The module "cumstd" of the Mastrave modelling library
Copyright © 2006,2007,2008,2009,2010,2011 Daniele de Rigo
The file cumstd.m is part of Mastrave.
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answer = cumstd( values , dim =  , mode = 0 )
Utility to extend the function std(.) providing cumulative standard deviations of the elements of the array values along a given dimension dim .
To mitigate unwanted numeric cancellations, all cumulative standard deviations 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 standard deviations 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 standard deviation to be computed. If omitted, its default value is: 0. Valid modes are: mode │ meaning ─────────────────┼──────────────────────────────────── 0 │ Compute the unbiased sample '--sample' │ standard deviation by normalizing │ the i-th standard deviation with │ (i-1) . Standard deviations of │ the first elements of values │ along dim are therefore NaN. ─────────────────┼──────────────────────────────────── 1 │ Compute the population standard '--population' │ deviation (or biased sample │ standard deviation) by normalizing │ the i-th standard deviation │ with i . Standard deviations 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 ) cs = cumstd( v ) check( cs(end), std(v) ); % Matrices: v = ceil( rand(5,7)* 100 ) cs = cumstd( v ) check( cs(end,:), std(v) ); % Passing a custom dimension cs = cumstd( v , 2 ) check( cs(:,end), std(v,0,2) ); % Dealing with multi-dimensional arrays v = ceil( rand(5,7,3)* 100 ) cs = cumstd( v ) cs = cumstd( v ,  ) check( cs(end,:,:), std(v) ); cs = cumstd( v , 3 ) check( cs(:,:,end), std(v,0,3) ); % Passing the kind of standard deviation to be computed % Unbiased sample standard deviation cs = cumstd( v , , '--sample' ) cs = cumstd( v , , 0 ) check( cs(end,:,:), std(v) ); % Population standard deviation (biased sample standard deviation) cs = cumstd( v , , '--population' ) cs = cumstd( v , , 1 ) check( cs(end,:,:), std(v,1,1) ); cs = cumstd( v , 2 , 1 ) check( cs(:,end,:), std(v,1,2) ); cs = cumstd( v , 3 , 1 ) check( cs(:,:,end), std(v,1,3) ); % Complex-valued elements of values v = ceil( rand(5,7)* 100 ) +1i * ceil( rand(5,7)* 100 ) cs = cumstd( v ) check( cs(end,:), std(v) ); cs = cumstd( v , 2 ) check( cs(:,end), std(v,0,2) );
Memory requirements: O( numel( values ) ) See also: cummean, cumvar, cumsumsq, groupfun Keywords: cumulative operators, scan Version: 0.3.3
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