# ITensor

An ITensor is a tensor with named indices (of type Index). The key feature of the ITensor is automatic contraction over all matching indices, similar to Einstein summation.

An ITensor is created with a fixed number of Index objects specifying its indices.
Because Index objects carry identifying information, most of the
ITensor interface does not depend on the Index order. For example,
given an ITensor constructed with indices `a`

and `b`

,
calling `elt(T,a=2,b=5)`

and `elt(T,b=5,a=2)`

accesses the same tensor element.

In addition to real-valued storage, ITensors can have other storage types such as complex storage or various sparse storage types.

If an ITensor is constructed with regular indices (Index objects `I`

for which
`hasQNs(I)==false`

) then its storage will be dense.

If instead an ITensor is constructed with indices carrying additional quantum number (QN)
block structure (Index objects `I`

for which
`hasQNs(I)==true`

) then its storage will be block-sparse.
(Up through version 2 of ITensor, such ITensors were called IQTensors.)

The `ITensor`

class is defined in the header "itensor/itensor.h"

## Synopsis

```
auto b1 = Index(5);
auto b3 = Index(8);
auto s2 = Index(2,"Site");
auto s3 = Index(2,"Site");
auto phi = ITensor(b1,s2,s3,b3);
phi.set(b1=2,s2=1,s3=2,b3=2, -0.5);
phi.set(b1=3,s2=2,s3=1,b3=6, 1.4);
//...
auto nrm = norm(phi); //save the original norm of phi
phi /= nrm; //division by a scalar
Print(norm(phi)); //prints: 1.0
//The * operator automatically contracts all matching indices.
//The prime(phi,b3) method primes the b3 Index of the second
//ITensor in the product so it is not contracted.
ITensor rho = phi * prime(phi,b3);
Print(order(rho)); //prints 2
Print(hasIndex(rho,b3)); //prints: true
Print(hasIndex(rho,prime(b3))); //prints: true
Print(hasIndex(rho,s2)); //prints: false
```

## Constructors and Accessor Methods

`ITensor()`

Default constructor.

A default-constructed ITensor evaluates to false in a boolean context.

To construct a order-zero (scalar) ITensor use the`ITensor(Cplx val)`

constructor below.`ITensor(Index i1, Index i2, ...)`

`ITensor(std::vector<Index> inds)`

`ITensor(std::array<Index> inds)`

`ITensor(std::initializer_list<Index> inds)`

Construct an ITensor with one or more indices. All elements are initially zero. For efficiency reasons no storage is actually allocated when calling this constructor, but automatically gets allocated when, for example, setting an element.

Indices can be provided as a list or in a vector, array, or initializer_list.

Click to Show Exampleauto s1 = Index(2,"Site"); auto s2 = Index(2,"Site"); auto T = ITensor(s1,s2);

`ITensor(Cplx val)`

Construct an order-zero, scalar ITensor with its single component set to val. If the imaginary part of

`val`

is exactly zero then the storage of the ITensor will be real.

Because Real numbers automatically convert to Cplx, calling`ITensor(3.14)`

calls this constructor.Click to Show Exampleauto R = ITensor(2.71); auto C = ITensor(3+4_i);

`randomITensor(Index i1, Index i2, ...)`

`randomITensorC(Index i1, Index i2, ...)`

`randomITensor(IndexSet inds)`

Create an ITensor with the provided indices and with random elements.

`randomITensorC`

makes an ITensor with random complex elements.Click to Show Exampleauto i = Index(2); auto j = Index(3); auto T = randomITensor(i,j); auto TC = randomITensorC(i,j); Print(isComplex(TC)); //prints: true

`matrixITensor(Matrix&& M, Index i1, Index i2)`

Create an ITensor with the two indices i1 and i2, which correspond to the row and column indices of the provided Matrix. The elements of the returned ITensor are set to be those of the Matrix provided.

The Matrix M is expected to be passed as an lvalue, either by passing a temporary or by calling std::move. Its storage will be moved into the returned ITensor and the Matrix will have empty storage afterward.

