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
11.482 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`
100.285 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();
3.905 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();
3.347 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();
3.850 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();
27.487 ms (1949728 allocations: 37.40 MiB)
28.199 ms (1950028 allocations: 45.03 MiB)
1.146 ms (728 allocations: 7.66 MiB)
1.599 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, $z); ## add a single row in place - fast
2.825 ms (212 allocations: 38.16 MiB)
1.116 μs (29 allocations: 1.50 KiB)
418.724 ns (16 allocations: 256 bytes)
Allowing missing as well as categorical slows down computations#
using StatsBase
function test(data) ## uses countmap function to test performance
println(eltype(data))
x = rand(data, 10^6)
y = categorical(x)
println(" raw:")
@btime countmap($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:
1.751 ms (8 allocations: 7.63 MiB)
categorical:
15.555 ms (1000004 allocations: 30.52 MiB)
String
raw:
16.500 ms (4 allocations: 448 bytes)
categorical:
26.715 ms (1000004 allocations: 30.52 MiB)
Union{Missing, Int64}
raw:
6.382 ms (4 allocations: 464 bytes)
categorical:
15.813 ms (1000004 allocations: 30.52 MiB)
Union{Missing, String}
raw:
19.140 ms (4 allocations: 448 bytes)
categorical:
29.456 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 |
⋮ | ⋮ | ⋮ |
2502349 | a | 1 |
2502350 | a | 1 |
2502351 | a | 1 |
2502352 | a | 1 |
2502353 | a | 1 |
2502354 | a | 1 |
2502355 | a | 1 |
2502356 | a | 1 |
2502357 | a | 1 |
2502358 | a | 1 |
2502359 | a | 1 |
2502360 | 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 |
⋮ | ⋮ | ⋮ |
2498446 | d | 1 |
2498447 | d | 1 |
2498448 | d | 1 |
2498449 | d | 1 |
2498450 | d | 1 |
2498451 | d | 1 |
2498452 | d | 1 |
2498453 | d | 1 |
2498454 | d | 1 |
2498455 | d | 1 |
2498456 | d | 1 |
2498457 | d | 1 |
traditional syntax, slow
@btime combine(v -> sum(v.y), $gdf)
17.556 ms (332 allocations: 19.11 MiB)
Row | x | x1 |
---|---|---|
Char | Int64 | |
1 | a | 2502360 |
2 | b | 2499998 |
3 | c | 2499185 |
4 | d | 2498457 |
use column selector
@btime combine($gdf, :y => sum)
7.011 ms (198 allocations: 10.14 KiB)
Row | x | y_sum |
---|---|---|
Char | Int64 | |
1 | a | 2502360 |
2 | b | 2499998 |
3 | c | 2499185 |
4 | d | 2498457 |
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 |
⋮ | ⋮ | ⋮ |
2502349 | a | 1 |
2502350 | a | 1 |
2502351 | a | 1 |
2502352 | a | 1 |
2502353 | a | 1 |
2502354 | a | 1 |
2502355 | a | 1 |
2502356 | a | 1 |
2502357 | a | 1 |
2502358 | a | 1 |
2502359 | a | 1 |
2502360 | 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 |
⋮ | ⋮ | ⋮ |
2498446 | d | 1 |
2498447 | d | 1 |
2498448 | d | 1 |
2498449 | d | 1 |
2498450 | d | 1 |
2498451 | d | 1 |
2498452 | d | 1 |
2498453 | d | 1 |
2498454 | d | 1 |
2498455 | d | 1 |
2498456 | d | 1 |
2498457 | d | 1 |
@btime combine($gdf, :y => sum)
6.874 ms (206 allocations: 10.62 KiB)
Row | x | y_sum |
---|---|---|
Cat… | Int64 | |
1 | a | 2502360 |
2 | b | 2499998 |
3 | c | 2499185 |
4 | d | 2498457 |
transform!(df, :x => PooledArray{Char} => :x)
