peakfinder(x0, thresh, extrema)

function varargout = peakfinder(x0, thresh, extrema)
%PEAKFINDER Noise tolerant fast peak finding algorithm
%   INPUTS:
%       x0 - A real vector from the maxima will be found (required)
%       thresh - The amount above surrounding data for a peak to be
%           identified (default = (max(x0)-min(x0))/4). Larger values mean
%           the algorithm is more selective in finding peaks.
%       extrema - 1 if maxima are desired, -1 if minima are desired
%           (default = maxima, 1)
%   OUTPUTS:
%       peakLoc - The indicies of the identified peaks in x0
%       peakMag - The magnitude of the identified peaks
%
%   [peakLoc] = peakfinder(x0) returns the indicies of local maxima that
%       are at least 1/4 the range of the data above surrounding data.
%
%   [peakLoc] = peakfinder(x0,thresh) returns the indicies of local maxima
%       that are at least thresh above surrounding data.
%
%   [peakLoc] = peakfinder(x0,thresh,extrema) returns the maxima of the
%       data if extrema > 0 and the minima of the data if extrema < 0
%
%   [peakLoc, peakMag] = peakfinder(x0,...) returns the indicies of the
%       local maxima as well as the magnitudes of those maxima
%
%   If called with no output the identified maxima will be plotted along
%       with the input data.
%
%   Note: If repeated values are found the first is identified as the peak
%
% Ex:
% t = 0:.0001:10;
% x = 12*sin(10*2*pi*t)-3*sin(.1*2*pi*t)+randn(1,numel(t));
% x(1250:1255) = max(x);
% peakfinder(x)
%
% Copyright Nathanael C. Yoder 2009 ([e-mail])

% Perform error checking and set defaults if not passed in
error(nargchk(1,3,nargin,'struct'));
error(nargoutchk(0,2,nargout,'struct'));

s = size(x0);
flipData =  s(1) < s(2);
len0 = numel(x0);
if len0 ~= s(1) && len0 ~= s(2)
    error('PEAKFINDER:Input','The input data must be a vector')
elseif isempty(x0)
    varargout = {[],[]};
    return;
end
if ~isreal(x0)
    warning('PEAKFINDER:NotReal','Absolute value of data will be used')
    x0 = abs(x0);
end

if nargin < 2 || isempty(thresh)
    thresh = (max(x0)-min(x0))/4;
elseif ~isnumeric(thresh) || ~isreal(thresh)
    thresh = (max(x0)-min(x0))/4;
    warning('PEAKFINDER:VectorThresh',...
        sprintf('The threshold must be a real scalar.  A threshold of %.4g will be used',thresh))
elseif numel(thresh) > 1
    warning('PEAKFINDER:VectorThresh','The threshold must be a scalar.  The first threshold in the vector will be used.')
    thresh = thresh(1);
end
if nargin < 3 || isempty(extrema)
    extrema = 1;
else
    extrema = sign(extrema(1)); % Should only be 1 or -1 but make sure
    if extrema == 0
        error('PEAKFINDER:ZeroMaxima','Either 1 (for maxima) or -1 (for minima) must be input for extrema');
    end
end

x0 = extrema*x0(:); % Make it so we are finding maxima regardless
dx0 = diff(x0); % Find derivative
dx0(dx0 == 0) = -eps; % This is so we find the first of repeated values
ind = find(dx0(1:end-1).*dx0(2:end) < 0)+1; % Find where the derivative changes sign

% Include endpoints in potential peaks and valleys
x = [x0(1);x0(ind);x0(end)];
ind = [1;ind;len0];

% x only has the peaks, valleys, and endpoints
len = numel(x);
minMag = min(x);


if len > 2 % Function with peaks and valleys
    
    % Set initial parameters for loop
    tempMag = minMag;
    foundPeak = false;
    leftMin = minMag;
    
    % Deal with first point a little differently since tacked it on
    % Calculate the sign of the derivative since we taked the first point
    %  on it does not neccessarily alternate like the rest.
    signDx = sign(diff(x(1:3)));
    if signDx(1) <= 0 % The first point is larger or equal to the second
        ii = 0;
        if signDx(1) == signDx(2) % Want alternating signs
            x(2) = [];
            ind(2) = [];
            len = len-1;
        end
    else % First point is smaller than the second
        ii = 1;
        if signDx(1) == signDx(2) % Want alternating signs
            x(1) = [];
            ind(1) = [];
            len = len-1;
        end
    end
    
    % Preallocate max number of maxima
    maxPeaks = ceil(len/2);
    peakLoc = zeros(maxPeaks,1);
    peakMag = zeros(maxPeaks,1);
    cInd = 1;
    % Loop through extrema which should be peaks and then valleys
    while ii < len
        ii = ii+1; % This is a peak
        % Reset peak finding if we had a peak and the next peak is bigger
        %   than the last or the left min was small enough to reset.
        if foundPeak && (x(ii) > peakMag(end) || leftMin < peakMag(end)-thresh)
            tempMag = minMag;
            foundPeak = false;
        end
        
        % Make sure we don't iterate past the length of our vector
        if ii == len
            break; % We assign the last point differently out of the loop
        end
        
        % Found new peak that was lager than temp mag and threshold larger
        %   than the minimum to its left.
        if x(ii) > tempMag && x(ii) > leftMin + thresh
            tempLoc = ii;
            tempMag = x(ii);
        end
        
        ii = ii+1; % Move onto the valley
        % Come down at least thresh from peak
        if ~foundPeak && tempMag > thresh + x(ii)
            foundPeak = true; % We have found a peak
            leftMin = x(ii);
            peakLoc(cInd) = tempLoc; % Add peak to index
            peakMag(cInd) = tempMag;
            cInd = cInd+1;
        elseif x(ii) < leftMin % New left minima
            leftMin = x(ii);
        end
    end
    
    % Check end point
    if x(end) > tempMag && x(end) > leftMin + thresh
        peakLoc(cInd) = len;
        peakMag(cInd) = x(end);
        cInd = cInd + 1;
    elseif ~foundPeak && tempMag > minMag % Check if we still need to add the last point
        peakLoc(cInd) = tempLoc;
        peakMag(cInd) = tempMag;
        cInd = cInd + 1;
    end
    
    % Create output
    peakInds = ind(peakLoc(1:cInd-1));
    peakMags = peakMag(1:cInd-1);
else % This is a monotone function where an endpoint is the only peak
    [peakMags,xInd] = max(x);
    if peakMags > minMag + thresh
        peakInds = ind(xInd);
    else
        peakMags = [];
        peakInds = [];
    end
end



% Rotate data if needed
if flipData
    peakMags = peakMags.';
    peakInds = peakInds.';
end
% Change sign of data if was finding minima
if extrema < 0
    peakMags = -peakMags;
    x0 = -x0;
end
% Plot if no output desired
if nargout == 0
    if isempty(peakInds)
        disp('No significant peaks found')
    else
        figure;
        plot(1:len0,x0,'.-',peakInds,peakMags,'ro','linewidth',2);
    end
else
    varargout = {peakInds,peakMags};
end