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 >> >> _______________________________________________ >> NumPy-Discussion mailing list >> NumPy-Discussion@scipy.org >> http://mail.scipy.org/mailman/listinfo/numpy-discussion >> > > > _______________________________________________ > NumPy-Discussion mailing list > NumPy-Discussion@scipy.org > http://mail.scipy.org/mailman/listinfo/numpy-discussion > >
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