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Structure of TCE So Hirata Pacific Northwest National Laboratory

Structure of TCE - LSUgb/TCE/Documentation/TCEtutorial.pdf · How TCE works ––– overview TCE derives working equations for a second quantized many-electron theory TCE is written

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Page 1: Structure of TCE - LSUgb/TCE/Documentation/TCEtutorial.pdf · How TCE works ––– overview TCE derives working equations for a second quantized many-electron theory TCE is written

Structure of TCE

So HirataPacific Northwest National Laboratory

Page 2: Structure of TCE - LSUgb/TCE/Documentation/TCEtutorial.pdf · How TCE works ––– overview TCE derives working equations for a second quantized many-electron theory TCE is written

This presentation will address

How TCE worksHow TCE-generated programs workHow TCE can be usedHow TCE can be enhancedOther sources of information

Page 3: Structure of TCE - LSUgb/TCE/Documentation/TCEtutorial.pdf · How TCE works ––– overview TCE derives working equations for a second quantized many-electron theory TCE is written

How TCE works ––– overview

TCE derives working equations for a second quantized many-electron theory

TCE is written in Python® programming language

TCE implements the working equations into parallel programs

For the NWChem© QC software suiteUsing ParSoft© Library

Page 4: Structure of TCE - LSUgb/TCE/Documentation/TCEtutorial.pdf · How TCE works ––– overview TCE derives working equations for a second quantized many-electron theory TCE is written

How TCE works ––– supported models

CISD MBPT(2)CCSDTEOM-CCSDCCSD lambda equation

CCSD dipole moments

( )( ) ( )( )[ ] PRRTTHHLLQ LC /10212110 ......exp... +++++++

( )( ) ( )ORRDEORRHHD 212121 +=++

( )( ) ( ) 02211 =++ OHDORRHD

( ) ( )[ ] 0exp 32121 =+++ OTTTHHT C

( ) ( )( )[ ] 0exp 112121 =+++ ORRTTHHD C

( ) ( ) ( )[ ][ ] 0exp1 212121 =++++ DTTHHLLO LC

( ) ( ) ( )[ ] 121121 exp1 HOTTHLLO C =+++

Page 5: Structure of TCE - LSUgb/TCE/Documentation/TCEtutorial.pdf · How TCE works ––– overview TCE derives working equations for a second quantized many-electron theory TCE is written

How TCE works ––– formula derivationInput a WFT model ansatz

Contraction of a creation and an annihilation operator

Identify equivalent terms and merge them together

Erase terms that will lead to vanishing contributions

FullyContracted?

Extract permutation operators

NOYES

Delete disconnected/unlinked terms

Working equations

Page 6: Structure of TCE - LSUgb/TCE/Documentation/TCEtutorial.pdf · How TCE works ––– overview TCE derives working equations for a second quantized many-electron theory TCE is written

How TCE works ––– program synthesis

Input WFT working equations

Strength reduction: X=ABCD → X=((BC)A)D

Factorization: X=AB+AC → X=A(B+C)

Intermediate reuse: X=AB+C(AB) → Y=AB, X=Y+CY

Operation Tree

Determine permutation symmetry of intermediates

Analyze the use of permutation symmetry in contraction

Generate Fortran77/Fortran90 programs

Page 7: Structure of TCE - LSUgb/TCE/Documentation/TCEtutorial.pdf · How TCE works ––– overview TCE derives working equations for a second quantized many-electron theory TCE is written

How TCE-generated programs work ––– challenges

Use of spin & spatial symmetry in tensor storage & contractionUse of permutation symmetry in tensor storage & contractionPermutation symmetry of intermediatesAbstraction of theoriesMemory managementScalablility to massively parallel regime

Page 8: Structure of TCE - LSUgb/TCE/Documentation/TCEtutorial.pdf · How TCE works ––– overview TCE derives working equations for a second quantized many-electron theory TCE is written

How TCE-generated programs work ––– permutation symmetry

Reduced storage size

Reduced operation cost

baji

abij tt <

<⇒

∑∑<

<<

<<⇒

dc

badc

dcji

cd

abcd

cdij vtvt 2

Page 9: Structure of TCE - LSUgb/TCE/Documentation/TCEtutorial.pdf · How TCE works ––– overview TCE derives working equations for a second quantized many-electron theory TCE is written

How TCE-generated programs work ––– intermediates

With no de-excitation (L) operator

With a de-excitation (L) operator

pn

qm

ggggggggi

lLlllL

lLlllL

<<<<<<<<′<<′<′<′′<<′<′<′

321321

321321

,,

ppn

qqm

pppphhhhggggpppphhhhggggi

<<<<<<<<<<<<′<<′<′<′′<<′<′<′′<<′<′<′

LLL

LLL321321321

321321321

,,,,

Page 10: Structure of TCE - LSUgb/TCE/Documentation/TCEtutorial.pdf · How TCE works ––– overview TCE derives working equations for a second quantized many-electron theory TCE is written