Click to Show Exampleauto M = Matrix(2,2); M(0,0) = 11; M(0,1) = 12; M(1,0) = 21; M(1,1) = 22; auto r = Index(2); auto c = Index(2); auto T = matrixITensor(std::move(M),r,c);

`inds(ITensor T) -> IndexSet const&`

Return a reference to the indices of this ITensor, as an IndexSet container. This method is useful for iterating over all of the indices of an ITensor.

Click to Show Exampleauto s1 = Index(2,"Site"); auto s2 = Index(2,"Site"); auto l1 = Index(10,"Link"); auto l2 = Index(24,"Link"); auto T = ITensor(l1,s1,s2,l2); //Print out just the Link indices of T for(auto& I : inds(T)) { if(hasTags(I,"Link")) println(I); }

`explicit operator bool()`

Evaluate an ITensor in a boolean context. Evaluates to

`false`

only if an ITensor is default constructed.Click to Show Exampleauto T1 = ITensor(); if(T1) println("T1 evaluates to true"); else println("T1 evaluates to false"); //prints: T1 evaluates to false auto T2 = ITensor(s1,s2); if(T2) println("T2 evaluates to true"); else println("T2 evaluates to false"); //prints: T2 evaluates to true

## Element Access Methods

`elt(ITensor T, IndexVal iv1, IndexVal iv2, ...) -> Real`

`eltC(ITensor T, IndexVal iv1, IndexVal iv2, ...) -> Cplx`

Returns the element of the ITensor

`T`

corresponding to the provided IndexVals.An IndexVal

`iv`

is a pairing of an Index`index(iv)`

and an integer`val(iv)`

. The element returned is the one corresponding to holding`index(iv1)`

equal to`val(iv1)`

,`index(iv2)`

equal to`val(iv2)`

, etc.For

`elt(...)`

, if the element to be accessed has a non-zero imaginary part, this method throws an exception.`eltC(...)`

behaves identically to the`elt(...)`

except its return type is a complex number. It succeeds whether the ITensor has complex or real storage.Click to Show Exampleauto i = Index(4,"i"); auto j = Index(4,"j"); auto k = Index(4,"k"); //Make a scalar ITensor auto S = ITensor(2.7); //Access its value (a real number) auto rs = elt(S); //Make a random order 3 ITensor auto T = randomITensor(i,j,k); //Get one of its elements auto rt = elt(T,j=2,k=1,i=4); //Make a complex scalar ITensor auto Sc = ITensor(2.7-4_i); //Access its value as a complex number auto zs = eltC(Sc);

`elt(ITensor T, int i1, int i2, ...) -> Real`

`eltC(ITensor T, int i1, int i2, ...) -> Cplx`

Simplified version of

`elt(ITensor, IndexVal, ...)`

(or`eltC(...)`

) when the ordering of the indices of the ITensor are known. In such a case, integers can be provided instead of IndexVal objects.For example, for ITensor T with indices ordered as j,i,k,

`elt(T,1,2,4)`

is equivalent to`elt(T,j=1,i=2,k=4)`

.Note that the ordering of the indices of an ITensor can be set using the

`permute(ITensor,IndexSet)`

function.Click to Show Exampleauto i = Index(4,"i"); auto j = Index(4,"j"); auto k = Index(4,"k"); //Make a random order 3 ITensor auto T = randomITensor(i,j,k); //Order the indices T = permute(T,{k,i,j}); //Get one of its elements auto rt = elt(T,2,1,4); Print(rt==elt(T,i=1,j=4,k=2)); //prints: true

`elt(ITensor T, std::vector<int> v) -> Real`

`eltC(ITensor T, std::vector<int> v) -> Cplx`

Version of

`elt(ITensor, IndexVal, ...)`

(or`eltC(...)`

) taking a`std::vector<int>`

when the ordering of the indices of the ITensor are known. In such a case, integers can be provided instead of IndexVal objects, and in this overload of`elt`

and`eltC`

the integers can be passed in a vector (dynamically sized array).Note that the ordering of the indices of an ITensor can be set using the

`permute(ITensor,IndexSet)`

function.`.set(IndexVal iv1, IndexVal iv2, ... , Cplx z)`

Set the element of this ITensor corresponding to the provided IndexVals to the value

`z`

.If

`z`

has exactly zero imaginary part and the ITensor storage is real, it will not be switched to complex storage.Because Real numbers are automatically convertible to Cplx, one can plug Real numbers into this method.

