matthiasm@8: function [x,n]=localmaxmin(y,xn)
matthiasm@8: %LOCALMAXMIN(Y) Local Maxima and Minima.
matthiasm@8: % X = LOCALMAXMIN(Y) or LOCALMAXMIN(Y,'max') for vector Y returns a logical
matthiasm@8: % vector X the same size as Y such that Y(X) contains the local maxima in Y.
matthiasm@8: %
matthiasm@8: % N = LOCALMAXMIN(Y,'min') for vector Y returns a logical vector N the same
matthiasm@8: % size as Y such that Y(N) contains the local minima in Y.
matthiasm@8: %
matthiasm@8: % [X,N] = LOCALMAXMIN(Y) for vector Y returns logical vectors X and N such
matthiasm@8: % that Y(X) contains the local maxima and Y(N) contains the local minima.
matthiasm@8: %
matthiasm@8: % When Y is a matrix, outputs are logical array(s) the same size as Y, and
matthiasm@8: % the minima and/or maxima are computed down the rows of each column in Y.
matthiasm@8: %
matthiasm@8: % See also MAX, MIN.
matthiasm@8: 
matthiasm@8: % D.C. Hanselman, University of Maine, Orono, ME 04469
matthiasm@8: % MasteringMatlab@yahoo.com
matthiasm@8: % Mastering MATLAB 7
matthiasm@8: % 2006-03-08
matthiasm@8: 
matthiasm@8: mm=['min';'max'];
matthiasm@8: if nargin==1
matthiasm@8:    xn='max';
matthiasm@8: elseif nargin~=2
matthiasm@8:    error('localmaxmin:NotEnoughInputArguments',...
matthiasm@8:          'One or Two Input Arguments Required.')
matthiasm@8: end
matthiasm@8: if ~ischar(xn) || isempty(strcmp(xn,mm))
matthiasm@8:    error('localmaxmin:UnknownArgument','Unknown Second Input Argument.')
matthiasm@8: end
matthiasm@8: if ~isnumeric(y) || ~isreal(y)
matthiasm@8:    error('localmaxmin:IncorrectDataType','Y Must be Real Valued.')
matthiasm@8: end
matthiasm@8: ysiz=size(y);
matthiasm@8: isrow=ysiz(1)==1;
matthiasm@8: if isrow % if row, convert to column for now
matthiasm@8:    y=y';
matthiasm@8:    ysiz(1)=ysiz(2);
matthiasm@8:    ysiz(2)=1;
matthiasm@8: end
matthiasm@8: if ysiz(1)<4
matthiasm@8:    error('localmaxmin:InsufficientData','Y Must Have at Least 4 Elements.')
matthiasm@8: end
matthiasm@8: x=false(ysiz);
matthiasm@8:    
matthiasm@8: sdiff=sign(diff(y));
matthiasm@8: zdiff=sdiff==0;
matthiasm@8: idz=find(sum(zdiff)); % columns where zero differences appear
matthiasm@8: 
matthiasm@8: if strcmp(xn,'min') || nargout==2   % get minima
matthiasm@8:    x(2:end-1,:)=diff(sdiff)==2;
matthiasm@8:    x(1,:)=sdiff(1,:)>0;
matthiasm@8:    x(end,:)=sdiff(end,:)<0;
matthiasm@8:    if any(zdiff)
matthiasm@8:       ir=1:ysiz(1);
matthiasm@8:       for k=idz % handle columns with zero differences
matthiasm@8:          itmp=ir;
matthiasm@8:          itmp(zdiff(:,k))=[];
matthiasm@8:          if all(sdiff(:,k)==0) % entire column is flat
matthiasm@8:             x(:,k)=true;
matthiasm@8:          else
matthiasm@8:             tmp=diff(sign(diff(y(itmp,k))))==2;
matthiasm@8:             x(itmp(tmp)+1,k)=true;
matthiasm@8:             if sdiff(1,k)==0
matthiasm@8:                nr=find(sdiff(:,k)>0,1);
matthiasm@8:                nf=find(sdiff(:,k)<0,1);
matthiasm@8:                if ~(isempty(nr)||isempty(nf))
matthiasm@8:                   x(1,k)=nr<nf;
matthiasm@8:                end
matthiasm@8:             end
matthiasm@8:             if sdiff(end,k)==0
matthiasm@8:                nr=find(sdiff(:,k)>0,1,'last');
matthiasm@8:                nf=find(sdiff(:,k)<0,1,'last');
matthiasm@8:                if ~(isempty(nr)||isempty(nf))
matthiasm@8:                   x(end,k)=nr<nf;
matthiasm@8:                end
matthiasm@8:             end
matthiasm@8:          end
matthiasm@8:       end
matthiasm@8:    end
matthiasm@8:    if isrow
matthiasm@8:       x=x.';
matthiasm@8:    end
matthiasm@8:    if nargout==2
matthiasm@8:       n=x;
matthiasm@8:    end
matthiasm@8: end
matthiasm@8: if strcmp(xn,'max') || nargout==2 % get maxima
matthiasm@8:    x=false(ysiz);
matthiasm@8:    x(2:end-1,:)=diff(sdiff)==-2;
matthiasm@8:    x(1,:)=sdiff(1,:)<0;
matthiasm@8:    x(end,:)=sdiff(end,:)>0;
matthiasm@8:    if any(zdiff)
matthiasm@8:       ir=1:ysiz(1);
matthiasm@8:       for k=idz % handle columns with zero differences
matthiasm@8:          itmp=ir;
matthiasm@8:          itmp(zdiff(:,k))=[];
matthiasm@8:          if all(sdiff(:,k)==0) % entire column is flat
matthiasm@8:             x(:,k)=true;
matthiasm@8:          else
matthiasm@8:             tmp=diff(sign(diff(y(itmp,k))))==-2;
matthiasm@8:             x(itmp(tmp)+1,k)=true;
matthiasm@8:             if sdiff(1,k)==0
matthiasm@8:                nr=find(sdiff(:,k)>0,1);
matthiasm@8:                nf=find(sdiff(:,k)<0,1);
matthiasm@8:                if ~(isempty(nr)||isempty(nf))
matthiasm@8:                   x(1,k)=nr>nf;
matthiasm@8:                end
matthiasm@8:             end
matthiasm@8:             if sdiff(end,k)==0
matthiasm@8:                nr=find(sdiff(:,k)>0,1,'last');
matthiasm@8:                nf=find(sdiff(:,k)<0,1,'last');
matthiasm@8:                if ~(isempty(nr)||isempty(nf))
matthiasm@8:                   x(end,k)=nr>nf;
matthiasm@8:                end
matthiasm@8:             end
matthiasm@8:          end
matthiasm@8:       end
matthiasm@8:    end
matthiasm@8:    if isrow
matthiasm@8:       x=x';
matthiasm@8:    end
matthiasm@8: end