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bagplot.m
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bagplot.m
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function result=bagplot(x,varargin)
% BAGPLOT draws a bagplot, which is a generalisation of the
% univariate boxplot to bivariate data. The original bagplot
% is described in :
%
% Rousseeuw, P.J., Ruts, I. and Tukey, J.W. (1999),
% "The bagplot: a bivariate boxplot",
% The American Statistician, 53, 382-387.
%
% The construction of this bagplot is based on the halfspacedepth
% (see also halfspacedepth.m). As the computation of the halfspacedepth
% is rather time-consuming, it is recommended at large datasets to
% perform the computations on a random subset of the data. The default
% size of the subset is 200, but this can be modified by the user.
%
% The bagplot can also be computed based on the adjusted outlyingness
% (see also adjustedoutlyingness.m).
%
% This method is described in:
%
% Hubert, M., and Van der Veeken, S. (2008),
% "Outlier detection for skewed data",
% Journal of Chemometrics, 22, 235-246.
%
% The bagplot based on the adjusted outlyingness can be obtained by
% setting the optional input argument 'type' equal to 'ao'.
%
% Required input arguments:
% x : bivariate data matrix (observations in the rows,
% variables in the columns)
%
% Optional input arguments:
% type : To draw the bagplot based on the halfspacedepth,
% this parameter should be equal to 'hd' (default).
% To draw the bagplot based on the adjusted outlyingness,
% it should be set to 'ao'.
% sizesubset : When drawing the bagplot based on the halfspacedepth,
% the size of the subset used to perform the main
% computations.
% plots : If equal to 1, a bagplot is drawn (default). If equal
% to zero, no plot is made.
% colorbag : The color of the bag.
% colorfence : The color of the fence.
% databag : If this parameter is 1, the data within the bag are
% plotted. If this parameter is set equal to 0, data
% points are not displayed.
% datafence : If this parameter is 1, the data within the fence
% are plotted. If this parameter is set equal to 0,
% data points are not displayed.
% scatsize : The size of the markers.
%
% I/O: result = bagplot( x, ...
% 'sizesubset', 200, ...
% 'type', 'hd', ...
% 'colorbag', [], ...
% 'colorfence', [], ...
% 'databag', 1, ...
% 'datafence', 1 );
%
% The user should only give the input arguments that have to change their
% default value.
% The name of the input arguments needs to be followed by their value.
% The order of the input arguments is of no importance.
%
% Examples:
% result=bagplot(x,'colorfence',[0.2 0.2 0.5],'databag',0)
% result=bagplot(x,'datafence',0,'colorbag',[1 0 0])
%
%
% The output of bagplot is a structure containing
%
% result.center : center of the data. When 'type=hd', this
% corresponds with the Tukey median. When
% 'type=ao', the point with smallest adjusted
% outlyingness.
% result.datatype : is 2 for observations in the bag, 1 for the
% observations in the fence and zero for outliers.
% result.flag : is 0 for outliers and equals 1 for regular
% points.
% result.depth : When 'type=hd' this is the halfspacedepth of
% each data point from the subset. The other
% observations receive depth = -1. When 'type=ao'
% this is the adjusted outlyingness (of all data
% points).
%
% This function is part of the Matlab Library for Robust Analysis,
% available at:
% http://wis.kuleuven.be/stat/robust.html
%
% Written by Fabienne Verwerft on 25/05/2005
% Update and revision by Stephan Van der Veeken 10/12/2007
% Last revision: 14/07/2010
% Modified by P.C. Luteijn 05/05/2021
%% Argument error handling
% ---------------------------------------------------------------------
% Undefined arguments
if nargin < 1
error('Input argument is undefined.')
end
% Dataset check
if size(x,1)<10
error('At least 10 datapoints are needed for the calculations.')
end
% Dataset dimension check
if size(x,2)~=2
error('The data should be twodimensional.')
end
%% Initial variables & default settings
% ---------------------------------------------------------------------
S = x;
counter = 1;
default = struct( ...
'colorbag', [0.6 0.6 1], ...
'colorfence', [0.8 0.8 1], ...
'sizesubset', 200,...
'databag', 1, ...
'datafence', 1, ...
'scatsize', 0.4, ...
'plots', 1, ...
