function [w,info] = perform_alpert_transform_2d(v,pos,alpert_vm, dir, options)

% perform_alpert_transform_2d - transform a 2D signal.
%
%
%   [w,info] = perform_alpert_transform_2d(v,pos,alpert_vm, dir, options);
%
%   'v' is a 1D vector, the value of the function at each sampling location.
%   'pos' is a 2D vector, pos(:,i) is the ith point.
%   'alpert_vm' is the number of vanishing moments (1=>Haar, 2=>linear basis ...).
%       * 'alpert_vm' can be an integer, and then the algorithm will use the same
%         order for X and Y direction.
%       * 'alpert_vm' can be a couple of integer alpert_vm=[kx,ky] and 'kx' will be the
%         order on the X direction, and 'ky' the order on the Y direction.
%       * 'alpert_vm' can be a set of monomial, see below ('degree_type') for
%         further comments.
%   'dir' is 1 for fwd transform and -1 for bwd.
%
%   'options' is a structure that can contains the followind field :
%   'degree_type' : Polynomial degree. By default, the multiresolution spaces are defined
%       as piecewise polynimals P that satisfy
%           degX(P)<alpert_vm(1) and degY(P)<alpert_vm(2).
%       If you want to use spaces defined by 
%           degX(P)+degY(P) < alpert_vm(1)
%       then you should specify degree_type='sum'
%       (default is degree_type='max').
%       If you want to define your own multiresolution space, 
%       you can provide your own monomials in 'alpert_vm' and then 
%       set degree_type='user_defined'. It's a bit tricky
%       because you have to provide an even number of monomials, 
%       twice more than needed. Suppose you want to use
%       as multiresolution basis the polynomials {1,X}, then you can set 
%           alpert_vm = [[0;0],[1;0],[0;1],[1;1]];
%   'part_type': for automatic partition, the way the algorithm
%       will perform the grouping (can be either '1axis', '2axis' or 'kmeans', 
%       type 'help dichotomic_grouping' for more info).
%   'part': if you don't want to use automatic grouping, then 
%       you can provide a cell array that contains a binary grouping of the points
%       (same format as 'dichotomic_grouping' function).
%
%   'w' is the transformed data.
%   'info' is a struct containing the localisation information for each
%       basis Alpert vector.
%       'info.l' is the scale of the vector (0=coarse scale).
%       'info.n' is the space location of the vector.
%       'info.k' is the number of multiwavelet (in [1,...,alpert_vm(1)*alpert_vm(2)]).
%
%   WARNING: the function will try to use the mex-compiled function
%       perform_moment_transform.dll if possible, and then it
%       won't retrun 'info'. Otherwise, it will use the slower
%       function 'perform_moment_transform_slow' and 
%       'info' will be returned.
%
%   Copyright (c) 2004 Gabriel Peyr