# ITensors indices access and manipulations **URL:** \ **Category:** ITensor Julia Questions\ **Created:** [August 22, 2023, 2:18pm UTC](https://itensor.discourse.group/t/itensors-indices-access-and-manipulations/1108 "2023-08-22T14:18:34Z")\ **Posts on this page:** 5\ **Page:** 1
**Author:** ![ste](https://avatars.discourse-cdn.com/v4/letter/s/76d3ee/32.png) [@ste](https://itensor.discourse.group/u/ste)\ **Post date:** [August 22, 2023, 2:18pm UTC](https://itensor.discourse.group/t/itensors-indices-access-and-manipulations/1108/1 "2023-08-22T14:18:34Z")
hi, thanks for the great work on itensors! I recently started playing around with it and love its features, though I have to say I’m a bit puzzled by the way tensor indices are handled, in particular, it seems to me that there’s no straightforward way of accessing and playing around with the indices of a given tensor - I understand that for a given tensor I can access those by calling `inds(A)` , but sometimes I’d like to be able to call an index with a given label, I thought the concept of ‘tags’ would be helpful there but I’m not sure what is the “recommended” way to use them in this context. A silly example, if I do the SVD of a matrix A\_{ij} and get a decomposition as U\_{iu} S\_{uv} Vd\_{vj}, is there a way to access, eg. to relabel or prime it, the “u” index in the matrix U ? The only way I could think of is to get both indices of U, and then “know” that “u” is the second one - but since labels can in principle float around (as long as they’re attached to the proper leg), I’m afraid that calling `inds(U)[2]` could give unpredictable results. Is there a way to call the index containing a “u” in its tag instead? Or say I want to extract the index of the physical leg of an MPS matrix, it would be the one containing a “Site” tag. I was digging through the documentation and I saw the `getfirst()` function, but its syntax is not clear to me (in particular what the matching function should look like, but maybe that’s my bad since I’m new to julia as well) - is that the intended way to deal with this use case? ---
**Author:** ![mtfishman](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/mtfishman/32/11_2.png) [@mtfishman](https://itensor.discourse.group/u/mtfishman)\ **Post date:** [August 22, 2023, 2:34pm UTC](https://itensor.discourse.group/t/itensors-indices-access-and-manipulations/1108/2 "2023-08-22T14:34:47Z")
Good question. Our recommended way of accessing the `u` index is through the `commonind` function, for example: ```julia i, j = Index.((2, 2)) A = randomITensor(i, j) U, S, V = svd(A, i) u = commonind(U, S) ``` Then you can use it like: ```julia dag(U) * prime(U, u) # Check if `U` is an isometry ``` More generally, you can think about sets of ITensors as networks of tensors, and usually you can uniquely determine a certain index or set of indices through the network connectivity, such as which indices are unique to a certain tensor or shared between pairs of tensors (which is how the `commonind` function is being used above). I find that I can almost always just use functions like `commonind[s]` or `uniqueind[s]` to access the indices that I want, and that is generally our goal when designing ITensor library code to make it as general as possible (as opposed to relying too much on tags to access a specific index, since then that relies on a certain convention for the names of tags which is more fragile). Often to do this properly it is helpful to have a drawing of the tensor network so you can think visually about which indices are connected to which tensors, our visualization packages like [https://github.com/ITensor/ITensors.jl/tree/main/ITensorVisualizationBase](https://github.com/ITensor/ITensors.jl/tree/main/ITensorVisualizationBase) can help with that. This network perspective on ITensors and tensor indices is one of the philosophies behind the new [GitHub - mtfishman/ITensorNetworks.jl: A package with general tools for working with higher-dimensional tensor networks based on ITensor.](https://github.com/mtfishman/ITensorNetworks.jl) package that we are developing. ---
**Author:** ![ste](https://avatars.discourse-cdn.com/v4/letter/s/76d3ee/32.png) [@ste](https://itensor.discourse.group/u/ste)\ **Post date:** [August 22, 2023, 4:05pm UTC](https://itensor.discourse.group/t/itensors-indices-access-and-manipulations/1108/3 "2023-08-22T16:05:02Z")
Thanks for the feedback! I see, indeed I had missed these [unique|common]inds functions, those are definitely helpful! But let’s say (sorry for coming up with awkward use cases) I want to compute some kind of weird “left” environment from two identical MPS, by contracting eg. an A^{[i]}\_{LRp} tensor (here I labelled the virtual Left, Right and physical legs) with itself over the legs L and p. How would I manage to single out the left (or the right) legs here ? Even if I started for simplicity from one edge where I’d have only one physical and one virtual indices, if I prime a copy of A, then all indices would get primed, even the physical one (which is something I don’t want). Would there be a clever way here to isolate a specific index without using eg. `inds(A)[1]` here ? Again, I realize this is a bit of a special scenario so probably not really your everyday use case, still I wonder if there’s some intended way of getting it in this case. ---
**Author:** ![mtfishman](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/mtfishman/32/11_2.png) [@mtfishman](https://itensor.discourse.group/u/mtfishman)\ **Post date:** [August 23, 2023, 1:37pm UTC](https://itensor.discourse.group/t/itensors-indices-access-and-manipulations/1108/4 "2023-08-23T13:37:22Z")
It’s a good question, it’s something that is really at the core of the philosophy of the ITensor library and Index system, and something we have discussed a lot internally when designing the library to come up with nice code patterns to handle those kinds of operations. How I think about it is that you shouldn’t really think of a tensor in isolation, but as part of a network. The indices are therefore defined through how they connect to neighboring tensors. So if you have an MPS `A`, you can perform various contractions of a tensor of `A` like this: ```julia n = 10 s = siteinds("S=1/2", n) A = randomMPS(s) i = 4 # Site we are interested in # Get indices of `A[i]` L = commonind(A[i - 1], A[i]) R = commonind(A[i], A[i + 1]) p = uniqueind(A[i], A[i - 1], A[i + 1]) # Could just use `p = s[i]` since we have `s` already # Contract over `L` and `p` dag(A[i]) * prime(A[i], R) # Contract over `L` only dag(A[i]) * prime(A[i], (R, p)) ``` Note that we provide shorthand functions `siteind` and `linkind`, so you could do: ```julia L = linkind(A, i - 1) R = linkind(A, i) p = siteind(A, i) ``` but those just use `commonind` and `uniqueind` internally. ---
**Author:** ![ste](https://avatars.discourse-cdn.com/v4/letter/s/76d3ee/32.png) [@ste](https://itensor.discourse.group/u/ste)\ **Post date:** [August 23, 2023, 2:56pm UTC](https://itensor.discourse.group/t/itensors-indices-access-and-manipulations/1108/5 "2023-08-23T14:56:15Z")
ok, I think I’m starting to get the philosophy behind it, makes sense! thanks a lot for the clarifications!