High-Performance Matrix Computations --- 2018

When: Summer semester 2018

CAMPUS #: 18ss-24886

Contact: Prof. Paolo Bientinesi

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Prerequisites

Basic knowledge of numerical linear algebra.
Principles of algorithms and programming.
Familiarity with Matlab and C.

Overview

The course centers around the idea of developing efficient numerical algorithms through a synergy between mathematics and architectures.

Tentative syllabus

• processor architecture (cpu, memory system, interconnect)
• floating point operations
• roofline model
• vectorization
• matrix-matrix product, BLAS
• factorizations
• method of relatively robust representations (MR3)
• blocked algorithms
• algorithms by block
• dynamic scheduling
• data parallelism
• shared memory vs. distributed memory paradigm
• synchronization vs. communication

Lectures & Exercises

• Tuesday, 16:15-17:45pm (lecture)
• Wednesday, 12:15-13:45pm (lecture + exercise)

Where: 1090|334 (klPhys)

Start: Wednesday, 11.04

Office hours

• Tuesdays, 11am-1pm, by appointment.
  AICES R432 (Rogowski Building - Schinkelstrasse 2)

Schedule

• Wednesday, 11.04	Intro [PDF] [script]
  	GER [PDF] [Mathematica notebook]

• Wednesday, 18.04	[script]
  	Performance [PDF]

• Tuesday, 24.04	[script]
  	[a * 0] [A + B]

• Wednesday, 25.04	[script]
  	[PDF to come]

• Tuesday, 08.05	[script]
  	Computational intensity, Roofline model [Paper]
  	LAMP - part 1 [script] [PDF]
  Wednesday, 09.05

• Tuesday, 15.05	[script]
  	FLAME: Generation of algorithms

• Wednesday, 16.05	[script]
  	Recursive, unblocked, blocked algorithms [LU diary]

• Tuesday, 29.05	[script+refs] [PDF]
  Wednesday, 30.05	From PME to algorithms [Sec 4.5] [Figs 4.1 & 4.4]

• Tuesday, 05.06	Linnea compiler [script] [Paper]
  Wednesday, 06.06

• Tuesday, 12.06

  Road to high-performance DGEMM [script]

• Wednesday, 13.06

  Project assignment [Projects]

• Tuesday, 19.06

  Extra Lecture: "Optimal Performance Numerical Code: Challenges and Solutions" by Prof. Markus Pueschel (ETH). 10:30-12:00 + 13:30-15:00, Room 115. [html] [PDF]

• Tuesday, 19.06	Regular Lecture. Projects. Algorithms by blocks [script] [Paper] [slides]
  Wednesday, 20.06

• Tuesday, 26.06	Application: GWAS [script] [Paper]
  Wednesday, 27.06

• Tuesday, 03.07

  Eigenproblem 1/4 [script]

• Wednesday, 04.07

  Eigenproblem 2/4 [script]

• Tuesday, 10.07

  Eigenproblem 3/4 [script]

• Wednesday, 11.07

  Eigenproblem 4/4 [script] [BX (Sec 2.3.1, 3.2.2)] [MR3] [Parallel Eigensolvers] [Slides]

Exams (by appointment)

• July: 19, 20, 31
• August: 7
• September: 17, 18, 24, 25