Use Octave coding conventions in all m-file %!test blocks * wavread.m, acosd.m, acot.m, acotd.m, acoth.m, acsc.m, acscd.m, acsch.m, asec.m, asecd.m, asech.m, asind.m, atand.m, cosd.m, cot.m, cotd.m, coth.m, csc.m, cscd.m, csch.m, sec.m, secd.m, sech.m, sind.m, tand.m, accumarray.m, accumdim.m, bitcmp.m, bitget.m, bitset.m, blkdiag.m, cart2pol.m, cart2sph.m, celldisp.m, chop.m, circshift.m, colon.m, common_size.m, cplxpair.m, cumtrapz.m, curl.m, dblquad.m, deal.m, divergence.m, flipdim.m, fliplr.m, flipud.m, genvarname.m, gradient.m, idivide.m, int2str.m, interp1.m, interp1q.m, interp2.m, interp3.m, interpft.m, interpn.m, isa.m, isdir.m, isequal.m, isequalwithequalnans.m, issquare.m, logspace.m, nargchk.m, narginchk.m, nargoutchk.m, nextpow2.m, nthargout.m, num2str.m, pol2cart.m, polyarea.m, postpad.m, prepad.m, profile.m, profshow.m, quadgk.m, quadv.m, randi.m, rat.m, repmat.m, rot90.m, rotdim.m, shift.m, shiftdim.m, sph2cart.m, structfun.m, trapz.m, triplequad.m, convhull.m, dsearch.m, dsearchn.m, griddata3.m, griddatan.m, rectint.m, tsearchn.m, __makeinfo__.m, doc.m, get_first_help_sentence.m, help.m, type.m, unimplemented.m, which.m, imread.m, imwrite.m, dlmwrite.m, fileread.m, is_valid_file_id.m, strread.m, textread.m, textscan.m, commutation_matrix.m, cond.m, condest.m, cross.m, duplication_matrix.m, expm.m, housh.m, isdefinite.m, ishermitian.m, issymmetric.m, logm.m, normest.m, null.m, onenormest.m, orth.m, planerot.m, qzhess.m, rank.m, rref.m, trace.m, vech.m, ans.m, bincoeff.m, bug_report.m, bzip2.m, comma.m, compare_versions.m, computer.m, edit.m, fileparts.m, fullfile.m, getfield.m, gzip.m, info.m, inputname.m, isappdata.m, isdeployed.m, ismac.m, ispc.m, isunix.m, list_primes.m, ls.m, mexext.m, namelengthmax.m, news.m, orderfields.m, paren.m, recycle.m, rmappdata.m, semicolon.m, setappdata.m, setfield.m, substruct.m, symvar.m, ver.m, version.m, warning_ids.m, xor.m, fminbnd.m, fsolve.m, fzero.m, lsqnonneg.m, optimset.m, pqpnonneg.m, sqp.m, matlabroot.m, __gnuplot_drawnow__.m, __plt_get_axis_arg__.m, ancestor.m, cla.m, clf.m, close.m, colorbar.m, colstyle.m, comet3.m, contourc.m, figure.m, gca.m, gcbf.m, gcbo.m, gcf.m, ginput.m, graphics_toolkit.m, gtext.m, hggroup.m, hist.m, hold.m, isfigure.m, ishghandle.m, ishold.m, isocolors.m, isonormals.m, isosurface.m, isprop.m, legend.m, line.m, loglog.m, loglogerr.m, meshgrid.m, ndgrid.m, newplot.m, orient.m, patch.m, plot3.m, plotyy.m, __print_parse_opts__.m, quiver3.m, refreshdata.m, ribbon.m, semilogx.m, semilogxerr.m, semilogy.m, stem.m, stem3.m, subplot.m, title.m, uigetfile.m, view.m, whitebg.m, compan.m, conv.m, deconv.m, mkpp.m, mpoles.m, pchip.m, poly.m, polyaffine.m, polyder.m, polyfit.m, polygcd.m, polyint.m, polyout.m, polyval.m, polyvalm.m, ppder.m, ppint.m, ppjumps.m, ppval.m, residue.m, roots.m, spline.m, intersect.m, ismember.m, powerset.m, setdiff.m, setxor.m, union.m, unique.m, autoreg_matrix.m, bartlett.m, blackman.m, detrend.m, fftconv.m, fftfilt.m, fftshift.m, freqz.m, hamming.m, hanning.m, ifftshift.m, sinc.m, sinetone.m, sinewave.m, unwrap.m, bicg.m, bicgstab.m, gmres.m, gplot.m, nonzeros.m, pcg.m, pcr.m, spaugment.m, spconvert.m, spdiags.m, speye.m, spfun.m, spones.m, sprand.m, sprandsym.m, spstats.m, spy.m, svds.m, treelayout.m, bessel.m, beta.m, betaln.m, factor.m, factorial.m, isprime.m, lcm.m, legendre.m, nchoosek.m, nthroot.m, perms.m, pow2.m, primes.m, reallog.m, realpow.m, realsqrt.m, hadamard.m, hankel.m, hilb.m, invhilb.m, magic.m, rosser.m, vander.m, __finish__.m, center.m, cloglog.m, corr.m, cov.m, gls.m, histc.m, iqr.m, kendall.m, kurtosis.m, logit.m, mahalanobis.m, mean.m, meansq.m, median.m, mode.m, moment.m, ols.m, ppplot.m, prctile.m, probit.m, quantile.m, range.m, ranks.m, run_count.m, runlength.m, skewness.m, spearman.m, statistics.m, std.m, table.m, var.m, zscore.m, betacdf.m, betainv.m, betapdf.m, betarnd.m, binocdf.m, binoinv.m, binopdf.m, binornd.m, cauchy_cdf.m, cauchy_inv.m, cauchy_pdf.m, cauchy_rnd.m, chi2cdf.m, chi2inv.m, chi2pdf.m, chi2rnd.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, expcdf.m, expinv.m, exppdf.m, exprnd.m, fcdf.m, finv.m, fpdf.m, frnd.m, gamcdf.m, gaminv.m, gampdf.m, gamrnd.m, geocdf.m, geoinv.m, geopdf.m, geornd.m, hygecdf.m, hygeinv.m, hygepdf.m, hygernd.m, kolmogorov_smirnov_cdf.m, laplace_cdf.m, laplace_inv.m, laplace_pdf.m, laplace_rnd.m, logistic_cdf.m, logistic_inv.m, logistic_pdf.m, logistic_rnd.m, logncdf.m, logninv.m, lognpdf.m, lognrnd.m, nbincdf.m, nbininv.m, nbinpdf.m, nbinrnd.m, normcdf.m, norminv.m, normpdf.m, normrnd.m, poisscdf.m, poissinv.m, poisspdf.m, poissrnd.m, stdnormal_cdf.m, stdnormal_inv.m, stdnormal_pdf.m, stdnormal_rnd.m, tcdf.m, tinv.m, tpdf.m, trnd.m, unidcdf.m, unidinv.m, unidpdf.m, unidrnd.m, unifcdf.m, unifinv.m, unifpdf.m, unifrnd.m, wblcdf.m, wblinv.m, wblpdf.m, wblrnd.m, kolmogorov_smirnov_test.m, kruskal_wallis_test.m, base2dec.m, bin2dec.m, blanks.m, cstrcat.m, deblank.m, dec2base.m, dec2bin.m, dec2hex.m, findstr.m, hex2dec.m, index.m, isletter.m, mat2str.m, rindex.m, str2num.m, strcat.m, strjust.m, strmatch.m, strsplit.m, strtok.m, strtrim.m, strtrunc.m, substr.m, validatestring.m, demo.m, example.m, fail.m, speed.m, addtodate.m, asctime.m, clock.m, ctime.m, date.m, datenum.m, datetick.m, datevec.m, eomday.m, etime.m, is_leap_year.m, now.m: Use Octave coding conventions in all m-file %!test blocks

