## Copyright (C) 2018 Anonymous
##
## 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; see the file COPYING.  If not, see
## <http://www.gnu.org/licenses/>.

## -*- texinfo -*-
## @deftypefn {Function File} {@var{ecc} =} n2ecc (@var{n})
## This returns the eccentricity given the third flattening (n)
##
## Examples:
##
## Scalar input:
## @example
## n_earth = 0.0016792;
## ecc_earth = n2ecc ( n_earth )
## => ecc_earth = 0.081819
## @end example 
##
## Vector input:
## @example
## n_vec = [ 0.0016792 0.033525 ];
## ecc = n2ecc ( n_vec )
## => ecc =
##	 0.081819     0.35432
## @end example
##
## @seealso{n2ecc}
function ecc = n2ecc ( n )
  if nargin < 1
    print_usage ( );
  end
  if ( ischar ( n ) )
    error ('n2ecc.m: numeric input expected');
  elseif ( n > 1 )
    error ('n2ecc.m: n should be <= 1' )
  else
    ecc = sqrt ( 4*n ./ ( 1 + n ) .^2 );
  end
%! test
%!
%! n_earth = 0.00167922;
%! n_jupiter = 0.0335246;
%! n_vec = [ n_earth n_jupiter ];
%! assert ( n2ecc ( n_earth ) , .081819221456 , 10e-12 ); 
%! assert ( n2ecc ( n_vec ),[0.08181922 0.3543164],10e-8)
%! error <numeric input expected> n2ecc ("n")
endfunction