Row | x | y |
---|---|---|
Char | Int64 | |
1 | a | 1 |
2 | b | 1 |
3 | c | 1 |
4 | c | 1 |
5 | a | 1 |
6 | a | 1 |
7 | d | 1 |
8 | d | 1 |
9 | a | 1 |
10 | b | 1 |
11 | b | 1 |
12 | b | 1 |
13 | a | 1 |
⋮ | ⋮ | ⋮ |
9999989 | a | 1 |
9999990 | a | 1 |
9999991 | d | 1 |
9999992 | d | 1 |
9999993 | d | 1 |
9999994 | c | 1 |
9999995 | b | 1 |
9999996 | b | 1 |
9999997 | b | 1 |
9999998 | a | 1 |
9999999 | c | 1 |
10000000 | a | 1 |
gdf = groupby(df, :x)
GroupedDataFrame with 4 groups based on key: x
Row | x | y |
---|---|---|
Char | Int64 | |
1 | a | 1 |
2 | a | 1 |
3 | a | 1 |
4 | a | 1 |
5 | a | 1 |
6 | a | 1 |
7 | a | 1 |
8 | a | 1 |
9 | a | 1 |
10 | a | 1 |
11 | a | 1 |
12 | a | 1 |
13 | a | 1 |
⋮ | ⋮ | ⋮ |
2502349 | a | 1 |
2502350 | a | 1 |
2502351 | a | 1 |
2502352 | a | 1 |
2502353 | a | 1 |
2502354 | a | 1 |
2502355 | a | 1 |
2502356 | a | 1 |
2502357 | a | 1 |
2502358 | a | 1 |
2502359 | a | 1 |
2502360 | a | 1 |
⋮
Row | x | y |
---|---|---|
Char | Int64 | |
1 | d | 1 |
2 | d | 1 |
3 | d | 1 |
4 | d | 1 |
5 | d | 1 |
6 | d | 1 |
7 | d | 1 |
8 | d | 1 |
9 | d | 1 |
10 | d | 1 |
11 | d | 1 |
12 | d | 1 |
13 | d | 1 |
⋮ | ⋮ | ⋮ |
2498446 | d | 1 |
2498447 | d | 1 |
2498448 | d | 1 |
2498449 | d | 1 |
2498450 | d | 1 |
2498451 | d | 1 |
2498452 | d | 1 |
2498453 | d | 1 |
2498454 | d | 1 |
2498455 | d | 1 |
2498456 | d | 1 |
2498457 | d | 1 |
@btime combine($gdf, :y => sum)
7.070 ms (200 allocations: 10.20 KiB)
Row | x | y_sum |
---|---|---|
Char | Int64 | |
1 | a | 2502360 |
2 | b | 2499998 |
3 | c | 2499185 |
4 | d | 2498457 |
Use views instead of materializing a new DataFrame#
x = DataFrame(rand(100, 1000), :auto)
@btime $x[1:1, :]
176.249 μs (3993 allocations: 159.07 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 | 0.287939 | 0.572906 | 0.66274 | 0.188851 | 0.881306 | 0.688795 | 0.809868 | 0.305628 | 0.628287 | 0.431636 | 0.460146 | 0.287203 | 0.917827 | 0.594192 | 0.984554 | 0.874009 | 0.859615 | 0.30106 | 0.907956 | 0.581831 | 0.925227 | 0.668358 | 0.71056 | 0.422462 | 0.728701 | 0.19335 | 0.620084 | 0.594948 | 0.13657 | 0.690162 | 0.580043 | 0.784896 | 0.189572 | 0.970589 | 0.0437869 | 0.21071 | 0.889412 | 0.222432 | 0.833584 | 0.886811 | 0.846198 | 0.615634 | 0.907751 | 0.280203 | 0.866202 | 0.463718 | 0.518148 | 0.450585 | 0.858622 | 0.487458 | 0.487388 | 0.415281 | 0.253844 | 0.890205 | 0.439333 | 0.212326 | 0.427554 | 0.131695 | 0.0433552 | 0.806975 | 0.119466 | 0.210352 | 0.290222 | 0.768752 | 0.399232 | 0.653529 | 0.640382 | 0.927122 | 0.637053 | 0.91059 | 0.522725 | 0.543098 | 0.792562 | 0.856469 | 0.485331 | 0.924605 | 0.315705 | 0.83893 | 0.0580339 | 0.0360773 | 0.454464 | 0.036376 | 0.544874 | 0.285235 | 0.333479 | 0.450541 | 0.210189 | 0.164295 | 0.162584 | 0.469341 | 0.54309 | 0.389203 | 0.868857 | 0.820107 | 0.95139 | 0.652192 | 0.755278 | 0.575802 | 0.86142 | 0.882691 | ⋯ |
@btime $x[1, :]
