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From: melahi_ahmed@yahoo.fr (ahmed)
Newsgroups: comp.lang.forth
Subject: Re: Differentiable Forth
Date: Wed, 17 Jul 2024 17:17:23 +0000
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On Wed, 17 Jul 2024 16:42:41 +0000, mhx wrote:

...
>
> Try the exponential matrix ( expm(A) where A
> is a square matrix ) next.
>
> -marcel

By expm(A) do you mean expm(A*t) where t is time (the independant
variable)
and A the matrix in the state model:

x_dot = A*x + B*u
y     = C*x + D*u

and PHI = expm(A*t) the transition matrix that permits to get the time
solution of the state model.

or you mean exactly expm(A), where A is the independant variable.
in the latter case I don't know how to calculate derivatives with
respect to matrices analytically.

for former case, time t is real, then we pass to dual numbers (t,1e) = t
+ 1e*eps where eps^2 =0
then we use the formulas known for floating point numbers
and generate versions for dual numbers and use them as in the posted
program.


Ahmed