Load and save DataFrames

Load and save DataFrames#

We do not cover all features of the packages. Please refer to their documentation to learn them.

Here we’ll load CSV.jl to read and write CSV files and Arrow.jl, JLSO.jl, and serialization, which allow us to work with a binary format and JSONTables.jl for JSON interaction. Finally we consider a custom JDF.jl format.

using DataFrames
using Arrow
using CSV
using Serialization
using JLSO
using JSONTables
using CodecZlib
using ZipFile
using JDF
using StatsPlots ## for charts
using Mmap ## for compression

Let’s create a simple DataFrame for testing purposes,

x = DataFrame(
    A=[true, false, true], B=[1, 2, missing],
    C=[missing, "b", "c"], D=['a', missing, 'c']
)
3×4 DataFrame
RowABCD
BoolInt64?String?Char?
1true1missinga
2false2bmissing
3truemissingcc

and use eltypes to look at the columnwise types.

eltype.(eachcol(x))

4-element Vector{Type}:
 Bool
 Union{Missing, Int64}
 Union{Missing, String}
 Union{Missing, Char}

CSV.jl#

Let’s use CSV to save x to disk; make sure x1.csv does not conflict with some file in your working directory.

CSV.write("x1.csv", x)

"x1.csv"

Now we can see how it was saved by reading x.csv.

print(read("x1.csv", String))

A,B,C,D
true,1,,a
false,2,b,
true,,c,c

We can also load it back as a data frame

y = CSV.read("x1.csv", DataFrame)
3×4 DataFrame
RowABCD
BoolInt64?String1?String1?
1true1missinga
2false2bmissing
3truemissingcc

Note that when loading in a DataFrame from a CSV the column type for columns :C :D have changed to use special strings defined in the InlineStrings.jl package.

eltype.(eachcol(y))

4-element Vector{Type}:
 Bool
 Union{Missing, Int64}
 Union{Missing, InlineStrings.String1}
 Union{Missing, InlineStrings.String1}

Serialization by JDF.jl and JLSO.jl#

Now we use serialization to save x.

There are two ways to perform serialization. The first way is to use the Serialization.serialize as below:

Note that in general, this process will not work if the reading and writing are done by different versions of Julia, or an instance of Julia with a different system image.

open("x.bin", "w") do io
    serialize(io, x)
end

Now we load back the saved file to y variable. Again y is identical to x. However, please beware that if you session does not have DataFrames.jl loaded, then it may not recognize the content as DataFrames.jl

y = open(deserialize, "x.bin")
3×4 DataFrame
RowABCD
BoolInt64?String?Char?
1true1missinga
2false2bmissing
3truemissingcc
eltype.(eachcol(y))

4-element Vector{Type}:
 Bool
 Union{Missing, Int64}
 Union{Missing, String}
 Union{Missing, Char}

JDF.jl#

JDF.jl is a relatively new package designed to serialize DataFrames. You can save a DataFrame with the savejdf function. For more details about design assumptions and limitations of JDF.jl please check out xiaodaigh/JDF.jl.

JDF.save("x.jdf", x);

To load the saved JDF file, one can use the loadjdf function

x_loaded = JDF.load("x.jdf") |> DataFrame
3×4 DataFrame
RowABCD
BoolInt64?String?Char?
1true1missinga
2false2bmissing
3truemissingcc

You can see that they are the same

isequal(x_loaded, x)

true

JDF.jl offers the ability to load only certain columns from disk to help with working with large files. set up a JDFFile which is a on disk representation of x backed by JDF.jl

x_ondisk = jdf"x.jdf"

JDF.JDFFile{String}("x.jdf")

We can see all the names of x without loading it into memory

names(x_ondisk)

4-element Vector{Symbol}:
 :A
 :B
 :C
 :D

The below is an example of how to load only columns :A and :D

xd = JDF.load(x_ondisk; cols=["A", "D"]) |> DataFrame
3×2 DataFrame
RowAD
BoolChar?
1truea
2falsemissing
3truec

JLSO.jl#

Another way to perform serialization is by using the JLSO.jl library:

