# Dot operator, 1. with array-indexing expression on the left-hand side and 2. with Matrix\*Vector-multiplication

**URL:** <https://discourse.julialang.org/t/dot-operator-1-with-array-indexing-expression-on-the-left-hand-side-and-2-with-matrix-vector-multiplication/62743>\
**Category:** Performance\
**Created:** [June 11, 2021, 2:40pm UTC](https://discourse.julialang.org/t/dot-operator-1-with-array-indexing-expression-on-the-left-hand-side-and-2-with-matrix-vector-multiplication/62743 "2021-06-11T14:40:16Z")\
**Posts on this page:** 19\
**Page:** 1

<div class="post-metadata">

**Author:** ![hardy](https://avatars.discourse-cdn.com/v4/letter/h/c5a1d2/32.png) [@hardy](https://discourse.julialang.org/u/hardy)\
**Post date:** [June 11, 2021, 2:40pm UTC](https://discourse.julialang.org/t/dot-operator-1-with-array-indexing-expression-on-the-left-hand-side-and-2-with-matrix-vector-multiplication/62743/1 "2021-06-11T14:40:17Z")

</div>

Hallo,  
I would like to understand how the dot operator works. There are two specific problems:

1. 

at [Performance Tips · The Julia Language](https://docs.julialang.org/en/v1/manual/performance-tips/#man-performance-tips) (headline: Consider using views for slicing)  
I learned that “…on the left-hand side of an assignment, where `array[1:5, :] = ...` assigns in-place to that portion of `array`”. As I understand it, no unnecessary copies are stored in memory.

Now I read here:  
[Functions · The Julia Language](https://docs.julialang.org/en/v1/manual/functions/#man-vectorized) that if I use the dot-operator .= :  
"If the left-hand side is an array-indexing expression, e.g. `X[begin+1:end] .= sin.(Y)` , then it translates to `broadcast!` on a `view`, e.g. `broadcast!(sin, view(X, firstindex(X)+1:lastindex(X)), Y)` , so that the left-hand side is updated in-place. "

Now I wonder why the dot near the equal sign in X[begin+1:end] .= sin.(Y) is necessary. Shouldn’t it be updated in-place anyway? What is the advantage of the View in this case?

1. 

If I have an expression like: Θ[:,k+1] = K\*Θ[:,k]+B  
and K is a 10x10 matrix , Θ[:,k] is a 10x1 vector and B is another 10x1 vector.  
Can I take advantage of the dot vector in this case?  
I can’t use . \* because I don’t want a broadcast. So I can’t use @.  
Because of the array-indexing expression on the left-hand side the .= seems unnecessary (it’s in-place anyway). And .+ without fusion doesn’t seem to make sense.  
Did I get that right?

It would be great if someone could explain this to me 😳

---

<div class="post-metadata">

**Author:** ![Oscar\_Smith](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/oscar_smith/32/25343_2.png) [@Oscar\_Smith](https://discourse.julialang.org/u/Oscar_Smith)\
**Post date:** [June 11, 2021, 3:06pm UTC](https://discourse.julialang.org/t/dot-operator-1-with-array-indexing-expression-on-the-left-hand-side-and-2-with-matrix-vector-multiplication/62743/2 "2021-06-11T15:06:42Z")

</div>

The difference between `=` and `.=` is whether you allocate an array for the answer before copying it to the view.

---

<div class="post-metadata">

**Author:** ![hardy](https://avatars.discourse-cdn.com/v4/letter/h/c5a1d2/32.png) [@hardy](https://discourse.julialang.org/u/hardy)\
**Post date:** [June 11, 2021, 3:22pm UTC](https://discourse.julialang.org/t/dot-operator-1-with-array-indexing-expression-on-the-left-hand-side-and-2-with-matrix-vector-multiplication/62743/3 "2021-06-11T15:22:02Z")

</div>

Is it wrong that an array-indexing expression at the left-hand side assignes in place by default?

---

<div class="post-metadata">

**Author:** ![mcabbott](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mcabbott/32/6603_2.png) [@mcabbott](https://discourse.julialang.org/u/mcabbott)\
**Post date:** [June 11, 2021, 3:49pm UTC](https://discourse.julialang.org/t/dot-operator-1-with-array-indexing-expression-on-the-left-hand-side-and-2-with-matrix-vector-multiplication/62743/4 "2021-06-11T15:49:01Z")

</div>

> [@hardy](#):
>
> Θ[:,k+1] = K\*Θ[:,k]+B

This allocates first a slice `Θ[:,k]`, then the product `K*Θ[:,k]`, then for the sum `+ B` before writing into `Θ`. Better would be `Θ[:,k+1] .= K*view(Θ,:,k) .+ B`, the `.+` is useful precisely because it can be fused with the `.=`. Even better would be

```julia
Θ[:,k+1] .= B
@views mul!(Θ[:,k+1], K, Θ[:,k], true, true)

