Re: symbolic differentiation of a scalar field
- To: mathgroup at smc.vnet.net
- Subject: [mg103358] Re: [mg103349] symbolic differentiation of a scalar field
- From: Leonid Shifrin <lshifr at gmail.com>
- Date: Thu, 17 Sep 2009 06:20:37 -0400 (EDT)
- References: <200909160948.FAA13142@smc.vnet.net>
Hi Llewlyn,
Here is one possibility (I changed your function f to make things a bit more
interesting):
In[1] =
Clear[f];
f[var_Symbol] := Sum[i*var[i]^2, {i, 10}]
In[2] =
Clear[x];
f[x]
Out[2] =
x[1]^2+2 x[2]^2+3 x[3]^2+4 x[4]^2+5 x[5]^2+6 x[6]^2+7 x[7]^2+8 x[8]^2+9
x[9]^2+10 x[10]^2
In[3] =
Clear[dfdk];
dfdk[var_Symbol][k_Integer][expr_] := D[expr, var[k]]
In[4] = Table[dfdk[x][i][f[x]], {i, 1, 10}]
Out[4] =
{2 x[1],4 x[2],6 x[3],8 x[4],10 x[5],12 x[6],14 x[7],16 x[8],18 x[9],20
x[10]}
Regards,
Leonid
On Wed, Sep 16, 2009 at 1:48 PM, Llewlyn <tommaso.biancalani at gmail.com>wrote:
> Greetings,
>
> I have a function depending by n (large) number of variables, that is f
> (x1 .. xn).
> I need to do to some symbolic calculus with this function, basically
> differentiation.
> Supposing n=10 here's my solution:
>
> f[ Array[a_, 10] ] := Sum [i*a[i], {i,10}]
> dfdk[ k_ ] := D[ f[Array[a_, 10]], a[k]]
>
> How do you think of? And how may i do for an unknown n, set of
> variables?
> I've tried searching tutorial for standard techinque but i didn't find
> one, links are really welcome.
>
> bests,
>
> Ll.
>
>
- References:
- symbolic differentiation of a scalar field
- From: Llewlyn <tommaso.biancalani@gmail.com>
- symbolic differentiation of a scalar field