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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{psi} =}  geocentricLatitude (@var{phi}, @var{flattening}) 
+## @deftypefnx {Function File} {@var{psi} =}  geocentricLatitude (@var{phi}, @var{flattening}, @var{angleUnit}) 
+## Return geocentric latitude (psi) given geodetic latitude (phi) and flattening.
+##
+## The default input and output is in degrees; use optional third parameter
+## @var{angleUnit} for radians.  @var{phi} 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
+## psi = geocentricLatitude (45, 0.0033528)
+## => psi =
+##  44.8076
+## @end example
+##
+## Also can use radians:
+## @example
+## psi = geocentricLatitude (pi/4, 0.0033528, "radians")
+## => psi =
+##  0.78204
+## @end example
+##
+## Vector Input:
+## @example
+## phi = 35:5:45;
+## psi = geocentricLatitude (phi, 0.0033528)
+## => psi =
+##  34.819      39.811      44.808
+## @end example
+##
+## @seealso{parametricLatitude, geodeticLatitudeFromGeocentric, geodeticLatitudeFromParametric} 
+## @end deftypefn
+
+## Function supplied by anonymous contributor, see:
+## https://savannah.gnu.org/patch/index.php?9640
+
+function psi = geocentricLatitude (phi, flattening, angleUnit="degrees")
+
+  if (nargin < 2 || isempty (angleUnit))
+    print_usage ();
+  endif
+  
+  if (! isnumeric (phi) || ! isreal (phi) || ...
+      ! isnumeric (flattening) || ! isreal (flattening))
+    error ("geocentricLatitude: numeric input expected for args #1 and #2");
+  elseif (! isscalar (flattening))
+    error ("geocentricLatitude: scalar value expected for flattening");
+  elseif (flattening < 0 || flattening >= 1)
+    error ("geocentricLatitude: flattening must lie in the real interval [0..1)" )
+  elseif (! ischar (angleUnit) || ! ismember (lower (angleUnit(1)), {"d", "r"}))
+    error ("geocentricLatitude: angleUnit should be one of 'degrees' or 'radians'");
+  endif
+
+  ## Make sure phi and (later on) flattening are element-wise conformant
+  if (strncmpi (angleUnit, "r", 1) == 1)
+    ## Insight From: Fundamentals of Astrodynamics and Applications,
+    ## (David Vallado 3rd edition pg 148)
+    psi = atan ((1 - flattening)^2 * tan (phi));
+  else
+    psi = atand ((1 - flattening)^2 * tand (phi));
+  end
+  
+endfunction
+
+
+%!test
+%! earth_flattening = 0.0033528;
+%! assert (geocentricLatitude (45, earth_flattening), 44.8075766, 10e-6);
+%! assert (geocentricLatitude (pi/4, earth_flattening, 'radians'), 0.78204, 10e-6);
+
+%!error <numeric input expected> geocentricLatitude (0.5, "flat")
+%!error <numeric input expected> geocentricLatitude (0.5, 5i)
+%!error <numeric input expected> geocentricLatitude ("phi", 0.0033528)
+%!error <numeric input expected> geocentricLatitude (5i, 0.0033528 )
+%!error <scalar value expected> geocentricLatitude ([45 50], [0.7 0.8])
+%!error <flattening must lie> geocentricLatitude (45, 1)
+%!error <angleUnit> geocentricLatitude (45, 0.0033528, "km")