differentiation of arbitrary matrix expressions

Thanks for your question.

Your code does seem to run into a Maxima bug; a simpler version of it is:

declare([X,Y],nonscalar);
integrate(f(x),x,0,X);     <<< does not give an error (arguable, but OK)
integrate(f(x),x,0,X.Y);  <<< gives an error that X.Y is non-real, but X.Y
can in fact be real/scalar

There is a simple workaround for this:

P : tau^(-2) *Phi(Q)^y*(1-Phi(Q))^(1-y)*phi(theta/tau);
subst(X.beta+theta,Q,P)

Sorry for the inconvenience.

You can reorganize the result using factor.

Re: The matrix() function seems designed for matrices of known dimensions

matrix(...) is a notation for writing explicit matrices in terms of their
entries, yes.  Not sure what your question is here.

Re:
It would also be nice if diff(Phi(x), x) gave me phi(x) instead of the
fully expanded solution.

Hmm, not sure what you want exactly here.  You could define

Phi(x) := integrate('phi(z),z,-inf,x)$

... in which case phi(z) will remain unevaluated, and diff(Phi(x),x) will
get you back phi.  Is that what you have in mind?

I think you'll have to tell us more about what sort of result you're trying
to get for us to help you more.

                -s

On Fri, Jun 28, 2013 at 2:42 PM, Ross Boylan <ross at biostat.ucsf.edu> wrote:

> I'm interested in working with things I know are matrices and vectors, but
> whose exact dimensions I don't want to specify.  I want to differentiate
> these things.  I have expressions like (using pseudo tex-ish notation)
> 1/tau^2 prod_i prod_j Phi(X_{ij} beta+theta_i)^y_{ij} phi(theta_i/tau)
> where X_{ij} is itself a matrix (a row vector for the j'th partner of
> respondent i).
> Phi is the cumulative standard normal distribution and phi is its density.
>
> I tried to start simple, without the ij.  So now
> phi(x) := exp(-x^2/2)/sqrt(2*%pi);
> 
> Phi(x) := integrate(phi(z), z, -inf, x);
> declare(X, nonscalar)
> declare(beta, nonscalar)
> P(beta, theta, tau, y) := tau^(-2) *Phi(X . beta+theta)^y*(1-Phi(X . beta
> + theta))^(1-y)*phi(theta/tau);
> log(P(beta, theta, tau, y))
> #0: Phi(x=X . beta+theta)
> #1: P(beta=beta,theta=theta,tau=**tau,y=y)
>  -- an error. To debug this try: debugmode(true);
>
> Phi(X . beta + theta);
> #0: Phi(x=X . beta+theta)
>  -- an error. To debug this try: debugmode(true);
>
> Phi(X*beta); --works
>
> The matrix() function seems designed for matrices of known dimensions
>
> 
> It would also be nice if diff(Phi(x), x) gave me phi(x) instead of the
> fully expanded solution.
>
> BTW,
> declare(X[i,j], nonscalar);  --error
>
> Thanks for any help.  cc's appreciated, as I'm having mail "issues".
>
> Ross Boylan
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