gusucode.com > 遗传算法 gaot工具箱matlab源码程序 > code_rar/gaot/dists.m
function D = dists(X1,X2,p,e)
%DISTS Calculates distances between vectors of points.
% D = dists(X1,X2,p,e)
% X1 = n x d matrix of n d-dimensional points
% X2 = m x d matrix of m d-dimensional points
% D = n x m matrix of distances
% = (n-1) x 1 vector of distances between X1 points, if X2 = []
% p = 2, Euclidean (default): D(i,j) = sqrt(sum((X1(i,:) - X2(j,:))^2))
% = 1, rectilinear: D(i,j) = sum(abs(X1(i,:) - X2(j,:))
% = Inf, Chebychev dist: D(i,j) = max(abs(X1(i,:) - X2(j,:))
% = (1 Inf), lp norm: D(i,j) = sum(abs(X1(i,:) - X2(j,:))^p)^(1/p)
% = 'rad', great circle distance in radians of a sphere
% (where X1 and X2 are decimal degree latitudes and longitudes)
% = 'mi' or 'sm', great circle distance in statute miles on the earth
% = 'km', great circle distance in kilometers on the earth
% e = epsilon for hyperboloid approximation gradient estimation
% = 0 (default); no error checking if any non-empty 'e' input
% ~= 0 => general lp used for rect., Cheb., and p outside [1,2]
%
% Great circle distances are calculated using the Haversine Formula (from R.W.
% Sinnott, "Virtues of the Haversine", Sky and Telescope, vol. 68, no. 2, 1984
% p. 159, as reported in "http://www.census.gov/cgi-bin/geo/gisfaq?Q5.1")
% Copyright (c) 1998 by Michael G. Kay
% Matlog Version 1.0 Apr-3-98
% Input Error Checking *******************************************************
if nargin == 4 & ~isempty(e) % No error checking is 'e' input
[n,d] = size(X1);
m = size(X2,1);
else % Do error checking
error(nargchk(1,4,nargin));
e = 0; % 'e' default
[n,d] = size(X1);
if n == 0 | ~isreal(X1)
error('X1 must be non-empty real matrix');
end
if nargin < 2 | isempty(X2) % Calc intra-seq dist b/w X1 points
m = 0; % X2 default
if n < 2
error('X1 must have more than 1 point');
end
else % Calc dist b/w X1 and X2 points
[m,dX2] = size(X2);
if m == 0 | ~isreal(X2)
error('X2 must be non-empty real matrix');
end
if d ~= dX2
error('Rows of X1 and X2 must have same dimensions');
end
end
if nargin < 3 | isempty(p)
p = 2; % 'p' default
elseif ~ischar(p) % lp distances
if length(p(:)) ~= 1 | ~isreal(p)
error('''p'' must be a real scalar number');
end
elseif ischar(p) % Great circle distances
p = lower(p);
if d ~= 2
error('Points must be 2-dimensional for great-circle distances');
end
if ~any(strcmp(p,{'rad','mi','sm','km'}))
error('''p'' must be either ''rad,'' ''mi,'' ''sm,'' or ''km''');
end
else
error('''p'' not valid value');
end
end
% End (Input Error Checking) ***********************************************
% Interchange if X2 is the only 1 point
intrchg = 0;
if n > 1 & m == 1
tmp = X2; X2 = X1; X1 = tmp;
m = n;n = 1;
intrchg = 1;
end
% 1-dimensional points
if d == 1
if e == 0
if m ~= 0
D = abs(X1(:,ones(1,m)) - X2(:,ones(1,n))');
else
D = abs(X1(1:n-1) - X1(2:n))'; % X1 intra-seq. dist.
end
else
if m ~= 0
D = sqrt((X1(:,ones(1,m)) - X2(:,ones(1,n))').^2 + e);
else
D = sqrt((X1(1:n-1) - X1(2:n)).^2 + e)';
end
end
% X1 only 1 point or intra-seq dist
elseif n == 1 | m == 0
if n == 1 % Expand X1 to match X2
X1 = X1(ones(1,m),:);
n = m;
else % X1 intra-seq. dist.