```

---

<div class="post-metadata">

**Author:** ![DNF](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dnf/32/10191_2.png) [@DNF](https://discourse.julialang.org/u/DNF)\
**Post date:** [June 11, 2021, 4:47pm UTC](https://discourse.julialang.org/t/dot-operator-1-with-array-indexing-expression-on-the-left-hand-side-and-2-with-matrix-vector-multiplication/62743/5 "2021-06-11T16:47:56Z")

</div>

> [@hardy](#):
>
> `X[begin+1:end] .= sin.(Y)`

In case it wasn’t clear, you absolutely do need the dotted assignment operator here. Without the dot, the values are assigned ‘in-place’ in the variable `X`. But before that happens, the expression `sin.(Y)` on the right hand side will create a temporary array. If you want to avoid that temporary array you must dot the entire expression, including the assignment operator.

Without the dot, this

```julia
X[begin+1:end] = sin.(Y)

```

is equivalent to this

```julia
temp = sin.(Y) # create temporary array
X[begin+1:end] = temp # assign in-place to X

```

---

<div class="post-metadata">

**Author:** ![hardy](https://avatars.discourse-cdn.com/v4/letter/h/c5a1d2/32.png) [@hardy](https://discourse.julialang.org/u/hardy)\
**Post date:** [June 11, 2021, 6:14pm UTC](https://discourse.julialang.org/t/dot-operator-1-with-array-indexing-expression-on-the-left-hand-side-and-2-with-matrix-vector-multiplication/62743/6 "2021-06-11T18:14:25Z")

</div>

Thanks a lot macabbott for that really helpful answer!  
But I’m still confused about  
`Θ[:,k+1] .= B`  
I’m not familiar with views. If I don’t assign a copy of B but a view, wouldn’t a subsequent change in Θ then also have to change B? I’ve tried it and seen that it doesn’t happen, but I still don’t understand how this works.

---

<div class="post-metadata">

**Author:** ![mcabbott](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mcabbott/32/6603_2.png) [@mcabbott](https://discourse.julialang.org/u/mcabbott)\
**Post date:** [June 11, 2021, 7:53pm UTC](https://discourse.julialang.org/t/dot-operator-1-with-array-indexing-expression-on-the-left-hand-side-and-2-with-matrix-vector-multiplication/62743/7 "2021-06-11T19:53:12Z")

</div>

> [@hardy](#):
>
> wouldn’t a subsequent change in Θ then also have to change B?

Maybe what you miss is that `Θ` is only one pointer deep. It owns a continuous block of memory. Or, it’s a mutable container of just numbers, not boxes which contain numbers. We can’t link part of it to `B`’s memory, all we can do is copy the numbers one by one from `B` to each overwrite one in `Θ`. Which is what `Θ[:,k+1] = B` and `Θ[:,k+1] .= B` and `Θ[:,k+1] .= view(B,:)` all do, although the precise chain of functions involved will differ.

---

<div class="post-metadata">

**Author:** ![hardy](https://avatars.discourse-cdn.com/v4/letter/h/c5a1d2/32.png) [@hardy](https://discourse.julialang.org/u/hardy)\
**Post date:** [June 11, 2021, 8:14pm UTC](https://discourse.julialang.org/t/dot-operator-1-with-array-indexing-expression-on-the-left-hand-side-and-2-with-matrix-vector-multiplication/62743/8 "2021-06-11T20:14:40Z")

</div>

That makes it a lot clearer to me. Thank you!  
Now I ask myself why I didn’t think of that 😊

---

<div class="post-metadata">

**Author:** ![hardy](https://avatars.discourse-cdn.com/v4/letter/h/c5a1d2/32.png) [@hardy](https://discourse.julialang.org/u/hardy)\
**Post date:** [June 12, 2021, 9:22pm UTC](https://discourse.julialang.org/t/dot-operator-1-with-array-indexing-expression-on-the-left-hand-side-and-2-with-matrix-vector-multiplication/62743/9 "2021-06-12T21:22:59Z")

</div>

Sorry for being so persistent.  
But I did

```julia
@time begin
       Θ[:,k+1] .= B
       @views mul!(Θ[:,k+1], K, Θ[:,k], true, true)
 end

```

and got 0.000030 seconds and 14 allocations: 400 bytes.

For  
`@time Θ[:,k+1] .= K*Θ[:,k] .+ B `

I got 0.000029 seconds and 8 allocations: 560 bytes

These are more allocations than expected!  
Is for efficiency only the number of allocated bytes critical or does every allocation cost time?

