Re: (complicated) matrix differentiation
- To: mathgroup at smc.vnet.net
- Subject: [mg43374] Re: (complicated) matrix differentiation
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Wed, 27 Aug 2003 04:05:01 -0400 (EDT)
- Organization: The University of Western Australia
- References: <bifg7u$jv1$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <bifg7u$jv1$1 at smc.vnet.net>, "Eugene Salinas" <eugenesalinas2003 at yahoo.com> wrote: > I'm writing an optimization routine and need to take derivatives (first > and second) of the objective function. This isn't really my area so > although I hope to do it analytically I would like to use the symbolic > subroutines to verify my argument. > > Anyway, here is the problem: > > Objective function F(Y)=tr[(X'BX)^-1 X'AX] > > I need dF(Y) and ddF(Y). > > To get dF(Y) I used the implicit definition where > tr[V'dF(Y)]=(d/dt)F(Y(t)) evaluated at t=0 for Y(t)=Y+tV. > > After some manipulations I get that > dF(Y)=-2(BX(X'BX)^-1)X'AX(X'BX)^-1+2AX(X'BX)^-1 > > now I guess I could just take the straight forward derivatives with > respect to X and it will be messy but presumably correct. Then I can use > these in the numerical part. There was an item on this in the Ins and Outs section of The Mathematica Journal 8(4). I have posted this item at http://physics.uwa.edu.au/pub/Mathematica/MathGroup/MatrixDerivative.nb 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