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
2.025 ns (0 allocations: 0 bytes)
@btime $x.x500; ## Slower
10.158 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`
91.196 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();
6.399 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();
5.701 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();
6.438 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();
23.482 ms (1949728 allocations: 37.40 MiB)
25.847 ms (1950028 allocations: 45.03 MiB)
1.514 ms (728 allocations: 7.66 MiB)
2.204 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, $z); ## add a single row in place - fast
5.250 ms (213 allocations: 38.16 MiB)
1.101 μs (30 allocations: 1.52 KiB)
383.557 ns (16 allocations: 256 bytes)
Allowing missing as well as categorical slows down computations#
using StatsBase
function test(data) ## uses countmap function to test performance
println(eltype(data))
x = rand(data, 10^6)
y = categorical(x)
println(" raw:")
@btime countmap($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:
2.337 ms (8 allocations: 7.63 MiB)
categorical:
9.388 ms (4 allocations: 576 bytes)
String
raw:
21.371 ms (4 allocations: 448 bytes)
categorical:
24.977 ms (4 allocations: 576 bytes)
Union{Missing, Int64}
raw:
7.312 ms (4 allocations: 464 bytes)
categorical:
22.333 ms (1000004 allocations: 30.52 MiB)
Union{Missing, String}
raw:
27.243 ms (4 allocations: 448 bytes)
categorical:
46.391 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 |
| ⋮ | ⋮ | ⋮ |
| 2500962 | a | 1 |
| 2500963 | a | 1 |
| 2500964 | a | 1 |
| 2500965 | a | 1 |
| 2500966 | a | 1 |
| 2500967 | a | 1 |
| 2500968 | a | 1 |
| 2500969 | a | 1 |
| 2500970 | a | 1 |
| 2500971 | a | 1 |
| 2500972 | a | 1 |
| 2500973 | a | 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 |
| ⋮ | ⋮ | ⋮ |
| 2500712 | d | 1 |
| 2500713 | d | 1 |
| 2500714 | d | 1 |
| 2500715 | d | 1 |
| 2500716 | d | 1 |
| 2500717 | d | 1 |
| 2500718 | d | 1 |
| 2500719 | d | 1 |
| 2500720 | d | 1 |
| 2500721 | d | 1 |
| 2500722 | d | 1 |
| 2500723 | d | 1 |
traditional syntax, slow
@btime combine(v -> sum(v.y), $gdf)
30.670 ms (333 allocations: 19.09 MiB)
| Row | x | x1 |
|---|---|---|
| Char | Int64 | |
| 1 | a | 2500973 |
| 2 | b | 2499799 |
| 3 | c | 2498505 |
| 4 | d | 2500723 |
use column selector
@btime combine($gdf, :y => sum)
11.341 ms (199 allocations: 9.41 KiB)
| Row | x | y_sum |
|---|---|---|
| Char | Int64 | |
| 1 | a | 2500973 |
| 2 | b | 2499799 |
| 3 | c | 2498505 |
| 4 | d | 2500723 |
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 |
| ⋮ | ⋮ | ⋮ |
| 2500962 | a | 1 |
| 2500963 | a | 1 |
| 2500964 | a | 1 |
| 2500965 | a | 1 |
| 2500966 | a | 1 |
| 2500967 | a | 1 |
| 2500968 | a | 1 |
| 2500969 | a | 1 |
| 2500970 | a | 1 |
| 2500971 | a | 1 |
| 2500972 | a | 1 |
| 2500973 | 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 |
| ⋮ | ⋮ | ⋮ |
| 2500712 | d | 1 |
| 2500713 | d | 1 |
| 2500714 | d | 1 |
| 2500715 | d | 1 |
| 2500716 | d | 1 |
| 2500717 | d | 1 |
| 2500718 | d | 1 |
| 2500719 | d | 1 |
| 2500720 | d | 1 |
| 2500721 | d | 1 |
| 2500722 | d | 1 |
| 2500723 | d | 1 |
@btime combine($gdf, :y => sum)
11.298 ms (209 allocations: 9.98 KiB)
| Row | x | y_sum |
|---|---|---|
| Cat… | Int64 | |
| 1 | a | 2500973 |
