b1_tenmat_doc.html

张量分析工具

     1     4     3

</pre><h2>Creating a tenmat from its constituent parts<a name="16"></a></h2><pre class="codeinput">B = tenmat(A.data,A.rdims,A.cdims,A.tsize) <span class="comment">%&lt;-- Recreates A</span>
</pre><pre class="codeoutput">B is a matrix corresponding to a tensor of size 3 x 2 x 2 x 2
	B.rindices = [ 2 ] (modes of tensor corresponding to rows)
	B.cindices = [ 1  4  3 ] (modes of tensor corresponding to columns)
	B.data = 
		     1     2     3    13    14    15     7     8     9    19    20    21
		     4     5     6    16    17    18    10    11    12    22    23    24
</pre><h2>Creating an empty tenmat<a name="17"></a></h2><pre class="codeinput">B = tenmat <span class="comment">%&lt;-- Empty tenmat.</span>
</pre><pre class="codeoutput">B is a matrix corresponding to a tensor of size [empty tensor]
	B.rindices = [  ] (modes of tensor corresponding to rows)
	B.cindices = [  ] (modes of tensor corresponding to columns)
	B.data = []
</pre><h2>Use double to convert a tenmat to a MATLAB matrix<a name="18"></a></h2><pre class="codeinput">double(A) <span class="comment">%&lt;-- converts A to a standard matrix</span>
</pre><pre class="codeoutput">
ans =

     1     2     3    13    14    15     7     8     9    19    20    21
     4     5     6    16    17    18    10    11    12    22    23    24

</pre><h2>Use tensor to convert a tenmat to a tensor<a name="19"></a></h2><pre class="codeinput">Y = tensor(A)
</pre><pre class="codeoutput">Y is a tensor of size 3 x 2 x 2 x 2
	Y(:,:,1,1) = 
	     1     4
	     2     5
	     3     6
	Y(:,:,2,1) = 
	     7    10
	     8    11
	     9    12
	Y(:,:,1,2) = 
	    13    16
	    14    17
	    15    18
	Y(:,:,2,2) = 
	    19    22
	    20    23
	    21    24
</pre><h2>Use size and tsize for the dimensions of a tenmat<a name="20"></a></h2><pre class="codeinput">size(A) <span class="comment">%&lt;-- Matrix size</span>
tsize(A) <span class="comment">%&lt;-- Corresponding tensor size</span>
</pre><pre class="codeoutput">
ans =

     2    12


ans =

     3     2     2     2

</pre><h2>Subscripted reference for a tenmat<a name="21"></a></h2><pre class="codeinput">A(2,1) <span class="comment">%&lt;-- returns the (2,1) element of the matrix.</span>
</pre><pre class="codeoutput">
ans =

     4

</pre><h2>Subscripted assignment for a tenmat<a name="22"></a></h2><pre class="codeinput">A(1:2,1:2) = ones(2) <span class="comment">%&lt;-- Replace part of the matrix.</span>
</pre><pre class="codeoutput">A is a matrix corresponding to a tensor of size 3 x 2 x 2 x 2
	A.rindices = [ 2 ] (modes of tensor corresponding to rows)
	A.cindices = [ 1  4  3 ] (modes of tensor corresponding to columns)
	A.data = 
		     1     1     3    13    14    15     7     8     9    19    20    21
		     1     1     6    16    17    18    10    11    12    22    23    24
</pre><h2>Use end for the last index<a name="23"></a></h2><pre class="codeinput">A(end,end) <span class="comment">%&lt;-- Same as X(2,12)</span>
</pre><pre class="codeoutput">
ans =

    24

</pre><h2>Basic operations for tenmat<a name="24"></a></h2><pre class="codeinput">norm(A) <span class="comment">%&lt;-- Norm of the matrix.</span>
</pre><pre class="codeoutput">
ans =

