1. Siddharth Manay Chandrika Kamath Center for Applied Scientific Computing 2 March 2005 Progress Report on Data Analysis Work at LLNL: Aug’04 - Feb’05 http://www.llnl.gov/casc/sapphire/ UCRL-PRES-209947-DRAFT This work was performed under the auspices of the U.S. Department of Energy by University of California Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48.

2. Sapphire/SDM AHM/SM 2 CASC Our progress on earlier applications Feature selection for EHOs (data from DIII-D) — IDL code + instructions transferred to Keith@GAT — visit to GAT + talk — interest in licensing Sapphire software — sample scenario ready for the web Separation of signals in climate data — a standalone C++ code available which uses our libraries for PCA/ICA — to be used in illustrating creation of workflows — sample scenario ready for the web Work done by Erick Cantu-Paz, Imola K. Fodor, Abel Gezahegne, Nu Ai Tang

3. Sapphire/SDM AHM/SM 3 CASC New application: tracking in NSTX data Joint work with PPPL (Klasky) Problem: track the plasma over time IDL code implementing a variant of block matching is too slow Prototyping other block-matching approaches National Spherical Torus Experiment Leveraging LDRD funding (CK); work done by Erick Cantu-Paz, Cyrus Harrison

4. Sapphire/SDM AHM/SM 4 CASC Joint work with PPPL (Klasky, Pomphrey, Monticello) Classify each of the nodes: quasiperiodic, islands, separatrix Connections between the nodes Want accurate and robust classification, valid when few points in each node New application: classification of puncture (Poincaré) plots for NCSX National Compact Stellarator Experiment Quasiperiodic IslandsSeparatrix

5. Piecewise Polynomial Models for Classification of Puncture Plots

6. Sapphire/SDM AHM/SM 6 CASC Polar Coordinates Transform the (x,y) data to Polar coordinates (r,  ). Advantages of polar coordinates: —Radial exaggeration reveals some features that are hard to see otherwise. —Automatically restricts analysis to radial band with data, ignoring inside and outside. —Easy to handle rotational invariance.

7. Sapphire/SDM AHM/SM 7 CASC Piecewise Polynomial Fitting: Dividing data into intervals. Use the  -histograms to find intervals. Need to divide the  domain into intervals that are: —Restricted to regions of  that have data. —Small enough so that polynomial will fit the data. —Large enough to span gaps where data is missing

8. Sapphire/SDM AHM/SM 8 CASC Piecewise Polynomial Fitting: Computing polynomials In each interval, compute the polynomial coefficients to fit 1 polynomial to the data. If the error is high, split the data into an upper and lower group. Fit 2 polynomials to the data, one to each group. Blue: data. Red: polynomials. Black: interval boundaries.

9. Sapphire/SDM AHM/SM 9 CASC Classification The number of polynomials needed to fit the data and the number of gaps gives the information needed to classify the node: Number of polynomials Gapsonetwo Zero Quasiperiodic Separatrix > ZeroIslands 2 Polynomials 2 Gaps  Islands 2 Polynomials 0 Gaps  Separatrix

10. Sapphire/SDM AHM/SM 10 CASC Results 3995 points, Separatrix250 points, 3 Islands Puncture 1, node 79 Zoom around  =1.6

11. Sapphire/SDM AHM/SM 11 CASC Results Puncture 1, node 11582 points, 13 Islands100 points, 13 Islands Puncture 1, node 17883 points, Quasiperiodic100 points, Quasiperiodic

12. Sapphire/SDM AHM/SM 12 CASC Results Puncture 1, node 462339 points, 1 Island250 points, 2 Islands Puncture 1, node 743744 points, Quasiperiodic500 points, Quasiperiodic

13. Sapphire/SDM AHM/SM 13 CASC Results Puncture 2, node 75500 points, 1 Island3795 points, Separatrix

14. Sapphire/SDM AHM/SM 14 CASC Results Puncture 2, node 422138 points, Separatrix750 points, Separatrix Puncture 2, node 592991 points, Separatrix250 points, Quasiperiodic

15. Sapphire/SDM AHM/SM 15 CASC Results 4548 points, 3 Islands500 points, 4 Islands Puncture 1, node 90 Zoomed around  =1.6

16. Sapphire/SDM AHM/SM 16 CASC Results 4899 points, Separatrix750 points, 1 Island Puncture 1, node 97 Zoomed around  =1.6

17. Sapphire/SDM AHM/SM 17 CASC Future work Set up web pages for climate and fusion scenarios NSTX data: continue building and testing block- matching algorithms NCSX data — continue interactions with Neil, Don, Scott — continue to refine and validate approach — investigate ways of making it more robust — investigate exploiting nearby nodes — design and implement in C++ for insertion into PPPL analysis pipeline