How TCE-generated programs work ––– spin & spatial symmetries

Spin symmetry

Spatial symmetry

∑∑ =indices

antContravariindices

Covariant

qq

pp ss

0

Iindices

Γ=Γ∏p

p

Page 11: Structure of TCE - LSUgb/TCE/Documentation/TCEtutorial.pdf · How TCE works ––– overview TCE derives working equations for a second quantized many-electron theory TCE is written

How TCE-generated programs work ––– tiling algorithm

DO iDO jIF (i>j)IF X(ij) IS NONZEROARITHMETIC

DO I (i1~i2)DO J (j1~j2)IF (I>J)IF X(IJ) IS NONZERODO iDO jARITHMETIC

IFIFIFIFIFIFIFIF

IFIFIFIFIFIFIFIF

IFIFIFIFIFIFIFIF

IFIFIFIFIFIFIFIF

IFIFIFIFIFIFIFIF

IFIFIFIFIFIFIFIF

IFIFIFIFIFIFIFIF

IFIFIFIFIFIFIFIF

IFIFIFIF

IFIFIFIF

IFIFIFIF

IFIFIFIF

Page 12: Structure of TCE - LSUgb/TCE/Documentation/TCEtutorial.pdf · How TCE works ––– overview TCE derives working equations for a second quantized many-electron theory TCE is written

How TCE-generated programs work ––– tiling algorithm

Spin, spatial, and permutation symmetriesNear-operation-minimumRuntime adjustment of peak memory sizeGranularity of dynamic load balancing parallelism

Page 13: Structure of TCE - LSUgb/TCE/Documentation/TCEtutorial.pdf · How TCE works ––– overview TCE derives working equations for a second quantized many-electron theory TCE is written

How TCE can be used –––preliminary

Use a Windows or LINUX machineDownload the latest Python® from www.python.org (free)

TCE codes (aee.py, ccc.py, oce.py, tce.py) will runObtain the latest NWChem development version for interfacing and running the TCE-generated codes

Minor modification of TCE’s code generator & development of interface will permit other QC software suites than NWChem

Page 14: Structure of TCE - LSUgb/TCE/Documentation/TCEtutorial.pdf · How TCE works ––– overview TCE derives working equations for a second quantized many-electron theory TCE is written

How TCE can be used ––– GUI based

Page 15: Structure of TCE - LSUgb/TCE/Documentation/TCEtutorial.pdf · How TCE works ––– overview TCE derives working equations for a second quantized many-electron theory TCE is written

How TCE can be used ––– text basedcf) Auer’s presentation

Page 16: Structure of TCE - LSUgb/TCE/Documentation/TCEtutorial.pdf · How TCE works ––– overview TCE derives working equations for a second quantized many-electron theory TCE is written

How TCE can be enhanced –––limitations of TCE

Tested for ...CC up to CCSDTQ, CI up to CISDTQ, ‘generalized’ MBPT up to MBPT(4), CC Λ up to CCSDTQ, EOM-CC (right & left) up to EOM-CCSDTQ

Anything else will probably need some workBut far less than a full manual implementation would!cf) Sadayappan’s presentation

Page 17: Structure of TCE - LSUgb/TCE/Documentation/TCEtutorial.pdf · How TCE works ––– overview TCE derives working equations for a second quantized many-electron theory TCE is written

How TCE can be enhanced –––collaborations

Join our effort!Partner with existing members (quantum chemists or computer scientists) to realize your new methods much more quicklyex) Professor Rodney Bartlett & Mr. Igor Schweigert ––– CC analytical derivativesex) Professor Piotr Piecuch, Dr. Karol Kowalski, Professor Mark S. Gordon –––Novel CC & EOM-CC methodsex) Professor Kimihiko Hirao, Dr. Takeshi Yanai ––– Relativistic correlation theories

Page 18: Structure of TCE - LSUgb/TCE/Documentation/TCEtutorial.pdf · How TCE works ––– overview TCE derives working equations for a second quantized many-electron theory TCE is written

Other sources of informationPapers

G. Baumgartner et al. Proc. Supercomp. (2002) [Performance optimization aspects]D. Cociorva et al. Lect. Notes Comput. Sci. 2228, 237 (2001). [Performance optimization aspects]S. Hirata, J.Phys.Chem.A 107, 9887 (2003) [TCE specs, and CISDTQ, CCSDTQ, MBPT(4) applications]S. Hirata et al., J.Chem.Phys. 120, 3297 (2004) [DK3 relativistic CCSDTQ applications]S. Hirata, submitted [EOM-CCSDTQ applications]

Webpagehttp://www.cis.ohio-state.edu/~gb/TCE/

TCE Manual

Page 19: Structure of TCE - LSUgb/TCE/Documentation/TCEtutorial.pdf · How TCE works ––– overview TCE derives working equations for a second quantized many-electron theory TCE is written

Acknowledgements

U.S. Department of EnergyNational Science Foundation

Professor Rodney J. BartlettDr. Wibe A. de JongDr. Michel DupuisProfessor Kimihiko HiraoDr. Takahito NakajimaDr. Jarek NieplochaDr. Theresa L. Windus Dr. Takeshi Yanai