Click to Show Example//Make an order 3 ITensor auto T = ITensor(i,j,k); //Set an element to a real number T.set(k=2,j=2,i=3, -1.24); //Set an element to a complex number T.set(k=4,j=1,i=2, 3.2-4.7_i);

`.set(int i1, int i2, ... , Cplx z)`

Shorthand notation for

`.set`

above when the ordering of the indices of the ITensor are known. For example, for ITensor T with indices ordered as j,i,k,`T.set(1,2,4, 3.2)`

is equivalent to`T.set(j=1,i=2,k=4, 3.2)`

.Note that the ordering of the indices of an ITensor can be set using the

`permute`

function described below.Click to Show Example//Make an order 3 ITensor auto T = ITensor(i,j,k); T = permute(T,j,i,k); //Set an element to a real number T.set(1,2,3,-1.24); Print(elt(T,j=1,i=2,k=3) == -1.24); //prints: true

## ITensor Prime and Tag Methods

ITensors have all of the same tagging and priming methods that are defined for IndexSets.

Note: all of the following functions listed of the form:

`.f(TagSet, ...)`

`.f(TagSet, TagSet, ...)`

`.f(int, ...)`

perform an in-place modification of the ITensor. `...`

stands for
optional arguments to specify a subset of indices of the ITensor
to apply the operation `.f()`

.

If no optional arguments are specified,

`.f()`

is applied to all indices of the input ITensor.If

`...`

is a list of indices, an IndexSet, or a collection of indices convertible to an IndexSet,`.f()`

is applied to only the specified indices.If

`...`

is a TagSet,`.f()`

is only applied to the indices in the IndexSet containing all tags in the TagSet.

Functions of the form:

`f(ITensor, TagSet, ...) -> ITensor`

`f(ITensor, TagSet, TagSet, ...) -> ITensor`

`f(ITensor, int, ...) -> ITensor`

perform the same operation as the above in-place operations and accept the same optional arguments, but do not modify the input ITensor and instead return a new, modified ITensor.

`.prime(int inc = 1, ...)`

`prime(ITensor is, int inc = 1, ...) -> ITensor`

Increment prime level of all indices by 1, or by the optional amount "inc".

Optionally, only modify the tags of the listed indices, or indices with the matching tags, as described at the top of the section.

Click to Show Exampleauto i1 = Index(2,"i,n=1"); auto i2 = Index(2,"i,n=2"); auto i3 = Index(2,"i,n=3"); auto A = randomITensor(i1,i2,i3); auto Ap = prime(A); Print(hasIndex(Ap,i1)); //prints: false Print(hasIndex(Ap,prime(i1))); //prints: true Print(hasIndex(Ap,prime(i2))); //prints: true Print(hasIndex(Ap,prime(i3))); //prints: true A.prime(2,"n=2"); Print(hasIndex(A,i1)); //prints: true Print(hasIndex(A,prime(i2,2))); //prints: true Print(hasIndex(A,i3)); //prints: true

`.setPrime(int plnew, ...)`

`setPrime(ITensor A, int plnew, ...) -> ITensor`

Set the prime level of all indices to plnew. Optionally, only set the prime levels of indices containing tags tsmatch

Optionally, only modify the tags of the listed indices, or indices with the matching tags, as described at the top of the section.

`.noPrime(...)`

`noPrime(ITensor is, ...) -> ITensor`

Set the prime level of all Index objects in the ITenssor to zero.

Optionally, only modify the tags of the listed indices, or indices with the matching tags, as described at the top of the section.

