function [ a, done ] = r8vec_mirror_next ( n, a )
%*****************************************************************************80
%
%% R8VEC_MIRROR_NEXT steps through all sign variations of an R8VEC.
%
% Discussion:
%
% In normal use, the user would set every element of A to be positive.
% The routine will take the input value of A, and output a copy in
% which the signs of one or more entries have been changed. Repeatedly
% calling the routine with the output from the previous call will generate
% every distinct "variation" of A; that is, all possible sign variations.
%
% When the output variable DONE is true (or equal to 1), then the
% output value of A is the last in the series.
%
% Note that A may have some zero values. The routine will essentially
% ignore such entries; more exactly, it will not stupidly assume that -0
% is a proper "variation" of 0!
%
% Also, it is possible to call this routine with the signs of A set
% in any way you like. The routine will operate properly, but it
% will nonethess terminate when it reaches the value of A in which
% every nonzero entry has negative sign.
%
% More efficient algorithms using the Gray code seem to require internal
% memory in the routine, or the passing back and forth of a "memory
% array", or the use of global variables, or unnatural demands on the
% user. This form of the routine is about as clean as I can make it.
%
% Example:
%
% Input Output
% --------- --------------
% A A DONE
% --------- -------- ----
% 1 2 3 -1 2 3 false
% -1 2 3 1 -2 3 false
% 1 -2 3 -1 -2 3 false
% -1 -2 3 1 2 -3 false
% 1 2 -3 -1 2 -3 false
% -1 2 -3 1 -2 -3 false
% 1 -2 -3 -1 -2 -3 false
% -1 -2 -3 1 2 3 true
%
% 1 0 3 -1 0 3 false
% -1 0 3 1 0 -3 false
% 1 0 -3 -1 0 -3 false
% -1 0 -3 1 0 3 true
%
% Licensing:
%
% This code is distributed under the GNU LGPL license.
%
% Modified:
%
% 19 April 2005
%
% Author:
%
% John Burkardt
%
% Reference:
%
% Albert Nijenhuis, Herbert Wilf,
% Combinatorial Algorithms,
% Academic Press, 1978, second edition,
% ISBN 0-12-519260-6.
%
% Input:
%
% integer N, the number of entries in the vector.
%
% real A(N), a vector of real numbers.
%
% Output:
%
% real A(N), some signs have been changed.
%
% logical DONE, is true if the input vector A was the last element
% in the series (every entry was nonpositive); the output vector is reset
% so that all entries are nonnegative, but presumably the ride is over!
%
%
% Seek the first strictly positive entry of A.
%
positive = 0;
for i = 1 : n
if ( 0.0 < a(i) )
positive = i;
break
end
end
%
% If there is no strictly positive entry of A, there is no successor.
%
if ( positive == 0 )
a(1:n) = - a(1:n);
done = true;
return
end
%
% Otherwise, negate A up to the positive entry.
%
a(1:positive) = -a(1:positive);
done = false;
return
end