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diff --git a/extrema2.m b/extrema2.m new file mode 100644 index 0000000..53a5e76 --- /dev/null +++ b/extrema2.m @@ -0,0 +1,174 @@ +function [xymax,smax,xymin,smin] = extrema2(xy,varargin)
+%EXTREMA2 Gets the extrema points from a surface.
+% [XMAX,IMAX,XMIN,IMIN] = EXTREMA2(X) returns the maxima and minima
+% elements of the matriz X ignoring NaN's, where
+% XMAX - maxima points in descending order (the bigger first and so on)
+% IMAX - linear indexes of the XMAX
+% XMIN - minima points in descending order
+% IMIN - linear indexes of the XMIN.
+% The program uses EXTREMA.
+%
+% The extrema points are searched only through the column, the row and
+% the diagonals crossing each matrix element, so it is not a perfect
+% mathematical program and for this reason it has an optional argument.
+% The user should be aware of these limitations.
+%
+% [XMAX,IMAX,XMIN,IMIN] = EXTREMA2(X,1) does the same but without
+% searching through the diagonals (less strict and perhaps the user gets
+% more output points).
+%
+% 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).
+%
+% Note: To change the linear index to (i,j) use IND2SUB.
+%
+% Example:
+% [x,y] = meshgrid(-2:.2:2,3:-.2:-2);
+% z = x.*exp(-x.^2-y.^2); z(10,7)= NaN; z(16:19,13:17) = NaN;
+% surf(x,y,z), shading interp
+% [zmax,imax,zmin,imin] = extrema2(z);
+% hold on
+% plot3(x(imax),y(imax),zmax,'bo',x(imin),y(imin),zmin,'ro')
+% for i = 1:length(zmax)
+% text(x(imax(i)),y(imax(i)),zmax(i),[' ' num2str(zmax(i))])
+% end
+% for i = 1:length(zmin)
+% text(x(imin(i)),y(imin(i)),zmin(i),[' ' num2str(zmin(i))])
+% end
+% hold off
+%
+% See also EXTREMA, MAX, MIN
+
+% Written by
+% Lic. on Physics Carlos Adrián Vargas Aguilera
+% Physical Oceanography MS candidate
+% UNIVERSIDAD DE GUADALAJARA
+% Mexico, 2005
+%
+% nubeobscura@hotmail.com
+
+% From : http://www.mathworks.com/matlabcentral/fileexchange
+% File ID : 12275
+% Submited at: 2006-09-14
+% 2006-11-11 : English translation from spanish.
+% 2006-11-17 : Accept NaN's.
+% 2006-11-22 : Fixed bug in INDX (by JaeKyu Suhr)
+% 2007-04-09 : Change name to MAXIMA2, and definition added.
+
+M = size(xy);
+if length(M) ~= 2
+ error('Entry must be a matrix.')
+end
+N = M(2);
+M = M(1);
+
+% Search peaks through columns:
+[smaxcol,smincol] = extremos(xy);
+
+% Search peaks through rows, on columns with extrema points:
+im = unique([smaxcol(:,1);smincol(:,1)]); % Rows with column extrema
+[smaxfil,sminfil] = extremos(xy(im,:).');
+
+% Convertion from 2 to 1 index:
+smaxcol = sub2ind([M,N],smaxcol(:,1),smaxcol(:,2));
+smincol = sub2ind([M,N],smincol(:,1),smincol(:,2));
+smaxfil = sub2ind([M,N],im(smaxfil(:,2)),smaxfil(:,1));
+sminfil = sub2ind([M,N],im(sminfil(:,2)),sminfil(:,1));
+
+% Peaks in rows and in columns:
+smax = intersect(smaxcol,smaxfil);
+smin = intersect(smincol,sminfil);
+
+% Search peaks through diagonals?
+if nargin==1
+ % Check peaks on down-up diagonal:
+ [iext,jext] = ind2sub([M,N],unique([smax;smin]));
+ [sextmax,sextmin] = extremos_diag(iext,jext,xy,1);
+
+ % Check peaks on up-down diagonal:
+ smax = intersect(smax,[M; (N*M-M); sextmax]);
+ smin = intersect(smin,[M; (N*M-M); sextmin]);
+
+ % Peaks on up-down diagonals:
+ [iext,jext] = ind2sub([M,N],unique([smax;smin]));
+ [sextmax,sextmin] = extremos_diag(iext,jext,xy,-1);
+
+ % Peaks on columns, rows and diagonals:
+ smax = intersect(smax,[1; N*M; sextmax]);
+ smin = intersect(smin,[1; N*M; sextmin]);
+end
+
+% Extrema points:
+xymax = xy(smax);
+xymin = xy(smin);
+
+% Descending order:
+[temp,inmax] = sort(-xymax); clear temp
+xymax = xymax(inmax);
+smax = smax(inmax);
+[xymin,inmin] = sort(xymin);
+smin = smin(inmin);
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+function [smax,smin] = extremos(matriz)
+% Peaks through columns or rows.
+
+smax = [];
+smin = [];
+
+for n = 1:length(matriz(1,:))
+ [temp,imaxfil,temp,iminfil] = extrema(matriz(:,n)); clear temp
+ if ~isempty(imaxfil) % Maxima indexes
+ imaxcol = repmat(n,length(imaxfil),1);
+ smax = [smax; imaxfil imaxcol];
+ end
+ if ~isempty(iminfil) % Minima indexes
+ imincol = repmat(n,length(iminfil),1);
+ smin = [smin; iminfil imincol];
+ end
+end
+
+
+function [sextmax,sextmin] = extremos_diag(iext,jext,xy,A)
+% Peaks through diagonals (down-up A=-1)
+
+[M,N] = size(xy);
+if A==-1
+ iext = M-iext+1;
+end
+[iini,jini] = cruce(iext,jext,1,1);
+[iini,jini] = ind2sub([M,N],unique(sub2ind([M,N],iini,jini)));
+[ifin,jfin] = cruce(iini,jini,M,N);
+sextmax = [];
+sextmin = [];
+for n = 1:length(iini)
+ ises = iini(n):ifin(n);
+ jses = jini(n):jfin(n);
+ if A==-1
+ ises = M-ises+1;
+ end
+ s = sub2ind([M,N],ises,jses);
+ [temp,imax,temp,imin] = extrema(xy(s)); clear temp
+ sextmax = [sextmax; s(imax)'];
+ sextmin = [sextmin; s(imin)'];
+end
+
+
+function [i,j] = cruce(i0,j0,I,J)
+% Indexes where the diagonal of the element io,jo crosses the left/superior
+% (I=1,J=1) or right/inferior (I=M,J=N) side of an MxN matrix.
+
+arriba = 2*(I*J==1)-1;
+
+si = (arriba*(j0-J) > arriba*(i0-I));
+i = (I - (J+i0-j0)).*si + J+i0-j0;
+j = (I+j0-i0-(J)).*si + J;
+
+
+% Carlos Adrián Vargas Aguilera. nubeobscura@hotmail.com
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