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ismembertol.m
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ismembertol.m
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########################################################################
##
## Copyright (C) 2000-2022 The Octave Project Developers
##
## See the file COPYRIGHT.md in the top-level directory of this
## distribution or <https://octave.org/copyright/>.
##
## This file is part of Octave.
##
## Octave 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.
##
## Octave 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 Octave; see the file COPYING. If not, see
## <https://www.gnu.org/licenses/>.
##
########################################################################
## -*- texinfo -*-
## @deftypefn {} {@var{tf} =} ismembertol (@var{a}, @var{s})
## @deftypefnx {} {@var{tf} =} ismembertol (@var{a}, @var{s}, @var{tol})
## @deftypefnx {} {@var{tf} =} ismembertol (@var{a}, @var{s}, @var{name}, @var{value})
## @deftypefnx {} {[@var{tf}, @var{s_idx}] =} ismembertol (@dots{})
##
## Return a logical matrix @var{tf} with the same shape as @var{a} which is
## true (1) if the element in @var{a} is @var{tol} close to @var{s} and false (0) if it
## is not. When @var{tol} is not provided, uses a default tolerance of @qcode{1e-6}.
##
## If a second output argument is requested then the index into @var{s} of each
## matching element is also returned.
##
## The inputs @var{a} and @var{s} are numberic values.
##
## @example
## @group
## a = [3, 10, 1];
## s = [0:9];
## [tf, s_idx] = ismembertol (a, s)
## @result{} tf = [1, 0, 1]
## @result{} s_idx = [4, 0, 2]
## @end group
## @end example
##
## Optional argument pair @var{name} and @var{value} might be given.
## The @var{value} is either @qcode{true} or @qcode{false} and the @var{name}
## might be given chosen from the following options:
## - @qcode{"ByRows"}: compares the rows of @var{a} and @var{s} by considering
## each column separately. Two rows, @var{u} and @var{v}, are within tolerance
## @qcode{if all(abs(u-v) <= tol*max(abs([a;s])))}.
## - @qcode{"OutputAllIndices"}: returns a cell array containing the indices for
## all elements in @var{s} that are within tolerance of the corresponding value
## in @var{s}.
## - @qcode{"DataScale"}: change the scale in the tolerance test to
## @qcode{abs(u-v) <= tol*DS}.
##
## Example:
## @example
## s = [1:6]'*pi;
## a = 10.^log10 (x);
## [tf, s_idx] = ismembertol (a, s);
## @end example
##
## @seealso{ismember, lookup, unique, union, intersect, setdiff, setxor}
## @end deftypefn
function [tf, s_idx] = ismembertol (a, s, varargin)
if (nargin < 2 || nargin > 9)
print_usage ()
endif
if nargin < 3 || ! isnumeric (varargin{1})
# defaut tolerance
tol = 1e-6;
else
tol = varargin{1};
endif
if ! isnumeric (a) || ! isnumeric (s)
print_usage ();
endif
if nargin > 2 && any (! ismember ( {varargin{ find(cellfun(@ischar,varargin)) }}, {"OutputAllIndices", "ByRows", "DataScale"}))
print_usage ();
endif
if nargin > 3 && (! all (cellfun(@(x) ischar(x) || islogical(x) || isnumeric(x), {varargin{2:end}})) || all (cellfun(@(x) isnumeric(x), {varargin{1:2}})))
print_usage ();
endif
by_rows_idx = find (strcmp ("ByRows", varargin));
by_rows = (! isempty (by_rows_idx) && logical (varargin{by_rows_idx+1}) );
all_indices_idx = find (strcmp ("OutputAllIndices", varargin));
all_indices = (! isempty (all_indices_idx) && logical (varargin{all_indices_idx+1}) );
data_scale_idx = find (strcmp ("DataScale", varargin));
data_scale = (! isempty (data_scale_idx) && isnumeric (varargin{data_scale_idx+1}) );
if data_scale
DS = varargin{data_scale_idx+1};
else
DS = max (abs ([a(:);s(:)]));
endif
if (! by_rows)
disp ('not by rows');
sa = size (a);
s = s(:);
a = a(:);
