Data Structures and Performance for Scientific Computing with Hadoop and Dumbo
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1 Data Structures and Performance for Scientific Computing with Hadoop and Dumbo Austin R. Benson Computer Sciences Division, UC-Berkeley ICME, Stanford University May 15, 2012
2 1 1 Matrix storage 2 Data 3 Example: outputting many small matrices 4 Example: Cholesky QR
3 Dense matrix storage A = How do we store the matrix in HDFS?
4 Dense matrix storage A = In HDFS: 1, [11, 12, 13, 14] 2, [21, 22, 23, 24] 3, [31, 32, 33, 34] 4, [41, 42, 43, 44]
5 Two rows per record or we might use: 1, [[11, 12, 13, 14], [21, 22, 23, 24]] 3, [[31, 32, 33, 34], [41, 42, 43, 44]]
6 Flattened list or maybe 1, [11, 12, 13, 14, 21, 22, 23, 24] 3, [31, 32, 33, 34, 41, 42, 43, 44]... but we do lose information here (maybe it s not important)
7 Full matrix or maybe 1, [[11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], [41, 42, 43, 44]]
8 What is the best way?
9 What is the best way? Depends on the application... we will look at an example later.
10 2 1 Matrix storage 2 Data 3 Example: outputting many small matrices 4 Example: Cholesky QR
11 Data Serialization Small optimizations 2.5x speedup! *all data from the NERSC Magellan cluster
12 Data Serialization Same experiment but different matrix size (200 columns): Again, 2.5x speedup!
13 Languages Switching from Python to C++... same general trend
14 More speedups Algorithm performance isn t the only place where we see speedups
15 Why can we expect these speedups? These are not high-performance implementations. We care about I/O performance.
16 3 1 Matrix storage 2 Data 3 Example: outputting many small matrices 4 Example: Cholesky QR
17 Suppose we need to write many small matrices to disk.
18 Code Code: git clone git://github.com/icme/mapreduce-workshop.git cd mapreduce-workshop/arbenson Files: speed test.py (tester) small matrix test.py (driver)
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23 4 1 Matrix storage 2 Data 3 Example: outputting many small matrices 4 Example: Cholesky QR
24 Algorithm Cholesky QR: R = chol(a T A, upper )
25 Implementation for MapReduce
26 Mapper implementation Which of these implementations is better?
27 Mapper implementation Which of these implementations is better? Answer: the one on the left (usually)
28 Why? 1 Shuffle time 2 Reduce bottleneck However, the left implementation could run out of memory.
29 Mapper implementation Can we do better? Yes
30 Questions? Austin R. Benson
TSQR, A t A, Cholesky QR, and Iterative Refinement using Hadoop on Magellan
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