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// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) 1999 - INRIA - Carlos Klimann
//
// This file must be used under the terms of the CeCILL.
// This source file is licensed as described in the file COPYING, which
// you should have received as part of this distribution. The terms
// are also available at
// http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt
//
function [s]=covar(x,y,fre)
//
//This function computes the covariance of two variables x
//and y where x is a numerical vector of length n, y is a
//numerical vector of length m and fre is an array of
//dimensions nxm. In fre the element of indices (i,j)
//corresponds to the number or frequencies of x_i&y_j.
//
//References: Wonacott, T.H. & Wonacott, R.J.; Introductory Statistics,
//J.Wiley & Sons, 1990.
//
//
//small correction (bug number 1072) date : 8 nov 2004
//
[lhs,rhs]=argn(0)
if rhs <> 3 then error(msprintf(gettext("%s: Wrong number of input arguments: %d expected.\n"),"covar",3)), end
if x==[] | y==[] then s=%nan; return, end
[lfre cfre]=size(fre);
[lx cx]=size(x)
[ly cy]=size(y)
if lx<>1 & cx<>1 then error(msprintf(gettext("%s: Wrong type for input argument #%d: Vector expected.\n"),"covar",1)), end
if ly<>1 & cy<>1 then error(msprintf(gettext("%s: Wrong type for input argument #%d: Vector expected.\n"),"covar",2)), end
fre(isnan(fre))=0
lx=lx*cx;
cy=ly*cy;
if lx<>lfre then error(msprintf(gettext("%s: Wrong value for input argument #%d: Same number of line as first input argument expected.\n"),"covar",3)), end
if cy<>cfre then error(msprintf(gettext("%s: Wrong value for input argument #%d: Same number of column as first input argument expected.\n"),"covar",3)), end
x=matrix(x,lx,1);
y=matrix(y,1,cy);
fr=fre/sum(fre)
s=sum(((x-sum(x.*sum(fr,"c")))*ones(1,cy)) ..
.* (fr) .* (ones(lx,1)*(y-sum(y.* sum(fr,"r")))))
endfunction
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