| 2 | b | 2499799 |
| 3 | c | 2498505 |
| 4 | d | 2500723 |
transform!(df, :x => PooledArray{Char} => :x)
| Row | x | y |
|---|---|---|
| Char | Int64 | |
| 1 | a | 1 |
| 2 | a | 1 |
| 3 | b | 1 |
| 4 | b | 1 |
| 5 | c | 1 |
| 6 | a | 1 |
| 7 | b | 1 |
| 8 | d | 1 |
| 9 | a | 1 |
| 10 | d | 1 |
| 11 | c | 1 |
| 12 | a | 1 |
| 13 | c | 1 |
| ⋮ | ⋮ | ⋮ |
| 9999989 | d | 1 |
| 9999990 | b | 1 |
| 9999991 | a | 1 |
| 9999992 | d | 1 |
| 9999993 | b | 1 |
| 9999994 | a | 1 |
| 9999995 | c | 1 |
| 9999996 | d | 1 |
| 9999997 | b | 1 |
| 9999998 | a | 1 |
| 9999999 | c | 1 |
| 10000000 | a | 1 |
gdf = groupby(df, :x)
GroupedDataFrame with 4 groups based on key: x
| Row | x | y |
|---|---|---|
| Char | Int64 | |
| 1 | a | 1 |
| 2 | a | 1 |
| 3 | a | 1 |
| 4 | a | 1 |
| 5 | a | 1 |
| 6 | a | 1 |
| 7 | a | 1 |
| 8 | a | 1 |
| 9 | a | 1 |
| 10 | a | 1 |
| 11 | a | 1 |
| 12 | a | 1 |
| 13 | a | 1 |
| ⋮ | ⋮ | ⋮ |
| 2500962 | a | 1 |
| 2500963 | a | 1 |
| 2500964 | a | 1 |
| 2500965 | a | 1 |
| 2500966 | a | 1 |
| 2500967 | a | 1 |
| 2500968 | a | 1 |
| 2500969 | a | 1 |
| 2500970 | a | 1 |
| 2500971 | a | 1 |
| 2500972 | a | 1 |
| 2500973 | a | 1 |
⋮
| Row | x | y |
|---|---|---|
| Char | Int64 | |
| 1 | d | 1 |
| 2 | d | 1 |
| 3 | d | 1 |
| 4 | d | 1 |
| 5 | d | 1 |
| 6 | d | 1 |
| 7 | d | 1 |
| 8 | d | 1 |
| 9 | d | 1 |
| 10 | d | 1 |
| 11 | d | 1 |
| 12 | d | 1 |
| 13 | d | 1 |
| ⋮ | ⋮ | ⋮ |
| 2500712 | d | 1 |
| 2500713 | d | 1 |
| 2500714 | d | 1 |
| 2500715 | d | 1 |
| 2500716 | d | 1 |
| 2500717 | d | 1 |
| 2500718 | d | 1 |
| 2500719 | d | 1 |
| 2500720 | d | 1 |
| 2500721 | d | 1 |
| 2500722 | d | 1 |
| 2500723 | d | 1 |
@btime combine($gdf, :y => sum)
11.448 ms (201 allocations: 9.47 KiB)
| Row | x | y_sum |
|---|---|---|
| Char | Int64 | |
| 1 | a | 2500973 |
| 2 | b | 2499799 |
| 3 | c | 2498505 |
| 4 | d | 2500723 |
Use views instead of materializing a new DataFrame#
x = DataFrame(rand(100, 1000), :auto)
@btime $x[1:1, :]
416.103 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 | 0.927191 | 0.925147 | 0.860232 | 0.367042 | 0.793031 | 0.271071 | 0.659231 | 0.603075 | 0.834824 | 0.256802 | 0.767116 | 0.611423 | 0.142812 | 0.550403 | 0.733392 | 0.5064 | 0.797749 | 0.777134 | 0.0341915 | 0.345416 | 0.255611 | 0.42972 | 0.605044 | 0.551389 | 0.306161 | 0.547919 | 0.47035 | 0.277387 | 0.258654 | 0.0161937 | 0.495312 | 0.109694 | 0.115507 | 0.882718 | 0.0900965 | 0.551132 | 0.901228 | 0.67187 | 0.780274 | 0.0817141 | 0.913372 | 0.912095 | 0.446414 | 0.0683816 | 0.52805 | 0.981285 | 0.890796 | 0.06733 | 0.458382 | 0.462061 | 0.409188 | 0.293576 | 0.207361 | 0.957921 | 0.866804 | 0.469245 | 0.584737 | 0.851847 | 0.263734 | 0.767993 | 0.721584 | 0.883568 | 0.40373 | 0.61615 | 0.664986 | 0.170156 | 0.263728 | 0.300801 | 0.762233 | 0.953721 | 0.414986 | 0.456428 | 0.189594 | 0.296596 | 0.194698 | 0.305515 | 0.783646 | 0.185751 | 0.60542 | 0.350535 | 0.217134 | 0.174845 | 0.999456 | 0.707654 | 0.37726 | 0.478549 | 0.699022 | 0.331679 | 0.510521 | 0.498565 | 0.818761 | 0.715034 | 0.991523 | 0.91223 | 0.759774 | 0.878493 | 0.609321 | 0.354186 | 0.868355 | 0.946109 | ⋯ |
@btime $x[1, :]
