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An Overview of : Packages for Parallel Formulation and Solution of Scientific and Engineering Problems Michael A. Heroux Sandia National Laboratories CScADS Workshop, July-August 2007

Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under contract DE-AC04-94AL85000. 31-July-07

Trilinos Contributors Dennis Ridzal Chris Baker Robert Hoekstra Lead Developer of Aristos Developer of Anasazi, RBGen Lead Developer of EpetraExt Developer of Epetra, Thyra, Tpetra Marzio Sala Ross Bartlett Lead Developer of Didasko, Galeri, IFPACK, WebTrilinos Lead Developer of MOOCHO, Stratimikos, RTOp, Russell Hooper Developer of ML, Amesos Thyra Developer of NOX Developer of Rythmos Andrew Salinger Vicki Howle Lead Developer of LOCA, Capo Paul Boggs Lead Developer of Meros Developer of Thyra Developer of Belos and Thyra Paul Sexton Developer of Epetra and Tpetra Erik Boman Jonathan Hu Lead Developer Isorropia Developer of ML Bob Shuttleworth Developer of Meros. Todd Coffey Sarah Knepper Lead Developer of Rythmos Developer of Komplex Chris Siefert Developer of ML Jason Cross Tammy Kolda Developer of Jpetra Lead Developer of NOX Bill Spotz Lead Developer of PyTrilinos David Day Joe Kotulski Developer of Epetra, New_Package Developer of Komplex Lead Developer of Pliris Ken Stanley Clark Dohrmann Rich Lehoucq Lead Developer of Amesos and New_Package Lead developer of CLAPS Developer of Anasazi and Belos Heidi Thornquist Michael Gee Kevin Long Lead Developer of Anasazi, Belos, RBGen and Teuchos Developer of ML, Moertel, NOX Lead Developer of Thyra Developer of Belos and Teuchos Ray Tuminaro Bob Heaphy Lead Developer of ML and Meros Lead developer of Trilinos SQA Roger Pawlowski Lead Developer of NOX Jim Willenbring Mike Heroux Developer of Epetra and New_Package. Trilinos Project Leader Michael Phenow Trilinos library manager Lead Developer of Epetra, AztecOO, Trilinos Webmaster Kokkos, Komplex, IFPACK, Thyra, Tpetra Lead Developer of New_Package Alan Williams Developer of Amesos, Belos, EpetraExt, Jpetra, Developer WebTrilinos Lead Developer Isorropia Teuchos Developer of Epetra, EpetraExt, AztecOO, Tpetra Eric Phipps Ulrich Hetmaniuk Lead developer Sacado Developer of Anasazi Developer of LOCA, NOX

1 3

Background/Motivation

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4 Target Problems: PDES and more…

Circuits

PDES

Inhomogeneous Fluids

And More… 31-July-07

2 5 Target Platforms: Any and All (Now and in the Future) ƒ Desktop: Development and more… ƒ Capability machines: Š Redstorm (XT3) , Clusters Š BG/L. Š Large-count multicore nodes. ƒ Parallel software environments: Š MPI of course. Š UPC, CAF, threads, vectors,… Š Combinations of the above. ƒ User “skins”: Š ++/C, Python Š . Š Web, CCA.

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6 Motivation For Trilinos ƒ Sandia does LOTS of solver work. ƒ When I started at Sandia in May 1998: Š Aztec was a mature package. Used in many codes. Š FETI, PETSc , DSCPack , Spooles , ARPACK , DASPK , and many other codes were (and are) in use. Š New projects were underway or planned in multi-level preconditioners, eigensolvers, non-linear solvers, etc… ƒ The challenges: Š Little or no coordination was in place to: • Efficiently reuse existing solver technology. • Leverage new development across various projects . • Support solver software processes. • Provide consistent solver APIs for applications. Š ASCI (now ASC) was forming software quality assurance/engineering (SQA/SQE) requirements: • Daunting requirements for any single solver effort to address alone.

