function som=integ2d(mat,x,y);%INTEG2D Approximate 2-D integral.%	SOM=INTEG2D(MAT,X,Y) approximates the 2-D integral of  %	matrix MAT according to abscissa X and ordinate Y.%%	MAT : MxN matrix to be integrated%	X   : N-row-vector indicating the abscissa integration path 	%				(default : 1:N)%	Y   : M-column-vector indicating the ordinate integration path %				(default : 1:M)	%	SOM : result of integration%%	Example :      %	 S = altes(256,0.1,0.45,10000) ;%	 [TFR,T,F] = tfrscalo(S,21:190,8,'auto') ;%	 E = integ2d(TFR,T,F)%%	See also INTEG.%	P. Goncalves, October 95%	Copyright (c) 1995 Rice University%%  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 2 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, write to the Free Software%  Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA[M,N]=size(mat);if nargin<1, error('At least one parameter required');elseif nargin==1, x=1:N; y=(1:M)';elseif nargin==2, y=(1:M)';end[xr,xc]=size(x);[yr,yc]=size(y);if (xr>xc & xr~=1), error('X must be a row-vector');elseif (yc>yr & yc~=1), error('Y must be a column-vector');elseif (N~=xc), error('MAT must have as many columns as X');elseif (M~=yr), error('MAT must have as many rows as Y');endmat = (sum(mat.').'-mat(:,1)/2-mat(:,N)/2).*(x(2)-x(1)) ;dmat = mat(1:M-1)+mat(2:M) ;dy = (y(2:M)-y(1:M-1))/2 ;som = sum(dmat.*dy) ;