Description of sltensor_svd

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sltensor_svd

PURPOSE

SLTENSOR_SVD Performs a Higher-Order SVD on a Tensor

SYNOPSIS

function varargout = sltensor_svd(T, n)

DESCRIPTION

SLTENSOR_SVD Performs a Higher-Order SVD on a Tensor

 $ Syntax $
   - [S, U1, U2, ...] = sltensor_svd(T)
   - [S, U1, U2, ...] = sltensor_svd(T, n)
   - [S, Us] = sltensor_svd(...)

 $ Description $
   - [S, U1, U2, ...] = sltensor_svd(T) Performs a Higher Order Singular Value
   Decomposition to a Tensor T. In the output arguments, S is the core
   tensor, U1, U2, ... are the singular vector matrices of mode 1, 2,...

   - [S, U1, U2, ...] = sltensor_svd(T, n) Here n specifies the order of the
   tensor T, n should be not less than ndims(T). If n > ndims(T) is just
   regarded as a tensor of dimensions d1xd2x...x1. 

   - [S, Us] = sltensor_svd(...) where all mode matrices are returned to Us,
   which is an 1 x n cell array, with each cell containing a mode matrix.
 
 $ History $
   - Created by Dahua Lin on Dec 17th, 2005

CROSS-REFERENCE INFORMATION

This function calls:

• sltensor_multiply SLTENSOR_MULTIPLY Multiplies a tensor and a matrix
• sltensor_unfold SLTENSOR_UNFOLD Unfolds a tensor to a matrix
• slignorevars SLIGNOREVARS Ignores the input variables

This function is called by:

SOURCE CODE

0001 function varargout = sltensor_svd(T, n)
0002 %SLTENSOR_SVD Performs a Higher-Order SVD on a Tensor
0003 %
0004 % $ Syntax $
0005 %   - [S, U1, U2, ...] = sltensor_svd(T)
0006 %   - [S, U1, U2, ...] = sltensor_svd(T, n)
0007 %   - [S, Us] = sltensor_svd(...)
0008 %
0009 % $ Description $
0010 %   - [S, U1, U2, ...] = sltensor_svd(T) Performs a Higher Order Singular Value
0011 %   Decomposition to a Tensor T. In the output arguments, S is the core
0012 %   tensor, U1, U2, ... are the singular vector matrices of mode 1, 2,...
0013 %
0014 %   - [S, U1, U2, ...] = sltensor_svd(T, n) Here n specifies the order of the
0015 %   tensor T, n should be not less than ndims(T). If n > ndims(T) is just
0016 %   regarded as a tensor of dimensions d1xd2x...x1.
0017 %
0018 %   - [S, Us] = sltensor_svd(...) where all mode matrices are returned to Us,
0019 %   which is an 1 x n cell array, with each cell containing a mode matrix.
0020 %
0021 % $ History $
0022 %   - Created by Dahua Lin on Dec 17th, 2005
0023 %
0024 
0025 %% parse and verify the arguments
0026 slchknargs(nargin, 1);
0027 n0 = ndims(T);
0028 if nargin == 1
0029     n = n0;
0030 else
0031     if n < n0;
0032         error('sltoolbox:invalidarg', ...
0033             'The order %d is too small', n);
0034     end
0035 end
0036 if nargout > 2 && nargout ~= n+1
0037     error('sltoolbox:invalidnargout', ...
0038         'The number of outputs is not valid');
0039 end
0040 
0041 %% compute
0042 
0043 Us = cell(n, 1);
0044 S = T;
0045 for i = 1 : n0
0046     M = sltensor_unfold(T, i);
0047     [d1, d2] = size(M);
0048     if d1 < d2
0049         [V, D, U] = svd(M', 0);
0050     else
0051         [U, D, V] = svd(M, 0);
0052     end
0053     slignorevars(D, V);
0054     clear D V;
0055     
0056     Us{i} = U;
0057     S = sltensor_multiply(S, U', i);
0058 end
0059 if n > n0
0060     for i = n0+1 : n
0061         Us{i} = 1;
0062     end
0063 end
0064 
0065 %% output
0066 varargout{1} = S;
0067 if nargout == 2
0068     varargout{2} = Us;
0069 else
0070     varargout(2:n+1) = Us;
0071 end
0072 
0073 
0074     
0075 
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0080 
0081     
0082

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