### A Pluto.jl notebook ###
# v0.15.1

using Markdown
using InteractiveUtils

# ╔═╡ 6617f01e-f252-11eb-1696-0f9f9b01245b
using MixedModels, PackageAnalyzer

# ╔═╡ 8be846d1-0872-41c0-9a97-776f8ade7185
using CairoMakie, MixedModelsMakie

# ╔═╡ ccf3aa24-756c-445a-a22c-99c748ccbc91
html"<button onclick='present()'>presentation mode</button>"

# ╔═╡ f9a85d0b-5e59-4dc1-83f1-48683dcb6acf
md"""
# Fitting mixed-models faster with MKL

Fitting a linear mixed-effects model (LMM) involves setting up a numerical representation of the model from which the objective function can be evaluated for a given value of the parameters.
The evaluation involves a considerable amount of linear algebra.

Intel's [Math Kernel Library](https://en.wikipedia.org/wiki/Math_Kernel_Library) provides an accelerated version of the Basic Linear Algebra Subroutines (BLAS) and some LAPACK subroutines.

Julia v1.7.0 will introduce a framework called `libblastrampoline` that allows for dynamic switching between BLAS libraries.
The binary [downloads](https://julialang.org/downloads) of Julia come with the [OpenBLAS](https://en.wikipedia.org/wiki/OpenBLAS) implementation, which is the default.  We will illustrate using MKL with a beta-test version of Julia v1.7.0

The active parts of this notebook use OpenBLAS.
We will simply quote the results from [lme4](https://github.com/lme4/lme4) for R and for [MixedModels](https://github.com/JuliaStats/MixedModels.jl) for Julia.
"""

# ╔═╡ 3052b69a-a9a8-4633-9df8-b1a70bbcabb7
md"""
## Linear mixed-effects models
- A linear mixed-effects (LMM) model allows for modeling several sources of variability (or *variance components*) in the response.
- A common example in Psychology or Linguistics would be a study in which each of several subjects is exposed to each of several items (e.g. words) under different experimental conditions, e.g. clear vs blurred image, primed by earlier exposure or not, and the response measured is the reaction time to, say, indicate if the image is a word or not.
- We expect an underlying variability in the response but also subject-to-subject variability and item-to-item variability.
- *Fixed-effects* are coefficients associated with repeatable conditions (e.g. clear vs blurred).
- *Random-effects* are coefficients in the linear predictor associated with *blocking factors* such as `subj` or `item` which are considered a selection from a population of possible values.
- *Mixed-effects* refers to a model with both fixed-effects parameters and random effects.
- The lme4 package for R allows for fitting models with *crossed* grouping factors for the random effects.  It is widely used because of this capability.
"""

# ╔═╡ ae102e47-1716-4861-84e5-76c19c054b6b
md"""
## An example
- Data from experiment 1 of [Masson, Rabe & Kliegl, 2017](https://doi.org/10.3758/s13421-016-0666-z) are available in [Arrow format](https://arrow.apache.org) with the [MixedModels package](https://github.com/JuliaStats/MixedModels.jl) for Julia.
- The data are stored in a directory in the `Artifacts` folder under the main Julia directory, which on my Linux system is `~/.julia/artifacts/`.
- The particular folder name is a long sequence of characters called a *hash* or *secure hash algorithm (SHA)*.  This particular SHA is in the [Artifacts.toml](https://github.com/JuliaStats/MixedModels.jl/blob/main/Artifacts.toml) file for the *MixedModels* package.
- The arrow file can be read in R using the `arrow` package or in Python/Pandas with the `pyarrow` package.  In both of these packages the `arrow` file format is called `feather` because it is also the Feather version 2 format.
"""

