On Wed, Feb 4, 2015 at 12:18 AM, Warren Weckesser <
warren.weckes...@gmail.com> wrote:

>
>
> On Tue, Feb 3, 2015 at 11:14 PM, Sturla Molden <sturla.mol...@gmail.com>
> wrote:
>
>> Warren Weckesser <warren.weckes...@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)
>

What's the usecase for a heaviside function?

I don't think I have needed one since I was using mathematica or maple.

(x < 0).astype(...)   (x <= 0).astype(...)
np.sign(x, dtype)
look useful enough for most cases, or not?

(What I wish numpy had is conditional place that doesn't calculate all the
values. (I think there is a helper function in scipy.stats for that))

Josef



>
>
>
> Warren
>
>
>
>>
>> Sturla
>>
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