JLSO.save("x.jlso", :data => x)

Now we can load back the file to y

y = JLSO.load("x.jlso")[:data]
3×4 DataFrame
RowABCD
BoolInt64?String?Char?
1true1missinga
2false2bmissing
3truemissingcc
eltype.(eachcol(y))

4-element Vector{Type}:
 Bool
 Union{Missing, Int64}
 Union{Missing, String}
 Union{Missing, Char}

JSONTables.jl#

Often you might need to read and write data stored in JSON format. JSONTables.jl provides a way to process them in row-oriented or column-oriented layout. We present both options below.

open(io -> arraytable(io, x), "x1.json", "w")

106

open(io -> objecttable(io, x), "x2.json", "w")

76

print(read("x1.json", String))

[{"A":true,"B":1,"C":null,"D":"a"},{"A":false,"B":2,"C":"b","D":null},{"A":true,"B":null,"C":"c","D":"c"}]

print(read("x2.json", String))

{"A":[true,false,true],"B":[1,2,null],"C":[null,"b","c"],"D":["a",null,"c"]}

y1 = open(jsontable, "x1.json") |> DataFrame
3×4 DataFrame
RowABCD
BoolInt64?String?String?
1true1missinga
2false2bmissing
3truemissingcc
eltype.(eachcol(y1))

4-element Vector{Type}:
 Bool
 Union{Missing, Int64}
 Union{Missing, String}
 Union{Missing, String}

y2 = open(jsontable, "x2.json") |> DataFrame
3×4 DataFrame
RowABCD
BoolInt64?String?String?
1true1missinga
2false2bmissing
3truemissingcc
eltype.(eachcol(y2))

4-element Vector{Type}:
 Bool
 Union{Missing, Int64}
 Union{Missing, String}
 Union{Missing, String}

Arrow.jl#

Finally we use Apache Arrow format that allows, in particular, for data interchange with R or Python.

Arrow.write("x.arrow", x)

"x.arrow"

y = Arrow.Table("x.arrow") |> DataFrame
3×4 DataFrame
RowABCD
BoolInt64?String?Char?
1true1missinga
2false2bmissing
3truemissingcc
eltype.(eachcol(y))

4-element Vector{Type}:
 Bool
 Union{Missing, Int64}
 Union{Missing, String}
 Union{Missing, Char}

Note that columns of y are immutable

try
    y.A[1] = false
catch e
    show(e)
end

ReadOnlyMemoryError()

This is because Arrow.Table uses memory mapping and thus uses a custom vector types:

y.A

3-element Arrow.BoolVector{Bool}:
 1
 0
 1

y.B

3-element Arrow.Primitive{Union{Missing, Int64}, Vector{Int64}}:
 1
 2
  missing

You can get standard Julia Base vectors by copying a data frame

y2 = copy(y)
3×4 DataFrame
RowABCD
BoolInt64?String?Char?
1true1missinga
2false2bmissing
3truemissingcc
y2.A

3-element Vector{Bool}:
 1
 0
 1

y2.B

3-element Vector{Union{Missing, Int64}}:
 1
 2
  missing

Basic benchmarking#

Next, we’ll create some files, so be careful that you don’t already have these files in your working directory! In particular, we’ll time how long it takes us to write a DataFrame with 1000 rows and 100000 columns.

bigdf = DataFrame(rand(Bool, 10^4, 1000), :auto)

bigdf[!, 1] = Int.(bigdf[!, 1])
bigdf[!, 2] = bigdf[!, 2] .+ 0.5
bigdf[!, 3] = string.(bigdf[!, 3], ", as string")

println("First run")