'type', 'hd' );
list = fieldnames(default);
result = default;
IN = length(list);
i = 1;
%% Argument input handling
% ---------------------------------------------------------------------
% Reading the user's input
if nargin > 1
%placing inputfields in array of strings
for j = 1:nargin-1
if rem(j,2)~=0
chklist{i}=varargin{j};
i=i+1;
end
end
% Checking which default parameters have to be changed
% and keep them in the structure 'result'.
while counter <= IN
index = strmatch( list(counter,:), chklist, 'exact' );
if ~isempty(index) % In case of similarity
% Searching the index of the accompanying field
for j=1:nargin-1
% Fieldnames are placed on odd index
if rem(j,2)~=0
if strcmp(chklist{index},varargin{j})
I=j;
end
end
end
result = setfield( result, chklist{index}, varargin{I+1} );
index = [];
end
counter=counter+1;
end
end
% Initialize setup parameters with mixed default/nargin
colorbag = result.colorbag;
colorfence = result.colorfence;
databag = result.databag;
datafence = result.datafence;
plots = result.plots;
type = result.type;
sizesubset = result.sizesubset;
scatsize = result.scatsize;
switch type
case 'hd'
s1 = S(:,1);
s2 = S(:,2);
Sextra = [ S, (1:size(S,1))' ];
Q = bagp( s1, s2, sizesubset );
bag = Q.interpol;
bigmatrix = [ sortrows( Sextra, [1 2] ), ...
sortrows( Q.datatyp, [1 2] ) ];
tussen = sortrows( bigmatrix, 3 );
datatyp = [ S, tussen(:,6) ];
tukm = Q.tukmed;
depth = Q.depth;
case 'ao'
s1 = S(:,1);
s2 = S(:,2);
n = length(s1);
Q = adjustedoutlyingness(S);
D = [ S, Q.adjout, Q.flag, (1:n)' ];
P = sortrows( D, 3 );
L = [ P(:,1), P(:,2) ];
n = size( P, 1 );
f = floor( n/2 );
g = sum( Q.flag );
h = n - g;
bag = L( (1:f), : );
hulp = [ ones(f,1); 2*ones(g-f,1); 3*ones(h,1) ];
d1 = [ P, hulp ];
d2 = sortrows( d1, 5 );
datatyp = [ d2(:,1), d2(:,2), d2(:,6) ];
tukm = L( 1, : );
depth = Q.adjout;
end
%% Data pre-processing
% ---------------------------------------------------------------------
i = find( datatyp(:,3) == 1 );
data1 = datatyp( i, 1:2 );
i = find( datatyp(:,3) == 2 );
data2 = datatyp( i, 1:2 );
data=[data1;data2];
plak = [ data; bag ];
k = convhull( plak(:,1), plak(:,2) );
whisk = plak( k, 1:2 );
i = find( datatyp(:,3) == 3 );
outl = datatyp( i, 1:2 );
% Bag convex hull
qb = convhull( bag(:,1), bag(:,2) );
bagq = bag( qb, 1:2 );
% Fence convex hull
gf = convhull( data2(:,1), data2(:,2) );
fence = data2( gf, 1:2 );
%% Plot creation
% ---------------------------------------------------------------------
if plots == 1
fill( whisk(:,1), whisk(:,2), colorfence, ...
'LineStyle', 'none', ...
'FaceAlpha', 0.5 );
% Plots all data on top of each other
hold on
% Only plots the data outside the bag
% Next fill function should be placed after the command
% plot(data...)
fill( bagq(:,1), bagq(:,2), colorbag, ...
'LineStyle', 'none', ...
'FaceAlpha', 0.5 )
% Set axis format to square
axis square
% Plot datapoint inside the bag
if databag == 1
scatter( data1(:,1), data1(:,2), ...
scatsize.*ones(size(data1(:,1))), ...
'MarkerEdgeColor', 'none', ...
'MarkerFaceColor', 'k')
end
% Plot datapoint outside the bag
if datafence == 1
scatter( data2(:,1), data2(:,2), ...
scatsize.*ones(size(data2(:,1))), ...
'MarkerEdgeColor', 'none', ...