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3 7 Evolving Trilinos Solution ƒ Trilinos1 is an evolving framework to address these challenges: Š Fundamental atomic unit is a package. Š Includes core set of vector, graph and matrix classes (Epetra/Tpetra packages). Š Provides a common abstract solver API (Thyra package). Š Provides a ready-made package infrastructure (new_package package): • Source code management (cvs, bonsai). • Build tools (autotools). • Automated regression testing (queue directories within repository). • Communication tools (mailman mail lists). Š Specifies requirements and suggested practices for package SQA. ƒ In general allows us to categorize efforts: Š Efforts best done at the Trilinos level (useful to most or all packages). Š Efforts best done at a package level (peculiar or important to a package). Š Allows package developers to focus only on things that are unique to their package.

1. Trilinos loose translation: “A string of pearls” 31-July-07

8 Continued Evolution

ƒ New capabilities extend scope: Š Sacado: AD Tools. (E. Phipps, D. Gay) Š Entrepid: Di screti zati ons ( P. Boch ev, D. Rid zal) . Š Others coming… ƒ Becoming more than just solvers.

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4 Trilinos Statistics Registered Users by Type (1632 Total)

Trilinos Statistics by Release 38 175 35 33 Developers 30 27 186 University Automated 28 19 Government Regression 11 Tested packages 9 Personal 925 Industry 17.80 Downloads 10.21 Other (100s) 7.36 4.40 308

9.54 Release 7.0 (9/06) Source lines 8.95 Release 6.0 (9/05) (100K) 7.16 Release 5.0 (3/05) 5.48 Release 4.0 (6/04) 27 General release 18 packages 17 16 Registered Users by Region (1632 Total) 16 30 25 Limited release 27 packages 26 77 22 Europe 32 219 Packages in 29 US (except Sandia) repository 26 22 579 Sandia (includes 0 10203040 unregistered) Counts Asia 208 Americas (except US)

Australia/NZ

Africa 508 Stats: Trilinos Download Page 06/14/2007.

10 External Visibility ƒ Awards: R&D 100, HPC SW Challenge (04). ƒ www.cfd-online.com: Trilinos A project led by Sandia to develop an object-oriented software framework for scientific computations. This is an active project which includes several state-of-the-art solvers and lots of other nice things a software engineer writing CFD codes would find useful. Everything is freely available for download once you have registered. Very good!

ƒ Industry Collaborations: Boeing, Goodyear, ExxonMobil. ƒ Linux distros: Debian, Mandriva. ƒ Star-P Interface. ƒ Over 4200 downloads since March 2005. ƒ Occasional unsolicited external endorsements such as the following two-ppgerson exchange on mathforum.org: > The consensus seems to be that OO has little, if anything, to offer > (except bloat) to numerical computing. I would completely disagree. A good example of using OO in numerics is Trilinos: http://software.sandia.gov/trilinos/

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5 11 Trilinos Presentation Forums

ƒ ACTS “Hands-on” Tutorial: Š Aug 21-23, 2007. Š At Lawrence Berkeley Lab, Berkeley, CA, USA. ƒ Next Trilinos User Group Meeting: Š Nov 6-8, 2007. Š At Sandia National Laboratories, Albuquerque, NM, USA.

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12 TOPS-2 Participation

ƒ Trilinos new member of TOPS. ƒ Activities start July 2008. ƒ Looking for application partners. ƒ Preparation activities: Š Interoperability with PETSc: • PETSc-Trilinos Data objects interoperable. • Interoperability at other levels in time. Š Fortran 9X User Interface: • Support construction of matrices/vectors via OO Fortran interface. • Support selection of solvers and parameters via Fortran. Š Attend meetings like this one.

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6 13

Trilinos Package Concepts

Package: The Atomic Unit

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14 Trilinos Packages ƒ Trilinos is a collection of Packages. ƒ Each package is: Š Focused on impp,ortant, state-of-the-art alggporithms in its problem regime. Š Developed by a small team of domain experts. Š Self-contained: No explicit dependencies on any other software packages (with some special exceptions). Š Configurable/buildable/documented on its own. ƒ Sample packages: NOX, AztecOO, ML, IFPACK, Meros. ƒ Special package collections: Š Petra (Epetra, Tpetra, Jpetra): Concrete Data Objects Š Thyra: Abstract Conceptual Interfaces Š Teuchos: Common Tools. Š New_package: Jumpstart prototype.

