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
3.095 ns (0 allocations: 0 bytes)
@btime $x.x500; ## Slower
11.272 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`
107.068 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();
3.802 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();
3.197 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();
3.853 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();
27.952 ms (1949728 allocations: 37.40 MiB)
28.930 ms (1950028 allocations: 45.03 MiB)
1.160 ms (728 allocations: 7.66 MiB)
1.605 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, $z); ## add a single row in place - fast
2.517 ms (212 allocations: 38.16 MiB)
1.168 μs (29 allocations: 1.50 KiB)
431.357 ns (16 allocations: 256 bytes)
Allowing missing as well as categorical slows down computations#
using StatsBase
function test(data) ## uses countmap function to test performance
println(eltype(data))
x = rand(data, 10^6)
y = categorical(x)
println(" raw:")
@btime countmap($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:
1.710 ms (8 allocations: 7.63 MiB)
categorical:
15.485 ms (1000004 allocations: 30.52 MiB)
String
raw:
21.243 ms (4 allocations: 448 bytes)
categorical:
31.704 ms (1000004 allocations: 30.52 MiB)
Union{Missing, Int64}
raw:
6.009 ms (4 allocations: 464 bytes)
categorical:
15.617 ms (1000004 allocations: 30.52 MiB)
Union{Missing, String}
raw:
21.557 ms (4 allocations: 448 bytes)
categorical:
32.430 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 |
⋮ | ⋮ | ⋮ |
2499501 | a | 1 |
2499502 | a | 1 |
2499503 | a | 1 |
2499504 | a | 1 |
2499505 | a | 1 |
2499506 | a | 1 |
2499507 | a | 1 |
2499508 | a | 1 |
2499509 | a | 1 |
2499510 | a | 1 |
2499511 | a | 1 |
2499512 | 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 |
⋮ | ⋮ | ⋮ |
2500206 | c | 1 |
2500207 | c | 1 |
2500208 | c | 1 |
2500209 | c | 1 |
2500210 | c | 1 |
2500211 | c | 1 |
2500212 | c | 1 |
2500213 | c | 1 |
2500214 | c | 1 |
2500215 | c | 1 |
2500216 | c | 1 |
2500217 | c | 1 |
traditional syntax, slow
@btime combine(v -> sum(v.y), $gdf)
15.907 ms (332 allocations: 19.08 MiB)
Row | x | x1 |
---|---|---|
Char | Int64 | |
1 | a | 2499512 |
2 | d | 2500017 |
3 | b | 2500254 |
4 | c | 2500217 |
use column selector
@btime combine($gdf, :y => sum)
6.867 ms (198 allocations: 10.14 KiB)
Row | x | y_sum |
---|---|---|
Char | Int64 | |
1 | a | 2499512 |
2 | d | 2500017 |
3 | b | 2500254 |
4 | c | 2500217 |
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 |
⋮ | ⋮ | ⋮ |
2499501 | a | 1 |
2499502 | a | 1 |
2499503 | a | 1 |
2499504 | a | 1 |
2499505 | a | 1 |
2499506 | a | 1 |
2499507 | a | 1 |
2499508 | a | 1 |
2499509 | a | 1 |
2499510 | a | 1 |
2499511 | a | 1 |
2499512 | 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 |
⋮ | ⋮ | ⋮ |
2500006 | d | 1 |
2500007 | d | 1 |
2500008 | d | 1 |
2500009 | d | 1 |
2500010 | d | 1 |
2500011 | d | 1 |
2500012 | d | 1 |
2500013 | d | 1 |
2500014 | d | 1 |
2500015 | d | 1 |
2500016 | d | 1 |
2500017 | d | 1 |
@btime combine($gdf, :y => sum)
6.851 ms (206 allocations: 10.62 KiB)
Row | x | y_sum |
---|---|---|
Cat… | Int64 | |
1 | a | 2499512 |
2 | b | 2500254 |
