Programming assignment No'1: Threaded Sparse Matrix Multiplication

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Programming assignment No.1 Threaded Sparse
Matrix Multiplication
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Objective

• Practice programming with threads
• Experience with practical issues in the steps for
  parallelization, in particular, load balancing.
• Write a parallel code that beats the state of the
  art production quality sequential code.

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Sparse matrix

• A matrix with a lot of zeros.
• Would work with dense matrix, but will be less
  efficient.

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Sparse matrix representation

• To get efficiency, one should only store and
  process non-zeros.
• Common Compressed Sparse Column (CSC) format and
  common Compressed Sparse Row (CSR) format.
• nonzero for data
• jc for row indices
• ir for the starting index
• of each column (CRC).

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CSC example

• How to find out the number of non-zeros in the
  matrix?
• SMGet(A, I, j)?
• SMPut(C, I, j, value)?

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The routine to be implemented

• A driver program will be provided so that you do
  not have to worry about I/O (main.c).
• But you will still need to learn the driver
  program.
• Internal array representations do not have to be
  CSC or CSR.
• E.g. a meshed linked lists (linked lists in two
  dimensions)

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A simple sparse matrix multiply algorithm

• void sparsemm (A, B, C)
• int I, j, k
• double tmp
• for (i0 ilta-gtrow i)
• for (j0 jltB-gtcol j)
• tmp 0.0
• for (k0 kltA-gtcol k)
• tmp smGet(A, I, k) smGet(B, k,
  j)
• smSet(C, I, j, tmp)

What is wrong with this? O(N4) algorithm for
Multiplying NxN matrices!
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A better algorithm

• sparsemm(A,B, C)
• int I, j
• double tmp
• triplet_item rowp, colp
• make AA, BB the meshed linked list
  representation for A and B
• for (i0 iltA-gtrow i)
• for(j0 jltB-gtcol j)
• rowp A-gtrowsi colp B-gtcolsj
• tmp 0
• while ((rowp!NULL) (colp !
  NULL))
• if (rowp-gtindex colp-gtindex)
  
• tmp rowp-gtvalue
  colp-gtvalue
• rowp rowp-gtnext colp
  colp-gtnext
• else if (rowp-gtindex lt
  colp-gtindex) rowp rowp-gtnext
• else colp colp-gtnext
• smset(CC, I, j, tmp)
• convert CC to C

This is a better algorithm. See the data
structures.
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For more information
For parallel sparse matrix multiply
For sequential sparse matrix multiply
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Grading

• Correctness and performance
• All program must be correct to get any points (a
  driver program is given so that you do not need
  to do I/O, just make sure your mm routines yields
  correct output format).
• 40 points for correct sequential code
• 20 points for 1.5x speedup compared to your own
  code for three large matrices on linprog
• 35 points for 1.5x speedup compared to the sample
  executable on linprog.
• Same code is based on the SMMP package from
  http//www.mgnet.org/douglas/ccd-free-software.ht
  ml
• 5 points for demo.

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Due dates

• Sept. 16, 1100am for sequential code
• Sept. 23, 1100am for threaded code
• Tar your project and send me the tar file (with
  makefile, README, and source code only).