2011/2/11 Stephen Montgomery-Smith <stephen@missouri.edu>

Bernardo Rocha wrote:

Hi everyone,

I've recently discovered GiNaC and I'm really excited about its
capabilities. There is one thing that I would like to know if it is able
to do that I haven't found in the tutorial.pdf or in any other place
that I've searched.

I would like to know if, given a function \Psi=\Psi(E), like the strain
energy function for the St. Venant-Kirchhoff material

\Psi(E) = 0.5 * \lambda * (tr E)^2 + \mu E:E

is it possible to differentiate it with respect to E, that is i would
like to compute \frac{\partial \Psi}{\partial E}. If this is possible,
could someone please send some examples or maybe point to which classes
should I use to do that?

That's all for now. Many thanks in advance.

Best regards,
Bernardo M. R.

Couldn't you do it this way? Write \Psi(E) as an expression involving the variables e11,e12,e13,...,e33 which are the entries of E. Then compute the partial derivatives \frac{\partial \Psi}{\partial eij} for 1<=i,j<=3. (Presumably you suppose that E is symmetric so only six partial derivatives need to be computed, but even if it is not necessarily symmetric you still only need 9 partial derivatives.) Just store this as something like:

expr dPsi_dE[3][3]

or

vector<expr> dPsi_dE

or something similar.