# ╔═╡ cf44a69e-7628-43f3-b395-05ebf62ca648
md"""
## Fitting a model using `lme4`
```
> library(lme4)
Loading required package: Matrix
> df <- read_feather("~/.julia/artifacts/6d31be16850ffb7b5c0b80cb25f85b5c10df6546/mrk17_exp1.arrow")
> str(df)
Classes ‘tbl_df’, ‘tbl’ and 'data.frame':	16409 obs. of  9 variables:
 $ subj : Factor w/ 73 levels "S01","S02","S03",..: 1 1 1 1 1 1 1 1 1 1 ...
 $ item : Factor w/ 240 levels "CAKE","PARTY",..: 1 2 3 4 5 6 7 8 9 10 ...
 $ trial: int  2 3 5 9 10 11 15 21 22 24 ...
 $ F    : Factor w/ 2 levels "LF","HF": 1 2 2 2 2 2 2 1 1 2 ...
 $ P    : Factor w/ 2 levels "unr","rel": 1 1 2 2 1 2 2 1 1 2 ...
 $ Q    : Factor w/ 2 levels "deg","clr": 1 2 2 1 1 2 1 1 2 2 ...
 $ lQ   : Factor w/ 2 levels "deg","clr": 1 1 1 1 1 1 1 2 1 1 ...
 $ lT   : Factor w/ 2 levels "NW","WD": 1 2 1 1 2 2 1 1 2 1 ...
 $ rt   : int  794 506 491 486 482 542 766 993 552 499 ...
> contrasts(df$F) <- contr.helmert(2)
> contrasts(df$P) <- contr.helmert(2)
> contrasts(df$Q) <- contr.helmert(2)
> contrasts(df$lQ) <- contr.helmert(2)
> contrasts(df$lT) <- contr.helmert(2)
> system.time(m6 <- lmer(1000/rt ~ 1+F*P*Q*lQ*lT+(1+P+Q+lQ+lT|item)+(1+F+P+Q+lQ+lT|subj), df, REML=FALSE))
boundary (singular) fit: see ?isSingular
   user  system elapsed 
603.279   0.023 603.317 
```
"""

# ╔═╡ d87d83aa-be17-4f14-b8ac-78a674db11b3
md"""
## Model summary
```
> summary(m6)
Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: 1000/rt ~ 1 + F * P * Q * lQ * lT + (1 + P + Q + lQ + lT | item) +  
    (1 + F + P + Q + lQ + lT | subj)
   Data: df

     AIC      BIC   logLik deviance df.resid 
  7285.8   7817.4  -3573.9   7147.8    16340 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-4.6350 -0.5990  0.0874  0.6620  5.5168 

Random effects:
 Groups   Name        Variance  Std.Dev. Corr                         
 item     (Intercept) 3.202e-03 0.056583                              
          P1          1.250e-04 0.011179  0.05                        
          Q1          1.582e-04 0.012577  0.36  0.40                  
          lQ1         8.777e-06 0.002963  0.76  0.33 -0.10            
          lT1         1.573e-04 0.012542 -0.11 -0.89  0.00 -0.60      
 subj     (Intercept) 3.061e-02 0.174957                              
          F1          3.838e-05 0.006195  0.39                        
          P1          1.282e-04 0.011324  0.35  0.95                  
          Q1          7.899e-04 0.028105  0.41  0.50  0.72            
          lQ1         1.153e-04 0.010738  0.06  0.02  0.22  0.58      
          lT1         1.044e-03 0.032314  0.26 -0.14 -0.01  0.37  0.50
 Residual             8.574e-02 0.292810                              
Number of obs: 16409, groups:  item, 240; subj, 73

Fixed effects:
                   Estimate Std. Error t value
(Intercept)       1.637e+00  2.093e-02  78.248
F1                1.925e-02  4.375e-03   4.401
P1                1.883e-02  2.747e-03   6.856
...
```
"""

# ╔═╡ e2306a42-dcb6-40e4-811f-7c5bb26e0c20
md"## The same model fit with MixedModels.jl"

# ╔═╡ cfb22981-bb2f-43fb-8dd4-59b62f3eed9c
mrk17 = MixedModels.dataset(:mrk17_exp1) # sample data set

# ╔═╡ 27647edb-a0c6-451a-93d8-4f8415be786b
contr = Dict(              # set the contrasts
	:subj => Grouping(),
	:item => Grouping(),
	:F => HelmertCoding(),
	:P => HelmertCoding(),
	:Q => HelmertCoding(),
	:lQ => HelmertCoding(),
	:lT => HelmertCoding(),
);

# ╔═╡ 26b3f46f-4dee-4e60-99ed-892137126c93
m6frm = @formula 1000/rt ~ 1+F*P*Q*lQ*lT + (1+P+Q+lQ+lT|item) + (1+F+P+Q+lQ+lT|subj);

# ╔═╡ 9a303a89-dafc-4736-a711-ccb19b0671fd
md"## First model fit"

# ╔═╡ 71b3b7a0-2f29-4bf0-b10b-d06fc8805b34
m6 = fit(MixedModel, m6frm, mrk17; contrasts=contr)

# ╔═╡ f96dd303-e501-4343-939f-2b9ddc05ee8a
md"""
## Comparative speed
- The first fit in Julia is somewhat slow (a little over 60 seconds on my laptop) because of the JIT compilation.
- The fit with `lmer` from `lme4` took over 600 seconds on my laptop.  Various options could have been used to speed up the fit but we just used the "vanilla" version.
- A progress indicator is shown during the optimization to minimize the objective (negative twice the log-likelihood) with respect to the parameters.  It doesn't appear in the Pluto output.  In this case it was
```
Minimizing 1312  Time: 0 Time: 0:00:34 (26.29 ms/it)
      From worker 3:	  objective:  7147.682158526245
```
"""

