%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  % Defines 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 afterwords.%% 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. % Finally, the transpose of an affine mapping exists and is defined as % an another affine mapping. Consequently, this routine also executes % W = AFFINE(W1,W2) if W1 and W2 are affine and B = AFFINE(A,W), if A % is a dataset and W is an 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% DATASETS, MAPPINGS% Copyright: R.P.W. Duin, r.p.w.duin@prtools.org% Faculty EWI, Delft University of Technology% P.O. Box 5031, 2600 GA Delft, The Netherlands% $Id: affine.m,v 1.14 2005/11/28 21:46:56 duin Exp $function w = affine(R,offset,lablist_in, lablist_out,size_in,size_out)	prtrace(mfilename);		if (nargin == 1) | (~isa(offset,'mapping'))		% 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,'dataset'))						% Copy labels from dataset			cost = lablist_in.cost;			[lablist_in,size_in] = get(lablist_in,'featlab','featsize');			% size_out = k; % Wrong for classifiers defined for 1D datasets		end				if (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 = mapping(mfilename,'trained',d,lablist_out,size_in,size_out);		w = setcost(w,cost);		elseif isa(R,'mapping') 		% 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 = mapping(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, OFFSET defines the mapping.		v = offset;		[m,k] = size(R);		d = +v;			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		w = setdat(R,x,v);			endreturn;