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LOCALIZATIONERROR - Compute psychoacoustic performance parameters for sound localization experiments
Program code:
function [varargout] = localizationerror(m,varargin)
%LOCALIZATIONERROR Compute psychoacoustic performance parameters for sound localization experiments
% Usage: [accL, precL, accP, precP, querr] = localizationerror(m)
% [res, meta, par] = localizationerror(m,errorflag)
%
% Input parameters:
%
% m : item list from a localization experiment.
%
% LOCALIZATIONERROR(m,errorflag) returns psychoacoustic performance
% parameters for experimental response patterns.
% m is a matrix. In each row of m, the information about the target
% and response in the columns must be provided.
%
% [res, meta, par] = LOCALIZATIONERROR(m,errorflag) calculates error
% metric res given by the string errorflag. meta contains additional
% metadata, par contains additional calculation results.
%
% The columns of 'm' comprise:
%
% - 1:4 azi_target,ele_target,azi_response,ele_response
%
% - 5:8 lat_target,pol_target,lat_response,pol_response
%
% - 9 F/B-C resolved pol_response
%
%
% The errorflag may be one of:
%
% 'accL' accuracy (average) in the lateral dimension
%
% 'precL' precision (std. dev.) in the lateral dimension
%
% 'precLcentral' 'precL' derived from responses close to horizontal meridian (+-30 deg elevation)
%
% 'accP' accuracy (average) in the polar dimension
%
% 'precP' precision (circular std. dev.) in the polar dimension
%
% 'querr' percentage of weighted polar errors > 45deg:[querr number_of_corrects total_number] = CalcAccPrec...
%
% 'accE' accuracy in the elevation
%
% 'absaccE' absolute accuracy in the elevation
%
% 'absaccL' absolute lateral accuracy
%
% 'accabsL' mean absolute lateral error
%
% 'accabsP' mean absolute polar error
%
% 'accPnoquerr' accP with quadrant errors removed
%
% 'precE' precision in the elevation
%
% 'querr90' precentage of weighted polar errors > 90deg
%
% 'precPmedian' unweighted polar precision error considering targets around the median plane only (+/-30deg lateral)
%
% 'precPmedianlocal' basing on precPmedian, quadrant errors (polar error >90 deg) are excluded. Similar to RMS local polar error (Middlebrooks, 1999)
%
% 'precPnoquerr' precP with quadrant errors removed
%
% 'rmsL' lateral RMS error according to Middlebrooks (1999)
%
% 'rmsPmedianlocal' unweighted polar RMS considering targets around
% the median plane only (+/-30deg lateral) and excluding quadrant
% errors (polar error > 90deg). Identical to RMS local polar error in Middlebrooks (1999).
%
% 'rmsPmedian' unweighted polar RMS considering targets around the median plane
% only (+/-30deg lateral). Includes quadrant errors.
%
% 'querrMiddlebrooks' quadrant errors as in Middlebrooks (1999). Use
% central positions within +/-30deg, querr is when polar
% error is >90deg [querr number_of_corrects total_number] = CalcAccPrec...
%
% 'corrcoefL' lateral correlation coeffficient. Output parameter: [cc, p]
%
% 'corrcoefP' polar correlation coeffficient, Only data within lateral +/-30deg are considered. Output parameter: [corr_coeff, p_of_significant_corr]
%
% 'SCC' spherical/spatial correlation coefficient (Carlile et al., 1997)
%
% 'gainLstats' performs linear regression to obtain lateral gain. See help of regress for a detailed description of the structure fields.
%
% 'gainL' lateral gain only
%
% 'pVeridicalL' Proportion of quasi-verdical responses in lateral
% dimension
%
% 'precLregress' lateral scatter around linear regression line (only quasi-veridical responses included).
%
% 'sirpMacpherson2000' performs an ad-hoc selective, iterative
% regression procedure (SIRP) as proposed in
% Macpherson & Middlebrooks (2000 JASA) in order
% to exclude outliers and reversals
% and isolate the main concentration of responses
% in the computation of the linear fits.