3 | c | 2500217 |
4 | d | 2500017 |
transform!(df, :x => PooledArray{Char} => :x)
Row | x | y |
---|---|---|
Char | Int64 | |
1 | a | 1 |
2 | a | 1 |
3 | d | 1 |
4 | b | 1 |
5 | a | 1 |
6 | d | 1 |
7 | a | 1 |
8 | b | 1 |
9 | c | 1 |
10 | b | 1 |
11 | a | 1 |
12 | c | 1 |
13 | c | 1 |
⋮ | ⋮ | ⋮ |
9999989 | c | 1 |
9999990 | c | 1 |
9999991 | d | 1 |
9999992 | c | 1 |
9999993 | b | 1 |
9999994 | b | 1 |
9999995 | d | 1 |
9999996 | c | 1 |
9999997 | d | 1 |
9999998 | c | 1 |
9999999 | d | 1 |
10000000 | d | 1 |
gdf = groupby(df, :x)
GroupedDataFrame with 4 groups based on key: x
Row | x | y |
---|---|---|
Char | Int64 | |
1 | a | 1 |
2 | a | 1 |
3 | a | 1 |
4 | a | 1 |
5 | a | 1 |
6 | a | 1 |
7 | a | 1 |
8 | a | 1 |
9 | a | 1 |
10 | a | 1 |
11 | a | 1 |
12 | a | 1 |
13 | a | 1 |
⋮ | ⋮ | ⋮ |
2499501 | a | 1 |
2499502 | a | 1 |
2499503 | a | 1 |
2499504 | a | 1 |
2499505 | a | 1 |
2499506 | a | 1 |
2499507 | a | 1 |
2499508 | a | 1 |
2499509 | a | 1 |
2499510 | a | 1 |
2499511 | a | 1 |
2499512 | a | 1 |
⋮
Row | x | y |
---|---|---|
Char | Int64 | |
1 | c | 1 |
2 | c | 1 |
3 | c | 1 |
4 | c | 1 |
5 | c | 1 |
6 | c | 1 |
7 | c | 1 |
8 | c | 1 |
9 | c | 1 |
10 | c | 1 |
11 | c | 1 |
12 | c | 1 |
13 | c | 1 |
⋮ | ⋮ | ⋮ |
2500206 | c | 1 |
2500207 | c | 1 |
2500208 | c | 1 |
2500209 | c | 1 |
2500210 | c | 1 |
2500211 | c | 1 |
2500212 | c | 1 |
2500213 | c | 1 |
2500214 | c | 1 |
2500215 | c | 1 |
2500216 | c | 1 |
2500217 | c | 1 |
@btime combine($gdf, :y => sum)
6.876 ms (200 allocations: 10.20 KiB)
Row | x | y_sum |
---|---|---|
Char | Int64 | |
1 | a | 2499512 |
2 | d | 2500017 |
3 | b | 2500254 |
4 | c | 2500217 |
Use views instead of materializing a new DataFrame#
x = DataFrame(rand(100, 1000), :auto)
@btime $x[1:1, :]
176.158 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 | 0.226699 | 0.863713 | 0.185664 | 0.991253 | 0.436737 | 0.321561 | 0.22017 | 0.997391 | 0.889487 | 0.521443 | 0.958576 | 0.735721 | 0.624697 | 0.560934 | 0.705801 | 0.802523 | 0.748778 | 0.0386374 | 0.832056 | 0.37978 | 0.411187 | 0.856293 | 0.799066 | 0.39061 | 0.485991 | 0.712236 | 0.411144 | 0.342315 | 0.962144 | 0.684008 | 0.892629 | 0.512254 | 0.576916 | 0.441884 | 0.286493 | 0.103342 | 0.143481 | 0.592531 | 0.775273 | 0.434635 | 0.14743 | 0.135948 | 0.406204 | 0.128172 | 0.948633 | 0.727155 | 0.413154 | 0.732688 | 0.386514 | 0.120765 | 0.0521672 | 0.178528 | 0.708148 | 0.457437 | 0.312459 | 0.0157715 | 0.399161 | 0.625863 | 0.220748 | 0.86596 | 0.559426 | 0.744871 | 0.683943 | 0.962464 | 0.947122 | 0.0529124 | 0.930145 | 0.24658 | 0.559914 | 0.135683 | 0.983599 | 0.224341 | 0.80823 | 0.978909 | 0.555534 | 0.882912 | 0.869087 | 0.444628 | 0.545685 | 0.215184 | 0.571798 | 0.910901 | 0.377452 | 0.56879 | 0.492264 | 0.453711 | 0.360586 | 0.386266 | 0.949954 | 0.416863 | 0.357312 | 0.329212 | 0.392536 | 0.0353349 | 0.49263 | 0.500132 | 0.509137 | 0.230268 | 0.179786 | 0.378619 | ⋯ |
@btime $x[1, :]
