## Learn to Use ITensor

# 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 `T.real(a(2),b(5))`

and `T.real(b(5),a(2))`

accesses the same tensor element.

In addition to the default dense real storage, ITensors can have other storage types such as complex storage or various sparse storage types.

The type `ITensor`

is defined in the header "itensor/itensor.h"; also see "itensor/itensor_interface.h" and "itensor/itensor_interface_impl.h".

## Synopsis

```
auto b1 = Index("bond 1",5);
auto b3 = Index("bond 3",8);
auto s2 = Index("site 2",2,Site);
auto s3 = Index("site 3",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(rank(rho)); //prints 2
Print(hasindex(rho,b3)); //prints: true
Print(hasindex(rho,prime(b3))); //prints: true
Print(hasindex(rho,b2)); //prints: false
```

## Constructors and Accessor Methods

`ITensor()`

Default constructor.

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

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

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

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.

Click to Show Exampleauto s1 = Index("Site 1",2,Site); auto s2 = Index("Site 2",2,Site); auto T = ITensor(s1,s2);

`ITensor(Cplx val)`

Construct a rank 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);

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

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

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

Construct an ITensor with indices provided in a vector, array, or initializer_list. All elements are initially set to zero.

`.r() -> int`

Return rank (number of indices) of this ITensor.

Click to Show Exampleauto s1 = Index("Site 1",2,Site); auto s2 = Index("Site 2",2,Site); auto T = ITensor(s1,s2); Print(T.r()); //prints: T.r() = 2

`.inds() -> 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("Site 1",2,Site); auto s2 = Index("Site 2",2,Site); auto l1 = Index("Link 1",10,Link); auto l2 = Index("Link 2",24,Link); auto T = ITensor(l1,s1,s2,l2); //Print out just the Link indices of T for(auto& I : T.inds()) { if(I.type() == 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

`.real(IndexVal iv1, IndexVal iv2, ...) -> Real`

Return the element of this ITensor corresponding to the provided IndexVals as a Real number.

An IndexVal

`iv`

is a pairing of an Index`iv.index`

and an integer`iv.val`

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

equal to`iv1.val`

;`iv2.index`

equal to`iv2.val`

; etc.If the element to be accessed as a non-zero imaginary part, this method throws an exception.

Click to Show Example//Make a scalar ITensor auto S = ITensor(2.7); //Access its value as a real number auto rs = S.real(); //Make a random rank 3 ITensor auto T = ITensor(i,j,k); randomize(T); //Get one of its elements auto rt = T.real(j(2),k(1),i(4));

`.real(int i1, int i2, ...) -> Real`

Shorthand notation for

`.real`

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.real(1,2,4)`

is equivalent to`T.real(j(1),i(2),k(4))`

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

`order`

function described below.Click to Show Example//Make a random rank 3 ITensor auto T = ITensor(i,j,k); randomize(T); //Order the indices T = order(T,k,i,j); //Get one of its elements auto rt = T.real(2,1,4); //Equivalent to T.real(k(2),i(1),j(4))

`.cplx(IndexVal iv1, IndexVal iv2, ...) -> Cplx`

Return the element of this ITensor corresponding to the provided IndexVals as a Cplx number.

This method behaves identically to the

`.real`

method described above, except its return type is a complex number. It succeeds whether the ITensor has complex or real storage.Click to Show Example//Make a complex scalar ITensor auto S = ITensor(2.7-4_i); //Access its value as a complex number auto zs = S.cplx();

`.cplx(int i1, int i2, ...) -> Cplx`

Shorthand notation for

`.cplx`

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.cplx(1,2,4)`

is equivalent to`T.cplx(j(1),i(2),k(4))`

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

`order`

function described below.`.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 a rank 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

`order`

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

## Prime Level Methods

`.noprime(IndexType type = All)`

Set the prime level of all indices to zero. (Optionally only those matching the specified IndexType.)

`.noprime(IndexType type1, IndexType type2, ...)`

Set the prime level of all indices matching the specified IndexTypes to zero.