   69.6994

</pre><pre class="codeinput">A' <span class="comment">%&lt;-- Calls ctranspose (also swaps mapped dimensions).</span>
</pre><pre class="codeoutput">ans is a matrix corresponding to a tensor of size 3 x 2 x 2 x 2
	ans.rindices = [ 1  4  3 ] (modes of tensor corresponding to rows)
	ans.cindices = [ 2 ] (modes of tensor corresponding to columns)
	ans.data = 
		     1     1
		     1     1
		     3     6
		    13    16
		    14    17
		    15    18
		     7    10
		     8    11
		     9    12
		    19    22
		    20    23
		    21    24
</pre><pre class="codeinput">+A <span class="comment">%&lt;-- Calls uplus.</span>
</pre><pre class="codeoutput">ans is a matrix corresponding to a tensor of size 3 x 2 x 2 x 2
	ans.rindices = [ 2 ] (modes of tensor corresponding to rows)
	ans.cindices = [ 1  4  3 ] (modes of tensor corresponding to columns)
	ans.data = 
		     1     1     3    13    14    15     7     8     9    19    20    21
		     1     1     6    16    17    18    10    11    12    22    23    24
</pre><pre class="codeinput">-A <span class="comment">%&lt;-- Calls uminus.</span>
</pre><pre class="codeoutput">ans is a matrix corresponding to a tensor of size 3 x 2 x 2 x 2
	ans.rindices = [ 2 ] (modes of tensor corresponding to rows)
	ans.cindices = [ 1  4  3 ] (modes of tensor corresponding to columns)
	ans.data = 
		    -1    -1    -3   -13   -14   -15    -7    -8    -9   -19   -20   -21
		    -1    -1    -6   -16   -17   -18   -10   -11   -12   -22   -23   -24
</pre><pre class="codeinput">A+A <span class="comment">%&lt;-- Calls plus.</span>
</pre><pre class="codeoutput">ans is a matrix corresponding to a tensor of size 3 x 2 x 2 x 2
	ans.rindices = [ 2 ] (modes of tensor corresponding to rows)
	ans.cindices = [ 1  4  3 ] (modes of tensor corresponding to columns)
	ans.data = 
		     2     2     6    26    28    30    14    16    18    38    40    42
		     2     2    12    32    34    36    20    22    24    44    46    48
</pre><pre class="codeinput">A-A <span class="comment">%&lt;-- Calls minus.</span>
</pre><pre class="codeoutput">ans is a matrix corresponding to a tensor of size 3 x 2 x 2 x 2
	ans.rindices = [ 2 ] (modes of tensor corresponding to rows)
	ans.cindices = [ 1  4  3 ] (modes of tensor corresponding to columns)
	ans.data = 
		     0     0     0     0     0     0     0     0     0     0     0     0
		     0     0     0     0     0     0     0     0     0     0     0     0
</pre><h2>Multiplying two tenmats<a name="30"></a></h2>
         <p>It is possible to compute the product of two tenmats and have a result that can be converted into a tensor.</p><pre class="codeinput">B = A * A' <span class="comment">%&lt;-- Tenmat that is the product of two tenmats.</span>
</pre><pre class="codeoutput">B is a matrix corresponding to a tensor of size 2 x 2
	B.rindices = [ 1 ] (modes of tensor corresponding to rows)
	B.cindices = [ 2 ] (modes of tensor corresponding to columns)
	B.data = 
		        1997        2384
		        2384        2861
</pre><pre class="codeinput">tensor(B) <span class="comment">%&lt;-- Corresponding tensor.</span>
</pre><pre class="codeoutput">ans is a tensor of size 2 x 2
	ans(:,:) = 
	        1997        2384
	        2384        2861
</pre><h2>Displaying a tenmat<a name="32"></a></h2>
         <p>Shows the original tensor dimensions, the modes mapped to rows, the modes mapped to columns, and the matrix.</p><pre class="codeinput">disp(A)
</pre><pre class="codeoutput">ans is a matrix corresponding to a tensor of size 3 x 2 x 2 x 2
	ans.rindices = [ 2 ] (modes of tensor corresponding to rows)
	ans.cindices = [ 1  4  3 ] (modes of tensor corresponding to columns)
	ans.data = 
		     1     1     3    13    14    15     7     8     9    19    20    21
		     1     1     6    16    17    18    10    11    12    22    23    24
</pre><p class="footer"><br>
            Published with MATLAB&reg; 7.2<br></p>
