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oclib: out of core optimization

Paul Sava

paul@sep.stanford.edu

My goal

• Quick introduction to the library

• Not much about inversion theory

• Ask the right questions

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Jon Claerbout’s optimization book

• Image estimation by example:Geophysical sounding image construction

Multidimensional autoregression

http://sepwww.stanford.edu/sep/prof

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Linear operators

dm LL: linear operator

m: image

d: data

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Linear operators

dm L

call operator_init(…)

stat=operator(adj,add,m,d)

m d L

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Least-squares inversion

dm *1* LLL

dm Ldmm

Lmin

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Simple inversion

R=Lm0-d

iterate {

g = L* R

G = L g

(m,R) <- step(m,R,g,G)

}

dm L m: model

d: data

L: physics

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Regularized inversion

0

dm

W

A

WL

W: weighting

A: regularization

: relative weight

dm L

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Preconditioned inversion

pm 1A

0

1 dp

W

I

WLA

p: preconditioned mdm L

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Why out-of-core optimization

• Least-squares imagingm: image

d: data

L: WE modeling operator

A: styling operator

W: weighting operator

• Velocity analysism: slowness perturbation

d: image perturbation

L: WE MVA operator

A: styling operator

W: weighting operator

0

dm

W

A

WL

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Linear operator example: WE MVA

stat = weimva(adj,add, dS,dR,SLop=weiop_sllN,SCop=weiop_bor1,WCop=weiop_mwcN,FKop=weiop_wem3,FXop=weiop_ssf3,IGop=weiop_hcig)

call weimva_init(SLin=weiop_sllN_init,SCin=weiop_bor1_init,

WCin=weiop_mwcN_init,FKin=weiop_wem3_init,FXin=weiop_ssf3_init,IGin=weiop_hcig_init)

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Outline

• Overview

• Solvers

• Examples

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Simple solver initdm L

R=Lm-diterate {

g=L* RG=L g(m,R) <- step(m,R,g,G)

}

call oc_mpi_solver_init (

impi,

ocniter,

ocmaxmem,

ocverb,

mmovie,

dmovie

)

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Simple solverdm L

R=Lm-diterate {

g=L* RG=L g(m,R) <- step(m,R,g,G)

}

call oc_mpi_solver (

L=weimva,

m_=dS,

d_=dR,

S=oc_cgstep,

op1=weiop_slo1,

op2=weiop_mwc1,

op3=weiop_bor1,

op4=weiop_wem3,

op5=weiop_ssf3,

op6=weiop_hcig

)

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Simple solverdm L

do i=1,ocniter

stat=L( T,F, g_, rd_, op1 … op9)

stat=L( F,F, g_, gd_, op1 … op9)

stat=S(forget,m_,g_,(/rd_/),(/gd_/),…)

end do

R=Lm-diterate {

g=L* RG=L g(m,R) <- step(m,R,g,G)

}

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Cluster executiondm L

do i=1,ocniter

stat=L( T,F, g_, rd_, op1 … op9)

stat=L( F,F, g_, gd_, op1 … op9)

stat=S(forget,m_,g_,(/rd_/),(/gd_/),…)

end do

R=Lm-diterate {

g=L* RG=L g(m,R) <- step(m,R,g,G)

}

mas

ter

node

1

node

2

node

3

node

4

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Solver with regularization

0

dm

W

A

WL

call oc_mpi_solverreg(L=weimva,m_=dS,d_=dR,A=oc_laplacian,S=oc_cgstep,op1=weiop_slo1,op2=weiop_mwc1,op3=weiop_bor1,op4=weiop_wem3,op5=weiop_ssf3,op6=weiop_hcig

)

paul@sep.stanford.edu

Solver with preconditioning

0

1 dp

W

I

WLA

call oc_mpi_solverpre(L=weimva,m_=dS,d_=dR,P=oc_ilaplacian,S=oc_cgstep,op1=weiop_slo1,op2=weiop_mwc1,op3=weiop_bor1,op4=weiop_wem3,op5=weiop_ssf3,op6=weiop_hcig

)

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Outline

• Overview

• Solvers

• Examples

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Example & Lab

• WE MVA for diffracted data• d: image perturbation• m: slowness perturbation

• Operator calls• forward: scattering mode• adjoint: backprojection mode

• Regularized inversion• model movie• data residual movie

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Example

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Example: d = Lm

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Example: m = L*d

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Example: m = [L*L+2A*A]-1L*d

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Iteration 1: Rd=d-Lm

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Iteration 2: Rd=d-Lm

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Iteration 3: Rd=d-Lm

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Iteration 4: Rd=d-Lm

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Iteration 5: Rd=d-Lm

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Summary

• Flexible, reusable f90 code

• Cluster ready

• Standard operator interface

• Conjugate-gradient solvers– Regularization– Preconditioning

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Resources (name@sep.stanford.edu)

• Developers:– Paul, Bob

• Manual– Marie

• Users– Antoine, Nick