`.mapPrime(int plold, int plnew, ...)`

`mapPrime(ITensor is, int plold, int plnew, ...) -> ITensor`

Set the prime level of all indices with

`plold`

to`plnew`

.Optionally, only modify the tags of the listed indices, or indices with the matching tags, as described at the top of the section (note that if the tagset used for matching contains an integer tag different from

`plold`

, this function won't do anything).`.swapPrime(int pl1, int pl2, ...)`

`swapPrime(ITensor is, int pl1, int pl1, ...) -> ITensor`

Swap the input prime levels, such that all indices with prime level

`pl1`

have prime level`pl2`

and vice versa.Optionally, only swap the prime levels of the listed indices, or indices with the matching tags, as described at the top of the section (note that if the tagset used for matching contains an integer tag different from one of the given prime levels, indices with those prime levels won't be modified).

`.addTags(TagSet tsadd, ...)`

`addTags(ITensor is, TagSet tsadd, ...) -> ITensor`

Add the tags in TagSet

`tsadd`

to the existing tags of the indices in this ITensor.Click to Show Exampleauto i1 = Index(2,"i,n=1"); auto i2 = Index(2,"i,n=2"); auto i3 = Index(2,"i,n=3"); auto A = randomITensor(i1,i2,i3); auto isx = addTags(A,"x","n=1"); Print(hasIndex(Ax,i1)); //prints: false Print(hasIndex(Ax,addTags(i1,"x"))); //prints: false Print(hasIndex(Ax,i2)); //prints: true Print(hasIndex(Ax,i3)); //prints: true

`.removeTags(TagSet tsremove, ...)`

`removeTags(ITensor is, TagSet tsremove, ...) -> ITensor`

Remove the tags in TagSet

`tsremove`

from the existing tags of the indices in this ITensor.`.replaceTags(TagSet tsold, TagSet tsnew, ...)`

`replaceTags(ITensor is, TagSet tsold, TagSet tsnew, ...) -> ITensor`

For any index containing all of the tags in

`tsold`

, replace these tags with those in`tsnew`

.`.swapTags(TagSet ts1, TagSet ts2, ...)`

`swapTags(ITensor is, TagSet ts1, TagSet ts2, ...) -> ITensor`

For any index containing all of the tags in

`ts1`

, replace these tags with those in`ts2`

and vice versa.`.setTags(TagSet tsnew, ...)`

`setTags(ITensor A, TagSet tsnew, ...) -> ITensor`

Set the tags of the indices in this ITensor to be exactly those in the TagSet

`tsnew`

.`.noTags(...)`

`noTags(ITensor A, TagSet tsnew, ...) -> ITensor`

Remove all tags of the indices in this ITensor.

## Operators Supported By ITensors

In this section, expressions like `ITensor * ITensor -> ITensor`

are pseudocode
indicating that two ITensors can be multiplied using the `*`

operator,
and that the result will be an ITensor.

`ITensor * ITensor -> ITensor`

`ITensor *= ITensor`

Contracting product.

`A * B`

contracts (sums) over all indices common to A and B. The`*=`

version overwrites the ITensor on the left afterward.Show Exampleauto l1 = Index(4); auto s2 = Index(2,"Site"); auto s3 = Index(2,"Site"); auto l3 = Index(4); auto A = ITensor(l1,s2,s3,l3); auto B = ITensor(l1,s2,prime(s3),prime(l3)); //... set components of A and B ... auto R = A * B; //contracts l1 and s2 Print(order(R)); //prints 4, the order of R Print(hasIndex(R,s3)); //prints "true" Print(hasIndex(R,l3)); //prints "true" Print(hasIndex(R,prime(s3))); //prints "true" Print(hasIndex(R,prime(l3))); //prints "true" Print(hasIndex(R,l1)); //prints "false"

`ITensor + ITensor -> ITensor`

`ITensor - ITensor -> ITensor`

`ITensor += ITensor`

`ITensor -= ITensor`

ITensor addition and subtraction. Adds ITensors element-wise. Both ITensors must have the same set of indices, though they can be in different orders.