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##### SOURCE BEGIN #####
%% Converting a tensor to a matrix and vice versa
% We show how to convert a tensor to a matrix stored with extra information
% so that it can be converted back to a tensor. Converting to a matrix
% requies an ordered mapping of the tensor indices to the rows and the
% columns of the matrix. 
%% Creating a tenmat (tensor as matrix) object
X = tensor(1:24,[3 2 2 2]) %<REPLACE_WITH_DASH_DASH Create a tensor.
%%
A = tenmat(X,[1 2],[3 4]) %<REPLACE_WITH_DASH_DASH Dims [1 2] map to rows, [3 4] to columns.
%%
B = tenmat(X,[2 1],[3 4]) %<REPLACE_WITH_DASH_DASH Order matters!
%%
C = tenmat(X,[1 2],[4 3]) %<REPLACE_WITH_DASH_DASH Order matters!
%% Creating a tenmat by specifying the dimensions mapped to the rows
% If just the row indices are specified, then the columns are arranged in
% increasing order.
A = tenmat(X,1) %<REPLACE_WITH_DASH_DASH Same as A = tenmat(X,1,2:4)
%% Creating a tenmat by specifying the dimensions mapped to the columns
% Likewise, just the columns can be specified if the 3rd argument is a 't'.
% The rows are arranged in increasing order.
A = tenmat(X, [2 3], 't') %<REPLACE_WITH_DASH_DASH Same as A = tenmat(X,[1 4],[2 3]).
%% Vectorize via tenmat
% All the dimensions can be mapped to the rows or the columnns.
A = tenmat(X,1:4,'t') %<REPLACE_WITH_DASH_DASH Map all the dimensions to the columns
%% Alternative ordering for the columns for mode-n matricization
% Mode-n matricization means that only mode n is mapped to the rows. 
% Different column orderings are available.
A = tenmat(X,2) %<REPLACE_WITH_DASH_DASH By default, columns are ordered as [1 3 4].
%% 
A = tenmat(X,2,[3 1 4]) %<REPLACE_WITH_DASH_DASH Explicit specification.
%%
A = tenmat(X,2,'fc') %<REPLACE_WITH_DASH_DASH Forward cyclic, i.e., [3 4 1].
%%
A = tenmat(X,2,'bc') %<REPLACE_WITH_DASH_DASH Backward cyclic, i.e., [1 4 3].
%% Constituent parts of a tenmat
A.data %<REPLACE_WITH_DASH_DASH The matrix itself.
%%
A.tsize %<REPLACE_WITH_DASH_DASH Size of the original tensor.
%%
A.rdims %<REPLACE_WITH_DASH_DASH Dimensions that were mapped to the rows.
%%
A.cdims %<REPLACE_WITH_DASH_DASH Dimensions that were mapped to the columns.
%% Creating a tenmat from its constituent parts
B = tenmat(A.data,A.rdims,A.cdims,A.tsize) %<REPLACE_WITH_DASH_DASH Recreates A
%% Creating an empty tenmat
B = tenmat %<REPLACE_WITH_DASH_DASH Empty tenmat.
%% Use double to convert a tenmat to a MATLAB matrix
double(A) %<REPLACE_WITH_DASH_DASH converts A to a standard matrix
%% Use tensor to convert a tenmat to a tensor
Y = tensor(A)
%% Use size and tsize for the dimensions of a tenmat
size(A) %<REPLACE_WITH_DASH_DASH Matrix size
tsize(A) %<REPLACE_WITH_DASH_DASH Corresponding tensor size
%% Subscripted reference for a tenmat
A(2,1) %<REPLACE_WITH_DASH_DASH returns the (2,1) element of the matrix.
%% Subscripted assignment for a tenmat
A(1:2,1:2) = ones(2) %<REPLACE_WITH_DASH_DASH Replace part of the matrix.
%% Use end for the last index
A(end,end) %<REPLACE_WITH_DASH_DASH Same as X(2,12)
%% Basic operations for tenmat
norm(A) %<REPLACE_WITH_DASH_DASH Norm of the matrix.
%%
A' %<REPLACE_WITH_DASH_DASH Calls ctranspose (also swaps mapped dimensions).
%%
+A %<REPLACE_WITH_DASH_DASH Calls uplus.
%%
-A %<REPLACE_WITH_DASH_DASH Calls uminus.
%%
A+A %<REPLACE_WITH_DASH_DASH Calls plus.
%%
A-A %<REPLACE_WITH_DASH_DASH Calls minus.
%% Multiplying two tenmats
% It is possible to compute the product of two tenmats and have a result
% that can be converted into a tensor.
B = A * A' %<REPLACE_WITH_DASH_DASH Tenmat that is the product of two tenmats.
%%
tensor(B) %<REPLACE_WITH_DASH_DASH Corresponding tensor.
%% Displaying a tenmat
% Shows the original tensor dimensions, the modes mapped to rows, the modes
% mapped to columns, and the matrix.
disp(A) 

##### SOURCE END #####
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