WIP Allow -E+n for modelnorm output

[PaulWessel]

See forum post for the origin of this PR.

Needs much work still - such as matching what the formum post seems to do?

[PaulWessel]

Can any of @GenericMappingTools/core see whaT I am missing repeatedly?

[wasjabloch]

I have successfully extracted the model variance using this branch. In order to plot an L-curve to determine the optimal number of singular values to use, I computed the data variance from the output grids as (python syntax):

datnorm = sqrt(sum(((pre - obs) / uncert) ** 2))

with predicted data values pre, observed data values obs and 1-sigma uncertainties (as supplied in the 4th column via -W) uncert.

It would be convenient to also output the data norm as an additional column into misfitfile.

During the course of my work, it turned out that the L-curve is not as easy to interpret as I wished to, so I ended up computing Akaikes Information Criterion (AIC)

aic = 2*k - 2*ln(L)

with number of singular values used k and the model likelihood L (of k). I assumed Gaussian uncertainties and computed L as:

L = product( exp(-(obs - pred)**2 /(2 * uncert)**2) / sqrt(2 * pi * uncert**2) )

The extra steps needed (apart from calculating the model norm modnorm) can all be done manually outside GMT. However, writing out all the grids and extracting pred can be quite time consuming, so it would be really nice if these metrics could be provided in dry-run mode, that is in concert with -C+n. I am unsure, however, if -C+n currently does allow to compute pred.

One glitch in the current implementation: modnorm should be sqrt(modnorm).

[PaulWessel]

Might you be able to submit a branch based off this one that implements what you describe?

[wasjabloch]

I could try getting started, but an important prerequisite would be to get the file output working. Until now, modnorm does not end up in misfitfile, but only 0s are written to the last column.

[PaulWessel]

OK, I have a fixed a bunch of issues:

1. modnorm is now sort (mod norm) and is written properly in the correct column.
2. The column headers are now written to output file

[PaulWessel]

I also merged in master so the branch is up to date with master plus the specific changes above.