function [ x, base ] = tuple_next_fast ( m, n, rank, base )
%*****************************************************************************80
%
%% tuple_next_fast() computes the next element of a tuple space, "fast".
%
% Discussion:
%
% The elements are N vectors. Each entry is constrained to lie
% between 1 and M. The elements are produced one at a time.
% The first element is
% (1,1,...,1)
% and the last element is
% (M,M,...,M)
% Intermediate elements are produced in lexicographic order.
%
% This code was written as a possibly faster version of TUPLE_NEXT.
%
% Example:
%
% N = 2,
% M = 3
%
% INPUT OUTPUT
% ------- -------
% Rank X
% ---- ----
% -1 -1 -1
%
% 0 1 1
% 1 1 2
% 2 1 3
% 3 2 1
% 4 2 2
% 5 2 3
% 6 3 1
% 7 3 2
% 8 3 3
% 9 1 1
%
% Licensing:
%
% This code is distributed under the MIT license.
%
% Modified:
%
% 04 June 2015
%
% Author:
%
% John Burkardt
%
% Input:
%
% integer M, the maximum entry in each component.
% M must be greater than 0.
%
% integer N, the number of components.
% N must be greater than 0.
%
% integer RANK, indicates the rank of the tuples.
% Typically, 0 <= RANK < N^M; values greater than this are
% legal and meaningful, being equivalent to the corresponding
% value mod N^M. RANK < 0 indicates that this is the first
% call for the given values of (M,N). Initialization is done,
% and X is set to a dummy value.
%
% integer BASE(N), a bookkeeping array.
% The user should allocate space for this array, but
% should not alter it between successive calls.
%
% Output:
%
% integer X(N), the next tuple of the given rank,
% or a dummy value if initialization is being done.
%
% integer BASE(N), the updated bookkeeping array.
%
if ( rank < 0 )
if ( m <= 0 )
fprintf ( 1, '\n' );
fprintf ( 1, 'TUPLE_NEXT_FAST - Fatal error!\n' );
fprintf ( 1, ' M <= 0 is illegal.\n' );
fprintf ( 1, ' M = %d\n', m );
error ( 'TUPLE_NEXT_FAST - Fatal error!' );
end
if ( n <= 0 )
fprintf ( 1, '\n' );
fprintf ( 1, 'TUPLE_NEXT_FAST - Fatal error!\n' );
fprintf ( 1, ' N <= 0 is illegal.\n' );
fprintf ( 1, ' N = %d\n', n );
error ( 'TUPLE_NEXT_FAST - Fatal error!' );
end
base(n) = 1;
for i = n - 1 : -1 : 1
base(i) = base(i+1) * m;
end
x(1:n) = -1;
else
x(1:n) = mod ( floor ( rank ./ base(1:n) ), m ) + 1;
end
return
end