X2 = X1(2:n,:); % X2 = ending points
n = n - 1;
X1 = X1(1:n,:); % X1 = beginning points
end
if p == 2 % Euclidean distance
D = sqrt(sum(((X1 - X2).^2 + e)'));
elseif ischar(p) % Great-circle distance
X1 = pi*X1/180;X2 = pi*X2/180;
D = 2*asin(min(1,sqrt(sin((X1(:,1) - X2(:,1))/2).^2 + ...
cos(X1(:,1)).*cos(X2(:,1)).* ...
sin((X1(:,2) - X2(:,2))/2).^2)))';
elseif p == 1 & e == 0 % Rectilinear distance
D = sum(abs(X1 - X2)');
elseif (p >= 1 & p <= 2) | (e ~= 0 & p > 0) % General lp distance
D = sum((((X1 - X2).^2 + e).^(p/2))').^(1/p);
elseif p == Inf & e == 0 % Chebychev distance
D = max(abs(X1 - X2)');
else % Otherwise
D = zeros(1,n);
for j = 1:n
D(j) = norm(X1(j,:) - X2(j,:),p);
end
end
% X1 and X2 are 2-dimensional points
elseif d == 2
if p == 2 % Euclidean distance
D = sqrt((X1(:, ones(1,m)) - X2(:, ones(1,n))').^2 + e + ...
(X1(:,2*ones(1,m)) - X2(:,2*ones(1,n))').^2 + e);
elseif ischar(p) % Great-circle distance
X1 = pi*X1/180;X2 = pi*X2/180;
cosX1lat = cos(X1(:,1));cosX2lat = cos(X2(:,1));
D = 2*asin(min(1,sqrt(...
sin((X1(:,ones(1,m)) - X2(:,ones(1,n))')/2).^2 + ...
cosX1lat(:,ones(1,m),1).*cosX2lat(:,ones(1,n))'.* ...
sin((X1(:,2*ones(1,m)) - X2(:,2*ones(1,n))')/2).^2)));
elseif p == 1 & e == 0 % Rectilinear distance
D = abs(X1(:,ones(1,m)) - X2(:,ones(1,n))') + ...
abs(X1(:,2*ones(1,m)) - X2(:,2*ones(1,n))');
elseif (p >= 1 & p <= 2) | (e ~= 0 & p > 0) % General lp distance
D = (((X1(:, ones(1,m)) - X2(:, ones(1,n))').^2 + e).^(p/2) + ...
((X1(:,2*ones(1,m)) - X2(:,2*ones(1,n))').^2 + e).^(p/2)).^(1/p);
elseif p == Inf & e == 0 % Chebychev distance
D = max(abs(X1(:,ones(1,m)) - X2(:,ones(1,n))'),...
abs(X1(:,2*ones(1,m)) - X2(:,2*ones(1,n))'));
else % Otherwise
D = zeros(n,m);
for i = 1:n
for j = 1:m
D(i,j) = norm(X1(i,:) - X2(j,:),p);
end
end
end
% X1 and X2 are 3 or more dim. point
else
if p == 2 % Euclidean distance
D = sqrt(sum((repmat(reshape(X1,[n 1 k]),1,m) - ...
repmat(reshape(X2,[1 m k]),n,1)).^2 + e,3));
elseif p == 1 & e == 0 % Rectilinear distance
D = sum(abs(repmat(reshape(X1,[n 1 k]),1,m) - ...
repmat(reshape(X2,[1 m k]),n,1)),3);
elseif (p >= 1 & p <= 2) | (e ~= 0 & p > 0) % General lp distance
D = sum(((repmat(reshape(X1,[n 1 k]),1,m) - ...
repmat(reshape(X2,[1 m k]),n,1)).^2 + e).^(p/2),3).^(1/p);
elseif p == Inf & e == 0 % Chebychev distance
D = max(abs(repmat(reshape(X1,[n 1 k]),1,m) - ...
repmat(reshape(X2,[1 m k]),n,1)),[],3);
else % Otherwise
D = zeros(n,m);
for i = 1:n
for j = 1:m
D(i,j) = norm(X1(i,:) - X2(j,:),p);
end
end
end
end
% Transpose D if X2 was interchanged or X1 intra-seq distances
if intrchg == 1 | m == 0
D = D.';
end
% Convert 'rad' to 'km' or 'mi' (or 'sm')
if ischar(p) & ~strcmp(p,'rad')
if strcmp(p,'km')
D = (6378.388 - 21.476*abs(sin(mean([X1(:,1);X2(:,1)]))))*D;
else % 'mi' or 'sm'
D = (3963.34 - 13.35*abs(sin(mean([X1(:,1);X2(:,1)]))))*D;
end
end