% As the original procedure does not necessarily
% converge, the implementation here runs up to 100
% iterations and selects the iteration that includes
% the most responses or excludes the least outliers,
% Outlier distance criterion is 40deg, output parameters
% [f,r] correspond to regression results for frontal and
% rear hemisphere respectively, see help of regress for
% a detailed description of the structure fields.
%
% 'gainPfront' frontal polar gain only
%
% 'gainPrear' rear polar gain only
%
% 'gainP' polar gain averaged between front and back
%
% 'slopePfront' slope in degrees of regression line (frontal only)
%
% 'slopePrear' slope in degrees of regression line (rear only)
%
% 'slopeP' slope in degrees of regression line (front and back)
%
% 'pVeridicalPfront' proportion of quasi-verdical polar responses in the front
%
% 'pVeridicalPrear' proportion of quasi-verdical polar responses in the back
%
% 'pVeridicalP' proportion of quasi-verdical polar responses in total
%
% 'precPregressFront' polar scatter around linear regression line for the front (only quasi-veridical responses included)
%
% 'precPregressRear' same as precPregressFront but for the back
%
% 'precPregress' average between precPregressFront and precPregressRear*
%
% 'perMacpherson2003' polar error rate used in Macpherson & Middlebrooks
% (2003). They measured the deviation of responses from the
% linear predictors obtained by an ad-hoc SIRP. Polar errors
% are defined by showing a deviation of >45deg
% (i.e., not being quasi-veridical) with respect
% to the linear flat stimulus prediction. Note that for this
% analysis the results from sirpMacpherson2000 are required
% and handled as LOCALIZATIONERROR(m,f,r,'perMacpherson2003')
%
%
% If no errorflag is provided, the function returns: accL, precL, precP, and querr
%
%
% References:
% J. C. Middlebrooks. Virtual localization improved by scaling
% nonindividualized external-ear transfer functions in frequency. J.
% Acoust. Soc. Am., 106:1493--1510, 1999.
%
% E. A. Macpherson and J. C. Middlebrooks. Vertical-plane sound
% localization probed with ripple-spectrum noise. J. Acoust. Soc. Am.,
% 114:430--445, 2003.
%
% S. Carlile, P. Leong, and S. Hyams. The nature and distribution of
% errors in sound localization by human listeners. Hearing research,
% 114(1):179--196, 1997.
%
%
% See also: baumgartner2014
%
% Url: http://amtoolbox.org/amt-1.3.0/doc/common/localizationerror.php
% #Author : Piotr Majdak (2021)
% #Author : Robert Baumgartner (2021)
% This file is licensed unter the GNU General Public License (GPL) either
% version 3 of the license, or any later version as published by the Free Software
% Foundation. Details of the GPLv3 can be found in the AMT directory "licences" and
% at <https://www.gnu.org/licenses/gpl-3.0.html>.
% You can redistribute this file and/or modify it under the terms of the GPLv3.
% This file is distributed without any warranty; without even the implied warranty
% of merchantability or fitness for a particular purpose.
