TensorSum - Revision history

Nathaniel: Minor update

2014-12-19T18:03:10Z

Minor update

Nathaniel at 15:01, 22 September 2014

2014-09-22T15:01:25Z

Nathaniel at 14:22, 20 September 2014

2014-09-20T14:22:24Z

Nathaniel at 02:49, 25 June 2013

2013-06-25T02:49:06Z

Nathaniel: Created page with "{{Function |name=TensorSum |desc=Computes a vector or operator from its tensor decomposition |rel=OperatorSchmidtDecomposition
SchmidtDecomposition |upd=November ..."

2012-12-03T14:56:47Z

Created page with "{{Function |name=TensorSum |desc=Computes a vector or operator from its tensor decomposition |rel=OperatorSchmidtDecomposition<br />SchmidtDecomposition |upd=November ..."

New page

{{Function
|name=TensorSum
|desc=Computes a vector or operator from its tensor decomposition
|rel=[[OperatorSchmidtDecomposition]]<br />[[SchmidtDecomposition]]
|upd=November 28, 2012
|v=1.00}}
<tt>'''TensorSum'''</tt> is a [[List of functions|function]] that computes a vector or operator from its tensor decomposition. It acts as an inverse of the <tt>[[OperatorSchmidtDecomposition]]</tt> and <tt>[[SchmidtDecomposition]]</tt> functions, but also works for multipartite decompositions.

==Syntax==
* <tt>TS = TensorSum(A1,A2,...)</tt>
* <tt>TS = TensorSum(S,A1,A2,...)</tt>

==Argument descriptions==
* <tt>A1,A2,...</tt>: Either matrices or cells containing matrices (and they should all be the same: either all matrices or all cells). If they are matrices, then the k-th column of each <tt>Ai</tt> will be tensored together for all k, and then the sum over k will be taken at the end. If they are cells, then the k-th element of each <tt>Ai</tt> will be tensored together for all k, and then the sum over k will be taken at the end.
* <tt>S</tt> (optional, default <tt>[1,1,...,1]</tt>): A vector of weights (such as Schmidt coefficients) that will be applied when summing the terms at the end of the computation.

==Examples==
===Inverse of <tt>[[SchmidtDecomposition]]</tt>===
This function acts as an inverse of the <tt>SchmidtDecomposition</tt> function:
<pre<noinclude></noinclude>>
>> vec = [1,2,3,4];
>> [s,u,v] = [[SchmidtDecomposition|SchmidtDecomposition(vec)]];
>> TensorSum(s,u,v)

ans =

1.0000
2.0000
3.0000
4.0000
</pre<noinclude></noinclude>>

===Inverse of <tt>[[OperatorSchmidtDecomposition]]</tt>===
This function also acts as an inverse of the <tt>OperatorSchmidtDecomposition</tt> function:
<pre<noinclude></noinclude>>
>> X = reshape(1:16,4,4)'

X =

1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16

>> [s,U,V] = [[OperatorSchmidtDecomposition|OperatorSchmidtDecomposition(X)]];
>> TensorSum(s,U,V)

ans =

1.0000 2.0000 3.0000 4.0000
5.0000 6.0000 7.0000 8.0000
9.0000 10.0000 11.0000 12.0000
13.0000 14.0000 15.0000 16.0000
</pre<noinclude></noinclude>>

@@ Line 4: / Line 4: @@
 |rel=[[FilterNormalForm]]<br />[[OperatorSchmidtDecomposition]]<br />[[SchmidtDecomposition]]
 |cat=[[List of functions#Basic_operations|Basic operation]]
-|upd=November 28, 2012
+|upd=December 19, 2014}}
 <tt>'''TensorSum'''</tt> is a [[List of functions|function]] that computes a vector or operator from its tensor decomposition. It acts as an inverse of the <tt>[[OperatorSchmidtDecomposition]]</tt> and <tt>[[SchmidtDecomposition]]</tt> functions, but also works for multipartite decompositions.

@@ Line 3: / Line 3: @@
 |desc=Computes a vector or operator from its tensor decomposition
 |rel=[[FilterNormalForm]]<br />[[OperatorSchmidtDecomposition]]<br />[[SchmidtDecomposition]]
 |upd=November 28, 2012
-|v=1.00}}
+|v=0.50}}
 <tt>'''TensorSum'''</tt> is a [[List of functions|function]] that computes a vector or operator from its tensor decomposition. It acts as an inverse of the <tt>[[OperatorSchmidtDecomposition]]</tt> and <tt>[[SchmidtDecomposition]]</tt> functions, but also works for multipartite decompositions.