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Rigo Dicochea University of California at Santa Cruz Research Advisor: Dr. Donald Gavel Research Supervisor: Marc Reinig. A Matrix Multiplication Implementation for Pre-Conditioning Back Propagated Errors on a Multi-Conjugate Adaptive Optics System. Mission Statement. - PowerPoint PPT Presentation
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Rigo DicocheaRigo Dicochea
University of California at Santa CruzUniversity of California at Santa Cruz
Research Advisor: Dr. Donald GavelResearch Advisor: Dr. Donald Gavel
Research Supervisor: Marc ReinigResearch Supervisor: Marc Reinig
A A Matrix Multiplication Implementation for Matrix Multiplication Implementation for Pre-Conditioning Back Propagated Errors Pre-Conditioning Back Propagated Errors
on a Multi-Conjugate Adaptive Optics on a Multi-Conjugate Adaptive Optics SystemSystem
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Mission StatementMission Statement
The goal is to implement a matrix multiplication on a The goal is to implement a matrix multiplication on a Field Programmable Gate Array (FPGA) to reduce Field Programmable Gate Array (FPGA) to reduce the total number of iterations necessary to solve a the total number of iterations necessary to solve a system of equations with unknown variables. system of equations with unknown variables.
Without AO With AO
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Background/Iterative ApproachBackground/Iterative Approach
Light Rays from Excited Sodium Ions
However, since each of these rays passes through different voxels, the total effect of the atmosphere on each of them is different.
We propagate our initial estimate of phase delay through each voxel.
Photo credit: Marc Reinig
A
B
C
D
E =
Possibly take 100’s of iteration to converge!
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Evolution of ProjectEvolution of Project A
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C
D
E =
State Machine
Hardware
Resources
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State Machine for Matrix State Machine for Matrix MultiplicationMultiplication
mult1by11
alu_input = ^b0001;
mult1by21
alu_input = ^b0001;
store1x11
alu_input = ^b0000;
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Pre-Conditioning ImplementationPre-Conditioning Implementation
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Resources Utilized Resources Utilized
208 FPGA Slices208 FPGA Slices– 18 Registers18 Registers– 1 ALU1 ALU– Control Logic/GatesControl Logic/Gates– MultiplexorMultiplexor– MANY Bus Lines(wires interconnecting different MANY Bus Lines(wires interconnecting different
hardware)hardware)
6 Virtex 4 FPGA’s
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TimingTiming
Initial Simulations yield a timing constraint of Initial Simulations yield a timing constraint of 200MHz.200MHz.
Must be able to converge in less than 1 milli-Must be able to converge in less than 1 milli-second.second.
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RESULTS!!RESULTS!!
Previous iterative solutions took in excess of Previous iterative solutions took in excess of 90 iterations to converge.90 iterations to converge.
With Matrix Multiplication/Pre-Conditioning With Matrix Multiplication/Pre-Conditioning we NOW converge in approximately 25 to we NOW converge in approximately 25 to 50 iterations!50 iterations!
A reduction of 50 to 75 iterations!A reduction of 50 to 75 iterations!
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What's Next?What's Next?
Implement fast Fourier transform which will Implement fast Fourier transform which will allow for more accurate convergent values.allow for more accurate convergent values.
Multiplex existing hardware to reduce Multiplex existing hardware to reduce resource consumption and cost.resource consumption and cost.
Determine the total number of FPGA’s Determine the total number of FPGA’s necessary to implement system on TMT necessary to implement system on TMT size telescope. size telescope.
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Illustration of Matrix Benefit Illustration of Matrix Benefit
CEV # 1
CEV # 2
CEV # 3
general solution space
reduced solution space due to reduced set of equations
post-processing (CN2)
-algorithm guarantees a solution set that satisfies the set of equations, but not necessarily the actual solution set
-post-processing data brings us closer to the actual solution set
actual solution set
No post-processing
Post-processing with CN2
Post-processing with CN2 and FFT
Iteration 1
CEV # 1
CEV # 2
CEV # 3
general solution space
reduced solution space due to reduced set of equations
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AcknowledgmentsAcknowledgments
Lab for Adaptive OpticsLab for Adaptive Optics– Dr. Don GavelDr. Don Gavel– Marc ReinigMarc Reinig– ATMAOS Project Leader Carlos Andres CabreraATMAOS Project Leader Carlos Andres Cabrera
Center for Adaptive OpticsCenter for Adaptive Optics XilinxXilinx
This project is supported by the National Science Foundation Science and Technology Center for Adaptive Optics, managed by the University of California at Santa Cruz under cooperative agreement No. AST - 9876783.