# ╔═╡ 349652e8-39ff-466d-9eb3-bf8af4cd3e33
md"""
## Model fits after the first will be faster
- For illustration we fit the same model but, in practice, we may be fitting alternative models
"""

# ╔═╡ 41eb523c-d897-4a87-9bf5-89cc2802c29e
fit(MixedModel, m6frm, mrk17; contrasts=contr);

# ╔═╡ ecded3b9-5a1f-4f42-9f05-b29a7cf803e7
md"""
- This takes about 33 seconds on my laptop.  The progress indicator ended up at
```
Minimizing 1312  Time: 0 Time: 0:00:32 (24.82 ms/it)
      From worker 3:	  objective:  7147.682158526245
```
- The time to do the optimizing is essentially the same as before but the JIT compilation no longer occurs.
"""

# ╔═╡ 191901d3-ea42-4e5c-8582-285dd5af4652
md"""
## Julia v1.7.0 is faster, especially with MKL
```
julia> m6 = fit(MixedModel, m6frm, mrk17; contrasts=contr);
Minimizing 1506  Time: 0 Time: 0:00:18 (12.51 ms/it)

julia> m6.objective
7147.55033778133

julia> using MKL

julia> m6 = fit(MixedModel, m6frm, mrk17; contrasts=contr);
Minimizing 1316  Time: 0 Time: 0:00:05 ( 4.28 ms/it)

julia> m6.objective
7147.550374727961
```
"""

# ╔═╡ 548589e2-5299-4ad1-a0ec-22ad3936d363
md"""
## Why is the Julia code so much faster?
- It is not the optimizer per se - lme4 and MixedModels use the same optimizer (BOBYQA) and the same implementation, [NLopt](https://github.com/stevengj/nlopt)
- Method instances are compiled with the JIT compiler (even better in v1.7.0)
- The flexibility of the system allows for things like swapping in another (binary) BLAS library
- The implementation in MixedModels is similar to that in lme4 but a bit more advanced
    + finer grain control of the linear algebra b/c of Julia's [LinearAlgebra package](https://docs.julialang.org/en/v1/stdlib/LinearAlgebra/)
    + I stumbled upon a cleaner way to evaluate a certain quantity needed to evaluate the objective
    + I don't think I would have been able to do this in the R implementation. MixedModels.jl is 100% Julia whereas lme4 is a hodge-podge of R, C, C++, Rcpp, RcppEigen, etc. (my fault, entirely - don't blame my co-authors)

## Characteristics of the MixedModels package
"""

# ╔═╡ 40b0b7e3-88d7-47ea-bb46-e0dfabefc4e1
analyze("MixedModels")

# ╔═╡ 03cdeea6-5f6b-4095-8ae3-3600906df570
md"""
## Internal representation is more fine-grained
- uses a blocked matrix representation for a penalized least squares problem rather than a generic sparse matrix
"""

# ╔═╡ 61cb5943-a6e9-4022-bb01-68b86df6fe36
BlockDescription(m6)

# ╔═╡ b151e0fb-b28b-41b0-aef4-38a81a7dfa78
sparseL(m6; full=true)

# ╔═╡ ab4b74a3-8e97-48a5-8cf8-91fdea464aa3
md"""
## Diagnostic plots
- One of the strengths of R is the data and diagnostic graphics
- Graphics packages take a long time to develop.  Julia graphics are still comparatively early stage.
- We do have some diagnostic plots for mixed-effects models in the `MixedModelsMakie` package.
"""

# ╔═╡ 8781b4e9-c2f0-4a44-a29f-4cbc8eb7d298
CairoMakie.activate!(type="svg")

# ╔═╡ 81001f33-3f66-401e-815a-a46e4d4309ab
md"## Shrinkage plots"

# ╔═╡ d6aada8f-511f-4a74-a8cd-19ef88512e65
shrinkageplot(m6) # random-effects by item

# ╔═╡ adaaae43-5c43-45e1-9bd7-3f4fb9efc768
md"## Shrinkage plots by subject"

# ╔═╡ ac2f5d62-49be-4850-90f0-95c58edece02
shrinkageplot(m6, :subj)

# ╔═╡ 7ce2e0d0-b3df-4006-9b07-70b64da3b29a
md"""
## Summary of my experiences
- After adjusting to the language, development of a compute-intensive package in Julia was much easier than in R
- Julia package is 100% Julia, R package was written in several languages
- Maintenance of the Julia package is more straightforward because tools (documentation, testing, continuous integration, pull requests, issues) are native.
- Performance is generally better in Julia
- Performance tools (profiling execution, memory allocation profiling) are native.
- Changes in the overall system can bring big performance bonuses.
- I can experiment in Julia much more easily than in a static language.
- Auxillary tools (formula language, graphics packages) needed polishing but are coming along.
- See also [Kyla McConnell's experiences](https://github.com/kyla-mcconnell/juliaR)
"""

