ScilabTEC2011 Keynote

7/25/2019 ScilabTEC2011 Keynote

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Scilab for Mathematical Education and

High Performance Computing

Tetsuya SAKURAI

University of Tsukuba


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Contents

! Scilab for Math Education

" Promoting the use of ICT in classroom

- Interactive white board, slate PC, projector, internet

" Math education with computer

" Hands-on with graphs

" Lecture in high school

" Touch interface for inputting Math expressions

! Scilab for High Performance Computing (HPC)

" Multicore and distributed computing platforms

" Developing high performance applications

" Examples

"

Scilab for application design

! Conclusions

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Scilab

for

Math Education

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Promoting the use of ICT in Classroom

! Promotion by MEXT (Ministry of Education, Culture, Sports, Science

and Technology of Japan):

"

assists improvements of ICT environment in school

- Interactive white board, PC, Internet, etc.

" pursues to utilize ICT in classrooms

" encourages to develop and to provide course materials

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http://www.mext.go.jp/

Good computer tools for education are required.


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Math Education with Computer

! Computers provide various hands-onlearning and teaching opportunities

in Math education

" Computers help students to understand various Math concepts

" The skills for search, curation, analysis, etc., are useful not only for Math

" Such experiences lead to skills for real-world problem solving using a

computer

! Animation of graphs

" effective to visualize Math concepts

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Graphs are static on a blackboard Graphs are dynamic on a screen


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Programming Tools

!

"

"

"

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We need an alternative programming tool


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Programming Tools

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Scilab

BASIC


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Programming Tools

!

"

"

"

"

"

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Hands-on with Graphs

Draw a graph of x2 124 x+ 1.

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Interval [-1, 1]

Interval [-20, 160]

Many students draw a graph

with the interval [-1, 1].

"The graph seems linear

. . . something wrong with the program"


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Draw a graph of data.

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Linear plot

Double logarithmic plot

Logarithmic plot gives rich information from the given data.


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x = linspace(0,10,100);

for t=1:3

y = x^2 - 4*t*x + 4*t^2 + t - 3;

plot2d(x,y,t,rect=[0,-4,10,10]);

end

y = (1/2)*x - 3;

plot2d(x,y,5);

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Find the common tangent line of

with t= 1, 2, 3.


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Scilab for Hands-on Tools

! Scilab is easy to make Math education tools with GUI

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Using Scilab as Backend Computing/Graphing Engine

Input Math Expressions Display Graph Output

Control Parameters

Display Numerical Results

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MathGUIde (frontend tool) calls Scilab as a computing/graphing engine

via Java interface

MathGUIde


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Students can predict a next event

by teacher's action

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Example: Lecture in High School

! Example of the use of a graphing tool at high school math class

Senior High School at Sakado, University of Tsukuba

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Input Interface for Math Expressions

Input Field

Hold Touch

sin

x +!

Multi-touch provides a good userbility

for inputting Math expressions

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Input Interface for Math Expressions

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Scilab

for

High Performance Computing (HPC)

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Multicore and Distributed Computing Platforms

! Multicore:

Clock frequency of CPU hit a peak around 2004.

-- Paradigm to increase a CPU performance had changed.

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We can not enjoy the automatic performance improvements

by clock speed.

Single-core Multi-core


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Multicore and Distributed Computing Platforms

! Distributed computing:

We need to develop high performance applications with over tens

of thousands of nodes for large-scale simulations.

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http://www.top500.org/

current future status

#CPUs 68,544 over 80,000

#cores

548,352

over 640,000

performance 8.17 Peta FLOPs over 10 Peta

K computer: next generation supercomputer in Japan


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Developing High Performance Applications

! Process for developing a high performance application

" Phase 1:Application design

"

Phase 2: Performance evaluation

" Phase 3:Tackle target problems

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Phase 1:

> Use a supercomputer with

middle size problems

> Implement parallel codes

> Find appropriate parameters

> Evaluate a performance

> Use a supercomputer with

large size problems

> Tackle target problems

> Solve real problems and

obtain physical results

> Try for grand challenge

> Use a workstation or a

small cluster with small

size problems

> Find appropriate

algorithms and solvers> Design an application

Phase 2: Phase 3:


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!

Systems of linear equations

Sumiyoshi, et.al. (1988)

A.K.Mann (1997)

Test problem: matrix size = 85,680 (750MB)

GCR method without

preconditioning

Number of iterations

Residual

GCR method with an

effective preconditioner


Residual

stagnated

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! Quantum dot simulation

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Asakura, et.al. (2010)

Polynomial eigenvalue problems

Hwang, et.al. (2004)

n=32,401,863

(5.4 GB)

n=1,532,255

(258 MB)


R

esidual

BiCGSTAB method without preconditioning

When the matrix size exceeds tenmillion, the BiCGSTAB method

without preconditioning does not

converge.

Even in Phase 1, we need to treatrelatively large-scale problems.

Software: C++/PETSc,Fortran90/OpenMP, . . .

Hardware: AMD 48cores + 256GB

of memory,

Xeon 8cores + 48GB

of memory + Tesla, . . .

Contour integral based eigensolver

(Nonlinear SS method)

n=186,543

(30 MB)

systems of linear equations


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8 32 128 512 2048

2500

1000

500

100

secComputational time on CRAY XT4

number of cores

Test problem:

Accelerator design* *R. Lee (2007)Matrix size = 1,100,242 (linear part)

Language: Fortran90/MPI

Linear solver: sparse direct solver

http://www.linearcollider.org/cms/

SS method

Lanczos method

! Contour integral based eigensolver (SS method*)

"

A target subspace is

constructed by a filter

using contour integral

" The filter is derived by

solving systems of linear

equations, simultaneously

coarse grained parallelism

Example of Phase 2 (Accelerator Design)*Sakurai, et.al. (2003),

Ikegami, et.al. (2010)

Input:random vectors

Solve systems of linearequations, simultaneously

Output:target eigenvectors

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Scilab for Application Design

! Scilab is useful in Phase 1

" Check matrix properties

"

Compare various algorithms

" Try new ideas

" Find good parameters

" . . .

! Memory limit is the major restriction

" Even in Phase 1, we need to treat relatively large-scale problems

"

Scilab for distributed computing is required

! We expect a toolbox for distributed computing which supports

"

Management of distributed data

"

Matrix-vector product, inner product, etc." Krylov subspace methods, QR decomposition, Sparse LU factorization, etc.

" Interface to libraries such as PETSc or Trilinos, etc.

(ex. Python + Trilinos)

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Conclusions

! Scilab for Math education

" Now digital equipments are ready in classroom

"

Scilab can be used for hands-on Math education

" Scilab is also useful as a backend computing/graphing engine

! Scilab for High Performance Computing

" Scilab is useful in a process of HPC application design

" Memory limit restricts scalability

" Distributed computing is required

" New features of Scilab 6-- new memory handling, thread safe, optimize for multicore,

Scilab gateway, etc.

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ScilabTEC2011 Keynote

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