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) 1996-2022 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.
##
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## 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{pdf} =} discrete_pdf (@var{x}, @var{v}, @var{p})
## For each element of @var{x}, compute the probability density function (PDF)
## at @var{x} of a univariate discrete distribution which assumes the values
## in @var{v} with probabilities @var{p}.
## @end deftypefn

function pdf = discrete_pdf (x, v, p)

  if (nargin != 3)
    print_usage ();
  endif

  if (! isvector (v))
    error ("discrete_pdf: V must be a vector");
  elseif (any (isnan (v)))
    error ("discrete_pdf: V must not have any NaN elements");
  elseif (! isvector (p) || (length (p) != length (v)))
    error ("discrete_pdf: P must be a vector with length (V) elements");
  elseif (! (all (p >= 0) && any (p)))
    error ("discrete_pdf: P must be a nonzero, non-negative vector");
  endif

  ## Reshape and normalize probability vector.  Values not in table get 0 prob.
  p = [0 ; p(:)/sum(p)];

  if (isa (x, "single") || isa (v, "single") || isa (p, "single"))
    pdf = NaN (size (x), "single");
  else
    pdf = NaN (size (x));
  endif

  k = ! isnan (x);
  [vs, vi] = sort (v(:));
  pdf(k) = p([0 ; vi](lookup (vs, x(k), 'm') + 1) + 1);

endfunction


%!shared x,v,p,y
%! x = [-1 0.1 1.1 1.9 3];
%! v = 0.1:0.2:1.9;
%! p = 1/length (v) * ones (1, length (v));
%! y = [0 0.1 0.1 0.1 0];
%!assert (discrete_pdf ([x, NaN], v, p), [y, NaN], 5*eps)

## Test class of input preserved
%!assert (discrete_pdf (single ([x, NaN]), v, p),
%!        single ([y, NaN]), 5*eps ("single"))
%!assert (discrete_pdf ([x, NaN], single (v), p),
%!        single ([y, NaN]), 5*eps ("single"))
%!assert (discrete_pdf ([x, NaN], v, single (p)),
%!        single ([y, NaN]), 5*eps ("single"))

## Test input validation
%!error <Invalid call> discrete_pdf ()
%!error <Invalid call> discrete_pdf (1)
%!error <Invalid call> discrete_pdf (1,2)
%!error discrete_pdf (1, ones (2), ones (2,1))
%!error discrete_pdf (1, [1 ; NaN], ones (2,1))
%!error discrete_pdf (1, ones (2,1), ones (1,1))
%!error discrete_pdf (1, ones (2,1), [1 -1])
%!error discrete_pdf (1, ones (2,1), [1 NaN])
%!error discrete_pdf (1, ones (2,1), [0  0])