%% Check input options
definput.import={'localizationerror'};
[flags,kv]=ltfatarghelper({'f','r'},definput,varargin);
if size(m,2)==1, m=m'; end
if isempty(flags.errorflag)
nargout=6;
thr=45;
accL=mean(m(:,7)-m(:,5));
varargout{1}=accL;
precL=sqrt(sum((m(:,7)-m(:,5)-accL).^2)/size(m,1));
varargout{2}=precL;
w=0.5*cos(deg2rad(m(:,7))*2)+0.5;
varargout{3}=mynpi2pi(circmean(m(:,8)-m(:,6),w));
[x,mag]=circmean(m(:,8)-m(:,6));
precP=rad2deg(acos(mag)*2)/2;
varargout{4}=precP;
idx=find((abs(mynpi2pi(m(:,8)-m(:,6))).*w)<=thr);
querr=100-size(idx,1)/size(m,1)*100;
varargout{5}=querr;
else
% if iscell(errorflag), errorflag=errorflag{1}; end
% if ~ischar(errorflag)
% error('ERR must be a string');
% end
% if size(errorflag,1)~=1, errorflag=errorflag'; end
nargout=3;
metadata=[];
par=[];
switch flags.errorflag
case 'accL'
accL=mean(m(:,7)-m(:,5));
varargout{1}=accL;
meta.ylabel='Lateral bias (deg)';
case 'absaccL'
accL=mean(m(:,7)-m(:,5));
varargout{1}=abs(accL);
meta.ylabel='Lateral absolute bias (deg)';
case 'accabsL'
accL=mean(abs(m(:,7)-m(:,5)));
varargout{1}=accL;
meta.ylabel='Lateral absolute error (deg)';
case 'corrcoefL'
[r,p] = corrcoef([m(:,5) m(:,7)]);
varargout{1}=r(1,2);
par.par1=p(1,2);
meta.ylabel='Lateral correlation coefficient';
meta.par1 = 'p for testing the hypothesis of no correlation';
case 'corrcoefP'
idx=find(abs(m(:,7))<=30);
[r,p] = corrcoef([m(idx,6) m(idx,8)]);
varargout{1}=r(1,2);
par.par1=p(1,2);
meta.ylabel='Polar correlation coefficient';
meta.par1 = 'p for testing the hypothesis of no correlation';
case 'precL'
accL=mean(m(:,7)-m(:,5));
precL=sqrt(sum((m(:,7)-m(:,5)-accL).^2)/size(m,1));
varargout{1}=precL;
meta.ylabel='Lateral precision error (deg)';
case 'precLcentral'
idx=find(abs(m(:,4))<=30); % responses close to horizontal meridian
accL=mean(m(idx,7)-m(idx,5));
precL=sqrt(sum((m(idx,7)-m(idx,5)-accL).^2)/length(idx));
varargout{1}=precL;
meta.ylabel='Central lateral precision error (deg)';
case 'rmsL'
idx=find(abs(m(:,7))<=60);
m=m(idx,:);
rmsL=sqrt(sum((mynpi2pi(m(:,7)-m(:,5))).^2)/size(m,1));
varargout{1}=rmsL;
meta.ylabel='Lateral RMS error (deg)';
case 'accP'
varargout{1}=mynpi2pi(circmean(m(:,8)-m(:,6)));
meta.ylabel='Polar bias (deg)';
case 'accabsP'
varargout{1}=mynpi2pi(circmean(abs(m(:,8)-m(:,6))));
meta.ylabel='Polar absolute bias (deg)';
case 'accPnoquerr'
w=0.5*cos(deg2rad(m(:,7))*2)+0.5;
idx=find(w>0.5);
m=m(idx,:); w=w(idx,:);
idx=find((abs(mynpi2pi(m(:,8)-m(:,6))).*w)<=45);
varargout{1}=mynpi2pi(circmean(m(idx,8)-m(idx,6)));
par.par1=length(idx);
meta.ylabel='Local polar bias (deg)';
meta.par1='Number of considered responses';
case 'precP'
w=0.5*cos(deg2rad(m(:,7))*2)+0.5;
precP=circstd(m(:,8)-m(:,6),w);
varargout{1}=precP;
meta.ylabel='Polar precision (deg)';
case 'precPnoquerr'
% w=0.5*cos(deg2rad(m(:,7))*2)+0.5;
% idx=find(w>0.5);
% thr=45; % threshold for the choice: quadrant error or not
% m=m(idx,:); w=w(idx,:);
range=360; % polar range of targets
thr=45; % threshold for the choice: quadrant error or not
latmax=0.5*180*(acos(4*thr/range-1))/pi;
idx=find(abs(m(:,7))<latmax); % targets outside not considered
m=m(idx,:);
w=0.5*cos((m(:,7))*2*pi/180)+0.5;
idx=find((abs(mynpi2pi(m(:,8)-m(:,6))).*w)<=thr);
m=m(idx,:);
w=0.5*cos((m(:,7))*pi/180*2)+0.5;
precP=circstd(m(:,8)-m(:,6),w);
