[Numpy-discussion] Any interest in a 'heaviside' ufunc?

Warren Weckesser warren.weckesser at gmail.com
Wed Feb 4 00:18:51 EST 2015


On Tue, Feb 3, 2015 at 11:14 PM, Sturla Molden <sturla.molden at gmail.com>
wrote:

> Warren Weckesser <warren.weckesser at gmail.com> wrote:
>
> >                     0    if x < 0
> >     heaviside(x) =  0.5  if x == 0
> >                     1    if x > 0
> >
>
> This is not correct. The discrete form of the Heaviside step function has
> the value 1 for x == 0.
>
> heaviside = lambda x : 1 - (x < 0).astype(int)
>
>
>


By "discrete form", do you mean discrete time (i.e. a function defined on
the integers)?  Then I agree, the discrete time unit step function is
defined as

    u(k) = 0  k < 0
           1  k >= 0

for integer k.

The domain of the proposed Heaviside function is not discrete; it is
defined for arbitrary floating point (real) arguments.  In this case, the
choice heaviside(0) = 0.5 is a common convention. See for example,

* http://mathworld.wolfram.com/HeavisideStepFunction.html
* http://www.mathworks.com/help/symbolic/heaviside.html
* http://en.wikipedia.org/wiki/Heaviside_step_function, in particular
http://en.wikipedia.org/wiki/Heaviside_step_function#Zero_argument

Other common conventions are the right-continuous version that you prefer
(heavisde(0) = 1), or the left-continuous version (heaviside(0) = 0).

We can accommodate the alternatives with an additional argument that sets
the value at 0:

    heaviside(x, zero_value=0.5)


Warren



>
> Sturla
>
> _______________________________________________
> NumPy-Discussion mailing list
> NumPy-Discussion at scipy.org
> http://mail.scipy.org/mailman/listinfo/numpy-discussion
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mail.python.org/pipermail/numpy-discussion/attachments/20150204/4378a49d/attachment.html>


More information about the NumPy-Discussion mailing list