But I gave an example where the output type can change depending on the
chosen timespan (eltype(y0)==Rational{Int}), so "eltype(f(y0))" can really
only be what the time integration algorithm actually produces, which means
you have to just run it and see what happens. It becomes a type-stability
issue because the internals of the functions are using similar(y0) to make
all the arrays (well, with some promotions before doing so), and so each
time you go through the loop you're banking on getting the same type. The
other way to handle this would be to make the arrays something like a Float
which just always kind of work, so this "bug" was likely introduced when
the integrator were upgraded to allow for output to be any type (That's
what introduced this issue in DifferentialEquations.jl, so I assume that's
what happened in ODE.jl as well).
The examples you gave are cases where the output is set (Int/Int returns on
Float no matter what), or where the type promotion isn't too difficult
(quadgtk is a linear combination of values from a to b, so just check the
element type of the intermediate values that you're using and promote
everything to that). But if you don't want to do the first, and you're
dealing with a case where type inference is essentially undecidable, you
will have this issue.
That said, using the heuristic of "eltype(f(y0))" will do better than it
currently does (it would catch the case where all inputs are an Int but one
application makes things floats, which is probably the most common problem).
On Monday, June 20, 2016 at 3:13:44 AM UTC+1, Gabriel Gellner wrote:
>
> I will admit my understanding of type stability in a jit compiler is
> shakey, but I don't see 0.5//2 as a type instability, rather it is a method
> error (the issues is a float does not convert to an int, but having a int
> become a float is a fair promotion, so I can't see why requiring y0 to be a
> float is at all similar -- it is very Julian to promote it). I understand
> type instability to mean that the output of function is not uniquely
> determined by its inputs. In this sense there is no type instability. The
> issue as I understand it is that we do eltype(y0) for the output type, when
> maybe it makes more sense to do eltype(f(y0)) which would then be type
> stable, since f is. This would even work if you did y0 = 3f0, etc.
>
> Again I could be missing something simple, but requiring the inputs
> to agree with the output of the input function feels like something far
> beyond any kind of Julia difference from other languages, and more a
> feature of it being a dynamic language and not purely static. Suggesting
> users, especially new users, to be worry about these situations doesn't
> jive with my understanding of Julia. It feels like premature optimization
> to me.
>
>
> On Sunday, June 19, 2016 at 6:38:37 PM UTC-7, Chris Rackauckas wrote:
>
>> I mean, it's the same type instability that you get if you try things
>> like .5//2. Many Julia function work with ints that give a float, but not
>> all do. If any function doesn't work (like convert will always fail if you
>> somehow got a float but initialized an array to be similar(arrInt)), then
>> you get this error.
>>
>> This can be probably be masked a little by pre-processing. I know that
>> ODE.jl makes the types compatible to start, but that doesn't mean they will
>> be after one step. For example, run an Euler step with try-catch and then
>> have it up the types to whatever is compatible, then solve the ODE. And
>> this has almost no performance penalty in most cases (and would be easy to
>> switch off). But I don't know if this goes into a low level "this uses this
>> method to solve the ODE" that ODE.jl implements. But even if you do this,
>> you won't catch all of the type errors. For example, if you want to use
>> Rational{Int}, it can take quite a few steps to overflow the numerator or
>> denominator, but once it does, you get an InexactError (and the solution is
>> to use Rational{BigInt}).
>>
>> You can use some try-catch phrases in the main solver, or put the solver
>> in a try-catch and have it fix types and re-run, but these are all things
>> that would be non-intuitive behavior and would have to be off by default.
>> But at that point, the user would probably know to just fix the type
>> problem.
>>
>> So honestly I don't think that there's a good way to make this "silent".
>> But this is the fundamental trade off in Julia that makes it fast, and it's
>> not something that is just encountered here, so users will need to learn
>> about it pretty quick or else they will see lots of other
>> functions/packages break.
>>
>> On Monday, June 20, 2016 at 2:07:30 AM UTC+1, Gabriel Gellner wrote:
>>>
>>> Is this truly a type instability?
>>>
>>> The function f has no type stability issues from my understanding of the
>>> concept. No matter the input types you always get a Float output so there
>>> is no type instability. Many of Julia's functions work this way, including
>>> division 1/2 -> float even though the inputs are ints.
