b2_sptenmat_doc.html

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</pre><h2>Creating an emtpy sptenmat<a name="19"></a></h2><pre class="codeinput">A = sptenmat <span class="comment">%&lt;-- A really empty sptenmat.</span>
</pre><pre class="codeoutput">A is an all-zero sptenmat from an sptensor of size [empty tensor]
	A.rindices = [  ] (modes of tensor corresponding to rows)
	A.cindices = [  ] (modes of tensor corresponding to columns)
</pre><h2>Use double to convert a sptenmat to a MATLAB sparse matrix<a name="20"></a></h2><pre class="codeinput">X = sptenrand([10 10 10 10],10); <span class="comment">%&lt;-- Create a tensor.</span>
A = sptenmat(X,1) <span class="comment">%&lt;-- Convert it to a sptenmat</span>
</pre><pre class="codeoutput">A is a sptenmat from an sptensor of size 10 x 10 x 10 x 10 with 10 nonzeros
	A.rindices = [ 1 ] (modes of tensor corresponding to rows)
	A.cindices = [ 2  3  4 ] (modes of tensor corresponding to columns)
	( 2,723)	0.783859
	( 3, 32)	0.986158
	( 4,647)	0.473343
	( 5,775)	0.902819
	( 5,236)	0.451059
	( 5,256)	0.804517
	( 5,357)	0.828864
	( 7,191)	0.16627
	( 7,447)	0.393906
	(10,434)	0.520757
</pre><pre class="codeinput">B = double(A) <span class="comment">%&lt;-- Convert it to a MATLAB sparse matrix</span>
</pre><pre class="codeoutput">
B =

   (3,32)      0.9862
   (7,191)     0.1663
   (5,236)     0.4511
   (5,256)     0.8045
   (5,357)     0.8289
  (10,434)     0.5208
   (7,447)     0.3939
   (4,647)     0.4733
   (2,723)     0.7839
   (5,775)     0.9028

</pre><pre class="codeinput">whos <span class="string">A</span> <span class="string">B</span> <span class="comment">%&lt;-- The storage for B (the sparse matrix) is larger than for A.</span>
</pre><pre class="codeoutput">  Name      Size                    Bytes  Class

  A        10x1000                    924  sptenmat object
  B        10x1000                   4124  double array (sparse)

Grand total is 53 elements using 5048 bytes

</pre><pre class="codeinput">C = B'; <span class="comment">%&lt;-- Transposing the result fixes the problem.</span>
whos <span class="string">C</span>
</pre><pre class="codeoutput">  Name      Size                    Bytes  Class

  C      1000x10                      164  double array (sparse)

Grand total is 10 elements using 164 bytes

</pre><h2>Use full to convert a sptenmath to a tenmat<a name="24"></a></h2><pre class="codeinput">B = sptenmat(sptenrand([3 3 3], 3), 1) <span class="comment">%&lt;-- Create a sptenmat</span>
</pre><pre class="codeoutput">B is a sptenmat from an sptensor of size 3 x 3 x 3 with 3 nonzeros
	B.rindices = [ 1 ] (modes of tensor corresponding to rows)
	B.cindices = [ 2  3 ] (modes of tensor corresponding to columns)
	(2,1)	0.759479
	(2,8)	0.949759
	(3,5)	0.557939
</pre><pre class="codeinput">C = full(B) <span class="comment">%&lt;-- Convert to a tenmat</span>
</pre><pre class="codeoutput">C is a matrix corresponding to a tensor of size 3 x 3 x 3
	C.rindices = [ 1 ] (modes of tensor corresponding to rows)
	C.cindices = [ 2  3 ] (modes of tensor corresponding to columns)
	C.data = 
		  Columns 1 through 8 
		         0         0         0         0         0         0         0         0
		    0.7595         0         0         0         0         0         0    0.9498
		         0         0         0         0    0.5579         0         0         0
		  Column 9 
		         0
		         0
		         0
</pre><h2>Use sptensor to convert a sptenmat to a sptensor<a name="26"></a></h2><pre class="codeinput">Y = sptensor(A) <span class="comment">%&lt;-- Convert a sptenmat to a sptensor</span>
</pre><pre class="codeoutput">Y is a sparse tensor of size 10 x 10 x 10 x 10 with 10 nonzeros
	( 2,3, 3,8)    0.7839
	( 3,2, 4,1)    0.9862
	( 4,7, 5,7)    0.4733
	( 5,5, 8,8)    0.9028
	( 5,6, 4,3)    0.4511
	( 5,6, 6,3)    0.8045
	( 5,7, 6,4)    0.8289
	( 7,1,10,2)    0.1663
	( 7,7, 5,5)    0.3939
	(10,4, 4,5)    0.5208
</pre><h2>Use size and tsize for the dimensions of a sptenmat<a name="27"></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 =

