I was practicing with some exercise like P3.jl. When I run following code, it hasn't any error and the answer is correct.
N = 10
A = rand(N,N)
SA = convert(SharedArray, A)
T = 100
Jacobi_parallel(SA,N,T)
But when I run with N=16386, it has an error:
This case is not supported yet
How can i resolve it?
Thank you.
In this part of the code:
#everywhere function Jacobi_blockwise_parallel_one_time_step(A,x,y,k,threshold)
if k <= threshold
Jacobi_serial_one_block_one_time_step(A,x,y,k)
else
k1 = floor(Int64, k/2)
k2 = k - k1
if (k1 != k2) error("This case is not supported yet") end
lrefs = [#spawn Jacobi_blockwise_parallel_one_time_step(A,x,y,k1,threshold),
#spawn Jacobi_blockwise_parallel_one_time_step(A,x+k1,y,k1,threshold),
#spawn Jacobi_blockwise_parallel_one_time_step(A,x,y+k1,k1,threshold),
#spawn Jacobi_blockwise_parallel_one_time_step(A,x+k1,y+k1,k1,threshold)];
pmap(fetch, lrefs)
end
end
When you call it the first time with k = N-2 (i.e. for N=2048 this triggers the error for me), k = 1023, and when you get to the 'spawn' statements, in the second call 'k' becomes 511 and k2 becomes 512, so this error is triggered.
Interestingly, the error does not appear if you run without adding extra worker processes first. Presumably the #spawn macro behaves differently / unexpectedly when there's no defined workers, I'm not sure. Either way though, I don't think the lrefs bit is doing what the author thinks it's doing (maybe it did in an older version of julia?)
Related
I'm very new to Julia but I've got a some background in Scheme/Rust/F#.
Today I wanted to make yesterday's AoC nicer without an explicit number of nested loops.
I arrived at this working solution, but I don't like the last if. In the languages mentioned above I would call a function (or use a computation expression) that gives me the first result that is not None. For Julia, I expected something to do that. It does, but unexpectedly in an eager fashion.
So When I tried return something(find(r, n, start + 1, which), find(r, n - 1, start + 1, extended)), that also evaluated the second argument when the first already had a result—and thus crashed.
Is there a macro/lazy version or something that I didn't find? How are you supposed to handle a case like that?
I also thought about (short-circuited) or'ing them together, but I guess Julia's strictness in that matter spoils that.
using DataStructures
function find(r::Array{Int}, n, start = 1, which = nil())::Union{Int,Nothing}
if start <= length(r)
extended = cons(start, which)
with_current = sum(i -> r[i], extended)
if with_current == 2020 && n == 1
return prod(i -> r[i], extended)
else
# Unfortunately no :(
#return something(find(r, n, start + 1, which), find(r, n - 1, start + 1, extended))
re = find(r, n, start + 1, which)
if isnothing(re)
return find(r, n - 1, start + 1, extended)
else
re
end
end
end
end
Let me comment more on it why it is not possible given the discussion in the comments.
In Julia function arguments are evaluated eagerly, so Julia evaluates both find(r, n, start + 1, which) and find(r, n - 1, start + 1, extended) before passing them to something function.
Now, with macros you have (I am not writing in a fully general case for simplicity and I hope I got the hygiene right :)):
julia> macro something(x, y)
quote
local vx = $(esc(x))
isnothing(vx) ? $(esc(y)) : vx
end
end
#something (macro with 1 method)
julia> #something 1 2
1
julia> #something nothing 2
2
julia> #something 1 sqrt(-1)
1
julia> #something nothing sqrt(-1)
ERROR: DomainError with -1.0:
sqrt will only return a complex result if called with a complex argument. Try sqrt(Complex(x)).
(in a full-blown version of the macro varargs and Some should be handled to replicate something exactly)
Piqued by Bogumił's answer I wanted to write my first Julia macro. It took some time and numerous attempts to figure out syntax, hygiene and escaping but I'm quite happy now.
I thought it might be worth sharing and provide opportunity for suggestions/improvements.
A lazy #something analog to Base.something
function _something_impl(thing)
:(something($(esc(thing))))
end
function _something_impl(thing, rest...)
quote
local evalued = $(esc(thing))
if isnothing(evalued)
$(_something_impl(rest...))
else
something(evalued)
end
end
end
macro something(things...)
