# Cannot compute dot product of ITensors due to mismatch of indices.

**URL:** <https://itensor.discourse.group/t/cannot-compute-dot-product-of-itensors-due-to-mismatch-of-indices/1839>\
**Category:** ITensor Julia Questions\
**Tags:** julia\
**Created:** [June 28, 2024, 11:55am UTC](https://itensor.discourse.group/t/cannot-compute-dot-product-of-itensors-due-to-mismatch-of-indices/1839 "2024-06-28T11:55:54Z")\
**Posts on this page:** 4\
**Page:** 1

<div class="post-metadata">

**Author:** ![Uranium92238](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/uranium92238/32/577_2.png) [@Uranium92238](https://itensor.discourse.group/u/Uranium92238)\
**Post date:** [June 28, 2024, 11:55am UTC](https://itensor.discourse.group/t/cannot-compute-dot-product-of-itensors-due-to-mismatch-of-indices/1839/1 "2024-06-28T11:55:54Z")

</div>

I am trying to write a piece of code which involves initializing entries of a matrix as dot products between ITensors. The code is shown below

```auto
function PerformDiis(R_iter_storage,p,T2_storage,R2_storage)
    B = zeros(p+1,p+1)
    Bpp = dot(R2_storage[p],R2_storage[p])
    for i in 1:p
        for j in 1:i
            # B[i,j] = SquareDot(R_iter_storage[i],R_iter_storage[j])/Bpp
            B[i,j] = dot(R2_storage[i],R2_storage[j])
            B[j,i] = B[i,j]
        end
    end
    # display(@views B[1:p,1:p])
    B[p+1, 1:p] .= -1
    B[1:p, p+1] .= -1
    B[p+1, p+1] = 0
    Id = zeros(p+1)
    Id[p+1]= -1
    C = B\Id
    pop!(C) # As C[p+1] is the Lagrange multiplier
    a_1, a_2, i_1, i_2 = inds(T2_storage[1])
    t = ITensor(zeros(size(R_iter_storage[1])),a_1,a_2,i_1,i_2)
    for i in 1:p
        t = t + C[i].*T2_storage[i]
    end
    # display(B)
    # display(C)
    return (t)
end

```

However, the line that would compute the off diagonal term throws the error

```auto
ERROR: DimensionMismatch: In scalar(T) or T[], ITensor T is not a scalar (it has indices ((dim=2|id=485|"a_1"), (dim=2|id=158|"a_2"), (dim=4|id=164|"i_1"), (dim=4|id=50|"i_2"), (dim=2|id=442|"a_1"), (dim=2|id=841|"a_2"), (dim=4|id=773|"i_1"), (dim=4|id=57|"i_2"))).
Stacktrace:
 [1] getindex
   @ ~/.julia/packages/ITensors/2Xz5q/src/itensor.jl:873 [inlined]
 [2] dot(A::ITensor, B::ITensor)
   @ ITensors ~/.julia/packages/ITensors/2Xz5q/src/itensor.jl:1932
 [3] PerformDiis(R_iter_storage::Vector{ITensor}, p::Int64, T2_storage::Vector{ITensor}, R2_storage::Vector{ITensor})
   @ Main ~/Desktop/Andreas/phase_2/julia-code/ccd/itensors/ccd-helper.jl:448
 [4] ccd_by_hand(maxitr::Int64)
   @ Main ~/Desktop/Andreas/phase_2/julia-code/ccd/itensors/ccd.jl:65
 [5] macro expansion
   @ ./timing.jl:279 [inlined]
 [6] top-level scope
   @ ~/Desktop/Andreas/phase_2/julia-code/ccd/itensors/ccd.jl:92

```

I guess that this is happening because even though the dimension of the `ITensor` `R2_storage[i]` and `R2_storage[j]` are the same, the memory location of their indices are different. Even though the names of the indices are same in both cases `a_1,a_2,a_3,a_4`. How can I possibly fix this error? As the dimensions are all same, can I make all them use the same indices so that I can do the dot product?

