R help - Nov 2006 - Partial derivatives of a matrix with respect to a single element

UseRs,

We are using projection matrices in demographic analyses, and one 
technique is to calculate partial derivatives of a matrix with respect 
to a variable appearing in one or more of its elements.  For example, 
consider the matrix A:

|  a*b a*c |
|   d   d  |


If I'm not mistaken, the partial derivative of matrix A w/ respect to 
variable 'a' is the matrix:

|  b  c  |
|  0  0  |

... just an element by element first order derivative of the notation, 
but would like to use R in a manner similar to our method:

We are doing this with symbolic notation, variable assignments, 
substitution, and the 'diff(matrix,variable)' function in Matlab; 
however, I'm always looking for GNU solutions to old procedure$, if you 
get my drift.  I've read and used the derivative functions in R, and 
could (probably) write a lengthy routine to duplicate this solution, but 
if there's a shortcut, I have no delusions about my own laziness and 
will greatly appreciate your input.

R. VanNimwegen

Kansas State University
Division of Biology
vanron at ksu.edu

Try the Ryacas package:
> library(Ryacas)
> a <- Sym("a"); b <- Sym("b"); c <-
Sym("c"); d <- Sym("d")
> M <- List(List(a*b, a*c), List(d, d))
> deriv(M, "a")
expression(list(list(b, c), list(0, 0)))

On 11/23/06, Ron E. VanNimwegen <vanron at ksu.edu>
wrote:
> UseRs,
>
> We are using projection matrices in demographic analyses, and one
> technique is to calculate partial derivatives of a matrix with respect
> to a variable appearing in one or more of its elements.  For example,
> consider the matrix A:
>
> |  a*b a*c |
> |   d   d  |
>
>
> If I'm not mistaken, the partial derivative of matrix A w/ respect to
> variable 'a' is the matrix:
>
> |  b  c  |
> |  0  0  |
>
> ... just an element by element first order derivative of the notation,
> but would like to use R in a manner similar to our method:
>
> We are doing this with symbolic notation, variable assignments,
> substitution, and the 'diff(matrix,variable)' function in Matlab;
> however, I'm always looking for GNU solutions to old procedure$, if you
> get my drift.  I've read and used the derivative functions in R, and
> could (probably) write a lengthy routine to duplicate this solution, but
> if there's a shortcut, I have no delusions about my own laziness and
> will greatly appreciate your input.
>
> R. VanNimwegen
>
> Kansas State University
> Division of Biology
> vanron at ksu.edu
>
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