Julia 笔记¶

主页
My New Workflow with Julia 1.0, mainly focus on how to develop a Julia package.
Timing in Julia
Publication quality plots in Julia

Version Control¶

download the “Generic Linux Binaries for x86 (64-bit)” of a particular version from Download Julia
put it into customed folder, such as src under home directory,
link it to the system path, such as

cd /usr/local/bin
sudo ln -s /home/weiya/src/julia-1.3.1/bin/julia julia1.3.1

Currently, I have installed the following different versions.

$ ll | grep julia
lrwxrwxrwx  1 root root      37 8月  31  2018 julia -> /home/weiya/src/julia-1.0.0/bin/julia*
lrwxrwxrwx  1 root root      37 7月  30  2019 julia1.1.1 -> /home/weiya/src/julia-1.1.1/bin/julia*
lrwxrwxrwx  1 root root      37 9月  18 15:28 julia1.2.0 -> /home/weiya/src/julia-1.2.0/bin/julia*
lrwxrwxrwx  1 root root      37 3月  18 10:25 julia1.3.1 -> /home/weiya/src/julia-1.3.1/bin/julia*

The source folders can be freely moved to another place, and only need to update the symbol links, which can be firstly deleted and then created, or use

sudo ln -sf TARGET LINK_NAME

to override current link. But, if the links is to a folder, then -n need to be added to override,

sudo ln -sfn TARGET LINK_NAME

otherwise, a soft link with the filename of TARGET will be created in the folder LINK_NAME.

since

-f: remove existing destination files
-n: treat LINK_NAME as a normal file if it is a symbolic link to a directory

refer to How to change where a symlink points

If LINK_NAME is ., then it would be the same file/folder name as in the TARGET by removing the path, and no need to specify -n for folders.

Also, note that the link to a folder should be deleted with

rm folder

instead of

rm -r folder/ # delete the original folder

Array¶

drop dimensions: dropdims, see for discussion on the necessity to specify the dims to drop
iterate each row of matrix: eachrow()
tuple to array: collect() or [i for i in t]
index of unique elements: unique(i->x[i], 1:length(x)), used in

pretty println¶

julia> println(a)
[0.4850429731437079 0.1694257866946448; 0.36463804331828364 0.6757027403913352; 0.1855162834299503 0.8954169294007691]

julia> display(a)
3×2 Matrix{Float64}:
 0.485043  0.169426
 0.364638  0.675703
 0.185516  0.895417

More advanced, maybe we can rewrite show to display as you want.

`.=` vs `=` when assigning a row/column vector¶

using StatsBase
a = zeros(2, 2)
b = randn(3, 2)
c = mean(b, dims = 1) # 1×2 Array{Float64,2}
a[1, :] = c # OK!
a[:, 1] = c # OK!
a[1, :] .= c # DimensionMismatch("cannot broadcast array to have fewer dimensions")
a[:, 1] .= c # DimensionMismatch("cannot broadcast array to have fewer dimensions")

similarly for column vector,

d = mean(randn(2, 2), dims = 2) # 2×1 Array{Float64,2}
a[1, :] .= d # DimensionMismatch("cannot broadcast array to have fewer dimensions")

one remedy is to reduce the dimension of the row/column vector

a[1, :] = c[:] # OK!
a[1, :] .= c[:] # OK!

an interesting phenomenon is the type returned after assigning regardless a[1,:] or a[:,1]

julia> a[:, 1] = c 
1×2 Array{Float64,2}:
julia> a[:, 1] = c[:]
2-element Array{Float64,1}:
julia> a[:, 1] .= c[:]
2-element view(::Array{Float64,2}, :, 1) with eltype Float64:

`dims=1`¶

总是记不太清 sum, mean 的时候 dims=1 是按行求和还是按列求和，经常先玩个 toy example 才能分辨出来。比如，

julia> a = rand(4, 3)
4×3 Array{Float64,2}:
 0.279181  0.0903167  0.148329
 0.486691  0.869156   0.0538834
 0.110781  0.836284   0.486467
 0.810343  0.208659   0.759561

julia> sum(a, dims=1)
1×3 Array{Float64,2}:
 1.687  2.00442  1.44824

即把 dims 所代表的维度元素加起来，或者说沿着 dims 进行运算。这一点与 R 的函数 apply 中 margin 参数作用刚好相反，

> a = matrix(rnorm(12), 4, 3)
> a
           [,1]        [,2]       [,3]
[1,]  1.1535199  0.03198768  0.2857126
[2,] -1.3616720  0.32325598  1.9242805
[3,] -0.6519595 -1.14800119 -0.3635221
[4,]  1.2713182  0.98515312  0.2269218
> apply(a, 1, sum)
[1]  1.4712202  0.8858644 -2.1634828  2.4833932

而 Python 的行为与 Julia 类似，先按列求和，再按行求和，但注意其指标从 0 开始，

>>> a = np.random.rand(3, 4);
>>> a
array([[0.47982003, 0.44339329, 0.08865359, 0.30770283],
       [0.03171438, 0.82452326, 0.62909043, 0.95733624],
       [0.51522304, 0.65602682, 0.95936926, 0.51930784]])
>>> np.sum(a, axis = 0)
array([1.02675744, 1.92394337, 1.67711328, 1.78434691])
>>> np.sum(a, axis = 0, keepdims = True)
array([[1.02675744, 1.92394337, 1.67711328, 1.78434691]])
>>> np.sum(a, axis = 1)
array([1.31956975, 2.44266431, 2.64992695])
>>> np.sum(a, axis = 1, keepdims = True)
array([[1.31956975],
       [2.44266431],
       [2.64992695]])

另外，Julia 中维度默认不会退化，即对应 Python 中 keepdims = False.

array in functions¶

julia> function g(x)
           x += [1, 2]
       end
g (generic function with 1 method)
julia> function g!(x)
           x .+= [1, 2]
       end
g! (generic function with 1 method)
julia> x = [1,2];

julia> g(x)'
1×2 Adjoint{Int64,Array{Int64,1}}:
 2  4

julia> x'
1×2 Adjoint{Int64,Array{Int64,1}}:
 1  2

julia> g!(x)'
1×2 Adjoint{Int64,Array{Int64,1}}:
 2  4

julia> x'
1×2 Adjoint{Int64,Array{Int64,1}}:
 2  4

Note that sometimes .+= may make the program much slower, such as en/code/2019-06-14-ML/GD2.jl

no reduction with `[1:1]`¶

Sometimes, I do not want to the array of array reduces to a single array, then [1:1] would help, instead of [1], see the following toy example.