>>>
>>> The real issue is that ode23 infers the type of the output from y0 which
>>> in this case is an int, but I don't see how this is the correct inference.
>>> Maybe it is desired, but I hardly see this as normal Julia behavior. I can
>>> happily mix input types to arguments in many Julia constructs, without
>>> forcing me to have to use the same input vs output type. matrix mult, sin,
>>> sqrt, etc etc. Isn't this exactly what convert functions are for?
>>>
>>> hell the developer docs say that literals in expressions should be ints
>>> so that conversions can be better. that is they say I should right 2*x not
>>> 2.0*x so that type promotions can work correctly. The issue in this case is
>>> that an implementation detail is being exposed to the user, that eltype(y0)
>>> is determining the output of the function. I don't see that this is
>>> standard Julian practice, though it might be desired in this case. For
>>> example I can use quadgk(f, 1, 2) and not have an error because of the
>>> integer a, b. And that is a very similar style function Base method.
>>>
>>> Maybe I am missing something simple, but I worry being to harsh about
>>> types when it feels unessary.
>>>
>>>
>>> On Sunday, June 19, 2016 at 5:28:39 PM UTC-7, Chris Rackauckas wrote:
>>>
>>>> I wouldn't call this a bug, it's a standard Julia thing for a reason.
>>>> You get an InexactError() because you start with an Int and you do an
>>>> operation which turns the Int into a Float so the program gets mad at the
>>>> type instability. You can just change everything to floats, but then
>>>> you're
>>>> getting rid of the user choice. For example, if you change everything to
>>>> floats, you can't solve it all using rationals of BigInts or whatever
>>>> crazy
>>>> numbers the user wants. However, if you let the number operations do as
>>>> they normally do, the user can get an answer in the same way that they
>>>> provide it. And it's not like this is a weird thing inside some
>>>> mathematical packages, this is normal Julia behavior.
>>>>
>>>> But this kind of thing will cause issues for first-timers in Julia. It
>>>> should be front and center in the Noteworthy Differences from Other
>>>> Languages that if you really want a float, start with a float.
>>>>
>>>> On Sunday, June 19, 2016 at 10:06:42 PM UTC+1, Gabriel Gellner wrote:
>>>>>
>>>>> You are passing in the initial condition `start` as an integer, but
>>>>> ode23 needs this to be a float. Change it to `const start = 3.0` and you
>>>>> are golden. This does feel like a bug you should file an issue at the
>>>>> github page.
>>>>>
>>>>> On Sunday, June 19, 2016 at 11:49:55 AM UTC-7, Joungmin Lee wrote:
>>>>>>
>>>>>> Hi,
>>>>>>
>>>>>> I am making simple examples of the ODE package in Julia, but I cannot
>>>>>> make a code without error for 1st order ODE.
>>>>>>
>>>>>> Here is my code:
>>>>>>
>>>>>> using ODE;
>>>>>>>
>>>>>>> function f(t, y)
>>>>>>> x = y
>>>>>>>
>>>>>>> dx_dt = (2-x)/5
>>>>>>>
>>>>>>> dx_dt
>>>>>>> end
>>>>>>>
>>>>>>> const start = 3;
>>>>>>> time = 0:0.1:30;
>>>>>>>
>>>>>>> t, y = ode23(f, start, time);
>>>>>>>
>>>>>>
>>>>>> It finally gives:
>>>>>> LoadError: InexactError()
>>>>>> while loading In[14], in expression starting on line 1
>>>>>>
>>>>>> in copy! at abstractarray.jl:310
>>>>>> in setindex! at array.jl:313
>>>>>> in oderk_adapt at C:\Users\user\.julia\v0.4\ODE\src\runge_kutta.jl:279
>>>>>> in oderk_adapt at C:\Users\user\.julia\v0.4\ODE\src\runge_kutta.jl:220
>>>>>> in ode23 at C:\Users\user\.julia\v0.4\ODE\src\runge_kutta.jl:210
>>>>>>
>>>>>> The example of 2nd order ODE at the GitHub works fine.
>>>>>>
>>>>>> How should I edit the code?
>>>>>>
>>>>>