22.833 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 | 0.226699 | 0.863713 | 0.185664 | 0.991253 | 0.436737 | 0.321561 | 0.22017 | 0.997391 | 0.889487 | 0.521443 | 0.958576 | 0.735721 | 0.624697 | 0.560934 | 0.705801 | 0.802523 | 0.748778 | 0.0386374 | 0.832056 | 0.37978 | 0.411187 | 0.856293 | 0.799066 | 0.39061 | 0.485991 | 0.712236 | 0.411144 | 0.342315 | 0.962144 | 0.684008 | 0.892629 | 0.512254 | 0.576916 | 0.441884 | 0.286493 | 0.103342 | 0.143481 | 0.592531 | 0.775273 | 0.434635 | 0.14743 | 0.135948 | 0.406204 | 0.128172 | 0.948633 | 0.727155 | 0.413154 | 0.732688 | 0.386514 | 0.120765 | 0.0521672 | 0.178528 | 0.708148 | 0.457437 | 0.312459 | 0.0157715 | 0.399161 | 0.625863 | 0.220748 | 0.86596 | 0.559426 | 0.744871 | 0.683943 | 0.962464 | 0.947122 | 0.0529124 | 0.930145 | 0.24658 | 0.559914 | 0.135683 | 0.983599 | 0.224341 | 0.80823 | 0.978909 | 0.555534 | 0.882912 | 0.869087 | 0.444628 | 0.545685 | 0.215184 | 0.571798 | 0.910901 | 0.377452 | 0.56879 | 0.492264 | 0.453711 | 0.360586 | 0.386266 | 0.949954 | 0.416863 | 0.357312 | 0.329212 | 0.392536 | 0.0353349 | 0.49263 | 0.500132 | 0.509137 | 0.230268 | 0.179786 | 0.378619 | ⋯ |
@btime view($x, 1:1, :)
22.833 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 | 0.226699 | 0.863713 | 0.185664 | 0.991253 | 0.436737 | 0.321561 | 0.22017 | 0.997391 | 0.889487 | 0.521443 | 0.958576 | 0.735721 | 0.624697 | 0.560934 | 0.705801 | 0.802523 | 0.748778 | 0.0386374 | 0.832056 | 0.37978 | 0.411187 | 0.856293 | 0.799066 | 0.39061 | 0.485991 | 0.712236 | 0.411144 | 0.342315 | 0.962144 | 0.684008 | 0.892629 | 0.512254 | 0.576916 | 0.441884 | 0.286493 | 0.103342 | 0.143481 | 0.592531 | 0.775273 | 0.434635 | 0.14743 | 0.135948 | 0.406204 | 0.128172 | 0.948633 | 0.727155 | 0.413154 | 0.732688 | 0.386514 | 0.120765 | 0.0521672 | 0.178528 | 0.708148 | 0.457437 | 0.312459 | 0.0157715 | 0.399161 | 0.625863 | 0.220748 | 0.86596 | 0.559426 | 0.744871 | 0.683943 | 0.962464 | 0.947122 | 0.0529124 | 0.930145 | 0.24658 | 0.559914 | 0.135683 | 0.983599 | 0.224341 | 0.80823 | 0.978909 | 0.555534 | 0.882912 | 0.869087 | 0.444628 | 0.545685 | 0.215184 | 0.571798 | 0.910901 | 0.377452 | 0.56879 | 0.492264 | 0.453711 | 0.360586 | 0.386266 | 0.949954 | 0.416863 | 0.357312 | 0.329212 | 0.392536 | 0.0353349 | 0.49263 | 0.500132 | 0.509137 | 0.230268 | 0.179786 | 0.378619 | ⋯ |
@btime $x[1:1, 1:20]
3.737 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 | 0.226699 | 0.863713 | 0.185664 | 0.991253 | 0.436737 | 0.321561 | 0.22017 | 0.997391 | 0.889487 | 0.521443 | 0.958576 | 0.735721 | 0.624697 | 0.560934 | 0.705801 | 0.802523 | 0.748778 | 0.0386374 | 0.832056 | 0.37978 |
@btime $x[1, 1:20]
23.447 ns (0 allocations: 0 bytes)
Row | x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x20 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | |
1 | 0.226699 | 0.863713 | 0.185664 | 0.991253 | 0.436737 | 0.321561 | 0.22017 | 0.997391 | 0.889487 | 0.521443 | 0.958576 | 0.735721 | 0.624697 | 0.560934 | 0.705801 | 0.802523 | 0.748778 | 0.0386374 | 0.832056 | 0.37978 |
@btime view($x, 1:1, 1:20)
28.233 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 | 0.226699 | 0.863713 | 0.185664 | 0.991253 | 0.436737 | 0.321561 | 0.22017 | 0.997391 | 0.889487 | 0.521443 | 0.958576 | 0.735721 | 0.624697 | 0.560934 | 0.705801 | 0.802523 | 0.748778 | 0.0386374 | 0.832056 | 0.37978 |
This notebook was generated using Literate.jl.