_something_impl(things...)
end
Version without exceptions
As I found exceptions raised from a macro like this not quite suitable, I also made a version that falls back to nothing.
function _something_nothing_impl(thing)
quote
local evaluated = $(esc(thing))
if isa(evaluated, Some)
evaluated.value
else
evaluated
end
end
end
function _something_nothing_impl(thing, rest...)
quote
local evalued = $(esc(thing))
if isnothing(evalued)
$(_something_nothing_impl(rest...))
else
something(evalued)
end
end
end
macro something_nothing(things...)
_something_nothing_impl(things...)
end
Now I guess the recursive middle function could also generated by a macro. :)
I have a function that optionally uses threads for its main loop, doing so when an argument usingthreads is true. At the moment, the code looks like this:
function dosomething(usingthreads::Bool)
n = 1000
if usingthreads
Threads.#threads for i = 1:n
#20 lines of code here
end
else
for i = 1:n
#same 20 lines of code repeated here
end
end
end
Less nasty than the above would be to put the "20 lines" in a separate function. Is there another way?
You could use a macro that changes its behavior depending on the result of Threads.nthreads():
macro maybe_threaded(ex)
if Threads.nthreads() == 1
return esc(ex)
else
return esc(:(Threads.#threads $ex))
end
end
Without threading, this macro will be a no-op:
julia> #macroexpand #maybe_threaded for i in 1:5
print(i)
end
:(for i = 1:5
#= REPL[2]:2 =#
print(i)
end)
But when threading is enabled and e.g. JULIA_NUM_THREADS=4 it will expand to the threaded version:
julia> #maybe_threaded for i in 1:5
print(i)
end
41325
Edit: Upon rereading the question, I realize this doesn't really answer it but it might be useful anyway.
You can use ThreadsX as suggested in this discourse link.
The answer from the thread (all credit to oxinabox):
using ThreadsX
function foo(multi_thread=true)
_foreach = multi_thread ? ThreadsX.foreach : Base.foreach
_foreach(1:10) do ii
#show ii
end
end
Like in R:
a <- 2
or even better
a ← 2
which should translate to
a = 2
and if possible respect method overloading.
= is overloaded (not in the multiple dispatch sense) a lot in Julia.
It binds a new variable. As in a = 3. You won't be able to use ← instead of = in this context, because you can't overload binding in Julia.
It gets lowered to setindex!. As in, a[i] = b gets lowered to setindex!(a, b, i). Unfortunately, setindex! takes 3 variables while ← can only take 2 variables. So you can't overload = with 3 variables.
But, you can use only 2 variables and overload a[:] = b, for example. So, you can define ←(a,b) = (a[:] = b) or ←(a,b) = setindex!(a,b,:).
a .= b gets lowered to (Base.broadcast!)(Base.identity, a, b). You can overload this by defining ←(a,b) = (a .= b) or ←(a,b) = (Base.broadcast!)(Base.identity, a, b).
So, there are two potentially nice ways of using ←. Good luck ;)
Btw, if you really want to use ← to do binding (like in 1.), the only way to do it is using macros. But then, you will have to write a macro in front of every single assignment, which doesn't look very good.
Also, if you want to explore how operators get lowered in Julia, do f(a,b) = (a .= b), for example, and then #code_lowered f(x,y).
No. = is not an operator in Julia, and cannot be assigned to another symbol.
Disclaimer: You are fully responsible if you will try my (still beginner's) experiments bellow! :P
MacroHelper is module ( big thanks to #Alexander_Morley and #DanGetz for help ) I plan to play with in future and we could probably try it here :
julia> module MacroHelper
# modified from the julia source ./test/parse.jl
function parseall(str)
pos = start(str)
exs = []
while !done(str, pos)
ex, pos = parse(str, pos) # returns next starting point as well as expr
ex.head == :toplevel ? append!(exs, ex.args) : push!(exs, ex)
end
if length(exs) == 0
throw(ParseError("end of input"))
elseif length(exs) == 1
return exs[1]
else
return Expr(:block, exs...) # convert the array of expressions
# back to a single expression
end
end
end;
With module above you could define simple test "language":
julia> module TstLang
export #tst_cmd
import MacroHelper
macro tst_cmd(a)
b = replace("$a", "←", "=") # just simply replacing ←
# in real life you would probably like
# to escape comments, strings etc
return MacroHelper.parseall(b)
end
end;
And by using it you could probably get what you want:
julia> using TstLang
julia> tst```
a ← 3
println(a)
a +← a + 3 # maybe not wanted? :P
```
3
9
What about performance?
