Accessing Arbitrary Dimensions

[Bill Denney-4]

Hi,

I'm trying to run code where I don't know the dimension that I'm wanting
to use a priori.  In other words, I want to take as an input argument
the dimension that I want to work on with a function that works
similarly to max (hhigh.m, attached).

A similar example to what I want to do is:

function y = test(x, dim)
  n = 5;
  sz = size(x);
  for i = 1:sz(dim)
    ## the next line should be corrected to
    points = x(:,:,:,max(1,i-n+1),:,:)
    y = max(x(points)
  endfor

I had the idea to use sub2ind to compute all the points that I need to
use, but I was wondering if there was a simpler (and possibly faster)
way than something like this in the loop:

sz = size (x);
idx = max(1, i-n+1)
sz_tmp = mat2cell(ones (length (idx),1)*sz, 1, length (sz));
sz_nodim = sz;
sz_nodim(dim) = [];
points = zeros (length (idx), prod (sz_nodim));
for j = 1:length(idx)
  sz_tmp2 = sz_tmp;
  sz_tmp2{dim} = idx;
  points(j,:) = sub2ind(sz, sz_tmp2{:});
endfor

All of the above was typed directly into this e-mail, and I'm pretty
sure that it doesn't do quite what I'm wanting, but hopefully it gets
the idea across.

Thanks,

Bill

## Copyright (C) 2008 Bill Denney
##
## This software 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.
##
## This software 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 this software; see the file COPYING.  If not, see
## <http://www.gnu.org/licenses/>.

## -*- texinfo -*-
## @deftypefn {Function File} {hhv} = hhigh (data)
## @deftypefnx {Function File} {hhv} = hhigh (data, nperiods)
## @deftypefnx {Function File} {hhv} = hhigh (data, nperiods, dim)
##
## Compute the highest high value of @var{data} for the past
## @var{nperiods} (default: 14) across the dimension, @var{dim}
## (default: 1).
##
## @seealso{llow}
## @end deftypefn

## Author: Bill Denney <bill@...>
## Created: 24 Feb 2008

function hhv = hhigh (data, nperiods, dim)

  if nargin < 1 || nargin > 3
    print_usage ();
  elseif ~ isvector (data)
    ## FIXME
    error ("cannot yet handle more than one dimensional data")
  endif
  if nargin < 2
    nperiods = 14;
  endif
  if nargin < 3
    ## Use the first non-singleton dimension
    dim = find (size (data) > 1, 1);
  endif

  if dim > ndims (data)
    error ("dim cannot be greater than the number of dimensions in data");
  endif

  sz = size (data);
  hhv = data;
  for i = 1:sz(dim)
    hhv(i) = max (data(max (i-nperiods+1, 1):i));
  endfor

endfunction

## Tests
%!shared c, h
%! c = [22.44 22.61 22.67 22.88 23.36 23.23 23.08 22.86 23.17 23.69 23.77 23.84 24.32 24.8 24.16 24.1 23.37 23.61 23.21 25];
%! h = [22.44 22.61 22.67 22.88 23.36 23.36 23.36 23.36 23.36 23.69 23.77 23.84 24.32 24.8 24.8 24.8 24.8 24.8 24.8 25];
%!assert(hhigh(c), h)
%!assert(hhigh(c'), h')

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[dbateman]

I've dealt with pretty much the same issue in the past. The sub2ind method is slow and not that flexible. I prefer two different solutions

1) Create a cell array of the correct dimensionality like

idx = cell(ndim, 1)
for i = 1, ndim
  idx {i} = ":";
endfor
idx{dim} = ??;

where ?? is replaced with whatever you want to replace it with to act of the dimension required. Then you can convert to a cs-list to use it as an index like x(idx{:}).

2) use permute/ipermute to more the desired dimension to be the first dimension and then treat the indexing as 2-D (even if the matrix is ND) and then permute back

D.