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// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) 2013 - Scilab Enterprises - Paul BIGNIER : m parameter added
// Copyright (C) 2013 - Samuel GOUGEON : http://bugzilla.scilab.org/11209 fixed
// Copyright (C) 2000 - 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, m] = variancef(x, fre, orien, m)
//
//This function computes the variance of the values of a vector or
//matrix x, each of them counted with a frequency signaled by the
//corresponding values of the integer vector or matrix fre with the same
//type of x.
//
//For a vector or matrix x, s=variancef(x,fre) (or s=variancef(x,fre,'*') returns
//in scalar s the variance of all the entries of x, each value counted
//with the multiplicity indicated by the corresponding value of fre.
//
//s=variancef(x,fre,'r')(or, equivalently, s=variancef(x,fre,1)) returns in each
//entry of the row vector s of type 1xsize(x,'c') the variance of each
//column of x, each value counted with the multiplicity indicated by the
//corresponding value of fre.
//
//s=variancef(x,fre,'c')(or, equivalently, s=variancef(x,fre,2)) returns in each
//entry of the column vector s of type size(x,'c')x1 the variance of
//each row of x, each value counted with the multiplicity indicated by
//the corresponding value of fre.
//
//The input argument m represents the a priori mean. If it is present, then the sum is
//divided by n. Otherwise ("sample variance"), it is divided by n-1.
//
//
[lhs,rhs] = argn(0)
if rhs<2 | rhs>4 then
msg = gettext("%s: Wrong number of input arguments: %d to %d expected.\n")
error(msprintf(msg, "variancef", 2, 4))
end
if x==[] | fre==[] | fre==0
s = %nan
return
end
if rhs==2 then
sumfre = sum(fre)
if sumfre <= 1 then
msg = gettext("%s: Wrong value for input argument #%d: Must be > %d.\n")
error(msprintf(msg, "variancef", 2, 1)), end
m = meanf(x,fre)
s = sum((abs(x-m).^2).*fre) / (sumfre-1)
return
end
biased = %f
if rhs==4 then
if typeof(m)~="constant" then
tmp = gettext("%s: Wrong value of m : a priori mean expected.\n")
error(msprintf(tmp, "variancef", ))
elseif orien=="*" then
if ~isscalar(m) then
tmp = gettext("%s: Wrong value of m : a priori mean expected.\n")
error(msprintf(tmp, "variancef", ))
end
elseif orien=="r" | orien==1 then
if size(m)~=[1 size(x,"c")] & ~isscalar(m) then
tmp = gettext("%s: Wrong value of m : a priori mean expected.\n")
error(msprintf(tmp, "variancef", ))
end
elseif orien=="c" | orien==2 then
if size(m)~=[size(x,"r") 1] & ~isscalar(m) then
tmp = gettext("%s: Wrong value of m : a priori mean expected.\n")
error(msprintf(tmp, "variancef", ))
end
end
if isnan(m) then
biased = %t; // Compute the biased variance
end
end
if orien=="*",
sumfre = sum(fre)
if sumfre <= 1 then
msg = _("%s: Wrong value for input argument #%d: Must be > %d.\n")
error(msprintf(msg, "variancef", 2, 1)),end
if rhs<4 then
m = meanf(x,fre)
s = sum((abs(x-m).^2).*fre) / (sumfre-1)
elseif biased == %t
m = meanf(x,fre)
s = sum((abs(x-m).^2).*fre) / sumfre
else
s = sum((abs(x-m).^2).*fre) / sumfre
end
elseif orien=="r" | orien==1,
sumfre = sum(fre, "r")
if or(sumfre==0) then
msg = _("%s: Wrong value for input argument #%d: Must be > %d.\n")
error(msprintf(msg, "variancef", 2, 1))
end
if rhs<4 | biased == %t then
m = meanf(x,fre,"r")
elseif isscalar(m) then
m = m*ones(1, size(x,"c"));
end
m2 = ones(size(x,"r"),1)*m
if rhs<4 then
s = sum((abs(x-m2).^2).*fre, "r") ./ (sumfre-1)
else
s = sum((abs(x-m2).^2).*fre, "r") ./ sumfre
end
elseif orien=="c" | orien==2,
sumfre = sum(fre, "c")
if or(sumfre==0) then
msg = _("%s: Wrong value for input argument #%d: Must be > %d.\n")
error(msprintf(msg, "variancef", 2, 1))
end
if rhs<4 | biased == %t then
m = meanf(x,fre,"c")
elseif isscalar(m) then
m = m*ones(size(x,"r"), 1);
end
m2 = m*ones(1,size(x,"c"))
if rhs<4 then
s = sum((abs(x-m2).^2).*fre, "c") ./ (sumfre-1)
else
s = sum((abs(x-m2).^2).*fre, "c") ./ sumfre
end
else
msg = _("%s: Wrong value for input argument #%d: ''%s'', ''%s'', ''%s'', %d or %d expected.\n")
error(msprintf(msg, "variancef", 3, "*", "c", "r", 1, 2))
end
endfunction
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