Performance issues many algebras

Hey,

I am currently implementing a new model specification language for longitudinal panel models. As "backend", I use OpenMx. Everything works but it is painfully slow.

The model specification language uses mean and kernel functions to describe a model on a Gaussian process. The mean function gets some variables as input (for example time) and returns the model implied mean for that input (for example time point). The covariance function gets two inputs (for example time point 1, and time point 2) and returns the model implied covariance for that input (for example covariance between time point1 and time point 2). Thus, model specification in this language consists of formulating parametric mean and covariance functions. The latent growth curve model (with no correlation between intercept and slope) looks like this in this language:

$$m(t;[\mu_{Int},\mu_{Slope}])=\mu_{Int}+\mu_{Slope} \quad k(s,t;[\sigma_{Int}^2,\sigma_{Slope}^2,\sigma_\epsilon^2])=\sigma_{Int}^2+st\sigma_{Slope}^2+\delta(s-t)\sigma_\epsilon^2$$
I use the same parameter names here as in (http://openmx.psyc.virginia.edu/docs/openmx/latest/TimeSeries_Path.html). $\delta(x)$ is 1 if $x=0$ and $0$ otherwise.

The model can be defined like that


gppModel('muInt+muSlope*t','varInt+varSlope*t*t!+omxApproxEquals(t,t!,0.0001)*error',myData).


To transform this into an OpenMx model, I use mxExpectationNormal and construct the appropriate covariance matrix and mean vector. That is, every entry of mean vector is an algebra, which is really only 'muI+muS*t' where t is replaced with the appropriate input, which is in the data set (myData). I use the same idea to create the appropriate algebra for every entry of the covariance matrix.

This all works fine. I get the same results using this approach as using the regular path specification approach for all models. However, it is painfully slow (like a couple of thousands times slower than the regular approach). It is also much slower than a matlab implementation of this language I did, which uses a completely different software as backend. I started profiling the code and it seems that, not surprisingly, a lot of time is spent evaluating the algebras. **Any ideas how to make this faster?**