---

<div class="post-metadata">

**Author:** ![DNF](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dnf/32/10191_2.png) [@DNF](https://discourse.julialang.org/u/DNF)\
**Post date:** [June 12, 2021, 10:18pm UTC](https://discourse.julialang.org/t/dot-operator-1-with-array-indexing-expression-on-the-left-hand-side-and-2-with-matrix-vector-multiplication/62743/10 "2021-06-12T22:18:33Z")

</div>

Don’t use the `@time` macro for micro benchmarks, it is not suitable. Install the BenchmarkTools package, read the manual, and then use that. The allocation estimates you get from `@time` do not tell you what you are looking for.

---

<div class="post-metadata">

**Author:** ![DNF](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dnf/32/10191_2.png) [@DNF](https://discourse.julialang.org/u/DNF)\
**Post date:** [June 12, 2021, 10:34pm UTC](https://discourse.julialang.org/t/dot-operator-1-with-array-indexing-expression-on-the-left-hand-side-and-2-with-matrix-vector-multiplication/62743/11 "2021-06-12T22:34:59Z")

</div>

To be honest, I wonder why `@time` is in Base. It seems like 99% of the time BenchmarkTools should be used instead. Perhaps it would be better if `@time` was removed, and then you would have to make a conscious choice when timing code, instead of relying on the built-in default.

---

<div class="post-metadata">

**Author:** ![hardy](https://avatars.discourse-cdn.com/v4/letter/h/c5a1d2/32.png) [@hardy](https://discourse.julialang.org/u/hardy)\
**Post date:** [June 13, 2021, 6:00am UTC](https://discourse.julialang.org/t/dot-operator-1-with-array-indexing-expression-on-the-left-hand-side-and-2-with-matrix-vector-multiplication/62743/12 "2021-06-13T06:00:23Z")

</div>

Do you mean that?

`@benchmark Θ[:,k+1] .= K*Θ[:,k] .+ B`

## BenchmarkTools.Trial: memory estimate: 560 bytes allocs estimate: 9

## minimum time: 1.324 μs (0.00% GC) median time: 1.373 μs (0.00% GC) mean time: 1.415 μs (0.00% GC) maximum time: 5.119 μs (0.00% GC)

samples: 10000  
evals/sample: 10

```julia-auto
@benchmark begin
              Θ[:,k+1] .= B
              @views mul!(Θ[:,k+1], K, Θ[:,k], true, true)
              end

```

## BenchmarkTools.Trial: memory estimate: 400 bytes allocs estimate: 15

## minimum time: 2.229 μs (0.00% GC) median time: 2.259 μs (0.00% GC) mean time: 2.316 μs (0.00% GC) maximum time: 5.337 μs (0.00% GC)

samples: 10000  
evals/sample: 9

---

<div class="post-metadata">

**Author:** ![hardy](https://avatars.discourse-cdn.com/v4/letter/h/c5a1d2/32.png) [@hardy](https://discourse.julialang.org/u/hardy)\
**Post date:** [June 13, 2021, 8:22am UTC](https://discourse.julialang.org/t/dot-operator-1-with-array-indexing-expression-on-the-left-hand-side-and-2-with-matrix-vector-multiplication/62743/13 "2021-06-13T08:22:20Z")

</div>

If I do

```julia-auto
@benchmark Θ[:,k+1] .= B

```

I would expect no allocations but I get:

## BenchmarkTools.Trial: memory estimate: 176 bytes allocs estimate: 7

## minimum time: 941.893 ns (0.00% GC) median time: 961.571 ns (0.00% GC) mean time: 1.002 μs (0.00% GC) maximum time: 8.047 μs (0.00% GC)

samples: 10000  
evals/sample: 28

And if I do

```julia-auto
@benchmark Θ[:,k+1] = B

```

## BenchmarkTools.Trial: memory estimate: 16 bytes allocs estimate: 1

## minimum time: 196.114 ns (0.00% GC) median time: 197.932 ns (0.00% GC) mean time: 204.880 ns (0.45% GC) maximum time: 9.356 μs (97.79% GC)

samples: 10000  
evals/sample: 621

I’m really confused about it 🙄

---

<div class="post-metadata">

**Author:** ![DNF](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dnf/32/10191_2.png) [@DNF](https://discourse.julialang.org/u/DNF)\
**Post date:** [June 13, 2021, 8:30am UTC](https://discourse.julialang.org/t/dot-operator-1-with-array-indexing-expression-on-the-left-hand-side-and-2-with-matrix-vector-multiplication/62743/14 "2021-06-13T08:30:13Z")

</div>

You must read the manual, specifically the part about variable interpolation.

