sympy / numba

[Peter230655]

I play around a lot with sympy.physics.mechanics, which invariably leads to numerically solving differentual equations.

I heared, that numba can speed up the execution, and I would like to test it.

Let's say I have a function like this:

force_vector_lam = sympy.lambdify(parameters, force_vector, cse=True)

Would this be correct:

from numba import jit

@jit
def force_vector_num(parameters):
return force_vector_lam(parameters)

Thanks a lot for any advice!!

[moorepants]

You should be able to use numba on any numerical function, i.e. whatever comes out of lambdify. Here is an PR that seems to show how someone else used it: https://github.com/sympy/sympy/pull/20088/files

[Peter230655]

Thanks a lot!
I will try it as soon as I am back home from my last business trip and can use my desk top again.
I will report what I will find out.

[brocksam]

My experience with Numba and lambdify has been that the Numba compilation times increase worse-than-linearly with the number of expressions in the lambdified function. So if you're trying to JIT a lambdified expression with a large number of expressions the compilation can take a while. But it does work well and results in much faster code than the Python code generated by vanilla lambdify. Worth it if you're going to be evaluating your callable many times.

I'd also suggest using numba.njit or numba.jit(nopython=True) rather than numba.jit (numba.njit and numba.jit(nopython=True) are equivalent). This ensures that Numba uses it's "nopython" mode (and doesn't fall back to "object" mode), which produces much faster numeric code.

[Peter230655]

Thanks for the hint!
Would 'njit' also speed up scipy functions, say if I do like this:

'@njit
def loesung(func, x0, parameters);
return fsolve(func, x0, parameters)

Thanks again!

[brocksam]

No, Numba would fail in that case because SciPy's fsolve is wrapping the Fortran library MINPACK, which is already compiled and highly optimised. As a rule of thumb Numba is best left for your own pure-Python functions.

[Peter230655]

Thanks!!
You guys know so many things!
I was too old when I got into python, etc! :-(

[asmeurer]

Numba is very strict, especially when using @njit, so the best thing to do if you want to know if it can work with something is to just try it. If it works, that means it can speed it up, and if it gives an error, that means it doesn't support it yet.

[Peter230655]

Thanks!!
If F(..) is some, say, scipy function, I can simply put
ergebnis = njit(F(..))
and if it does not give an error, fine - if it gives an error, too bad?
What I mean: it will not run without error but give a wrong result?
Thanks again!

[asmeurer]

@jit
def force_vector_num(parameters):
return force_vector_lam(parameters)

By the way, you don't need the level of indirection here. Putting @njit on top of a function definition is the same as doing njit(function). So you can just do

force_vector_lam = njit(sympy.lambdify(parameters, force_vector, cse=True))

[Peter230655]

Thanks!!