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7 Objective Package(s) Trilinos Linear algebra objects Epetra, Jpetra, Tpetra Package Krylov solvers AztecOO, Belos, Komplex Summary ILU-type preconditioners AztecOO, IFPACK Multilevel preconditioners ML, CLAPS Basic Linear Algebra classes Eiggpenvalue problems Anasazi Block Krylov Methods: Block preconditioners Meros Linear: CG, GMRES Direct sparse linear solvers Amesos ScalableEigen: LOBPCG, block Davidson, Preconditionersblock Krylov-Schur Direct dense solvers Epetra, Teuchos, Pliris 3rd Party Direct Solver Package. Abstract interfaces Thyra Nonlinear system solvers NOX, LOCA Abstract Interfaces. Time Integrators/DAEs Rythmos C++ utilities, (some) I/O Teuchos, EpetraExt, Kokkos Trilinos Tutorial Didasko “Skins” PyTrilinos, WebTrilinos, Star-P, Stratimikos Optimization MOOCHO, Aristos Archetype package NewPackage Others Galeri, Isorropia, Moertel, RTOp, Sacado

Full “Vertical” Solver Coverage Trilinos Packages

· Optimization Problems:

n · Unconstrained: Find ufu∈ℜ that minimizes () mn MOOCHO · Constrained: Find yu∈ℜ and ∈ℜ that minimizes fyu( , ) s.t. cyu( , )= 0

· Transient Problems: SlSolve ftf (()x& t , x ())()tt , )0= 0 ′ tTxxxx∈[0, ], (0)==00 , &(0) Rythmos · DAEs/ODEs: for xt( )∈ℜn , t ∈ [0, T ] nm+ n · Nonlinear Problems: Given nonlinear op cxu ( , )∈ℜ →ℜ n NOX · Nonlinear equations: Solve cx( )=∈ℜ 0 for x ∂c · Stability analysis: For cxu ( , )=∈∋ 0 find space u U singular LOCA ∂x

· Implicit Linear Problems: Given linear ops (matrices) AB , ∈ℜnn× AztecOO, Belos, · Linear equations: Solve Ax=∈ℜ b for x n Ifpack,ML,etc. · Eigen problems: Solve Av= λλ Bv for (all) v ∈ℜn , ∈ℜ Anasazi · Explicit Linear Problems:

mn× mn× · Matrix/graph equations: Compute yAxAAGA==; ( ); ∈ℜ∈ , G n Epetra, Tpetra · Vector problems: Compute yxw=+αβα; =<> xyxy,; , ∈ℜ

8 17 New in Trilinos 8.0 ƒ Sacado (E. Phipps, D. Gay) AD tools via templated types: Š Write residual evaluation using template scalar type. Š Get Jacobian “for free.” ƒ Belos ((q,)H. Thornquist, M. Parks) Block Kr ylov Linear solvers: Š Block CG. Š Block GMRES: • Modular implementation: e.g., orthogonalization interface, several adapters. • All BLAS 3 kernels. Š Pseudo-Block GMRES: • Synch’ed independent GMRES’s. • BLAS 3 SpMM, SpSM. Š Single RHS GCRO-DR: Recyygcling GMRES: • Useful for sequences of systems: i i i A x = b , i = 1,K ƒ Aristos (D. Ridzal) Nonlinear continuous optimization package : Š Based on full-space SQP methods. Š Specifically designed for large-scale constrained optimization problems with inexact linearized constraint equations solves.

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18

Managing Parallel Data

The Petra Object Model

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9 A Simple Epetra/AztecOO Program

// Header files omitted… int main(int argc, char *argv[]) { // ***** Create x and b vectors ***** MPI_Init(&argc,&argv); // Initialize MPI, MpiComm Epetra_Vector x(Map); Epetra_ Mpp(iComm Comm( MPI__ COMM WORLD ); Epetra_ Vector b((p);Map); b.Random(); // Fill RHS with random #s // ***** Map puts same number of equations on each pe ***** // ***** Create Linear Problem ***** int NumMyElements = 1000 ; Epetra_LinearProblem problem(&A, &x, &b); Epetra_Map Map(-1, NumMyElements, 0, Comm); int NumGlobalElements = Map.NumGlobalElements(); // ***** Create/define AztecOO instance, solve ***** AztecOO solver(problem); // ***** Create an Epetra_Matrix tridiag(-1,2,-1) ***** solver.SetAztecOption(AZ_precond, AZ_Jacobi); solver.Iterate(1000, 1.0E-8); Epetra_CrsMatrix A(Copy, Map, 3); double negOne = -1.0; double posTwo = 2.0;

for (int i=0; i

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24 Practice Categories

Each practice falls into one of three categories:

VSR Veryygy Strongly Recommended - Practices necessaryyp for Epetra to p erform well.

