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
11.834 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`
97.949 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();
3.903 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();
3.322 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();
3.870 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();
26.094 ms (1949728 allocations: 37.40 MiB)
27.518 ms (1950028 allocations: 45.03 MiB)
1.207 ms (728 allocations: 7.66 MiB)
1.648 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, $z); ## add a single row in place - fast
2.735 ms (213 allocations: 38.16 MiB)
1.099 μs (30 allocations: 1.52 KiB)
429.291 ns (16 allocations: 256 bytes)
Allowing missing as well as categorical slows down computations#
using StatsBase
function test(data) ## uses countmap function to test performance
println(eltype(data))
x = rand(data, 10^6)
y = categorical(x)
println(" raw:")
@btime countmap($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:
1.932 ms (8 allocations: 7.63 MiB)
categorical:
16.107 ms (1000004 allocations: 30.52 MiB)
String
raw:
23.543 ms (4 allocations: 448 bytes)
categorical:
33.864 ms (1000004 allocations: 30.52 MiB)
Union{Missing, Int64}
raw:
7.415 ms (4 allocations: 464 bytes)
categorical:
16.489 ms (1000004 allocations: 30.52 MiB)
Union{Missing, String}
raw:
17.170 ms (4 allocations: 448 bytes)
categorical:
27.073 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 |
| ⋮ | ⋮ | ⋮ |
| 2499613 | a | 1 |
| 2499614 | a | 1 |
| 2499615 | a | 1 |
| 2499616 | a | 1 |
| 2499617 | a | 1 |
| 2499618 | a | 1 |
| 2499619 | a | 1 |
| 2499620 | a | 1 |
| 2499621 | a | 1 |
| 2499622 | a | 1 |
| 2499623 | a | 1 |
| 2499624 | a | 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 |
| ⋮ | ⋮ | ⋮ |
| 2499583 | b | 1 |
| 2499584 | b | 1 |
| 2499585 | b | 1 |
| 2499586 | b | 1 |
| 2499587 | b | 1 |
| 2499588 | b | 1 |
| 2499589 | b | 1 |
| 2499590 | b | 1 |
| 2499591 | b | 1 |
| 2499592 | b | 1 |
| 2499593 | b | 1 |
| 2499594 | b | 1 |
traditional syntax, slow
@btime combine(v -> sum(v.y), $gdf)
17.181 ms (333 allocations: 19.08 MiB)
| Row | x | x1 |
|---|---|---|
| Char | Int64 | |
| 1 | a | 2499624 |
| 2 | c | 2499816 |
| 3 | d | 2500966 |
| 4 | b | 2499594 |
use column selector
@btime combine($gdf, :y => sum)
7.076 ms (199 allocations: 9.41 KiB)
| Row | x | y_sum |
|---|---|---|
| Char | Int64 | |
| 1 | a | 2499624 |
| 2 | c | 2499816 |
| 3 | d | 2500966 |
| 4 | b | 2499594 |
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 |
| ⋮ | ⋮ | ⋮ |
| 2499613 | a | 1 |
| 2499614 | a | 1 |
| 2499615 | a | 1 |
| 2499616 | a | 1 |
| 2499617 | a | 1 |
| 2499618 | a | 1 |
| 2499619 | a | 1 |
| 2499620 | a | 1 |
| 2499621 | a | 1 |
| 2499622 | a | 1 |
| 2499623 | a | 1 |
| 2499624 | 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 |
| ⋮ | ⋮ | ⋮ |
| 2500955 | d | 1 |
| 2500956 | d | 1 |
| 2500957 | d | 1 |
| 2500958 | d | 1 |
| 2500959 | d | 1 |
| 2500960 | d | 1 |
| 2500961 | d | 1 |
| 2500962 | d | 1 |
| 2500963 | d | 1 |
| 2500964 | d | 1 |
| 2500965 | d | 1 |
| 2500966 | d | 1 |
@btime combine($gdf, :y => sum)
7.012 ms (207 allocations: 9.89 KiB)
| Row | x | y_sum |
|---|---|---|
| Cat… | Int64 | |
| 1 | a | 2499624 |
| 2 | b | 2499594 |
| 3 | c | 2499816 |
