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// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) 2000 - INRIA - Carlos Klimann
// Copyright (C) 2013 - Samuel GOUGEON
//
// 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] = variance(x, orien, m)
//
//This function computes the variance of the values of a vector or
//matrix x.
//
//For a vector or a matrix x, s=variance(x) returns in the scalar s the
//variance of all the entries of x.
//
//s=variance(x,'r') (or, equivalently, s=variance(x,1)) is the rowwise
//variance. It returns in each entry of the row vector s the variance of
//each column of x.
//
//s=variance(x,'c') (or, equivalently, s=variance(x,2)) is the columnwise standard
//deviation. It returns in each entry of the column vector y the
//variance of each row of x.
//
//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.
//
// Checking and normalizing input arguments:
// ----------------------------------------
[lhs,rhs] = argn(0)
if rhs==0 then
tmp = gettext("%s: Wrong number of input arguments: %d to %d expected.\n")
error(msprintf(tmp, "variance", 1, 2))
end
if x==[] then
s = %nan
return
end
if ~isdef("orien","local") then
orien = "*"
end
if rhs==3 then
if typeof(m)~="constant" then
tmp = gettext("%s: Wrong value of m : a priori mean expected.\n")
error(msprintf(tmp, "variance"))
elseif orien=="*" then
if ~isscalar(m) then
tmp = gettext("%s: Wrong value of m : a priori mean expected.\n")
error(msprintf(tmp, "variance"))
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, "variance"))
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, "variance"))
end
end
end
transposed = %f // to refer and process as in "r", we priorly transpose any "c" request
if orien=="r" | orien==1 | orien=="c" | orien==2 | orien=="*"
if orien=="c" | orien==2 then
x = x.'
transposed = %t
orien = "r"
end
else
tmp = gettext("%s: Wrong value for input argument #%d: ''%s'', ''%s'', %d or %d expected.\n")
error(msprintf(tmp, "variance", 2, "c", "r", 1, 2))
end
// Calculations
// ------------
d = size(x, orien) - 1 + exists("m","local") // Denominator. If m is given, then the a priori mean is known and we divide by size(n,orien)
if rhs == 3 & isnan(m) then
// This will compute the "biased variance": the denominator is size(x,orien) but the a priori mean is not considered as provided.
rhs = 2
end
if orien=="*" then
if rhs < 3 then
m = mean(x)
end
else
if rhs < 3 then
m = mean(x, orien).*.ones(size(x,1),1)
else
if isscalar(m) then
if or(m==[0 1]) then
tmp = _("%s: The significance of input argument #%d has been modified. Please refer to the variance help page.\n")
warning(msprintf(tmp, "variance", 3))
end
// If m is a scalar, extend it to the size of x.
// If lhs==1, we do not need to perform this operation, because in the following 'x - m', m can be a scalar
m = m*ones(x)
else
if transposed then
m = m.';
end
m = m.*.ones(size(x,1),1)
end
end
end
s = sum(abs(x - m).^2, orien) / d
m = m(1, :);
if transposed then
s = s.'
m = m.'
end
endfunction
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