Combiner ITensor

A combiner is a type of ITensor used to "reshape" several indices into one Index whose size is the product of the smaller indices. The same combiner can be used to reverse this process.

To construct a combiner ITensor, call the combiner method with the indices you want to combine as arguments.

To retrieve the "combined" index that results from merging all of the indices provided, use the combinedIndex` function (see below).

Internally, a combiner is implemented as a type of ITensor with a special storage type. This storage performs no allocation of any elements whatsoever; when a combiner ITensor is contracted with another ITensor, special optimized routines are called to reshape the regular ITensor into the resulting ITensor with combined indices as efficiently as possible.

Synopsis

auto i = Index(3);
auto j = Index(5);
auto k = Index(7);
auto l = Index(9);

auto T = randomITensor(i,j,k,l);

auto [C,c] = combiner(i,k);

//
// Combine
// 
auto cT = C * T; //or T * C, which has same effect

Print(hasindex(cT,i)); //prints: false
Print(hasindex(cT,j)); //prints: true
Print(hasindex(cT,k)); //prints: false
Print(hasindex(cT,l)); //prints: true
Print(hasindex(cT,c)); //prints: true

Print(order(cT)); //prints: 3

Print(c == commonIndex(C,cT)); //prints: true

Print(dim(c)); //prints 21 = 7*3

//
// Uncombine
// 
auto nT = cT * C;

//Check that nT == T
Print(norm(nT-T)); //prints: 0.0

Specification

• combiner(IndexSet is, Args args = Args::global()) -> std::tuple<ITensor,Index>

  combiner(Index i1, Index i2, ...) -> std::tuple<ITensor,Index>

  Given an IndexSet, a container convertible to IndexSet, or a list of one or more indices, return a combiner ITensor which can be used to combine these indices into a single, new Index c, as well as the new Index c, in a tuple.

  The resulting ITensor will have all of the indices provided, plus one new Index c whose size is the product of sizes dim(is(1)) * dim(is(2)) * ....

  The first version also recognizes the following optional named arguments:

  • "Tags" (default: "Link,CMB") — set the tags of the new, combined Index

Related functions

• combinedIndex(ITensor C) -> Index

  Returned the "combined" index of the combiner C. This is the new Index that C has which resulted from merging the indices passed to the combiner function.

  In debug mode, performs a run-time check that the ITensor C actually has combiner storage as it should. If this is not the case, an exception is thrown.

This page current as of version 3.0.0