| 4 | d | 2500966 |
transform!(df, :x => PooledArray{Char} => :x)
| Row | x | y |
|---|---|---|
| Char | Int64 | |
| 1 | a | 1 |
| 2 | c | 1 |
| 3 | c | 1 |
| 4 | c | 1 |
| 5 | d | 1 |
| 6 | a | 1 |
| 7 | c | 1 |
| 8 | b | 1 |
| 9 | b | 1 |
| 10 | b | 1 |
| 11 | a | 1 |
| 12 | b | 1 |
| 13 | b | 1 |
| ⋮ | ⋮ | ⋮ |
| 9999989 | b | 1 |
| 9999990 | b | 1 |
| 9999991 | b | 1 |
| 9999992 | c | 1 |
| 9999993 | b | 1 |
| 9999994 | a | 1 |
| 9999995 | d | 1 |
| 9999996 | c | 1 |
| 9999997 | d | 1 |
| 9999998 | b | 1 |
| 9999999 | c | 1 |
| 10000000 | d | 1 |
gdf = groupby(df, :x)
GroupedDataFrame with 4 groups based on key: x
| Row | x | y |
|---|---|---|
| Char | Int64 | |
| 1 | a | 1 |
| 2 | a | 1 |
| 3 | a | 1 |
| 4 | a | 1 |
| 5 | a | 1 |
| 6 | a | 1 |
| 7 | a | 1 |
| 8 | a | 1 |
| 9 | a | 1 |
| 10 | a | 1 |
| 11 | a | 1 |
| 12 | a | 1 |
| 13 | a | 1 |
| ⋮ | ⋮ | ⋮ |
| 2499613 | a | 1 |
| 2499614 | a | 1 |
| 2499615 | a | 1 |
| 2499616 | a | 1 |
| 2499617 | a | 1 |
| 2499618 | a | 1 |
| 2499619 | a | 1 |
| 2499620 | a | 1 |
| 2499621 | a | 1 |
| 2499622 | a | 1 |
| 2499623 | a | 1 |
| 2499624 | a | 1 |
⋮
| Row | x | y |
|---|---|---|
| Char | Int64 | |
| 1 | b | 1 |
| 2 | b | 1 |
| 3 | b | 1 |
| 4 | b | 1 |
| 5 | b | 1 |
| 6 | b | 1 |
| 7 | b | 1 |
| 8 | b | 1 |
| 9 | b | 1 |
| 10 | b | 1 |
| 11 | b | 1 |
| 12 | b | 1 |
| 13 | b | 1 |
| ⋮ | ⋮ | ⋮ |
| 2499583 | b | 1 |
| 2499584 | b | 1 |
| 2499585 | b | 1 |
| 2499586 | b | 1 |
| 2499587 | b | 1 |
| 2499588 | b | 1 |
| 2499589 | b | 1 |
| 2499590 | b | 1 |
| 2499591 | b | 1 |
| 2499592 | b | 1 |
| 2499593 | b | 1 |
| 2499594 | b | 1 |
@btime combine($gdf, :y => sum)
7.083 ms (201 allocations: 9.47 KiB)
| Row | x | y_sum |
|---|---|---|
| Char | Int64 | |
| 1 | a | 2499624 |
| 2 | c | 2499816 |
| 3 | d | 2500966 |
| 4 | b | 2499594 |
Use views instead of materializing a new DataFrame#
x = DataFrame(rand(100, 1000), :auto)
@btime $x[1:1, :]
472.793 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 | 0.170676 | 0.482524 | 0.165371 | 0.28671 | 0.975893 | 0.195169 | 0.815353 | 0.799585 | 0.253567 | 0.533303 | 0.525501 | 0.230238 | 0.531516 | 0.00957515 | 0.745903 | 0.792815 | 0.728319 | 0.133442 | 0.981423 | 0.46901 | 0.641219 | 0.787587 | 0.692759 | 0.595666 | 0.496043 | 0.17451 | 0.642836 | 0.215083 | 0.156066 | 0.937662 | 0.788349 | 0.446731 | 0.0264751 | 0.608187 | 0.0496019 | 0.209162 | 0.318499 | 0.286048 | 0.382011 | 0.263219 | 0.243171 | 0.772068 | 0.891277 | 0.126665 | 0.17446 | 0.152157 | 0.428155 | 0.120195 | 0.534041 | 0.77409 | 0.697785 | 0.151386 | 0.456728 | 0.253105 | 0.0494999 | 0.805595 | 0.553076 | 0.68742 | 0.732219 | 0.51402 | 0.148861 | 0.404823 | 0.383418 | 0.512849 | 0.083324 | 0.41738 | 0.903677 | 0.0680598 | 0.437073 | 0.883555 | 0.633713 | 0.0927744 | 0.746247 | 0.718136 | 0.220564 | 0.190088 | 0.673532 | 0.845 | 0.864176 | 0.0940294 | 0.25463 | 0.729672 | 0.911144 | 0.207148 | 0.897171 | 0.50063 | 0.643739 | 0.524316 | 0.305217 | 0.97115 | 0.48895 | 0.0511832 | 0.641521 | 0.00818834 | 0.0542199 | 0.146498 | 0.941823 | 0.216359 | 0.262421 | 0.769855 | ⋯ |
@btime $x[1, :]
