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+## Copyright (C) 2018-2020 Philip Nienhuis
+## 
+## This program 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.
+## 
+## This program 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
+## this program; if not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{phi} =} geodeticLatitudeFromParametric (@var{beta}, @var{flattening}) 
+## @deftypefnx {Function File} {@var{phi} =} geodeticLatitudeFromParametric (@var{beta}, @var{flattening}, @var{angleUnit}) 
+## Returns geodetic latitude (phi) given parametric latitude and flattening.
+##
+## Parametric latitude (@var{beta}) is also known as a reduced latitude.
+## The default input and output is in degrees; use optional third parameter
+## @var{angleUnit} for radians.  @var{beta} can be a scalar, vector, matrix
+## or any ND array.  @var{flattening} must be a scalar value in the interval
+## [0..1).
+##
+## Examples:
+## Scalar input:
+## @example
+## phi = geodeticLatitudeFromParametric (45, 0.0033528)
+## => phi =
+##  45.096
+## @end example
+##
+## Also can use radians:
+## @example
+## phi = geodeticLatitudeFromParametric (pi/4, 0.0033528, "radians")
+## => phi =
+##  0.78708
+## @end example
+##
+## Vector Input:
+## @example
+## beta = 35:5:45;
+## phi = geodeticLatitudeFromParametric (beta, 0.0033528)
+## => phi =
+##  35.09      40.095      45.096
+## @end example
+##
+## @seealso{geocentricLatitude, geodeticLatitudeFromGeocentric, parametricLatitude} 
+## @end deftypefn
+
+## Function supplied by anonymous contributor, see:
+## https://savannah.gnu.org/patch/index.php?9640
+
+function phi = geodeticLatitudeFromParametric (beta, flattening, angleUnit="degrees")
+  
+  if (nargin < 2)
+    print_usage ();
+  endif
+
+  if (! isnumeric (beta) || ! isreal (beta) || ...
+      ! isnumeric (flattening) || ! isreal (flattening))
+    error ("geodeticLatitudeFromParametric : numeric input expected");
+  elseif (! isscalar (flattening))
+    error ("geodeticLatitudeFromParametric: scalar value expected for flattening");
+  elseif (flattening < 0 || flattening >= 1)
+    error ("geodeticLatitudeFromParametric: flattening must lie in the real interval [0..1)" );
+  elseif (! ischar (angleUnit) ||! ismember (lower (angleUnit(1)), {"d", "r"}))
+    error ("geodeticLatitudeFromParametric: angleUnit should be one of 'degrees' or 'radians'");
+  endif
+
+  if (strncmpi (angleUnit, "r", 1) == 1)
+    phi = atan2 (tan (beta), (1 - flattening)) ;
+  else 
+    phi = atan2d (tand (beta), (1 - flattening)) ;
+  endif
+  
+endfunction
+
+%!test
+%! earth_flattening  =  0.0033528 ;
+%! assert ( geodeticLatitudeFromParametric (45, earth_flattening), 45.0962122, 10e-6);
+%! assert ( geodeticLatitudeFromParametric (pi/4, earth_flattening, 'radians'), 0.78708, 10e-6);
+
+%!error <numeric input expected> geodeticLatitudeFromParametric (0.5, "flat")
+%!error <numeric input expected> geodeticLatitudeFromParametric (0.5, 5i)
+%!error <numeric input expected> geodeticLatitudeFromParametric ("beta", 0.0033528)
+%!error <numeric input expected> geodeticLatitudeFromParametric (5i, 0.0033528 )
+%!error <scalar value expected> geodeticLatitudeFromParametric ([45 50], [0.7 0.8])
+%!error <flattening must lie> geodeticLatitudeFromParametric (45, 1)
+%!error <angleUnit> geodeticLatitudeFromParametric (45, 0.0033528, "km")