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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{retval} =} einstein_sum (@var{x})
## @deftypefnx {Function File} {@var{retval} =} einstein_sum (@var{x}, @var{y})
##
## Return the Einstein sum of the input.
## The Einstein sum of two real scalars x and y is: (x + y) / (1 + x * y)
##
## For one vector argument, apply the Einstein sum to all of the elements
## of the vector. (The Einstein sum is associative.) For one
## two-dimensional matrix argument, return a vector of the Einstein sum
## of each column.
##
## For two vectors or matrices of identical dimensions, or for one scalar and
## one vector or matrix argument, return the pairwise Einstein sum.
##
## @seealso{algebraic_product, algebraic_sum, bounded_difference, bounded_sum, drastic_product, drastic_sum, einstein_product, hamacher_product, hamacher_sum}
## @end deftypefn
## Author: L. Markowsky
## Keywords: fuzzy-logic-toolkit fuzzy einstein_sum
## Directory: fuzzy-logic-toolkit/inst/
## Filename: einstein_sum.m
## Last-Modified: 26 Jul 2024
function retval = einstein_sum (x, y = 0)
if (nargin == 0 || nargin > 2 ||
!is_real_matrix (x) || !is_real_matrix (y))
error ("invalid arguments to function einstein_sum\n");
elseif (nargin == 1)
if (isvector (x))
retval = vector_arg (x);
elseif (ndims (x) == 2)
retval = matrix_arg (x);
else
error ("invalid arguments to function einstein_sum\n");
endif
elseif (nargin == 2)
if (isequal (size (x), size (y)))
retval = arrayfun (@scalar_args, x, y);
elseif (isscalar (x) && ismatrix (y))
x = x * ones (size (y));
retval = arrayfun (@scalar_args, x, y);
elseif (ismatrix (x) && isscalar (y))
y = y * ones (size (x));
retval = arrayfun (@scalar_args, x, y);
else
error ("invalid arguments to function einstein_sum\n");
endif
endif
endfunction
function retval = scalar_args (x, y)
retval = (x + y) / (1 + x * y);
endfunction
function retval = vector_arg (real_vector)
x = 0;
for i = 1 : length (real_vector)
y = real_vector(i);
x = (x + y) / (1 + x * y);
endfor
retval = x;
endfunction
function retval = matrix_arg (x)
num_cols = columns (x);
retval = zeros (1, num_cols);
for i = 1 : num_cols
retval(i) = vector_arg (x(:, i));
endfor
endfunction
%!test
%! x = [5 3];
%! z = einstein_sum(x);
%! assert(z, 0.5000);
%!test
%! x = [5 2 3 6];
%! y = [-1 1 2 3];
%! z = einstein_sum(x, y);
%! assert(z, [-1.000 1.000 0.7143 0.4737], 1e-4);
## Test input validation
%!error <invalid arguments to function einstein_sum>
%! einstein_sum()
%!error <invalid arguments to function einstein_sum>
%! einstein_sum(2j)
%!error <invalid arguments to function einstein_sum>
%! einstein_sum(1, 2j)
%!error <invalid arguments to function einstein_sum>
%! einstein_sum([1 2j])
%!error <einstein_sum: function called with too many inputs>
%! einstein_sum(1, 2, 3)
%!error <invalid arguments to function einstein_sum>
%! einstein_sum([1 2], [1 2 3])
%!error <invalid arguments to function einstein_sum>
%! einstein_sum([1 2], [1 2; 3 4])
%!error <invalid arguments to function einstein_sum>
%! einstein_sum(0:100, [])
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