'MarkerFaceColor', 'k')
end
% Plot outliers
scatter( outl(:,1), outl(:,2), ...
scatsize.*ones(size(outl(:,1))), ...
'MarkerEdgeColor', 'none', ...
'MarkerFaceColor', 'r')
% Depth median (crosshair)
% i.e. point with highest halfspace depth
plot( tukm(1), tukm(2), 'o', ... circle around
'MarkerFaceColor', 'w', ...
'MarkerEdgeColor', 'w', ...
'MarkerSize',10 );
plot( tukm(1), tukm(2), '+k', ... cross inside
'MarkerFaceColor', 'k', ...
'MarkerEdgeColor', 'k', ...
'LineWidth', 1.2, ...
'Markersize', 6 )
% Set method to title name
switch type
case 'ao'
title('bagplot based on adjusted outlyingness')
set( gcf, ...
'Name', 'Bagplot based on adjusted outlyingness', ...
'NumberTitle', 'off' );
case 'hd'
title('bagplot based on halfspacedepth')
set( gcf, ...
'Name', 'Bagplot based on halfspacedepth', ...
'NumberTitle', 'off');
end
% Axis manipulation
xmin = min( datatyp(:,1) );
xmax = max( datatyp(:,1) );
small = 0.05*( xmax - xmin );
xaxis1 = xmin - small;
xaxis2 = xmax + small;
ymin = min( datatyp(:,2) );
ymax = max( datatyp(:,2) );
small = 0.05*( ymax - ymin );
xaxis3 = ymin - small;
xaxis4 = ymax + small;
axis([xaxis1 xaxis2 xaxis3 xaxis4]);
% Closing arguments
box on
hold off
end
%% Data structure creation
% ---------------------------------------------------------------------
Datatyp2=datatyp(:,3);
flag=zeros(size(S,1),1);
for i = 1:(size(S,1))
if Datatyp2(i)==3
flag(i)=0;
else
flag(i)=1;
end
end
datatype=zeros(size(S,1),1);
for i = 1:(size(S,1))
if Datatyp2(i)==3
datatype(i)=0;
else
if Datatyp2(i)==2
datatype(i)=1;
else
datatype(i)=2;
end
end
end
% Return structure
result = struct( ...
'center', tukm, ...
'datatype', datatype, ...
'flag', flag, ...
'depth', depth, ...
'bag', bagq, ...
'fence', fence );
%% FUNCTIONS
% -------------------------------------------------------------------------
function [kount,ADK,empty]=isodepth(x,y,d,varargin)
% ISODEPTH is an algoritm that computes the depth region of a bivariate
% dataset corresponding to depth d.
%
% First, we have to check whether the data points are in general position.
% If not, a very small random number is added to each of the data points
% until the dataset comes in general position. All this is done in the
% m-file dithering. Then all special k-dividers must be found. The
% coordinates of the vertices of the depth region we are looking for are
% intersection points of these special k-dividers. So, consequently, every
% intersection point in turn has to be tested, for example by computing its
% depth (see halfspacedepth.m), to check whether it is a vertex of the
% depth region.
%
% The ISODEPTH algoritm is described in:
% Ruts, I., Rousseeuw, P.J. (1996),
% "Computing depth contours of bivariate point clouds",
% Computational Statistics and Data Analysis, 23, 153-168.
%
% Required input arguments:
% x : vector containing the first coordinates of all the data points
% y : vector containing the second coordinates of all the data points
% d : the depth of which the depth region has to be constructed
%
% I/O: [kount, ADK, empty]= isodepth(x,y,d);
%
% The output of isodepth is given by
%
% kount : the total number of vertices of the depth region
% ADK : the coordinates of the vertices of the depth region
% empty : logical value (1 if the depth region is empty, 0 if not)
%
% This function is part of the Matlab Library for Robust Analysis,
% available at:
% http://wis.kuleuven.be/stat/robust.html
%
% Last Update: 29/04/2005
n=length(x);
eps=0.0000001;
%
% Checking input
%
if length(x)==1
error('x is not a vector')
elseif not(length(x)==length(y))
error('The vectors x and y must have the same length.')
end
if sum(isnan(x))>=1 || sum(isnan(y))>=1
error('Missing values are not allowed')
end
if sum(x==x(1))==n
error('All data points lie on a vertical line.')
elseif sum(y==y(1))==n
error('All data points lie on a horizontal line.')
else
R=corrcoef(x,y);
if abs(R(1,2))==1
error('All data points are collineair.')
end
end
%
% Check whether the data is in general position. If not, add a very small random
% number to each of the data points.
