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
4.147 ns (0 allocations: 0 bytes)
@btime $x.x500; ## Slower
15.320 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`
187.119 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();
4.258 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();
3.201 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();
3.802 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();
27.688 ms (1949728 allocations: 37.40 MiB)
28.602 ms (1950028 allocations: 45.03 MiB)
1.078 ms (728 allocations: 7.66 MiB)
1.518 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, $z); ## add a single row in place - fast
2.363 ms (212 allocations: 38.16 MiB)
1.135 μs (29 allocations: 1.50 KiB)
397.607 ns (16 allocations: 256 bytes)
Allowing missing as well as categorical slows down computations#
using StatsBase
function test(data) ## uses countmap function to test performance
println(eltype(data))
x = rand(data, 10^6)
y = categorical(x)
println(" raw:")
@btime countmap($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:
1.519 ms (8 allocations: 7.63 MiB)
categorical:
14.711 ms (1000004 allocations: 30.52 MiB)
String
raw:
20.785 ms (4 allocations: 448 bytes)
categorical:
31.675 ms (1000004 allocations: 30.52 MiB)
Union{Missing, Int64}
raw:
5.560 ms (4 allocations: 464 bytes)
categorical:
14.751 ms (1000004 allocations: 30.52 MiB)
Union{Missing, String}
raw:
20.356 ms (4 allocations: 448 bytes)
categorical:
30.319 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 |
⋮ | ⋮ | ⋮ |
2500219 | d | 1 |
2500220 | d | 1 |
2500221 | d | 1 |
2500222 | d | 1 |
2500223 | d | 1 |
2500224 | d | 1 |
2500225 | d | 1 |
2500226 | d | 1 |
2500227 | d | 1 |
2500228 | d | 1 |
2500229 | d | 1 |
2500230 | 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 |
⋮ | ⋮ | ⋮ |
2499628 | b | 1 |
2499629 | b | 1 |
2499630 | b | 1 |
2499631 | b | 1 |
2499632 | b | 1 |
2499633 | b | 1 |
2499634 | b | 1 |
2499635 | b | 1 |
2499636 | b | 1 |
2499637 | b | 1 |
2499638 | b | 1 |
2499639 | b | 1 |
traditional syntax, slow
@btime combine(v -> sum(v.y), $gdf)
18.085 ms (322 allocations: 19.09 MiB)
Row | x | x1 |
---|---|---|
Char | Int64 | |
1 | d | 2500230 |
2 | a | 2502381 |
3 | c | 2497750 |
4 | b | 2499639 |
use column selector
@btime combine($gdf, :y => sum)
6.758 ms (198 allocations: 10.14 KiB)
Row | x | y_sum |
---|---|---|
Char | Int64 | |
1 | d | 2500230 |
2 | a | 2502381 |
3 | c | 2497750 |
4 | b | 2499639 |
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 |
⋮ | ⋮ | ⋮ |
2502370 | a | 1 |
2502371 | a | 1 |
2502372 | a | 1 |
2502373 | a | 1 |
2502374 | a | 1 |
2502375 | a | 1 |
2502376 | a | 1 |
2502377 | a | 1 |
2502378 | a | 1 |
2502379 | a | 1 |
2502380 | a | 1 |
2502381 | 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 |
⋮ | ⋮ | ⋮ |
2500219 | d | 1 |
2500220 | d | 1 |
2500221 | d | 1 |
2500222 | d | 1 |
2500223 | d | 1 |
2500224 | d | 1 |
2500225 | d | 1 |
2500226 | d | 1 |
2500227 | d | 1 |
2500228 | d | 1 |
2500229 | d | 1 |
2500230 | d | 1 |
@btime combine($gdf, :y => sum)
6.450 ms (206 allocations: 10.62 KiB)
Row | x | y_sum |
---|---|---|
Cat… | Int64 | |
1 | a | 2502381 |
2 | b | 2499639 |
