Thanks a lot for all your help! The [f(a=i,x=j,b=k) for i,j,k in zip
(v,w,z)] way looks useful, as I can easily see what is inserted for
what. Looking at the other examples, I realised that most of my time
series are likely to be imported as numpy arrays, so I will have to
look in more detail at the numpy way. Is there an easy way of
converting a function f into a numpy function?
Here is what I tried:
sage: import numpy
sage: var('a b')
sage: f = a*x^2 + b
sage: v = numpy.array([1,2,3])
sage: w = numpy.array([4,5,6])
sage: z = numpy.array([7,8,9])
sage: f(a=v,x=w,b=z)
Traceback (click to the left for traceback)
...
TypeError: 'numpy.ndarray' object is not callable
sage: a = v
sage: b = w
sage: x = z
sage: f
array([
b + 49 a,
b + 64 a,
b + 81 a], dtype=object)
sage: a*x^2 + b
array([53, 133, 249], dtype=object)
The last output is what I want, but I don't want to type the whole
equation in again. I am collecting all the methods and ideas that help
me and I hope that I will be able to put it all into a tutorial one
day.
Cheers
Stan
On Nov 19, 6:27 pm, "David Joyner" <[EMAIL PROTECTED]> wrote:
> On Wed, Nov 19, 2008 at 12:19 PM, Jason Grout
>
>
>
> <[EMAIL PROTECTED]> wrote:
>
> > Stan Schymanski wrote:
> >> Hi Mike and Jason,
>
> >> Thanks a lot for the quick response. My problem becomes a bit more
> >> obvious if I have a function of several variables. Then the map
> >> function becomes somehow impractical because I can't define which list
> >> is used for which variable. List comprehensions also get a lot more
> >> difficult. Example:
>
> >> sage: var('a b c')
> >> sage: f = a*x^2+b
> >> sage: w = [4,5,6]
> >> sage: z = [7,8,9]
> >> sage: map(f,v,w,z)
> >> [53, 133, 249]
> >> sage: map(f,w,v,z)
> >> [197, 322, 489]
>
> >> I wouldn't even know how to do this with a list comprehension in one
> >> step. Since the functions I work with have to be applied to time
> >> series of quite a few variables, I am really desperate for a practical
> >> way of doing this. So far, all mathematical programs I worked with
> >> were able to do this and I bet that many people are used to applying
> >> functions to lists and arrays. Isn't this a lot faster than defining
> >> loops?
>
> > I would generally use list comprehensions over map. So, you could do:
>
> > sage: [f(a=i,x=j,b=k) for i,j,k in zip(v,w,z)]
>
> Or just
>
> sage: f = lambda x: x[1]*x[0]^2+x[2]
> sage: v = [1,2,3]
> sage: w = [4,5,6]
> sage: z = [7,8,9]
> sage: map(f,zip(v,w,z))
> [11, 28, 63]
>
>
>
> > Note that numpy has the concept of "universal functions" which
> > automatically thread over a list, much like Matlab would.
>
> > sage: np.sin(np.array((0., 30., 45., 60., 90.)) * np.pi / 180. )
>
> > Also, if you want threadable functions, you can do it easily with pure
> > python functions and a decorator:
>
> > def threadable(f):
> > def threadable_f(*args,**kwds):
> > return [f(*tuple, **kwds) for tuple in zip(*args)]
> > return threadable_f
>
> > @threadable
> > def f(x,y,z):
> > return x*y^2+z
>
> > f([1,2,3],[4,5,6],[7,8,9])
>
> > This last call produces:
>
> > [23, 58, 117]
>
> > Jason
>
>
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