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Parallel Multi-Reference Configuration Interaction on JAZZ. Ron Shepard (CHM) Mike Minkoff (MCS) Mike Dvorak (MCS). The COLUMBUS Program System. Molecular Electronic Structure Collection of individual programs that communicate through external files
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Parallel Multi-Reference Configuration Interaction on JAZZ Ron Shepard (CHM)Mike Minkoff (MCS)Mike Dvorak (MCS)
The COLUMBUS Program System • Molecular Electronic Structure • Collection of individual programs that communicate through external files • 1: Atomic-Orbital Integral Generation2: Orbital Optimization (MCSCF, SCF)3: Integral Transformation4: MR-SDCI5: CI Density6: Properties (energy gradient, geometry optimization)
Real Symmetric Eigenvalue Problem • Use the iterative Davidson Method for the lowest (or lowest few) eigenpairs • Direct CI: H is not explicitly constructed, w=Hv are constructed in “operator” form • Matrix dimensions are 104 to 109 • All floating point calculations are 64-bit
Davidson Method Generate an initial vector x1 MAINLOOP: DO n=1, NITER Compute and save wn = Hxn Compute the nth row and column of G = XTHX = WTX Compute the subspace Ritz pair: (G – 1) c = 0 Compute the residual vector r = W c – X c Check for convergence using |r|, c, , etc. IF (converged) THEN EXIT MAINLOOP ELSE Generate a new expansion vector xn+1 from r, , v=Xc, etc. ENDIF ENDDO MAINLOOP
Matrix Elements • Hmn = <m| Hop |n> • |n> = |(r1)1(r2)2 … (rn)n | with j=,
…Matrix Elements • hpq and gpqrs are computed and stored as arrays (with index symmetry) • <m|Epq|n> and <m|epqrs|n> are coupling coefficients; these are sparse and are recomputed as needed
Matrix-Vector Products • w = H x • The challenge is to bring together the different factors in order to compute w efficiently
Coupling Coefficient Evaluation • Graphical Unitary Group Approach (GUGA) • Define a directed graph with nodes and arcs: Shavitt Graph • Nodes correspond to spin-coupled states consisting of a subset of the total number of orbitals • Arcs correspond to the (up to) four allowed spin couplings when an orbital is added to the graph
…Coupling Coefficient Evaluation graph head Internal orbitals w,x,y,z External orbitals graph tail
Integral Types • 0: gpqrs • 1: gpqra • 2: gpqab, gpa,qb • 3: gpabc • 4: gabcd
Original Program (1980) • Need to optimize wave functions for Ncsf=105 to 106 • Available memory was typically 105 words • Must segment the vectors, v and w, and partition the matrix H into subblocks, then work with one subblock at a time.
…First Parallel Program (1990) • Networked workstations using TCGMSG • Each matrix subblock corresponds to a compute task • Different tasks require different resources (pay attention to load balancing) • Same vector segmentation for all gpqrs types • gpqrs, <m| epqrs |n>, w, and v were stored on external shared files (file contention bottlenecks)
Current Parallel Program • Eliminate shared file I/O by distributing data across the nodes with the GA Library • Parallel efficiency depends on the vector segmentation and corresponding H subblocking • Apply different vector segmentation for different gpqrs types • Tasks are timed each Davidson iteration, then sorted into decreasing order and reassigned for the next iteration in order to optimize load balancing • Manual tuning of the segmentation is required for optimal performance • Capable of optimizing expansions up to Ncsf=109
Mike Dvorak, Mike Minkoff MCS Division Ron Shepard Chemistry Division Argonne National Lab COLUMBUS-PetaflopsApplication
Notes on software engineering • PCIUDG parallel code • Fortran 77/90 • Compiled with Intel/Myrinet on Jazz • 70k lines in PCIUDG • 14 files containing ~205 subroutines • Versioning system • Currently distributed in a tar file • Created a LCRC CVS repository for personal code mods
Notes on Software Engineering (cont) • Homegrown preprocessing system • Uses “*mdc*if parallel” statements to comment/uncomment parts of the code • Could/should be replaced with CPP directives • Global Arrays library • Provides global address space for matrix computation • Used mainly for chemistry codes but applicable for other applications • Ran with most current version --> no perf gain • Installed on Softenv on Jazz (version 3.2.6)
Gprof Output • 270 subroutines called • loopcalc subroutine using ~20% of simulation time • Added user defined MPE states to 50 loopcalc calls • Challenge due to large number of subroutines in file • 2 GB file size severe limiter on number of procs • Broken logging • Show actual output
Live Demo of a 20 proc run Jumpshot/MPE Instrumentation
Using FPMPI • Relinked code with FPMPI • Tell you total number of MPE calls made • Output file size smalled (compared to other tools i.e. Jumpshot) • Produces a histogram of message sizes • Not installed in Softenv on Jazz yet • ~riley/fpmpi-2.0 • Problem for runs • Double Zeta C2H4 without optimizing the load balance
COLUMBUS Performance Data R. Shepard, M. Dvorak, M. Minkoff