SR Strongly Recommended - Practices that are definitely a good thing or that have proved to be valuable.

R Recommended - Practices that are probably a good idea.

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12 25 Data Model Wrap-Up

ƒ Our target apps and computer platforms require flexible data model. ƒ Petra Object Model (POM) supports: Š Arbitraryyp placement of vector, ,g grap h, matrix entries on p arallel machine. Š Arbitrary redistribution, ghosting and collection of distributed data. Š Coarse-grain abstraction for key objects. ƒ This flexibility is needed by LALs: Š Algebraic and multi-level preconditioners. Š Concrete distributed matrix kernels. Š Direct methods. ƒ Also needed for future architectures: Multicore, GPUs, CELL, etc. ƒ Also needed for future parallel languages & libraries: UPC, CAF, etc. ƒ Final Notes: Š POM is complex: BUT Non-LALs (ANAs) do not rely on it. Š Parallel Data Redistribution is a huge topic I must skip for this talk (ask about it at break if interested).

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26

Templates and Generic Programming

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13 27 Investment in Generic Programming

ƒ 2nd Generation Trilinos packages are templated on: Š OrdinalType (think int). Š ScalarType (think double). ƒ Examples: Teuchos::SerialDenseMatrix A; Teuchos::SerialDenseMatrix B; ƒ Scalar/Ordinal Traits mechanism completes support for genericity. ƒ The following packages support templates:

Teuchos (Basic Tools) Thyra (Abstract Interfaces) Tpetra (including MPI support) Belos (Krylov and Block Krylov Linear), IFPACK (algebraic preconditioners, next version), Anasazi (Eigensolvers), Sacado (AD), MOOCHO(Optimization)

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28 Potential Benefits of Templated Types

Templated scalar (and ordinal) types have great potential: ƒ Generic: Algorithms expressed over abstract field. ƒ High Performance: Partial template specialization + Fortran. ƒ Facilitate variety of algorithmic studies. ƒ Allow study of asymptotic behavior of discretizations. ƒ Facilitate debugging: Reduces FP error as source error. ƒ UQ, QMU st udies . ƒ Use your imagination… ƒ All new Trilinos packages are templated. ƒ Dark side: Compilation times can soar (but don’t have to).

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14 29

Other Interface Packages: “Skins”

PyTrilinos, WebTrilinos, ForTrilinos

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30 PyTrilinos

ƒ PyTrilinos provides Python access to Trilinos packages. ƒ Uses SWIG to generate bindings. ƒ Epetra, AztecOO, Galeri, IFPACK, ML, NOX, LOCA, Teuchos, Thyra, Anasazi, Amesos and NewPackage are support. ƒ Possible to: Š Define RowMatrix implementation in Python. Š Use from Trilinos C++ code. ƒ Performance for large grain is equivalent to C++. ƒ Several times hit for very fine grain code.

