external/other/find_extrema.m
function [xmax,imax,xmin,imin] = find_extrema(x)
% Gets the global extrema points from a time series.
%
% INPUTS:
%    - xmax : maxima points in descending order
%    - imax : indexes of the XMAX
%    - xmin : minima points in descending order
%    - imin : indexes of the XMIN
%
% DEFINITION (from http://en.wikipedia.org/wiki/Maxima_and_minima):
%     In mathematics, maxima and minima, also known as extrema, are points in
%     the domain of a function at which the function takes a largest value
%     (maximum) or smallest value (minimum), either within a given
%     neighbourhood (local extrema) or on the function domain in its entirety
%     (global extrema).
%
% AUTHORS:  
%     Carlos Adrin Vargas Aguilera, nubeobscura@hotmail.com, 2004
%     Physical Oceanography MS candidate
%     UNIVERSIDAD DE GUADALAJARA 

xmax = [];
imax = [];
xmin = [];
imin = [];

% Vector input?
Nt = numel(x);
if Nt ~= length(x)
    error('Entry must be a vector.')
end

% NaN's:
inan = find(isnan(x));
indx = 1:Nt;
if ~isempty(inan)
    indx(inan) = [];
    x(inan) = [];
    Nt = length(x);
end

% Difference between subsequent elements:
dx = diff(x);

% Is an horizontal line?
if ~any(dx)
    return
end

% Flat peaks? Put the middle element:
a = find(dx~=0);              % Indexes where x changes
lm = find(diff(a)~=1) + 1;    % Indexes where a do not changes
d = a(lm) - a(lm-1);          % Number of elements in the flat peak
a(lm) = a(lm) - floor(d/2);   % Save middle elements
a(end+1) = Nt;

% Peaks?
xa  = x(a);             % Serie without flat peaks
b = (diff(xa) > 0);     % 1  =>  positive slopes (minima begin)
% 0  =>  negative slopes (maxima begin)
xb  = diff(b);          % -1 =>  maxima indexes (but one)
% +1 =>  minima indexes (but one)
imax = find(xb == -1) + 1; % maxima indexes
imin = find(xb == +1) + 1; % minima indexes
imax = a(imax);
imin = a(imin);

nmaxi = length(imax);
nmini = length(imin);

% Maximum or minumim on a flat peak at the ends?
if (nmaxi==0) && (nmini==0)
    if x(1) > x(Nt)
        xmax = x(1);
        imax = indx(1);
        xmin = x(Nt);
        imin = indx(Nt);
    elseif x(1) < x(Nt)
        xmax = x(Nt);
        imax = indx(Nt);
        xmin = x(1);
        imin = indx(1);
    end
    return
end

% Maximum or minumim at the ends?
if (nmaxi==0)
    imax(1:2) = [1 Nt];
elseif (nmini==0)
    imin(1:2) = [1 Nt];
else
    if imax(1) < imin(1)
        imin(2:nmini+1) = imin;
        imin(1) = 1;
    else
        imax(2:nmaxi+1) = imax;
        imax(1) = 1;
    end
    if imax(end) > imin(end)
        imin(end+1) = Nt;
    else
        imax(end+1) = Nt;
    end
end
xmax = x(imax);
xmin = x(imin);

% NaN's:
if ~isempty(inan)
    imax = indx(imax);
    imin = indx(imin);
end

% Same size as x:
imax = reshape(imax,size(xmax));
imin = reshape(imin,size(xmin));

% Descending order:
[temp,inmax] = sort(-xmax);
xmax = xmax(inmax);
imax = imax(inmax);
[xmin,inmin] = sort(xmin);
imin = imin(inmin);


