Re: Jacobian
- To: mathgroup at smc.vnet.net
- Subject: [mg117550] Re: Jacobian
- From: Peter Pein <petsie at dordos.net>
- Date: Tue, 22 Mar 2011 05:09:03 -0500 (EST)
- References: <im7bt9$t86$1@smc.vnet.net>
Am 21.03.2011 12:13, schrieb Duarte:
> Hi everyone.
>
> I just recently started using mathematica. I have version 6.0.
> I have a project in which I need toi calculate the jacobian matrix of a function G:R4 - R4.
>
> My question is wether there is a command that computes the jacobian or do I need to compute each partiall derivate individually? What command gives the partial derivatives?
>
> Thank you
>
Hi,
define vectors f and x:
In[1]:= vars = Subscript[x,#]& /@ Range[4];
f=Subscript[y, #][Sequence @@ vars]& /@ Range[4];
In[3]:= j1=D[f,{vars}];
In[4]:= j2=Outer[D,f,vars];
In[5]:= j1===j2
Out[5]= True
due to the long function name "Derivative" I shorten the following output:
In[6]:= j1
Out[6]= {{Derivative[1, 0, 0, 0][Subscript[y, 1]][Subscript[x, 1],
Subscript[x, 2], Subscript[x, 3],
Subscript[x, 4]],
Derivative[0, 1, 0, 0][Subscript[y, 1]][Subscript[x, 1], ..},
...,
{..,
Subscript[x, 2], Derivative[0, 0, 0, 1][Subscript[y, 4]][
Subscript[x, 1], Subscript[x, 2], Subscript[x, 3],
Subscript[x, 4]]}}
hth,
Peter