varargout{1}=real(precP);
meta.ylabel='Local polar precision error (deg)';
case 'querr'
range=360; % polar range of targets
thr=45; % threshold for the choice: quadrant error or not
latmax=0.5*180*(acos(4*thr/range-1))/pi;
idx=find(abs(m(:,7))<latmax); % targets outside not considered
m=m(idx,:);
w=0.5*cos(pi*(m(:,7))/180*2)+0.5; % weigthing of the errors
corrects=size(find((abs(mynpi2pi(m(:,8)-m(:,6))).*w)<=thr),1);
totals=size(m,1);
chancerate=2*thr/range./w;
wrongrate=100-mean(chancerate)*100;
querr=100-corrects/totals*100;
varargout{1}=querr;
meta.ylabel='Weighted quadrant errors (%)';
par.par1=corrects;
meta.par1='Number of correct responses';
par.par2=totals;
meta.par2='Number of responses within the lateral range';
par.par3=wrongrate; % valid only for targets between 0 and 180°
meta.par3='Wrong rate, valid only for targets between 0 and 180°';
case 'querrMiddlebrooks' % as in Middlebrooks (1999); comparable to COC from Best et al. (2005)
idx=abs(m(:,7))<=30;
m=m(idx,:);
idx=find((abs(mynpi2pi(m(:,8)-m(:,6))))<=90);
querr=100-size(idx,1)/size(m,1)*100;
% chance performance (FIXME: not working with exp_baumgartner2014!)
% tang = m(:,6);
% rang = min(tang):max(tang); % assume listener knows target range
% p = ones(length(rang),length(tang)); % equally distributed response probabilities
% chance = baumgartner2014_pmv2ppp(p,tang,rang,'QE');
varargout{1}=querr;
meta.ylabel='Quadrant errors (%)';
par.par1=size(idx,1);
meta.par1='Number of confusions';
par.par2=size(m,1);
meta.par2='Number of responses within the lateral range';
% par.chance=chance;
% meta.chance='Chance performance';
case 'querrMiddlebrooksRAU' % as in Middlebrooks (1999) but calculated in rau
idx=find(abs(m(:,7))<=30);
m=m(idx,:);
idx=find((abs(mynpi2pi(m(:,8)-m(:,6))))<=90);
querr=100-size(idx,1)/size(m,1)*100;
varargout{1}=rau(querr,size(m,1));
meta.ylabel='RAU quadrant errors';
par.par1=size(idx,1);
meta.par1='Number of confusions';
par.par2=size(m,1);
meta.par2='Number of responses within the lateral range';
case 'accE'
varargout{1}=mynpi2pi(circmean(m(:,4)-m(:,2)));
meta.ylabel='Elevation bias (deg)';
case 'absaccE'
varargout{1}=abs(mynpi2pi(circmean(m(:,4)-m(:,2))));
meta.ylabel='Absolute elevation bias (deg)';
case 'precE'
precE=circstd(m(:,4)-m(:,2));
varargout{1}=precE;
meta.ylabel='Elevation precision error (deg)';
case 'lateral' % obsolete
nargout=2;
varargout{1}=accL;
varargout{2}=precL;
case 'polar' % obsolete
nargout=3;
varargout{1}=accP;
varargout{2}=precP;
varargout{3}=querr;
case 'precPmedianlocal'
idx=find(abs(m(:,7))<=30);
m=m(idx,:);
idx=find(abs(mynpi2pi(m(:,8)-m(:,6)))<90);
if isempty(idx), error('Quadrant errors of 100%, local bias is NaN'); end
precPM=circstd(m(idx,8)-m(idx,6));
varargout{1}=precPM;
meta.ylabel='Local central precision error (deg)';
case 'precPmedian'
idx=find(abs(m(:,7))<=30);
m=m(idx,:);
precPM=circstd(m(:,8)-m(:,6));
varargout{1}=precPM;
meta.ylabel='Central precision error (deg)';
case 'rmsPmedianlocal'
idx=find(abs(m(:,7))<=30);
m=m(idx,:);
idx=find(abs(mynpi2pi(m(:,8)-m(:,6)))<90);
rmsPlocal=sqrt(sum((mynpi2pi(m(idx,8)-m(idx,6))).^2)/size(idx,1));
varargout{1}=rmsPlocal;
meta.ylabel='Local central RMS error (deg)';
% chance performance (FIXME: not working with exp_baumgartner2014!)
