doc: Ensure documentation lists output argument when it exists for all m-files. For new users of Octave it is best to show explicit calling forms in the documentation and to show a return argument when it exists. * bp-table.cc, shift.m, accumarray.m, accumdim.m, bincoeff.m, bitcmp.m, bitget.m, bitset.m, blkdiag.m, celldisp.m, cplxpair.m, dblquad.m, flip.m, fliplr.m, flipud.m, idivide.m, int2str.m, interpft.m, logspace.m, num2str.m, polyarea.m, postpad.m, prepad.m, randi.m, repmat.m, rng.m, rot90.m, rotdim.m, structfun.m, triplequad.m, uibuttongroup.m, uicontrol.m, uipanel.m, uipushtool.m, uitoggletool.m, uitoolbar.m, waitforbuttonpress.m, help.m, __additional_help_message__.m, hsv.m, im2double.m, im2frame.m, javachk.m, usejava.m, argnames.m, char.m, formula.m, inline.m, __vectorize__.m, findstr.m, flipdim.m, strmatch.m, vectorize.m, commutation_matrix.m, cond.m, cross.m, duplication_matrix.m, expm.m, orth.m, rank.m, rref.m, trace.m, vech.m, cast.m, compare_versions.m, delete.m, dir.m, fileattrib.m, grabcode.m, gunzip.m, inputname.m, license.m, list_primes.m, ls.m, mexext.m, movefile.m, namelengthmax.m, nargoutchk.m, nthargout.m, substruct.m, swapbytes.m, ver.m, verLessThan.m, what.m, fminunc.m, fsolve.m, fzero.m, optimget.m, __fdjac__.m, matlabroot.m, savepath.m, campos.m, camroll.m, camtarget.m, camup.m, camva.m, camzoom.m, clabel.m, diffuse.m, legend.m, orient.m, rticks.m, specular.m, thetaticks.m, xlim.m, xtickangle.m, xticklabels.m, xticks.m, ylim.m, ytickangle.m, yticklabels.m, yticks.m, zlim.m, ztickangle.m, zticklabels.m, zticks.m, ellipsoid.m, isocolors.m, isonormals.m, stairs.m, surfnorm.m, __actual_axis_position__.m, __pltopt__.m, close.m, graphics_toolkit.m, pan.m, print.m, printd.m, __ghostscript__.m, __gnuplot_print__.m, __opengl_print__.m, rotate3d.m, subplot.m, zoom.m, compan.m, conv.m, poly.m, polyaffine.m, polyder.m, polyint.m, polyout.m, polyreduce.m, polyvalm.m, roots.m, prefdir.m, prefsfile.m, profexplore.m, profexport.m, profshow.m, powerset.m, unique.m, arch_rnd.m, arma_rnd.m, autoreg_matrix.m, bartlett.m, blackman.m, detrend.m, durbinlevinson.m, fftconv.m, fftfilt.m, fftshift.m, fractdiff.m, hamming.m, hanning.m, hurst.m, ifftshift.m, rectangle_lw.m, rectangle_sw.m, triangle_lw.m, sinc.m, sinetone.m, sinewave.m, spectral_adf.m, spectral_xdf.m, spencer.m, ilu.m, __sprand__.m, sprand.m, sprandn.m, sprandsym.m, treelayout.m, beta.m, betainc.m, betaincinv.m, betaln.m, cosint.m, expint.m, factorial.m, gammainc.m, gammaincinv.m, lcm.m, nthroot.m, perms.m, reallog.m, realpow.m, realsqrt.m, sinint.m, hadamard.m, hankel.m, hilb.m, invhilb.m, magic.m, pascal.m, rosser.m, toeplitz.m, vander.m, wilkinson.m, center.m, corr.m, cov.m, discrete_cdf.m, discrete_inv.m, discrete_pdf.m, discrete_rnd.m, empirical_cdf.m, empirical_inv.m, empirical_pdf.m, empirical_rnd.m, kendall.m, kurtosis.m, mad.m, mean.m, meansq.m, median.m, mode.m, moment.m, range.m, ranks.m, run_count.m, skewness.m, spearman.m, statistics.m, std.m, base2dec.m, bin2dec.m, blanks.m, cstrcat.m, deblank.m, dec2base.m, dec2bin.m, dec2hex.m, hex2dec.m, index.m, regexptranslate.m, rindex.m, strcat.m, strjust.m, strtrim.m, strtrunc.m, substr.m, untabify.m, __have_feature__.m, __prog_output_assert__.m, __run_test_suite__.m, example.m, fail.m, asctime.m, calendar.m, ctime.m, date.m, etime.m: Add return arguments to @deftypefn macros where they were missing. Rename variables in functions (particularly generic "retval") to match documentation. Rename some return variables for (hopefully) better clarity (e.g., 'ax' to 'hax' to indicate it is a graphics handle to an axes object).

