Feature/wjiang/sphere pert

[weiyuan-jiang]

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[weiyuan-jiang]

[weiyuan-jiang]

Sphere Perturbation Performance Results

• Benchmark grid: 720 longitude by 360 latitude points (0.5 degree)
• MPI ranks: 40

Measurements

xcorr/ycorr	Filter order	Sphere filter build	Sphere field draw
2 degrees	Mord=1	7.6359 s	0.2725 s
10 degrees	Mord=2	0.0624 s	0.2566 s

Both generated sphere fields had zero mean to displayed precision and unit
standard deviation. The 2-degree field had range -3.89724 to 4.21915; the
10-degree field had range -3.05700 to 3.23377.

Realization Figure Runs

The realization figures were generated with four MPI ranks using the same
720 by 360 grid. These are the timings from the runs that produced
compare_pert_xcorr2.png and compare_pert_xcorr10.png.

xcorr/ycorr	Rectangle build	Rectangle draw	Sphere build	Sphere draw
2 degrees	0.0206 s	0.0251 s	12.1048 s	0.2158 s
10 degrees	0.0313 s	0.0277 s	0.0201 s	0.0645 s

Optimization

xcorr=2 switches to the stable Mord=1 direct-Legendre covariance path.
The current implementation distributes m-mode covariance and Cholesky work
across node-local MPI ranks and stores factors in shared memory. Previous
40-rank measurements for the non-distributed full-covariance path were about
119 seconds to build; the current 40-rank build is about 7.6 seconds.

[weiyuan-jiang]

=== pert_statistics: recovered xcorr from generated fields ===
grid=720x360, MPI ranks=4
samples per rank=64
rectangle_random_fields: target= 2.00 deg, samples=256,
recovered xcorr= 1.984 deg (error= -0.016 deg)
build_sphere_filter: |Im(root)|= 911.7 > threshold; using direct Legendre covariance (Mord=1, stable)
sphere_random_fields: target= 2.00 deg, samples=256,
recovered xcorr= 1.989 deg (error= -0.011 deg)
rectangle_random_fields: target= 10.00 deg, samples=256,
recovered xcorr= 9.728 deg (error= -0.272 deg)
sphere_random_fields: target= 10.00 deg, samples=256,
recovered xcorr= 10.800 deg (error= 0.800 deg)