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## -*- texinfo -*-
## @deftypefn  {} {@var{r} =} corr (@var{x})
## @deftypefnx {} {@var{r} =} corr (@var{x}, @var{y})
## Compute matrix of correlation coefficients.
##
## If each row of @var{x} and @var{y} is an observation and each column is
## a variable, then the @w{(@var{i}, @var{j})-th} entry of
## @code{corr (@var{x}, @var{y})} is the correlation between the
## @var{i}-th variable in @var{x} and the @var{j}-th variable in @var{y}.
## @tex
## $$
## {\rm corr}(x,y) = {{\rm cov}(x,y) \over {\rm std}(x) \, {\rm std}(y)}
## $$
## @end tex
## @ifnottex
##
## @example
## corr (@var{x},@var{y}) = cov (@var{x},@var{y}) / (std (@var{x}) * std (@var{y}))
## @end example
##
## @end ifnottex
## If called with one argument, compute @code{corr (@var{x}, @var{x})},
## the correlation between the columns of @var{x}.
## @seealso{cov}
## @end deftypefn

function r = corr (x, y = [])

  if (nargin < 1)
    print_usage ();
  endif

  ## Input validation is done by cov.m.  Don't repeat tests here

  ## Special case, scalar is always 100% correlated with itself
  if (isscalar (x))
    if (isa (x, "single"))
      r = single (1);
    else
      r = 1;
    endif
    return;
  endif

  ## No check for division by zero error, which happens only when
  ## there is a constant vector and should be rare.
  if (nargin == 2)
    ## Adjust for Octave 9.1.0 compatability behavior change in two-input cov.
    ## cov now treats cov(x,y) as cov(x(:),y(:)), returning a 2x2 covariance
    ## of the two univariate distributions x and y.  corr will now pass [x,y]
    ## as cov([x,y]), which for m x n inputs will return 2n x 2n outputs, with
    ##  the off diagonal matrix quarters containing what was previously
    ## returned by cov(x,y).

    ## FIXME: Returning a larger than needed arary and discarding 3/4 of the
    ##        information is nonideal.  Consider implementing a more
    ##        efficient cov here as a subfunction to corr.

    nx = columns(x);
    c = cov ([x, y]);
    c = c(1:nx, nx+1:end);
    s = std (x)' * std (y);
    r = c ./ s;
  else
    c = cov (x);
    s = sqrt (diag (c));
    r = c ./ (s * s');
  endif

endfunction


%!test
%! x = rand (10);
%! cc1 = corr (x);
%! cc2 = corr (x, x);
%! assert (size (cc1) == [10, 10] && size (cc2) == [10, 10]);
%! assert (cc1, cc2, sqrt (eps));

%!test
%! x = [1:3]';
%! y = [3:-1:1]';
%! assert (corr (x, y), -1, 5*eps);
%! assert (corr (x, flipud (y)), 1, 5*eps);
%! assert (corr ([x, y]), [1 -1; -1 1], 5*eps);

%!test
%! x = single ([1:3]');
%! y = single ([3:-1:1]');
%! assert (corr (x, y), single (-1), 5*eps);
%! assert (corr (x, flipud (y)), single (1), 5*eps);
%! assert (corr ([x, y]), single ([1 -1; -1 1]), 5*eps);

%!assert (corr (5), 1)
%!assert (corr (single (5)), single (1))

## Test input validation
%!error <Invalid call> corr ()
%!error corr ([1; 2], ["A", "B"])
%!error corr (ones (2,2,2))
%!error corr (ones (2,2), ones (2,2,2))