          10        1000


ans =

    10    10    10    10

</pre><h2>Subscripted reference for a sptenmat<a name="28"></a></h2>
         <p>This is not supported beyond getting the constituent parts.</p>
         <h2>Subscripted assignment for a sptenmat<a name="29"></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 sptenmat from an sptensor of size 10 x 10 x 10 x 10 with 14 nonzeros
	A.rindices = [ 1 ] (modes of tensor corresponding to rows)
	A.cindices = [ 2  3  4 ] (modes of tensor corresponding to columns)
	( 1,  1)	1
	( 1,  2)	1
	( 2,  1)	1
	( 2,  2)	1
	( 2,723)	0.783859
	( 3, 32)	0.986158
	( 4,647)	0.473343
	( 5,236)	0.451059
	( 5,256)	0.804517
	( 5,357)	0.828864
	( 5,775)	0.902819
	( 7,191)	0.16627
	( 7,447)	0.393906
	(10,434)	0.520757
</pre><h2>Use end for the last index<a name="30"></a></h2>
         <p>End is not supported.</p>
         <h2>Basic operations for sptenmat<a name="31"></a></h2><pre class="codeinput">norm(A) <span class="comment">%&lt;-- Norm of the matrix.</span>
</pre><pre class="codeoutput">
ans =

    2.9356

</pre><pre class="codeinput">+A <span class="comment">%&lt;-- Calls uplus.</span>
</pre><pre class="codeoutput">ans is a sptenmat from an sptensor of size 10 x 10 x 10 x 10 with 14 nonzeros
	ans.rindices = [ 1 ] (modes of tensor corresponding to rows)
	ans.cindices = [ 2  3  4 ] (modes of tensor corresponding to columns)
	( 1,  1)	1
	( 1,  2)	1
	( 2,  1)	1
	( 2,  2)	1
	( 2,723)	0.783859
	( 3, 32)	0.986158
	( 4,647)	0.473343
	( 5,236)	0.451059
	( 5,256)	0.804517
	( 5,357)	0.828864
	( 5,775)	0.902819
	( 7,191)	0.16627
	( 7,447)	0.393906
	(10,434)	0.520757
</pre><pre class="codeinput">-A <span class="comment">%&lt;-- Calls uminus.</span>
</pre><pre class="codeoutput">ans is a sptenmat from an sptensor of size 10 x 10 x 10 x 10 with 14 nonzeros
	ans.rindices = [ 1 ] (modes of tensor corresponding to rows)
	ans.cindices = [ 2  3  4 ] (modes of tensor corresponding to columns)
	( 1,  1)	-1
	( 1,  2)	-1
	( 2,  1)	-1
	( 2,  2)	-1
	( 2,723)	-0.783859
	( 3, 32)	-0.986158
	( 4,647)	-0.473343
	( 5,236)	-0.451059
	( 5,256)	-0.804517
	( 5,357)	-0.828864
	( 5,775)	-0.902819
	( 7,191)	-0.16627
	( 7,447)	-0.393906
	(10,434)	-0.520757
</pre><h2>Use aatx to efficiently compute A * A' * x for a sptenmat<a name="34"></a></h2><pre class="codeinput">x = ones(10,1); <span class="comment">%&lt;-- Create vector</span>
aatx(A,x) <span class="comment">%&lt;-- Compute A * A' * x</span>
</pre><pre class="codeoutput">
ans =

    4.0000
    4.6144
    0.9725
    0.2241
    2.3528
         0
    0.1828
         0
         0
    0.2712

</pre><pre class="codeinput">double(A) * double(A)' * x <span class="comment">%&lt;-- Same as above but less efficient</span>
</pre><pre class="codeoutput">
ans =

    4.0000
    4.6144
    0.9725
    0.2241
    2.3528
         0
    0.1828
         0
         0
    0.2712

</pre><h2>Displaying a tenmat<a name="36"></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 sptenmat from an sptensor of size 10 x 10 x 10 x 10 with 14 nonzeros
	ans.rindices = [ 1 ] (modes of tensor corresponding to rows)
	ans.cindices = [ 2  3  4 ] (modes of tensor corresponding to columns)
	( 1,  1)	1
	( 1,  2)	1
	( 2,  1)	1
	( 2,  2)	1
	( 2,723)	0.783859
	( 3, 32)	0.986158
	( 4,647)	0.473343
	( 5,236)	0.451059
	( 5,256)	0.804517
	( 5,357)	0.828864
	( 5,775)	0.902819
	( 7,191)	0.16627
	( 7,447)	0.393906
	(10,434)	0.520757
</pre><p class="footer"><br>
            Published with MATLAB&reg; 7.2<br></p>
      </div>
      <!--
##### SOURCE BEGIN #####
%% Converting sparse tensors to matrices and vice versa
% We show how to convert a sptensor to a matrix stored in _coordinate_
% format and with extra information so that it can be converted back to a
% sptensor.