% tang = m(:,6);
% rang = min(tang):max(tang); % assume listener knows target range
% p = ones(length(rang),length(tang)); % equally distributed response probabilities
% chance = baumgartner2014_pmv2ppp(p,tang,rang,'PE');
% par.chance = chance;
% meta.chance = 'Chance performance';
case 'rmsPmedian'
idx=find(abs(m(:,7))<=30);
m=m(idx,:);
rmsP=sqrt(sum((mynpi2pi(m(:,8)-m(:,6))).^2)/size(m,1));
varargout{1}=rmsP;
meta.ylabel='Central RMS error (deg)';
case 'SCC'
trgt = m(:,[1 2]);
resp = m(:,[3 4]);
T = pol2dcos(trgt);
R = pol2dcos(resp);
sxy = T' * R;
sxx = T' * T;
syy = R' * R;
scc = det(sxy) / sqrt(det(sxx) * det(syy));
varargout{1}=scc;
meta.ylabel='Spatial correlation coefficient';
case 'gainLstats'
[l.b,l.bint,l.r,l.rint,l.stats]=regress(m(:,7),[ones(length(m),1) m(:,5)]);
varargout{1}=l;
meta.ylabel='Lateral gain';
case 'gainL'
l = localizationerror(m,'gainLstats');
varargout{1}=l.b(2);
meta.ylabel='Lateral gain';
case 'precLregress'
l = localizationerror(m,'gainLstats');
x = -90:90;
y = l.b(2)*m(:,5) + l.b(1); % linear regression
dev = m(:,7) - y; % deviation
dev = dev(abs(dev)<=45); % include only quasi-veridical responses
prec = rms(dev);
varargout{1} = prec;
meta.ylabel = 'Lateral scatter (deg)';
case 'pVeridicalL'
tol = 45; % tolerance of lateral angle error for quasi-veridical responses
l = localizationerror(m,'gainLstats');
x = -90:90;
y = l.b(2)*m(:,5) + l.b(1); % linear regression
dev = m(:,7) - y; % deviation wrapped to +-180 deg
prop = sum(abs(dev)<=tol)/length(dev);
varargout{1} = prop*100;
meta.ylabel = '% lateral quasi-veridical';
case 'sirpMacpherson2000'
delta = 40; % outlier tolerance in degrees
Nmin = 5; % minimum number of responses used for regression
maxiter = 100; % max number of iterations
% Only responses for targets located within 30 degrees of the median plane are included
m = m( abs(m(:,5))<=30,: );
for frontback = 1:2 % Analyze front and back hemispheres separately
if frontback == 1 % Front
mhemi = m( m(:,6)<=90 ,:); % frontal target locations
idinit = mhemi(:,8)<=90; % initialization with correct responses
else % Back
mhemi = m( m(:,6)>=90 ,:); % rear targets
idinit = mhemi(:,8)>=90; % initialization with correct responses
end
if length(idinit)<Nmin
r.b = nan(1,2);
r.stats = nan(1,4);
else
iditer = false(length(idinit),maxiter);
y = mhemi(:,8); % response
x = mhemi(:,6); % target
for iter = 1:maxiter
B=regress(y(idinit),[ones(sum(idinit),1) mhemi(idinit,6)]);
yhat=B(2)*x+B(1);
dev = mod( (y-yhat) +180,360) -180; % deviation wrapped to +-180 deg
iditer(:,iter)= abs(dev) < delta;
if isequal(iditer(:,iter),idinit)
break % because it converged
else
idinit = iditer(:,iter);
end
end
[nselect,iopt] = max(sum(iditer));
idselect = iditer(:,iopt);
[r.b,r.bint,r.r,r.rint,r.stats]=regress(...
