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## Copyright (C) 1996-2021 The Octave Project Developers
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## -*- texinfo -*-
## @deftypefn {} {} std (@var{x})
## @deftypefnx {} {} std (@var{x}, @var{w})
## @deftypefnx {} {} std (@var{x}, @var{w}, @var{dim})
## @deftypefnx {} {} std (@var{x}, @var{w}, @qcode{"ALL"})
## Compute the standard deviation of the elements of the vector @var{x}.
##
## The standard deviation is defined as
## @tex
## $$
## {\rm std} (x) = \sigma = \sqrt{{\sum_{i=1}^N (x_i - \bar{x})^2 \over N - 1}}
## $$
## where $\bar{x}$ is the mean value of @var{x} and $N$ is the number of elements of @var{x}.
## @end tex
## @ifnottex
##
## @example
## @group
## std (@var{x}) = sqrt ( 1/(N-1) SUM_i (@var{x}(i) - mean(@var{x}))^2 )
## @end group
## @end example
##
## @noindent
## where @math{N} is the number of elements of the @var{x} vector.
## @end ifnottex
##
## If @var{x} is a matrix, compute the standard deviation for each column and
## return them in a row vector.
##
## The argument @var{w} determines the weighting scheme to use.
## Valid values are
##
## @table @asis
## @item 0:
## normalize with @math{N-1}, provides the square root of the best unbiased
## estimator of the variance [default]
##
## @item 1:
## normalize with @math{N}, this provides the square root of the second
## moment around the mean
##
## @item a vector:
## compute the weighted standard deviation with nonnegative scalar weights,
## the length of @var{w} must be equal to the size of @var{x} along dimension
## @var{dim}
## @end table
##
## The optional variable @var{dim} can be used to force @code{std} to operate
## over the specified dimension. @var{dim} can either be a scalar dimension or
## a vector of non-repeating dimensions over which to operate. Dimensions are
## positive integers. When @var{dim} is a vector, @var{w} must be either 0 or
## 1, and the standard deviation is calculated over the array slice defined by
## @var{dim}.
##
## Specifying dimension @qcode{"ALL"} will force @code{std} to operate
## on all elements of @var{x}, when @var{w} is either 0 or 1, and is equivalent
## to @code{std (@var{x}(:))}.
## @seealso{var, bounds, mad, range, iqr, mean, median}
## @end deftypefn
function retval = std (varargin)
retval = sqrt (var (varargin{:}));
endfunction
%!test
%! x = ones (10, 2);
%! y = [1, 3];
%! assert (std (x), [0, 0]);
%! assert (std (y), sqrt (2), sqrt (eps));
%! assert (std (x, 0, 2), zeros (10, 1));
%!assert (std (ones (3, 1, 2), 0, 2), zeros (3, 1, 2))
%!assert (std ([1 2], 0), sqrt (2)/2, 5*eps)
%!assert (std ([1 2], 1), 0.5, 5*eps)
%!assert (std (1), 0)
%!assert (std (single (1)), single (0))
%!assert (std ([1 2 3], [], 3), [0 0 0])
##Test empty inputs
%!assert (std ([]), NaN)
%!assert (std ([],[],1), NaN(1,0))
%!assert (std ([],[],2), NaN(0,1))
%!assert (std ([],[],3), [])
%!assert (std (ones (0,1)), NaN)
%!assert (std (ones (1,0)), NaN)
%!assert (std (ones (1,0), [], 1), NaN(1,0))
%!assert (std (ones (1,0), [], 2), NaN)
%!assert (std (ones (1,0), [], 3), NaN(1,0))
%!assert (std (ones (0,1)), NaN)
%!assert (std (ones (0,1), [], 1), NaN)
%!assert (std (ones (0,1), [], 2), NaN(0,1))
%!assert (std (ones (0,1), [], 3), NaN(0,1))
%!assert (std (ones (1,3,0,2)), NaN(1,1,0,2))
%!assert (std (ones (1,3,0,2), [], 1), NaN(1,3,0,2))
%!assert (std (ones (1,3,0,2), [], 2), NaN(1,1,0,2))
%!assert (std (ones (1,3,0,2), [], 3), NaN(1,3,1,2))
%!assert (std (ones (1,3,0,2), [], 4), NaN(1,3,0))
## Test input validation
%!error std ()
%!error std (['A'; 'B'])
%!error std (1, 2)
%!error std (1, [], ones (2,2))
%!error std (1, [], 1.5)
%!error std (1, [], 0)