Lambdify'ed expression raises TypeError when u

Question

I'm using sympy to create an expression that is then displayed as latex with sympy.init_printing(). The expression is used in calculations after being lambdified to a function named f.

However, when using an array or a Series object as an argument to f I get a TypeError, if the lambdified expression contains a sympy object (e.g. sympy.sqrt()). If I had used **.5 instead of the sqrt I would get no error (but it wouldn't display the root in IPython).

Question:
How can I use arrays or Series on a function I created through sympy.lambdify()?

---

The following code is a (simplified) demo of the problem:

import sympy
import numpy
sympy.init_printing()

x = sympy.symbols('x')

_f = lambda x: sympy.sqrt(x)
f = sympy.lambdify(x, _f(x), (sympy, numpy))

f(x)

This results in a pretty root:

Then, trying to use

import pandas
df = pandas.DataFrame([1,2,3], columns=['a'])

f(df['a'])

I get:

TypeError                                 Traceback (most recent call last)
/home/gold/venvs/venv_python3.5/lib/python3.5/site-packages/sympy/core/cache.py in wrapper(*args, **kwargs)
     92                 try:
---> 93                     retval = cfunc(*args, **kwargs)
     94                 except TypeError:

/home/gold/venvs/venv_python3.5/lib/python3.5/site-packages/pandas/core/generic.py in __hash__(self)
    830         raise TypeError('{0!r} objects are mutable, thus they cannot be'
--> 831                         ' hashed'.format(self.__class__.__name__))
    832 

TypeError: 'Series' objects are mutable, thus they cannot be hashed

During handling of the above exception, another exception occurred:

SympifyError                              Traceback (most recent call last)
<ipython-input-25-d0ba59fbbc02> in <module>()
      2 df = pandas.DataFrame([1,2,3], columns=['a'])
      3 
----> 4 f(df['a'])

/home/gold/venvs/venv_python3.5/lib/python3.5/site-packages/sympy/__init__.py in <lambda>(_Dummy_21)

/home/gold/venvs/venv_python3.5/lib/python3.5/site-packages/sympy/functions/elementary/miscellaneous.py in sqrt(arg)
    113     """
    114     # arg = sympify(arg) is handled by Pow
--> 115     return Pow(arg, S.Half)
    116 
    117 

/home/gold/venvs/venv_python3.5/lib/python3.5/site-packages/sympy/core/cache.py in wrapper(*args, **kwargs)
     93                     retval = cfunc(*args, **kwargs)
     94                 except TypeError:
---> 95                     retval = func(*args, **kwargs)
     96                 return retval
     97 

/home/gold/venvs/venv_python3.5/lib/python3.5/site-packages/sympy/core/power.py in __new__(cls, b, e, evaluate)
    168         from sympy.functions.elementary.exponential import exp_polar
    169 
--> 170         b = _sympify(b)
    171         e = _sympify(e)
    172         if evaluate:

/home/gold/venvs/venv_python3.5/lib/python3.5/site-packages/sympy/core/sympify.py in _sympify(a)
    353 
    354     """
--> 355     return sympify(a, strict=True)
    356 
    357 

/home/gold/venvs/venv_python3.5/lib/python3.5/site-packages/sympy/core/sympify.py in sympify(a, locals, convert_xor, strict, rational, evaluate)
    275 
    276     if strict:
--> 277         raise SympifyError(a)
    278 
    279     if iterable(a):

SympifyError: SympifyError: 0    1
1    2
2    3
Name: a, dtype: int64

Answer 1

With "numpy", this works:

In [845]: df=pd.DataFrame([1,2,3], columns=['a'])
In [846]: arr=np.array([1,2,3])
In [847]: f = sympy.lambdify(x, sympy.sqrt(x),"numpy")

In [849]: f(arr)
Out[849]: array([ 1.        ,  1.41421356,  1.73205081])
In [850]: f(df)
Out[850]: 
          a
0  1.000000
1  1.414214
2  1.732051

but the sympy substitute does not:

In [851]: f(x)
...
AttributeError: 'Symbol' object has no attribute 'sqrt'

I haven't studied the lambdify docs enough to know if I can make both work in one function or not.

f = sympy.lambdify(x, sympy.sqrt(x),modules=("sympy", "numpy"))

handles the sympy but not the numpy arguments.

It looks like not specifying modules should be the same as modules = ["math", "mpmath", "sympy", "numpy"].

An expression with operators works nicely, even combining symbols and arrays:

In [926]: f = sympy.lambdify((x,y), x+y, ("numpy","sympy"))
In [927]: f(x,y)
Out[927]: x + y
In [928]: f(arr,arr)
Out[928]: array([2, 4, 6])
In [929]: f(arr,x)
Out[929]: array([x + 1, x + 2, x + 3], dtype=object)

I probably haven't discovered anything that you haven't already.