julia> x
2-element Array{Array{Int64,1},1}:
 [1, 2, 3]
 [1, 2]

julia> x[1]
3-element Array{Int64,1}:
 1
 2
 3

julia> x[1:1]
1-element Array{Array{Int64,1},1}:
 [1, 2, 3]

convert a matrix into an array of array¶

julia> a = zeros(3, 4)
3×4 Array{Float64,2}:
 0.0  0.0  0.0  0.0
 0.0  0.0  0.0  0.0
 0.0  0.0  0.0  0.0

julia> mapslices(x->[x], a, dims = 2)
3×1 Array{Array{Float64,1},2}:
 [0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0]

julia> mapslices(x->[x], a, dims = 2)[:]
3-element Array{Array{Float64,1},1}:
 [0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0]

refer to

Converting a matrix into an array of arrays

Conversely, we can converting the array of arrays to a matrix, refer to How to convert an array of array into a matrix?

julia> b = mapslices(x->[x], a, dims = 2)[:]
julia> hcat(b...)
4×3 Array{Float64,2}:
 0.0  0.0  0.0
 0.0  0.0  0.0
 0.0  0.0  0.0
 0.0  0.0  0.0
julia> reduce(hcat, b)
4×3 Array{Float64,2}:
 0.0  0.0  0.0
 0.0  0.0  0.0
 0.0  0.0  0.0
 0.0  0.0  0.0

index from 0¶

using OffsetArrays package, refer to

Github: OffsetArrays

Base¶

Relative path in `include` vs `read`¶

Suppose we have two files

# file: relpath/a.jl
f(x) = x + 1

and

# file: relpath/a.jl
include("a.jl")

println(f(1))

println(String(read("a.jl")))

If we run the scripts from docs/julia/MWE

# file: relpath/b.jl
$ julia relpath/b.jl

it will throw an error that a.jl is not found. But note that include also use the same relative path. The reason is that

help?> include
...During including, a task-local include path is set to the
  directory containing the file.

连等号赋值¶

如果采用 a=b=c=ones(10) 形式赋值的话，则如果后面改变 a 的值，b 和 c 的值也将随之改变。

但如果 a=b=c=1 为常值的话，则三个变量的值还是独立的。

ERROR: `expected Type{T}`¶

参考 ERROR: LoadError: TypeError: Type{…} expression: expected Type{T}, got Module

其中举了一个小例子

module Foo end
Foo{Int64}

会爆出这样的错误。但是一开始竟然没有仔细类比，最后在 REPL 中逐行试验才发现是，using SharedArrays 后直接用 SharedArrays{Float64}(10)，这与上面 Foo 的错误形式完全一样，竟然没有仔细类比。哎，看来以后多思考一下错误可能的原因，不要一味蛮力试验。

type, instance, and object¶

看两个句子：

A type union is a special abstract type which includes as objects all instances of any of its argument types
Nothing is the singleton type whose only instance is the object nothing.

从中分析知道，instance 相对于 types，而 object 相对 instance。一个 type 可能有多个 instance，每个 instance 称之为 object。

instance of some types
object of some instances

Control Flow¶

priority of `&`¶

use

(x[1] <= width) & (x[1] >= 0) & (x[2] <= height) & (x[2] >=0)

instead of

x[1] <= width & x[1] >= 0 & x[2] <= height & x[2] >=0

`ifelse` vs `?`¶

ifelse differs from ? or if in that it is an ordinary function, so all the arguments are evaluated first.

For example, it will try to evaluate the second clause,

julia> isnothing(nothing) ? "" : @sprintf "%.4f" nothing
""

julia> ifelse(isnothing(nothing), "" , @sprintf "%.4f" nothing)
ERROR: MethodError: no method matching isfinite(::Nothing)

Adopted from Clouds#32

Tip

The specifiers in @sprintf should be consists of ones in C++, and the detailed explanation refers to Print Format – C/C++

Note that, %g uses the shorter representation between %e and %f.

`for` in array¶

julia> for i = 1:3
           a = [i for i = i:3]
           println(a)
       end
[1, 2, 3]
[2, 3]
[3]

same iterative variable i, but it works well.

Distributed¶

`@distributed`¶

如果配合 sharedarrays 使用时，需要加上 @sync, 参考@fetch

`@sync` vs `@async`¶

julia> @time sleep(2)
  2.003579 seconds (5 allocations: 128 bytes)

julia> @time @async sleep(2)
  0.015021 seconds (6.57 k allocations: 379.004 KiB)
Task (runnable) @0x00007f24428409d0

julia> @time @sync @async sleep(2)
  2.008425 seconds (1.62 k allocations: 79.125 KiB)
Task (done) @0x00007f24429ebd00

@async: for whatever falls within its scope, Julia will start this task running but then proceed to whatever comes next in the script without waiting for the task to be complete
@sync: wait until all lexically-enclosed uses of @async, @spawn, @spawnat and @distributed are complete, where complete matters how you define the tasks within the scope, such as remotecall_fetch (only finished when it gets the message from the worker that its task is complete) vs remotecall (finished once it has sent the worker the job to do)

With setting

using Distributed
cell(N) = Vector{Any}(undef, N)

addprocs(2)

Nonesync + asyncNone + asyncasync + Nonesync+async + None

julia> @time begin
       a = cell(nworkers())
       for (idx, pid) in enumerate(workers())
           a[idx] = remotecall_fetch(sleep, pid, 2)
       end
   end
  4.270026 seconds (28.35 k allocations: 1.384 MiB)

julia> @time begin
       a = cell(nworkers())
       @sync for (idx, pid) in enumerate(workers())
           @async a[idx] = remotecall_fetch(sleep, pid, 2)
       end
   end
  2.031801 seconds (2.50 k allocations: 144.907 KiB)

julia> @time begin
       a = cell(nworkers())
       for (idx, pid) in enumerate(workers())
           println("sending work to $pid")
           @async a[idx] = remotecall_fetch(sleep, pid, 2)
       end
   end
sending work to 2
sending work to 3
0.020147 seconds (2.10 k allocations: 121.017 KiB)

julia> a
2-element Array{Any,1}:
 #undef
 #undef

# wait around 2 seconds
julia> a
2-element Array{Any,1}:
 nothing
 nothing

julia> @time begin
       a = cell(nworkers())
       @async for (idx, pid) in enumerate(workers())
           println("sending work to $pid")
           a[idx] = remotecall_fetch(sleep, pid, 2)
       end
   end
  sending work to 2
0.000141 seconds (32 allocations: 2.867 KiB)
Task (runnable) @0x00007f2442843d00

# wait around 2 seconds, it prints
julia> sending work to 3

julia> @time begin
       a = cell(nworkers())
       @sync @async for (idx, pid) in enumerate(workers())
           a[idx] = remotecall_fetch(sleep, pid, 2)
       end
   end
  4.017451 seconds (13.96 k allocations: 692.136 KiB)
Task (done) @0x00007f2442dfdfc0

refer to How and When to Use @async and @sync in Julia - Stack Overflow

And as the official documentation said,

@async is similar to @spawnat, but only runs tasks on the local process. We use it to create a “feeder” task for each process. Each task picks the next index that needs to be computed, then waits for its process to finish, then repeats until we run out of indices. Note that the feeder tasks do not begin to execute until the main task reaches the end of the @sync block, at which point it surrenders control and waits for all the local tasks to complete before returning from the function.