%
[x,y, Index, angl, ind1,ind2]=dithering(x,y);
%
% Main part
%
if (n==1)&&(d==1)
kount=n;
ADK=[x,y];
empty=0;
return
end
%
if (d>floor(n/2))
kount=0;
ADK=0;
empty=1;
return
end
%
if n<=3
kount=n;
ADK=[x,y];
empty=1;
return
end
%
nrank(Index)=(1:n);
%
% Let the line rotate from zero to angle(1)
%
ncirq=Index;
kount=1;
halt=0;
M=length(angl);
if angl(1)>(pi/2)
L=1;
D1=ind1(L);
IV1=nrank(D1);
D2=ind2(L);
IV2=nrank(D2);
IV=ncirq(IV1);
ncirq(IV1)=ncirq(IV2);
ncirq(IV2)=IV;
IV=IV1;
nrank(D1)=IV2;
nrank(D2)=IV;
%
if ((IV1==d) && (IV2==(d+1)))||((IV2==d) && (IV1==(d+1)))||((IV1==(n-d)) && (IV2==(n-d+1)))||((IV2==(n-d)) && (IV1==(n-d+1)))
if angl(L)<(pi/2)
dum=angl(L)+(pi/2);
else
dum=angl(L)-(pi/2);
end
if (IV1==d && IV2==(d+1))||(IV2==d && IV1==(d+1))
if dum<=(pi/2)
alfa(kount)=angl(L)+pi;
else
alfa(kount)=angl(L);
end
end
if or((IV1==(n-d) && IV2==(n-d+1)),(IV2==(n-d) && IV1==(n-d+1)))
if dum<=(pi/2)
alfa(kount)=angl(L);
else
alfa(kount)=angl(L)+pi;
end
end
kand1(kount)=ind1(L);
kand2(kount)=ind2(L);
D(kount)=sin(alfa(kount))*x(ind1(L))-cos(alfa(kount))*y(ind1(L));
kount=kount+1;
end
halt=1;
end
%
L=2;
stay=1;
% jflag keeps track of which angle we have to test next
while stay==1
stay=0;
kontrol=0;
if (pi<=(angl(L)+(pi/2))) && ((angl(L)-(pi/2))< angl(1))
D1=ind1(L);
IV1=nrank(D1);
D2=ind2(L);
IV2=nrank(D2);
IV=ncirq(IV1);
ncirq(IV1)=ncirq(IV2);
ncirq(IV2)=IV;
IV=IV1;
nrank(D1)=IV2;
nrank(D2)=IV;
%
if ((IV1==d) && (IV2==(d+1)))||((IV2==d) && (IV1==(d+1)))||((IV1==(n-d)) && (IV2==(n-d+1)))||((IV2==(n-d)) && (IV1==(n-d+1)))
if angl(L)<(pi/2)
dum=angl(L)+(pi/2);
else
dum=angl(L)-(pi/2);
end
if (IV1==d && IV2==(d+1))||(IV2==d && IV1==(d+1))
if dum<=(pi/2)
alfa(kount)=angl(L)+pi;
else
alfa(kount)=angl(L);
end
end
if or((IV1==(n-d) && IV2==(n-d+1)),(IV2==(n-d) && IV1==(n-d+1)))
if dum<=(pi/2)
alfa(kount)=angl(L);
else
alfa(kount)=angl(L)+pi;
end
end
kand1(kount)=ind1(L);
kand2(kount)=ind2(L);
D(kount)=sin(alfa(kount))*x(ind1(L))-cos(alfa(kount))*y(ind1(L));
kount=kount+1;
end
kontrol=1;
end
L=L+1;
if kontrol==1
halt=1;
end
if (L==(M+1)) && (kontrol==1)
jflag=1;
stay=2;
end
if not(stay==2)
if ((halt==1)&&(kontrol==0))||(L==(M+1))
stay=3;
else
stay=1;
end
end
end
if not(stay==2)
if (L>1)
jflag=L-1;
else
jflag=M;
end
end
%
halt2=0;
if not(stay==2)
J=0;
%
% If the first switch didnt occur between 0 and the angle angl(1) look for it
% between the following angles.
