function unique_num = r8vec_sorted_unique_count ( n, a, tol )
%*****************************************************************************80
%
%% r8vec_sorted_unique_count() counts the unique elements in a sorted R8VEC.
%
% Discussion:
%
% Because the array is sorted, this algorithm is O(N).
%
% If the tolerance is large enough, then the concept of uniqueness
% can become ambiguous. If we have a tolerance of 1.5, then in the
% list ( 1, 2, 3, 4, 5, 6, 7, 8, 9 ) is it fair to say we have only
% one unique entry? That would be because 1 may be regarded as unique,
% and then 2 is too close to 1 to be unique, and 3 is too close to 2 to
% be unique and so on.
%
% This seems wrongheaded. So I prefer the idea that an item is not
% unique under a tolerance only if it is close to something that IS unique.
% Thus, the unique items are guaranteed to cover the space if we include
% a disk of radius TOL around each one.
%
% Licensing:
%
% This code is distributed under the GNU LGPL license.
%
% Modified:
%
% 30 April 2004
%
% Author:
%
% John Burkardt
%
% Input:
%
% integer N, the number of elements of A.
%
% real A(N), the sorted array to examine.
%
% real TOL, a nonnegative tolerance for equality.
%
% Output:
%
% integer UNIQUE_NUM, the number of unique elements of A.
%
unique_num = 0;
if ( n < 1 )
return;
end
unique_num = 1;
j1 = 1;
for j2 = 2 : n
if ( tol < abs ( a(j1) - a(j2) ) )
unique_num = unique_num + 1;
j1 = j2;
end
end
return
end