Performance tips#
using DataFrames
using BenchmarkTools
using CategoricalArrays
using PooledArrays
using Random
Access by column number is faster than by name#
x = DataFrame(rand(5, 1000), :auto)
@btime $x[!, 500]; ## Faster
3.086 ns (0 allocations: 0 bytes)
@btime $x.x500; ## Slower
11.443 ns (0 allocations: 0 bytes)
When working with data DataFrame use barrier functions or type annotation#
function f_bad() ## this function will be slow
Random.seed!(1)
x = DataFrame(rand(1000000, 2), :auto)
y, z = x[!, 1], x[!, 2]
p = 0.0
for i in 1:nrow(x)
p += y[i] * z[i]
end
p
end
@btime f_bad();
# if you run @code_warntype f_bad() then you notice
# that Julia does not know column types of `DataFrame`
106.113 ms (5999022 allocations: 122.06 MiB)
solution 1 is to use barrier function (it should be possible to use it in almost any code) for the calculation. You will notice much less memopry allocations and faster performance.
function f_inner(y, z)
p = 0.0
for i in eachindex(y, z)
p += y[i] * z[i]
end
p
end
function f_barrier()
Random.seed!(1)
x = DataFrame(rand(1000000, 2), :auto)
f_inner(x[!, 1], x[!, 2])
end
@btime f_barrier();
3.813 ms (44 allocations: 30.52 MiB)
or use inbuilt function if possible
using LinearAlgebra
function f_inbuilt()
Random.seed!(1)
x = DataFrame(rand(1000000, 2), :auto)
dot(x[!, 1], x[!, 2])
end
@btime f_inbuilt();
3.239 ms (44 allocations: 30.52 MiB)
solution 2 is to provide the types of extracted columns. However, there are cases in which you will not know these types.
function f_typed()
Random.seed!(1)
x = DataFrame(rand(1000000, 2), :auto)
y::Vector{Float64}, z::Vector{Float64} = x[!, 1], x[!, 2]
p = 0.0
for i in 1:nrow(x)
p += y[i] * z[i]
end
p
end
@btime f_typed();
3.780 ms (44 allocations: 30.52 MiB)
In general for tall and narrow tables it is often useful to use Tables.rowtable
, Tables.columntable
or Tables.namedtupleiterator
for intermediate processing of data in a type-stable way.
Consider using delayed DataFrame
creation technique#
also notice the difference in performance between copying vs non-copying data frame creation
function f1()
x = DataFrame([Vector{Float64}(undef, 10^4) for i in 1:100], :auto, copycols=false) ## we work with a DataFrame directly
for c in 1:ncol(x)
d = x[!, c]
for r in 1:nrow(x)
d[r] = rand()
end
end
x
end
function f1a()
x = DataFrame([Vector{Float64}(undef, 10^4) for i in 1:100], :auto) ## we work with a DataFrame directly
for c in 1:ncol(x)
d = x[!, c]
for r in 1:nrow(x)
d[r] = rand()
end
end
x
end
function f2()
x = Vector{Any}(undef, 100)
for c in 1:length(x)
d = Vector{Float64}(undef, 10^4)
for r in eachindex(d)
d[r] = rand()
end
x[c] = d
end
DataFrame(x, :auto, copycols=false) ## we delay creation of DataFrame after we have our job done
end
function f2a()
x = Vector{Any}(undef, 100)
for c in eachindex(x)