## Copyright (C) 2009-2012 Kai Habel
##
## 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
## <http://www.gnu.org/licenses/>.

## -*- texinfo -*-
## @deftypefn  {Function File} {[@var{cx}, @var{cy}, @var{cz}, @var{v}] =} curl (@var{x}, @var{y}, @var{z}, @var{fx}, @var{fy}, @var{fz})
## @deftypefnx {Function File} {[@var{cz}, @var{v}] =} curl (@var{x}, @var{y}, @var{fx}, @var{fy})
## @deftypefnx {Function File} {[@dots{}] =} curl (@var{fx}, @var{fy}, @var{fz})
## @deftypefnx {Function File} {[@dots{}] =} curl (@var{fx}, @var{fy})
## @deftypefnx {Function File} {@var{v} =} curl (@dots{})
## Calculate curl of vector field given by the arrays @var{fx}, @var{fy}, and
## @var{fz} or @var{fx}, @var{fy} respectively.
## @tex
## $$ curl F(x,y,z) = \left( {\partial{d} \over \partial{y}} F_z - {\partial{d} \over \partial{z}} F_y, {\partial{d} \over \partial{z}} F_x - {\partial{d} \over \partial{x}} F_z, {\partial{d} \over \partial{x}} F_y - {\partial{d} \over \partial{y}} F_x \right)$$
## @end tex
## @ifnottex
##
## @example
## @group
##                   / d         d       d         d       d         d     \
## curl F(x,y,z)  =  | -- Fz  -  -- Fy,  -- Fx  -  -- Fz,  -- Fy  -  -- Fx |
##                   \ dy        dz      dz        dx      dx        dy    /
## @end group
## @end example
##
## @end ifnottex
## The coordinates of the vector field can be given by the arguments @var{x},
## @var{y}, @var{z} or @var{x}, @var{y} respectively.  @var{v} calculates the
## scalar component of the angular velocity vector in direction of the z-axis
## for two-dimensional input.  For three-dimensional input the scalar
## rotation is calculated at each grid point in direction of the vector field
## at that point.
## @seealso{divergence, gradient, del2, cross}
## @end deftypefn

