux = t_aux + 1;
end;

fwhm_positions = (tp - t_aux):(tp + t_aux);
fwhm_values = x((tp - t_aux):(tp + t_aux));
endfunction;

t = 1:1000;
m = 350;
s = 180;
x = exp(-(1/(2*s))*(t - m).^2); // 'x' is a gaussian function

plot(t, x);
plot(fwhm_positions, fwhm_values, 'r.-');

Now, look the result following.

Thanks CV, you helped us too much!
God bless you.

Gary Nelson said...

I copied the code into scilab editor, saved it and tried to execute it. It plots a gaussian, but yields an undefined variable for fwhm_positions here
plot(fwhm_positions, fwhm_values, 'r.-');

so the red dots don't plot. It looks as if the function does not execute. This is what I copied and tried to run. Also ran it from the console--same result

function [fwhm_positions, fwhm_values] = fwhm(x, positions)
tp = positions; //assign the peak position into tp

t_aux = 1;
while x(tp) < 2*x(tp + t_aux),
t_aux = t_aux + 1;
end;

fwhm_positions = (tp - t_aux):(tp + t_aux);
fwhm_values = x((tp - t_aux):(tp + t_aux));
endfunction;

t = 1:1000;
m = 350;
s = 180;
x = exp(-(1/(2*s))*(t - m).^2); // 'x' is a gaussian function

plot(t, x);
plot(fwhm_positions, fwhm_values, 'r.-');

What to do??

Gary Nelson said...

I validated that the function does not execute. After execution, variables after the endfunction can be validated from the console, but t_aux and tp are undefined.

Why does not the function execute?

Thanks

Sheep said...

Hi Gery,

try it:

t = 1:1000;
m = 350;
s = 180;
x = exp(-(1/(2*s))*(t - m).^2); // 'x' is a gaussian function

plot(t, x);

[fwhm_positions, fwhm_values] = fwhm(x, m);
plot(fwhm_positions, fwhm_values, 'r.-');

After 'endfunction'

Gary Nelson said...

Well, I tried it as suggested and get the same error. I copy the suggested code from the web page into the scilab editor, save it, and execute it.

in console we see

-->exec('/fwhmtest.sce', -1)
plot(fwhm_positions, fwhm_values, 'r.-');
!--error 4
Undefined variable: fwhm_positions

at line 19 of exec file called by :
exec('/fwhmtest.sce', -1)

Obviously, you don't get this result. I don't see any error in what I am doing, but the result is non-positive.

Sheep said...

My friend Gary, this is the full code:

function [fwhm_positions, fwhm_values] = fwhm(x, positions)
tp = positions; //assign the peak position into tp

t_aux = 1;
while x(tp) < 2*x(tp + t_aux),
t_aux = t_aux + 1;
end;

fwhm_positions = (tp - t_aux):(tp + t_aux);
fwhm_values = x((tp - t_aux):(tp + t_aux));
endfunction;

t = 1:1000;
m = 350;
s = 180;
x = exp(-(1/(2*s))*(t - m).^2); // 'x' is a gaussian function

plot(t, x);

[fwhm_positions, fwhm_values] = fwhm(x, m);
plot(fwhm_positions, fwhm_values, 'r.-');

Try to execute the code using "ctrl + l", directly from the editor.

Thank you for your contribution, again.

See you.

CV said...

Hi Sheep!
Thanks for sharing!