d = Vector{Float64}(undef, 10^4)
for r in eachindex(d)
d[r] = rand()
end
x[c] = d
end
DataFrame(x, :auto) ## we delay creation of DataFrame after we have our job done
end
@btime f1();
@btime f1a();
@btime f2();
@btime f2a();
27.633 ms (1949728 allocations: 37.40 MiB)
28.487 ms (1950028 allocations: 45.03 MiB)
1.142 ms (728 allocations: 7.66 MiB)
1.563 ms (1028 allocations: 15.29 MiB)
You can add rows to a DataFrame in place and it is fast#
x = DataFrame(rand(10^6, 5), :auto)
y = DataFrame(transpose(1.0:5.0), :auto)
z = [1.0:5.0;]
@btime vcat($x, $y); ## creates a new DataFrame - slow
@btime append!($x, $y); ## in place - fast
x = DataFrame(rand(10^6, 5), :auto) ## reset to the same starting point
@btime push!($x, $z); ## add a single row in place - fast
2.687 ms (212 allocations: 38.16 MiB)
1.192 μs (29 allocations: 1.50 KiB)
443.960 ns (16 allocations: 256 bytes)
Allowing missing as well as categorical slows down computations#
using StatsBase
function test(data) ## uses countmap function to test performance
println(eltype(data))
x = rand(data, 10^6)
y = categorical(x)
println(" raw:")
@btime countmap($x)
println(" categorical:")
@btime countmap($y)
nothing
end
test(1:10)
test([randstring() for i in 1:10])
test(allowmissing(1:10))
test(allowmissing([randstring() for i in 1:10]))
Int64
raw:
1.882 ms (8 allocations: 7.63 MiB)
categorical:
15.506 ms (1000004 allocations: 30.52 MiB)
String
raw:
18.031 ms (4 allocations: 448 bytes)
categorical:
28.813 ms (1000004 allocations: 30.52 MiB)
Union{Missing, Int64}
raw:
6.026 ms (4 allocations: 464 bytes)
categorical:
15.741 ms (1000004 allocations: 30.52 MiB)
Union{Missing, String}
raw:
20.340 ms (4 allocations: 448 bytes)
categorical:
30.785 ms (1000004 allocations: 30.52 MiB)
When aggregating use column selector and prefer integer, categorical, or pooled array grouping variable#
df = DataFrame(x=rand('a':'d', 10^7), y=1);
gdf = groupby(df, :x)
GroupedDataFrame with 4 groups based on key: x
Row | x | y |
---|---|---|
Char | Int64 | |
1 | a | 1 |
2 | a | 1 |
3 | a | 1 |
4 | a | 1 |
5 | a | 1 |
6 | a | 1 |
7 | a | 1 |
8 | a | 1 |
9 | a | 1 |
10 | a | 1 |
11 | a | 1 |
12 | a | 1 |
13 | a | 1 |
⋮ | ⋮ | ⋮ |
2500722 | a | 1 |
2500723 | a | 1 |
2500724 | a | 1 |
2500725 | a | 1 |
2500726 | a | 1 |
2500727 | a | 1 |
2500728 | a | 1 |
2500729 | a | 1 |
2500730 | a | 1 |
2500731 | a | 1 |
2500732 | a | 1 |
2500733 | a | 1 |
⋮
Row | x | y |
---|---|---|
Char | Int64 | |
1 | c | 1 |
2 | c | 1 |
3 | c | 1 |
4 | c | 1 |
5 | c | 1 |
6 | c | 1 |
7 | c | 1 |
8 | c | 1 |
9 | c | 1 |
10 | c | 1 |
11 | c | 1 |
12 | c | 1 |
13 | c | 1 |
⋮ | ⋮ | ⋮ |
2501221 | c | 1 |
2501222 | c | 1 |
2501223 | c | 1 |
2501224 | c | 1 |
2501225 | c | 1 |
2501226 | c | 1 |
2501227 | c | 1 |
2501228 | c | 1 |
2501229 | c | 1 |
2501230 | c | 1 |
2501231 | c | 1 |
