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## Copyright (C) 2011-2025 L. Markowsky <lmarkowsky@gmail.com>
##
## This file is part of the fuzzy-logic-toolkit.
##
## The fuzzy-logic-toolkit 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 3 of
## the License, or (at your option) any later version.
##
## The fuzzy-logic-toolkit 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 the fuzzy-logic-toolkit; see the file COPYING. If not,
## see <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {@var{sqr_dist} =} square_distance_matrix (@var{X}, @var{V})
##
## Return a k x n matrix of ||x - v||^2 values (the squares of the
## distances between input data points x and cluster centers v), where
## k is the number of cluster centers and n is the number of data points.
##
## The element sqr_dist(i, j) will contain the square of the distance
## between the cluster center V(i, :) and the data point X(j, :).
##
## @end deftypefn
## Author: L. Markowsky
## Keywords: fuzzy-logic-toolkit fuzzy private
## Directory: fuzzy-logic-toolkit/inst/private/
## Filename: square_dist_matrix.m
## Last-Modified: 5 Jun 2024
function sqr_dist = square_distance_matrix (X, V)
sqr_dist = (sumsq (X, 2) + (sumsq (V, 2))' - 2 * X * V')';
endfunction
%!test
%! ## Test the faster version of this function (above) by comparing its
%! ## output with the output of the previous, nested-for-loop version (below).
%! ##
%! ## The test is run 100 times (but is reported by the Octave interpreter as
%! ## "1 test"). In each of the 100 test runs, the vectorized and loop versions
%! ## of the function are called using randomly generated matrices X, V.
%! ##
%! ## The sizes of X and V, however, aren't random: X has 100 rows, 8 cols,
%! ## and V has 5 rows, 8 cols. That is, the entries in X and V are random
%! ## values in the range [0, 1], but the sizes of X and V are hard-coded.
%! ##
%! ## The test is passed if all entries of the two results differ by less than
%! ## a tolerance of 10e-9 in all 100 test runs.
%!
%! function sqr_dist = square_distance_matrix_using_for_loops (X, V)
%! k = rows (V);
%! n = rows (X);
%! sqr_dist = zeros (k, n);
%! for i = 1 : k
%! Vi = V(i, :);
%! for j = 1 : n
%! Vi_to_Xj = X(j, :) - Vi;
%! sqr_dist(i, j) = sum (Vi_to_Xj .* Vi_to_Xj);
%! endfor
%! endfor
%! endfunction
%!
%! ## Fixed array sizes and tolerance for the test.
%!
%! n = 100;
%! f = 8;
%! k = 5;
%! tolerance = 10e-9;
%!
%! ## Run the test 100 times, in a loop. Each test run is successful if
%! ## the vectorized and nested-for-loop version of the function produce
%! ## results within the hard-coded tolerance.
%!
%! for i = 1 : 100
%! X = rand (n, f);
%! V = rand (k, f);
%! vec_result = square_distance_matrix (X, V);
%! loop_result = square_distance_matrix_using_for_loops (X, V);
%! assert (abs (vec_result - loop_result) < tolerance)
%! endfor
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