Important note: if the left-hand-side ITensor is default initialized, doing += or -= will assign the right-hand ITensor to it (click to see example below). This is for convenience when summing multiple ITensors in a loop.

Show Exampleauto l1 = Index(4); auto s2 = Index(2,"Site"); auto s3 = Index(2,"Site"); auto l3 = Index(4); auto A = ITensor(l1,s2,s3,l3); auto B = ITensor(l3,s3,s2,l1); //...set components of A and B... ITensor S = A + B; //sum of A and B ITensor D = A - B; //difference of A and B // // Calling += on a default-initialized ITensor // auto T1 = ITensor(); auto T2 = ITensor(l1,l2); if(not T1) print("T1 is default initialized"); T1 += T2; if(T1) print("T1 is now initialized and equals T2");

`-ITensor -> ITensor`

Negate each element of an ITensor.

`ITensor * Real -> ITensor`

`Real * ITensor -> ITensor`

`ITensor / Real -> ITensor`

`ITensor *= Real`

`ITensor /= Real`

Multiply or divide each element of an ITensor by a real scalar.

`ITensor * Cplx -> ITensor`

`Cplx * ITensor -> ITensor`

`ITensor / Cplx -> ITensor`

`ITensor *= Cplx`

`ITensor /= Cplx`

Multiply or divide each element of an ITensor by a complex scalar.

If the ITensor initially has real storage and the complex scalar has a non-zero imaginary part, the storage automatically converts to complex storage. If the complex number has exactly zero imaginary part, the ITensor will continue to have real storage.

`ITensor / ITensor -> ITensor`

`ITensor /= ITensor`

Non-contracting product (has no relationship to division).

`A / B`

creates a new tensor out of A and B by "merging" any common indices according to the rule R_{ijk}= A_{ik}B_{jk}(no sum over k). (Here i, j, and k could be individual indices or represent groups of indices.)Show Exampleauto s2 = Index(2,"Site"); auto s3 = Index(2,"Site"); auto l3 = Index(4); auto A = ITensor(s2,s3,l3); auto B = ITensor(s3,l3); //...set components of A and B... ITensor R = A / B; //merge indices s3 and l3 Print(order(R)); //prints 3, order of R Print(hasIndex(R,s2)); //prints "true" Print(hasIndex(R,s3)); //prints "true" Print(hasIndex(R,l3)); //prints "true"

`ITensor * setElt(IndexVal) -> ITensor`

`setElt(IndexVal) * ITensor -> ITensor`

`ITensor *= setElt(IndexVal)`

When multiplied by an ITensor, a setElt(IndexVal) behaves like a order-1 (single Index) ITensor whose only non-zero element is the element corresponding to the IndexVal, which has the value 1.0.

Show Exampleauto i = Index(3); auto j = Index(4); auto T = ITensor(i,j); randomize(T); auto S = T * setElt(i(2)); // Now S will have only Index j // and will correspond to the "slice" // of T with i fixed to the value 2 Print(S.elt(j=3) - T.elt(i=2,j=3)); //prints: 0.0

## Complex ITensor Methods

`.conj()`

`conj(ITensor T) -> ITensor`

Complex conjugate each element of this ITensor.

`.takeReal()`

Replace each element of this ITensor with their real part. Afterwards the ITensor will have real storage.

`.takeImag()`

Replace each element of this ITensor with their imaginary part. Afterwards the ITensor will have real storage.

`.dag()`

`dag(ITensor T) -> ITensor`

Complex conjugate each element of this ITensor. Same as

`.conj()`

but useful for interface compatibility with IQTensor.

## Elementwise Transformation Methods

`.fill(Cplx z)`

Replace all elements with the number z. If z has zero imaginary part, the ITensor will have real storage afterward. Note that Real scalars automatically convert to Cplx so this method can be used for either type.

