serpind.m

Version 1.0.0.0 (2,29 KB) von
serpentine traversal of an N-dimensional array
Aktualisiert 31. Mär 2016

Lizenz anzeigen

function [p,ip,m] = serpind(s)
% Return serpentine indexing list for array size s.
%
% syntax:
% p = serpind(s);
% [p,ip] = serpind(s);
% [p,ip,m] = serpind(s);
%
% input arg:
%
% s (size-[1,N] array of non-negative integers): array size
%
% output args:
%
% p (size-[M,1] array of non-negative integers; M = prod(s)): flat indexing list for
% serpentine array traversal (p is a permutation of (1:M).'.)
%
% ip (size-[M,1] array of non-negative integers; optional output): inverse permutation
% of p
%
% m (size-[M,N] array of non-negative integers; optional output): N-dimensional array
% subscripts corresponding to p
%
% Each element p(j) corresponds to a multidimensional array subscript list m(j,1:N)
% defined by
% [m(j,1), m(j,2), ... m(j,N)] = ind2sub(s,p(j))
% The subscript lists m(1,:), m(2,:), ... traverse the set of all indices for a size-s
% array (i.e., 1 <= m(j,k) <= s(k) for each j = 1:M, k = 1:N). The "serpentine"
% traversal order has the property that m(j,:) and m(j+1,:) differ in only one dimension
% index, and the difference in that index is either +1 or -1.
%
% The index list p is a permutation of (1:M).', and its inverse is ip (i.e., p(ip) =
% (1:M).'). Thus, for an array A, the two sequential operations
% A = A(p);
% A = A(ip);
% are equivalent to
% A = A(:);
%
% The elements of a size-s array A can be sequenced in serpentine order as follows,
% s = size(A);
% [p,ip] = serpind(s);
% A = A(p);
% The original array can then be reconstructed as follows:
% A = reshape(A(ip),s);
%
% Version 04/09/2006
% Author: Kenneth C. Johnson
% software.kjinnovation.com
%
% See ZipInterp.pdf, Section 9.4 ("Seed chaining"), on the KJ Innovation website for an
% application example illustrating the use of serpind.m.
%
N = length(s);
M = prod(s);
p = zeros(M,1);
if M==0
if nargout>=2
ip = p;
if nargout>=3
m = zeros(0,N);
end
end
return
end
p(1) = 1;
len = 1;
stride = 1;
for k = 1:N
L = len;
for j=2:s(k)
p(len+1:len+L) = p(len:-1:len-L+1)+stride;
len = len+L;
end
stride = stride*s(k);
end
if nargout>=2
ip(p,1) = (1:M).';
if nargout>=3
[m{1:N}] = ind2sub(s,p);
m = cell2mat(m);
end
end

Zitieren als

Kenneth Johnson (2024). serpind.m (https://www.mathworks.com/matlabcentral/fileexchange/10756-serpind-m), MATLAB Central File Exchange. Abgerufen .

Kompatibilität der MATLAB-Version
Erstellt mit R2006a
Kompatibel mit allen Versionen
Plattform-Kompatibilität
Windows macOS Linux
Kategorien
Mehr zu Matrices and Arrays finden Sie in Help Center und MATLAB Answers

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!
Version Veröffentlicht Versionshinweise
1.0.0.0