Languages for Scientific Computing 1 --- 2009-10

Prerequisites:

Basic knowledge of numerical methods, numerical linear algebra, programming languages, algorithms.


Overview:

We will compare and contrast languages especially suitable for numerical computations, symbolic computations, and high-performance computations: Mathematica, Matlab, C, Fortran. We will also cover standard tools and libraries for scientific and parallel computations: BLAS, LAPACK, MPI, OpenMP... An introduction to Python should conclude the semester. Different programming paradigms will be introduced: functional vs. imperative, discrete vs. numerical vs. symbolic. Programs will be evaluated with respect to metrics like performance, size, elegance. This first module focuses on numerical computations, high-performance and parallelism. The course is hands on. The students are expected to solve (and compete on) simple programming assignments and to present approach & results in front of the class.



• Winter semester 2009-10.


• CAMPUS #: 09ws-14775


• Lectures begin: Thursday, October 15th. In the afternoon.




• Lectures & Exercises:
  Thursdays, 10.30-12.00, Rogowski 115 - AICES seminar room (Schinkelstrasse 2)
  Thursdays, 17.00-18.30, Rogowski 115 - AICES seminar room (Schinkelstrasse 2)


• Office hours: Tuesdays, 11am-1pm, AICES R432 (Rogowski Building - Schinkelstrasse 2)




• Lectures:
  
  
  • Oct.22nd: Introduction to Programming [Lectures 1 & 2].
    History of Programming Languages [Poster].
    
    [Assignment #1]
    [Solution] Elegant solution to Problem #1 and possible approaches to Problems #2 and #3. (by Andreas Bollermann)
  
  
  
  • Oct.29th: Mathematica. Replacements rules, assignments, functions.
    Mathematica pt2: Lists, functional constructs, programming constructs.
    [Intro to Mathematica].
    
    [Assignment #2]
    [Solutions], including a replacement rules-based Quicksort (by Fabian Kuerten). Challenge winner: Tadeus Prastowo.
  
  
  
  • Nov.5th: Classes moved to January 15th.
  
  
  
  • Nov.12th: Floating point arithmetic. [Lecture]
    Mathematica: Numerics. [Notes & Solution to HW2]
    
    [Assignment #3]
  
  
  
  • Nov.19th: Matlab demo. Fast Fourier Transform. [Lecture] <- updated
    Mathematica: [Razz], [Sound].
  
  
  
  • Nov.26th: Visualization in Matlab. [Lecture]
    
    [Assignment #4] (team assignment)
    Files: [F.m] [P.m] [Image]
  
  
  
  • Dec.3rd: Intro to C (part 1). [Lecture]
    Book: "The C Programming Language", by Brian Kernighan & Dennis Ritchie.
    
    Visualization in Mathematica. [Lecture]
  
  
  
  • Dec.10rd: Intro to C (part 2). [Lecture] [MV.c]
    Shell scripting. [Lecture]
  
  
  
  • Dec.17rd: Numerical Linear Algebra libraries. High-performance. [Lecture]
    
    BLAS [Source] [Reference]
    LAPACK [Source]
    
    [Assignment #5]
  
  
  
  • Jan.7th: FLAME, a language and a library for dense linear algebra.
  
  
  
  • Jan.14th & 15th: Python and extreme programming. [Lectures & Material]
  
  
  
  • Jan.21st: Makefiles. [Examples]
    TRMV challenge. Winner: Torsten Kammer.
    
    Final assignment: Razz simulation.
    [Assignment #6] <-- To be discussed at the final exam.
  
  
  
  • Jan.28th: Programming the Cell Broadband Engine.
  
  
  
  • Feb.2nd: How to give a presentation. [HOWTO-Presentations].
    Afternoon: Eigensolvers for Multicore Processors and Massively Parallel Supercomputers.

Automatic Generation and Analysis of Algorithms --- 2009

Prerequisites:

Basic knowledge of numerical linear algebra.
Principles of algorithms and programming.
Familiarity with at least one of the following languages: Mathematica, Maple, Matlab, C.


