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
4.018 ns (0 allocations: 0 bytes)
@btime $x.x500; ## Slower
15.420 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`
187.409 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();
4.243 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();
3.652 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();
4.253 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();
27.118 ms (1949728 allocations: 37.40 MiB)
28.267 ms (1950028 allocations: 45.03 MiB)
1.154 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, $z); ## add a single row in place - fast
2.471 ms (212 allocations: 38.16 MiB)
1.104 μs (29 allocations: 1.50 KiB)
421.090 ns (16 allocations: 256 bytes)
Allowing missing as well as categorical slows down computations#
using StatsBase
function test(data) ## uses countmap function to test performance
println(eltype(data))
x = rand(data, 10^6)
y = categorical(x)
println(" raw:")
@btime countmap($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:
1.789 ms (8 allocations: 7.63 MiB)
categorical:
15.489 ms (1000004 allocations: 30.52 MiB)
String
raw:
17.567 ms (4 allocations: 448 bytes)
categorical:
28.681 ms (1000004 allocations: 30.52 MiB)
Union{Missing, Int64}
raw:
6.007 ms (4 allocations: 464 bytes)
categorical:
16.462 ms (1000004 allocations: 30.52 MiB)
Union{Missing, String}
raw:
15.014 ms (4 allocations: 448 bytes)
categorical:
25.889 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 | 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 |
⋮ | ⋮ | ⋮ |
2500964 | d | 1 |
2500965 | d | 1 |
2500966 | d | 1 |
2500967 | d | 1 |
2500968 | d | 1 |
2500969 | d | 1 |
2500970 | d | 1 |
2500971 | d | 1 |
2500972 | d | 1 |
2500973 | d | 1 |
2500974 | d | 1 |
2500975 | d | 1 |
⋮
Row | x | y |
---|---|---|
Char | Int64 | |
1 | b | 1 |
2 | b | 1 |
3 | b | 1 |
4 | b | 1 |
5 | b | 1 |
6 | b | 1 |
7 | b | 1 |
8 | b | 1 |
9 | b | 1 |
10 | b | 1 |
11 | b | 1 |
12 | b | 1 |
13 | b | 1 |
⋮ | ⋮ | ⋮ |
2498815 | b | 1 |
2498816 | b | 1 |
2498817 | b | 1 |
2498818 | b | 1 |
2498819 | b | 1 |
2498820 | b | 1 |
2498821 | b | 1 |
2498822 | b | 1 |
2498823 | b | 1 |
2498824 | b | 1 |
2498825 | b | 1 |
2498826 | b | 1 |
traditional syntax, slow
@btime combine(v -> sum(v.y), $gdf)
18.332 ms (322 allocations: 19.09 MiB)
Row | x | x1 |
---|---|---|
Char | Int64 | |
1 | d | 2500975 |
2 | c | 2496821 |
3 | a | 2503378 |
4 | b | 2498826 |
use column selector
@btime combine($gdf, :y => sum)
6.858 ms (198 allocations: 10.14 KiB)
Row | x | y_sum |
---|---|---|
Char | Int64 | |
1 | d | 2500975 |
2 | c | 2496821 |
3 | a | 2503378 |
4 | b | 2498826 |
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 |
⋮ | ⋮ | ⋮ |
2503367 | a | 1 |
2503368 | a | 1 |
2503369 | a | 1 |
2503370 | a | 1 |
2503371 | a | 1 |
2503372 | a | 1 |
2503373 | a | 1 |
2503374 | a | 1 |
2503375 | a | 1 |
2503376 | a | 1 |
2503377 | a | 1 |
2503378 | 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 |
⋮ | ⋮ | ⋮ |
2500964 | d | 1 |
2500965 | d | 1 |
2500966 | d | 1 |
2500967 | d | 1 |
2500968 | d | 1 |
2500969 | d | 1 |
2500970 | d | 1 |
2500971 | d | 1 |
2500972 | d | 1 |
2500973 | d | 1 |
2500974 | d | 1 |
2500975 | d | 1 |
@btime combine($gdf, :y => sum)
