%AFFINE Construct affine (linear) mapping from parameters
%
% W = AFFINE(R,OFFSET,LABLIST_IN,LABLIST_OUT,SIZE_IN,SIZE_OUT)
% W = AFFINE(R,OFFSET,A)
% W = AFFINE(W1,W2)
%
% INPUT
% R Matrix of a linear mapping from a K- to an L-dimensional space
% OFFSET Shift applied after R; a row vector of the length L
% (optional; default: zeros(1,L))
% LABLIST_IN Labels of the features of the input space
% (optional; default: (1:K)')
% LABLIST_OUT Labels of the features of the output space, e.g. class names
% for linear classifiers (optional; default: (1:L)')
% SIZE_IN If based on images: size vector of the input dimensionality
% (optional; default: K)
% SIZE_OUT If based on images: size vector of the output dimensionality
% (optional; default: L)
% A Dataset (LAB_IN_LIST and SIZE_IN are derived from A)
% W1,W2 Affine mappings
%
% OUTPUT
% W Affine mapping
%
% DESCRIPTION
% This is a low level basic PRTools routine, not intended for direct use.
% It efines a mapping W based on a linear transformation R and an offset.
% R should be a [K x L] matrix describing a linear transformation from
% a K-dimensional space to an L-dimensional space. If K=1, then R is
% interpreted as the diagonal of an [L x L] diagonal matrix. OFFSET is
% a row vector of the length L, added afterwards.
%
% Affine mappings are treated by PRTools in a special way. A scaling
% defined for an affine mapping, e.g. by W = SETSCALE(W,SCALE) is directly
% executed by a multiplication of the coefficients. Also, the product of
% two affine mappings is directly converted to a new affine mapping.
% This routine also executes W = AFFINE(W1,W2), if W1 and W2 are affine.
% B = AFFINE(A,W), if A is a dataset and W is an affine mapping.
% Finally, the transpose of an affine mapping exists and is defined as
% an another affine mapping.
%
% An [M x K] dataset A can be mapped as D = A*W. The result is equivalent
% to [+A, ones(M,1)]*[R; OFFSET]. The dataset D has feature labels stored
% in LABLIST. The number of this labels should, thereby, be at least L.
%
% SEE ALSO (<a href="http://37steps.com/prtools">PRTools Guide</a>)
% DATASETS, MAPPINGS
% Copyright: R.P.W. Duin, r.p.w.duin@37steps.com
% Faculty EWI, Delft University of Technology
% P.O. Box 5031, 2600 GA Delft, The Netherlands
% $Id: affine.m,v 1.10 2009/03/17 10:03:51 duin Exp $
function w = affine(R,offset,lablist_in, lablist_out,size_in,size_out)
if (nargin == 1) | (~isa(offset,'prmapping'))
% Definition of an affine mapping
[m,k] = size(R);
if (nargin < 6)
prwarning(5,'SIZE_OUT is not specified. The number of columns of R, %d, is assumed.', k);
size_out = k;
end
if (nargin < 5)
prwarning(5,'SIZE_IN is not specified. The number of rows of R, %d, is assumed.', m);
size_in = m;
end
if (nargin < 4)
prwarning(5,'LABLIST_OUT is not specified, [1:%d]'' assumed.', k);
lablist_out = [];
end
if (nargin < 3)
prwarning(5,'LABLIST_IN is not specified, [1:%d]'' assumed.', m);
lablist_in = [];
end
if (nargin < 2) | (isempty(offset))
prwarning(3,'OFFSET not specified, a zero vector assumed.');
offset = zeros(1,k);
end
% Check consistencies
if (~isa(R,'double'))
error('No proper transformation matrix stored.')
end
if (size_in == 1) & nargin < 3 % R is a scaling vector
size_in = size_out;
end
if (isempty(lablist_in))
lablist_in = genlab(1,[1:size_in]');
end
cost = [];
if (isa(lablist_in,'prdataset')) % Copy labels from dataset/datafile
cost = lablist_in.cost;
size_in = getfeatsize(lablist_in);
lablist_in = getfeatlab(lablist_in);
%if isempty(lablist_in)
% lablist_in = num2str([1:size_in]');
%end
% size_out = k; % Wrong for classifiers defined for 1D datasets
end
if ~isempty(lablist_in) & (size(lablist_in,1) < m)
error('Wrong number of input labels supplied.')
end
if isempty(lablist_out)
lablist_out = genlab(1,[1:size_out]');
end
if (size(lablist_out,1) < k)
error('Wrong number of output labels supplied.')
end
if any(size(offset) ~= [1,k])
error('Offset is not a row vector of the correct size.')
end
% Store the results:
d.rot = R;
d.offset = offset;
d.lablist_in = lablist_in;
w = prmapping(mfilename,'trained',d,lablist_out,size_in,size_out);
w = setcost(w,cost);
elseif isa(R,'prmapping')
% Two mappings, stored in R and OFFSET, should be combined.
w1 = R;
w2 = offset;
if (~isclassifier(w1)) & (~isclassifier(w2)) & (strcmp(getmapping_file(w1),'affine')) & (strcmp(getmapping_file(w2),'affine'))
% Combine two affine mappings
% If d1.rot or d2.rot are vectors, they have to be interpreted as
% the diagonal matrices, unless the inner dimension does not fit.
d1 = +w1;
d2 = +w2;
if (size(d1.rot,1) == 1) % d1.rot is a vector
if (size(d2.rot) == 1) % d2.rot is a vector
d.rot = d1.rot.*d2.rot;
d.offset = d1.offset.*d2.rot + d2.offset;
else % d2.rot is a matrix
d.rot = repmat(d1.rot',1,size(d2.rot,2)).*d2.rot;
d.offset = d1.offset*d2.rot + d2.offset;
end
else % d1.rot is a matrix
%RD Here comes a bug fix that I needed to continue, I am not sure it
%RD is sufficient It may even introduce new problems, especially for
% 1D datasets.
%if size(d2.rot,1) == 1 % d2.rot is vector
if (size(d1.rot,2) > 1) & (size(d2.rot,1) == 1) % d2.rot is a vector
d.rot = d1.rot.*repmat(d2.rot,size(d1.rot,1),1);
d.offset = d1.offset.*d2.rot + d2.offset;
else % d2.rot is a matrix
d.rot = d1.rot*d2.rot;
d.offset = d1.offset*d2.rot + d2.offset;
end
end
d.lablist_in = d1.lablist_in;
w = prmapping(mfilename,'trained',d,getlabels(w2),getsize_in(w1),getsize_out(w2));
else
% Store a sequential mapping.
w = sequential(w1,w2);
end
else
% Execution of the affine mapping.
% R is a dataset or double, OFFSET defines the mapping.
v = offset;
[m,k] = size(R);
d = +v;
if all(size(v) == 0)
d.rot = repmat(d.rot,1,k);
d.offset = zeros(1,k);
end
if (size(d.rot,1) == 1) & (k > 1)
% No rotation, just a scaling
x = zeros(m,k);
Rdat = +R;
if (m > k) % Necessary switch for handling large feature sizes.
for j=1:k
x(:,j) = Rdat(:,j)*d.rot(j);
end
else
for i=1:m
x(i,:) = Rdat(i,:).*d.rot;
end
end
x = x + repmat(d.offset,m,1);
else % Rotation.
x = [+R,ones(m,1)] * [d.rot;d.offset];
end
if size(v,2) == 2 & size(x,2) == 1
x = [x -x];
end
if isdataset(R)
w = setdat(R,x,v);
else
w = x;
end
end
return;