[Tutor] How to vectorize a constant function?

[Jose Amoreira]

Hello!
In "A Primer on Scientific Programming with Python", they define a vectorized 
function as a scalar function that, when called with a vector argument, 
returns a vector with the values of the function for each of the values stored 
in the argument vector.

I am trying to define a constant vectorized function, that is, one that 
returns 1. (for instance) when called with a scalar argument x and that 
returns array([1.,1.,1.]) when the argument is a three-element array, etc.

Here are a few snippets of an interactive session displaying my failed 
attempts:
---------------------------
In [1]: from numpy import *
In [2]: def f(x):
   ...:     return 1.
In [3]: x=linspace(0,1,5)
In [4]: print f(x)
------> print(f(x))
1.0
-------------------------
That's not what I want, that's a scalar, not a five element array. Next 
option:
-------------------------
In [13]: def g(x):
   ....:     return where(True,1.,0.)
In [14]: print g(x)
-------> print(g(x))
1.0
---------------------------
Still not right. But here is something strange. The values in x are non-
negative, therefore the test x>=0 yelds True for each element in x. One might 
then think that g(x) as defined above would, in this case, be equivalent to 
h(x) defined below:
--------------------------
In [16]: def h(x):
   ....:     return where(x>=0,1.,0)
---------------------------
However,
---------------------------
In [18]: print h(x)
-------> print(h(x))
[ 1.  1.  1.  1.  1.]
---------------------------
So my questions are:
1. What's the proper way to vectorize a constant function (I know that we 
really don't have to, but I'd like to do it in a first step towards a more 
sophisticated calculation)?
2. Why do g(x) and h(x) return different results?
3. Why doesn't f(x) work?
Thanks
Jose