function [ undx, xdnu ] = r8vec_undex ( x_num, x_val, x_unique_num, tol )
%*****************************************************************************80
%
%% r8vec_undex() returns unique sorted indexes for an R8VEC.
%
% Discussion:
%
% An R8VEC is a vector of R8 values.
%
% The goal of this routine is to determine a vector UNDX,
% which points, to the unique elements of X, in sorted order,
% and a vector XDNU, which identifies, for each entry of X, the index of
% the unique sorted element of X.
%
% This is all done with index vectors, so that the elements of
% X are never moved.
%
% The first step of the algorithm requires the indexed sorting
% of X, which creates arrays INDX and XDNI. (If all the entries
% of X are unique, then these arrays are the same as UNDX and XDNU.)
%
% We then use INDX to examine the entries of X in sorted order,
% noting the unique entries, creating the entries of XDNU and
% UNDX as we go.
%
% Once this process has been completed, the vector X could be
% replaced by a compressed vector XU, containing the unique entries
% of X in sorted order, using the formula
%
% XU(1:X_UNIQUE_NUM) = X(UNDX(1:X_UNIQUE_NUM)).
%
% We could then, if we wished, reconstruct the entire vector X, or
% any element of it, by index, as follows:
%
% X(I) = XU(XDNU(I)).
%
% We could then replace X by the combination of XU and XDNU.
%
% Later, when we need the I-th entry of X, we can locate it as
% the XDNU(I)-th entry of XU.
%
% Here is an example of a vector X, the sort and inverse sort
% index vectors, and the unique sort and inverse unique sort vectors
% and the compressed unique sorted vector.
%
% I X Indx Xdni XU Undx Xdnu
% ----+-----+-----+-----+--------+-----+-----+
% 1 : 11. 1 1 : 11, 1 1
% 2 : 22. 3 5 : 22, 2 2
% 3 : 11. 6 2 : 33, 4 1
% 4 : 33. 9 8 : 55, 5 3
% 5 : 55. 2 9 : 4
% 6 : 11. 7 3 : 1
% 7 : 22. 8 6 : 2
% 8 : 22. 4 7 : 2
% 9 : 11. 5 4 : 1
%
% INDX(2) = 3 means that sorted item(2) is X(3).
% XDNI(2) = 5 means that X(2) is sorted item(5).
%
% UNDX(3) = 4 means that unique sorted item(3) is at X(4).
% XDNU(8) = 2 means that X(8) is at unique sorted item(2).
%
% XU(XDNU(I))) = X(I).
% XU(I) = X(UNDX(I)).
%
% Licensing:
%
% This code is distributed under the GNU LGPL license.
%
% Modified:
%
% 26 October 2008
%
% Author:
%
% John Burkardt
%
% Input:
%
% integer X_NUM, the number of data values.
%
% real X_VAL(X_NUM), the data values.
%
% integer X_UNIQUE_NUM, the number of unique values in X_VAL.
% This value is only required for languages in which the size of
% UNDX must be known in advance.
%
% real TOL, a tolerance for equality.
%
% Output:
%
% integer UNDX(X_UNIQUE_NUM), the UNDX vector.
%
% integer XDNU(X_NUM), the XDNU vector.
%
%
% Implicitly sort the array.
%
indx = r8vec_sort_heap_index_a ( x_num, x_val );
%
% Walk through the implicitly sorted array X.
%
i = 1;
j = 1;
undx(j) = indx(i);
xdnu(indx(i)) = j;
for i = 2 : x_num
if ( tol < abs ( x_val(indx(i)) - x_val(undx(j)) ) )
j = j + 1;
undx(j) = indx(i);
end
xdnu(indx(i)) = j;
end
return
end