## Author: Kai Habel <kai.habel@gmx.de>

function varargout = curl (varargin)

  fidx = 1;
  if (nargin == 2)
    sz = size (varargin{fidx});
    dx = (1:sz(2))(:);
    dy = (1:sz(1))(:);
  elseif (nargin == 3)
    sz = size (varargin{fidx});
    dx = (1:sz(2))(:);
    dy = (1:sz(1))(:);
    dz = (1:sz(3))(:);
  elseif (nargin == 4)
    fidx = 3;
    dx = varargin{1}(1,:);
    dy = varargin{2}(:,1);
  elseif (nargin == 6)
    fidx = 4;
    dx = varargin{1}(1,:,1)(:);
    dy = varargin{2}(:,1,1)(:);
    dz = varargin{3}(1,1,:)(:);
  else
    print_usage();
  endif

  if ((nargin == 4) || (nargin == 2))
    if (!size_equal (varargin{fidx}, varargin{fidx + 1}))
      error ("curl: size of X and Y must match");
    elseif (ndims (varargin{fidx}) != 2)
      error ("curl: expected two-dimensional matrices X and Y");
    elseif ((length (dx) != columns (varargin{fidx}))
         || (length (dy) != rows (varargin{fidx})))
      error ("curl: size of dx and dy must match the respective dimension of X and Y");
    endif

    dFx_dy = gradient (varargin{fidx}.', dy, dx).';
    dFy_dx = gradient (varargin{fidx + 1}, dx, dy);
    rot_z = dFy_dx - dFx_dy;
    av = rot_z / 2;
    if (nargout == 0 || nargout == 1)
      varargout{1} = av;
    else
      varargout{1} = rot_z;
      varargout{2} = av;
    endif

  elseif ((nargin == 6) || (nargin == 3))
    if (!size_equal (varargin{fidx}, varargin{fidx + 1}, varargin{fidx + 2}))
      error ("curl: size of X, Y, and Z must match");
    elseif (ndims (varargin{fidx}) != 3)
      error ("curl: expected two-dimensional matrices X, Y, and Z");
    elseif ((length (dx) != size (varargin{fidx}, 2))
         || (length (dy) != size (varargin{fidx}, 1))
         || (length (dz) != size (varargin{fidx}, 3)))
      error ("curl: size of dx, dy, and dz must match the respective dimesion of X, Y, and Z");
    endif

    [~, dFx_dy, dFx_dz] = gradient (varargin{fidx}, dx, dy, dz);
    [dFy_dx, ~, dFy_dz] = gradient (varargin{fidx + 1}, dx, dy, dz);
    [dFz_dx, dFz_dy] = gradient (varargin{fidx + 2}, dx, dy, dz);
    rot_x = dFz_dy - dFy_dz;
    rot_y = dFx_dz - dFz_dx;
    rot_z = dFy_dx - dFx_dy;
    l = sqrt(varargin{fidx}.^2 + varargin{fidx + 1}.^2 + varargin{fidx + 2}.^2);
    av = (rot_x .* varargin{fidx} +
          rot_y .* varargin{fidx + 1} +
          rot_z .* varargin{fidx + 2}) ./ (2 * l);

    if (nargout == 0 || nargout == 1)
      varargout{1} = av;
    else
      varargout{1} = rot_x;
      varargout{2} = rot_y;
      varargout{3} = rot_z;
      varargout{4} = av;
    endif
  endif

endfunction


%!test
%! [X,Y] = meshgrid (-20:20,-22:22);
%! av = curl (2*(X-Y), Y);
%! assert (all (av(:) == 1));
%! [cz,av] = curl (2*(X-Y), Y);
%! assert (all (cz(:) == 2));
%! assert (all (av(:) == 1));
%! [cz,av] = curl (X/2, Y/2, 2*(X-Y), Y);
%! assert (all (cz(:) == 4));
%! assert (all (av(:) == 2));
%! assert (size_equal (X,Y,cz,av));