Evaluate sympy expression from an array of values
I'm experimenting with sympy and I've hit upon an issue I can't work out.
Using scipy I can write an expression and evaluate it for an array of x values as follows:
import scipy
xvals = scipy.arange(-100,100,0.1)
f = lambda x: x**2
f(xvals)
Using sympy I can write the same expression as follows:
import sympy
x = sympy.symbols('x')
g = x**2
I can evaluate this expression for a single value by doing the following:
g.evalf(subs={x:10})
However I can't work out how to evaluate it for an array of x values, like I did with scipy. How would I do this?
Answer
First of all, at the moment SymPy does not guarantee support for numpy arrays which is what you want in this case. Check this bug report http://code.google.com/p/sympy/issues/detail?id=537
Second, If you want to evaluate something numerically for many values SymPy is not the best choice (it is a symbolic library after all). Use numpy and scipy.
However, a valid reason to evaluate something numerically will be that deriving the expression to be evaluated was hard so you derive it in SymPy and then evaluate it in NumPy/SciPy/C/Fortran. To translate an expression to numpy just use
from sympy.utilities.lambdify import lambdify
func = lambdify(x, big_expression_containing_x,'numpy') # returns a numpy-ready function
numpy_array_of_results = func(numpy_array_of_arguments)
Check the docstring of lambdify for more details. Be aware that lambdify still has some issues and may need a rewrite.
And just as a side note, if you want to evaluate the expressions really many times, you can use the codegen/autowrap module from sympy in order to create fortran or C code that is wrapped and callable from python.
EDIT: An updates list of ways to do numerics in SymPy can be found on the wiki https://github.com/sympy/sympy/wiki/Philosophy-of-Numerics-and-Code-Generation-in-SymPy