julia> function test1()
a = 3
a += a + 3
end;
julia> function test2()
tst```
a ← 3
a +← a + 3
```
end;
julia> test1(); #time test1();
0.000002 seconds (4 allocations: 160 bytes)
julia> test2(); #time test2();
0.000002 seconds (4 allocations: 160 bytes)
If you like to see syntax highlight (for example in atom editor) then you need to use it differently:
function test3()
#tst_cmd begin
a ← 3
a ← a + a + 3 # parser don't allow you to use "+←" here!
end
end;
We could hope that future Julia IDEs could syntax highlight cmd macros too. :)
What could be problem with "solution" above? I am not so experienced julian so many things. :P (in this moment something about "macro hygiene" and "global scope" comes to mind...)
But what you want is IMHO good for some domain specific languages and not to redefine basic of language! It is because readability very counts and if everybody will redefine everything then it will end in Tower of Babel...
What happens for a global variable when running in the parallel mode?
I have a global variable, "to_be_optimized_parameterIndexSet", which is a vector of indexes that should be optimized using gamultiobj and I have set its value only in the main script(nowhere else).
My code works properly in serial mode but when I switch to parallel mode (using "matlabpool open" and setting proper values for 'gaoptimset' ) the mentioned global variable becomes empty (=[]) in the fitness function and causes this error:
??? Error using ==> parallel_function at 598
Error in ==> PF_gaMultiFitness at 15 [THIS LINE: constants(to_be_optimized_parameterIndexSet) = individual;]
In an assignment A(I) = B, the number of elements in B and
I must be the same.
Error in ==> fcnvectorizer at 17
parfor (i = 1:popSize)
Error in ==> gamultiobjMakeState at 52
Score =
fcnvectorizer(state.Population(initScoreProvided+1:end,:),FitnessFcn,numObj,options.SerialUserFcn);
Error in ==> gamultiobjsolve at 11
state = gamultiobjMakeState(GenomeLength,FitnessFcn,output.problemtype,options);
E rror in ==> gamultiobj at 238
[x,fval,exitFlag,output,population,scores] = gamultiobjsolve(FitnessFcn,nvars, ...
Error in ==> PF_GA_mainScript at 136
[x, fval, exitflag, output] = gamultiobj(#(individual)PF_gaMultiFitness(individual, initialConstants), ...
Caused by:
Failure in user-supplied fitness function evaluation. GA cannot continue.
I have checked all the code to make sure I've not changed this global variable everywhere else.
I have a quad-core processor.
Where is the bug? any suggestion?
EDIT 1: The MATLAB code in the main script:
clc
clear
close all
format short g
global simulation_duration % PF_gaMultiFitness will use this variable
global to_be_optimized_parameterIndexSet % PF_gaMultiFitness will use this variable
global IC stimulusMoment % PF_gaMultiFitness will use these variables
[initialConstants IC] = oldCICR_Constants; %initialize state
to_be_optimized_parameterIndexSet = [21 22 23 24 25 26 27 28 17 20];
LB = [ 0.97667 0.38185 0.63529 0.046564 0.23207 0.87484 0.46014 0.0030636 0.46494 0.82407 ];
UB = [1.8486 0.68292 0.87129 0.87814 0.66982 1.3819 0.64562 0.15456 1.3717 1.8168];
PopulationSize = input('Population size? ') ;
GaTimeLimit = input('GA time limit? (second) ');
matlabpool open
nGenerations = inf;
options = gaoptimset('PopulationSize', PopulationSize, 'TimeLimit',GaTimeLimit, 'Generations', nGenerations, ...
'Vectorized','off', 'UseParallel','always');
[x, fval, exitflag, output] = gamultiobj(#(individual)PF_gaMultiFitness(individual, initialConstants), ...
length(to_be_optimized_parameterIndexSet),[],[],[],[],LB,UB,options);
matlabpool close
some other piece of code to show the results...
