function?[mdminmax]?=?spxy（XYN）

%?Algorithm?for?Sample?set?Partitioning?based?on?joint?X-Y?distances
%?[mdminmax]?=?spxy（XYN）;
%
%?X?-->?Matrix?of?instrumental?responses
%?Y?-->?Matrix?of?parameters
%?N?-->?Number?of?samples?to?be?selected?（minimum?of?2）
%
%?m?-->?Indexes?of?the?selected?samples
%
%?dminmax（1）?=?0;
%?dminmax（2）?=?Joint?XY?distance?between?the?two?first?samples?selected?by?the?algorithm
%?dminmax（i）?=?Smallest?joint?XY?distance?between?the?i-th?selected?sample?and?the?previously?selected?ones?（i?>?2）
%
%?Reference:
%?R.?K.?H.?Galvao?M.?C.?U.?Araujo?G.?E.?Jose?M.?J.?C.?Pontes?E.?C.?Silva?T.?C.?B.?Saldanha
%?A?method?for?calibration?and?validation?subset?partitioning
%?Talanta?vol.?67?pp.?736-740?2005.
%
%?Web?site:?www.ele.ita.br/~kawakami/spa/

dminmax?=?zeros（1N）;?%?Initializes?the?vector?of?minimum?distances
M?=?size（X1）;?%?Number?of?rows?in?X?（samples）
samples?=?1:M;

%?Auto-scales?the?Y?matrix
for?i=1:size（Y2）?%?For?each?parameter?in?Y
????yi?=?Y（:i）;
????Y（:i）?=?（yi?-?mean（yi））/std（yi）;
end

D?=?zeros（MM）;?%?Initializes?the?matrix?of?X?distances
Dy?=?zeros（MM）;?%?Initializes?the?matrix?of?Y?distances

for?i=1:M-1
????xa?=?X（i:）;
????ya?=?Y（i:）;
????for?j?=?i+1:M
??????xb?=?X（j:）;
??????yb?=?Y（j:）;
??????D（ij）?=?norm（xa?-?xb）;
??????Dy（ij）?=??norm（ya?-?yb）;
????end
end

Dmax?=?max（max（D））;
Dymax?=?max（max（Dy））;

D?=?D/Dmax?+?Dy/Dymax;?%?Combines?the?distances?in?X?and?Y

%?D:?Upper?Triangular?Matrix
%?D（ij）?=?Euclidean?distance?between?objects?i?and?j?（j?>?i）