Info

Applications in my project: parallel.job, where it is much like the feeder, although it might be quite fast.

Gurobi¶

Currently (2022-09-23) no way to enable Gurobi.jl in GitHub Actions.
hide message of Set parameter ...: GRBsetintparam(GRB_ENV, GRB_INT_PAR_OUTPUTFLAG, 0). Inspired by the way for C++ API of Gurobi, and

JLD vs JLD2¶

JLD depends on HDF5, whose installation requires to login in, while JLD2 avoid the dependence of HDF5.

Source

Juno¶

Info

An IDE on Atom.

Shortcuts¶

Ctrl+J Ctrl+E: switch from REPL to editor, refer to the correct shortcut is be Ctrl-J Ctrl-E (and the command is called Julia Client: Focus Last Editor), an inspiration is that I can check it via Ctrl-Shift-P.

Bug when `Cltr + Enter`¶

当我使用 Ctrl + Enter 运行下列语句时，

using Images, ImageView
img = load(download("https://juliaimages.org/latest/assets/segmentation/horse.jpg"));
imshow(img)

REPL 冻住了，一直停在

Dict{String,Any} with 4 entries:

而我如果直接将上述语句复制到 REPL 中运行时，一切 OK，正常显示为

Dict{String,Any} with 4 entries:
  "gui"         => Dict{String,Any}("window"=>GtkWindowLeaf(name="", parent, wi…
  "roi"         => Dict{String,Any}("redraw"=>50: "map(clim-mapped image, input…
  "annotations" => 3: "input-2" = Dict{UInt64,Any}() Dict{UInt64,Any}
  "clim"        => 2: "CLim" = CLim{RGB{Float64}}(RGB{Float64}(0.0,0.0,0.0), RG…

找到类似的 Issue: [BUG] Evaluation in Editor freezes Atom occasionally

虽然其解决方案不太清楚，是有关 notification-daemon，但是维护者 @pfitzseb 的回复

OS level notifications are disabled completly in the latest Juno release because they were causing crashes on Mac and didn’t really seem to work on other platforms.

提醒我或许是因为 Juno 的版本问题，当前版本为 v0.7.2, 最新版本为 v0.8.1

仅仅更新 Juno.jl 的版本似乎还不行，另外将 Atom.jl 从 v0.12.8 更新到 v0.12.9

最后竟然真的解决了！

System Proxy¶

当在 .bashrc 添加 http_proxy 和 https_proxy 中并 source 之后，直接在 shell 里面开的 julia session 中，验证当前 ip

run(`curl ifconfig.me`)

或者直接查看

ENV["http_proxy"]

发现可以使用系统代理。但是在 Atom 中开的 julia，则不行。找到 Atom 一条相关的 issue: [Atom 1.32.0] Does not inherit environment variables when launched not from the command line，但是我已经是最新版了，不应该存在这个问题。但是当我通过 Ctrl-Shift-i 打开 devtools，验证 process.env["http_proxy"]，显示 undefined；而且直接在 source 之后的 terminal 中打开，也显示 undefined。猜想，只对 PATH 有效？或者因为 Juno.jl?

跳过这个问题，最后直接在 startup.jl 文件中添加

ENV["http_proxy"] =
ENV["https_proxy"]

进行设置，这参考了 Install packages behind the proxy

Function¶

function redefinition in `if`¶

WrongCorrect: anonymous functions

julia> function f()
        flag = true
        if flag
            g(x) = 1
        else
            g(x) = 2
        end
        println(g(1))
    end
WARNING: Method definition g(Any) in module Main at REPL[1]:4 overwritten at REPL[1]:6.
f (generic function with 1 method)

julia> f()
2

julia> function f()
        flag = true
        if flag
            g = x->1
        else
            g = x->2
        end
        println(g(1))
    end
f (generic function with 1 method)

julia> f()
1

The correct way is to use the anonymous function, see also Defining a function inside if…else..end NOT as expected? - New to Julia - JuliaLang

invoke function via string¶

julia> getfield(Main, Symbol("exp"))(1)
2.718281828459045

refer to reflection - Julia: invoke a function by a given string - Stack Overflow

default argument and optional arguments¶

julia> function f(x, y=nothing; z=1)
           if isnothing(y)
               println("x + z = $(x+z)")
           else
               println("x + y + z = $(x+y+z)")
           end
       end

julia> f(1)
x + z = 2

julia> f(1, 2)
x + y + z = 4

with this format, we can avoid define two functions f(x; ) and f(x, y;) respectively.

function in function¶

julia> function f2()
           a = 10
           function g()
               a = a+10
           end
           g()
           println(a)
       end
f2 (generic function with 1 method)

julia> f2()
20

but

julia> function f2()
           a = 10
           g() = a + 10
           g()
           println(a)
       end
f2 (generic function with 1 method)

julia> f2()
10

since the first one does not have return, but g() has return and the addition is not on a.

Pkg¶

Pkg + BinaryBuilder: binary objects that are not Julia packages

PyCall¶

Update Matplotlib¶

Info

Post: 2022-04-09 19:13:48

julia> pyplot()
[ Info: Precompiling PyPlot [d330b81b-6aea-500a-939a-2ce795aea3ee]
┌ Warning: You are using Matplotlib 3.1.3, which is no longer
│ officialy supported by the Plots community. To ensure smooth Plots.jl
│ integration update your Matplotlib library to a version >= 3.4.0
│ 
│ If you have used Conda.jl to install PyPlot (default installation),
│ upgrade your matplotlib via Conda.jl and rebuild the PyPlot.
│ 
│ If you are not sure, here are the default instructions:
│ 
│ In Julia REPL:
│ ```
│ import Pkg;
│ Pkg.add("Conda")
│ import Conda
│ Conda.update()
│ Pkg.build("PyPlot")
│ ```
│ 
└ @ Plots ~/.julia/packages/Plots/9C6z9/src/backends/pyplot.jl:29

Then follow the instruction,

julia> import Conda

julia> Conda.update()
[ Info: Running `conda update -y --all conda` in root environment
Collecting package metadata (current_repodata.json): done
Solving environment: done

## Package Plan ##

  environment location: /home/weiya/.julia/conda/3

  added / updated specs:
    - conda

it implies that the env created by Conda.jl is ~/.julia/conda/3

If I check all env in the shell, it returns

$ conda env list
# conda environments:
#
                         /home/weiya/.julia/conda/3
                         /home/weiya/.julia/conda/3/envs/_ORCA_jl_
base                     /home/weiya/anaconda3
py37                     /home/weiya/anaconda3/envs/py37
...