mhemi(idselect,8),[ones(nselect,1) mhemi(idselect,6)]);
end
varargout{frontback}=r;
end
par='SIRP results';
case 'gainPfront'
f = localizationerror(m,'sirpMacpherson2000');
varargout{1}=f.b(2);
meta.ylabel='Frontal polar gain';
case 'gainPrear'
[tmp,r] = localizationerror(m,'sirpMacpherson2000');
varargout{1}=r.b(2);
meta.ylabel='Rear polar gain';
case 'gainP'
[f,r] = localizationerror(m,'sirpMacpherson2000');
varargout{1}=(f.b(2)+r.b(2))/2;
meta.ylabel='Polar gain';
case 'slopePfront'
g = localizationerror(m,'gainPfront');
varargout{1} = rad2deg(acos(1./sqrt(g.^2+1)));
meta.ylabel='Frontal polar regression slope';
case 'slopePrear'
g = localizationerror(m,'gainPrear');
varargout{1} = rad2deg(acos(1./sqrt(g.^2+1)));
meta.ylabel='Rear polar regression slope';
case 'slopeP'
g = localizationerror(m,'gainP');
varargout{1} = rad2deg(acos(1./sqrt(g.^2+1)));
meta.ylabel='Polar regression slope';
case 'pVeridicalPfront'
tol = 45; % tolerance of polar angle error for quasi-veridical responses
f = localizationerror(m,'sirpMacpherson2000');
mf = m( abs(m(:,5))<=30 & m(:,6)< 90 ,:); % frontal central data only
x = -90:270;
yf=f.b(2)*mf(:,6)+f.b(1); % linear prediction for flat, frontal targets
devf = mod( (mf(:,8)-yf) +180,360) -180; % deviation wrapped to +-180 deg
pVer = sum(abs(devf) <= tol) / length(devf);
varargout{1}=pVer*100;
meta.ylabel = '% quasi-veridical (frontal)';
case 'pVeridicalPrear'
tol = 45; % tolerance of polar angle error for quasi-veridical responses
[~,r] = localizationerror(m,'sirpMacpherson2000');
mr = m( abs(m(:,5))<=30 & m(:,6)>=90 ,:); % rear central data only
x = -90:270;
yr = r.b(2)*mr(:,6) + r.b(1); % linear prediction for flat, rear targets
devr = mod( (mr(:,8)-yr) +180,360) -180; % deviation wrapped to +-180 deg
pVer = sum(abs(devr) <= tol) / length(devr);
varargout{1}=pVer*100;
meta.ylabel = '% quasi-veridical (rear)';
case 'pVeridicalP'
tol = 45; % tolerance of polar angle error for quasi-veridical responses
[f,r] = localizationerror(m,'sirpMacpherson2000');
mf = m( abs(m(:,5))<=30 & m(:,6)< 90 ,:); % frontal central targets
mr = m( abs(m(:,5))<=30 & m(:,6)>=90 ,:); % rear central targets
x = -90:270;
yf = f.b(2)*mf(:,6) + f.b(1); % linear prediction for flat, frontal targets
yr = r.b(2)*mr(:,6) + r.b(1); % linear prediction for flat, rear targets
devf = mod( (mf(:,8)-yf) +180,360) -180; % deviation wrapped to +-180 deg
devr = mod( (mr(:,8)-yr) +180,360) -180; % deviation wrapped to +-180 deg
pVerf = sum(abs(devf) <= tol) / length(devf);
pVerr = sum(abs(devr) <= tol) / length(devr);
pVer = (pVerf + pVerr)/2;
varargout{1}=pVer*100;
meta.ylabel = '% quasi-veridical';
case 'precPregressFront'
tol = 45; % tolerance of polar angle error for quasi-veridical responses
f = localizationerror(m,'sirpMacpherson2000');
mf = m( abs(m(:,5))<=30 & m(:,6)< 90 ,:); % frontal central targets only
x = -90:270;
