# What does passing a vector as \`dims\` to \`Statistics.std\` mean?

**URL:** <https://discourse.julialang.org/t/what-does-passing-a-vector-as-dims-to-statistics-std-mean/83295>\
**Category:** General Usage\
**Tags:** question\
**Created:** [June 24, 2022, 8:37am UTC](https://discourse.julialang.org/t/what-does-passing-a-vector-as-dims-to-statistics-std-mean/83295 "2022-06-24T08:37:01Z")\
**Posts on this page:** 4\
**Page:** 1

<div class="post-metadata">

**Author:** ![Saransh-cpp](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/saransh-cpp/32/34579_2.png) [@Saransh-cpp](https://discourse.julialang.org/u/Saransh-cpp)\
**Post date:** [June 24, 2022, 8:37am UTC](https://discourse.julialang.org/t/what-does-passing-a-vector-as-dims-to-statistics-std-mean/83295/1 "2022-06-24T08:37:01Z")

</div>

I have been trying to use the `std` function on a batch of images. For instance, this is a batch of 2 images having 3 channels each -

```julia
xs = rand(3, 3, 3, 2)

```

I want to find the standard deviation of the first image which can be achieved using -

```julia
std(xs[:, :, :, 1])

```

Now I want to achieve the same thing using the `dims` kwarg, but I cannot figure out the usage of the same. More precisely, what is the function actually calculating if I pass in a vector as dims? I couldn’t find any examples of this on the internet or in Julia’s documentation. An example with the batch of images defined above -

```julia
julia> xs
3×3×3×2 Array{Float64, 4}:
[:, :, 1, 1] =
 0.775483 0.804976 0.805342
 0.502332 0.571661 0.788025
 0.627064 0.175482 0.733361

[:, :, 2, 1] =
 0.744905 0.861811 0.236851
 0.493482 0.672934 0.954064
 0.382317 0.368025 0.0896878

[:, :, 3, 1] =
 0.287127 0.505461 0.280565
 0.637652 0.07373 0.132018
 0.493528 0.173168 0.0917483

[:, :, 1, 2] =
 0.993559 0.85186 0.974956
 0.962802 0.20569 0.171647
 0.344311 0.158447 0.0416952

[:, :, 2, 2] =
 0.0756434 0.800149 0.0489549
 0.868386 0.197549 0.56844
 0.00663242 0.131731 0.614948

[:, :, 3, 2] =
 0.154051 0.93772 0.143768
 0.196975 0.0213649 0.0269268
 0.0658219 0.913233 0.179747

julia> std(xs, dims=[3,1])
1×3×1×2 Array{Float64, 4}:
[:, :, 1, 1] =
 0.16137 0.287385 0.354948

[:, :, 1, 2] =
 0.412971 0.39161 0.332775

```

Could someone please explain to me how is the final `1x3x1x2` Array has been calculated? Thank you!

---

<div class="post-metadata">

**Author:** ![Karthik-d-k](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/karthik-d-k/32/35438_2.png) [@Karthik-d-k](https://discourse.julialang.org/u/Karthik-d-k)\
**Post date:** [June 24, 2022, 9:34am UTC](https://discourse.julialang.org/t/what-does-passing-a-vector-as-dims-to-statistics-std-mean/83295/2 "2022-06-24T09:34:36Z")

</div>

Hi @Saransh-cpp

`dims` is used to specify on which dimensions you want to calculate the `std` on…  
Let’s say for example we have two 3-channel images of size (4, 4) as below →

```julia
julia> using Statistics

# two 3-channel images of size (4, 4)
julia> xs = rand(3, 4, 4, 2)
3×4×4×2 Array{Float64, 4}:
[:, :, 1, 1] =
 0.638898 0.0607577 0.248664 0.134614
 0.359026 0.045089 0.934976 0.208916
 0.574276 0.00640597 0.916209 0.146101

[:, :, 2, 1] =
 0.337945 0.385004 0.941823 0.879369
 0.00222145 0.191058 0.53481 0.513988
 0.760298 0.589457 0.286568 0.510345

[:, :, 3, 1] =
 0.815596 0.157969 0.623036 0.0807889
 0.557733 0.813058 0.474988 0.159235
 0.893057 0.386838 0.570377 0.518802

[:, :, 4, 1] =
 0.104052 0.380098 0.268024 0.578795
 0.413343 0.998084 0.449842 0.224211
 0.864892 0.808143 0.0459052 0.457739

[:, :, 1, 2] =
 0.24586 0.870185 0.770928 0.31385
 0.3981 0.391596 0.845867 0.146243
 0.114382 0.0579019 0.247182 0.0315621

[:, :, 2, 2] =
 0.306497 0.418139 0.713051 0.87407
 0.14916 0.302198 0.621749 0.0677304
 0.753772 0.00230659 0.938192 0.106774

[:, :, 3, 2] =
 0.624643 0.598719 0.160968 0.766046
 0.755545 0.0378673 0.397636 0.86422
 0.809038 0.915949 0.0150156 0.0320573

[:, :, 4, 2] =
 0.128597 0.0363205 0.862884 0.957192
 0.646652 0.159509 0.553012 0.71586
 0.5693 0.270781 0.950244 0.844724

# std on over all numbers (on all dims)
julia> std(xs, dims=[1, 2, 3, 4])
1×1×1×1 Array{Float64, 4}:
[:, :, 1, 1] =
 0.308191790621495
# we will just get a single number, preserving input shape (x, x, x, x)

# std on batch dimension (i.e, last dim), we specify 1st 3 dims to calc std on
julia> std(xs, dims=[1, 2, 3])
1×1×1×2 Array{Float64, 4}:
[:, :, 1, 1] =
 0.29192537121237955

[:, :, 1, 2] =
 0.32666112721755525
# we will just get two numbers, each for one image

# std on channel dimension (i.e, first dim), we specify last 3 dims to calc std on
julia> std(xs, dims=[2, 3, 4])
3×1×1×1 Array{Float64, 4}:
[:, :, 1, 1] =
 0.30341597287159655
 0.2841992921298127
 0.34238183603676203
# we will just get three numbers, each for one channel

```

Input shape will be preserved in outputs, IMO there is no real benefit of thinking in terms of output dim, rather we can just think of it as numbers with `length` == `dim length you wanted the output to be on`.

---

<div class="post-metadata">

**Author:** ![Saransh-cpp](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/saransh-cpp/32/34579_2.png) [@Saransh-cpp](https://discourse.julialang.org/u/Saransh-cpp)\
**Post date:** [June 24, 2022, 12:35pm UTC](https://discourse.julialang.org/t/what-does-passing-a-vector-as-dims-to-statistics-std-mean/83295/3 "2022-06-24T12:35:57Z")

</div>

Thank you for the detailed explanation and the examples! I have been using the `WHCN` format for images (as used by `Flux`) and tweaking your examples just by a tiny bit did the trick. Additionally, I discovered that the dims can also be specified like this -

```julia
julia> std(xs, dims=1:3)

```

---

<div class="post-metadata">

**Author:** ![Karthik-d-k](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/karthik-d-k/32/35438_2.png) [@Karthik-d-k](https://discourse.julialang.org/u/Karthik-d-k)\
**Post date:** [June 24, 2022, 1:17pm UTC](https://discourse.julialang.org/t/what-does-passing-a-vector-as-dims-to-statistics-std-mean/83295/4 "2022-06-24T13:17:16Z")

</div>

> [@Saransh-cpp](#):
>
> I discovered that the dims can also be specified like this -
> 
> ```julia
> julia> std(xs, dims=1:3)
> 
> ```

That’s cool ! 🙌