Couldn’t find libpython error¶

ENV["PYTHON"]=""; Pkg.build("PyCall")

to install its own private Miniconda distribution for you, in a way that won’t interfere with your other Python installations.

Refer to Couldn’t find libpython error #199

Actually, using PyPlot also encounters the similar question, cannot find matplotlib, then I changed to the conda environment contained such package, and then

ENV["PYTHON"]="the-python-path";
# change to package command line
build PyCall

it works. And it seems that it does NOT depend on conda environment any more, i.e., PyPlot still works for different conda environment, even without matplotlib package in such environment.

In the words of the official documentation,

If you use Python virtualenvs, then be aware that PyCall uses the virtualenv it was built with by default, even if you switch virtualenvs. If you want to switch PyCall to use a different virtualenv, then you should switch virtualenvs and run rm(Pkg.dir(“PyCall”,”deps”,”PYTHON”)); Pkg.build(“PyCall”).

which supports my above guess.

Record for install `PyCall`¶

Switch to py37 conda environment, then run julia1.2.0

(v1.2) pkg> add PyCall

Then test to import module in the same REPL,

julia> using PyCall
[ Info: Recompiling stale cache file /home/weiya/.julia/compiled/v1.2/PyCall/GkzkC.ji for PyCall [438e738f-606a-5dbb-bf0a-cddfbfd45ab0]

julia> math = pyimport("math")
PyObject <module 'math' from '/home/weiya/anaconda3/lib/python3.7/lib-dynload/math.cpython-37m-x86_64-linux-gnu.so'>

Now open a new julia session under different conda environment (or no any conda environment), re-run the above code

julia> using PyCall

julia> math = pyimport("math")
PyObject <module 'math' from '/home/weiya/anaconda3/lib/python3.7/lib-dynload/math.cpython-37m-x86_64-linux-gnu.so'>

As you can see, no any compiling info when using PyCall, and return the same math module. However such module does not corresponds to the py37 conda environment. The official documentation says

On GNU/Linux systems, PyCall will default to using the python3 program (if any, otherwise python) in your PATH.

Then to specify the version of python such as

julia> ENV["PYTHON"] = Sys.which("python")
"/home/weiya/anaconda3/envs/py37/bin/python3.7"

and rebuild, note that need to restart the julia session to recompiling,

julia> using PyCall
[ Info: Recompiling stale cache file /home/weiya/.julia/compiled/v1.2/PyCall/GkzkC.ji for PyCall [438e738f-606a-5dbb-bf0a-cddfbfd45ab0]

julia> pyimport("math")
PyObject <module 'math' from '/home/weiya/anaconda3/envs/py37/lib/python3.7/lib-dynload/math.cpython-37m-x86_64-linux-gnu.so'>

then the module corresponds to the specified conda environment, and then like the above test, it also can be used in other conda environment without recompiling.

RCall¶

rcopy(NA) return missing,

julia> rcopy(R"lm($dop ~ 0 + $H)$coefficients")
100-element reshape(::Array{Union{Missing, Float64},1}, 100) with eltype Union{Missing, Float64}:
     missing
   -1.909321682273283e-23

A related error is

julia> Array{Float64}(rcopy(R"lm($dop ~ 0 + $H)$coefficients"))
ERROR: MethodError: Cannot `convert` an object of type Missing to an object of type Float64
Closest candidates are:
  convert(::Type{T}, ::T) where T<:Number at number.jl:6
  convert(::Type{T}, ::Number) where T<:Number at number.jl:7
  convert(::Type{T}, ::Base.TwicePrecision) where T<:Number at twiceprecision.jl:250

Random¶

Warning

Caution for Random.seed!(). Be careful to use it in a function. Adapt it from

Case 1: Two files¶

Suppose I have the following two files,

a.jlb.jl

using Random
import StatsBase.sample
function g(seed = 1234)
    println(sample(Random.seed!(seed), 1:5, 5))
end

include("a.jl")

function f()
    println(rand(3))
    g(1234)
    println(rand(3))
end

after first different results, it repeats to show the same results.

julia> include("b.jl")
f (generic function with 1 method)

julia> f()
[0.8484503038106239, 0.6270935436096212, 0.8958165220379257]
[3, 4, 5, 4, 1]
[0.3728458178193992, 0.2631210819875911, 0.9886904946486306]

julia> f()
[0.4898584067326506, 0.4252112774882528, 0.37976500269509095]
[3, 4, 5, 4, 1]
[0.3728458178193992, 0.2631210819875911, 0.9886904946486306]

julia> f()
[0.4898584067326506, 0.4252112774882528, 0.37976500269509095]
[3, 4, 5, 4, 1]
[0.3728458178193992, 0.2631210819875911, 0.9886904946486306]

Case 2: a single file¶

The above phenomenon can be observed in a single file,

using Random

function f(seed)
    println(rand(Random.seed!(seed)))
end

function g(seed)
    println(rand())
    f(seed)
    println(rand())
end

julia> include("c.jl")
g (generic function with 1 method)

julia> g(1)
0.8797616728308622
0.23603334566204692
0.34651701419196046

julia> g(1)
0.3127069683360675
0.23603334566204692
0.34651701419196046

julia> g(1)
0.3127069683360675
0.23603334566204692
0.34651701419196046

A Correct Way¶

replace Random.seed!(seed) with MersenneTwister

using Random

function f(seed)
    println(rand(MersenneTwister(seed)))
end

function g(seed)
    println(rand())
    f(seed)
    println(rand())
end

it behaves as expected,

julia> include("d.jl")
g (generic function with 1 method)

julia> g(1)
0.12495220703448995
0.23603334566204692
0.41171274946529546

julia> g(1)
0.7243446710747494
0.23603334566204692
0.3672395293576307

julia> g(1)
0.5368102592873767
0.23603334566204692
0.6466136938696847

Revise¶

Is there a way to undo `using` in Julia?¶

NO

Although we cannot remove some defined function, with the powerful Revise.jl, we can update the functions without reloading the scripts.

Statistics (StatsBase, Distributions)¶

关于 `mean()`¶

using Statistics 后才能用 mean()，而 using Distributions 后也能用 mean()。前者表示 generic function with 5 methods，后者称 generic function with 78 methods.

`Normal` 中标准差为 0 的问题¶

可知，最低可以支持 1e-323，所以似乎也支持 sqrt(1e-646)，但并没有，而且当 sqrt(1e-324) 时精度就不够了，似乎 sqrt(x) 的精度与 x 的精度相当。

SymPy: Symbolic Math¶

julia> using SymPy
[ Info: Precompiling SymPy [24249f21-da20-56a4-8eb1-6a02cf4ae2e6]
ERROR: InitError: PyError (PyImport_ImportModule

The Python package sympy could not be imported by pyimport. Usually this means
that you did not install sympy in the Python version being used by PyCall.