2501232 | c | 1 |
traditional syntax, slow
@btime combine(v -> sum(v.y), $gdf)
17.042 ms (332 allocations: 19.09 MiB)
Row | x | x1 |
---|---|---|
Char | Int64 | |
1 | a | 2500733 |
2 | d | 2497020 |
3 | b | 2501015 |
4 | c | 2501232 |
use column selector
@btime combine($gdf, :y => sum)
6.893 ms (198 allocations: 10.14 KiB)
Row | x | y_sum |
---|---|---|
Char | Int64 | |
1 | a | 2500733 |
2 | d | 2497020 |
3 | b | 2501015 |
4 | c | 2501232 |
transform!(df, :x => categorical => :x);
gdf = groupby(df, :x)
GroupedDataFrame with 4 groups based on key: x
Row | x | y |
---|---|---|
Cat… | Int64 | |
1 | a | 1 |
2 | a | 1 |
3 | a | 1 |
4 | a | 1 |
5 | a | 1 |
6 | a | 1 |
7 | a | 1 |
8 | a | 1 |
9 | a | 1 |
10 | a | 1 |
11 | a | 1 |
12 | a | 1 |
13 | a | 1 |
⋮ | ⋮ | ⋮ |
2500722 | a | 1 |
2500723 | a | 1 |
2500724 | a | 1 |
2500725 | a | 1 |
2500726 | a | 1 |
2500727 | a | 1 |
2500728 | a | 1 |
2500729 | a | 1 |
2500730 | a | 1 |
2500731 | a | 1 |
2500732 | a | 1 |
2500733 | a | 1 |
⋮
Row | x | y |
---|---|---|
Cat… | Int64 | |
1 | d | 1 |
2 | d | 1 |
3 | d | 1 |
4 | d | 1 |
5 | d | 1 |
6 | d | 1 |
7 | d | 1 |
8 | d | 1 |
9 | d | 1 |
10 | d | 1 |
11 | d | 1 |
12 | d | 1 |
13 | d | 1 |
⋮ | ⋮ | ⋮ |
2497009 | d | 1 |
2497010 | d | 1 |
2497011 | d | 1 |
2497012 | d | 1 |
2497013 | d | 1 |
2497014 | d | 1 |
2497015 | d | 1 |
2497016 | d | 1 |
2497017 | d | 1 |
2497018 | d | 1 |
2497019 | d | 1 |
2497020 | d | 1 |
@btime combine($gdf, :y => sum)
6.834 ms (206 allocations: 10.62 KiB)
Row | x | y_sum |
---|---|---|
Cat… | Int64 | |
1 | a | 2500733 |
2 | b | 2501015 |
3 | c | 2501232 |
4 | d | 2497020 |
transform!(df, :x => PooledArray{Char} => :x)
Row | x | y |
---|---|---|
Char | Int64 | |
1 | a | 1 |
2 | a | 1 |
3 | d | 1 |
4 | d | 1 |
5 | d | 1 |
6 | b | 1 |
7 | d | 1 |
8 | a | 1 |
9 | a | 1 |
10 | d | 1 |
11 | b | 1 |
12 | b | 1 |
13 | c | 1 |
⋮ | ⋮ | ⋮ |
9999989 | d | 1 |
9999990 | b | 1 |
9999991 | c | 1 |
9999992 | c | 1 |
9999993 | a | 1 |
9999994 | b | 1 |
9999995 | b | 1 |
9999996 | d | 1 |
9999997 | d | 1 |
9999998 | b | 1 |
9999999 | a | 1 |
10000000 | c | 1 |
gdf = groupby(df, :x)
GroupedDataFrame with 4 groups based on key: x
Row | x | y |
---|---|---|
Char | Int64 | |
1 | a | 1 |
2 | a | 1 |
3 | a | 1 |
4 | a | 1 |
5 | a | 1 |
6 | a | 1 |
7 | a | 1 |
8 | a | 1 |
9 | a | 1 |
10 | a | 1 |
11 | a | 1 |
12 | a | 1 |
13 | a | 1 |
⋮ | ⋮ | ⋮ |
2500722 | a | 1 |
2500723 | a | 1 |
2500724 | a | 1 |
2500725 | a | 1 |
2500726 | a | 1 |
2500727 | a | 1 |
2500728 | a | 1 |
2500729 | a | 1 |
2500730 | a | 1 |
2500731 | a | 1 |
2500732 | a | 1 |
2500733 | a | 1 |
⋮
Row | x | y |
---|---|---|
Char | Int64 | |
1 | c | 1 |
2 | c | 1 |
3 | c | 1 |
4 | c | 1 |
5 | c | 1 |
6 | c | 1 |
7 | c | 1 |
8 | c | 1 |
9 | c | 1 |
10 | c | 1 |
11 | c | 1 |
12 | c | 1 |
13 | c | 1 |
⋮ | ⋮ | ⋮ |
