Unexpected error on 1st order ODE using ODE package

[Joungmin Lee]

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?

[Gabriel Gellner]

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.

[Chris Rackauckas]

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.

[Gabriel Gellner]

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.

[Chris Rackauckas]

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.

[Gabriel Gellner]

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.

[Chris Rackauckas]

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).

[Gabriel Gellner]

Fair enough. I guess if the urge is to support strangely generic code then the inputs should never be expected to be promoted. But I just don't see what you are describing as being a "standard" in Julia. ODE.jl and your project maybe try to attain this level of genericity, but most of Base seems to do this kind of promotion, and doesn't always return the types, or give an inexact error, when you provide certain inputs (like returning Rational if you input Rational). Optim.jl, Roots.jl, Disributions.jl doesn't do this, quadgk doesn't give back rationals, etc. The standard libraries I use the most often I guess.

A user that is told that type in type out is the standard in Julia, and that strange error messages like the OP had are not bugs, would have great reason to be skeptical that this is actually a contract that is commonly followed. Maybe this is the way Julia is going. I hope that doing the common case will never get too annoying (like throwing a type error so I can have the unlikely case that I an use Rational inputs for an ode solver ;), and that all my code would be expected to be filled with eltypes and inexact errors. We shall see.

[Joungmin Lee]

Thank you all for the discussion!

I have recently moved from Python to Julia, so I didn't know that. :)

Joungmin

2016년 6월 20일 월요일 오전 3시 49분 55초 UTC+9, Joungmin Lee 님의 말:

[Mauro]

I'd say this is a bug. `sin(5)` works, so `ode23(f, 0, [0,1])` should
work too by promoting `y0=0` and `tspan=[0,1]` to appropriate types.
Note that `eltype(tspan)` needs to be promoted to some kind of floating
point number; I don't think rationals make sense for
differential-equations. I pushed a fix, at least for the Runge-Kutta
solvers of ODE.jl: https://github.com/JuliaLang/ODE.jl/pull/96

[Chris Rackauckas]

I agree rationals don't make sense in most cases (I did it once just for fun), but how would it work with other defined numbers as they come? Will the promotions "just work?"

But as mentioned, applying f once and using the types from there would catch most cases. 

[Mauro]

On Mon, 2016-06-20 at 10:32, Chris Rackauckas <rack...@gmail.com> wrote:
> I agree rationals don't make sense in most cases (I did it once just for
> fun), but how would it work with other defined numbers as they come? Will
> the promotions "just work?"

No. It is the duty of the type-creator to embed their new type into the
promotion system of Julia.

> But as mentioned, applying f once and using the types from there would
> catch most cases.

Yes, that is the general strategy but I find it quite hard to do it
correctly (otherwise, I'd have caught this before...)

> On Monday, June 20, 2016 at 9:00:28 AM UTC+1, Mauro wrote:
>>
>> I'd say this is a bug. `sin(5)` works, so `ode23(f, 0, [0,1])` should
>> work too by promoting `y0=0` and `tspan=[0,1]` to appropriate types.
>> Note that `eltype(tspan)` needs to be promoted to some kind of floating
>> point number; I don't think rationals make sense for
>> differential-equations. I pushed a fix, at least for the Runge-Kutta
>> solvers of ODE.jl: https://github.com/JuliaLang/ODE.jl/pull/96
>>
>> On Mon, 2016-06-20 at 07:09, Gabriel Gellner <gabriel...@gmail.com