Siddharth ManayChandrika 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.

Sapphire/SDM AHM/SM 2CASC

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

Sapphire/SDM AHM/SM 3CASC

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 SphericalTorus Experiment

Leveraging LDRD funding (CK); work done by Erick Cantu-Paz, Cyrus Harrison

Sapphire/SDM AHM/SM 4CASC

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 Islands Separatrix

Piecewise Polynomial Models for Classification of Puncture Plots

Sapphire/SDM AHM/SM 6CASC

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.

Sapphire/SDM AHM/SM 7CASC

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

Sapphire/SDM AHM/SM 8CASC

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.

Sapphire/SDM AHM/SM 9CASC

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

Gaps one two

ZeroQuasiperiodic

Separatrix

> Zero Islands

2 Polynomials2 Gaps Islands

2 Polynomials0 Gaps Separatrix

Sapphire/SDM AHM/SM 10CASC

Results

3995 points, Separatrix 250 points, 3 Islands

Puncture 1, node 79

Zoom around =1.6 Zoom around =1.6

Sapphire/SDM AHM/SM 17CASC

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