## Check sort status, because we expect the array will often be sorted.
if (issorted (s))
is = [];
else
[s, is] = sort (s);
endif
## Remove NaNs from table because lookup can't handle them
if (isreal (s) && ! isempty (s) && isnan (s(end)))
s = s(1:(end - sum (isnan (s))));
endif
if ! data_scale
DS = max (abs ([a(:);s(:)]));
endif
[s_i, s_j] = find (abs (transpose (s) - a) < tol * DS);
if ! all_indices
disp ('not all indices');
s_idx = zeros (size (a));
[~, I] = unique (s_i);
s_j = s_j(I);
s_idx(s_i(I)) = s_j;
tf = logical (s_idx);
if (! isempty (is))
s_idx(tf) = is(s_idx(tf));
endif
s_idx = reshape (s_idx, sa);
tf = reshape (tf, sa);
else # all_indices
disp ('all indices');
disp ([s_i'; s_j']);
s_idx = cell (size(a));
tf = zeros (size(a));
C = unique (s_j);
for ic = C',
printf ("ic = %d\n",ic);
ii = find (s_j == ic);
disp (ii);
for sii = s_i(ii)'
printf ("adding %d to s_idx{%d}\n",ic,sii);
if ! isempty (is)
s_idx{sii} = [s_idx{sii} is(ic)];
else
s_idx{sii} = [s_idx{sii} ic];
endif
endfor
disp (s_idx{ic});
tf(ic) = 1;
endfor
endif
else # "rows" argument
disp ('by rows');
if (isempty (a) || isempty (s))
tf = false (rows (a), 1);
s_idx = zeros (rows (a), 1);
else
if (rows (s) == 1)
tf = all (bsxfun (@eq, a, s), 2);
s_idx = double (tf);
else
# Two rows, u and v, are within tolerance if all(abs(u-v) <= tol*max(abs([A;B]))).
na = rows (a);
if ! all_indices
s_idx = zeros (na, 1);
else
s_idx = cell (na, 1);
endif
if length (DS) == 1,
DS = repmat (DS, 1, columns (a));
endif
for i = 1:na,
if ! all_indices
s_i = find ( all (abs (a(i,:) - s) < tol * DS, 2), 1);
if ! isempty (s_i), s_idx(i) = s_i; endif
else
s_i = find ( all (abs (a(i,:) - s) < tol * DS, 2));
if ! isempty (s_i), s_idx{i} = s_i; endif
endif
endfor
if ! all_indices
tf = logical (s_idx);
else
tf = cellfun(@(x) ! isempty (x) && all (x(:)!=0), s_idx);
endif
endif
endif
endif
endfunction
%!demo
%! A = rand(1000,2);
%! B = [(0:.2:1)',0.5*ones(6,1)];
%! [LIA,LocAllB] = ismembertol(B, A, 0.1, 'ByRows', true, 'OutputAllIndices', true, 'DataScale', [1,Inf]);
%! hold on
%! plot(B(:,1),B(:,2),'x')
%! for k = 1:length(LocAllB)
%! plot(A(LocAllB{k},1), A(LocAllB{k},2),'.');
%! endfor
%!assert (isempty (ismembertol ([], [1, 2])), true)
%!fail ("ismembertol ([], {1, 2})")
%!fail ("ismembertol ({[]}, {1, 2})")
%!fail ("ismembertol ({}, {1, 2})")
%!fail ("ismembertol ({1}, {'1', '2'})")
%!fail ("ismembertol ({'1'}, {'1' '2'},'ByRows',true)")
%!fail ("ismembertol ([1 2 3], [5 4 3 1], 'ByRows',true)")
%!test
%! [result, s_idx] = ismembertol ([1; 2], []);
