# Vectorization and passing a matrix as an argument

**URL:** <https://discourse.julialang.org/t/vectorization-and-passing-a-matrix-as-an-argument/9114>\
**Category:** General Usage\
**Created:** [February 16, 2018, 4:05pm UTC](https://discourse.julialang.org/t/vectorization-and-passing-a-matrix-as-an-argument/9114 "2018-02-16T16:05:52Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![gideonsimpson](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/gideonsimpson/32/1928_2.png) [@gideonsimpson](https://discourse.julialang.org/u/gideonsimpson)\
**Post date:** [February 16, 2018, 4:05pm UTC](https://discourse.julialang.org/t/vectorization-and-passing-a-matrix-as-an-argument/9114/1 "2018-02-16T16:05:52Z")

</div>

I have an energy type function that I’ve written:

```julia
function energy(r,A)
    return 0.5 * dot(r, A*r)
end

```

where `r` is an n dimensional array and `A` is an nxn matrix which may or may not be sparse. Evaluating this on a single `r` and `A` works fine. However, for a fixed `A`, if I try to evaluate on many `r`’s via vectorization, I get the error:

```julia
ERROR: DimensionMismatch("arrays could not be broadcast to a common size")

```

Here is a complete sample code that produces this error:

```julia
 function energy(r,A)
       return 0.5 * dot(r, A*r)
end

A = [1. 2.; 2. 1.]
r = [1.,0.5]
energy(r,A) # this works fine

x = linspace(-1,1, 10)|>collect
y = linspace(-1,1, 10)|>collect

rvals = [[x[j],y[i]] for i=1:length(y), j = 1:length(x)];

energy.(rvals,A) # this generates the error

```

---

<div class="post-metadata">

**Author:** ![rdeits](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rdeits/32/286_2.png) [@rdeits](https://discourse.julialang.org/u/rdeits)\
**Post date:** [February 16, 2018, 4:22pm UTC](https://discourse.julialang.org/t/vectorization-and-passing-a-matrix-as-an-argument/9114/2 "2018-02-16T16:22:38Z")

</div>

Julia is interpreting your command as an attempt to broadcast over the elements of `rvals` and the elements of `A` simultaneously, but you actually want it to use the entirety of `A` for every call. In essence you want `rvals` to be treated like an array in the broadcast, but for `A` to be treated like a scalar so that it is passed intact to each call to `energy`. You can make any item behave like a scalar in broadcasting by simply wrapping it in a one-element tuple:

```julia
julia> energy.(rvals, (A,))
10×10 Array{Float64,2}:
  3.0 2.35802 1.76543 1.22222 0.728395 0.283951 -0.111111 -0.45679 -0.753086 -1.0     
  2.35802 1.81481 1.32099 0.876543 0.481481 0.135802 -0.160494 -0.407407 -0.604938 -0.753086
  1.76543 1.32099 0.925926 0.580247 0.283951 0.037037 -0.160494 -0.308642 -0.407407 -0.45679 
  1.22222 0.876543 0.580247 0.333333 0.135802 -0.0123457 -0.111111 -0.160494 -0.160494 -0.111111
  0.728395 0.481481 0.283951 0.135802 0.037037 -0.0123457 -0.0123457 0.037037 0.135802 0.283951
  0.283951 0.135802 0.037037 -0.0123457 -0.0123457 0.037037 0.135802 0.283951 0.481481 0.728395
 -0.111111 -0.160494 -0.160494 -0.111111 -0.0123457 0.135802 0.333333 0.580247 0.876543 1.22222 
 -0.45679 -0.407407 -0.308642 -0.160494 0.037037 0.283951 0.580247 0.925926 1.32099 1.76543 
 -0.753086 -0.604938 -0.407407 -0.160494 0.135802 0.481481 0.876543 1.32099 1.81481 2.35802 
 -1.0 -0.753086 -0.45679 -0.111111 0.283951 0.728395 1.22222 1.76543 2.35802 3.0     

```