%% Creating a sptenmat (sparse tensor as sparse matrix) object
% A sparse tensor can be converted to a sparse matrix. The matrix, however,
% is not stored as a MATLAB sparse matrix because that format is sometimes
% inefficient for converted sparse tensors. Instead, the row and column
% indices are stored explicitly.
%%
% First, we create a sparse tensor to be converted.
X = sptenrand([10 10 10 10],10) %<REPLACE_WITH_DASH_DASH Generate some data.
%%
% All the same options for tenmat are available as for tenmat.
A = sptenmat(X,1) %<REPLACE_WITH_DASH_DASH Mode-1 matricization.
%%
A = sptenmat(X,[2 3]) %<REPLACE_WITH_DASH_DASH More than one mode is mapped to the columns.
%%
A = sptenmat(X,[2 3],'t') %<REPLACE_WITH_DASH_DASH Specify column dimensions (transpose).
%%
A = sptenmat(X,1:4) %<REPLACE_WITH_DASH_DASH All modes mapped to rows, i.e., vectorize.
%%
A = sptenmat(X,2) %<REPLACE_WITH_DASH_DASH By default, columns are ordered as [1 3 4].
%% 
A = sptenmat(X,2,[3 1 4]) %<REPLACE_WITH_DASH_DASH Explicit column ordering.
%%
A = sptenmat(X,2,'fc') %<REPLACE_WITH_DASH_DASH Foward cyclic.
%%
A = sptenmat(X,2,'bc') %<REPLACE_WITH_DASH_DASH Backward cyclic.
%% Constituent parts of a sptenmat
A.subs %<REPLACE_WITH_DASH_DASH Subscripts of the nonzeros.
%%
A.vals %<REPLACE_WITH_DASH_DASH The corresponding nonzero values.
%%
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 sptenmat from its constituent parts
B = sptenmat(A.subs,A.vals,A.rdims,A.cdims,A.tsize) %<REPLACE_WITH_DASH_DASH Copies A
%%
B = sptenmat(double(A),A.rdims,A.cdims,A.tsize) %<REPLACE_WITH_DASH_DASH More efficient to pass a matrix.
%% Creating a sptenmat with no nonzeros
A = sptenmat([],[],A.rdims,A.cdims,A.tsize) %<REPLACE_WITH_DASH_DASH An empty sptenmat.
%% Creating an emtpy sptenmat
A = sptenmat %<REPLACE_WITH_DASH_DASH A really empty sptenmat.
%% Use double to convert a sptenmat to a MATLAB sparse matrix
X = sptenrand([10 10 10 10],10); %<REPLACE_WITH_DASH_DASH Create a tensor.
A = sptenmat(X,1) %<REPLACE_WITH_DASH_DASH Convert it to a sptenmat
%%
B = double(A) %<REPLACE_WITH_DASH_DASH Convert it to a MATLAB sparse matrix
%%
whos A B %<REPLACE_WITH_DASH_DASH The storage for B (the sparse matrix) is larger than for A.
%%
C = B'; %<REPLACE_WITH_DASH_DASH Transposing the result fixes the problem.
whos C
%% Use full to convert a sptenmath to a tenmat
B = sptenmat(sptenrand([3 3 3], 3), 1) %<REPLACE_WITH_DASH_DASH Create a sptenmat
%%
C = full(B) %<REPLACE_WITH_DASH_DASH Convert to a tenmat
%% Use sptensor to convert a sptenmat to a sptensor
Y = sptensor(A) %<REPLACE_WITH_DASH_DASH Convert a sptenmat to a sptensor
%% Use size and tsize for the dimensions of a sptenmat
size(A) %<REPLACE_WITH_DASH_DASH Matrix size
tsize(A) %<REPLACE_WITH_DASH_DASH Corresponding tensor size
%% Subscripted reference for a sptenmat
% This is not supported beyond getting the constituent parts.
%% Subscripted assignment for a sptenmat
A(1:2,1:2) = ones(2) %<REPLACE_WITH_DASH_DASH Replace part of the matrix.
%% Use end for the last index
% End is not supported.
%% Basic operations for sptenmat
norm(A) %<REPLACE_WITH_DASH_DASH Norm of the matrix.
%%
+A %<REPLACE_WITH_DASH_DASH Calls uplus.
%%
-A %<REPLACE_WITH_DASH_DASH Calls uminus.
%% Use aatx to efficiently compute A * A' * x for a sptenmat
x = ones(10,1); %<REPLACE_WITH_DASH_DASH Create vector
aatx(A,x) %<REPLACE_WITH_DASH_DASH Compute A * A' * x
%%
double(A) * double(A)' * x %<REPLACE_WITH_DASH_DASH Same as above but less efficient
%% 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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