6.936 ms (206 allocations: 10.62 KiB)
Row | x | y_sum |
---|---|---|
Cat… | Int64 | |
1 | a | 2503378 |
2 | b | 2498826 |
3 | c | 2496821 |
4 | d | 2500975 |
transform!(df, :x => PooledArray{Char} => :x)
Row | x | y |
---|---|---|
Char | Int64 | |
1 | d | 1 |
2 | d | 1 |
3 | c | 1 |
4 | c | 1 |
5 | d | 1 |
6 | c | 1 |
7 | d | 1 |
8 | d | 1 |
9 | a | 1 |
10 | c | 1 |
11 | c | 1 |
12 | b | 1 |
13 | c | 1 |
⋮ | ⋮ | ⋮ |
9999989 | b | 1 |
9999990 | d | 1 |
9999991 | c | 1 |
9999992 | d | 1 |
9999993 | d | 1 |
9999994 | a | 1 |
9999995 | b | 1 |
9999996 | d | 1 |
9999997 | c | 1 |
9999998 | a | 1 |
9999999 | d | 1 |
10000000 | c | 1 |
gdf = groupby(df, :x)
GroupedDataFrame with 4 groups based on key: x
Row | x | y |
---|---|---|
Char | Int64 | |
1 | d | 1 |
2 | d | 1 |
3 | d | 1 |
4 | d | 1 |
5 | d | 1 |
6 | d | 1 |
7 | d | 1 |
8 | d | 1 |
9 | d | 1 |
10 | d | 1 |
11 | d | 1 |
12 | d | 1 |
13 | d | 1 |
⋮ | ⋮ | ⋮ |
2500964 | d | 1 |
2500965 | d | 1 |
2500966 | d | 1 |
2500967 | d | 1 |
2500968 | d | 1 |
2500969 | d | 1 |
2500970 | d | 1 |
2500971 | d | 1 |
2500972 | d | 1 |
2500973 | d | 1 |
2500974 | d | 1 |
2500975 | d | 1 |
⋮
Row | x | y |
---|---|---|
Char | Int64 | |
1 | b | 1 |
2 | b | 1 |
3 | b | 1 |
4 | b | 1 |
5 | b | 1 |
6 | b | 1 |
7 | b | 1 |
8 | b | 1 |
9 | b | 1 |
10 | b | 1 |
11 | b | 1 |
12 | b | 1 |
13 | b | 1 |
⋮ | ⋮ | ⋮ |
2498815 | b | 1 |
2498816 | b | 1 |
2498817 | b | 1 |
2498818 | b | 1 |
2498819 | b | 1 |
2498820 | b | 1 |
2498821 | b | 1 |
2498822 | b | 1 |
2498823 | b | 1 |
2498824 | b | 1 |
2498825 | b | 1 |
2498826 | b | 1 |
@btime combine($gdf, :y => sum)
6.845 ms (200 allocations: 10.20 KiB)
Row | x | y_sum |
---|---|---|
Char | Int64 | |
1 | d | 2500975 |
2 | c | 2496821 |
3 | a | 2503378 |
4 | b | 2498826 |
Use views instead of materializing a new DataFrame#
x = DataFrame(rand(100, 1000), :auto)
@btime $x[1:1, :]
177.912 μs (3993 allocations: 159.03 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 | 0.533832 | 0.740286 | 0.853234 | 0.777097 | 0.611464 | 0.324563 | 0.499339 | 0.749408 | 0.927847 | 0.870377 | 0.965651 | 0.72197 | 0.574052 | 0.478148 | 0.983111 | 0.556064 | 0.374839 | 0.916984 | 0.0193792 | 0.755716 | 0.975626 | 0.730709 | 0.821956 | 0.390936 | 0.556354 | 0.41773 | 0.835759 | 0.293013 | 0.198553 | 0.862085 | 0.10988 | 0.172973 | 0.919261 | 0.806478 | 0.878556 | 0.23524 | 0.902018 | 0.913381 | 0.372442 | 0.90486 | 0.131084 | 0.608427 | 0.733988 | 0.380072 | 0.776194 | 0.0334767 | 0.611489 | 0.940687 | 0.958361 | 0.231076 | 0.178097 | 0.0510354 | 0.0784132 | 0.0703268 | 0.195266 | 0.256965 | 0.691982 | 0.173461 | 0.186191 | 0.438712 | 0.242839 | 0.368379 | 0.988625 | 0.850556 | 0.900574 | 0.462683 | 0.666923 | 0.339847 | 0.658977 | 0.502627 | 0.271695 | 0.291988 | 0.844242 | 0.81607 | 0.818286 | 0.177858 | 0.976994 | 0.786026 | 0.10908 | 0.675134 | 0.556752 | 0.249779 | 0.277854 | 0.334831 | 0.997643 | 0.904662 | 0.128419 | 0.134903 | 0.441624 | 0.935133 | 0.97847 | 0.938362 | 0.405337 | 0.119887 | 0.516625 | 0.997316 | 0.39703 | 0.599507 | 0.997173 | 0.713875 | ⋯ |
@btime $x[1, :]
