Re: Multi-variable first-order perturbation analysis?
- To: mathgroup at smc.vnet.net
- Subject: [mg104572] Re: Multi-variable first-order perturbation analysis?
- From: dh <dh at metrohm.com>
- Date: Wed, 4 Nov 2009 01:34:56 -0500 (EST)
- References: <hcl3i9$blv$1@smc.vnet.net>
Hi,
what you are looking for is called the Jacobian and may be obtained by "D":
funs = {f1[x1, x2], f2[x1, x2]};
D[funs, {{x1, x2}}] /. {x1 -> x10, x2 -> x20}
Daniel
AES wrote:
> I have a half dozen functions f1, f2, ?, each of which depends on some
> or all of half a dozen variables x1, x2, ?, all of these functions
> pretty vanilla in character.
>
> Objective is to obtain the same number of first-order perturbation
> expansions df1, df2, ?, where df1 means all the relevant derivatives
>
> (df1/dx1) * dx1 + (df2/dx2) * dx2 + . . .
>
> evaluated at initial values x1=x10, x2=x20, ? and so on -- all of this
> totally symbolic in character, and with *no* cross-products dx1 dx2 or
> similar.
>
> I know I can code this various ways -- but what's the "cleanest" way to
> accomplish this?
>
> [Notes: The results for df1, df2, ? don't have to be neatly readable,
> e.g., the terms multiplying dx1 for a given dfi don't all have to be
> neatly collected inside a single set of brackets; the resulting
> expressions just have to be correct. And, by "cleanest" I don't
> necessarily mean the tersest, most arcane way of coding this.]
>