Refresh CCMA code

[rmcgibbo]

@peastman and I spent some time looking at the CCMA code today, as part of trying to build a new test case. The code is kind of hard to follow mathematically, and doesn't really track exactly with the paper.

• The scaling of the inverse Jacobian by d[i]/d[j] isn't mentioned in a comment or anything, but is important. (The variable that appears to be the inverse jacobian is not actually the inverse jacobian, it's actually the inverse jacobian times d[i]/d[j]). This is a little tricky and is probably an optimization.
• In the apply() function, the construction of the error term looks looks like it's a kind of squared relative error, but in the paper it's an absolute error (not relative) and also not squared. OTOH, the construction of the jacobian tracks the paper very closely (e.g. eq. 4 and this code) This makes it a little tricky to figure out what's going on during the newton-raphson iterations.
• the theory section of the user guide doesn't have any info about constraint algorithms.

The code is overall pretty ancient, I think. It would be nice to refresh it and add some documentation.

[jchodera]

+1

Also, would there be a correction applied to the manuscript (if the scaling is indeed critical)?

[rmcgibbo]

I think the scaling is just an optimization that absorbs some constants into the variable holding the inverse jacobian, but I'm not sure exactly how it all comes together.