lapack

LAPACK

BLAS and LAPACK are:

• linear algebra packages

• de-facto standards

• non-parallel

• originally written in Fortran

• also have C interfaces available

  It might be a good idea to understand how to interface Fortran with C before the C interfaces.

Many implementations have been made, so they may be considered interfaces derived from an initial implementation nowadays.

BLAS

http://www.netlib.org/blas/

BLAS contains low level functions such as:

• vector norm
• vector sum
• vector scalar multiplication
• vector matrix multiplication
• matrix matrix multiplication

LAPACK uses BLAS

BLAS vs LAPACK

LAPACK contains higher level functions such as:

• solving linear systems
• least squares
• eigenvalue/eigenvector calculations

It now includes an official C interface called LAPACKE, which other implementations also implement.

Implementations

ScaLAPACK

http://www.netlib.org/scalapack/

Continuation of LAPACK.

Considers parallelism distributed across machines.

ATLAS

http://math-atlas.sourceforge.net/

Automatically tuned BLAS LAPACK. Not sure what this means, but sounds good!

Implements full BLAS, but only part of LAPACK.

Has C interface.

OpenBLAS

https://github.com/xianyi/OpenBLAS

PBLAS

https://en.wikipedia.org/wiki/PBLAS

Created and used by ScaLAPACK.

MKL

Intel's closed source implementation.

C interface

The BLAS project provides cblas.h, which contains a C interface for BLAS (TODO but also an implementation?)

Via atlas:

sudo apt-get install libatlas-dev
gcc -lcblas

Via LAPACKE (libblas-dev already contains cblas.h):

sudo apt-get install liblapacke-dev
gcc -lblas

Levels

1: array array. ex: array sum. 2: matrix array. ex: solve linear system. 3: matrix matrix. ex: multiply two matrices.

Function naming conventions

http://www.netlib.org/lapack/lug/node24.html

The functions are named according to the pattern:

XYYZZZ

Where:

• X: data type:

  • S: single precision (C float)
  • D: double precision
  • C: complex
  • Z: double complex

• YY: known type the type of input matrices:

  • GE: general
  • TR: triangular

  The more restrict the matrix type, the more efficient algorithms can be.

• ZZ: computation to be done:

  • SV: SolVe linear system
  • MM: Matrix Multiply
  • LS: Least Squares (overdetermined system)

Sources

• function signatures: in source code olny http://www.netlib.org/lapack/double/

• naming convention http://www.cs.rochester.edu/~bh/cs400/using_lapack.html

• user's guide. algorithm info http://www.netlib.org/lapack/lug/

• http://www.tat.physik.uni-tuebingen.de/~kley/lehre/ftn77/tutorial/blas.html

LAPACKE

http://stackoverflow.com/questions/26875415/difference-between-lapacke-and-lapack