d_ktensor_doc.html

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	Y.core is a sparse tensor of size 2 x 2 x 2 with 2 nonzeros
	(1,1,1)    5.0000
	(2,2,2)    0.2500
	Y.U{1} = 
		    0.9501    0.8913
		    0.2311    0.7621
		    0.6068    0.4565
		    0.4860    0.0185
	Y.U{2} = 
		    0.8214    0.7919
		    0.4447    0.9218
		    0.6154    0.7382
	Y.U{3} = 
		    0.1763    0.9355
		    0.4057    0.9169
</pre><pre class="codeinput">norm(full(X)-full(Y)) <span class="comment">%&lt;-- They are the same.</span>
</pre><pre class="codeoutput">
ans =

  3.8057e-016

</pre><h2>Use ndims and size for the dimensions of a ktensor<a name="16"></a></h2><pre class="codeinput">ndims(X) <span class="comment">%&lt;-- Number of dimensions.</span>
</pre><pre class="codeoutput">
ans =

     3

</pre><pre class="codeinput">size(X) <span class="comment">%&lt;-- Row vector of the sizes.</span>
</pre><pre class="codeoutput">
ans =

     4     3     2

</pre><pre class="codeinput">size(X,2) <span class="comment">%&lt;-- Size of the 2nd mode.</span>
</pre><pre class="codeoutput">
ans =

     3

</pre><h2>Subscripted reference for a ktensor<a name="19"></a></h2><pre class="codeinput">X(1,1,1) <span class="comment">%&lt;-- Assemble the (1,1,1) element (requires computation).</span>
</pre><pre class="codeoutput">
ans =

    0.8529

</pre><pre class="codeinput">X.lambda(2) <span class="comment">%&lt;-- Weight of 2nd factor.</span>
</pre><pre class="codeoutput">
ans =

    0.2500

</pre><pre class="codeinput">X.U{2} <span class="comment">%&lt;-- Extract a matrix.</span>
</pre><pre class="codeoutput">
ans =

    0.8214    0.7919
    0.4447    0.9218
    0.6154    0.7382

</pre><pre class="codeinput">X{2} <span class="comment">%&lt;-- Same as above.</span>
</pre><pre class="codeoutput">
ans =

    0.8214    0.7919
    0.4447    0.9218
    0.6154    0.7382

</pre><h2>Subscripted assignment for a ktensor<a name="23"></a></h2><pre class="codeinput">X.lambda = ones(size(X.lambda)) <span class="comment">%&lt;-- Insert new multipliers.</span>
</pre><pre class="codeoutput">X is a ktensor of size 4 x 3 x 2
	X.lambda = [ 1  1 ]
	X.U{1} = 
		    0.9501    0.8913
		    0.2311    0.7621
		    0.6068    0.4565
		    0.4860    0.0185
	X.U{2} = 
		    0.8214    0.7919
		    0.4447    0.9218
		    0.6154    0.7382
	X.U{3} = 
		    0.1763    0.9355
		    0.4057    0.9169
</pre><pre class="codeinput">X.lambda(1) = 7 <span class="comment">%&lt;-- Change a single element of lambda.</span>
</pre><pre class="codeoutput">X is a ktensor of size 4 x 3 x 2
	X.lambda = [ 7  1 ]
	X.U{1} = 
		    0.9501    0.8913
		    0.2311    0.7621
		    0.6068    0.4565
		    0.4860    0.0185
	X.U{2} = 
		    0.8214    0.7919
		    0.4447    0.9218
		    0.6154    0.7382
	X.U{3} = 
		    0.1763    0.9355
		    0.4057    0.9169
</pre><pre class="codeinput">X{3}(1:2,1) = [1;1] <span class="comment">%&lt;-- Change the matrix for mode 3.</span>
</pre><pre class="codeoutput">X is a ktensor of size 4 x 3 x 2
	X.lambda = [ 7  1 ]
	X.U{1} = 
		    0.9501    0.8913
		    0.2311    0.7621
		    0.6068    0.4565
		    0.4860    0.0185
	X.U{2} = 
		    0.8214    0.7919
		    0.4447    0.9218
		    0.6154    0.7382
	X.U{3} = 
		    1.0000    0.9355
		    1.0000    0.9169
</pre><h2>Use end for the last array index.<a name="26"></a></h2><pre class="codeinput">X(3:end,1,1)  <span class="comment">%&lt;-- Calculated X(3,1,1) and X((4,1,1).</span>
</pre><pre class="codeoutput">
ans =

