# At dot of function of five arguments against five vectors to five dimensional array
**URL:** https://discourse.julialang.org/t/at-dot-of-function-of-five-arguments-against-five-vectors-to-five-dimensional-array/114146
**Category:** New to Julia
**Tags:** broadcast, arrays
**Created:** [May 11, 2024, 5:32pm UTC](https://discourse.julialang.org/t/at-dot-of-function-of-five-arguments-against-five-vectors-to-five-dimensional-array/114146 "2024-05-11T17:32:52Z")
**Posts on this page:** 7
**Page:** 1
### Author:  [@PeterSP](https://discourse.julialang.org/u/PeterSP)
#### Post date: [May 11, 2024, 5:32pm UTC](https://discourse.julialang.org/t/at-dot-of-function-of-five-arguments-against-five-vectors-to-five-dimensional-array/114146/1 "2024-05-11T17:32:52Z")
I’ve seen many examples that generate a two dimensional array (matrix) from a function of two arguments against two vectors:
```julia
x = 1:100
y = 1:100
f(x,y) = x*y
z = @. f(x', y)
```
I want to do something analagous, but five-dimensional:
```julia
v = 1:100
w = 1:100
x = 1:100
y = 1:100
z = 1:100
g(v,w,x,y,z) = v*w*x*y*z
u = @. g(reshape(v,(1,1,1,1,100)),reshape(w,(1,1,1,100,1)),reshape(x,(1,1,100,1,1)),reshape(y,(1,100,1,1,1,1)),reshape(z,(100,1,1,1,1)))
```
But when I try to do the latter I get
```julia
ERROR: DimensionMismatch: arrays could not be broadcast to a common size; got a dimension with lengths 100 and 5
```
(I also tried nonsense like `v''''` but that just results in `v` again because it limits itself to 2 dimensions)
Is there a good way to do what I’m trying to do?
---
### Author:  [@GunnarFarneback](https://discourse.julialang.org/u/GunnarFarneback)
#### Post date: [May 11, 2024, 5:38pm UTC](https://discourse.julialang.org/t/at-dot-of-function-of-five-arguments-against-five-vectors-to-five-dimensional-array/114146/2 "2024-05-11T17:38:05Z")
`@.` is too powerful for what you want to do, it fails to broadcast the reshape calls. Try
```julia
u = g.(reshape(v,(1,1,1,1,100)),reshape(w,(1,1,1,100,1)),reshape(x,(1,1,100,1,1)),reshape(y,(1,100,1,1,1,1)),reshape(z,(100,1,1,1,1)))
```
instead.
---
### Author:  [@PeterSP](https://discourse.julialang.org/u/PeterSP)
#### Post date: [May 11, 2024, 5:39pm UTC](https://discourse.julialang.org/t/at-dot-of-function-of-five-arguments-against-five-vectors-to-five-dimensional-array/114146/3 "2024-05-11T17:39:48Z")
> [@GunnarFarneback](#):
>
> `u = g.(reshape(v,(1,1,1,1,100)),reshape(w,(1,1,1,100,1)),reshape(x,(1,1,100,1,1)),reshape(y,(1,100,1,1,1,1)),reshape(z,(100,1,1,1,1)))`
That gives me an out of memory error, which is promising! Thanks! (Same as I’d get for `collect(1:100^5)` which makes sense)
---
### Author:  [@Dan](https://discourse.julialang.org/u/Dan)
#### Post date: [May 11, 2024, 7:55pm UTC](https://discourse.julialang.org/t/at-dot-of-function-of-five-arguments-against-five-vectors-to-five-dimensional-array/114146/4 "2024-05-11T19:55:13Z")
Perhaps adding a utility function can make the expression simpler. Here is an example:
```julia
alongdim(v,d,D) = reshape(v,ntuple(t->t==d ? D : 1))
alongdim(v,d) = alongdim(v,d,d)
```
Using `alongdim` in this context:
```julia
julia> u = (sin∘prod∘vcat).(alongdim.(Ref(1:2),1:4)...)
2×2×2×2 Array{Float64, 4}:
[:, :, 1, 1] =
0.841471 0.909297
0.909297 -0.756802
[:, :, 2, 1] =
0.909297 -0.756802
-0.756802 0.989358
[:, :, 1, 2] =
0.909297 -0.756802
-0.756802 0.989358
[:, :, 2, 2] =
-0.756802 0.989358
0.989358 -0.287903
```
`alongdim(v,d,D)` would return an array of dimension `D` with the vector `v` laid out a long dimension `d`.
```julia
u = g.(reshape(v,(1,1,1,1,100)),reshape(w,(1,1,1,100,1)),reshape(x,(1,1,100,1,1)),reshape(y,(1,100,1,1,1,1)),reshape(z,(100,1,1,1,1)))
```
can be rewritten as:
```julia
u = g.(
alongdim(v,5,5),
alongdim(w,4,5),
alongdim(x,3,5),
alongdim(y,2,5),
alongdim(z,1,5)
)
```
or even shorter:
```julia
u = g.(alongdim.((v,w,x,y,z),5:-1:1,5)...)
```
---
### Author:  [@rocco\_sprmnt21](https://discourse.julialang.org/u/rocco_sprmnt21)
#### Post date: [May 11, 2024, 8:15pm UTC](https://discourse.julialang.org/t/at-dot-of-function-of-five-arguments-against-five-vectors-to-five-dimensional-array/114146/5 "2024-05-11T20:15:00Z")
```julia
Base.splat(g).(Iterators.product(v,w,x,y,z))
```
```julia
g.([v;],[w...;;],[x...;;;],[y...;;;;],[z...;;;;;])
```
```julia
a=[v,w,x,y,z]
args=ntuple(i->cat(a[i]...,dims=i),5)
g.(args...)
```
```julia
nn=ntuple(i->ntuple(j->j==i ? (:) : 1,5),5)
g.(reshape.(a,nn)...)
```
---
### Author:  [@Dan](https://discourse.julialang.org/u/Dan)
#### Post date: [May 11, 2024, 10:00pm UTC](https://discourse.julialang.org/t/at-dot-of-function-of-five-arguments-against-five-vectors-to-five-dimensional-array/114146/6 "2024-05-11T22:00:49Z")
```julia
u = [g(V, W, X, Y, Z) for Z in z, Y in y, X in x, W in w, V in v]
```
---
### Author:  [@rafael.guerra](https://discourse.julialang.org/u/rafael.guerra)
#### Post date: [May 12, 2024, 6:13pm UTC](https://discourse.julialang.org/t/at-dot-of-function-of-five-arguments-against-five-vectors-to-five-dimensional-array/114146/7 "2024-05-12T18:13:25Z")
Writing this using TensorCast.jl is compact and has the merit of clarity in tracking indices:
```julia
using TensorCast
@cast u[i,j,k,l,m] := g(v[i], w[j], x[k], y[l], z[m])
```