Overview:

This course is research-oriented; it covers novel techniques on automation.
In this course "automation" means that a computer makes decisions and performs operations much like a human would do. This is in constrast to the scenario in which automation means that a computer is used to test a very large number of cases.
Starting from a problem expressed in symbolic (algebraic) form (example: Lx = b), it is possible to automatically generate algorithms and code to solve the problem with only minimal human intevention. Not only are the algorithms generated automatically, but they are provably correct!
We will study the generation methodology and we will explore the following topics: generation of parallel algorithms for multi-core processors, cost analysis, error analysis.



• Summer semester 2009.


• CAMPUS #: 09ss-24886


• First meeting: Thursday, April 16th - 17.15 in Wullnerstrasse.
  Lectures begin: Thursday, April 23rd - 10.30am.


• Lectures:
  Thursdays, 10.00-11.30, 2356|5055 (Ahornstrasse 55)
  Thursdays, 17.15-18.45, 1810|013 (Wullnerstrasse 5 u.7)


• Office hours:
  Tuesdays, 11am-1pm, AICES R432 (Rogowski Building - Schinkelstrasse 2)


• Lectures:
  
  
  • Preliminaries: [Lectures 1 & 2].
  
  
  • Lectures 3 & 4: Matrix partitionings; intro to Mathematica pt.1.
    Presentations: [Code generation], [ATLAS].
  
  
  • Lectures 5 & 6: Semantics of Expressions and Commands.
    Assignment: Are the following three statements equivalent?
    1. While Exp do Com endw
    2. If Exp then Com; While Exp do Com endw else null fi
    3. If Exp then Com else null fi; While Exp do Com endw
  
  
  • Lectures 7 & 8: Fundamental Theorem of Invariance.
    Presentations: [Theorem provers], [ACL2].
  
  
  • HOMEWORK #2: [Partitioning and Repartitioning].
    Material: [Mathematica primer].
  
  
  • Lectures 9 & 10: Partitioned Matrix Expression.
    
  
  
  • Lectures 12 & 13: Algorithm Generation.
    Material: [FLAME paper], [Dissertation (Chapters 2 & 3)].
    Project assignment: Automatic cost analysis.]
  
  
  • Lectures 14 & 15: From PMEs to high-performance. [Slides]
    Presentation: [Overview of Spiral].
  
  
  • Lectures 16 & 17: Floating point arithmetic and error analysis.
    Material: [Dissertation (Chapter 4)].
    Presentation: [Spiral: parallelization and vectorization].
  
  
  • Lectures 18 & 19: Modular and systematic error analysis.
    Material: [Dissertation (Chapter 4)], [Stability paper].
    Presentation: [Overview of FFTW].
  
  
  • Lectures 20 & 21: Stability analisys: TRSV, TRSM, LU, Blocked LU.
    Material: [Dissertation (Chapter 4)], [Stability paper].
    Presentation: Performance of FFTW.
  
  
  • Lecture 22: Cost analysis: projects.
    Lecture 23: How to give a presentation. [HOWTO-Presentations].
    

Languages for Scientific Computing --- 2008-09

• Winter semester 2008-09.


• CAMPUS #: 08ws-14775




• Lectures: Thursdays, 1.15-2.45pm, RS 5 (Rochusstrasse 2-14)


• Exercises: Wednesdays, 10-11.30am, MeT P 11 (Kopernikusstrasse 14)


• Office hours: Tuesdays, 11am-1pm, AICES R432 (Rogowski Building - Schinkelstrasse 2)





• Lectures:
  
  
  • Lecture 1: Intro to Programming
  
  
  • Lecture 2: Intro to Matlab
  
  
  • Lecture 3: Matlab Part2
  
  
  • November 12 & 13: PETSc tutorial.
  
  
  • November 20: Intro to C.
    
  
  
  • November 27: BLAS. [Source] [Reference]
    
  
  
  • December 3 & 4: Pair Programming. Pointers to functions.
  
  
  • Intro to Mathematica & functional programming.
    
  
  
  • January 15: Floating Point Arithmetic.
  
  
  • January 22: LAPACK. [Source]
  
  
  • January 29: FLAME. [Source]
  
  
  • February 4: make / Makefile, Valgrind
    February 5: Shell scripting