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
2.785 ns (0 allocations: 0 bytes)
@btime $x.x500; ## Slower
11.743 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`
101.866 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();
4.647 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();
4.055 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();
4.665 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();
26.756 ms (1949728 allocations: 37.40 MiB)
28.565 ms (1950028 allocations: 45.03 MiB)
1.200 ms (728 allocations: 7.66 MiB)
1.865 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, $z); ## add a single row in place - fast
2.517 ms (213 allocations: 38.16 MiB)
1.084 μs (30 allocations: 1.52 KiB)
411.472 ns (16 allocations: 256 bytes)
Allowing missing as well as categorical slows down computations#
using StatsBase
function test(data) ## uses countmap function to test performance
println(eltype(data))
x = rand(data, 10^6)
y = categorical(x)
println(" raw:")
@btime countmap($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:
1.891 ms (8 allocations: 7.63 MiB)
categorical:
10.152 ms (4 allocations: 576 bytes)
String
raw:
18.666 ms (4 allocations: 448 bytes)
categorical:
22.295 ms (4 allocations: 576 bytes)
Union{Missing, Int64}
raw:
7.176 ms (4 allocations: 464 bytes)
categorical:
21.785 ms (1000004 allocations: 30.52 MiB)
Union{Missing, String}
raw:
18.502 ms (4 allocations: 448 bytes)
categorical:
34.761 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 | 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 |
| ⋮ | ⋮ | ⋮ |
| 2500234 | b | 1 |
| 2500235 | b | 1 |
| 2500236 | b | 1 |
| 2500237 | b | 1 |
| 2500238 | b | 1 |
| 2500239 | b | 1 |
| 2500240 | b | 1 |
| 2500241 | b | 1 |
| 2500242 | b | 1 |
| 2500243 | b | 1 |
| 2500244 | b | 1 |
| 2500245 | b | 1 |
⋮
| 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 |
| ⋮ | ⋮ | ⋮ |
| 2501668 | d | 1 |
| 2501669 | d | 1 |
| 2501670 | d | 1 |
| 2501671 | d | 1 |
| 2501672 | d | 1 |
| 2501673 | d | 1 |
| 2501674 | d | 1 |
| 2501675 | d | 1 |
| 2501676 | d | 1 |
| 2501677 | d | 1 |
| 2501678 | d | 1 |
| 2501679 | d | 1 |
traditional syntax, slow
@btime combine(v -> sum(v.y), $gdf)
17.486 ms (333 allocations: 19.09 MiB)
| Row | x | x1 |
|---|---|---|
| Char | Int64 | |
| 1 | b | 2500245 |
| 2 | c | 2500332 |
| 3 | a | 2497744 |
| 4 | d | 2501679 |
use column selector
@btime combine($gdf, :y => sum)
6.963 ms (199 allocations: 9.41 KiB)
| Row | x | y_sum |
|---|---|---|
| Char | Int64 | |
| 1 | b | 2500245 |
| 2 | c | 2500332 |
| 3 | a | 2497744 |
| 4 | d | 2501679 |
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 |
| ⋮ | ⋮ | ⋮ |
| 2497733 | a | 1 |
| 2497734 | a | 1 |
| 2497735 | a | 1 |
| 2497736 | a | 1 |
| 2497737 | a | 1 |
| 2497738 | a | 1 |
| 2497739 | a | 1 |
| 2497740 | a | 1 |
| 2497741 | a | 1 |
| 2497742 | a | 1 |
| 2497743 | a | 1 |
| 2497744 | 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 |
| ⋮ | ⋮ | ⋮ |
| 2501668 | d | 1 |
| 2501669 | d | 1 |
| 2501670 | d | 1 |
| 2501671 | d | 1 |
| 2501672 | d | 1 |
| 2501673 | d | 1 |
| 2501674 | d | 1 |
| 2501675 | d | 1 |
| 2501676 | d | 1 |
| 2501677 | d | 1 |
| 2501678 | d | 1 |
| 2501679 | d | 1 |
@btime combine($gdf, :y => sum)
7.006 ms (209 allocations: 9.98 KiB)
| Row | x | y_sum |
|---|---|---|