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15 31 #include "mpi.h" #include "Epetra_MpiComm.h" #include "Epetra_Vector.h" #include "Epetra_Time.h" #include "Epetra_RowMatrix.h" C++ vs. Python: Equivalent Code #include "Epetra_CrsMatrix.h" #include "Epetra_Time.h" #include "Epetra_LinearProblem.h" #include "Trilinos_Util_CrsMatrixGallery.h" using namespace Trilinos_Util; #! /usr/bin/env python int main(int argc, char *argv[]) from PyTrilinos import Epetra, Triutils { EIi()Epetra.Init() MPI_Init(&argc, &argv); Comm = Epetra.PyComm() Epetra_MpiComm Comm(MPI_COMM_WORLD); int nx = 1000; nx = 1000 int ny = 1000 * Comm.NumProc(); ny = 1000 * Comm.NumProc() CrsMatrixGallery Gallery("laplace_2d", Comm); Gallery = Triutils.CrsMatrixGallery("laplace_2d", Gallery.Set("ny", ny); Comm) Gallery.Set("nx", nx); Gallery.Set("nx", nx) Gallery.Set("problem_size",nx*ny); Gallery.Set("ny", ny) Gallery.Set("map_type", "linear"); Epetra_LinearProblem* Problem = Gallery.Set("problem_size", nx * ny) Gallery.GetLinearProblem(); Gallery.Set("map_type", "linear") assert (Problem != 0); Matrix = Galleryy().GetMatrix() // retrieve pointers to solution (lhs), right-hand side (rhs) LHS = Gallery.GetStartingSolution() // and matrix itself (A) RHS = Gallery.GetRHS() Epetra_MultiVector* lhs = Problem->GetLHS(); Epetra_MultiVector* rhs = Problem->GetRHS(); Time = Epetra.Time(Comm) Epetra_RowMatrix* A = Problem->GetMatrix(); for i in xrange(10): Epetra_Time Time(Comm); Matrix.Multiply(False, LHS, RHS) for (int i = 0 ; i < 10 ; ++i) print Time.ElapsedTime() A->Multiply(false, *lhs, *rhs); Epetra.Finalize() cout << Time.ElapsedTime() << endl; MPI_Finalize(); return(EXIT_SUCCESS); } // end of main() 31-July-07

Web 32 Interface ƒ Yet another Trilinos Package ƒ Supports: Š Use of Trilinos via simple Web Editor Š User or generated data sets. Š CiliCompilation and execution on webserver.

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16 33 Sample Page

ƒ Intended use: Š Installation on departmental intranet. Š Allows first time users easy access. Š Supports “just-in- time” use of solvers.

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34 Fortran Interface

ƒ Presently Trilinos has no full-featured Fortran interface. ƒ Plans in place to develop OO Fortran 9X interface. ƒ Will Develop as part of SciDAC TOPS-2 effort. ƒ Interested in a target Fortran application for collaboration.

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17 35

Formal Software Engineering

CSE Software is not IT Software

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36 SQA/SQE

ƒ Software Quality Assurance/Engineering is important. ƒ Not sufficient to say, “We do a good job.” ƒ Trilinos facilitates SQA/SQE development/processes for packages: Š 10 of 30 ASC SQE practices are directly handled by Trilinos (no requirements on packages). Š Trilinos provides infrastructure support for the remaining 20. Š Trilinos Dev Guide Part II: Specific to ASC requirements. Š Trili nos sof tware engi neeri ng poli ci es provid e a read y-made infrastructure for new packages. Š Trilinos philosophy: Few requirements. Instead mostly suggested practices. Provides package with option to provide alternate process.

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18 37 Trilinos Service SQE Practices Impact Yearly Trilinos User Group Meeting (TUG) and Developer Forum: — All Requirements steps: gathering, Once a year gathering for tutorials, package feature updates, derivation, documentation, feasibility,etc. user/developer requirements discussion and developer training. — User and Developer training. Monthly Trilinos leaders meetings: —Developer Training. Trilinos leaders, including package development leaders, key managers, —Design reviews. funding sources and other stakeholders participate in monthly phone —Policy decisions across all development meetings to discuss any timely issues related to the Trilinos Project. phases. Trilinos and package mail lists: —Developer/user/client communication. Trilinos lists for leaders, announcements, developers, users, checkins and —Requirements/design/testing artifacts. similar lists at the package level support a variety of communication. All —Announcement/documenting of releases. lists are archived, providing critical artifacts for assessments and audits.

Trilinos and Trilinos3PL source repositories: —Source management. All source code, development and user documentation is retained and —Versioning. tracked. In addition, reference versions of all external software, including —Third-party software management. BLAS, LAPACK, Umfpack, etc. are retained in Trilinos3PL.