`.prime(int inc = 1)`

Increment the prime level of all indices by 1, or an optional amount

`inc`

.`.prime(Index i1, Index i2, ..., int inc = 1)`

Increment the prime level of the specified indices by 1, or by an optional amount

`inc`

.`.prime(IndexType type1, IndexType type2, ..., int inc = 1)`

Increment the prime level of all indices of the specified types by 1, or by an optional amount

`inc`

.`.primeExcept(Index i1, Index i2, ..., int inc = 1)`

Increment the prime level of all indices,

*except*those specified, by 1, or by an optional amount`inc`

.`.primeExcept(IndexType type1, IndexType type2, ..., int inc = 1)`

Increment the prime level of all indices,

*except*those matching the specified types, by 1, or by an optional amount`inc`

.`.mapprime(int plevold, int plevnew, IndexType type = All)`

Change the prime level of all indices of level

`plevold`

to have level`plevnew`

.This applies to all indices by default. The optional argument

`type`

can be used to map only indices of a certain IndexType (such as Site or Link).`.mapprime(int plevold, int plevnew, IndexType type = All)`

Change the prime level of all indices of level

`plevold`

to have level`plevnew`

.This applies to all indices by default. The optional argument

`type`

can be used to map only indices of a certain IndexType (such as Site or Link)..mapprime(..., IndexType t, int oldtlev, int newtlev, ... Index i, int oldilev, int newilev, ...)

This version of mapprime takes an unlimited arguments, but arguments must come in groups of three, either

`IndexType t, int oldtlev, int newtlev`

or`Index i, int oldilev , int newilev`

For arguments of type 1, all indices of

`IndexType t`

with prime level`oldtlev`

have their prime level changed to`newtlev`

.For arguments of type 2, if a copy of

`Index i`

is found with prime level`oldilev`

, it is changed to prime level`newilev`

.The operation of this function is such that each Index of the ITensor is visited only once, and compared to all of the arguments from left to right until there is a match. If so, the Index is modified and then the function proceeds to the next Index of the ITensor.

Click to Show Exampleauto b1 = Index("bond 1",5,Link); auto b3 = Index("bond 3",8,Link); auto s2 = Index("Site 2",2,Site); auto s3 = Index("Site 3",2,Site); auto T = ITensor(b1,prime(b3,2),s2,s3); T.mapprime(Site,0,4,b3,2,5); //Now s2 and s3 will have prime level 4 //and b3 will have prime level 5

## 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("link 1",4); auto s2 = Index("Site 2",2,Site); auto s3 = Index("Site 3",2,Site); auto l3 = Index("link 3",4); auto A = ITensor(l1,s2,s3,l3); auto B = ITensor(l1,s2,prime(s3),prime(l3)); //... set components of A and B ... ITensor R = A * B; //contracts l1 and s2 Print(rank(R)); //prints 4, the rank 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("link 1",4); auto s2 = Index("Site 2",2,Site); auto s3 = Index("Site 3",2,Site); auto l3 = Index("link 3",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("Site 2",2,Site); auto s3 = Index("Site 3",2,Site); auto l3 = Index("link 3",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(rank(R)); //prints 3, rank of R Print(hasindex(R,s2)); //prints "true" Print(hasindex(R,s3)); //prints "true" Print(hasindex(R,l3)); //prints "true"

`ITensor * IndexVal -> ITensor`

`IndexVal * ITensor -> ITensor`

`ITensor *= IndexVal`

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

In other words, an IndexVal behaves as if it has been plugged into the setElt function before being contracted.

Note that multiplying an IndexVal by another IndexVal or multiplying an IndexVal by a scalar also results in an ITensor. For more information, see the IndexVal documentation.

Show Exampleauto i = Index("i",3); auto j = Index("j",4); auto T = ITensor(i,j); randomize(T); auto S = T * 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.real(j(3)) - T.real(i(2),j(3))); //prints: 0.0

## Complex ITensor Methods

`.conj()`

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()`

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.To iterate over all non-zero elements of an ITensor

`T`

, use`iterInds(T)`

to obtain an iterator returning a`std::vector<IndexVal>`

for each non-zero element. The order of the`IndexVal`

obtained in the vectors will follow the same internal order of indices in the tensor.This can be helpful when dealing with tensor slices or other structural manipulations of tensors when paired with

`.set()`

,`.real()`

,`.cplx()`

, which take such vectors as arguments.

## Functions for Creating ITensors

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

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

`randomTensor(IndexSet inds)`

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

`randomTensorC`

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

`matrixTensor(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("r",2); auto c = Index("c",2); auto T = matrixTensor(std::move(M),r,c);

## Functions for Modifying ITensors

`randomize(ITensor & T, 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); randomize(T); randomize(T,{"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.`order(ITensor T, Index i1, Index i2, ...) -> ITensor`

Given an ITensor T and a 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 = ITensor(i,j,k); randomize(T); T = order(T,j,i,k); Print(T.real(1,2,4) == T.real(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});

`conj(ITensor T) -> ITensor`

`dag(ITensor T) -> ITensor`

Return the complex conjugate of T.

`dag(T)`

has the same result as`conj(T)`

and is defined for interface compatibility with IQTensor.`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.