PyCall is currently configured to use the Python version at:

/home/weiya/anaconda3/envs/py37/bin/python3.7

and you should use whatever mechanism you usually use (apt-get, pip, conda,
etcetera) to install the Python package containing the sympy module.

julia> @vars x
(x,)

julia> exp(-x^2/2)/sqrt(2pi)
                     2 
                   -x  
                   ────
                    2  
0.398942280401433⋅ℯ    

julia> f(x) = exp(-x^2/2)/sqrt(2pi)
f (generic function with 1 method)

julia> integrate(f(x), x)
                           ⎛√2⋅x⎞
0.199471140200716⋅√2⋅√π⋅erf⎜────⎟
                           ⎝ 2  ⎠

julia> integrate(f(x), (x, -Inf, Inf))
0.398942280401433⋅√2⋅√π

julia> integrate(x*f(x), (x, -Inf, Inf))
0

julia> integrate(x*f(x), x)
                      2 
                    -x  
                    ────
                     2  
-0.398942280401433⋅ℯ    

julia> integrate(x*f(x), (x, -Inf, Inf))
0

julia> integrate(f(x)^2, (x, -Inf, Inf))
0.159154943091895⋅√π

julia> integrate(f(x)^2, x)
0.0795774715459477⋅√π⋅erf(x)

where erf is https://en.wikipedia.org/wiki/Error_function

parallel¶

references

pbsdsh (unsolved)¶

Submit a pbsdsh job and specify multiply nodes with multiply cores, say nodes=2:ppn=4

error log file (see full file in the cluster: dshmcmc.e21907):

fatal: error thrown and no exception handler available.
InitError(mod=:Base, error=ArgumentError(msg="Package Sockets not found in current path:
- Run `Pkg.add("Sockets")` to install the Sockets package.
"))
rec_backtrace at /buildworker/worker/package_linux64/build/src/stackwalk.c:94
record_backtrace at /buildworker/worker/package_linux64/build/src/task.c:246
jl_throw at /buildworker/worker/package_linux64/build/src/task.c:577
require at ./loading.jl:817
init_stdio at ./stream.jl:237
jfptr_init_stdio_4446.clone_1 at /opt/share/julia-1.0.0/lib/julia/sys.so (unknown line)
jl_apply_generic at /buildworker/worker/package_linux64/build/src/gf.c:2182
reinit_stdio at ./libuv.jl:121
__init__ at ./sysimg.jl:470
jl_apply_generic at /buildworker/worker/package_linux64/build/src/gf.c:2182
jl_apply at /buildworker/worker/package_linux64/build/src/julia.h:1536 [inlined]
jl_module_run_initializer at /buildworker/worker/package_linux64/build/src/toplevel.c:90
_julia_init at /buildworker/worker/package_linux64/build/src/init.c:811
julia_init__threading at /buildworker/worker/package_linux64/build/src/task.c:302
main at /buildworker/worker/package_linux64/build/ui/repl.c:227
__libc_start_main at /lib64/libc.so.6 (unknown line)
_start at /opt/share/julia-1.0.0/bin/julia (unknown line)

But when I just use single node, and arbitrary cores, say nodes=1:ppn=2, it works well.

references¶

julia local package 失败折腾记录¶

no error after add ~/GitHub/adm.jl, but using adm cannot work. refer to Adding a local package
set startup.jl but still not work. refer to How does Julia find a module?
one possible way: Finalizing Your Julia Package: Documentation, Testing, Coverage, and Publishing

Variable Scopes¶

`for` loop¶

mwe1.jlmwe2.jlmwe3.jl

i = 0
for j = 1:2
    if j != i
        println("ok")
    end
end

i = 0
for j = 1:2
    if j != i
        println("ok")
    end
    i = j
end

i = 0
for j = 1:2
    if j != i
        println("ok")
    end
    global i = j
end

The results are

$ julia mwe1.jl
ok
ok
$ julia mwe2.jl
ERROR: LoadError: UndefVarError: i not defined
# more information given in julia1.5.2
$ julia1.5.2 mwe2.jl
┌ Warning: Assignment to `i` in soft scope is ambiguous because a global variable by the same name exists: `i` will be treated as a new local. Disambiguate by using `local i` to suppress this warning or `global i` to assign to the existing global variable.
ERROR: LoadError: UndefVarError: i not defined
$ julia mwe3.jl
ok
ok

Thus, the reason is that $i$ is a global variable, we cannot modify a global variable in a local block without global keyword, i.e., global i = i + 1, but we can read i in the for loop.

Alternatively, we can use let block,

let
i = 0
for j = 1:2
    i = i + 1
end
i
end

then i isn’t really a global variable anymore.

References:

`while` loop¶

function test_while(flag)
    if flag
        a = 1
    else
        while true
            a = 2
            break
        end
    end
    println(a)
end
function test_while2(flag)
    while true
        a = 2
        break
    end
    println(a)
end

the results are

julia> test_while(false)
2

julia> test_while2(false)
ERROR: UndefVarError: a not defined

自定义 `==` and `hash()`¶

对于自定义的 mutable struct, 直接用 == 返回 false，因此需要自己定义等号，比如

Base.:(==)(x::Reaction, y::Reaction) = all([
    x.substrate == y.substrate,
    x.product == y.product,
    x.reversible == y.reversible,
    x.species == y.species])

而如果想用 unique 函数的话，其基于 isequal 函数，而 isequal 是通过判断 hash 值来判定的，所以仅仅定义了 == 仍不够，还需要定义 hash 函数，这很简单，比如

function Base.hash(obj::Reaction, h::UInt)
    return hash((obj.substrate, obj.product, obj.reversible, obj.species), h)
end

hash（散列、杂凑）函数，是将任意长度的数据映射到有限长度的域上。直观解释起来，就是对一串数据m进行杂糅，输出另一段固定长度的数据h，作为这段数据的特征（指纹）。

or

HASH函数是这么一种函数，他接受一段数据作为输入，然后生成一串数据作为输出，从理论上说，设计良好的HASH函数，对于任何不同的输入数据，都应该以极高的概率生成不同的输出数据，因此可以作为“指纹”使用，来判断两个文件是否相同。数据 ---->输入 HASH 函数 ---->输出指纹数据

参考

import vs using

Instead of explicitly redefine function with Module.function name, we can first import it, e.g., pdf, we need to use import Distributions.pdf.

`MethodError: objects of type Module are not callable`¶

check if the function is mistaken by the module name, such as AxisArray vs. AxisArrays.

