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Re: Numerically computing partial derivatives
*To*: mathgroup at smc.vnet.net
*Subject*: [mg47989] Re: Numerically computing partial derivatives
*From*: Paul Abbott <paul at physics.uwa.edu.au>
*Date*: Tue, 4 May 2004 07:03:23 -0400 (EDT)
*Organization*: The University of Western Australia
*References*: <c72d7k$jk$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
In article <c72d7k$jk$1 at smc.vnet.net>,
Mark Coleman <mark at markscoleman.com> wrote:
> I am working with a maximum likelihood problem in econometrics. With
> some effort I can get Mathematica v5.0 to maximize the function. In order to
> derive standard errors of the estimates, however, I need to calculate
> the Hessian of the function at the optimal solution. This requires, of
> course, calculating the set of second derivatives of the function. Due
> to the nature of the function, however, neither the built-in D or ND
> operator seem to work (note: The function contains a term of the form
> Log[Det[I-rho*W]], where I is the nxn Identity matrix, rho is a real,
> and W is a non-symmetric (sparse) matrix of reals, or order n. In
> practice, n > 1000 at times. As a result, symbolic differentiation is
> not feasible. In addition, when I use ND [], I get nonsensical answers.
I assume you realize that
Log[Det[I-rho W]] == Sum[Log[1-rho lambda[i]],{i,n}]
where lambda[i] is the i-th eigenvalue of W. Can't you use this to
achieve symbolic differentiation?
Cheers,
Paul
--
Paul Abbott Phone: +61 8 9380 2734
School of Physics, M013 Fax: +61 8 9380 1014
The University of Western Australia (CRICOS Provider No 00126G)
35 Stirling Highway
Crawley WA 6009 mailto:paul at physics.uwa.edu.au
AUSTRALIA http://physics.uwa.edu.au/~paul
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