%
stay2=1;
if (L==M+1) && (kontrol==0)
halt=0;
halt2=0;
J=J+1;
if J==(M+1)
J=1;
end
L=J+1;
if L==(M+1)
L=1;
end
while stay2==1
stay2=0;
kontrol=0;
if (angl(L)+pi/2)<pi
ang1=angl(L)+pi/2;
else
ang1=angl(L)-pi/2;
end
if J==M
jj=1;
if halt2==0
angl(1)=angl(1)+pi;
end
else
jj=J+1;
end
if (angl(J)<=ang1) && (ang1<angl(jj))
if angl(1)>pi
angl(1)=angl(1)-pi;
end
D1=ind1(L);
IV1=nrank(D1);
D2=ind2(L);
IV2=nrank(D2);
IV=ncirq(IV1);
ncirq(IV1)=ncirq(IV2);
ncirq(IV2)=IV;
IV=IV1;
nrank(D1)=IV2;
nrank(D2)=IV;
%
if ((IV1==d) && (IV2==(d+1)))||((IV2==d) && (IV1==(d+1)))||((IV1==(n-d)) && (IV2==(n-d+1)))||((IV2==(n-d)) && (IV1==(n-d+1)))
if angl(L)<(pi/2)
dum=angl(L)+(pi/2);
else
dum=angl(L)-(pi/2);
end
if (IV1==d && IV2==(d+1))||(IV2==d && IV1==(d+1))
if dum<=(pi/2)
alfa(kount)=angl(L)+pi;
else
alfa(kount)=angl(L);
end
end
if or((IV1==(n-d) && IV2==(n-d+1)),(IV2==(n-d) && IV1==(n-d+1)))
if dum<=(pi/2)
alfa(kount)=angl(L);
else
alfa(kount)=angl(L)+pi;
end
end
kand1(kount)=ind1(L);
kand2(kount)=ind2(L);
D(kount)=sin(alfa(kount))*x(ind1(L))-cos(alfa(kount))*y(ind1(L));
kount=kount+1;
end
kontrol=1;
end
if angl(1)>pi
angl(1)=angl(1)-pi;
end
if L==M
L=1;
else
L=L+1;
end
if kontrol==1
halt=1;
end
if (halt==1)&&(kontrol==0)
if halt2==1
stay2=2;
end
if not(stay2==2)
if L>1
jflag=L-1;
else
jflag=M;
end
stay2=0;
end
else
if L==jj
if jj==1
halt2=1;
end
J=J+1;
if J==(M+1)
J=1;
end
L=J+1;
if L==(M+1)
L=1;
end
stay2=1;
else
stay2=1;
end
end
end
end
end
%
if not(stay2==2)
%
% The first switch has occurred. Now start looking for the next ones,
% between the following angles.
%
for i=(J+1):(M-1)
L=jflag;
stay=1;
while stay==1
stay=0;
kontrol=0;
if ((angl(L)+pi/2)<pi)
ang1=angl(L)+pi/2;
else
ang1=angl(L)-pi/2;
end
if (angl(i)<=ang1)&&(ang1<angl(i+1))
D1=ind1(L);
IV1=nrank(D1);
D2=ind2(L);
IV2=nrank(D2);
IV=ncirq(IV1);
ncirq(IV1)=ncirq(IV2);
ncirq(IV2)=IV;
IV=IV1;
nrank(D1)=IV2;
nrank(D2)=IV;
%
if ((IV1==d) && (IV2==(d+1)))||((IV2==d) && (IV1==(d+1)))||((IV1==(n-d)) && (IV2==(n-d+1)))||((IV2==(n-d)) && (IV1==(n-d+1)))
if angl(L)<(pi/2)
dum=angl(L)+(pi/2);
else
dum=angl(L)-(pi/2);
end
if (IV1==d && IV2==(d+1))||(IV2==d && IV1==(d+1))
if dum<=(pi/2)
alfa(kount)=angl(L)+pi;
else
alfa(kount)=angl(L);
end
end
if or((IV1==(n-d) && IV2==(n-d+1)),(IV2==(n-d) && IV1==(n-d+1)))
if dum<=(pi/2)
alfa(kount)=angl(L);
else
alfa(kount)=angl(L)+pi;
end
end
kand1(kount)=ind1(L);
kand2(kount)=ind2(L);
D(kount)=sin(alfa(kount))*x(ind1(L))-cos(alfa(kount))*y(ind1(L));
kount=kount+1;
end
kontrol=1;
end
if kontrol==0
jflag=L;
else
if not(L==M)
L=L+1;
else
L=1;
end
stay=1;
end
end
end
L=jflag;
%
% Finally, look for necessary switches between the last angle and zero.
