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Diffstat (limited to 'modules/statistics/macros/variancef.sci')
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1 files changed, 136 insertions, 0 deletions
diff --git a/modules/statistics/macros/variancef.sci b/modules/statistics/macros/variancef.sci new file mode 100755 index 000000000..e593de8ea --- /dev/null +++ b/modules/statistics/macros/variancef.sci @@ -0,0 +1,136 @@ + +// 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 |