%! assert (result, [false; false]);
%! assert (s_idx, [0; 0]);
%!test
%! [result, s_idx] = ismembertol ([], [1, 2]);
%! assert (result, logical ( [] ));
%! assert (s_idx, []);
%!test
%! [result, s_idx] = ismembertol ([1 2 3 4 5], [3]);
%! assert (result, logical ([0 0 1 0 0]));
%! assert (s_idx , [0 0 1 0 0]);
%!test
%! [result, s_idx] = ismembertol ([1 6], [1 2 3 4 5 1 6 1]);
%! assert (result, [true true]);
%! assert (s_idx(2), 7);
%!test
%! [result, s_idx] = ismembertol ([3,10,1], [0,1,2,3,4,5,6,7,8,9]);
%! assert (result, [true false true]);
%! assert (s_idx, [4 0 2]);
%!test
%! [result, s_idx] = ismembertol ([1:3; 5:7; 4:6], [0:2; 1:3; 2:4; 3:5; 4:6], "ByRows", true);
%! assert (result, [true; false; true]);
%! assert (s_idx, [2; 0; 5]);
%!test
%! [result, s_idx] = ismembertol ([1.1,1.2,1.3; 2.1,2.2,2.3; 10,11,12], [1.1,1.2,1.3; 10,11,12; 2.12,2.22,2.32], "ByRows", true);
%! assert (result, [true; false; true]);
%! assert (s_idx, [1; 0; 2]);
%!test
%! [result, s_idx] = ismembertol ([1:3; 5:7; 4:6; 0:2; 1:3; 2:4], [1:3], "ByRows", true);
%! assert (result, logical ([1 0 0 0 1 0]'));
%! assert (s_idx, [1 0 0 0 1 0]');
%!test
%! [tf, s_idx] = ismembertol ([5, 4-3j, 3+4j], [5, 4-3j, 3+4j]);
%! assert (tf, logical ([1 1 1]));
%! assert (s_idx, [1 2 3]);
%!test
%! [tf, s_idx] = ismembertol ([5, 4-3j, 3+4j], 5);
%! assert (tf, logical ([1 0 0]));
%! assert (s_idx, [1 0 0]);
%!test
%! [tf, s_idx] = ismembertol ([5, 5, 5], 4-3j);
%! assert (tf, logical ([0 0 0]));
%! assert (s_idx, [0 0 0]);
%!test
%! [tf, s_idx] = ismembertol ([5, 4-3j, 3+4j; 5, 4-3j, 3+4j], [5, 5, 5], "ByRows", true);
%! assert (tf, logical ([0; 0]));
%! assert (s_idx, [0; 0]);
%!test
%! [tf, s_idx] = ismembertol ([5, 5, 5], [5, 4-3j, 3+4j; 5, 5, 5], "ByRows", true);
%! assert (tf, true);
%! assert (s_idx, 2);
%!test
%! tf = ismembertol ([5, 4-3j, 3+4j], 5);
%! assert (tf, logical ([1 0 0]));
%! [~, s_idx] = ismembertol ([5, 4-3j, 3+4j], 5);
%! assert (s_idx, [1 0 0]);
%!test
%! [tf, s_idx] = ismembertol (-1-1j, [-1-1j, -1+3j, -1+1j]);
%! assert (tf, true);
%! assert (s_idx, 1);
%!test
%! [tf, s_idx] = ismembertol ([0.9 1.9 3.1 4.2], [1 2 3], 0.1);
%! assert (tf, [true true true false]);
%! assert (s_idx, [1 2 3 0]);
%!test
%! [tf, s_idx] = ismembertol ([1:10] + 0.01 * (rand (1,10) - 0.5), [1:10], 0.01);
%! assert (tf, logical ([1:10]));
%! assert (s_idx, [1:10]);
## Test input validation
%!error <Invalid call> ismembertol ()
%!error <Invalid call> ismembertol (1)
%!error <Invalid call> ismembertol (1,2,3,4)