[R] Partial derivatives of a matrix with respect to a single element

[Ron E. VanNimwegen]

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