First run

println("CSV.jl")
csvwrite1 = @elapsed @time CSV.write("bigdf1.csv", bigdf)
println("Serialization")
serializewrite1 = @elapsed @time open(io -> serialize(io, bigdf), "bigdf.bin", "w")
println("JDF.jl")
jdfwrite1 = @elapsed @time JDF.save("bigdf.jdf", bigdf)
println("JLSO.jl")
jlsowrite1 = @elapsed @time JLSO.save("bigdf.jlso", :data => bigdf)
println("Arrow.jl")
arrowwrite1 = @elapsed @time Arrow.write("bigdf.arrow", bigdf)
println("JSONTables.jl arraytable")
jsontablesawrite1 = @elapsed @time open(io -> arraytable(io, bigdf), "bigdf1.json", "w")
println("JSONTables.jl objecttable")
jsontablesowrite1 = @elapsed @time open(io -> objecttable(io, bigdf), "bigdf2.json", "w")
println("Second run")
println("CSV.jl")
csvwrite2 = @elapsed @time CSV.write("bigdf1.csv", bigdf)
println("Serialization")
serializewrite2 = @elapsed @time open(io -> serialize(io, bigdf), "bigdf.bin", "w")
println("JDF.jl")
jdfwrite2 = @elapsed @time JDF.save("bigdf.jdf", bigdf)
println("JLSO.jl")
jlsowrite2 = @elapsed @time JLSO.save("bigdf.jlso", :data => bigdf)
println("Arrow.jl")
arrowwrite2 = @elapsed @time Arrow.write("bigdf.arrow", bigdf)
println("JSONTables.jl arraytable")
jsontablesawrite2 = @elapsed @time open(io -> arraytable(io, bigdf), "bigdf1.json", "w")
println("JSONTables.jl objecttable")
jsontablesowrite2 = @elapsed @time open(io -> objecttable(io, bigdf), "bigdf2.json", "w")

CSV.jl
  6.625767 seconds (44.69 M allocations: 1.127 GiB, 3.21% gc time, 64.54% compilation time)
Serialization
  0.280890 seconds (224.29 k allocations: 10.821 MiB, 29.82% compilation time)
JDF.jl
  0.165195 seconds (68.08 k allocations: 147.946 MiB, 23.08% gc time, 46.89% compilation time)
JLSO.jl
  1.295517 seconds (284.83 k allocations: 20.372 MiB, 0.76% gc time, 8.74% compilation time)
Arrow.jl
  6.013596 seconds (5.45 M allocations: 275.670 MiB, 0.58% gc time, 97.57% compilation time)
JSONTables.jl arraytable
 20.560618 seconds (229.62 M allocations: 5.422 GiB, 15.39% gc time, 0.08% compilation time)
JSONTables.jl objecttable
  0.617348 seconds (96.64 k allocations: 309.085 MiB, 48.29% gc time, 17.88% compilation time)
Second run
CSV.jl
  1.690940 seconds (44.40 M allocations: 1.113 GiB, 9.06% gc time)
Serialization
  0.216240 seconds (15.01 k allocations: 400.680 KiB, 7.44% compilation time)
JDF.jl
  0.124376 seconds (35.13 k allocations: 146.223 MiB, 17.17% gc time)
JLSO.jl
  1.183068 seconds (33.41 k allocations: 7.465 MiB)
Arrow.jl
  0.113700 seconds (81.35 k allocations: 5.426 MiB)
JSONTables.jl arraytable
 15.777456 seconds (229.62 M allocations: 5.422 GiB, 14.61% gc time, 0.10% compilation time)
JSONTables.jl objecttable
  0.532067 seconds (20.71 k allocations: 305.221 MiB, 54.40% gc time, 2.10% compilation time)

