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Re: More universal way of writing gradient

  • To: mathgroup at smc.vnet.net
  • Subject: [mg112925] Re: More universal way of writing gradient
  • From: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>
  • Date: Wed, 6 Oct 2010 03:15:20 -0400 (EDT)
  • References: <i8erhh$hv6$1@smc.vnet.net>

Wouldn't mapping at the deepest level work?

foo[u_] := Map[bar, u, {-1}]

or in your example:

grad[u_] := Map[{Derivative[1, 0][#], Derivative[0, 1][#]} &, u, {-1}]

Cheers -- Sjoerd

On Oct 5, 11:35 am, Sam Takoy <sam.ta... at yahoo.com> wrote:
> Hi,
>
> My question is not related to the gradient at all, but rather strictly
> the grammar of Mathematica. Gradient is just an example.
>
> My question is: what's the elegant way to write the following function
> so that it applies to single functions as well as ("rectangular") lists
> of functions?
>
> grad[u_] := {Derivative[1, 0][u], Derivative[0, 1][u]}
> gradList[u_] := {Map[Derivative[1, 0], u, {2}],
>    Map[Derivative[0, 1], u, {Length[Dimensions[u]]}]}
>
> f[x_, y_] := Sin[x] Exp[y]
> Through[grad[f][x, y]] // MatrixForm
> gradList[{{f, f}, {f, f}}] //
>    Map[Apply[#, {x, y}] &, #, {Length[Dimensions[#]]}] & // MatrixFor=
m
>
> I'm sure I could wrap grad and gradList into a function with an If, but
> I'm sure there is a more natural way.
>
> Thank you in advance,
>
> Sam
>
> PS: Using Map[Apply[]] in the second case because Through doesn't seem
> to work with Lists of Lists. This is the subject of an earlier post...



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