yf = f.b(2)*mf(:,6) + f.b(1); % linear prediction for flat, frontal targets
devf = mod( (mf(:,8)-yf) +180,360) -180; % deviation wrapped to +-180 deg
dev = devf(abs(devf)<=tol); % include only quasi-veridical responses
prec = rms(dev);
varargout{1} = prec;
meta.ylabel = 'Frontal polar scatter (deg)';
case 'precPregressRear'
tol = 45; % tolerance of polar angle error for quasi-veridical responses
[~,r] = localizationerror(m,'sirpMacpherson2000');
mr = m( abs(m(:,5))<=30 & m(:,6)>=90 ,:); % rear central targets only
x = -90:270;
yr = r.b(2)*mr(:,6) + r.b(1); % linear prediction for flat, rear targets
devr = mod( (mr(:,8)-yr) +180,360) -180; % deviation wrapped to +-180 deg
dev = devr(abs(devr)<=tol); % include only quasi-veridical responses
prec = rms(dev);
varargout{1} = prec;
meta.ylabel = 'Rear polar scatter (deg)';
case 'precPregress'
precF = localizationerror(m,'precPregressFront');
precR = localizationerror(m,'precPregressRear');
prec = (precF+precR)/2;
varargout{1} = prec;
meta.ylabel = 'Polar scatter (deg)';
case 'perMacpherson2003'
if isempty(kv.f) || isempty(kv.r)
amt_disp('Regression coefficients missing! Input is interpreted as baseline data!','documentation');
amt_disp('For this analysis the results from `sirpMacpherson2000()` for baseline data','documentation');
amt_disp('are required and must be handled as `localizationerror(m,f,r,...)`.','documentation');
[kv.f,kv.r] = localizationerror(m,'sirpMacpherson2000');
end
plotflag = false;
tol = 45; % tolerance of polar angle to be not counted as polar error
mf = m( abs(m(:,5))<=30 & m(:,6)< 90 ,:); % frontal central targets only
mr = m( abs(m(:,5))<=30 & m(:,6)>=90 ,:); % rear central targets only
x = -90:270;
yf=kv.f.b(2)*mf(:,6)+kv.f.b(1); % linear prediction for flat, frontal targets
yr=kv.r.b(2)*mr(:,6)+kv.r.b(1); % linear prediction for flat, rear targets
devf = mod( (mf(:,8)-yf) +180,360) -180; % deviation wrapped to +-180 deg
devr = mod( (mr(:,8)-yr) +180,360) -180;
f.pe = sum(abs(devf) > tol);
r.pe = sum(abs(devr) > tol);
per = (f.pe + r.pe) / size(m,1) * 100; % polar error rate
varargout{1} = per;
meta.ylabel = 'Polar error rate (%)';
if plotflag
plot(m(:,6),m(:,8),'ko');
axis equal
axis tight
hold on
plot(mf(:,6),yf,'LineWidth',2);
plot(mr(:,6),yr,'LineWidth',2);
plot(mf(:,6),yf+45,'r','LineWidth',2);
plot(mf(:,6),yf-45,'r','LineWidth',2);
plot(mr(:,6),yr+45,'r','LineWidth',2);
plot(mr(:,6),yr-45,'r','LineWidth',2);
title(['PER: ' num2str(per,2) '%'])
end
otherwise
error(['Unknown ERR: ' err]);
end
if length(varargout) < 2
varargout{2}=meta;
end
if length(varargout) < 3
varargout{3}=par;
end
end
end
function out_deg=mynpi2pi(ang_deg)
ang=ang_deg/180*pi;
out_rad=sign(ang).*((abs(ang)/pi)-2*ceil(((abs(ang)/pi)-1)/2))*pi;
out_deg=out_rad*180/pi;
end
function [phi,mag]=circmean(azi,dim)
% [PHI,MAG]=circmean(AZI,DIM)
%
% Calculate the average angle of AZI according
% to the circular statistics (Batschelet, 1981).
