I'm lambdifying a sympy piecewise function trying to do something like this:
f = Piecewise((1,(p > -1e-10) & (p < 1e-10)), (1/p, True))
g = lambdify(p,f,"numpy")
While
>>> f.subs(p,0)
1
I get
>>> g(0)
/usr/lib/python2.7/dist-packages/numpy/__init__.py:1: RuntimeWarning: divide by zero encountered in true_divide
"""
array(1.0)
It seems, that (the lambdified ?)-Piecewise evaluates all expressions before returning the one with the true condition. Is there a way around this?
The NumPy code printer used by lambdify translates Piecewise to
numpy.select(conditions, expressions, default=numpy.nan)
This means that the array expressions is computed in its entirety before numpy.select selects one element of that array. Some ways to get around it are:
1) Change the backend to math (or mpmath, or anything other than numpy), which will cause Piecewise to be translated as a nested if statement.
g = lambdify(p, f, "math")
g(0) # 1, no warnings
2) Rewrite the formula in terms of Max/Min/Abs/sign, which can express some piecewise functions and lambdify easily. This isn't always possible but in your case,
f = 0.5 * (sign(p + 1e-10) + sign(p - 1e-10)) / Max(1e-10, Abs(p)) + 0.5 * (sign(p + 1e-10) - sign(p - 1e-10))
does the job. The trick is that 0.5 * (sign(p + 1e-10) + sign(p - 1e-10)) is sign(p) when p is not too close to 0, and is 0 when it is. Similarly, 0.5 * (sign(p + 1e-10) - sign(p - 1e-10)) is 1 if p is not too close to 0 and is 0 when it is. These factors cause the formula to switch from one mode to the other, and Max in the denominator avoids the division by zero error in any case.