---

<div class="post-metadata">

**Author:** ![hardy](https://avatars.discourse-cdn.com/v4/letter/h/c5a1d2/32.png) [@hardy](https://discourse.julialang.org/u/hardy)\
**Post date:** [June 13, 2021, 12:46pm UTC](https://discourse.julialang.org/t/dot-operator-1-with-array-indexing-expression-on-the-left-hand-side-and-2-with-matrix-vector-multiplication/62743/15 "2021-06-13T12:46:57Z")

</div>

I did, but I’m not sure what to do. Both Θ[:,k+1] and B are globals in my little trial.

---

<div class="post-metadata">

**Author:** ![hardy](https://avatars.discourse-cdn.com/v4/letter/h/c5a1d2/32.png) [@hardy](https://discourse.julialang.org/u/hardy)\
**Post date:** [June 13, 2021, 1:11pm UTC](https://discourse.julialang.org/t/dot-operator-1-with-array-indexing-expression-on-the-left-hand-side-and-2-with-matrix-vector-multiplication/62743/16 "2021-06-13T13:11:03Z")

</div>

I put it inside a function like

```julia
function dotequal(A,B)
       A.=B
       end

@benchmark dotequal(Θ[:,k+1],B)

```

but get the same result for the function with and the one without the dot.

I think I will put this aside for now.  
Nevertheless, thank you very much for your patience.

---

<div class="post-metadata">

**Author:** ![DNF](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dnf/32/10191_2.png) [@DNF](https://discourse.julialang.org/u/DNF)\
**Post date:** [June 13, 2021, 2:30pm UTC](https://discourse.julialang.org/t/dot-operator-1-with-array-indexing-expression-on-the-left-hand-side-and-2-with-matrix-vector-multiplication/62743/17 "2021-06-13T14:30:14Z")

</div>

Look up variable interpolation using `$` in the BenchmarkTools manual.

---

<div class="post-metadata">

**Author:** ![Seif\_Shebl](https://avatars.discourse-cdn.com/v4/letter/s/eada6e/32.png) [@Seif\_Shebl](https://discourse.julialang.org/u/Seif_Shebl)\
**Post date:** [June 13, 2021, 3:28pm UTC](https://discourse.julialang.org/t/dot-operator-1-with-array-indexing-expression-on-the-left-hand-side-and-2-with-matrix-vector-multiplication/62743/18 "2021-06-13T15:28:34Z")

</div>

They mean you should use the interpolation operator `$` to get proper timings:

```julia
julia> @benchmark $Θ[:,$k+1] .= $B
BenchmarkTools.Trial:
  memory estimate: 0 bytes
  allocs estimate: 0
  --------------
  minimum time: 21.866 ns (0.00% GC)
  median time: 21.966 ns (0.00% GC)
  mean time: 22.064 ns (0.00% GC)
  maximum time: 51.956 ns (0.00% GC)
  --------------
  samples: 10000
  evals/sample: 997

julia> @benchmark $Θ[:,$k+1] = $B
BenchmarkTools.Trial:
  memory estimate: 0 bytes
  allocs estimate: 0
  --------------
  minimum time: 15.315 ns (0.00% GC)
  median time: 15.315 ns (0.00% GC)
  mean time: 15.476 ns (0.00% GC)
  maximum time: 126.126 ns (0.00% GC)
  --------------
  samples: 10000
  evals/sample: 999

julia> @benchmark $Θ[:,$k+1] .= $K * $Θ[:,$k] .+ $B
BenchmarkTools.Trial:
  memory estimate: 320 bytes
  allocs estimate: 2
  --------------
  minimum time: 160.842 ns (0.00% GC)
  median time: 167.347 ns (0.00% GC)
  mean time: 179.127 ns (1.53% GC)
  maximum time: 868.750 ns (75.86% GC)
  --------------
  samples: 10000
  evals/sample: 784

julia> @benchmark begin
           $Θ[:,$k+1] .= $B
           @views mul!($Θ[:,$k+1], $K, $Θ[:,$k], true, true)
       end
BenchmarkTools.Trial:
  memory estimate: 0 bytes
  allocs estimate: 0
  --------------
  minimum time: 98.835 ns (0.00% GC)
  median time: 99.894 ns (0.00% GC)
  mean time: 104.734 ns (0.00% GC)
  maximum time: 208.369 ns (0.00% GC)
  --------------
  samples: 10000
  evals/sample: 944

```

---

<div class="post-metadata">

**Author:** ![hardy](https://avatars.discourse-cdn.com/v4/letter/h/c5a1d2/32.png) [@hardy](https://discourse.julialang.org/u/hardy)\
**Post date:** [June 13, 2021, 3:52pm UTC](https://discourse.julialang.org/t/dot-operator-1-with-array-indexing-expression-on-the-left-hand-side-and-2-with-matrix-vector-multiplication/62743/19 "2021-06-13T15:52:56Z")

</div>

Thank you so much!  
I I’ve tried that too, but forgot the $ next to k+1 and it didn’t work.