CODEWITHSUNDEEP
pythonsympy
soap
soap

Reputation: 761

Wrong result when integrating piecewise function in sympy

I am starting to use sympy. I computed a convolution, but the result was not correct:

enter image description here

enter image description here

This result is wrong: The correct result is

enter image description here

So what did I do wrong? I had used sympy to integrate piecewise fucntions before, with no problems...

The code:

from sympy import *
init_session()

f = lambda x: Piecewise( (1 , (x >= -1) & (x <= 1)) , (0 , True) )
Conv = lambda x: integrate( f(x-y)*f(y) , (y, -oo, +oo) )

Upvotes: 3

Views: 1879

Answers (1)

user6655984
user6655984

Reputation:

There is nothing that you did wrong. It's Sympy having an issue with the product of two piecewise expressions. By calling piecewise_fold(f(x-y)*f(y)) you can see that it does not manage to sort this product out, leaving it as a nested Piecewise construction. 

Piecewise((Piecewise((1, And(x - y <= 1, x - y >= -1)), (0, True)), And(y <= 1, y >= -1)), (0, True))

The symbolic integration routine trips up on this nested thing, which may be worth filing an issue on GitHub.

Workaround

If you flatten this nested Piecewise by hand, the integration works correctly.

g = Piecewise((1, And(x-y <= 1, x-y >= -1, y <= 1, y >= -1)), (0, True))
integrate(g, (y, -oo, +oo))

outputs Min(1, x + 1) - Min(1, x + 1, Max(-1, x - 1)) which is correct although perhaps not in the form one would expect.

Upvotes: 1

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