%
stay=1;
while stay==1
kontrol=0;
stay=0;
if (angl(L)+pi/2)<pi
ang1=angl(L)+pi/2;
else
ang1=angl(L)-pi/2;
end
if (angl(M)<=ang1)&&(ang1<pi)
D1=ind1(L);
IV1=nrank(D1);
D2=ind2(L);
IV2=nrank(D2);
IV=ncirq(IV1);
ncirq(IV1)=ncirq(IV2);
ncirq(IV2)=IV;
IV=IV1;
nrank(D1)=IV2;
nrank(D2)=IV;
%
if ((IV1==d) && (IV2==(d+1)))||((IV2==d) && (IV1==(d+1)))||((IV1==(n-d)) && (IV2==(n-d+1)))||((IV2==(n-d)) && (IV1==(n-d+1)))
if angl(L)<(pi/2)
dum=angl(L)+(pi/2);
else
dum=angl(L)-(pi/2);
end
if (IV1==d && IV2==(d+1))||(IV2==d && IV1==(d+1))
if dum<=(pi/2)
alfa(kount)=angl(L)+pi;
else
alfa(kount)=angl(L);
end
end
if or((IV1==(n-d) && IV2==(n-d+1)),(IV2==(n-d) && IV1==(n-d+1)))
if dum<=(pi/2)
alfa(kount)=angl(L);
else
alfa(kount)=angl(L)+pi;
end
end
kand1(kount)=ind1(L);
kand2(kount)=ind2(L);
D(kount)=sin(alfa(kount))*x(ind1(L))-cos(alfa(kount))*y(ind1(L));
kount=kount+1;
end
kontrol=1;
end
if kontrol==1
if not(L==M)
L=L+1;
else
L=1;
end
stay=1;
end
end
end
num=kount-1; % num is the total number of special k-dividers
%
% Sort the num special k-dividers. Permute kand1, kand2 and D in the same
% way.
%
[alfa,In]=sort(alfa);
kand1=kand1(In);
kand2=kand2(In);
D=D(In);
%
IW1=1;
IW2=2;
Jfull=0;
NDK=0;
stay2=1;
while stay2==1
stay2=0;
ndata=0;
%
% Compute the intersection point.
%
while abs(-sin(alfa(IW2))*cos(alfa(IW1))+sin(alfa(IW1))*cos(alfa(IW2)))<eps
IW2=IW2+1;
ndata=0;
if IW2==(num+1)
IW2=1;
end
end
%
xcord=(cos(alfa(IW2))*D(IW1)-cos(alfa(IW1))*D(IW2))/(-sin(alfa(IW2))*cos(alfa(IW1))+sin(alfa(IW1))*cos(alfa(IW2)));
ycord=(-sin(alfa(IW2))*D(IW1)+sin(alfa(IW1))*D(IW2))/(-sin(alfa(IW1))*cos(alfa(IW2))+sin(alfa(IW2))*cos(alfa(IW1)));
%
% Test whether the intersection point is a data point. If so,
% adjust IW1 and IW2.
