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.

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

LAPACK contains higher level functions such as:

solving linear systems
eigenvalue/eigenvector calculations

It now includes an official C interface called LAPACKE.

This does not ship with the Ubuntu liblapack-dev package at the time of writing, but there is a liblapacke-dev package available which provides it.

ScaLAPACK

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

Continuation of LAPACK.

Considers parallelism.

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.

C interface

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

Via atlas:

sudo aptitude install libatlas-dev
gcc -lcblas

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

sudo aptitude 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

README.md

BLAS and LAPACK

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