2501221 | c | 1 |
2501222 | c | 1 |
2501223 | c | 1 |
2501224 | c | 1 |
2501225 | c | 1 |
2501226 | c | 1 |
2501227 | c | 1 |
2501228 | c | 1 |
2501229 | c | 1 |
2501230 | c | 1 |
2501231 | c | 1 |
2501232 | c | 1 |
@btime combine($gdf, :y => sum)
6.892 ms (200 allocations: 10.20 KiB)
Row | x | y_sum |
---|---|---|
Char | Int64 | |
1 | a | 2500733 |
2 | d | 2497020 |
3 | b | 2501015 |
4 | c | 2501232 |
Use views instead of materializing a new DataFrame#
x = DataFrame(rand(100, 1000), :auto)
@btime $x[1:1, :]
178.012 μs (3993 allocations: 159.07 KiB)
Row | x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x100 | ⋯ |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | ⋯ | |
1 | 0.42789 | 0.967359 | 0.918973 | 0.906407 | 0.601049 | 0.141497 | 0.269524 | 0.362511 | 0.302767 | 0.49287 | 0.903798 | 0.185448 | 0.910387 | 0.292795 | 0.420275 | 0.855791 | 0.665596 | 0.710955 | 0.596022 | 0.399665 | 0.419189 | 0.541056 | 0.839193 | 0.134896 | 0.578652 | 0.480068 | 0.129179 | 0.277899 | 0.255473 | 0.950498 | 0.91113 | 0.899886 | 0.478308 | 0.64995 | 0.900101 | 0.723188 | 0.677891 | 0.311735 | 0.399226 | 0.228016 | 0.275472 | 0.449918 | 0.00146114 | 0.734431 | 0.727605 | 0.838324 | 0.397414 | 0.415977 | 0.431987 | 0.822608 | 0.983384 | 0.813928 | 0.747125 | 0.720962 | 0.878377 | 0.398502 | 0.52517 | 0.905648 | 0.721429 | 0.913815 | 0.38545 | 0.175032 | 0.751491 | 0.734684 | 0.949456 | 0.765581 | 0.730452 | 0.710118 | 0.528839 | 0.842054 | 0.324576 | 0.0909811 | 0.437877 | 0.663287 | 0.441392 | 0.0640868 | 0.408951 | 0.0406273 | 0.48404 | 0.965489 | 0.324505 | 0.0609265 | 0.205014 | 0.730064 | 0.456885 | 0.658836 | 0.796033 | 0.725453 | 0.314003 | 0.0794224 | 0.372323 | 0.405437 | 0.677053 | 0.27065 | 0.993129 | 0.945871 | 0.295412 | 0.498531 | 0.842625 | 0.934196 | ⋯ |
@btime $x[1, :]
17.889 ns (0 allocations: 0 bytes)
Row | x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x100 | ⋯ |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | ⋯ | |
1 | 0.42789 | 0.967359 | 0.918973 | 0.906407 | 0.601049 | 0.141497 | 0.269524 | 0.362511 | 0.302767 | 0.49287 | 0.903798 | 0.185448 | 0.910387 | 0.292795 | 0.420275 | 0.855791 | 0.665596 | 0.710955 | 0.596022 | 0.399665 | 0.419189 | 0.541056 | 0.839193 | 0.134896 | 0.578652 | 0.480068 | 0.129179 | 0.277899 | 0.255473 | 0.950498 | 0.91113 | 0.899886 | 0.478308 | 0.64995 | 0.900101 | 0.723188 | 0.677891 | 0.311735 | 0.399226 | 0.228016 | 0.275472 | 0.449918 | 0.00146114 | 0.734431 | 0.727605 | 0.838324 | 0.397414 | 0.415977 | 0.431987 | 0.822608 | 0.983384 | 0.813928 | 0.747125 | 0.720962 | 0.878377 | 0.398502 | 0.52517 | 0.905648 | 0.721429 | 0.913815 | 0.38545 | 0.175032 | 0.751491 | 0.734684 | 0.949456 | 0.765581 | 0.730452 | 0.710118 | 0.528839 | 0.842054 | 0.324576 | 0.0909811 | 0.437877 | 0.663287 | 0.441392 | 0.0640868 | 0.408951 | 0.0406273 | 0.48404 | 0.965489 | 0.324505 | 0.0609265 | 0.205014 | 0.730064 | 0.456885 | 0.658836 | 0.796033 | 0.725453 | 0.314003 | 0.0794224 | 0.372323 | 0.405437 | 0.677053 | 0.27065 | 0.993129 | 0.945871 | 0.295412 | 0.498531 | 0.842625 | 0.934196 | ⋯ |