0.532235469

groupedbar(
    repeat(["CSV.jl", "Serialization", "JDF.jl", "JLSO.jl", "Arrow.jl", "JSONTables.jl\nobjecttable"],
        inner=2),
    [csvwrite1, csvwrite2, serializewrite1, serializewrite1, jdfwrite1, jdfwrite2,
        jlsowrite1, jlsowrite2, arrowwrite1, arrowwrite2, jsontablesowrite2, jsontablesowrite2],
    group=repeat(["1st", "2nd"], outer=6),
    ylab="Second",
    title="Write Performance\nDataFrame: bigdf\nSize: $(size(bigdf))"
)
_images/476d0fa3c7b2efa6e960e6fda4d96998a297ededeef6d221175cbfdd5e0c77eb.png 
data_files = ["bigdf1.csv", "bigdf.bin", "bigdf.arrow", "bigdf1.json", "bigdf2.json"]
df = DataFrame(file=data_files, size=getfield.(stat.(data_files), :size))
append!(df, DataFrame(file="bigdf.jdf", size=reduce((x, y) -> x + y.size,
    stat.(joinpath.("bigdf.jdf", readdir("bigdf.jdf"))),
    init=0)))
sort!(df, :size)
6×2 DataFrame
Rowfilesize
StringInt64
1bigdf.arrow1742906
2bigdf.bin5199352
3bigdf.jdf5223402
4bigdf1.csv55083649
5bigdf2.json55087650
6bigdf1.json124028757
@df df plot(:file, :size / 1024^2, seriestype=:bar, title="Format File Size (MB)", label="Size", ylab="MB")
_images/aa5a984f4029f8daa88b10e411c4f6986b651845be2c9257ada24bd7df76f681.png 
println("First run")
println("CSV.jl")
csvread1 = @elapsed @time CSV.read("bigdf1.csv", DataFrame)
println("Serialization")
serializeread1 = @elapsed @time open(deserialize, "bigdf.bin")
println("JDF.jl")
jdfread1 = @elapsed @time JDF.load("bigdf.jdf") |> DataFrame
println("JLSO.jl")
jlsoread1 = @elapsed @time JLSO.load("bigdf.jlso")
println("Arrow.jl")
arrowread1 = @elapsed @time df_tmp = Arrow.Table("bigdf.arrow") |> DataFrame
arrowread1copy = @elapsed @time copy(df_tmp)
println("JSONTables.jl arraytable")
jsontablesaread1 = @elapsed @time open(jsontable, "bigdf1.json")
println("JSONTables.jl objecttable")
jsontablesoread1 = @elapsed @time open(jsontable, "bigdf2.json")
println("Second run")
csvread2 = @elapsed @time CSV.read("bigdf1.csv", DataFrame)
println("Serialization")
serializeread2 = @elapsed @time open(deserialize, "bigdf.bin")
println("JDF.jl")
jdfread2 = @elapsed @time JDF.load("bigdf.jdf") |> DataFrame
println("JLSO.jl")
jlsoread2 = @elapsed @time JLSO.load("bigdf.jlso")
println("Arrow.jl")
arrowread2 = @elapsed @time df_tmp = Arrow.Table("bigdf.arrow") |> DataFrame
arrowread2copy = @elapsed @time copy(df_tmp)
println("JSONTables.jl arraytable")
jsontablesaread2 = @elapsed @time open(jsontable, "bigdf1.json")
println("JSONTables.jl objecttable")
jsontablesoread2 = @elapsed @time open(jsontable, "bigdf2.json");

First run
CSV.jl
  2.638622 seconds (3.55 M allocations: 208.195 MiB, 0.98% gc time, 138.18% compilation time)
Serialization
  0.395702 seconds (9.50 M allocations: 155.494 MiB, 9.00% gc time, 9.19% compilation time)
JDF.jl
  0.217561 seconds (169.93 k allocations: 158.469 MiB, 12.14% gc time, 76.63% compilation time)
JLSO.jl
  0.350374 seconds (9.52 M allocations: 158.102 MiB, 6.15% gc time, 8.30% compilation time)
Arrow.jl
  0.481468 seconds (550.37 k allocations: 26.328 MiB, 98.46% compilation time)
  0.068915 seconds (14.50 k allocations: 10.259 MiB)
JSONTables.jl arraytable
  6.826233 seconds (271.07 k allocations: 1.838 GiB, 9.73% gc time)
JSONTables.jl objecttable
  0.352800 seconds (7.43 k allocations: 403.793 MiB, 4.50% gc time, 0.02% compilation time)
Second run
  0.546310 seconds (152.65 k allocations: 34.427 MiB)
Serialization
  0.340662 seconds (9.48 M allocations: 154.588 MiB, 5.76% gc time)
JDF.jl
  0.371574 seconds (77.27 k allocations: 153.746 MiB, 86.69% gc time)
JLSO.jl
  0.352822 seconds (9.50 M allocations: 157.233 MiB, 4.64% gc time)
Arrow.jl
  0.008759 seconds (86.57 k allocations: 3.731 MiB)
  0.049918 seconds (14.50 k allocations: 10.259 MiB)
JSONTables.jl arraytable
  6.749524 seconds (271.07 k allocations: 1.838 GiB, 9.91% gc time)
JSONTables.jl objecttable
  0.354865 seconds (7.08 k allocations: 403.777 MiB, 1.90% gc time)

