I am fitting a 2D depth surface (z_mod) to some 170 data points (z_obs) using greenspline. To account for noise in the data, I’m using singular value decomposition to model the surface and am currently choosing a eigenvalue cut-off subjectively, using: gmt greenspline $dep -G$svd -L $R -Z2 -I$I -W -C+c -E$mis -V then plotting a bunch of the resulting files. I’d now like to arrive at a more objective cut-off value by plotting the famous “L-curve” (data variance vs. model variance), frequently used for determining the damping parameter in inverse problems: data variance ^ | | function of svd cut-off value | | | | | | | | | \ | \* Optimal damping | \_________________________ | +--------------------------------------- > model variance I can compute the data variance as sum((z_mod - z_obs)**2). However, I’m having problem plotting the model variance. Essentially, I’m unable to access the spline coefficients alpha in the greenspline source. I’ve tried various combinations of -E -C+f, but was unable to access the model parameters. Or am I overseeing something? Can I compute it from the eigenvalues (supplied by the -E option)? Best fix: Is it me, have I missed something? Dirty fix: Can I compile greenspline easily, so I can send alpha to stdout? Elegant fix: Would it be possible to implement e.g. an option -C+afile: “For each cutoff eigenvalue, write out the alpha coefficients to file (we automatically insert “###” before the extension, see +c and +i).”

Dear community I could compile the greenspline source without major issues and now have my private version in which I write out the model norm as an INFORMATION. for (e = 0; e < (uint64_t)n_use; e++) { /* Only loop over the first n_use eigenvalues (if restricted) */ GMT_Report (API, GMT_MSG_INFORMATION, "Evaluate spline for eigenvalue # %d\n", (int)e); gmt_M_memcpy (s, ssave, nm, double); /* Restore original values before call */ (void)gmt_solve_svd (GMT, A, (unsigned int)nm, (unsigned int)nm, v, s, b, 1U, obs, (double)e, GMT_SVD_EIGEN_NUMBER_CUTOFF); /* obs (hence alpha) now has the solution for the coefficients based on the first e eigenvalues */ for (k = 0; k < nm; k++) modnorm += obs[k] * obs[k]; GMT_Report (API, GMT_MSG_INFORMATION, "Used Eigenvalues, Model norm = %d, %g\n", e, modnorm); Thanks for the nicely maintained and commented source code and easy compilation instructions :slight_smile:

@pwessel : Is it worth implementing into gmt with an extra option now that @wsja has basically done it?

Looking at this, could your modnorm value be added as a column to the output file that -E sets? Would be pretty simple for me to add that, possibly via a -E modifier.

But first, why were you unable to use -C+f? Append +f file to save the eigenvalues to the specified file for further analysis

The eigenvalues is not what I need, I need the alphas, dependent on n_use. From C+f I get what I think would be what be the singular values (The diagonal elements of S, from G = USV^T; they are in the 1e18 - 1e0 range. I would expect the alphas to span at most 5 or 6 orders of magnitude). Moreover, I only get one set of e values (e = number of data points = number of model parameters), not e times e. [image] pwessel: Looking at this, could your modnorm value be added as a column to the output file that -E sets? Would be pretty simple for me to add that, possibly via a -E modifier. Yes, that would probably be the easiest one. In fact, two extra columns would be nice: model norm (as modnorm, above) and data norm (with the weights applied just as in the misfit function).

OK, got you this time. Let me see if I can whip out a branch for your testing,

[image] wsja: modnorm += *obs * *obs; I dont know what you mean here. obs is an array.

OK, that is what I did. See if you can test this branch and comment on what is missing: https://github.com/GenericMappingTools/gmt/pull/7358

I think there is some syntactical mishap: Should it be: -E+nfile (this throws an: [Session greenspline (0)]: Error returned from GMT API: GMT_ERROR_ON_FOPEN (15)) or -Efile+n (which does not recognize the +n flag, but simply appends an “+n” to the file name)

Syntax is -E[misfitfile][+n] There is no modifier to set the filename (existing syntax) but you gotta append the new modifier +n if you want effect.

Access greenspline's model coefficients

Q&A

pwessel April 4, 2023, 5:13pm 10

I dont know what you mean here. obs is an array.

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Access greenspline's model coefficients

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