| Cat… | Int64 | |
| 1 | a | 2497744 |
| 2 | b | 2500245 |
| 3 | c | 2500332 |
| 4 | d | 2501679 |
transform!(df, :x => PooledArray{Char} => :x)
| Row | x | y |
|---|---|---|
| Char | Int64 | |
| 1 | b | 1 |
| 2 | c | 1 |
| 3 | a | 1 |
| 4 | b | 1 |
| 5 | d | 1 |
| 6 | d | 1 |
| 7 | b | 1 |
| 8 | a | 1 |
| 9 | b | 1 |
| 10 | c | 1 |
| 11 | b | 1 |
| 12 | a | 1 |
| 13 | d | 1 |
| ⋮ | ⋮ | ⋮ |
| 9999989 | c | 1 |
| 9999990 | b | 1 |
| 9999991 | d | 1 |
| 9999992 | b | 1 |
| 9999993 | d | 1 |
| 9999994 | d | 1 |
| 9999995 | d | 1 |
| 9999996 | a | 1 |
| 9999997 | d | 1 |
| 9999998 | c | 1 |
| 9999999 | d | 1 |
| 10000000 | d | 1 |
gdf = groupby(df, :x)
GroupedDataFrame with 4 groups based on key: x
| Row | x | y |
|---|---|---|
| Char | Int64 | |
| 1 | b | 1 |
| 2 | b | 1 |
| 3 | b | 1 |
| 4 | b | 1 |
| 5 | b | 1 |
| 6 | b | 1 |
| 7 | b | 1 |
| 8 | b | 1 |
| 9 | b | 1 |
| 10 | b | 1 |
| 11 | b | 1 |
| 12 | b | 1 |
| 13 | b | 1 |
| ⋮ | ⋮ | ⋮ |
| 2500234 | b | 1 |
| 2500235 | b | 1 |
| 2500236 | b | 1 |
| 2500237 | b | 1 |
| 2500238 | b | 1 |
| 2500239 | b | 1 |
| 2500240 | b | 1 |
| 2500241 | b | 1 |
| 2500242 | b | 1 |
| 2500243 | b | 1 |
| 2500244 | b | 1 |
| 2500245 | b | 1 |
⋮
| Row | x | y |
|---|---|---|
| Char | Int64 | |
| 1 | d | 1 |
| 2 | d | 1 |
| 3 | d | 1 |
| 4 | d | 1 |
| 5 | d | 1 |
| 6 | d | 1 |
| 7 | d | 1 |
| 8 | d | 1 |
| 9 | d | 1 |
| 10 | d | 1 |
| 11 | d | 1 |
| 12 | d | 1 |
| 13 | d | 1 |
| ⋮ | ⋮ | ⋮ |
| 2501668 | d | 1 |
| 2501669 | d | 1 |
| 2501670 | d | 1 |
| 2501671 | d | 1 |
| 2501672 | d | 1 |
| 2501673 | d | 1 |
| 2501674 | d | 1 |
| 2501675 | d | 1 |
| 2501676 | d | 1 |
| 2501677 | d | 1 |
| 2501678 | d | 1 |
| 2501679 | d | 1 |
@btime combine($gdf, :y => sum)
7.031 ms (201 allocations: 9.47 KiB)
| Row | x | y_sum |
|---|---|---|
| Char | Int64 | |
| 1 | b | 2500245 |
| 2 | c | 2500332 |
| 3 | a | 2497744 |
| 4 | d | 2501679 |
Use views instead of materializing a new DataFrame#
x = DataFrame(rand(100, 1000), :auto)
@btime $x[1:1, :]
463.867 μs (3015 allocations: 143.79 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 | 0.934263 | 0.681707 | 0.916354 | 0.45278 | 0.198325 | 0.767602 | 0.183158 | 0.118934 | 0.548764 | 0.638947 | 0.336727 | 0.880418 | 0.97969 | 0.0936676 | 0.201878 | 0.0659746 | 0.765655 | 0.73299 | 0.116682 | 0.548067 | 0.241901 | 0.12975 | 0.0665906 | 0.0826919 | 0.131193 | 0.251029 | 0.505611 | 0.479015 | 0.775606 | 0.174039 | 0.794976 | 0.243669 | 0.320148 | 0.203104 | 0.824043 | 0.267315 | 0.712735 | 0.27403 | 0.0556481 | 0.682453 | 0.378992 | 0.00639638 | 0.889112 | 0.0458452 | 0.515194 | 0.319812 | 0.361336 | 0.135419 | 0.833253 | 0.15026 | 0.678403 | 0.143559 | 0.748848 | 0.625254 | 0.370249 | 0.211714 | 0.28072 | 0.42219 | 0.0469383 | 0.118914 | 0.105784 | 0.958931 | 0.579923 | 0.948524 | 0.259139 | 0.973252 | 0.558309 | 0.440189 | 0.806435 | 0.373211 | 0.14354 | 0.898967 | 0.543327 | 0.942933 | 0.250959 | 0.358954 | 0.994501 | 0.522274 | 0.796337 | 0.422856 | 0.351537 | 0.794464 | 0.81633 | 0.349748 | 0.684969 | 0.304787 | 0.600808 | 0.0405932 | 0.779506 | 0.600779 | 0.0795234 | 0.990703 | 0.747754 | 0.525823 | 0.785462 | 0.991345 | 0.622194 | 0.174585 | 0.0711777 | 0.55187 | ⋯ |
@btime $x[1, :]