Exclude JSONTables due to much longer timing

groupedbar(
    repeat(["CSV.jl", "Serialization", "JDF.jl", "JLSO.jl", "Arrow.jl", "Arrow.jl\ncopy", ##"JSON\narraytable",
            "JSON\nobjecttable"], inner=2),
    [csvread1, csvread2, serializeread1, serializeread2, jdfread1, jdfread2, jlsoread1, jlsoread2,
        arrowread1, arrowread2, arrowread1 + arrowread1copy, arrowread2 + arrowread2copy,
        # jsontablesaread1, jsontablesaread2,
        jsontablesoread1, jsontablesoread2],
    group=repeat(["1st", "2nd"], outer=7),
    ylab="Second",
    title="Read Performance\nDataFrame: bigdf\nSize: $(size(bigdf))"
)
_images/1f29761aac8a320ccdd6e8b976dbae7f80cbc755a9253f1d105d6a982ebdd44d.png

Using gzip compression#

A common user requirement is to be able to load and save CSV that are compressed using gzip. Below we show how this can be accomplished using CodecZlib.jl. The same pattern is applicable to JSONTables.jl compression/decompression. Again make sure that you do not have file named df_compress_test.csv.gz in your working directory. We first generate a random data frame.

df = DataFrame(rand(1:10, 10, 1000), :auto)
10×1000 DataFrame
900 columns omitted
Rowx1x2x3x4x5x6x7x8x9x10x11x12x13x14x15x16x17x18x19x20x21x22x23x24x25x26x27x28x29x30x31x32x33x34x35x36x37x38x39x40x41x42x43x44x45x46x47x48x49x50x51x52x53x54x55x56x57x58x59x60x61x62x63x64x65x66x67x68x69x70x71x72x73x74x75x76x77x78x79x80x81x82x83x84x85x86x87x88x89x90x91x92x93x94x95x96x97x98x99x100⋯
Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64⋯
15710108693194742764786245564344729898129694155991091981067411051671135748259651719127888813101938381783638⋯
258276654244561367311079769298897741016219198461101010512396419104433843112108736551091083105391741043312510974101⋯
31327891042937821414193863610684371010271656941891067825972103108933442513104884445139922310358693341275326797⋯
477828836762941011095528710248499108933193152132892895373997884105743693310399559104721336105539444310618210431⋯
5441091074775968461015410998855221034658924910274419211643849110147325369929283552101892953103942510437266110444⋯
61173484746664683584952510188731873186816349743102107632971885629210646676810789833151037721241047910849421071⋯
727510110531434101077821095710127275107615722658457162104591236958329686239453257547634111018416351047287261182⋯
8418396510177339879559271077162536253811091041074835181031495821068834723610786886810710410810922873210628249731019⋯
957621896574521941184192844141010171935366841102441785111052127857856259276632895210663108810658323369396237⋯
101022321088775723101093781419782910810621068531091544249965431810679866468833628451010189913685810210417510295239109⋯