The MATLAB code of the fitness function, "PF_gaMultiFitness":
function objectives =PF_gaMultiFitness(individual, constants)
global simulation_duration IC stimulusMoment to_be_optimized_parameterIndexSet
%THIS FUNCTION RETURNS MULTI OBJECTIVES AND PUTS EACH OBJECTIVE IN A COLUMN
constants(to_be_optimized_parameterIndexSet) = individual;
[smcState , ~, Time]= oldCICR_CompCore(constants, IC, simulation_duration,2);
targetValue = 1; % [uM]desired [Ca]i peak concentration
afterStimulus = smcState(Time>stimulusMoment,14); % values of [Ca]i after stimulus
peak_Ca_value = max(afterStimulus); % smcState(:,14) is [Ca]i
if peak_Ca_value < 0.8 * targetValue
objectives(1,1) = inf;
else
objectives(1, 1) = abs(peak_Ca_value - targetValue);
end
pkIDX = peakFinder(afterStimulus);
nPeaks = sum(pkIDX);
if nPeaks > 1
peakIndexes = find(pkIDX);
period = Time(peakIndexes(2)) - Time(peakIndexes(1));
objectives(1,2) = 1e5* 1/period;
elseif nPeaks == 1 && peak_Ca_value > 0.8 * targetValue
objectives(1,2) = 0;
else
objectives(1,2) = inf;
end
end
Global variables do not get passed from the MATLAB client to the workers executing the body of the PARFOR loop. The only data that does get sent into the loop body are variables that occur in the text of the program. This blog entry might help.
it really depends on the type of variable you're putting in. i need to see more of your code to point out the flaw, but in general it is good practice to avoid assuming complicated variables will be passed to each worker. In other words anything more then a primitive may need to be reinitialized inside a parallel routine or may need have specific function calls (like using feval for function handles).
My advice: RTM
Ok, first up, this is NOT for a class, test, or other student type activity.
I'm a scripter for a game, and am trying to implement the math library for all to use, and unfortunately, all I have available to me is very basic lua. The implemented version cannot be changed, and does not include any libraries. For those wondering, its for scripting in Fold.It.
Here's what I have...
math={}
math.fact = function(b) if(b==1)or(b==0) then return 1 end e=1 for c=b,1,-1 do e=e*c end return e end
math.pow = function(b,p) e=b if(p==0) then return 1 end if(p<0) then p=p*(-1) end for c=p,2,-1 do e=e*b end return e end
math.cos = function(b,p) e=0 p=p or 10 for i=1,p do e=e+(math.pow(-1,i)*math.pow(b,2*i)/math.fact(2*i)) end return e end
To clarify above, math.fact returns factorial, which is returning accurate to about 10 points of precision, and is a new function I've done to aid in cosine calculation.
The math.pow is also a new function to handle returning powers, also working as expected.
The issue is with the cosine function. Its returning unexpected values. Here's an easier to digest version (I've been writing my library stuff ultra lean)...
function math.cos(value,precision)
result=0
precision=precision or 10
for i=1,precision do
result=result+(math.pow(-1,i)*math.pow(value,2*i)/math.fact(2*i))
end
return e
end
The problem is, with those functions, for print(math.cos(90)) it returns 4.77135... when I'm expecting -0.44807... (based on calc in scientific mode, or using an online tool to cos(90)).
I'm also having issues with sin and tan, however they are similarly written to cos, which seems to have been done in many languages. If I can figure out what I'm doing wrong, I can get them all fixed.
EDIT: Corrected typo
First, your lua doesn't run. Second, you need to make your variables local. Third, cosine starts with a one.
The problem is because the Taylor series you are using only converges on the correct values of cosine close to zero. You would have to use a far more terms of the series to get it to handle 90 correctly. You can fix this for your implementation two ways:
Add a pi constant. Then use a while loop to adjust the value such that abs(value) < 2*pi:
math.pi = 3.14159265358
while value > math.pi*2 do
value = value - math.pi * 2
end
while value < -math.pi*2 do
value = value + math.pi * 2
end
Or - find or implement a version of fmod in lua.
Here is the corrected code (you can minify it):
math={}
math.fact = function(b)
if(b==1)or(b==0) then
return 1
end
local e=1
for c=b,1,-1 do
e=e*c
end
return e
end
math.pow = function(b,p)
local e=b
if(p==0) then
return 1
end
if(p<0) then
p=p*(-1)
end
for c=p,2,-1 do
e=e*b
end
return e
end
math.cos = function(b,p)
local e=1
b = math.correctRadians(b)
p=p or 10
for i=1,p do
e=e+(math.pow(-1,i)*math.pow(b,2*i)/math.fact(2*i))
end
return e
end
math.pi = 3.1415926545358
math.correctRadians = function( value )
while value > math.pi*2 do
value = value - math.pi * 2
end
while value < -math.pi*2 do
value = value + math.pi * 2
end
return value
end
interactive lua run:
imac:~ root$ lua -i temp.lua
Lua 5.1.4 Copyright (C) 1994-2008 Lua.org, PUC-Rio
> print( math.cos( 90 ) )
-0.44807359244883
>