Click to Show Exampleauto T = ITensor(i,j,k); T.fill(1.); T.fill(2.+3._i); PrintData(T);

`.generate(Func f)`

Set each element of this ITensor by repeatedly calling the function

`f()`

.For example, if

`f`

is a random number generator, then the ITensor elements will be randomized by calling`f`

once for each element.Click to Show Exampleauto T = ITensor(i,j,k); //create a lambda function //which return a scalar auto c = 1.0; auto countUp = [&c]() { return c++; }; T.generate(countUp); PrintData(T);

`.apply(Func f)`

Transform this ITensor by applying the function

`f`

to each element and replacing the element with the return value of`f`

.If the ITensor has real storage, the function

`f`

is only required to accept Real arguments (accepting a Cplx argument works too since Real is automatically convertible to Cplx).Click to Show Exampleauto T = ITensor(i,j,k); randomize(T); //create a lambda function //which returns the square of its argument auto square = [](Real r) { return r*r; }; T.apply(square); PrintData(T);

`.visit(Func f)`

Apply the function

`f`

to each element of this ITensor. Calling`visit`

has no effect on an ITensor but is useful for inspecting each element. For example, it could be print elements meeting a certain criterion.Click to Show Exampleauto T = ITensor(i,j,k); randomize(T); //create a lambda function //which remembers the largest //magnitude number given to it Real max_mag = 0.; auto maxComp = [&max_mag](Real r) { if(std::fabs(r) > max_mag) max_mag = std::fabs(r); }; T.visit(maxComp); println("Largest magnitude elt of T is ",max_mag);

## Other Facts About ITensors

An ITensor

`T`

can be read from or written to a stream using`read(s,T)`

or`write(s,T)`

.Printing an ITensor shows its indices and some other information such as its norm.

To view all non-zero elements of an ITensor

`T`

, do one of the following:PrintData(T);

printfln("T = %f",T);

In the

`printfln`

command, the`%s`

formatting token does not display ITensor elements, whereas the`%f`

token shows all non-zero elements.

## Functions for Modifying ITensors

`.randomize(Args args = Args::global())`

Randomize all elements the ITensor T. Optimized more for speed than for true randomness. Afterward all elements will be real by default.

Optionally

`.randomize()`

accepts a named argument "Complex" which if set to`true`

will make the ITensor have random complex elements.Click to Show Exampleauto T = ITensor(i,j,k); T.randomize(T); T.randomize({"Complex",true});

## Functions for Transforming ITensors

`apply(ITensor T, Func f) -> ITensor`

Return the ITensor resulting from transforming each element of T by calling

`f(x) -> y`

. Works similarly to the`.apply`

method discussed above but creates a new ITensor instead of modifying an ITensor in-place.`permute(ITensor T, IndexSet is) -> ITensor`

`permute(ITensor T, Index i1, Index i2, ...) -> ITensor`

Given an ITensor T and an IndexSet or list of all of its indices in a particular order, return an ITensor with indices in that order. The data of the output ITensor is the appropriate permutation of the data of the ITensor T.

Click to Show Exampleauto T = randomITensor(i,j,k); auto Tp = permute(T,{j,i,k}); Print(elt(Tp,1,2,4) == elt(Tp,j=1,i=2,k=4)); //prints "true"

`random(ITensor T, Args args = Args::global()) -> ITensor`

Return a new ITensor with the same indices as T but with randomized, real elements.

Optionally

`random`

accepts a named argument "Complex" which if set to`true`

will make the returned ITensor have random complex elements.Click to Show Exampleauto T = ITensor(i,j,k); auto RT = random(T); auto CT = random(T,{"Complex",true});

`realPart(ITensor T) -> ITensor`

Return just the real part of an ITensor T.

`imagPart(ITensor T) -> ITensor`

Return just the imaginary part of an ITensor T.

## Extracting Properties of ITensors

`order(ITensor T) -> long`

Return the order (number of indices) of the ITensor T.

Click to Show Exampleauto s1 = Index(2,"Site"); auto s2 = Index(2,"Site"); auto T = ITensor(s1,s2); Print(order(T)); //prints: order(T) = 2

`maxDim(ITensor T) -> long`

Return the maximum dimension of all indices in the ITensor.