3 | c | 2497750 |
4 | d | 2500230 |
transform!(df, :x => PooledArray{Char} => :x)
Row | x | y |
---|---|---|
Char | Int64 | |
1 | d | 1 |
2 | a | 1 |
3 | c | 1 |
4 | b | 1 |
5 | a | 1 |
6 | b | 1 |
7 | b | 1 |
8 | a | 1 |
9 | d | 1 |
10 | b | 1 |
11 | c | 1 |
12 | d | 1 |
13 | c | 1 |
⋮ | ⋮ | ⋮ |
9999989 | b | 1 |
9999990 | a | 1 |
9999991 | d | 1 |
9999992 | d | 1 |
9999993 | a | 1 |
9999994 | c | 1 |
9999995 | b | 1 |
9999996 | c | 1 |
9999997 | d | 1 |
9999998 | a | 1 |
9999999 | d | 1 |
10000000 | a | 1 |
gdf = groupby(df, :x)
GroupedDataFrame with 4 groups based on key: x
Row | x | y |
---|---|---|
Char | Int64 | |
1 | d | 1 |
2 | d | 1 |
3 | d | 1 |
4 | d | 1 |
5 | d | 1 |
6 | d | 1 |
7 | d | 1 |
8 | d | 1 |
9 | d | 1 |
10 | d | 1 |
11 | d | 1 |
12 | d | 1 |
13 | d | 1 |
⋮ | ⋮ | ⋮ |
2500219 | d | 1 |
2500220 | d | 1 |
2500221 | d | 1 |
2500222 | d | 1 |
2500223 | d | 1 |
2500224 | d | 1 |
2500225 | d | 1 |
2500226 | d | 1 |
2500227 | d | 1 |
2500228 | d | 1 |
2500229 | d | 1 |
2500230 | d | 1 |
⋮
Row | x | y |
---|---|---|
Char | Int64 | |
1 | b | 1 |
2 | b | 1 |
3 | b | 1 |
4 | b | 1 |
5 | b | 1 |
6 | b | 1 |
7 | b | 1 |
8 | b | 1 |
9 | b | 1 |
10 | b | 1 |
11 | b | 1 |
12 | b | 1 |
13 | b | 1 |
⋮ | ⋮ | ⋮ |
2499628 | b | 1 |
2499629 | b | 1 |
2499630 | b | 1 |
2499631 | b | 1 |
2499632 | b | 1 |
2499633 | b | 1 |
2499634 | b | 1 |
2499635 | b | 1 |
2499636 | b | 1 |
2499637 | b | 1 |
2499638 | b | 1 |
2499639 | b | 1 |
@btime combine($gdf, :y => sum)
6.504 ms (200 allocations: 10.20 KiB)
Row | x | y_sum |
---|---|---|
Char | Int64 | |
1 | d | 2500230 |
2 | a | 2502381 |
3 | c | 2497750 |
4 | b | 2499639 |
Use views instead of materializing a new DataFrame#
x = DataFrame(rand(100, 1000), :auto)
@btime $x[1:1, :]
157.715 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 | 0.857709 | 0.868882 | 0.387681 | 0.488023 | 0.834645 | 0.866347 | 0.55441 | 0.0824349 | 0.213983 | 0.918295 | 0.465122 | 0.666802 | 0.219003 | 0.833122 | 0.332478 | 0.891696 | 0.798761 | 0.328678 | 0.872907 | 0.16932 | 0.731264 | 0.0498152 | 0.0452986 | 0.86139 | 0.224454 | 0.676093 | 0.702068 | 0.630011 | 0.212997 | 0.54692 | 0.953215 | 0.246759 | 0.285561 | 0.830933 | 0.208419 | 0.298392 | 0.856182 | 0.0363883 | 0.963636 | 0.981062 | 0.512305 | 0.752976 | 0.354239 | 0.818094 | 0.193617 | 0.941641 | 0.603115 | 0.146802 | 0.543513 | 0.494639 | 0.348184 | 0.282977 | 0.755999 | 0.355126 | 0.440887 | 0.306459 | 0.773269 | 0.818225 | 0.195117 | 0.532733 | 0.630013 | 0.348014 | 0.0122188 | 0.980042 | 0.323457 | 0.250844 | 0.97999 | 0.853918 | 0.227002 | 0.206662 | 0.315433 | 0.949148 | 0.38365 | 0.449628 | 0.0649162 | 0.288904 | 0.047182 | 0.0564574 | 0.0831607 | 0.859313 | 0.691922 | 0.386613 | 0.354105 | 0.211295 | 0.132831 | 0.174855 | 0.754809 | 0.268924 | 0.551961 | 0.218701 | 0.328155 | 0.779858 | 0.985688 | 0.629967 | 0.520666 | 0.634212 | 0.831947 | 0.563328 | 0.136819 | 0.954159 | ⋯ |
@btime $x[1, :]
