Evaluate sympy expression from an array of values

Question

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 1

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

Answer 2

While the accepted answer makes it clear that the OP was looking for numerical evaluation, I'll still point out that one can also have symbolic evaluation by using symarray:

import sympy
xs = sympy.symarray('x', 10)
f = lambda x: x**2
f(xs)

yields

array([x_0**2, x_1**2, x_2**2, x_3**2, x_4**2, x_5**2, x_6**2, x_7**2,
       x_8**2, x_9**2], dtype=object)

Note that this also uses a numpy array internally, but one filled with sympy.Expressions.

Answer 3

Or you can do it via numpy.vectorize. I am using x, g, and xvals from the question body.

scalar_func = lambda xx: float(g.evalf(subs={x: xx}))
vector_func = numpy.vectorize(scalar_func)
vector_func(xvals) # returns a numpy array [10000.0, 9980.01, 9960.04, ...]

Answer 4

try

import sympy
x = sympy.symbols('x')
f = lambda x: x**2
print [f(k) for k in range(4)]

or you can also try

g = x**2
print [g.subs(x,k) for k in range(4)]