# Inner product grammar is neater than sum(index) in JuMP modeling, But triggers Warning?

**URL:** https://discourse.julialang.org/t/inner-product-grammar-is-neater-than-sum-index-in-jump-modeling-but-triggers-warning/124528
**Category:** Optimization (Mathematical)
**Tags:** jump
**Created:** [January 8, 2025, 9:35am UTC](https://discourse.julialang.org/t/inner-product-grammar-is-neater-than-sum-index-in-jump-modeling-but-triggers-warning/124528 "2025-01-08T09:35:37Z")
**Posts on this page:** 1
**Showing post:** 29

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### Author: ![WalterMadelim](https://avatars.discourse-cdn.com/v4/letter/w/3e96dc/32.png) [@WalterMadelim](https://discourse.julialang.org/u/WalterMadelim)
#### Post date: [May 6, 2025, 2:34am UTC](https://discourse.julialang.org/t/inner-product-grammar-is-neater-than-sum-index-in-jump-modeling-but-triggers-warning/124528/29 "2025-05-06T02:34:44Z")

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Given the discussion [here](https://discourse.julialang.org/t/dot-product/128704/6). I think we are motivated to fathom whether there is a standard (or at least recommended) way to write JuMP code that attains the optimal performance. @odow

Some very common cases include

```julia
import JuMP
using LinearAlgebra
model = JuMP.Model();
JuMP.@variable(model, x[1:3]);
JuMP.@variable(model, X[1:3, 1:3]);

JuMP.@expression(model, lin_scalar_1, rand(3)' * x)
JuMP.@expression(model, lin_scalar_2, dot(rand(3), x))

JuMP.@expression(model, quad_scalar_1, x' * rand(3, 3) * x)
JuMP.@expression(model, quad_scalar_2, dot(x, rand(3, 3), x))

JuMP.@expression(model, matrix_lin_scalar_1, rand(3)' * X * rand(3))
JuMP.@expression(model, matrix_lin_scalar_2, dot(rand(3), X, rand(3)))

JuMP.@expression(model, mat_lin_scalar_1, sum(rand(3, 3) .* X))
JuMP.@expression(model, mat_lin_scalar_2, dot(rand(3, 3), X))

```

It appears that they will have _different_ dispatches in `MutableArithmetics`, thus possibly different performances.

For a reference, notice the word `Unlike` in the following docstring

```julia
help?> *

  *(A, B::AbstractMatrix, C)
  A * B * C * D

  If the last factor is a vector, or the first a transposed vector, then it is efficient to deal with      
  these first. In particular x' * B * y means (x' * B) * y for an ordinary column-major B::Matrix. Unlike  
  dot(x, B, y), this allocates an intermediate array.

```

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_[View the full topic](https://discourse.julialang.org/t/inner-product-grammar-is-neater-than-sum-index-in-jump-modeling-but-triggers-warning/124528)._