15.762 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 | 0.927191 | 0.925147 | 0.860232 | 0.367042 | 0.793031 | 0.271071 | 0.659231 | 0.603075 | 0.834824 | 0.256802 | 0.767116 | 0.611423 | 0.142812 | 0.550403 | 0.733392 | 0.5064 | 0.797749 | 0.777134 | 0.0341915 | 0.345416 | 0.255611 | 0.42972 | 0.605044 | 0.551389 | 0.306161 | 0.547919 | 0.47035 | 0.277387 | 0.258654 | 0.0161937 | 0.495312 | 0.109694 | 0.115507 | 0.882718 | 0.0900965 | 0.551132 | 0.901228 | 0.67187 | 0.780274 | 0.0817141 | 0.913372 | 0.912095 | 0.446414 | 0.0683816 | 0.52805 | 0.981285 | 0.890796 | 0.06733 | 0.458382 | 0.462061 | 0.409188 | 0.293576 | 0.207361 | 0.957921 | 0.866804 | 0.469245 | 0.584737 | 0.851847 | 0.263734 | 0.767993 | 0.721584 | 0.883568 | 0.40373 | 0.61615 | 0.664986 | 0.170156 | 0.263728 | 0.300801 | 0.762233 | 0.953721 | 0.414986 | 0.456428 | 0.189594 | 0.296596 | 0.194698 | 0.305515 | 0.783646 | 0.185751 | 0.60542 | 0.350535 | 0.217134 | 0.174845 | 0.999456 | 0.707654 | 0.37726 | 0.478549 | 0.699022 | 0.331679 | 0.510521 | 0.498565 | 0.818761 | 0.715034 | 0.991523 | 0.91223 | 0.759774 | 0.878493 | 0.609321 | 0.354186 | 0.868355 | 0.946109 | ⋯ |
@btime view($x, 1:1, :)
16.860 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 | 0.927191 | 0.925147 | 0.860232 | 0.367042 | 0.793031 | 0.271071 | 0.659231 | 0.603075 | 0.834824 | 0.256802 | 0.767116 | 0.611423 | 0.142812 | 0.550403 | 0.733392 | 0.5064 | 0.797749 | 0.777134 | 0.0341915 | 0.345416 | 0.255611 | 0.42972 | 0.605044 | 0.551389 | 0.306161 | 0.547919 | 0.47035 | 0.277387 | 0.258654 | 0.0161937 | 0.495312 | 0.109694 | 0.115507 | 0.882718 | 0.0900965 | 0.551132 | 0.901228 | 0.67187 | 0.780274 | 0.0817141 | 0.913372 | 0.912095 | 0.446414 | 0.0683816 | 0.52805 | 0.981285 | 0.890796 | 0.06733 | 0.458382 | 0.462061 | 0.409188 | 0.293576 | 0.207361 | 0.957921 | 0.866804 | 0.469245 | 0.584737 | 0.851847 | 0.263734 | 0.767993 | 0.721584 | 0.883568 | 0.40373 | 0.61615 | 0.664986 | 0.170156 | 0.263728 | 0.300801 | 0.762233 | 0.953721 | 0.414986 | 0.456428 | 0.189594 | 0.296596 | 0.194698 | 0.305515 | 0.783646 | 0.185751 | 0.60542 | 0.350535 | 0.217134 | 0.174845 | 0.999456 | 0.707654 | 0.37726 | 0.478549 | 0.699022 | 0.331679 | 0.510521 | 0.498565 | 0.818761 | 0.715034 | 0.991523 | 0.91223 | 0.759774 | 0.878493 | 0.609321 | 0.354186 | 0.868355 | 0.946109 | ⋯ |
@btime $x[1:1, 1:20]
8.795 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 | 0.927191 | 0.925147 | 0.860232 | 0.367042 | 0.793031 | 0.271071 | 0.659231 | 0.603075 | 0.834824 | 0.256802 | 0.767116 | 0.611423 | 0.142812 | 0.550403 | 0.733392 | 0.5064 | 0.797749 | 0.777134 | 0.0341915 | 0.345416 |
@btime $x[1, 1:20]
19.222 ns (0 allocations: 0 bytes)
| Row | x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x20 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | |
| 1 | 0.927191 | 0.925147 | 0.860232 | 0.367042 | 0.793031 | 0.271071 | 0.659231 | 0.603075 | 0.834824 | 0.256802 | 0.767116 | 0.611423 | 0.142812 | 0.550403 | 0.733392 | 0.5064 | 0.797749 | 0.777134 | 0.0341915 | 0.345416 |
@btime view($x, 1:1, 1:20)
19.501 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 | 0.927191 | 0.925147 | 0.860232 | 0.367042 | 0.793031 | 0.271071 | 0.659231 | 0.603075 | 0.834824 | 0.256802 | 0.767116 | 0.611423 | 0.142812 | 0.550403 | 0.733392 | 0.5064 | 0.797749 | 0.777134 | 0.0341915 | 0.345416 |
This notebook was generated using Literate.jl.