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Re: More universal way of writing gradient
*To*: mathgroup at smc.vnet.net
*Subject*: [mg112919] Re: More universal way of writing gradient
*From*: Bob Hanlon <hanlonr at cox.net>
*Date*: Wed, 6 Oct 2010 03:14:12 -0400 (EDT)
Perhaps a different approach would work easier
Clear[grad]
grad[f_][arg__] := Module[{v, vars},
vars = Table[v[i], {i, Length[{arg}]}];
(D[f @@ vars, #] & /@ vars) /.
Thread[vars -> {arg}]]
grad[f_List][arg__] := grad[#][arg] & /@ f
grad[f][x, y]
{Derivative[1, 0][f][x, y], Derivative[0, 1][f][x, y]}
grad[f][1, 2]
{Derivative[1, 0][f][1, 2], Derivative[0, 1][f][1, 2]}
grad[{f, g}][x, y]
{{Derivative[1, 0][f][x, y], Derivative[0, 1][f][x, y]},
{Derivative[1, 0][g][x, y], Derivative[0, 1][g][x, y]}}
grad[{{f, g}, {h, i}}][x, y]
{{{Derivative[1, 0][f][x, y], Derivative[0, 1][f][x, y]},
{Derivative[1, 0][g][x, y], Derivative[0, 1][g][x, y]}},
{{Derivative[1, 0][h][x, y], Derivative[0, 1][h][x, y]},
{Derivative[1, 0][i][x, y], Derivative[0, 1][i][x, y]}}}
Bob Hanlon
---- Sam Takoy <sam.takoy 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[#]]}] & // MatrixForm
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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