19.132 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 | 0.857709 | 0.868882 | 0.387681 | 0.488023 | 0.834645 | 0.866347 | 0.55441 | 0.0824349 | 0.213983 | 0.918295 | 0.465122 | 0.666802 | 0.219003 | 0.833122 | 0.332478 | 0.891696 | 0.798761 | 0.328678 | 0.872907 | 0.16932 | 0.731264 | 0.0498152 | 0.0452986 | 0.86139 | 0.224454 | 0.676093 | 0.702068 | 0.630011 | 0.212997 | 0.54692 | 0.953215 | 0.246759 | 0.285561 | 0.830933 | 0.208419 | 0.298392 | 0.856182 | 0.0363883 | 0.963636 | 0.981062 | 0.512305 | 0.752976 | 0.354239 | 0.818094 | 0.193617 | 0.941641 | 0.603115 | 0.146802 | 0.543513 | 0.494639 | 0.348184 | 0.282977 | 0.755999 | 0.355126 | 0.440887 | 0.306459 | 0.773269 | 0.818225 | 0.195117 | 0.532733 | 0.630013 | 0.348014 | 0.0122188 | 0.980042 | 0.323457 | 0.250844 | 0.97999 | 0.853918 | 0.227002 | 0.206662 | 0.315433 | 0.949148 | 0.38365 | 0.449628 | 0.0649162 | 0.288904 | 0.047182 | 0.0564574 | 0.0831607 | 0.859313 | 0.691922 | 0.386613 | 0.354105 | 0.211295 | 0.132831 | 0.174855 | 0.754809 | 0.268924 | 0.551961 | 0.218701 | 0.328155 | 0.779858 | 0.985688 | 0.629967 | 0.520666 | 0.634212 | 0.831947 | 0.563328 | 0.136819 | 0.954159 | ⋯ |
@btime view($x, 1:1, :)
19.132 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 | 0.857709 | 0.868882 | 0.387681 | 0.488023 | 0.834645 | 0.866347 | 0.55441 | 0.0824349 | 0.213983 | 0.918295 | 0.465122 | 0.666802 | 0.219003 | 0.833122 | 0.332478 | 0.891696 | 0.798761 | 0.328678 | 0.872907 | 0.16932 | 0.731264 | 0.0498152 | 0.0452986 | 0.86139 | 0.224454 | 0.676093 | 0.702068 | 0.630011 | 0.212997 | 0.54692 | 0.953215 | 0.246759 | 0.285561 | 0.830933 | 0.208419 | 0.298392 | 0.856182 | 0.0363883 | 0.963636 | 0.981062 | 0.512305 | 0.752976 | 0.354239 | 0.818094 | 0.193617 | 0.941641 | 0.603115 | 0.146802 | 0.543513 | 0.494639 | 0.348184 | 0.282977 | 0.755999 | 0.355126 | 0.440887 | 0.306459 | 0.773269 | 0.818225 | 0.195117 | 0.532733 | 0.630013 | 0.348014 | 0.0122188 | 0.980042 | 0.323457 | 0.250844 | 0.97999 | 0.853918 | 0.227002 | 0.206662 | 0.315433 | 0.949148 | 0.38365 | 0.449628 | 0.0649162 | 0.288904 | 0.047182 | 0.0564574 | 0.0831607 | 0.859313 | 0.691922 | 0.386613 | 0.354105 | 0.211295 | 0.132831 | 0.174855 | 0.754809 | 0.268924 | 0.551961 | 0.218701 | 0.328155 | 0.779858 | 0.985688 | 0.629967 | 0.520666 | 0.634212 | 0.831947 | 0.563328 | 0.136819 | 0.954159 | ⋯ |
@btime $x[1:1, 1:20]
3.517 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 | 0.857709 | 0.868882 | 0.387681 | 0.488023 | 0.834645 | 0.866347 | 0.55441 | 0.0824349 | 0.213983 | 0.918295 | 0.465122 | 0.666802 | 0.219003 | 0.833122 | 0.332478 | 0.891696 | 0.798761 | 0.328678 | 0.872907 | 0.16932 |
@btime $x[1, 1:20]
19.745 ns (0 allocations: 0 bytes)
Row | x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x20 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | |
1 | 0.857709 | 0.868882 | 0.387681 | 0.488023 | 0.834645 | 0.866347 | 0.55441 | 0.0824349 | 0.213983 | 0.918295 | 0.465122 | 0.666802 | 0.219003 | 0.833122 | 0.332478 | 0.891696 | 0.798761 | 0.328678 | 0.872907 | 0.16932 |
@btime view($x, 1:1, 1:20)
18.199 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 | 0.857709 | 0.868882 | 0.387681 | 0.488023 | 0.834645 | 0.866347 | 0.55441 | 0.0824349 | 0.213983 | 0.918295 | 0.465122 | 0.666802 | 0.219003 | 0.833122 | 0.332478 | 0.891696 | 0.798761 | 0.328678 | 0.872907 | 0.16932 |
This notebook was generated using Literate.jl.