`minDim(ITensor T) -> long`

Return the minimum dimension of all indices in the ITensor.

`norm(ITensor T) -> Real`

Return the Euclidean norm of this ITensor (the square root of the sum of squares of its elements). Equivalent to, but much more efficient than,

`sqrt(real(eltC(dag(T)*T)))`

`isReal(ITensor T) -> bool`

Return

`true`

if the ITensor has real valued storage, otherwise`false`

.`isComplex(ITensor T) -> bool`

Return

`true`

if the ITensor has complex valued storage, otherwise`false`

. Returns true even if the norm of the imaginary part happens to be zero.`sumels(ITensor const& T) -> Real`

`sumelsC(ITensor const& T) -> Cplx`

Return the sum of all elements of this ITensor. If the ITensor has a non-zero imaginary part, throws an exception.

For a function that works for real or complex ITensors, use

`sumelsC`

.

## Analyzing ITensor Indices

`hasInds(ITensor T, IndexSet is) -> bool`

Returns

`true`

if ITensor`T`

has all of the indices in the IndexSet`is`

`hasIndex(ITensor T, Index i) -> bool`

Returns

`true`

if ITensor T has an Index exactly matching`i`

(including its tags).`findInds(ITensor T, TagSet tsmatch) -> IndexSet`

Find all indices of the ITensor containing tags in the specified TagSet.

`findIndex(ITensor T, TagSet tags) -> Index`

Return the first Index of T that contains tags in

`tags`

. If no such Index is found, returns a default-constructed Index (which evaluates to`false`

in a boolean context).If more than one Index is found, throws an error.

Click to Show Exampleauto s = Index(3,"Site"); auto l = Index(10,"Link"); auto T = ITensor(s,l); auto x = findIndex(T,"Site"); if(x) println("Found Index with tag Site: ",x); auto y = findIndex(T,"x"); if(!y) println("T does not have an Index with tag x");

`commonInds(ITensor A, ITensor B[, TagSet tags]) -> IndexSet`

Return the indices found on both ITensors A and B. If A and B have no Index in common, returns a default constructed IndexSet (one with no Indices).

If the optional TagSet

`tags`

is provided, only common Indices with the specified tags will be returned.Click to Show Exampleauto i = Index(2,"i"); auto j = Index(2,"j"); auto k = Index(2,"k"); auto l = Index(2,"l"); auto A = ITensor(i,j,k); auto B = ITensor(j,k,l); auto c = commonInds(A,B); Print(hasSameInds(c,{i,j})); //prints: true

`commonIndex(ITensor A, ITensor B[, TagSet tags]) -> Index`

Return the Index found on both A and B. If A and B have no Index in common, returns a default constructed Index (which will evaluate to

`false`

in a boolean context). Throws an error if more than one index is found (if A and B may have more than one common Index, consider using the function`commonInds`

).If the optional TagSet

`tags`

is provided, only the common Index with the specified tags will be returned if found.Click to Show Exampleauto A = ITensor(i,j,k); auto B = ITensor(k,m,n); auto c = commonIndex(A,B); if(c) println("Common Index of A and B is ",c);

`uniqueInds(ITensor A, ITensor B) -> IndexSet`

`uniqueInds(ITensor A, std::vector<ITensor> const& B) -> IndexSet`

`uniqueInds(ITensor A, std::initializer_list<ITensor> B) -> IndexSet`

Return all indices of A not found in ITensor B (or not found in a vector of ITensors).

