The module "cumvar" of the Mastrave modelling library
Copyright © 2006,2007,2008,2009,2010,2011 Daniele de Rigo
The file cumvar.m is part of Mastrave.
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answer = cumvar( values , dim =  , mode = 0 )
Utility to extend the function var(.) providing cumulative variances of the elements of the array values along a given dimension dim .
To mitigate unwanted numeric cancellations, all cumulative variances are first approximated by centering values elements with their corresponding non-cumulative means and then refined by correcting the centering with the correct cumulative means. This way, if N is the total number of elements of values and n is the size of the dimension dim of values , then the computation remains O( n * N ).
values ::numeric:: Vector, matrix or multi-dimensional array of numbers. dim ::scalar_index|empty:: Scalar positive integer representing the dimension along which the cumulative variances have to be computed. If dim is an empty array  , the dimension is the first non-singleton dimension. In case values is a vector, this definition means that the default dimension is the one along which the elements of the vector values are aligned. If omitted, the default value is . mode ::numstring:: Boolean or string declaring the kind of variance to be computed. If omitted, its default value is: 0. Valid modes are: mode │ meaning ─────────────────┼─────────────────────────────────── 0 │ Compute the unbiased sample '--sample' │ variance by normalizing the i-th │ variance with (i-1) . Variances │ of the first elements of values │ along dim are therefore NaN. ─────────────────┼─────────────────────────────────── 1 │ Compute the population variance '--population' │ (or biased sample variance) by │ normalizing the i-th variance │ with i . Variances of the first │ elements of values along dim │ are therefore zeros.
% Correctness check function check = @(computed,expected)assert( ... abs( (computed - expected)./expected ) < 10*eps ... ) % Basic usage % Vectors: v = ceil( rand(1,7)* 100 ) cv = cumvar( v ) check( cv(end), var(v) ); % Matrices: v = ceil( rand(5,7)* 100 ) cv = cumvar( v ) check( cv(end,:), var(v) ); % Passing a custom dimension cv = cumvar( v , 2 ) check( cv(:,end), var(v,0,2) ); % Dealing with multi-dimensional arrays v = ceil( rand(5,7,3)* 100 ) cv = cumvar( v ) cv = cumvar( v ,  ) check( cv(end,:,:), var(v) ); cv = cumvar( v , 3 ) check( cv(:,:,end), var(v,0,3) ); % Passing the kind of variance to be computed % Unbiased sample variance cv = cumvar( v , , '--sample' ) cv = cumvar( v , , 0 ) check( cv(end,:,:), var(v) ); % Population variance (biased sample variance) cv = cumvar( v , , '--population' ) cv = cumvar( v , , 1 ) check( cv(end,:,:), var(v,1,1) ); cv = cumvar( v , 2 , 1 ) check( cv(:,end,:), var(v,1,2) ); cv = cumvar( v , 3 , 1 ) check( cv(:,:,end), var(v,1,3) ); % Complex-valued elements of values v = ceil( rand(5,7)* 100 ) +1i * ceil( rand(5,7)* 100 ) cv = cumvar( v ) check( cv(end,:), var(v) ); cv = cumvar( v , 2 ) check( cv(:,end), var(v,0,2) );
Memory requirements: O( numel( values ) ) See also: cummean, cumstd, cumsumsq, groupfun Keywords: cumulative operators, scan Version: 0.3.3
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