%
% For vectors, CIRCMEAN(AZI) is the mean value of the elements in AZI. For
% matrices, CIRCMEAN(AZI) is a row vector containing the mean value of
% each column. For N-D arrays, CIRCMEAN(azi) is the mean value of the
% elements along the first non-singleton dimension of AZI.
%
% circmean(AZI,DIM) takes the mean along the dimension DIM of AZI.
%
% PHI is the average angle in deg, 0..360�
% MAG is the magnitude showing the significance of PHI (kind of dispersion)
% MAG of zero shows that there is no average of AZI.
% MAG of one shows a highest possible significance
% MAG can be represented in terms of standard deviation in deg by using
% rad2deg(acos(MAG)*2)/2
%
% [PHI,MAG]=circmean(AZI,W) calculates a weighted average where each sample
% in AZI is weighted by the corresponding entry in W.
%
% Piotr Majdak, 6.3.2007
if isempty(azi) % no values
phi=NaN;
mag=NaN;
return;
end
if prod(size(azi))==1 % one value only
phi=azi;
mag=1;
return;
end
if ~exist('dim') % find the dimension
dim = min(find(size(azi)~=1));
w=ones(size(azi));
elseif prod(size(dim))~=1
% dim vector represents weights
w=dim;
dim = min(find(size(azi)~=1));
end
x=deg2rad(azi);
s=mean(sin(x).*w,dim)/mean(w);
c=mean(cos(x).*w,dim)/mean(w);
y=zeros(size(s));
for ii=1:length(s)
if s(ii)>0 & c(ii)>0
y(ii)=atan(s(ii)/c(ii));
elseif c(ii)<0
y(ii)=atan(s(ii)/c(ii))+pi;
elseif s(ii)<0 & c(ii)>0
y(ii)=atan(s(ii)/c(ii))+2*pi;
elseif s(ii)==0
y(ii)=0;
else
y(ii)=NaN;
end
end
mag=sqrt(s.*s+c.*c);
phi=wrapTo360(rad2deg(y));
end
function mag=circstd(azi,dim)
% MAG=circstd(AZI,DIM)
%
% Calculate the standard deviation angle (in deg) of AZI (in deg) according
% to the circular statistics (Batschelet, 1981).
%
% For vectors, CIRCSTD(AZI) is the std of the elements in AZI. For
% matrices, CIRCSTD(AZI) is a row vector containing the std of
% each column. For N-D arrays, CIRCSTD(azi) is the std value of the
% elements along the first non-singleton dimension of AZI.
%
% CIRCSTD(AZI,DIM) takes the std along the dimension DIM of AZI.
%
%
% MAG=CIRCSTD(AZI,W) calculates a weighted std where each vector strength
% of AZI is weighted by the corresponding entry in W.
%
% Piotr Majdak, 21.08.2008
if isempty(azi) % no values
mag=NaN;
return;
end
if prod(size(azi))==1 % one value only
mag=0;
return;
end
if ~exist('dim') % find the dimension
[phi,mag]=circmean(azi);
elseif prod(size(dim))~=1
[phi,mag]=circmean(azi,dim);
end
mag=rad2deg(sqrt(2*(1-mag)));
end
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