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I'm new to python and trying to do a HW assignment and it keeps throwing this error back at me (in iPython Notebook):

"TypeError: unsupported operand type(s) for ** or pow(): 'list' and 'float'"

Here's the formula i'm trying to imitate: h(x)=(1/√2π)*e^−(1/2)^x^2

import numpy as np
import math
from math import *


def h_scalar(x):
    return (1 / sqrt(2 * pi)) * exp(-.50** x ** 2.00)

I'm trying to get the same out put as my teacher.

l = [-10.0, -1.0, 0.0, 1.0, 10.0] #
print h_scalar(l)
>>> [1.4867195147342977e-06, 0.24197072451914337, 0.3989422804014327,
0.24197072451914337, 1.4867195147342977e-06]

Here's the teachers question btw:

First of all, write a function called h_scalar. The function should expect a list (or in general an item that is iterable). It will expect that the list contains floating point values. It should return a new list of floats that are the h(x) for each x value in the input list. You should name your function h_scalar()

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  • 2
    1.) Your exponential should be -.50 * x ** 2.00. 2.) You cannot broadcast an operation like **2.00 across a standard python array. To do this, convert x to a np.array. 3.) If you don't want to use numpy, consider using a for loop to compute the formula for each element in x. Store these values in another array, which you then return. Alternatively, use a list comprehension. Commented Oct 2, 2013 at 14:54

6 Answers 6

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8

You will achieve a better performance using numpy's sqrt and exp, which will operate elementwise:

import numpy as np
from numpy import sqrt, exp, pi
def h_scalar(x):
    x = np.array(x)
    return (1/sqrt(2*pi)) * exp(-0.50*x**2)

You can use it like:

x = [-10.0, -1.0, 0.0, 1.0, 10.0]
h_scalar(x)
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3 Comments

+1 this is the only solution so far that gains a proper performance advantage from vectorization
To meet the requirements of the input being a list (or any iterable) you should insert x=np.array(x, copy=False) as the first line of the function h_scalar.
@Dave, thank you! I haven't paid enough attention to that requirement! In this case I think you cannot avoid the copy...
7

If you want to use numpy.vectorize this is one option:

>>> import numpy as np
>>> h_scalar = np.vectorize(lambda x: (1 / np.sqrt(2 * np.pi)) * np.exp( -.50** x ** 2.00 ))
>>> l = np.array([-10.0, -1.0, 0.0, 1.0, 10.0])
>>> h_scalar(l)
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1 Comment

Bear in mind that np.vectorize doesn't really give any performance benefit over a plain list comprehension - you'll still end up looping in Python rather than C
0

What you want is list comprehension.

Like this:

def h_scalar(sca):
    return [(1 / sqrt(2 * pi)) * exp(-.50** x ** 2.00) for x in sca]
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0

To perform an operation on all items in a list (or another iterable object), creating a new list from the return values of the operation, you can do something like this:

>>> l = [1,2,3,4,5]
>>> l2 = [ 2 * x for x in l ]
>>> print l2
[2, 4, 6, 8, 10]

The Python language feature used on the second line here is called a list comprehension, and it's very well suited to the homework task you've been given.

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0

you are trying to use power on a list instead of a list item. I may have the exact function wrong here, but try something like this to take a list and return a list.

def h_scalar(x):
    return [(1/sqrt(2*pi))*exp(-.50 ** i ** 2.0) for i in x]

I'm not sure you have the right equation though, could you re-format it?

In [14]: h_scalar(l)                                              
Out[14]: 
[0.3989422804014327,                                              
 0.24197072451914337,                                             
 0.14676266317373993,                                             
 0.24197072451914337,                                             
 0.3989422804014327]
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3 Comments

Thank you, i didn't know i was doing that. I can now receive output, but it's not matching my teachers. My output is now "[0.3989422804014327, 0.24197072451914337, 0.14676266317373993, 0.24197072451914337, 0.3989422804014327]" whereas my instructor's is "[1.4867195147342977e-06, 0.24197072451914337, 0.3989422804014327, 0.24197072451914337, 1.4867195147342977e-06]" Am i calculating something wrong still?
list comprehension like svk and Piotr pointed out is one way to go. Like I said, you'll want to double check your equation, but I can't tell from your formatting what you're trying to get.
Does this look like your original equation: link
0

import numpy as np import math from math import *

def h_scalar(x): return (1 / sqrt(2 * pi)) * exp(-.50** x ** 2.00)

l = [-10.0, -1.0, 0.0, 1.0, 10.0]

h_scalar = np.vectorize(h_scalar) ## you are missing this line in your code

print h_scalar(l)

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