    3.8274
    2.8080

</pre><pre class="codeinput">X(1,1,1:end-1)  <span class="comment">%&lt;-- Calculates X(1,1,1).</span>
</pre><pre class="codeoutput">
ans =

    6.1234

</pre><pre class="codeinput">X{end}  <span class="comment">%&lt;-- Or use inside of curly braces. This is X{3}.</span>
</pre><pre class="codeoutput">
ans =

    1.0000    0.9355
    1.0000    0.9169

</pre><h2>Adding and subtracting ktensors<a name="29"></a></h2>
         <p>Adding two ktensors is the same as concatenating the matrices</p><pre class="codeinput">X = ktensor({rand(4,2),rand(2,2),rand(3,2)}) <span class="comment">%&lt;-- Data.</span>
Y = ktensor({rand(4,2),rand(2,2),rand(3,2)}) <span class="comment">%&lt;-- More data.</span>
</pre><pre class="codeoutput">X is a ktensor of size 4 x 2 x 3
	X.lambda = [ 1  1 ]
	X.U{1} = 
		    0.4289    0.6822
		    0.3046    0.3028
		    0.1897    0.5417
		    0.1934    0.1509
	X.U{2} = 
		    0.6979    0.8600
		    0.3784    0.8537
	X.U{3} = 
		    0.5936    0.8216
		    0.4966    0.6449
		    0.8998    0.8180
Y is a ktensor of size 4 x 2 x 3
	Y.lambda = [ 1  1 ]
	Y.U{1} = 
		    0.6602    0.5341
		    0.3420    0.7271
		    0.2897    0.3093
		    0.3412    0.8385
	Y.U{2} = 
		    0.5681    0.7027
		    0.3704    0.5466
	Y.U{3} = 
		    0.4449    0.7948
		    0.6946    0.9568
		    0.6213    0.5226
</pre><pre class="codeinput">Z = X + Y <span class="comment">%&lt;-- Concatenates the factor matrices.</span>
</pre><pre class="codeoutput">Z is a ktensor of size 4 x 2 x 3
	Z.lambda = [ 1  1  1  1 ]
	Z.U{1} = 
		    0.4289    0.6822    0.6602    0.5341
		    0.3046    0.3028    0.3420    0.7271
		    0.1897    0.5417    0.2897    0.3093
		    0.1934    0.1509    0.3412    0.8385
	Z.U{2} = 
		    0.6979    0.8600    0.5681    0.7027
		    0.3784    0.8537    0.3704    0.5466
	Z.U{3} = 
		    0.5936    0.8216    0.4449    0.7948
		    0.4966    0.6449    0.6946    0.9568
		    0.8998    0.8180    0.6213    0.5226
</pre><pre class="codeinput">Z = X - Y <span class="comment">%&lt;-- Concatenates as with plus, but changes the weights.</span>
</pre><pre class="codeoutput">Z is a ktensor of size 4 x 2 x 3
	Z.lambda = [ 1  1 -1 -1 ]
	Z.U{1} = 
		    0.4289    0.6822    0.6602    0.5341
		    0.3046    0.3028    0.3420    0.7271
		    0.1897    0.5417    0.2897    0.3093
		    0.1934    0.1509    0.3412    0.8385
	Z.U{2} = 
		    0.6979    0.8600    0.5681    0.7027
		    0.3784    0.8537    0.3704    0.5466
	Z.U{3} = 
		    0.5936    0.8216    0.4449    0.7948
		    0.4966    0.6449    0.6946    0.9568
		    0.8998    0.8180    0.6213    0.5226
</pre><pre class="codeinput">norm( full(Z) - (full(X)-full(Y)) ) <span class="comment">%&lt;-- Should be zero.</span>
</pre><pre class="codeoutput">
ans =

