function [ x, constraint, more ] = vector_constrained_next3 ( ...
n, x_min, x_max, x, more )
%*****************************************************************************80
%
%% vector_constrained_next3() returns the "next" constrained vector.
%
% Discussion:
%
% This routine addresses the same problem as VECTOR_CONSTRAINED_NEXT2,
% and differs only in that real arithmetic is used, rather than
% integer arithmetic. Integer arithmetic allows us to do an exact
% calculation, but we run into overflow problems in simple cases
% where N is 10 and the X_MAX entries are of order 10, for instance.
%
% We consider all vectors of dimension N whose components
% satisfy X_MIN(1:N) <= X(1:N) <= X_MAX(1:N).
%
% We are only interested in the subset of these vectors which
% satisfy the following constraint:
%
% sum ( 1 <= I <= N ) ( X(I) / X_MAX(I) ) <= 1
%
% Example:
%
% N = 3
% X_MIN: 1 1 1
% X_MAX: 5 6 4
%
% P = 120
%
% # X(1) X(2) X(3) CONSTRAINT
%
% 1 1 1 1 0.62
% 2 2 1 1 0.82
% 3 1 2 1 0.78
% 4 2 2 1 0.98
% 5 1 3 1 0.95
% 6 1 1 2 0.87
%
% Licensing:
%
% This code is distributed under the MIT license.
%
% Modified:
%
% 27 April 2006
%
% Author:
%
% John Burkardt
%
% Input:
%
% integer N, the number of components in the vector.
%
% integer X_MIN(N), X_MAX(N), the minimum and maximum
% values allowed in each component.
%
% integer X(N). On first call (with MORE = FALSE),
% the input value of X is not important. On subsequent calls, the
% input value of X should be the output value from the previous call.
%
% logical MORE. On input, if the user has set MORE
% FALSE, the user is requesting the initiation of a new sequence
% of values. If MORE is TRUE, then the user is requesting "more"
% values in the current sequence.
%
% Output:
%
% integer X(N). On output, (with MORE = TRUE), the value of X will be the "next"
% vector in the reverse lexicographical list of vectors that satisfy
% the condition. However, on output with MORE = FALSE, the vector
% X is meaningless, because there are no more vectors in the list.
%
% real CONSTRAINT, the constraint value for X.
% Valid vectors X will have a CONSTRAINT value between
% product(X_MIN(1:N)) / product(X_MAX(1:N))
% and 1.0.
%
% logical MORE. On output, if MORE is TRUE,
% then another value was found and returned in X, but if MORE is
% FALSE, then there are no more values in the sequence, and X is
% NOT the next value.
%
if ( ~ more )
x(1:n) = x_min(1:n);
constraint = sum ( x(1:n) ./ x_max(1:n) );
if ( 1.0 < constraint )
more = false;
else
more = true;
end
return
else
i = 1;
while ( true )
if ( x(i) < x_max(i) )
x(i) = x(i) + 1;
constraint = sum ( x(1:n) ./ x_max(1:n) );
if ( constraint <= 1.0 )
break
end
end
x(i) = x_min(i);
i = i + 1;
if ( n < i )
more = false;
break
end
end
end
return
end