TensorSum
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TensorSum | |
Computes a vector or operator from its tensor decomposition | |
Other toolboxes required | none |
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Related functions | FilterNormalForm OperatorSchmidtDecomposition SchmidtDecomposition |
TensorSum is a function that computes a vector or operator from its tensor decomposition. It acts as an inverse of the OperatorSchmidtDecomposition and SchmidtDecomposition functions, but also works for multipartite decompositions.
Syntax
- TS = TensorSum(A1,A2,...)
- TS = TensorSum(S,A1,A2,...)
Argument descriptions
- A1,A2,...: 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 Ai 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 Ai will be tensored together for all k, and then the sum over k will be taken at the end.
- S (optional, default [1,1,...,1]): 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 SchmidtDecomposition
This function acts as an inverse of the SchmidtDecomposition function:
>> vec = [1,2,3,4];
>> [s,u,v] = SchmidtDecomposition(vec);
>> TensorSum(s,u,v)
ans =
1.0000
2.0000
3.0000
4.0000
Inverse of OperatorSchmidtDecomposition
This function also acts as an inverse of the OperatorSchmidtDecomposition function:
>> 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(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
Source code
Click here to view this function's source code on github.