Bugzill a P rod ucts: —RiRequirements/f /flaults capturi ng and Each package has its own Bugzilla Product with standard components. tracking. Trilinos configure script and M4 macros: —Portability. The Trilinos configure script and related macros support portable —Software release. installation of Trilinos and its packages Trilinos test harness: —Pre-checkin and regression testing. Trilinos provides a base testing plan and automated testing across —Software metrics. multiple platforms, plus creation of testing artifacts. Test harness results are used to derive a variety of metrics for SQE. 31-July-07

38 “Promotional” Model

Phase k Promotional Phase k+1 Event

•Lower formality •Higher formality •Fewer Artifacts •Sufficient Artifacts •Lean/Agile •Bullet proof •Maintainable

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19 39 Trilinos Software Lifecycle Model

ƒ Three phases: Š Research. Š Production Growth. Š Production Maintenance. ƒ Each phase contains its own lifecycle model. ƒ Promotional events: Š Required for transition from one phase to next. Š Signify change in behaviors and attitude. ƒ Phase assigned individually to each package.

Willenbring, J. M., Heroux, M. A., and Heaphy, R. T. 2007. The Trilinos Software Lifecycle Model. In Proceedings of the 3rd international Workshop on Software Engineering For High Performance Computing Applications (May 20 - 26, 2007). International Conference on Software Engineering. IEEE Computer Society, Washington, DC, 6.

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40

A Few More Useful Things

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20 41 Stratimikos

ƒ New package in Trilinos 7.0. ƒ Single point of access to Trilinos preconditioners/solvers: Š Uniform interface to all preconditioners. Š Uniform interface to all solvers, linear and non-linear. Š Selection of preconditioner/solver via parameter list. ƒ Simplest way to access the suite of Trilinos capabilities ƒ Simple driver code available on website.

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42 Dynamic External Package Support

ƒ New directory Trilinos/packages/external. ƒ Supports seamless integration of externally developed packages via package registration. ƒ Your package: “WorldsBestPreconditioner” Š Understands configure/make. Š Can have its own options: --enable-superfast-mode ƒ Copy source into Trilinos/packages/external. ƒ In Trilinos/ppgackages/external, ,yp type: ./CustomizeExternal.csh WorldsBestPreconditioner ƒ Build Trilinos in the usual way using configure/make. Š Include arguments such as --enable-superfast-mode: They will be passed down to your package.

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21 43

The Trilinos Tutorial Package

ƒ Trilinos is large (and still growing…) Š More than 900K code lines Š Many packages • a lot of functionalities … • … and also a lot to learn ƒ Trilinos tutorial is also delivered as a package: Didasko.

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44 What DIDASKO is not

ƒ DIDASKO, as a tutorial, cannot cover the most advanced features of Trilinos: Š Only the “stable” features are covered

ƒ DIDASKO is not a substitute of each package’s documentation and examples, which remain of fundamental importance

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22 45 Covered Packages

ƒ At present, we cover

Epetra TiTriutil s IFPACK Teuchos AztecOO ML NOX Amesos EpetraExt Anasazi Tpetra

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46 Some Upcoming Efforts

ƒ Exploiting new architecture opportunities: Š Multicore especially. ƒ Redefining the scope of Trilinos beyond solvers: Š CSE enabling technologies distribution. ƒ Expanding accessibility: Š Fortran Interfaces. Š Easier installation (esp. on Windows).

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23 47 Challenges

ƒ Support and perfective maintenance of existing software: Š Presently done through growth, changes in system architecture. Š Not sustaibllinable long term. ƒ Adaptation of software engineering research to CSE software. Š Imposition of standard IT approach worse than ineffective. Š Must have counter-proposals of our own.

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48 Trilinos Availability/Information ƒ Trilinos and related packages are available via LGPL. ƒ Current release (7.0) is “click release”. Unlimited availability. ƒ Trilinos Release 8: September 2007. ƒ More information: Š http://trilinos.sandia.gov Š http://software.sandia.gov Š Additional documentation at my website: http://www.cs.sandia.gov/~mheroux. ƒ 5th Annual Trilinos User Group Meeting: November 6-8, 2007 at Sandia National Laboratories, Albuquerque, NM, USA.

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24 49 Summary

ƒ Trilinos is a large, growing, modular software delivery framework: Š SiiiliSome initial investment i idn understandi didiiilng design is typical (especially if unfamiliar with C++, configure/make, OO principles) Š Modularity allows focusing on your scope of interest. ƒ Interested in new collaborations.

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25