The module "cummean" of the Mastrave modelling library

Copyright and license notice of the function cummean

Copyright © 2005,2006,2007,2008,2009,2010,2011 Daniele de Rigo

The file cummean.m is part of Mastrave.

Mastrave is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

Mastrave is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with Mastrave. If not, see http://www.gnu.org/licenses/.

Function declaration

answer = cummean( values       ,
                  dim    = []  ,
                  mode   = 'a' )

Description

Utility to extend the function mean(.) providing cumulative means of the elements of the array values along a given dimension dim .

Input arguments

 values            ::numeric::
                   Vector, matrix or multi-dimensional array of numbers.

 dim               ::scalar_index|empty::
                   Scalar positive integer representing the dimension along
                   which the cumulative means 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              ::string::
                   String declaring the kind of mean to be computed.
                   If omitted, its default value is: 'a'.
                   Valid modes are:

                        mode        │      meaning
                   ─────────────────┼──────────────────────────────────
                     'a'            │ Compute the ordinary arithmetic
                     '--arithmetic' │ mean.
                   ─────────────────┼──────────────────────────────────
                     'g'            │ Compute the geometric mean.
                     '--geometric'  │
                   ─────────────────┼──────────────────────────────────
                     'h'            │ Compute the harmonic mean.
                     '--harmonic'   │

Example of usage

   % Basic usage

   % Vectors:
   m  = ceil( rand(1,7)* 100 )
   cm = cummean( m )
   assert( cm(end) == mean(m) )

   % Matrices:
   m  = ceil( rand(5,7)* 100 )
   cm = cummean( m )
   assert( cm(end,:) == mean(m) )
   

   % Passing a custom dimension
   cm = cummean( m , 2 )
   assert( cm(:,end) == mean(m,2) )

   % Dealing with multi-dimensional arrays
   m  = ceil( rand(5,7,3)* 100 )
   cm = cummean( m )
   cm = cummean( m , [] )
   assert( cm(end,:,:) == mean(m) )

   cm = cummean( m , 3 )
   assert( cm(:,:,end) == mean(m,3) )
   

   % Passing the kind of mean to be computed
   cm = cummean( m , [], '--arithmetic' )
   cm = cummean( m , [], 'a' )
   assert( cm(end,:,:) == mean(m) )

   % Geometric mean
   cm = cummean( m , [], '--geometric' )
   cm = cummean( m , [], 'g' )
   assert( cm(end,:,:) == prod(m,1).^(1/size(m,1)) )
   cm = cummean( m , 2, 'g' )
   assert( cm(:,end,:) == prod(m,2).^(1/size(m,2)) )

   % Harmonic mean
   cm = cummean( m , [], '--harmonic' )
   cm = cummean( m , [], 'h' )
   assert( cm(end,:,:) == size(m,1)./sum(1./m,1) )
   cm = cummean( m , 3, '--harmonic' )
   assert( cm(:,:,end) == size(m,3)./sum(1./m,3) )

Memory requirements:
   O( numel(  values  ) )



See also:
   cumstd, cumvar, cumsumsq, groupfun



Keywords:
   cumulative operators, scan



Version: 0.4.3

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