@btime view($x, 1:1, :)
17.889 ns (0 allocations: 0 bytes)
Row | x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x100 | ⋯ |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | ⋯ | |
1 | 0.42789 | 0.967359 | 0.918973 | 0.906407 | 0.601049 | 0.141497 | 0.269524 | 0.362511 | 0.302767 | 0.49287 | 0.903798 | 0.185448 | 0.910387 | 0.292795 | 0.420275 | 0.855791 | 0.665596 | 0.710955 | 0.596022 | 0.399665 | 0.419189 | 0.541056 | 0.839193 | 0.134896 | 0.578652 | 0.480068 | 0.129179 | 0.277899 | 0.255473 | 0.950498 | 0.91113 | 0.899886 | 0.478308 | 0.64995 | 0.900101 | 0.723188 | 0.677891 | 0.311735 | 0.399226 | 0.228016 | 0.275472 | 0.449918 | 0.00146114 | 0.734431 | 0.727605 | 0.838324 | 0.397414 | 0.415977 | 0.431987 | 0.822608 | 0.983384 | 0.813928 | 0.747125 | 0.720962 | 0.878377 | 0.398502 | 0.52517 | 0.905648 | 0.721429 | 0.913815 | 0.38545 | 0.175032 | 0.751491 | 0.734684 | 0.949456 | 0.765581 | 0.730452 | 0.710118 | 0.528839 | 0.842054 | 0.324576 | 0.0909811 | 0.437877 | 0.663287 | 0.441392 | 0.0640868 | 0.408951 | 0.0406273 | 0.48404 | 0.965489 | 0.324505 | 0.0609265 | 0.205014 | 0.730064 | 0.456885 | 0.658836 | 0.796033 | 0.725453 | 0.314003 | 0.0794224 | 0.372323 | 0.405437 | 0.677053 | 0.27065 | 0.993129 | 0.945871 | 0.295412 | 0.498531 | 0.842625 | 0.934196 | ⋯ |
@btime $x[1:1, 1:20]
3.769 μs (70 allocations: 3.09 KiB)
Row | x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x20 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | |
1 | 0.42789 | 0.967359 | 0.918973 | 0.906407 | 0.601049 | 0.141497 | 0.269524 | 0.362511 | 0.302767 | 0.49287 | 0.903798 | 0.185448 | 0.910387 | 0.292795 | 0.420275 | 0.855791 | 0.665596 | 0.710955 | 0.596022 | 0.399665 |
@btime $x[1, 1:20]
18.499 ns (0 allocations: 0 bytes)
Row | x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x20 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | |
1 | 0.42789 | 0.967359 | 0.918973 | 0.906407 | 0.601049 | 0.141497 | 0.269524 | 0.362511 | 0.302767 | 0.49287 | 0.903798 | 0.185448 | 0.910387 | 0.292795 | 0.420275 | 0.855791 | 0.665596 | 0.710955 | 0.596022 | 0.399665 |
@btime view($x, 1:1, 1:20)
18.499 ns (0 allocations: 0 bytes)
Row | x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x20 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | |
1 | 0.42789 | 0.967359 | 0.918973 | 0.906407 | 0.601049 | 0.141497 | 0.269524 | 0.362511 | 0.302767 | 0.49287 | 0.903798 | 0.185448 | 0.910387 | 0.292795 | 0.420275 | 0.855791 | 0.665596 | 0.710955 | 0.596022 | 0.399665 |
This notebook was generated using Literate.jl.