`uniqueIndex(ITensor A, ITensor B[, TagSet tsmatch]) -> Index`

`uniqueIndex(ITensor A, std::vector<ITensor> B[, TagSet tsmatch]) -> Index`

`uniqueIndex(ITensor A, std::initializer_list<ITensor> B[, TagSet tsmatch]) -> Index`

Return the Index of A not found in ITensor B (or not found in a vector of ITensors). Optionally, return the unique Index of the specified TagSet

`tsmatch`

.If all of A's indices are also present on the other ITensors provided, this function returns a default constructed Index (which will evaluate to

`false`

in a boolean context).If more than one Index is found, throw an error (and consider using

`uniqueInds`

instead).Click to Show Exampleauto A = ITensor(i,j,k,l); auto B = ITensor(k,j); auto C = ITensor(l); auto u = uniqueIndex(A,{B,C}); Print(u == i); //prints "true"

## Other Functions

`multSiteOps(ITensor A, ITensor B) -> ITensor`

Multiply two operators whose index structure follows the ITensor convention for operators.

A and B are expected to have indices with a "Site" tag s1, s2, s3, ... and s1', s2', s3', ... and no other indices with a "Site" tag.

This function:

- Increments the prime level of A's "Site" indices by 1
- Contracts A with B
- Maps all "Site" indices with prime level 2 back to prime level 1.

Click to Show Exampleauto s1 = Index(3,"Site"); auto s2 = Index(3,"Site"); auto A = ITensor(s1,s2,prime(s1),prime(s2)); auto B = ITensor(s1,s2,prime(s1),prime(s2)); //...set elements of A and B... auto C = multSiteOps(A,B); //ASCII art drawing: s1'' s2'' | | s1'' s2'' s1' s2' [ A ] | | | | | | = [ C ] -> [ C ] [ B ] | | | | | | s1 s2 s1 s2 s1 s2

`.replaceInds(IndexSet is1, IndexSet is2)`

`replaceInds(ITensor T, IndexSet is1, IndexSet is2) -> ITensor`

Search the input ITensor for the indices in IndexSet

`is1`

. For any Index`i`

in`is1`

found in the ITensor, replace with the corresponding index in`is2`

(i.e., if`i`

is the 3rd index in`is1`

and is found in ITensor`T`

, it is replaced by`is2(3)`

).Any indices of the ITensor not listed in

`is1`

are left unchanged.Note that for ITensors with QN conservation, the directions of the indices are kept the same as the original ones.

Click to Show Exampleauto s1 = Index(2,"Site,s=1"); auto s2 = Index(2,"Site,s=2"); auto s3 = Index(2,"Site,s=3"); auto s4 = Index(2,"Site,s=4"); auto T12 = randomITensor(s1,prime(s1),s2,prime(s2)); auto T34 = replaceInds(T12,{s1,s2,prime(s1),prime(s2)},{s3,s4,prime(s3,2),prime(s4,2)}); //ASCII art drawing: s1' s2' s3'' s4'' | | | | [T12] -> [T34] | | | | s1 s2 s3 s4

`.swapInds(IndexSet is1, IndexSet is2)`

`swapInds(ITensor T, IndexSet is1, IndexSet is2) -> ITensor`

Swap the indices

`is1`

with the indices`is2`

in the ITensor.This is the same as calling

`.replaceInds({is1,is2},{is2,is1})`

.Click to Show Exampleauto s1 = Index(2,"Site,s=1"); auto s2 = Index(2,"Site,s=2"); auto T12 = randomITensor(s1,prime(s1),s2,prime(s2)); auto T21 = swapInds(T12,{s1,prime(s1)},{s2,prime(s2)}); //ASCII art drawing: s1' s2' s2' s1' | | | | [T12] -> [T21] | | | | s1 s2 s2 s1

## Advanced / Developer Methods

`.store() -> storage_ptr&`

Access the storage pointer, which is of an opaque "box" type called

`ITData`

. Useful for writing new methods that "dynamically overload" on the storage type using the doTask system.`ITensor(IndexSet iset, StorageType&& store, LogNum scale = 1.)`

`ITensor(IndexSet iset, storage_ptr&& pstore, LogNum scale = 1.)`

Construct an ITensor having IndexSet

`iset`

, storage`dat`

, and optional scale. The storage object must be a temporary or moved using`std::move`

. The type of the storage object must be one of the registered types in "itensor/itdata/storage_types.h".Alternatively a

`storage_ptr`

can be passed instead of a storage object.

*This page current as of version 3.0.0*

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