Improve the accuracy of wave_queue::compute_offsets().

[campreilly]

Using folds in the wavefront to detect edges produces better results in surface ducts, but creates accuracy problems for the pedersen deep tests. The problems with propagation loss accuracy has been traced to problems in the accuracy of the inverse Hessian method currently used by compute_offsets. Investigate other methods.

[campreilly]

Investigating options on the improve_offset branch (efcb444fe457e2a45a05d8e3aa005efdd0cb8f1f).

Our current scheme is basically a one step Newton Raphson method (http://en.wikipedia.org/wiki/Newton%27s_method_in_optimization). When the distance squared is a smoothly varying function of travel time, launch D/E, and launch AZ (in neighborhood around the CPA) this method should provide us with a very accurate answer. But, there are known shortcomings and that seesms to be the source of our problems.

We are investigating iterative schemes like the Golden Sector Search (http://en.wikipedia.org/wiki/Golden_section_search) and Brent's Method (http://en.wikipedia.org/wiki/Brent%27s_method) as alternatives.

[campreilly]

We have prototyped both the Golden Sector Search and Brent's Method in Matlab, and they hold promise. Our next steps are:

• Implement Golden Sector Search in a unit test, using our specific case, just to work out the kinks of moving it to C++.
• Create a new class that implements a generalized Golden Sector Search.
• Integrate the Golden Sector Search into wave_queue::compute_offsets().
• Test the accuracy and speed of WaveQ3D using the Golden Sector Search.
• Create a new class that builds on Golden Sector Search to create Brent's Method.

[campreilly]

There were several iterations of this that exposed small errors in the solution. Before declaring success, we performed extensive re-testing:

• Linux Debug mode
  • Re-ran ray_speed, usml_test. eigneray_extra_test, pedersen test. No errors detected, but did not run Matlab tests.
• Linux Release mode
  • Re-ran ray_speed and cmp_speed and found that they are slightly faster (7.34 and 6.28 sec respectively on Sean's computer) than the last time we computed these benchmarks.
  • Re-ran usml_test. eigneray_extra_test, pedersen test. No errors detected, but did not run Matlab tests.
• Linux Release with valgrind memcheck
  • ray_speed -> no leaks are possible
  • usml_test -> boost::unit_test seems to leak 8 bytes, but our stuff has no leaks. We feel this is acceptable
• Doxygen on linux runs with no errors
• Re-based to squash update using Linux and moved over to Windows testing
• In Visual C++ 10.0, batch build the INSTALL target in both Release and Debug
• Windows Debug
  • Re-ran ray_speed, usml_test. eigneray_extra_test, pedersen test. No errors detected, but did not run Matlab tests.
  • The pedersen_deep_sensitivity test took well over 15 mins in Debug mode. That must b why is was commented out in last release.
• Windows Release
  • Re-ran ray_speed and cmp_speed and found that they are significantly slower (11.29 and 11.63 sec respectively on Sean's computer) than the same benchmarks on the Linux virtual machine.
  • Re-ran usml_test. eigneray_extra_test, pedersen test. No errors detected,
• Matlab testing of waveq3d module
  • proploss_test
  • Lloyd's mirror vs. range as good as original test report.
  • Lloyd's mirror vs. depth significantly better than original test report.
  • refraction_surface_duct test
  • select AZ=0 and DE <= +/- 3.8311 to limit display to rays trapped in the duct.
  • Using the "follow" option and marching forward in time allow you to visualize the select of on_edge points.
  • Most other waveq3d tests produce results consistent with original test report.
  • refraction_test
  • reflect_loss_range_freq
  • eigneray_basic_raytrace
  • eigenray_concave_raytrace
  • munk_raytrace
  • proploss_llyods_range_raytrace
  • proploss_llyods_depth_raytrace
• Matlab testing of eigenray_extra_test study
  • The eigenray_lloyds.m results are similar to those the report, but accuracies are a factor of 10 worse than shown in the original test report.
  • But, they no longer have increased errors at short ranges.
  • The eigneray_lloyds_zoom has a finer ray fan than in the original test report, so the range scale had to be decreased.
• Matlab testing of pedersen study
  • The pedersen_shallow_compare and pedersen_deep_compare both show results that are as good or better than the original test report.
  • The pedersen_shallow_raytrace and pedersen_deep_raytrace also worked fine.
  • The pedersen_deep_sensitivity showed signicant errors for ray spacing finer than 0.1 deg. But this is similar to what was seem in eariler tests.