%
if or(kand1(IW1)==kand1(IW2),kand1(IW1)==kand2(IW2))
ndata=kand1(IW1);
end
if or(kand2(IW1)==kand1(IW2),kand2(IW1)==kand2(IW2))
ndata=kand2(IW1);
end
if not(ndata==0)
iv=0;
stay=1;
while stay==1
stay=0;
next=IW2+1;
iv=iv+1;
if next==(num+1)
next=1;
end
if not(next==IW1)
if or(ndata==kand1(next),ndata==kand2(next))
IW2=IW2+1;
if (IW2==(num+1))
IW2=1;
end
stay=1;
end
end
end
if iv==(num-1)
kount=1;
ADK=[x(ndata),y(ndata)];
empty=0;
return
end
end
if IW2==num
kon=1;
else
kon=IW2+1;
end
if kon==IW1
kon=kon+1;
end
if kon==(num+1)
kon=1;
end
%
% Test whether the intersection point lies to the left of the special
% k-divider which corresponds to alfa(kon). If so, compute its depth.
%
stay3=1;
stay4=1;
if (sin(alfa(kon))*xcord-cos(alfa(kon))*ycord-D(kon))<=eps
hdep1=halfspacedepth(xcord,ycord,x,y);
if hdep1==d
NDK=1;
else
hdep2=halfspacedepth(xcord-0.000001,ycord-0.000001,x,y);
hdep3=halfspacedepth(xcord+0.000001,ycord+0.000001,x,y);
hdep4=halfspacedepth(xcord-0.000001,ycord+0.000001,x,y);
hdep5=halfspacedepth(xcord+0.000001,ycord-0.000001,x,y);
hdepvector=[hdep1;hdep2;hdep3;hdep4;hdep5];
if (NDK==0)&&(sum(hdepvector>=d)>=1)
NDK=1;
end
if (hdep1<d)&&(hdep2<d)&&(hdep3<d)&&(hdep4<d)&&(hdep5<d)&&(NDK==1)
%
% The intersection point is not the correct one, try the next
% special k-divider.
%
IW2=IW2+1;
if IW2==(num+1)
IW2=1;
end
stay2=1;
end
end
if not(stay2==1)
%
% Store IW2 and IW1 in kornr. If kornr has already been filled,
% check wether we have encountered this intersection point before.
%
if (IW2>IW1)&&(Jfull==0)
kornr(IW1:(IW2-1),1)=kand1(IW1);
kornr(IW1:(IW2-1),2)=kand2(IW1);
kornr(IW1:(IW2-1),3)=kand1(IW2);
kornr(IW1:(IW2-1),4)=kand2(IW2);
else
if IW2>IW1
i=IW1;
stay3=1;
while stay3==1
if (kornr(i,1)==kand1(IW1))&&(kornr(i,2)==kand2(IW1))&&(kornr(i,3)==kand1(IW2))&&(kornr(i,4)==kand2(IW2))
stay3=0;
else
m1=(y(kornr(i,2))-y(kornr(i,1)))/(x(kornr(i,2))-x(kornr(i,1)));
m2=(y(kornr(i,4))-y(kornr(i,3)))/(x(kornr(i,4))-x(kornr(i,3)));
if not(m1==m2)
xcord1=(m1*x(kornr(i,1))-y(kornr(i,1))-m2*x(kornr(i,3))-y(kornr(i,3)))/(m1-m2);
ycord1=(m2*(m1*x(kornr(i,1))-y(kornr(i,1)))-m1*(m2*x(kornr(i,3))-y(kornr(i,3))))/(m1-m2);
end
if (abs(xcord1-xcord)<eps)&&(abs(ycord1-ycord)<eps)
stay3=0;
end
if stay3==1
kornr(i,1)=kand1(IW1);
kornr(i,2)=kand2(IW1);
kornr(i,3)=kand1(IW2);
kornr(i,4)=kand2(IW2);
end
end
if stay3==1
i=i+1;
if i==IW2
stay3=2;
i=i-1;
end
end
end
else
Jfull=1;
kornr(IW1:num,1)=kand1(IW1);
kornr(IW1:num,2)=kand2(IW1);
kornr(IW1:num,3)=kand1(IW2);
kornr(IW1:num,4)=kand2(IW2);
i=1;
stay4=1;
if IW2==1
stay4=3;
end
while stay4==1
if (kornr(i,1)==kand1(IW1))&&(kornr(i,2)==kand2(IW1))&&(kornr(i,3)==kand1(IW2))&&(kornr(i,4)==kand2(IW2))
stay4=0;
else
m1=(y(kornr(i,2))-y(kornr(i,1)))/(x(kornr(i,2))-x(kornr(i,1)));
warning off MATLAB:divideByZero