Thanks for the answer (and for the question too). I had been thinking of a
way to implement methods that would be independent of number of
coordinates. I just ran some test code and this method works great. I think
I can use this for the proposed vector calculus module. Also, I suppose we
can use this for calculating gradients, and perhaps with some changes, for
calculating curl too (by providing Lambda with a tuple of functions for
each component of the vector field).
On Thursday, April 18, 2013 5:02:13 AM UTC+5:30, Aaron Meurer wrote:
>
> You can do the whole thing symbolically with Lambda
>
> [Lambda(f, Derivative(f, coord)) for coord in coordinates]
>
> Unlike the normal list comprehension, Derivative is unevaluated, so
> you create the object before you actually have f, and unlike the
> lambda version, you can access and manipulate the object using .args
> .subs and all the other standard SymPy constructs.
>
> The disadvantage here is that when you call the functions, it will
> give you an unevaluated Derivative. You'll have to call .doit() to
> evaluate them. Maybe we should create a Doit() object that calls
> doit() on its argument and returns as an unevaluated Doit() if nothing
> changes. Something like
>
> class Doit(Expr):
> def __new__(cls, obj):
> obj_doit = obj.doit()
> if obj_doit == obj:
> return super(Doit, cls).__new__(cls, obj)
> return obj_doit
>
> Then you could use
>
> Dx, Dy, Dz = [Lambda(f, Doit(Derivative(f, coord))) for coord in
> coordinates]
>
> and Dx(f) would evaluate if the derivative of f can be computed,
> otherwise it would give Doit(Derivative(f, x)), which would still
> automatically do itself if you later substitute f with something that
> can be differentiated. If you want it to work only the first time, it
> would be something like
>
> class DoitNow(Expr):
> def __new__(cls, obj, evaluate=True):
> if evaluate:
> return obj.doit()
> return super(DoitNow, cls).__new__(cls, obj)
>
> Dx, Dy, Dz = [Lambda(f, DoitNow(Derivative(f, coord), evaluate=False))
> for coord in coordinates]
>
> Really, though, we should just build this behavior into Lambda as an
> option.
>
> Aaron Meurer
>
> On Wed, Apr 17, 2013 at 2:59 PM, thomas hisch <t.h...@gmail.com<javascript:>>
> wrote:
> > Maybe you want to use nested lambdas:
> >
> > map(lambda c: lambda f: Diff(f,c), coords)
> >
> >
> > On Wednesday, April 17, 2013 10:11:14 PM UTC+2, brombo wrote:
> >>
> >> Consider the following
> >>
> >> coords = symbols('x,y,z')
> >>
> >> I wish to contruct the list of functions:
> >>
> >> [Dx,Dy,Dx]
> >>
> >> where
> >>
> >> def Dx(f):
> >> return(diff(f,coord[0]))
> >>
> >> etc.
> >>
> >> but I want to build the list [Dx,Dy,Dz] with a for loop and not have to
> >> do a separate
> >>
> >> def Dx(f):
> >> return(diff(f,coord[0]))
> >>
> >> def Dy(f):
> >> return(diff(f,coord[1]))
> >>
> >> def Dz(f):
> >> return(diff(f,coord[2]))
> >>
> >> since when I am writing the code I don't know how long coords will be.
> >
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>
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