  1.7110e-016

</pre><h2>Basic operations with a ktensor<a name="33"></a></h2><pre class="codeinput">+X <span class="comment">%&lt;-- Calls uplus.</span>
</pre><pre class="codeoutput">ans is a ktensor of size 4 x 2 x 3
	ans.lambda = [ 1  1 ]
	ans.U{1} = 
		    0.4289    0.6822
		    0.3046    0.3028
		    0.1897    0.5417
		    0.1934    0.1509
	ans.U{2} = 
		    0.6979    0.8600
		    0.3784    0.8537
	ans.U{3} = 
		    0.5936    0.8216
		    0.4966    0.6449
		    0.8998    0.8180
</pre><pre class="codeinput">-X <span class="comment">%&lt;-- Calls uminus.</span>
</pre><pre class="codeoutput">ans is a ktensor of size 4 x 2 x 3
	ans.lambda = [ -1 -1 ]
	ans.U{1} = 
		    0.4289    0.6822
		    0.3046    0.3028
		    0.1897    0.5417
		    0.1934    0.1509
	ans.U{2} = 
		    0.6979    0.8600
		    0.3784    0.8537
	ans.U{3} = 
		    0.5936    0.8216
		    0.4966    0.6449
		    0.8998    0.8180
</pre><pre class="codeinput">5*X <span class="comment">%&lt;-- Calls mtimes.</span>
</pre><pre class="codeoutput">ans is a ktensor of size 4 x 2 x 3
	ans.lambda = [ 5  5 ]
	ans.U{1} = 
		    0.4289    0.6822
		    0.3046    0.3028
		    0.1897    0.5417
		    0.1934    0.1509
	ans.U{2} = 
		    0.6979    0.8600
		    0.3784    0.8537
	ans.U{3} = 
		    0.5936    0.8216
		    0.4966    0.6449
		    0.8998    0.8180
</pre><h2>Use permute to reorder the modes of a ktensor<a name="36"></a></h2><pre class="codeinput">permute(X,[2 3 1]) <span class="comment">%&lt;-- Reorders modes of X</span>
</pre><pre class="codeoutput">ans is a ktensor of size 2 x 3 x 4
	ans.lambda = [ 1  1 ]
	ans.U{1} = 
		    0.6979    0.8600
		    0.3784    0.8537
	ans.U{2} = 
		    0.5936    0.8216
		    0.4966    0.6449
		    0.8998    0.8180
	ans.U{3} = 
		    0.4289    0.6822
		    0.3046    0.3028
		    0.1897    0.5417
		    0.1934    0.1509
</pre><h2>Use arrange to normalize the factors of a ktensor<a name="37"></a></h2>
         <p>The function <tt>arrange</tt> normalizes the columns of the factors and then arranges the rank-one pieces in decreasing order of size.
         </p><pre class="codeinput">X = ktensor({rand(3,2),rand(4,2),rand(2,2)})  <span class="comment">% &lt;-- Unit weights.</span>
</pre><pre class="codeoutput">X is a ktensor of size 3 x 4 x 2
	X.lambda = [ 1  1 ]
	X.U{1} = 
		    0.8801    0.2714
		    0.1730    0.2523
		    0.9797    0.8757
	X.U{2} = 
		    0.7373    0.1991
		    0.1365    0.2987
		    0.0118    0.6614
		    0.8939    0.2844
	X.U{3} = 
		    0.4692    0.9883
		    0.0648    0.5828
</pre><pre class="codeinput">arrange(X) <span class="comment">%&lt;-- Normalized a rearranged.</span>
</pre><pre class="codeoutput">ans is a ktensor of size 3 x 4 x 2
	ans.lambda = [ 0.87781     0.73416 ]
	ans.U{1} = 
		    0.2855    0.6626
		    0.2653    0.1302