`/lib/x86_64-linux-gnu/libz.so.1: version`ZLIB_1.2.9’ not found`¶

ref to https://stackoverflow.com/questions/48306849/lib-x86-64-linux-gnu-libz-so-1-version-zlib-1-2-9-not-found

work with GPU¶

An Introduction to GPU Programming in Julia
Re-build after install cudnn, refer to GPU on cluster: conversion to pointer not defined for CuArray{Float32,2}

load `ImageView` on Server¶

when using ImageView, it throws an error,

ERROR: LoadError: InitError: Cannot open display:

fixed by ssh -X. If further ssh on the node, it still works.

`-i` vs `-L`¶

if need to REPL and also arguments, then -i would be suitable.

And note that -- should be separated the switches and program files. (but seems not necessary)

Julia docs: Getting Started

Unable to display plot using the REPL. GKS errors¶

The reason would be relate to the GR package,

cd .julia/packages/GR/ZI5OE/deps/gr/bin/
ldd gksqt

and then get

linux-vdso.so.1 =>  (0x00007ffdc1e58000)
libQt5Widgets.so.5 => not found
libQt5Gui.so.5 => not found
libQt5Network.so.5 => not found
libQt5Core.so.5 => not found
libGL.so.1 => /lib64/libGL.so.1 (0x00002ae608a73000)
libpthread.so.0 => /lib64/libpthread.so.0 (0x00002ae608ce5000)
libstdc++.so.6 => /lib64/libstdc++.so.6 (0x00002ae608f01000)
libm.so.6 => /lib64/libm.so.6 (0x00002ae609209000)
libgcc_s.so.1 => /lib64/libgcc_s.so.1 (0x00002ae60950b000)
libc.so.6 => /lib64/libc.so.6 (0x00002ae609721000)
libexpat.so.1 => /lib64/libexpat.so.1 (0x00002ae609aef000)
libxcb-dri3.so.0 => /lib64/libxcb-dri3.so.0 (0x00002ae609d19000)
libxcb-xfixes.so.0 => /lib64/libxcb-xfixes.so.0 (0x00002ae609f1c000)
libxcb-present.so.0 => /lib64/libxcb-present.so.0 (0x00002ae60a125000)
libxcb-sync.so.1 => /lib64/libxcb-sync.so.1 (0x00002ae60a328000)
libxshmfence.so.1 => /lib64/libxshmfence.so.1 (0x00002ae60a52f000)
libglapi.so.0 => /lib64/libglapi.so.0 (0x00002ae60a733000)
libselinux.so.1 => /lib64/libselinux.so.1 (0x00002ae60a963000)
libXext.so.6 => /lib64/libXext.so.6 (0x00002ae60ab8a000)
libXdamage.so.1 => /lib64/libXdamage.so.1 (0x00002ae60ad9d000)
libXfixes.so.3 => /lib64/libXfixes.so.3 (0x00002ae60afa0000)
libX11-xcb.so.1 => /lib64/libX11-xcb.so.1 (0x00002ae60b1a6000)
libX11.so.6 => /lib64/libX11.so.6 (0x00002ae60b3a9000)
libxcb.so.1 => /lib64/libxcb.so.1 (0x00002ae60b6e7000)
libxcb-glx.so.0 => /lib64/libxcb-glx.so.0 (0x00002ae60b90f000)
libxcb-dri2.so.0 => /lib64/libxcb-dri2.so.0 (0x00002ae60bb2b000)
libXxf86vm.so.1 => /lib64/libXxf86vm.so.1 (0x00002ae60bd30000)
libdrm.so.2 => /lib64/libdrm.so.2 (0x00002ae60bf36000)
libdl.so.2 => /lib64/libdl.so.2 (0x00002ae60c148000)
/lib64/ld-linux-x86-64.so.2 (0x0000557abc358000)
libXau.so.6 => /lib64/libXau.so.6 (0x00002ae60c34c000)
libpcre.so.1 => /lib64/libpcre.so.1 (0x00002ae60c551000)

(refer to one comment in Error: GKS: can’t connect to GKS socket application)

So it seems that it is due to the missing of libqt5. If I have the sudo privilege, maybe just type

sudo apt-get install qt5-default

but I cannot. But I noticed that I have installed miniconda3, and the qt is installed,

qmake -v
# QMake version 3.1
# Using Qt version 5.9.7 in /users/xxx/miniconda3/lib

So a natural way is to append the library path of qt to LD_LIBRARY_PATH, that is,

# in .bashrc
export LD_LIBRARY_PATH=/users/xxx/miniconda3/lib:$LD_LIBRARY_PATH

then rebuild GR package in the julia REPL.

This solution should work, but actually it failed at the first time. Do not be too frustrated, I found the reason is that I type miniconda3 as minconda3 in the path.

It works now, although it still throw an error,

julia> libGL error: unable to load driver: swrast_dri.so
libGL error: failed to load driver: swrast

reset `kw...` value¶

In the following situation, I want to reset a particular argument in kw....

function f(; kw...)
    g(; kw...)
end

Note that the type of kw is Base.Iterators.Pairs, firstly I want to directly reset the value via

h(;kw...) = kw
h(a=1).data.a = 2

but it throws

ERROR: setfield! immutable struct of type NamedTuple cannot be changed
Stacktrace:
 [1] setproperty!(::NamedTuple{(:a,),Tuple{Int64}}, ::Symbol, ::Int64) at ./Base.jl:21
 [2] top-level scope at none:0

So I need to find new method, or give up such idea. Fortunately, the official documentation of Julia says

The nature of keyword arguments makes it possible to specify the same argument more than once. For example, in the call plot(x, y; options..., width=2) it is possible that the options structure also contains a value for width.

Thus, I can write

function f(; kw...)
    g(; kw..., b = 6)
end

to solve my problem, where b is the argument I want to reset.

some interesting behavior¶

d = Dict{Int, Int}()
d[1] = 1

if we access

d.vals
# d.keys

it will return a 16-element Array{Int64,1}, but if we use

values(d)
keys(d)

it correctly returns the exactly one elements, but with type Base.ValueIterator for a Dict{Int64,Int64} with 1 entry.

pass array into function¶

julia> a = [1,2]
2-element Array{Int64,1}:
 1
 2

julia> function f(a)
           a = a .+ 1
       end
f (generic function with 1 method)

julia> f(a)
2-element Array{Int64,1}:
 2
 3

julia> a
2-element Array{Int64,1}:
 1
 2

julia> function g(a)
           a .= a .+ 1
       end
g (generic function with 1 method)

julia> g(a)
2-element Array{Int64,1}:
 2
 3

julia> a
2-element Array{Int64,1}:
 2
 3

check whether array entry is undef¶

b = Array{Array{Int, 1}}(undef, 3)
isdefined(b, 1)
# or
isassigned(b, 1)
# not
# isdefined(b[1])

refer to Julia: check whether array entry is undef

Memory Allocation¶

Usage of `GC.gc()`¶

Manually run GC.gc() can release the occupied memory,

The experiments are as follows,

open a julia1.6 session
run tseries = zeros(1024,1024, 5, 50);, it allocates 1.953GB, roughtly 1.953/16 = 12%, while the column MEM% displayed by htop indeed show 11.4.
repeat to run, then MEM% increses to 21.5
run GC.gc(), then MEM% decreases to 11.0
repeat to run 2 times, then MEM% increases to 31.2
run GC.gc(), then MEM% decreases to 11.0
set tseries = nothing, and run GC.gc(), it disappears from the top line of htop, i.e., (nearly) zero memory.