21.908 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 | 0.934263 | 0.681707 | 0.916354 | 0.45278 | 0.198325 | 0.767602 | 0.183158 | 0.118934 | 0.548764 | 0.638947 | 0.336727 | 0.880418 | 0.97969 | 0.0936676 | 0.201878 | 0.0659746 | 0.765655 | 0.73299 | 0.116682 | 0.548067 | 0.241901 | 0.12975 | 0.0665906 | 0.0826919 | 0.131193 | 0.251029 | 0.505611 | 0.479015 | 0.775606 | 0.174039 | 0.794976 | 0.243669 | 0.320148 | 0.203104 | 0.824043 | 0.267315 | 0.712735 | 0.27403 | 0.0556481 | 0.682453 | 0.378992 | 0.00639638 | 0.889112 | 0.0458452 | 0.515194 | 0.319812 | 0.361336 | 0.135419 | 0.833253 | 0.15026 | 0.678403 | 0.143559 | 0.748848 | 0.625254 | 0.370249 | 0.211714 | 0.28072 | 0.42219 | 0.0469383 | 0.118914 | 0.105784 | 0.958931 | 0.579923 | 0.948524 | 0.259139 | 0.973252 | 0.558309 | 0.440189 | 0.806435 | 0.373211 | 0.14354 | 0.898967 | 0.543327 | 0.942933 | 0.250959 | 0.358954 | 0.994501 | 0.522274 | 0.796337 | 0.422856 | 0.351537 | 0.794464 | 0.81633 | 0.349748 | 0.684969 | 0.304787 | 0.600808 | 0.0405932 | 0.779506 | 0.600779 | 0.0795234 | 0.990703 | 0.747754 | 0.525823 | 0.785462 | 0.991345 | 0.622194 | 0.174585 | 0.0711777 | 0.55187 | ⋯ |
@btime view($x, 1:1, :)
22.067 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 | 0.934263 | 0.681707 | 0.916354 | 0.45278 | 0.198325 | 0.767602 | 0.183158 | 0.118934 | 0.548764 | 0.638947 | 0.336727 | 0.880418 | 0.97969 | 0.0936676 | 0.201878 | 0.0659746 | 0.765655 | 0.73299 | 0.116682 | 0.548067 | 0.241901 | 0.12975 | 0.0665906 | 0.0826919 | 0.131193 | 0.251029 | 0.505611 | 0.479015 | 0.775606 | 0.174039 | 0.794976 | 0.243669 | 0.320148 | 0.203104 | 0.824043 | 0.267315 | 0.712735 | 0.27403 | 0.0556481 | 0.682453 | 0.378992 | 0.00639638 | 0.889112 | 0.0458452 | 0.515194 | 0.319812 | 0.361336 | 0.135419 | 0.833253 | 0.15026 | 0.678403 | 0.143559 | 0.748848 | 0.625254 | 0.370249 | 0.211714 | 0.28072 | 0.42219 | 0.0469383 | 0.118914 | 0.105784 | 0.958931 | 0.579923 | 0.948524 | 0.259139 | 0.973252 | 0.558309 | 0.440189 | 0.806435 | 0.373211 | 0.14354 | 0.898967 | 0.543327 | 0.942933 | 0.250959 | 0.358954 | 0.994501 | 0.522274 | 0.796337 | 0.422856 | 0.351537 | 0.794464 | 0.81633 | 0.349748 | 0.684969 | 0.304787 | 0.600808 | 0.0405932 | 0.779506 | 0.600779 | 0.0795234 | 0.990703 | 0.747754 | 0.525823 | 0.785462 | 0.991345 | 0.622194 | 0.174585 | 0.0711777 | 0.55187 | ⋯ |
@btime $x[1:1, 1:20]
9.738 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 | 0.934263 | 0.681707 | 0.916354 | 0.45278 | 0.198325 | 0.767602 | 0.183158 | 0.118934 | 0.548764 | 0.638947 | 0.336727 | 0.880418 | 0.97969 | 0.0936676 | 0.201878 | 0.0659746 | 0.765655 | 0.73299 | 0.116682 | 0.548067 |
@btime $x[1, 1:20]
24.750 ns (0 allocations: 0 bytes)
| Row | x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x20 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | |
| 1 | 0.934263 | 0.681707 | 0.916354 | 0.45278 | 0.198325 | 0.767602 | 0.183158 | 0.118934 | 0.548764 | 0.638947 | 0.336727 | 0.880418 | 0.97969 | 0.0936676 | 0.201878 | 0.0659746 | 0.765655 | 0.73299 | 0.116682 | 0.548067 |
@btime view($x, 1:1, 1:20)
26.471 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 | 0.934263 | 0.681707 | 0.916354 | 0.45278 | 0.198325 | 0.767602 | 0.183158 | 0.118934 | 0.548764 | 0.638947 | 0.336727 | 0.880418 | 0.97969 | 0.0936676 | 0.201878 | 0.0659746 | 0.765655 | 0.73299 | 0.116682 | 0.548067 |
This notebook was generated using Literate.jl.