########################################################################
##
## Copyright (C) 1993-2022 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{c} =} cond (@var{A})
## @deftypefnx {} {@var{c} =} cond (@var{A}, @var{p})
## Compute the @var{p}-norm condition number of a matrix with respect to
## inversion.
##
## @code{cond (@var{A})} is defined as
## @tex
## $ {\parallel A \parallel_p * \parallel A^{-1} \parallel_p .} $
## @end tex
## @ifnottex
## @code{norm (@var{A}, @var{p}) * norm (inv (@var{A}), @var{p})}.
## @end ifnottex
##
## By default, @code{@var{p} = 2} is used which implies a (relatively slow)
## singular value decomposition.  Other possible selections are
## @code{@var{p} = 1, Inf, "fro"} which are generally faster.  For a full
## discussion of possible @var{p} values, @pxref{XREFnorm,,@code{norm}}.
##
## The condition number of a matrix quantifies the sensitivity of the matrix
## inversion operation when small changes are made to matrix elements.  Ideally
## the condition number will be close to 1.  When the number is large this
## indicates small changes (such as underflow or round-off error) will produce
## large changes in the resulting output.  In such cases the solution results
## from numerical computing are not likely to be accurate.
## @seealso{condest, rcond, condeig, norm, svd}
## @end deftypefn

function c = cond (A, p = 2)

  if (nargin < 1)
    print_usage ();
  endif

  if (ndims (A) > 2)
    error ("cond: A must be a 2-D matrix");
  endif

  if (p == 2)
    if (isempty (A))
      c = 0.0;
    elseif (any (! isfinite (A(:))))
      error ("cond: A must not contain Inf or NaN values");
    else
      sigma   = svd (A);
      sigma_1 = sigma(1);
      sigma_n = sigma(end);
      if (sigma_1 == 0 || sigma_n == 0)
        c = Inf;
      else
        c = sigma_1 / sigma_n;
      endif
    endif
  else
    c = norm (A, p) * norm (inv (A), p);
  endif

endfunction


%!test
%! y = [7, 2, 3; 1, 3, 4; 6, 4, 5];
%! tol = 1e-6;
%! type = {1, 2, "fro", "inf", inf};
%! for n = 1:numel (type)
%!   rcondition(n) = 1 / cond (y, type{n});
%! endfor
%! assert (rcondition, [0.017460, 0.019597, 0.018714, 0.012022, 0.012022], tol);

%!assert (cond ([1, 2; 2, 1]), 3, sqrt (eps))
%!assert (cond ([1, 2, 3; 4, 5, 6; 7, 8, 9]) > 1.0e+16)

%!error <Invalid call> cond ()
%!error <A must be a 2-D matrix> cond (ones (1,3,3))
%!error <A must not contain Inf or NaN value> cond ([1, 2;Inf 4])
%!error <A must not contain Inf or NaN value> cond ([1, 2;NaN 4])