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########################################################################
##
## Copyright (C) 1995-2024 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{y} =} center (@var{x})
## @deftypefnx {} {@var{y} =} center (@var{x}, @var{dim})
## Center data by subtracting its mean.
##
## If @var{x} is a vector, subtract its mean.
##
## If @var{x} is a matrix, do the above for each column.
##
## If the optional argument @var{dim} is given, operate along this dimension.
##
## Programming Note: @code{center} has obvious application for normalizing
## statistical data. It is also useful for improving the precision of general
## numerical calculations. Whenever there is a large value that is common
## to a batch of data, the mean can be subtracted off, the calculation
## performed, and then the mean added back to obtain the final answer.
## @seealso{zscore}
## @end deftypefn
function y = center (x, dim)
if (nargin < 1)
print_usage ();
endif
if (! (isnumeric (x) || islogical (x)))
error ("center: X must be a numeric vector or matrix");
endif
if (isinteger (x))
x = double (x);
endif
nd = ndims (x);
sz = size (x);
if (nargin != 2)
## Find the first non-singleton dimension.
(dim = find (sz > 1, 1)) || (dim = 1);
else
if (! (isscalar (dim) && dim == fix (dim) && dim > 0))
error ("center: DIM must be an integer and a valid dimension");
endif
endif
n = size (x, dim);
if (n == 0)
y = x;
else
## FIXME: Use bsxfun, rather than broadcasting, until broadcasting
## supports diagonal and sparse matrices (Bugs #41441, #35787).
y = bsxfun (@minus, x, mean (x, dim));
## y = x - mean (x, dim); # automatic broadcasting
endif
endfunction
%!assert (center ([1,2,3]), [-1,0,1])
%!assert (center (single ([1,2,3])), single ([-1,0,1]))
%!assert (center (int8 ([1,2,3])), [-1,0,1])
%!assert (center (logical ([1, 0, 0, 1])), [0.5, -0.5, -0.5, 0.5])
%!assert (center (ones (3,2,0,2)), zeros (3,2,0,2))
%!assert (center (ones (3,2,0,2, "single")), zeros (3,2,0,2, "single"))
%!assert (center (magic (3)), [3,-4,1;-2,0,2;-1,4,-3])
%!assert (center ([1 2 3; 6 5 4], 2), [-1 0 1; 1 0 -1])
%!assert (center (1, 3), 0)
## Test input validation
%!error <Invalid call> center ()
%!error <DIM must be an integer> center (1, ones (2,2))
%!error <DIM must be an integer> center (1, 1.5)
%!error <DIM must be .* a valid dimension> center (1, 0)
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