GzipCompressorStream comes from CodecZlib

open("df_compress_test.csv.gz", "w") do io
    stream = GzipCompressorStream(io)
    CSV.write(stream, df)
    close(stream)
end

df2 = CSV.File(transcode(GzipDecompressor, Mmap.mmap("df_compress_test.csv.gz"))) |> DataFrame
10×1000 DataFrame
900 columns omitted
Rowx1x2x3x4x5x6x7x8x9x10x11x12x13x14x15x16x17x18x19x20x21x22x23x24x25x26x27x28x29x30x31x32x33x34x35x36x37x38x39x40x41x42x43x44x45x46x47x48x49x50x51x52x53x54x55x56x57x58x59x60x61x62x63x64x65x66x67x68x69x70x71x72x73x74x75x76x77x78x79x80x81x82x83x84x85x86x87x88x89x90x91x92x93x94x95x96x97x98x99x100⋯
Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64Int64⋯
15710108693194742764786245564344729898129694155991091981067411051671135748259651719127888813101938381783638⋯
258276654244561367311079769298897741016219198461101010512396419104433843112108736551091083105391741043312510974101⋯
31327891042937821414193863610684371010271656941891067825972103108933442513104884445139922310358693341275326797⋯
477828836762941011095528710248499108933193152132892895373997884105743693310399559104721336105539444310618210431⋯
5441091074775968461015410998855221034658924910274419211643849110147325369929283552101892953103942510437266110444⋯
61173484746664683584952510188731873186816349743102107632971885629210646676810789833151037721241047910849421071⋯
727510110531434101077821095710127275107615722658457162104591236958329686239453257547634111018416351047287261182⋯
8418396510177339879559271077162536253811091041074835181031495821068834723610786886810710410810922873210628249731019⋯
957621896574521941184192844141010171935366841102441785111052127857856259276632895210663108810658323369396237⋯
101022321088775723101093781419782910810621068531091544249965431810679866468833628451010189913685810210417510295239109⋯
df == df2

true

Using zip files#

Sometimes you may have files compressed inside a zip file. In such a situation you may use ZipFile.jl in conjunction an an appropriate reader to read the files. Here we first create a ZIP file and then read back its contents into a DataFrame.

df1 = DataFrame(rand(1:10, 3, 4), :auto)
3×4 DataFrame
Rowx1x2x3x4
Int64Int64Int64Int64
16279
241089
35842
df2 = DataFrame(rand(1:10, 3, 4), :auto)
3×4 DataFrame
Rowx1x2x3x4
Int64Int64Int64Int64
18932
28168
3411010

And we show yet another way to write a DataFrame into a CSV file: Writing a CSV file into the zip file

w = ZipFile.Writer("x.zip")

f1 = ZipFile.addfile(w, "x1.csv")
write(f1, sprint(show, "text/csv", df1))

# write a second CSV file into zip file
f2 = ZipFile.addfile(w, "x2.csv", method=ZipFile.Deflate)
write(f2, sprint(show, "text/csv", df2))

close(w)

Now we read the compressed CSV file we have written:

z = ZipFile.Reader("x.zip");
# find the index index of file called x1.csv
index_xcsv = findfirst(x -> x.name == "x1.csv", z.files)
# to read the x1.csv file in the zip file
df1_2 = CSV.read(read(z.files[index_xcsv]), DataFrame)
3×4 DataFrame
Rowx1x2x3x4
Int64Int64Int64Int64
16279
241089
35842
df1_2 == df1

true

# find the index index of file called x2.csv
index_xcsv = findfirst(x -> x.name == "x2.csv", z.files)
# to read the x2.csv file in the zip file
df2_2 = CSV.read(read(z.files[index_xcsv]), DataFrame)
3×4 DataFrame
Rowx1x2x3x4
Int64Int64Int64Int64
18932
28168
3411010
df2_2 == df2

true

Note that once you read a given file from z object its stream is all used-up (reaching its end). Therefore to read it again you need to close the file object z and open it again. Also do not forget to close the zip file once you are done.

close(z)

Remove generated files

rm("x.arrow")
rm("x.bin")
rm("x.zip")
rm("x.jlso")
rm("x1.csv")
rm("x1.json")
rm("x2.json")
rm("x.jdf", recursive=true)
rm("bigdf.jdf", recursive=true)
rm("df_compress_test.csv.gz")
rm("bigdf1.json")
rm("bigdf1.csv")
rm("bigdf2.json")
rm("bigdf.jlso")
rm("bigdf.bin")
rm("bigdf.arrow")

This notebook was generated using Literate.jl.