Type error in Python 2.7 for some simple recursive code

Question

I'm having a type error with some recursive code in Python 2.7. The code below is essentially a riemann integral, where you add up the area of rectangles underneath a curve. It works perfectly when 'step' is 0.25 or greater, but the type error occurs when it is less than 0.25. Why does this happen and how can I fix it?

The following error occurs for the last line of code:

  File "/home/i/PycharmProjects/6.00.1x/prob3/radiationExposure.py", line 25, in radiationExposure
return f(stop - step) * step + radiationExposure(start, (stop - step), step)

TypeError: unsupported operand type(s) for +: 'float' and 'NoneType'

My code is as follows:

def f(x):
    import math
    return 10*math.e**(math.log(0.5)/5.27 * x)

def radiationExposure(start, stop, step):

'''
    Computes and returns the amount of radiation exposed
    to between the start and stop times. Calls the
    function f to obtain the value of the function at any point.

    start: integer, the time at which exposure begins
    stop: integer, the time at which exposure ends
    step: float, the width of each rectangle. You can assume that
      the step size will always partition the space evenly.

    returns: float, the amount of radiation exposed to
      between start and stop times.
    '''

    if stop - step == start:
        return f(stop - step) * step
    elif stop - step > start:
        return f(stop - step) * step + radiationExposure(start, (stop - step), step)

Note to those with ethics: This is to satisfy my own curiosity. There is no grade for the archived MIT course on edx.org, and recursive code isn't required for this problem.

khelwood · Accepted Answer · 2015-01-07 07:54:17Z

1

The function radiationExposure given in your question returns None when stop-step < start because neither of the if conditions is met.

if stop - step == start:
    return f(stop - step) * step
elif stop - step > start:
    return f(stop - step) * step + radiationExposure(start, (stop - step), step)
# If the execution reaches this point and the function ends, it will return None

If you are expecting arithmetic to give you exactly stop-step==start, then don't use floating point variables, because they are approximations.

If you instead had:

if stop - step <= start:
    return f(stop - step) * step
else:
    return f(stop - step) * step + radiationExposure(start, stop - step, step)

that would at least ensure that the function returned a number instead of None.

answered Jan 7, 2015 at 7:54

khelwood

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1 Comment

istinson Over a year ago

That makes perfect sense. Thank you for taking the time to help me, khelwood.

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