MATLAB Central Newsreader - local maxima lines:MATLAB CODE

local maxima lines:MATLAB CODE

carlosmvmendes@gmail.com — Fri, 04 May 2007 04:11:19 -0400

Hello!

Is there any Matlab function to obtain the local maxima lines?

Wavemenu in the wavelet toolbox does it but i can=B4t find the actual
Matlab command line function.

If that fucntion doesn=B4t exist in Matlab function, is there any free
available Matlab code to perform it?

Thanks in advance.

Carlos

Re: local maxima lines:MATLAB CODE

Paul Mennen — Fri, 04 May 2007 19:10:46 -0400

> Is there any Matlab function to obtain the local
> maxima lines?
> Carlos

I assume you just want to find the local maxima in a vector?
If so, a fairly simple minded expression to return the indexes of all
the local maxima of a vector "a" follows:

find(a>=[a(2:end) inf] & a>[inf a(1:end-1)])

If the maxima is a sequence of several equal values, this will return
the index of the first of those. If you wanted it to return the index
of the last one, just swap the >= and the >. If you wanted to
include endpoints of the sequence as possible local maxima, just
change the two instances of "inf" to "-inf".

If you think about how this works, I think you will find it
easy to extend it to look for local minima as well.

This may be good enough for most applications, although the reason I
called it "simple minded" is that it can be fooled by a plateau. For
instance a sequence such as [1 2 3 3 3 4 4] has no local maximum, but
one will be identified by my simple minded approach.

Suppose we take this 15 element example:

a = [1 2 2 3 2 1 1 5 1 17 17 17 15 20 1 ];
% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 - index of a

A better algorithm that handles plateaus should return the following
indices as local maxima: 4, 8, 10, 14. And for local minima is should
return indicies: 6, 9, 13

This is tricky, but I think you will find that the following code
produces this result exactly:

--------------------------------------------------------------
p = 1:length(a);
b = diff([inf a])~=0;
aa = a(b); pp = p(b);
maxima = pp(find(aa>[aa(2:end) inf] & aa>[inf aa(1:end-1)]))
minima = pp(find(aa<[aa(2:end) -inf] & aa<[-inf aa(1:end-1)]))
---------------------------------------------------------------

~Paul

Re: local maxima lines:MATLAB CODE

Pavle Boskoski — Sun, 11 May 2008 15:32:02 -0400

carlosmvmendes@gmail.com wrote in message
<1178277079.853382.320360@n59g2000hsh.googlegroups.com>...
> Hello!
>
> Is there any Matlab function to obtain the local maxima lines?
>
> Wavemenu in the wavelet toolbox does it but i can=B4t find
the actual
> Matlab command line function.
>
> If that fucntion doesn=B4t exist in Matlab function, is
there any free
> available Matlab code to perform it?
>
> Thanks in advance.
>
> Carlos
>

Here is some script that recreates the plot that you can see
from the wave menu:

% First generate the wavelet coefficients
% sig is your signal normal use of CWT command
r=cwt(sig,'haar',15000);

%clear some stuff if you run this over and over
clear coefs coefs_max coefs_fin;

indBeg = size(r,1);
scales = a_coefs;
coefs = r;
%--------------------
[tmp,I1] = sort(scales);
[tmp,I2] = sort(I1);
coefs = coefs(I2,:);
coefs_max = localmax(coefs,indBeg); %localmax is a built-in
in wavelet toolbox
coefs_fin = coefs_max(I1,:);

clear coefs coefs_max;

% Prepare the plot
[nbRow,nbCol] = size(coefs_fin);
markersize = 2;
marker = 'o';
linestyle = 'none';
color = wtbutils('colors','cw1d','spy');
x = [1:nbCol];

[iRow, iCol]= find(coefs_fin);

%Plot the maxima
plot(x(iCol),a_coefs(iRow), ...
   'marker',marker, ...
   'markersize',markersize, ...
   'linestyle',linestyle, ...
   'color','r');

I hope this was the thing that you were looking for.

Pavle

Re: local maxima lines:MATLAB CODE

Pavle Boskoski — Sun, 11 May 2008 15:39:03 -0400

There was a small error in my previous script:

r=cwt(sig,'haar',15000);

should be:

r=cwt(sig,a_coefs,'haar');

where a_coefs are the scales on which you would like to
perform the CWT

Pavle