TypeError: can't convert expression to float

Question

I am a python newbie. I am trying to evaluate Planck equation using python. I have written a simple program. But when I give input to it is giving me an error. can anyone hep me where I am going wrong? Here is the program and the error:

Program:

from __future__ import division
from sympy.physics.units import *
from math import *
import numpy
from scipy.interpolate import interp1d

#Planck's Law evaluation at a single wavelength and temperature
def planck_law(wavelength,temperature):
    T=temperature
    f=c/wavelength
    h=planck
    k=boltzmann
    U=2*h/(c**3)*(f**3)/(exp(h*f/(k*T))-1)
    return U.evalf()

Input: I have imported the function as 'cp' and the input is as follows

value = (cp.planck_law(400,2000))

Error:

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>`enter code here`
  File "Camera_performance.py", line 14, in planck_law
  U=2*h/(c**3)*(f**3)/(exp(h*f/(k*T))-1)
  File "/usr/lib/python2.7/dist-packages/sympy/core/expr.py", line 221, in __float__
  raise TypeError("can't convert expression to float")

TypeError: can't convert expression to float

Answer 1

It seem like you are mixing namespaces, since your are using from ... import *. You wanted to use sympy.exp() but your code uses math.exp(). It is good practice to keep the namespaces separated, i.e. never use from ... import * - it might seem like more typing at first, but will produce much cleaner easier comprehensible code in the end. Try:

import sympy as sy
import sympy.physics.units as units

def planck_law(wavelength,temperature):
     """Planck's Law evaluation at a single wavelength and temperature """   
     T=temperature
     f=units.c/wavelength
     h=units.planck
     k=units.boltzmann
     U=2*h/(units.c**3)*(f**3)/(sy.exp(h*f/(k*T))-1)
     return U.evalf()

# Test:
print(planck_law(640e-9*units.m, 500*units.K))
# Result: 1.503553603007e-34*kg/(m*s)

Answer 2

When you call your function, you need to pass units to the temperature and wavelength argument. Calling cp.planck_law(400*meters,2000*K) gives the expected 1.15133857387385e-33*kg/(m*s).

The problem arose with the exponential function, which, rightfully, expects to receive a dimensionless argument. Since the arguments you were passing did not include units, Sympy treated them as dimensionless floats, rather than a temperature and a length, as required.

Answer 3

Your term h*f/(k*T) isn't unitless, so you cannot pass it to exp(). Doesn't make sense in a physical context, either ;-)

You can get a result if you divide it by K and m:

exp(h*f/(k*T)/K/m)

but that surely makes no sense. It's just to make the program run (into nonsense).

I guess you will have to check your formula and find out how you really want to compute the value you want to pass to exp().

EDIT:

As Pascal pointed out, you are just missing the units for the arguments you pass. Try it with:

planck_law(400e-9*m,2000*K)

Returns:

3.20224927538564e-22*kg/(m*s)