Linear Algebra software

The BLAS

The Basic Linear Algebra Subroutines are extensively used in LAPACK, in other linear algebra packages, and elsewhere.

There are three levels of BLAS:

• Level 1: Scalar and vector operations
• Level 2: Matrix-vector operations
• Level 3: Matrix-matrix operations

For general information about BLAS see http://www.netlib.org/blas/faq.html.

Optimized versions of the BLAS are available for many computer architectures. See

• OpenBLAS
• GotoBLAS

See also:

• Automatically Tuned Linear Algebra Software (ATLAS)
• BLACS Basic Linear Algebra Communication Subprograms with message passing.
• PSBLAS – Parallel sparse BLAS.

LAPACK

• LAPACK
• LAPACK User’s Guide
• http://en.wikipedia.org/wiki/LAPACK
• ScaLAPACK for parallel distributed memory machines

To install BLAS and LAPACK to work with gfortran, see:

• http://gcc.gnu.org/wiki/GfortranBuild

On some linux systems, including the VM for the class, you can install both BLAS and LAPACK via:

$ sudo apt-get install liblapack-dev

Direct methods for sparse systems

Although iterative methods are often used for sparse systems, there are also excellent software packages for direct methods (such as Gaussian elimination):

• UMFPACK
• SuperLU
• MUMPS
• Pardiso

Other references

• LAPACK examples for some examples.
• Recent list of freely available linear algebra software