## ITensor Prime Level Transformations

`swapPrime(ITensor T, int plev1, int plev2) -> ITensor`

Return a copy of the ITensor T modified such that any Index having prime level

`plev1`

now has`plev2`

and any Index having prime level`plev2`

has`plev1`

.Any Index with a prime level other than

`plev1`

or`plev2`

remains unchanged.Click to Show Exampleauto T = ITensor(i,prime(i)); T.set(i(1),prime(i)(2), 12); T.set(i(2),prime(i)(1), 21); auto TT = swapPrime(T,0,1); Print(T.real(i(1),prime(i)(2))); //prints: 21 Print(T.real(i(2),prime(i)(1))); //prints: 12

For the following functions, the symbol `...`

is pseudocode
which signifies these functions forward their arguments
internally to the ITensor class method with the same name.

See the ITensor prime level methods for details about the possible arguments to these functions.

`prime(ITensor T, ...) -> ITensor`

Return a copy of T, calling

`.prime(...)`

on this copy before returning it.`primeExcept(ITensor T, ...) -> ITensor`

Return a copy of T, calling

`.primeExcept(...)`

on this copy before returning it.`noprime(ITensor T, ...) -> ITensor`

Return a copy of T, calling

`.noprime(...)`

on this copy before returning it.`mapprime(ITensor T, ...) -> ITensor`

Return a copy of T, calling

`.mapprime(...)`

on this copy before returning it.

## Extracting Properties of ITensors

`rank(ITensor T) -> long`

`ord(ITensor T) -> long`

Return the number of indices of 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.`norm() -> 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((T*T).real())`

.For complex ITensors, it is equivalent to

`sqrt((dag(T)*T).cplx().real())`

`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

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

Returns

`true`

if ITensor T has an Index exactly matching`i`

(including its prime level).`findtype(ITensor T, IndexType type) -> Index`

Return the first Index of T whose IndexType matches

`type`

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

in a boolean context).Click to Show Exampleauto s = Index("s",3,Site); auto l = Index("l",10,Link); auto T = ITensor(s,l); auto x = findtype(T,Site); if(x) println("Found Site Index ",x); auto y = findtype(T,MyType); if(!y) println("T does not have a MyType Index");

`commonIndex(ITensor A, ITensor B, IndexType t = All) -> Index`

Return the first 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).If the optional IndexType

`t`

is provided, only a common Index of that type 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);

`uniqueIndex(ITensor A, ITensor B, IndexType t = All) -> Index`

Return the first Index of A found NOT to be on B.

If all of A's indices are also present on B, returns a default constructed Index (which will evaluate to

`false`

in a boolean context).If the optional IndexType

`t`

is provided, only a unique Index of that type will be returned if found.Click to Show Exampleauto A = ITensor(i,j); auto B = ITensor(k,j); auto u = uniqueIndex(A,B); Print(u == i); //prints "true"

`uniqueIndex(ITensor A, ITensor B, ITensor C, ...) -> Index`

Return the first Index of A found NOT to be on the ITensors B, C, ... (up to any number of additional tensors provided).

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).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"

`findindex(ITensor T, Cond c) -> Index`

Return the first Index of T for which the condition function

`c(i)`

returns`true`

. If no Index matches the condition, returns a default-constructed Index (which evaluates to`false`

in a boolean context).Click to Show Exampleauto s = Index("s",3,Site); auto l = Index("l",10,Link); auto T = ITensor(s,l); auto sizeIs3 = [](Index const& i) { return i.m()==3; }; auto x = findindex(T,sizeIs3); if(x) printfln("Found Index %s with size of 3",x);

## 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

`Site`

type indices s1, s2, s3, ... and indices s1', s2', s3', ... and no othe`Site`

indices.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("s1",3,Site); auto s2 = Index("s2",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' [ A ] | | | | = [ C ] [ B ] | | | | s1 s2 s1 s2

- Increments the prime level of A's

`reindex(ITensor T, Index old1, Index new1, Index old2, Index new2, ...) -> ITensor`

Given an ITensor T which has indices

`old1`

,`old2`

, and possibly other indices or other copies of`old1`

etc. with various prime levels, this function returns a new ITensor with the same components but with`old1`

replaced by`new1`

,`old2`

replaced by`new2`

, etc. This includes all different copies of the old indices which might be part of the index set with various prime levels. Any other indices of T which are not mentioned in the arguments to`reindex`

are left unchanged.Click to Show Exampleauto s1 = Index("s1",2,Site); auto s2 = Index("s2",2,Site); auto s3 = Index("s3",2,Site); auto s4 = Index("s4",2,Site); auto T12 = ITensor(s1,prime(s1),s2,prime(s2)); auto T34 = reindex(T12,s1,s3,s2,s4); //ASCII art drawing: s1' s2' s3' s4' | | | | [T12] -> [T34] | | | | s1 s2 s3 s4

## 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 2.1.1*

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