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% This file is part of NS2DDV.                                                      %
%                                                                                   %
% Copyright(C) 2011-2018    C. Calgaro  (caterina.calgaro@math.univ-lille1.fr)      %
%                           E. Creusé   (emmanuel.creuse@math.univ-lille1.fr)       %
%                           T. Goudon   (thierry.goudon@inria.fr)                   %
%                           A. Mouton   (alexandre.mouton@math.univ-lille1.fr)      %
%                                                                                   %
% NS2DDV 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.           %
%                                                                                   %
% NS2DDV 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      %
% NS2DDV. If not, see <http://www.gnu.org/licenses/>.                               %
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function[RENUMBERING] = renumbering_P1P1BP2(MESH, PARAMETERS)

	% INPUT
	% MESH					An incomplete mesh metadata
	% PARAMETERS 			List of simulation parameters
	%
	% OUTPUT
	% RENUMBERING			List of renumbering permutation matrices

	% Assembling P1 mass matrix with P1 dof and P1B (resp. P2) mass matrix with P1B dof (resp P2 dof)
	% WARNING : we must provide a P1 discretization of rho = 1 to the mass assembling routine
	rho_Id = ones(MESH.np1,1);
	M_p1 = assembling_mass(MESH, 'P1', rho_Id, 'P1', PARAMETERS);
	M_p1b = assembling_mass(MESH, 'P1B', rho_Id, 'P1', PARAMETERS);
	M_p2 = assembling_mass(MESH, 'P2', rho_Id, 'P1', PARAMETERS);

	% Permutation using M_p1, M_p1b and M_p2 matrices (resp. with P1, P1B and P2 dof)
	switch PARAMETERS.MESH.RENUMBERING
		case {'AMD'}
			RENUMBERING.perm_p1  = amd(M_p1);
			RENUMBERING.perm_p1b = amd(M_p1b);
			RENUMBERING.perm_p2  = amd(M_p2);
		case {'CMK'}
			RENUMBERING.perm_p1  = symrcm(M_p1);
			RENUMBERING.perm_p1b = symrcm(M_p1b);
			RENUMBERING.perm_p2  = symrcm(M_p2);    
		otherwise
		    error(sprintf('Unknown renumbering technique.\n'));
	end
end