## Copyright (C) 2000 Paul Kienzle
##
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2 of the License, or
## (at your option) any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program; if not, write to the Free Software
## Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

## usage: idx = lookup(table, y)
##
## Lookup values in a sorted table.  Usually used as a prelude to
## interpolation.
##
## If table is strictly increasing and idx=lookup(table, y), then
##    table(idx(i)) <= y(i) < table(idx(i+1))
## for all y(i) within the table.  If y(i) is before the table, then 
## idx(i) is 0. If y(i) is after the table then idx(i) is table(n).
## If the table is strictly decreasing, then the tests are reversed.
## No guarantees for tables which are non-monotonic or are not strictly
## monotonic.
##
## To get an index value which lies within an interval of the table
## use:
##      idx = lookup(table(2:length(table)-1), y) - 1
## This puts values before the table into the first interval, and values
## after the table into the last interval.

## Changed from binary search to sort.
## Thanks to Kai Habel <kai.habel@gmx.de> for the suggestion.

## TODO: sort-based lookup is significantly slower given a large table
## TODO: and small lookup vector.  This shouldn't be a problem since
## TODO: interpolation (the reason for the table lookup in the first
## TODO: place) usually involves subsampling of an existing table.  The
## TODO: other use of interpolation, looking up values one at a time, is
## TODO: unfortunately significantly slower for large tables.  
## TODO:    sort is order O((lt+lx)*log(lt+lx)) 
## TODO:    search is order O(lx*log(lt))
## TODO: Clearly, search is asymptotically better than sort, but sort
## TODO: is compiled and search is not.  Could support both, or recode
## TODO: search in C++, or assume things are good enough as they stand.
function idx=lookup(table,xi)
  if isempty (table)
    idx = zeros(size(xi));
  elseif is_vector(table)
    [nr, nc] = size(xi);
    lt=length(table);
    if ( table(1) > table(lt) )
      ## decreasing table
      [v, p] = sort ([xi(:) ; table(:)]);
      idx (p) = cumsum (p > nr*nc);
      idx = lt - idx (1 : nr*nc);
    else
      ## increasing table
      [v, p] = sort ([table(:) ; xi(:) ]);
      idx (p) = cumsum (p <= lt);
      idx = idx (lt+1 : lt+nr*nc);
    endif
    idx = reshape (idx, nr, nc);
  else
    error ("lookup: table must be a vector");
  endif
endfunction
  
%!assert (lookup(1:3, 0.5), 0)     # value before table
%!assert (lookup(1:3, 3.5), 3)     # value after table error
%!assert (lookup(1:3, 1.5), 1)     # value within table error
%!assert (lookup(1:3, [3,2,1]), [3,2,1])
%!assert (lookup([1:4]', [1.2, 3.5]'), [1, 3]');
%!assert (lookup([1:4], [1.2, 3.5]'), [1, 3]');
%!assert (lookup([1:4]', [1.2, 3.5]), [1, 3]);
%!assert (lookup([1:4], [1.2, 3.5]), [1, 3]);
%!assert (lookup(1:3, [3, 2, 1]), [3, 2, 1]);
%!assert (lookup([3:-1:1], [3.5, 3, 1.2, 2.5, 2.5]), [0, 1, 2, 1, 1])
%!assert (isempty(lookup([1:3], [])))
%!assert (isempty(lookup([1:3]', [])))
%!assert (lookup(1:3, [1, 2; 3, 0.5]), [1, 2; 3, 0]);