22.904 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 | 0.170676 | 0.482524 | 0.165371 | 0.28671 | 0.975893 | 0.195169 | 0.815353 | 0.799585 | 0.253567 | 0.533303 | 0.525501 | 0.230238 | 0.531516 | 0.00957515 | 0.745903 | 0.792815 | 0.728319 | 0.133442 | 0.981423 | 0.46901 | 0.641219 | 0.787587 | 0.692759 | 0.595666 | 0.496043 | 0.17451 | 0.642836 | 0.215083 | 0.156066 | 0.937662 | 0.788349 | 0.446731 | 0.0264751 | 0.608187 | 0.0496019 | 0.209162 | 0.318499 | 0.286048 | 0.382011 | 0.263219 | 0.243171 | 0.772068 | 0.891277 | 0.126665 | 0.17446 | 0.152157 | 0.428155 | 0.120195 | 0.534041 | 0.77409 | 0.697785 | 0.151386 | 0.456728 | 0.253105 | 0.0494999 | 0.805595 | 0.553076 | 0.68742 | 0.732219 | 0.51402 | 0.148861 | 0.404823 | 0.383418 | 0.512849 | 0.083324 | 0.41738 | 0.903677 | 0.0680598 | 0.437073 | 0.883555 | 0.633713 | 0.0927744 | 0.746247 | 0.718136 | 0.220564 | 0.190088 | 0.673532 | 0.845 | 0.864176 | 0.0940294 | 0.25463 | 0.729672 | 0.911144 | 0.207148 | 0.897171 | 0.50063 | 0.643739 | 0.524316 | 0.305217 | 0.97115 | 0.48895 | 0.0511832 | 0.641521 | 0.00818834 | 0.0542199 | 0.146498 | 0.941823 | 0.216359 | 0.262421 | 0.769855 | ⋯ |
@btime view($x, 1:1, :)
22.843 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 | 0.170676 | 0.482524 | 0.165371 | 0.28671 | 0.975893 | 0.195169 | 0.815353 | 0.799585 | 0.253567 | 0.533303 | 0.525501 | 0.230238 | 0.531516 | 0.00957515 | 0.745903 | 0.792815 | 0.728319 | 0.133442 | 0.981423 | 0.46901 | 0.641219 | 0.787587 | 0.692759 | 0.595666 | 0.496043 | 0.17451 | 0.642836 | 0.215083 | 0.156066 | 0.937662 | 0.788349 | 0.446731 | 0.0264751 | 0.608187 | 0.0496019 | 0.209162 | 0.318499 | 0.286048 | 0.382011 | 0.263219 | 0.243171 | 0.772068 | 0.891277 | 0.126665 | 0.17446 | 0.152157 | 0.428155 | 0.120195 | 0.534041 | 0.77409 | 0.697785 | 0.151386 | 0.456728 | 0.253105 | 0.0494999 | 0.805595 | 0.553076 | 0.68742 | 0.732219 | 0.51402 | 0.148861 | 0.404823 | 0.383418 | 0.512849 | 0.083324 | 0.41738 | 0.903677 | 0.0680598 | 0.437073 | 0.883555 | 0.633713 | 0.0927744 | 0.746247 | 0.718136 | 0.220564 | 0.190088 | 0.673532 | 0.845 | 0.864176 | 0.0940294 | 0.25463 | 0.729672 | 0.911144 | 0.207148 | 0.897171 | 0.50063 | 0.643739 | 0.524316 | 0.305217 | 0.97115 | 0.48895 | 0.0511832 | 0.641521 | 0.00818834 | 0.0542199 | 0.146498 | 0.941823 | 0.216359 | 0.262421 | 0.769855 | ⋯ |
@btime $x[1:1, 1:20]
9.859 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 | 0.170676 | 0.482524 | 0.165371 | 0.28671 | 0.975893 | 0.195169 | 0.815353 | 0.799585 | 0.253567 | 0.533303 | 0.525501 | 0.230238 | 0.531516 | 0.00957515 | 0.745903 | 0.792815 | 0.728319 | 0.133442 | 0.981423 | 0.46901 |
@btime $x[1, 1:20]
25.006 ns (0 allocations: 0 bytes)
| Row | x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x20 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | |
| 1 | 0.170676 | 0.482524 | 0.165371 | 0.28671 | 0.975893 | 0.195169 | 0.815353 | 0.799585 | 0.253567 | 0.533303 | 0.525501 | 0.230238 | 0.531516 | 0.00957515 | 0.745903 | 0.792815 | 0.728319 | 0.133442 | 0.981423 | 0.46901 |
@btime view($x, 1:1, 1:20)
24.956 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 | 0.170676 | 0.482524 | 0.165371 | 0.28671 | 0.975893 | 0.195169 | 0.815353 | 0.799585 | 0.253567 | 0.533303 | 0.525501 | 0.230238 | 0.531516 | 0.00957515 | 0.745903 | 0.792815 | 0.728319 | 0.133442 | 0.981423 | 0.46901 |
This notebook was generated using Literate.jl.