CODEWITHSUNDEEP
pythonsympy
JohnDoe122
JohnDoe122

Reputation: 688

Replacing numbers with parameters in sympy

I have some SymPy expressions of the form: 2*x1**2+7*cos(8*x2)+2*Pi (mine are longer and more complicated, but this should be enough for my question). How can I turn all the numbers appearing in this expression into parameters, something like this: a*x1**2+b*cos(c*x2)+d. Basically, I have a program which is able to give me an approximate function able to fit some data, but the parameters are integers or some well known numbers, such as pi or e (this is the first expression I provided). Then, I want to take that expression and fine tune these numbers (using gradient descent), such that to obtain the actual parameters (one can assume that the functional form is right, just the parameters need to be adjusted). For example, in the end, the right equation could be: 2.87*x1**2+6.95*cos(8.05*x2)+6.27. Is there a way to do this? Thank you!

Upvotes: 0

Views: 89

Answers (1)

smichr
smichr

Reputation: 19115

It's a little tricky because you say "all numbers" but you are ignoring exponents. In your example you are only replacing numerical factors in a term with new symbols. To do that (and to get you on your way with a possible solution) try using replace, telling it you are looking for a Mul and then telling it what you want to do with the Mul when you have it:

from sympy import *
from sympy.abc import x,y

eq=2*x**2+7*cos(8*y)+2*pi

def nfact2dum(m):
    assert m.is_Mul
    nonnum = sift(m.args, lambda i:i.is_number, binary=True)[1]
    return Mul(*([Dummy()] + nonnum))

deq = eq.replace(
    lambda x:x.is_Mul, 
    lambda x: nfact2dum(x))

print(
    deq.subs(list(zip(deq.atoms(Dummy),numbered_symbols('c')))))

output: c0*x**2 + c2*cos(c1*y) + c3

Upvotes: 1

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