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 | 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 | 0.287939 | 0.572906 | 0.66274 | 0.188851 | 0.881306 | 0.688795 | 0.809868 | 0.305628 | 0.628287 | 0.431636 | 0.460146 | 0.287203 | 0.917827 | 0.594192 | 0.984554 | 0.874009 | 0.859615 | 0.30106 | 0.907956 | 0.581831 | 0.925227 | 0.668358 | 0.71056 | 0.422462 | 0.728701 | 0.19335 | 0.620084 | 0.594948 | 0.13657 | 0.690162 | 0.580043 | 0.784896 | 0.189572 | 0.970589 | 0.0437869 | 0.21071 | 0.889412 | 0.222432 | 0.833584 | 0.886811 | 0.846198 | 0.615634 | 0.907751 | 0.280203 | 0.866202 | 0.463718 | 0.518148 | 0.450585 | 0.858622 | 0.487458 | 0.487388 | 0.415281 | 0.253844 | 0.890205 | 0.439333 | 0.212326 | 0.427554 | 0.131695 | 0.0433552 | 0.806975 | 0.119466 | 0.210352 | 0.290222 | 0.768752 | 0.399232 | 0.653529 | 0.640382 | 0.927122 | 0.637053 | 0.91059 | 0.522725 | 0.543098 | 0.792562 | 0.856469 | 0.485331 | 0.924605 | 0.315705 | 0.83893 | 0.0580339 | 0.0360773 | 0.454464 | 0.036376 | 0.544874 | 0.285235 | 0.333479 | 0.450541 | 0.210189 | 0.164295 | 0.162584 | 0.469341 | 0.54309 | 0.389203 | 0.868857 | 0.820107 | 0.95139 | 0.652192 | 0.755278 | 0.575802 | 0.86142 | 0.882691 | ⋯ |
@btime view($x, 1:1, :)
17.899 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 | 0.287939 | 0.572906 | 0.66274 | 0.188851 | 0.881306 | 0.688795 | 0.809868 | 0.305628 | 0.628287 | 0.431636 | 0.460146 | 0.287203 | 0.917827 | 0.594192 | 0.984554 | 0.874009 | 0.859615 | 0.30106 | 0.907956 | 0.581831 | 0.925227 | 0.668358 | 0.71056 | 0.422462 | 0.728701 | 0.19335 | 0.620084 | 0.594948 | 0.13657 | 0.690162 | 0.580043 | 0.784896 | 0.189572 | 0.970589 | 0.0437869 | 0.21071 | 0.889412 | 0.222432 | 0.833584 | 0.886811 | 0.846198 | 0.615634 | 0.907751 | 0.280203 | 0.866202 | 0.463718 | 0.518148 | 0.450585 | 0.858622 | 0.487458 | 0.487388 | 0.415281 | 0.253844 | 0.890205 | 0.439333 | 0.212326 | 0.427554 | 0.131695 | 0.0433552 | 0.806975 | 0.119466 | 0.210352 | 0.290222 | 0.768752 | 0.399232 | 0.653529 | 0.640382 | 0.927122 | 0.637053 | 0.91059 | 0.522725 | 0.543098 | 0.792562 | 0.856469 | 0.485331 | 0.924605 | 0.315705 | 0.83893 | 0.0580339 | 0.0360773 | 0.454464 | 0.036376 | 0.544874 | 0.285235 | 0.333479 | 0.450541 | 0.210189 | 0.164295 | 0.162584 | 0.469341 | 0.54309 | 0.389203 | 0.868857 | 0.820107 | 0.95139 | 0.652192 | 0.755278 | 0.575802 | 0.86142 | 0.882691 | ⋯ |
@btime $x[1:1, 1:20]
3.729 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 | 0.287939 | 0.572906 | 0.66274 | 0.188851 | 0.881306 | 0.688795 | 0.809868 | 0.305628 | 0.628287 | 0.431636 | 0.460146 | 0.287203 | 0.917827 | 0.594192 | 0.984554 | 0.874009 | 0.859615 | 0.30106 | 0.907956 | 0.581831 |
@btime $x[1, 1:20]
18.510 ns (0 allocations: 0 bytes)
Row | x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x20 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | |
1 | 0.287939 | 0.572906 | 0.66274 | 0.188851 | 0.881306 | 0.688795 | 0.809868 | 0.305628 | 0.628287 | 0.431636 | 0.460146 | 0.287203 | 0.917827 | 0.594192 | 0.984554 | 0.874009 | 0.859615 | 0.30106 | 0.907956 | 0.581831 |
@btime view($x, 1:1, 1:20)
18.510 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 | 0.287939 | 0.572906 | 0.66274 | 0.188851 | 0.881306 | 0.688795 | 0.809868 | 0.305628 | 0.628287 | 0.431636 | 0.460146 | 0.287203 | 0.917827 | 0.594192 | 0.984554 | 0.874009 | 0.859615 | 0.30106 | 0.907956 | 0.581831 |
This notebook was generated using Literate.jl.