20.701 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 | 0.533832 | 0.740286 | 0.853234 | 0.777097 | 0.611464 | 0.324563 | 0.499339 | 0.749408 | 0.927847 | 0.870377 | 0.965651 | 0.72197 | 0.574052 | 0.478148 | 0.983111 | 0.556064 | 0.374839 | 0.916984 | 0.0193792 | 0.755716 | 0.975626 | 0.730709 | 0.821956 | 0.390936 | 0.556354 | 0.41773 | 0.835759 | 0.293013 | 0.198553 | 0.862085 | 0.10988 | 0.172973 | 0.919261 | 0.806478 | 0.878556 | 0.23524 | 0.902018 | 0.913381 | 0.372442 | 0.90486 | 0.131084 | 0.608427 | 0.733988 | 0.380072 | 0.776194 | 0.0334767 | 0.611489 | 0.940687 | 0.958361 | 0.231076 | 0.178097 | 0.0510354 | 0.0784132 | 0.0703268 | 0.195266 | 0.256965 | 0.691982 | 0.173461 | 0.186191 | 0.438712 | 0.242839 | 0.368379 | 0.988625 | 0.850556 | 0.900574 | 0.462683 | 0.666923 | 0.339847 | 0.658977 | 0.502627 | 0.271695 | 0.291988 | 0.844242 | 0.81607 | 0.818286 | 0.177858 | 0.976994 | 0.786026 | 0.10908 | 0.675134 | 0.556752 | 0.249779 | 0.277854 | 0.334831 | 0.997643 | 0.904662 | 0.128419 | 0.134903 | 0.441624 | 0.935133 | 0.97847 | 0.938362 | 0.405337 | 0.119887 | 0.516625 | 0.997316 | 0.39703 | 0.599507 | 0.997173 | 0.713875 | ⋯ |
@btime view($x, 1:1, :)
20.700 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 | 0.533832 | 0.740286 | 0.853234 | 0.777097 | 0.611464 | 0.324563 | 0.499339 | 0.749408 | 0.927847 | 0.870377 | 0.965651 | 0.72197 | 0.574052 | 0.478148 | 0.983111 | 0.556064 | 0.374839 | 0.916984 | 0.0193792 | 0.755716 | 0.975626 | 0.730709 | 0.821956 | 0.390936 | 0.556354 | 0.41773 | 0.835759 | 0.293013 | 0.198553 | 0.862085 | 0.10988 | 0.172973 | 0.919261 | 0.806478 | 0.878556 | 0.23524 | 0.902018 | 0.913381 | 0.372442 | 0.90486 | 0.131084 | 0.608427 | 0.733988 | 0.380072 | 0.776194 | 0.0334767 | 0.611489 | 0.940687 | 0.958361 | 0.231076 | 0.178097 | 0.0510354 | 0.0784132 | 0.0703268 | 0.195266 | 0.256965 | 0.691982 | 0.173461 | 0.186191 | 0.438712 | 0.242839 | 0.368379 | 0.988625 | 0.850556 | 0.900574 | 0.462683 | 0.666923 | 0.339847 | 0.658977 | 0.502627 | 0.271695 | 0.291988 | 0.844242 | 0.81607 | 0.818286 | 0.177858 | 0.976994 | 0.786026 | 0.10908 | 0.675134 | 0.556752 | 0.249779 | 0.277854 | 0.334831 | 0.997643 | 0.904662 | 0.128419 | 0.134903 | 0.441624 | 0.935133 | 0.97847 | 0.938362 | 0.405337 | 0.119887 | 0.516625 | 0.997316 | 0.39703 | 0.599507 | 0.997173 | 0.713875 | ⋯ |
@btime $x[1:1, 1:20]
3.796 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 | 0.533832 | 0.740286 | 0.853234 | 0.777097 | 0.611464 | 0.324563 | 0.499339 | 0.749408 | 0.927847 | 0.870377 | 0.965651 | 0.72197 | 0.574052 | 0.478148 | 0.983111 | 0.556064 | 0.374839 | 0.916984 | 0.0193792 | 0.755716 |
@btime $x[1, 1:20]
21.999 ns (0 allocations: 0 bytes)
Row | x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x20 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | |
1 | 0.533832 | 0.740286 | 0.853234 | 0.777097 | 0.611464 | 0.324563 | 0.499339 | 0.749408 | 0.927847 | 0.870377 | 0.965651 | 0.72197 | 0.574052 | 0.478148 | 0.983111 | 0.556064 | 0.374839 | 0.916984 | 0.0193792 | 0.755716 |
@btime view($x, 1:1, 1:20)
21.957 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 | 0.533832 | 0.740286 | 0.853234 | 0.777097 | 0.611464 | 0.324563 | 0.499339 | 0.749408 | 0.927847 | 0.870377 | 0.965651 | 0.72197 | 0.574052 | 0.478148 | 0.983111 | 0.556064 | 0.374839 | 0.916984 | 0.0193792 | 0.755716 |
This notebook was generated using Literate.jl.