Refer to the following video for the whole experiments.

Another experiments are for for loop,

julia> for i = 1:6
           tseries = zeros(1024,1024, 5, 50);
           sleep(3)
           if i % 3 == 0
               println("gc...")
               GC.gc(); sleep(3)
           end
       end

It can be observed that MEM% increses from ~10 to ~20, and then ~30, then decreases to ~10 after first GC.

With monitoring the memory from top, we can use the following memuse() function to get the memory usage of the current process.

function memuse()
    pid = getpid()
    return round(Int,parse(Int,read(`ps -p $pid -o rss=`, String))/1024)
end

println("init mem = ", memuse(), "MB")
for i = 1:6
    # tseries = zeros(1024,1024, 5, 50);
    r = R"rnorm(1024*1024*5*50)"
    # sleep(3)
    println("i = ", i, ", mem = ", memuse(), "MB")
    if i % 3 == 0
        finalize(r)
        GC.gc(); GC.gc(); GC.gc(); GC.gc(); 
        R"gc()"; R"gc()";
        sleep(3)
        println("after gc..., mem = ", memuse(), "MB")
    end
end

function test()
  for i = 1:2   println("\ni=$i")
    a = rand(10000,10000)
    println("Created a $(memuse())")
    a = 0
    GC.gc()
    println("Release a $(memuse())\n")

    b = rand(10000,10000)
    println("Created b $(memuse())")
    b = 0
    GC.gc()
    println("Release b $(memuse())\n")

    c = rand(10000,10000)
    println("Created c $(memuse())")
    c =0
    GC.gc()
    println("Release c $(memuse())\n")
  end
end

memory allocation of `undef`¶

julia> @time Array{Array{Int, 1}, 2}(undef, 100, 100);
  0.000024 seconds (6 allocations: 78.359 KiB)
julia> @time zeros(100,100, 1);
  0.000014 seconds (6 allocations: 78.359 KiB)
julia> @time zeros(100,100, 10);
  0.000077 seconds (6 allocations: 781.484 KiB)

wrong arrangement of multiple figures in a grid¶

Hi, I am confused by the arrangement of multiple figures in a grid. I begin with the example code in the README,

gui = imshow_gui((300, 300), (2, 1))  # 2 columns, 1 row of images (each initially 300×300)
canvases = gui["canvas"]
imshow(canvases[1,1], testimage("lighthouse"))
imshow(canvases[1,2], testimage("mandrill"))
Gtk.showall(gui["window"])

it throws an error when accessing canvases[1,2]

julia> imshow(canvases[1,2], testimage("mandrill"))
ERROR: BoundsError: attempt to access 2×1 Array{Any,2} at index [1, 2]

and I check the size of canvases is

julia> size(canvases)
(2, 1)

it seems that the canvases will arrage by column while the gui declares it should be by rows.

On the other hand, if I run

gui = imshow_gui((300, 300), (2, 1))  # 2 columns, 1 row of images (each initially 300×300)
canvases = gui["canvas"]
imshow(canvases[1,1], testimage("lighthouse"))
imshow(canvases[2,1], testimage("mandrill"))
Gtk.showall(gui["window"])

gui = imshow_gui((300, 300), (1, 2))  # 2 columns, 1 row of images (each initially 300×300)
canvases = gui["canvas"]
imshow(canvases[1,1], testimage("lighthouse"))
imshow(canvases[1,2], testimage("mandrill"))
Gtk.showall(gui["window"])

Then I guess it might due to the version of some packages…

同时安装多个 package¶

用空格隔开，如

add Distributions Combinatorics MATLAB PyPlot LightGraphsFlows LightGraphs Clp Plots

内地镜像源¶

安装 PkgMirrors，则可以用中科大或者浙大的镜像源了

初次设置后，以后直接 using PkgMirrors 便切换到设置好的镜像，以后直接通过镜像源安装。

select text in the output pdf¶

Several weeks ago, the text, such as the label, title or legend, in the output pdf via savefig("xxx.pdf") can be selected, but recently I found that I cannot select the text in the pdf. The reason would be the version of the packages.

I had tried GRUtils, and GRUtils.savefig can output pdf to select the texts, so I think the reason is some changes in Plots package.

And I found that with Plots@0.27.0 in Julia1.0, I can select the text, but currently the newer Plots@1.2.0 cannot produce such pdf. To determine the change, maybe I need more effort to try different versions. But now I can downgrade the version to satisfy my requirement.

`colorviews` for images¶

check the help document by ?colorviews, and there are some examples to illustrate its usage, but here I add some examples that I used in my projects.

julia> colorview(RGB, rand(3,10,10))
10×10 reshape(reinterpret(RGB{Float64}, ::Array{Float64,3}), 10, 10) with eltype RGB{Float64}:

and we need to permutate the dims such that the first dim matches with RGB.

julia> colorview(RGB, permutedims(rand(10, 10, 3), (3, 1, 2)))
10×10 reshape(reinterpret(RGB{Float64}, ::Array{Float64,3}), 10, 10) with eltype RGB{Float64}:

we also can append the alpha channel to an image, such as

julia> colorview(RGBA, colorview(RGB, rand(3, 10, 10)), rand(10, 10))
10×10 mappedarray(RGBA{Float64}, ImageCore.extractchannels, reshape(reinterpret(RGB{Float64}, ::Array{Float64,3}), 10, 10), ::Array{Float64,2}) with eltype RGBA{Float64}:

but directly append the array does not work,

julia> colorview(RGBA, rand(3, 10, 10), rand(10, 10))
ERROR: DimensionMismatch("arrays do not all have the same axes (got (Base.OneTo(3), Base.OneTo(10), Base.OneTo(10)) and (Base.OneTo(10), Base.OneTo(10)))")

which should be replaced with

julia> colorview(RGBA, rand(4, 10, 10))
10×10 reshape(reinterpret(RGBA{Float64}, ::Array{Float64,3}), 10, 10) with eltype RGBA{Float64}:

