Description of slrangespace

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slrangespace

PURPOSE

SLRANGESPACE Determines the subspace of the range of X

SYNOPSIS

function [U, Uc] = slrangespace(tar, varargin)

DESCRIPTION

SLRANGESPACE Determines the subspace of the range of X

 $ Syntax $
   - U = slrangespace(tar)
   - U = slrangespace(tar, ...)
   - [U, Uc] = slrangespace(...)

 $ Arguments $
   - tar:      the target, can be a sample matrix or covariance
   - U:        the basis for the range space
   - Uc:       the basis for the orthogonal complement of the range

 $ Description $
   - U = slrangespace(tar) determines the range space of tar in default 
     settings. That is to set the dimension to be the rank of tar. Note
     that tar can have two forms: a sample matrix or a covariance
     given by the syntax {'cov', C}.

   - U = slrangespace(tar, ...) determines the range space of X using
     the specified dimension determination schemes. The arguments 
     input following X will be delivered to sldim_by_eigval for dimension
     determination.

   - [U, Uc] = slrangespace(...) also returns orthogonal complement of U.

 $ History $
   - Created by Dahua Lin on Apr 25, 2005

CROSS-REFERENCE INFORMATION

This function calls:

• slsymeig SLSYMEIG Compute the eigenvalues and eigenvectors for symmetric matrix
• sldim_by_eigval SLDIM_BY_EIGVAL Determines the dimension of principal subspace by eigenvalues

This function is called by:

• sldlda SLDLDA Performs Direct Linear Discriminant Analysis
• slnullspace SLRANGESPACE Determines the null-space of the range of X

SOURCE CODE

0001 function [U, Uc] = slrangespace(tar, varargin)
0002 %SLRANGESPACE Determines the subspace of the range of X
0003 %
0004 % $ Syntax $
0005 %   - U = slrangespace(tar)
0006 %   - U = slrangespace(tar, ...)
0007 %   - [U, Uc] = slrangespace(...)
0008 %
0009 % $ Arguments $
0010 %   - tar:      the target, can be a sample matrix or covariance
0011 %   - U:        the basis for the range space
0012 %   - Uc:       the basis for the orthogonal complement of the range
0013 %
0014 % $ Description $
0015 %   - U = slrangespace(tar) determines the range space of tar in default
0016 %     settings. That is to set the dimension to be the rank of tar. Note
0017 %     that tar can have two forms: a sample matrix or a covariance
0018 %     given by the syntax {'cov', C}.
0019 %
0020 %   - U = slrangespace(tar, ...) determines the range space of X using
0021 %     the specified dimension determination schemes. The arguments
0022 %     input following X will be delivered to sldim_by_eigval for dimension
0023 %     determination.
0024 %
0025 %   - [U, Uc] = slrangespace(...) also returns orthogonal complement of U.
0026 %
0027 % $ History $
0028 %   - Created by Dahua Lin on Apr 25, 2005
0029 %
0030 
0031 %% parse and verify input arguments
0032 
0033 if isnumeric(tar)   
0034     target_type = 1;        % target is sample
0035     
0036     if ndims(tar) ~= 2
0037         error('sltoolbox:invalidarg', ...
0038             'When tar is sample matrix, it should be a 2D matrix');
0039     end
0040     
0041     X = tar;
0042     d = size(X, 1);
0043     
0044 elseif iscell(tar)
0045     
0046     if length(tar) == 2 && ischar(tar{1}) ...
0047             && strcmpi(tar{1}, 'cov')
0048         
0049         target_type = 2;        % target is covariance
0050         
0051         C = tar{2};
0052         d = size(C, 1);
0053         
0054         if ~isequal(size(C), [d d])
0055             error('sltoolbox:invalidarg', ...
0056                 'A covariance matrix should be square');
0057         end
0058         
0059     else        
0060         error('sltoolbox:invalidarg', ...
0061             'The target should be a sample matrix or a covariance given by cell');        
0062     end
0063     
0064 else
0065     
0066     error('sltoolbox:invalidarg', ...
0067         'The target should be a sample matrix or a covariance given by cell');        
0068 end
0069 
0070 if nargout == 0
0071     return;
0072 elseif nargout == 1
0073     need_complement = false;
0074 else
0075     need_complement = true;
0076 end
0077     
0078 
0079 %% compute
0080 
0081 switch target_type
0082     
0083     case 1      % sample matrix
0084         
0085         if ~need_complement
0086             [U, D] = svd(X, 0);
0087         else
0088             [U, D] = svd(X);
0089         end
0090         
0091         evals = diag(D) .^ 2;
0092         clear D;
0093                                         
0094     case 2      % covariance
0095         
0096         [evals, U] = slsymeig(C);
0097         
0098 end
0099     
0100 evals = max(evals, 0);
0101 k = sldim_by_eigval(evals, varargin{:});
0102 
0103 %% output
0104 
0105 if ~need_complement
0106     U = U(:, 1:k);
0107 else
0108     if k == size(U, 2)
0109         Uc = zeros(d, 0);
0110     else
0111         Uc = U(:, k+1:end);
0112         U  = U(:, 1:k);
0113     end
0114 end
0115

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