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uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
version = "1.0.1"

[[deps.Tables]]
deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "TableTraits", "Test"]
git-tree-sha1 = "d0c690d37c73aeb5ca063056283fde5585a41710"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.5.0"

[[deps.Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"

[[deps.TensorCore]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "1feb45f88d133a655e001435632f019a9a1bcdb6"
uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50"
version = "0.1.1"

[[deps.Test]]
deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

[[deps.TiffImages]]
deps = ["ColorTypes", "DocStringExtensions", "FileIO", "FixedPointNumbers", "IndirectArrays", "Inflate", "OffsetArrays", "OrderedCollections", "PkgVersion", "ProgressMeter"]
git-tree-sha1 = "03fb246ac6e6b7cb7abac3b3302447d55b43270e"
uuid = "731e570b-9d59-4bfa-96dc-6df516fadf69"
version = "0.4.1"

[[deps.TimeZones]]
deps = ["Dates", "Future", "LazyArtifacts", "Mocking", "Pkg", "Printf", "RecipesBase", "Serialization", "Unicode"]
git-tree-sha1 = "81753f400872e5074768c9a77d4c44e70d409ef0"
uuid = "f269a46b-ccf7-5d73-abea-4c690281aa53"
version = "1.5.6"

[[deps.Tokei_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "8ccf563fc2dd590fbc91c8634ba66b0e0ab94a5f"
uuid = "3ac119c9-1236-5556-b556-adc8150b0244"
version = "12.1.2+2"

[[deps.TranscodingStreams]]
deps = ["Random", "Test"]
git-tree-sha1 = "216b95ea110b5972db65aa90f88d8d89dcb8851c"
uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
version = "0.9.6"

[[deps.URIs]]
git-tree-sha1 = "97bbe755a53fe859669cd907f2d96aee8d2c1355"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.3.0"

[[deps.UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[deps.Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

[[deps.UnicodeFun]]
deps = ["REPL"]
git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
version = "0.4.1"

[[deps.WoodburyMatrices]]
deps = ["LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "59e2ad8fd1591ea019a5259bd012d7aee15f995c"
uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
version = "0.5.3"

[[deps.XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "1acf5bdf07aa0907e0a37d3718bb88d4b687b74a"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.9.12+0"

[[deps.XSLT_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
version = "1.1.34+0"

[[deps.Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.6.9+4"

[[deps.Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.9+4"

[[deps.Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fe47bd2247248125c428978740e18a681372dd4"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.3+4"

[[deps.Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.4+4"

[[deps.Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.10+4"

[[deps.Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.0+3"

[[deps.Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.13.0+3"

[[deps.Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.4.0+3"

[[deps.ZipFile]]
deps = ["Libdl", "Printf", "Zlib_jll"]
git-tree-sha1 = "c3a5637e27e914a7a445b8d0ad063d701931e9f7"
uuid = "a5390f91-8eb1-5f08-bee0-b1d1ffed6cea"
version = "0.9.3"

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "cc4bf3fdde8b7e3e9fa0351bdeedba1cf3b7f6e6"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.0+0"

[[deps.isoband_jll]]
deps = ["Libdl", "Pkg"]
git-tree-sha1 = "a1ac99674715995a536bbce674b068ec1b7d893d"
uuid = "9a68df92-36a6-505f-a73e-abb412b6bfb4"
version = "0.2.2+0"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "acc685bcf777b2202a904cdcb49ad34c2fa1880c"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.14.0+4"

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "7a5780a0d9c6864184b3a2eeeb833a0c871f00ab"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "0.1.6+4"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"

[[deps.libsodium_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "848ab3d00fe39d6fbc2a8641048f8f272af1c51e"
uuid = "a9144af2-ca23-56d9-984f-0d03f7b5ccf8"
version = "1.0.20+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "c45f4e40e7aafe9d086379e5578947ec8b95a8fb"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+0"

[[deps.licensecheck_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "36fd7569c95add047b52be1fb99c485e91f374f6"
uuid = "4ecb348a-8b88-51ea-b912-4c460483ee91"
version = "0.3.1+1"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "d713c1ce4deac133e3334ee12f4adff07f81778f"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2020.7.14+2"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "487da2f8f2f0c8ee0e83f39d13037d6bbf0a45ab"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.0.0+3"
"""

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