To use RGB{N0f8}, the input array should be UInt8 not Int,

julia> colorview(RGB{N0f8}, Array{UInt8}(fill(1,3,10,10)))
10×10 reshape(reinterpret(RGB{N0f8}, view(::Array{UInt8,3}, [1, 2, 3], :, :)), 10, 10) with eltype RGB{Normed{UInt8,8}}:

return values of function¶

julia> versioninfo()
Julia Version 1.4.0
Commit b8e9a9ecc6 (2020-03-21 16:36 UTC)
Platform Info:
  OS: Linux (x86_64-pc-linux-gnu)
  CPU: Intel(R) Core(TM) i5-6300HQ CPU @ 2.30GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-8.0.1 (ORCJIT, skylake)

julia> function f(a, b, c, d)
           return a, b, c, d
       end
julia> a = f(1,2,3,4);

julia> a
(1, 2, 3, 4)

julia> a, b = f(1,2,3,4);

julia> a
1

julia> b
2

julia> a, b, c = f(1,2,3,4);

julia> a
1

julia> b
2

julia> c
3

String¶

padding zero on the left¶

For example, convert “1” to “001”,

JuliaPython

julia> lpad(1, 3, '0')
"001"

>>> a = 1
>>> f"{a:03}"
'001'

check if substring¶

JuliaPython

julia> occursin("tech", "techNotes")
true

>>> "tech" in "techNotes"
True

single/double quoting¶

julia> a = 'www'
ERROR: syntax: invalid character literal

julia> a = 'w'
'w': ASCII/Unicode U+0077 (category Ll: Letter, lowercase)

julia> a = "ww"
"ww"

refer to #105.

run command line¶

For example, to combine different figures,

run(`convert p1.png p2.png +append p12.png`)

but if there are two many figures to combine, the correct way is to keep the multiple figure name as an array,

figs = "p" .* string.(1:10) .* ".png"
run(`convert $figs +append pall.png`)

instead of trying to convert the array to a string,

# WRONG!!!
julia> figs = prod("p" .* string.(1:10) .* ".png ")
julia> run(`convert $figs +append pall.png`)
convert: unable to open image 'p1.png p2.png ... p10.png '

or writting all command as a string

# WRONG!!!
command = "convert " * prod("p" .* string.(1:10) .* ".png ") * "+append pall.png"
run(`$command`)

Special characters #{}()[]<>|&*?~; need to be quoted,

julia> run(`ls *.toml`)
ERROR: LoadError: parsing command `ls *.toml`: special characters "#{}()[]<>|&*?~;" must be quoted in commands

the quote is not just for the special character, which will fix the filename in the above example,

julia> run(`ls "*.toml"`)
ls: cannot access '*.toml': No such file or directory

but quoting is not enough,

julia> run(`"ls *.toml"`)
ERROR: IOError: could not spawn `'ls *.toml'`: no such file or directory (ENOENT)

the right way is

julia> run(`bash -c "ls *.toml"`)
Manifest.toml  Project.toml
Process(`bash -c 'ls *.toml'`, ProcessExited(0))

refer to Quoting in shell commands - General Usage - JuliaLang

foreach¶

julia> foreach(readdir(".")) do filename
           println(filename)
       end
# or a more concise way
julia> foreach(println, readdir("."))

an example

Regex¶

julia> split("juliaxxxjulia", "julia")
3-element Array{SubString{String},1}:
 ""
 "xxx"
 ""

# ^ requires `Regex`
julia> split("juliaaaajulia", "^julia")
1-element Array{SubString{String},1}:
"juliaaaajulia"


julia> split("juliaxxxjulia", Regex("^julia"))
2-element Array{SubString{String},1}:
 ""
 "xxxjulia"

julia> x = "xxx"
"xxx"

julia> split("juliaxxxjulia", Regex("^julia$x"))
2-element Array{SubString{String},1}:
 ""
 "julia"

adopted from pattern = Regex("^"*pattern)

Underscores¶

julia> function ff()
           return 1, 2, 3
       end
ff (generic function with 1 method)

julia> _, _, a = ff()
(1, 2, 3)

julia> a
3

julia> _
ERROR: all-underscore identifier used as rvalue

where the formal definition for rvalue refers to Value categories

Julia 笔记¶

Version Control¶

Array¶

pretty println¶

.= vs = when assigning a row/column vector¶

dims=1¶

array in functions¶

no reduction with [1:1]¶

convert a matrix into an array of array¶

index from 0¶

Base¶

Relative path in include vs read¶

连等号赋值¶

ERROR: expected Type{T}¶

type, instance, and object¶

Control Flow¶

priority of &¶

ifelse vs ?¶

for in array¶

Distributed¶

@distributed¶

@sync vs @async¶

Gurobi¶

JLD vs JLD2¶

Juno¶

Shortcuts¶

Bug when Cltr + Enter¶

System Proxy¶

Function¶

function redefinition in if¶

invoke function via string¶

default argument and optional arguments¶

function in function¶

Pkg¶

PyCall¶

Update Matplotlib¶

Couldn’t find libpython error¶

Record for install PyCall¶

RCall¶

Random¶

Case 1: Two files¶

Case 2: a single file¶

A Correct Way¶

Revise¶

Is there a way to undo using in Julia?¶

Statistics (StatsBase, Distributions)¶

关于 mean()¶

Normal 中标准差为 0 的问题¶

SymPy: Symbolic Math¶

parallel¶

pbsdsh (unsolved)¶

references¶

julia local package 失败折腾记录¶

Variable Scopes¶

for loop¶

while loop¶

自定义 == and hash()¶

MethodError: objects of type Module are not callable¶

/lib/x86_64-linux-gnu/libz.so.1: versionZLIB_1.2.9’ not found`¶

work with GPU¶

load ImageView on Server¶

-i vs -L¶

Unable to display plot using the REPL. GKS errors¶

reset kw... value¶

some interesting behavior¶

pass array into function¶

check whether array entry is undef¶

Memory Allocation¶

Usage of GC.gc()¶

memory allocation of undef¶

wrong arrangement of multiple figures in a grid¶

同时安装多个 package¶

内地镜像源¶

select text in the output pdf¶

colorviews for images¶

return values of function¶

String¶

padding zero on the left¶

check if substring¶

single/double quoting¶

`.=` vs `=` when assigning a row/column vector¶

`dims=1`¶

no reduction with `[1:1]`¶

Relative path in `include` vs `read`¶

ERROR: `expected Type{T}`¶

priority of `&`¶

`ifelse` vs `?`¶

`for` in array¶

`@distributed`¶

`@sync` vs `@async`¶

Bug when `Cltr + Enter`¶

function redefinition in `if`¶

Record for install `PyCall`¶

Is there a way to undo `using` in Julia?¶

关于 `mean()`¶

`Normal` 中标准差为 0 的问题¶

`for` loop¶

`while` loop¶

自定义 `==` and `hash()`¶

`MethodError: objects of type Module are not callable`¶

`/lib/x86_64-linux-gnu/libz.so.1: version`ZLIB_1.2.9’ not found`¶

load `ImageView` on Server¶

`-i` vs `-L`¶

reset `kw...` value¶

Usage of `GC.gc()`¶

memory allocation of `undef`¶

`colorviews` for images¶