Integer constants + how to use atan2

[benlabbeus]

Hi all!

1. Is there a way to constrain the constant to only use specific integers? In my case, 1 and 2.

2. Is there also a way to use a atan2 function? It seems that Julia doesn't have this.

Much appreciated!

[MilesCranmer]

1. Yes, the trick for this is to avoid constants altogether, and give 1 and 2 as features. For example:

data_cols = 5
integer_cols = 2
X = np.random.randn(100, data_cols + integer_cols)  # Normal data is first 5 columns
X[:, data_cols+0] = 1
X[:, data_cols+1] = 2

We have generated some random data and then set the last two columns equal to the constants we wish for PySR to use.

Then, we need to disable PySR from finding its own constants, by making them prohibitively expensive (and also disabling the constant optimization routine to speed things up):

settings_to_disable_constants = dict(
    complexity_of_constants=100,  # Make constants too expensive to use
    should_optimize_constants=False,  # =speed up
    weight_mutate_constant=0.0  # =speed up
)

model = PySRRegressor(**your_settings, **settings_to_disable_constants)
model.fit(X, y, variable_names=["x1", "x2", "x3", "x4", "x5", "_1", "_2"])

The equation will show _1 and _2 as features, but they are integers. This is just to prevent SymPy from eagerly simplifying things.

Julia's atan can be used as a binary operator, in which case it is the same as typical atan2. i.e., atan(x) is normal atan, and atan(x, y) is atan2.

Hope this helps!
Miles

[benlabbeus]

Amazing! Thanks for the prompt reply Miles!

Just wanted to say this is an amazing tech you've built!

[MilesCranmer]

Thanks! 🙂

[benlabbeus]

Again, really appreciate your help!

I can't seem to get atan2 working, I have the following:

`
binary_operators=["*", "+", "-", "/", "^", "greater", "atan2"],

extra_sympy_mappings={"atan2": lambda x, y: sympy.atan(x,y)},
`

and am getting the error:

julia.core.JuliaError: Exception 'UndefVarError: atan2not defined' occurred while calling julia code: [*, +, -, /, ^, greater, atan2]

[benlabbeus]

Nvm! Got it working:

binary_operators=["*", "+", "-", "/", "^", "greater", "atan2(x, y) = atan(x, y)"],