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// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) 2013 - Scilab Enteprises - Paul Bignier: added mean squared deviation
// (third input argument)
// 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 sd = stdev(x, o, m)
//
//This function computes the standard deviation of the values of a
//vector or matrix x.
//
//For a vector or a matrix x, s=stdev(x) returns in the scalar s the
//standard deviation of all the entries of x.
//
//s=stdev(x,'r') (or, equivalently, s=stdev(x,1)) is the rowwise
//standard deviation. It returns in each entry of the row vector s the
//standard deviation of each column of x.
//
//s=stdev(x,'c') (or, equivalently, s=stdev(x,2)) is the columnwise
//standard deviation. It returns in each entry of the column vector y
//the standard deviation of each row of x.
//
//The input argument m represents the a priori mean. If it is present, then the sum is
//divided by size(x,"*"). Otherwise ("sample standard deviation"), it is divided by size(x,"*")-1.
//
[lhs, rhs] = argn(0);
if rhs < 1 then
error(msprintf(_("%s: Wrong number of input arguments: %d to %d expected.\n"),"stdev",1,3));
end
if rhs < 2 then
o = "*"
on = 0
else
select o
case "*" then
on = 0
case "r" then
on = 1
case "c" then
on = 2
else
if type(o) <> 1 | size(o, "*") <> 1 | o < 0 | floor(o) <> o then
error(msprintf(_("%s: Wrong value for input argument #%d: ''%s'', ''%s'', ''%s'' or a positive integer expected.\n"),"stdev",2,"*","r","c")),
else
on = o
end
end
end
if typeof(x) == "hypermat" then
if rhs == 3 then
sd = %hm_stdev(x, o, m);
else
sd = %hm_stdev(x, o);
end
return
end
if type(x) ~= 1 | ~isreal(x) then
tmp = _("%s: Wrong type for input argument #%d: A real matrix expected.\n")
error(msprintf(tmp, "stdev", 1))
end
siz = size(x);
if rhs == 3 then
if and(typeof(m) ~= ["constant" "hypermat"]) | ~isreal(m) then
tmp = _("%s: Wrong type for input argument #%d: A real matrix expected.\n")
error(msprintf(tmp, "stdev", 3))
elseif on == 0 then
if ~isscalar(m) then
tmp = _("%s: Wrong size for input argument #%d.\n")
error(msprintf(tmp, "stdev", 3))
end
elseif on == 1 then
if or(size(m) ~= [1 siz(2:$)]) then
if isscalar(m) then
m = resize_matrix(m, [1 siz(2:$)], m);
else
tmp = _("%s: Wrong size for input argument #%d.\n")
error(msprintf(tmp, "stdev", 3))
end
end
elseif on == 2 then
if or(size(m) ~= [siz(1) 1 siz(3:$)]) then
if isscalar(m) then
m = resize_matrix(m, [siz(1) 1 siz(3:$)], m);
else
tmp = _("%s: Wrong size for input argument #%d.\n")
error(msprintf(tmp, "stdev", 3))
end
end
end
end
if x == [] then
sd = %nan;
return
end
if rhs == 3 & isnan(m) then
// This will compute the "biased variance": the denominator will be size(x,orien)
// but the a priori mean is not considered as provided.
rhs = 2
end
// Remove the mean
if on == 0 then
if rhs == 3
y = x - m;
else
y = x - mean(x);
end
elseif on == 2 then
if rhs == 3
y = x - m*ones(x(1,:));
else
y = x - mean(x,on)*ones(x(1,:));
end
elseif on == 1 then
if rhs == 3
y = x - ones(x(:,1))*m;
else
y = x - ones(x(:,1))*mean(x,1);
end
else // on > ndims(x) then
sd = 0*x;
return
end
mn = size(x, o);
if mn == 1 then
sd = 0*y;
else
if rhs <= 2 & exists("m", "local") == 0 then // If m is provided but rhs=2, that means we want the biased deviation
sd = sqrt(sum(y.^2,o)/(mn-1));
else
sd = sqrt(sum(y.^2,o)/mn);
end
end
endfunction
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