Heyoka time value as float

[naoya-kumagai]

I am trying to create an event detection using heyoka, following the Event Detection Overview in the tutorial.
Below, the function f is a self defined function that evaluates when the object that is the target of integration (coordinate expressed by x) and another object approached each other close enough to be below a threshold.

    ev = hy.nt_event(
            # The left-hand side of the event equation
            f(x, hk.time),
            # The callback.
            callback = cb)

However, this results in errors such as
TypeError: float() argument must be a string or a number, not 'heyoka.core.expression'
How can I explicitly get the value of hk.time as a float value, so as not to have such errors?

[bluescarni]

Hi,

could you please post here the full error message with traceback? Is the error happening when creating the event or when running the integration?

In general, it should not be needed to pass the time variable as an argument to f(), as you can directly use hk.time inside the implementation of f() if your event equation is time-dependent.

(I am on vacation until the end of the week, so apologies if my replies are a bit delayed)

[naoya-kumagai]

Essentially, this is what happens (There isn't much meaning in the definition of f, this is just an example). I am using a library that internally converts the given type to float and causes the error.

    TypeError                                 Traceback (most recent call last)
    <ipython-input-15-648e45bc850a> in <module>
         24 ev = hy.nt_event(
         25         # The left-hand side of the event equation
    ---> 26         f(x, hy.time),
         27         # The callback.
         28         callback = cb)
    
    <ipython-input-15-648e45bc850a> in f(x, hy_time)
          2 
          3 def f(x, hy_time):
    ----> 4     if float(hy_time) < 10:
          5         return x
          6     return x*2
    
    TypeError: float() argument must be a string or a number, not 'heyoka.core.expression'

[bluescarni]

@naoya-kumagai the event equation must be a mathematical expression which can contain the state variables and the time variable. In other words, an event equation must be formulated in the same way the equations of motion are, i.e., by constructing a mathematical expression via the built-in functions and operators supported by heyoka.

Note that the heyoka expression system currently does not provide an if ... then construct, so the type of logic that you are showing in the example function f() above cannot be implemented directly. There are ways to emulate an if ... then branch in the expression system, if you need that sort of functionality I can try to help you implement it if you can provide more details on what you are trying to do.

[naoya-kumagai]

@bluescarni
I have a function f that given time t, returns the keplerian elements of the object at t.
I then need to convert that into r,v vectors using pykep's par2ic. (This is where the float error occurs)
I then use the r vector to detect a close encounter with the object that I am integrating for. Defining this close encounter will also require an if statement, as I will need to detect "if" the two objects' distance from each other is less than a threshold.

[bluescarni]

@naoya-kumagai

I have a function f that given time t, returns the keplerian elements of the object at t.

If you want to use such a function, it must be implemented using the mathematical primitives of the heyoka expression system, and it must be a continuous, differentiable function of t. Otherwise, you won't be able to use it in the definition of an event.

I then need to convert that into r,v vectors using pykep's par2ic. (This is where the float error occurs)

You cannot use pykep's par2ic function in the definition of an event equation, because par2ic is not implemented using the heyoka primitives.

I then use the r vector to detect a close encounter with the object that I am integrating for. Defining this close encounter will also require an if statement, as I will need to detect "if" the two objects' distance from each other is less than a threshold.

I think I understand what you are trying to do now, but that is not the way of doing it in heyoka.

If you want to detect when two bodies are at a distance R, the corresponding mathematical condition would be something like (assuming 2D to simplify):

(x1 - x2)**2 + (y1 - y2)**2 == R**2

For writing such an event equation in heyoka, you need to move everything to the left-hand side, so that the expression to use when creating the event becomes:

(x1 - x2)**2 + (y1 - y2)**2 - R**2

As I understand, in your case one body is part of the dynamical system and thus you can use its cartesian state variables directly in the event expression. For the other body, the position is an explicit function of time which must be converted from orbital elements to cartesian coordinates (as far as I have understood). You will have to implement such conversion using heyoka's mathematical functions, you cannot rely on an external function such as par2ic for this purpose.

It is possible to implement the orbital elements -> cartesian coordinates conversion within the heyoka expression system, and indeed I have been working on this recently. However I believe that to implement this conversion you will need the atan2() function which is only available in the development version of heyoka currently.

Please let me know if I have understood the issue correctly...

[naoya-kumagai]

@bluescarni
Thank you very much for the explanation. You understood everything correctly!

Since I do not have time to implement all these functions to use the heyoka expression system, the best way to go seems to generate a fine grid and evaluating the event a posteriori from the integration result.