---

<div class="post-metadata">

**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:** [June 28, 2024, 12:51pm UTC](https://itensor.discourse.group/t/cannot-compute-dot-product-of-itensors-due-to-mismatch-of-indices/1839/2 "2024-06-28T12:51:58Z")

</div>

Can you turn your example code into something we can run ourselves, for example by also including in your script example (maybe random) ITensors that you would put into that function, and how you would call that function with those random ITensor inputs? As an example, see how I turned your previous post into a minimal runnable example here: [How to update a tensor element-wise in ITensors ? - #5 by mtfishman](https://itensor.discourse.group/t/how-to-update-a-tensor-element-wise-in-itensors/1814/5).

I’ve asked you multiple times in previous posts you have made that when you share example code that you should share code that we can run ourselves, and that is also instructed in [Please Read: Make It Easier to Help You](https://itensor.discourse.group/t/please-read-make-it-easier-to-help-you/7) which I have pointed out to you to read multiple times. What that means is that we should be able to copy and paste your code exactly as you have written it, and it will run on our computers, say if we copy and paste your code into a file and run the file in Julia with `include("...")`. We’re happy to help, but please help us help you.

As you have identified, `dot` only works on ITensors that share indices, so you could either make sure that the ITensor indices match from the start, or make them match by contracting with `delta` tensors or using a function such as `replaceinds` to replace the indices of one ITensor to make them match with the other one.

---

<div class="post-metadata">

**Author:** ![Uranium92238](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/uranium92238/32/577_2.png) [@Uranium92238](https://itensor.discourse.group/u/Uranium92238)\
**Post date:** [June 28, 2024, 1:11pm UTC](https://itensor.discourse.group/t/cannot-compute-dot-product-of-itensors-due-to-mismatch-of-indices/1839/3 "2024-06-28T13:11:40Z")

</div>

> [@mtfishman](#):
>
> using a function such as `replaceinds` to replace the indices of one ITensor to make them match with the other one.

This seemed to solve the problem when I forced all the ITensors to have the same indices by adding the following lines to my code

```auto
    a_1, a_2, i_1, i_2 = inds(T2_storage[1])
    for i in 1:p
        R2_storage[i] = replaceinds(R2_storage[i], inds(R2_storage[i]) => (a_1,a_2,i_1,i_2))
    end

```

Also, I understand that I should provide a minimal example that reproduces the problem that I am faced with and will keep that in mind in subsequent discussions.

---

<div class="post-metadata">

**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:** [June 28, 2024, 2:12pm UTC](https://itensor.discourse.group/t/cannot-compute-dot-product-of-itensors-due-to-mismatch-of-indices/1839/4 "2024-06-28T14:12:49Z")

</div>

For you and others, I would not recommend writing code like `replaceinds(a, inds(a) => new_inds)`, that can easily lead to incorrect results if you input `a` with different Index ordering, for example:

```julia
julia> using ITensors: Index, inds, permute, random_itensor, replaceinds

julia> i, j = Index.((2, 2))
((dim=2|id=183), (dim=2|id=167))

julia> a = random_itensor(i, j)
ITensor ord=2 (dim=2|id=183) (dim=2|id=167)
NDTensors.Dense{Float64, Vector{Float64}}

julia> a[i => 1, j => 2]
-0.6311743998126356

julia> k, l = Index.((2, 2))
((dim=2|id=282), (dim=2|id=60))

julia> b = replaceinds(a, inds(a) => (k, l))
ITensor ord=2 (dim=2|id=282) (dim=2|id=60)
NDTensors.Dense{Float64, Vector{Float64}}

julia> a = permute(a, j, i)
ITensor ord=2 (dim=2|id=167) (dim=2|id=183)
NDTensors.Dense{Float64, Vector{Float64}}

julia> c = replaceinds(a, inds(a) => (k, l))
ITensor ord=2 (dim=2|id=282) (dim=2|id=60)
NDTensors.Dense{Float64, Vector{Float64}}

julia> b[k => 1, l => 2], c[k => 1, l => 2]
(-0.6311743998126356, 0.7321160309889322)

```