[R] Solving equations

Spencer Graves spencer.graves at pdf.com
Wed Mar 26 16:24:25 CET 2003

	  What do you mean "solve"?  Do you want to solve for "t" in f(t) = 
A*exp(B*t), where A and B are given square matrices?  Is "t" a scalar or 
also a square matrix or something else, and does "*" refer to 
element-wise multiplication (as in R) or matrix multiplication (written 
"%*%" in R)?

	  Suppose we want to solve

	  F = A %*% exp(B%*%t)

where A, B, and F are given square matrices.  I might approach it as 

	  Ainv.F <- solve(A, F) # compute inverse(A)%*%F

	  AiF.eig <- eigen(Ainv.F)

#  Then check to make sure there are no repeated eigenvalues,
#  or if there are that a Jordon canonical form is still diagonal.
#  This will give Ainv.F in a form
#        Evec %*% diag(Lam) %*% inverse(Evec)
#  The natural log of this is just
#        Evec %*% diag(log(Lam)) %*% inverse(Evec)

 From this point, you can solve for "t"

Does this help?
Sorry this is a bit cryptic, but I don't have time to write and debug 
code for this myself right now.

Hope this helps,
Spencer Graves

schlegel at cs.uni-duesseldorf.de wrote:
> Hello,
> Does somebody knows if there exists a function which solves a set of
> equation, say f(vars),
> for the variables vars (similar to Solve in mathematica).
> The functions I am considering are of the form f(t) ~ A*exp(B*t), where
> A and B are matrices.
> Thanks Thomas
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