# Slicing tensor with QN

**URL:** <https://itensor.discourse.group/t/slicing-tensor-with-qn/878>\
**Category:** ITensor Julia Questions\
**Created:** [May 17, 2023, 10:30am UTC](https://itensor.discourse.group/t/slicing-tensor-with-qn/878 "2023-05-17T10:30:00Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![qumaciel](https://avatars.discourse-cdn.com/v4/letter/q/edb3f5/32.png) [@qumaciel](https://itensor.discourse.group/u/qumaciel)\
**Post date:** [May 17, 2023, 10:30am UTC](https://itensor.discourse.group/t/slicing-tensor-with-qn/878/1 "2023-05-17T10:30:00Z")

</div>

Hi there,

Suppose I have the following block-sparse tensor:

```julia
using ITensors

let
  A = [1.0 0.0 0.0 0.0;
       0.0 1e-9 0.0 0.0;
       0.0 0.0 2.0 3.0;
       0.0 0.0 1e-10 4.0];
		
       i = Index([QN(0)=>2, QN(1)=>2], "i");

       T = ITensor(A, i', dag(i));
end

```

Is it possible to slice `T` such that I can `@show`/manipulate the blocks corresponding to `QN(0)` or `QN(1)` individually?

Something like

```auto
B = [1.0 0.0;
     0.0 1e-9];

C = [2.0 3.0;
     1e-10 4.0];

T[(slice of block QN(0)] = B;
T[(slice of block QN(1)] = C;

#or slicing to show

@show T[(slice of block QN(0)] 

## Output: block B

```

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<div class="post-metadata">

**Author:** ![JanReimers](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/janreimers/32/171_2.png) [@JanReimers](https://itensor.discourse.group/u/JanReimers)\
**Post date:** [May 17, 2023, 2:58pm UTC](https://itensor.discourse.group/t/slicing-tensor-with-qn/878/2 "2023-05-17T14:58:41Z")

</div>

Hi qumaciel, This is a good question you are asking. In order to work with QN blocks directly like this you sometimes need to work at the NDTensors level, which is a library underneath ITensors. There may be a better way to do what you want, but here is one way:

```auto
using ITensors
import NDTensors: blockview,tensor,nzblocks
let
    B = [1.0 0.0;0.0 1e-9];
    C = [2.0 3.0;1e-10 4.0];
    i = Index([QN(0)=>2, QN(1)=>2], "i");
    T = ITensor(0.0, i', dag(i));
    blockview(tensor(T),nzblocks(T)[1]).=B
    blockview(tensor(T),nzblocks(T)[2]).=C
    @show T
end

```

In real code you cannot rely on the ordering of nzblocks(T), so you will need to add code that looks at the indices of the blocks to make sure you get the data inserted into the correct blocks.

I hope this helps.  
JR

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<div class="post-metadata">

**Author:** ![JanReimers](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/janreimers/32/171_2.png) [@JanReimers](https://itensor.discourse.group/u/JanReimers)\
**Post date:** [May 17, 2023, 3:04pm UTC](https://itensor.discourse.group/t/slicing-tensor-with-qn/878/3 "2023-05-17T15:04:29Z")

</div>

Here is an alternate method working at the ITensors level:

```auto
using ITensors
let
       iB=Index([QN(0)=>2], "iB");
       iC=Index([QN(1)=>2], "iC");
       B=ITensor([1.0 0.0;0.0 1e-9], prime(iB), dag(iB));
       C=ITensor([2.0 3.0;1e-10 4.0], prime(iC), dag(iC));
       T,Tinds=directsum(B=>inds(B),C=>inds(C))
       @show dense(T) 
end

```

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<div class="post-metadata">

**Author:** ![qumaciel](https://avatars.discourse-cdn.com/v4/letter/q/edb3f5/32.png) [@qumaciel](https://itensor.discourse.group/u/qumaciel)\
**Post date:** [May 18, 2023, 6:52am UTC](https://itensor.discourse.group/t/slicing-tensor-with-qn/878/4 "2023-05-18T06:52:14Z")

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Thanks @JanReimers ! I’m transitioning from C++ ITensor to julia ITensor and I’m still learning how to approach things in julia.

> [@JanReimers](#):
>
> In real code you cannot rely on the ordering of nzblocks(T), so you will need to add code that looks at the indices of the blocks to make sure you get the data inserted into the correct blocks.

Do you know what makes `nzblocks(T)` ordering unreliable?

Just a side note, look the difference between both approaches in terms of runtime and memory allocation:

```auto
# blockview approach
0.472095 seconds (774.64 k allocations: 51.870 MiB, 2.75% gc time, 99.64% compilation time)

# directsum approach
3.412558 seconds (10.92 M allocations: 712.118 MiB, 6.12% gc time, 99.88% compilation time)

```

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<div class="post-metadata">

**Author:** ![JanReimers](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/janreimers/32/171_2.png) [@JanReimers](https://itensor.discourse.group/u/JanReimers)\
**Post date:** [May 18, 2023, 2:11pm UTC](https://itensor.discourse.group/t/slicing-tensor-with-qn/878/5 "2023-05-18T14:11:52Z")

</div>

I am also transitioning from C++ to Julia … I believe the effort is worth it. Regarding nzblocks ordering: I think it is arbitrary by design, in the interests of efficiency. At any point new allowed blocks might be inserted under the hood. Also blocks can get combined or removed (if they are all zeros). It should be possible to optmize the algo for directsum to get better performance.