Sympy to numpy causes the AttributeError: 'Symbol' object has no attribute 'cos'

Question

I am trying to do partial derivatives using sympy and I want to convert it to a function so that I can substitute values and estimate the derivatives at some values of t_1, t_2. The code I am using is as follows:

import sympy as sp
import numpy as np
from sympy import init_printing
init_printing()
t_1,t_2,X_1,X_2,Y_1,Y_2,X_c1,X_c2,Y_c1,Y_c2,a_1,a_2,psi_1,psi_2,b_1,b_2= sp.symbols('t_1 t_2 X_1 X_2 Y_1 Y_2 X_c1 X_c2 Y_c1 Y_c2 a_1 a_2 psi_1 psi_2 b_1 b_2')

X_1=X_c1 + (a_1 * sp.cos(t_1) * sp.cos(psi_1)) - ((b_1) * sp.sin(t_1)* sp.sin(psi_1))

X_2=X_c2 + (a_2 * sp.cos(t_2) * sp.cos(psi_2)) - ((b_2) * sp.sin(t_2)* sp.sin(psi_2))

Y_1=Y_c1 + (a_1 * sp.cos(t_1) * sp.sin(psi_1)) + ((b_1) * sp.sin(t_1)* sp.cos(psi_1))

Y_2=Y_c2 + (a_2 * sp.cos(t_2) * sp.sin(psi_2)) + ((b_2) * sp.sin(t_2)* sp.sin(psi_2))

D=(((X_2-X_1)**2) + ((Y_2-Y_1)**2))**0.5

y_1=sp.diff(D,t_1)

y_2=sp.diff(D,t_2)

f=sp.lambdify(t_1, y_1, "numpy")

g=sp.lambdify(t_2, y_2, "numpy")

When I try to substitute a value for t_1 using,

f(np.pi/2)

I get the following error:

AttributeError   Traceback (most recent call last)
<ipython-input-26-f37892b21c8b> in <module>()
----> 1 f(np.pi/2)

/users/vishnu/anaconda3/lib/python3.5/site-packages/numpy    /__init__.py in <lambda>(_Dummy_23)

AttributeError: 'Symbol' object has no attribute 'cos'

I referred to the following links:

What causes this error (AttributeError: 'Mul' object has no attribute 'cos') in Python?

Python AttributeError:cos

but I think my imports of numpy and sympy are not clashing unlike the cases mentioned in those links. Any help is appreciated.

Solution

This type of error occurs when you call np.cos(a_symbol), which apparently translates under-the-hood in numpy to a_symbol.cos().

lambdify is for numeric calculations - it replaces all sp calls with np calls. But what you're doing is symbolic. This is enough for your problem:

f1 = lambda t: y_1.subs({t_1: t})
f2 = lambda t: y_2.subs({t_2: t})

Comments

[Vishnu]

Thank you, this answers the question correctly. Do you know why if I use f1(np.pi/2) it substitutes cos(t_1) as 6.123*10**-17. How do I make it substitute zero?

[Eric]

You use sp.pi instead

[Vishnu]

Works perfectly. Thanks again. :)