High-Performance Matrix Computations --- 2016
When: Summer semester 2016
CAMPUS #: 16ss-24886
Contact: Prof. Paolo Bientinesi
Basic knowledge of numerical linear algebra.
Principles of algorithms and programming.
Familiarity with Matlab and C.
The course centers around the idea of developing efficient numerical algorithms
through a synergy between mathematics and architectures.
- processor architecture (cpu, memory system, interconnect)
- floating point operations
- roofline model
- matrix-matrix product, BLAS
- 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
- Tuesdays, 4.15-5.45pm (lecture)
- Thursdays, 4.15-5.45pm (lecture + exercise)
Where: 1090|334 (klPhys), Rogowski Building, Schinkelstrasse 2
Start: Tuesday, April 19, 4.15pm
Tuesdays, 11am-1pm, by appointment.
AICES R432 (Rogowski Building - Schinkelstrasse 2)
Tuesday, 19.04 Introduction [script]
Thursday, 21.04 Performance [GER] [slides] [script]
Tuesday, 26.04 Locality [A+B] [op] [script]
Thursday, 28.04 Defs, coding [slides] [GER] [GEMM] [script]
Tuesday, 03.05 ELAPS [GitHub]
Tuesday, 10.05 BLAS [slides] [reference]. Roofline Model [Paper] [script]
Thursday, 12.05 Blocked vs. unblocked algorithms: Cholesky factorization. HW #1 [PDF] Deadline: Friday, May 20th, midnight
Tuesday, 24.05 Partitioned Matrix Expression, variants [slides] [Cluster].
Tuesday, 31.05 High performance matrix matrix product [PPX] [references]
Thursday, 02.06 Strassen [PPX]
Tuesday, 07.06 Multithreading, dependencies [elaps experiments] [script]
Thursday, 09.06 Algorithms by blocks - pt.1 [Paper] [slides] [script]
Tuesday, 14.06 Algorithms by blocks - pt.2 [slides] [script]
Thursday, 16.06 Sequence of least squares problems [Paper] [script]
Tuesday, 21.06 Out-of-core algorithms. Double buffering [Paper]
Thursday, 23.06 Eigenproblems, preliminaries, accuracy, reductions. [script]
Tuesday, 28.06 Reduction to tridiagonal form [script] [notes]
Thursday, 30.06 Householder vs. SBR
[Final projects] (Org mode, it's just a text file)
Tuesday, 05.07 Final projects. Bisection.
Tuesday, 12.07 Computation of eigenvalues; basics, power method
Thursday, 14.07 Computation of eigenvectors; inverse iterations, MR3 [Paper] [Slides]
Tuesday, 19.07 MR3, MR3-SMP, PMRRR [Paper] [Slides]
Thursday, 21.07 Matrix distributions [Slides, pp.19-28]
- [Final projects] updated (Sept 9th)
- July 26
- July 28
- August 2
- September 27
- September 29