NHSE Software Catalog

LAPACK -- Linear Algebra PACKage

url

http://www.netlib.org/lapack/index.html

title_line

routines for linear system solving, least squares,
and eigenproblems, designed for single processors and shared memory machines

abstract

LAPACK provides routines for solving systems of simultaneous linear
equations, least-squares solutions of linear systems of equations,
eigenvalue problems, and singular value problems. The associated
matrix factorizations (LU, Cholesky, QR, SVD, Schur, generalized
Schur) are also provided, as are related computations such as
reordering of the Schur factorizations and estimating condition numbers.
Dense and banded matrices are handled, but not general sparse
matrices. In all areas, similar functionality is provided for real and
complex matrices, in both single and double precision.

The original goal of the LAPACK project was to make the widely used
EISPACK and LINPACK libraries run efficiently on shared-memory
vector and parallel processors. On these machines, LINPACK and
EISPACK are inefficient because their memory access patterns
disregard the multi-layered memory hierarchies of the machines,
thereby spending too much time moving data instead of doing useful
floating-point operations. LAPACK addresses this problem by
reorganizing the algorithms to use block matrix operations, such as
matrix multiplication, in the innermost loops. These block operations
can be optimized for each architecture to account for the memory
hierarchy, and so provide a transportable way to achieve high efficiency
on diverse modern machines.

LAPACK routines are written so that as much as possible of the
computation is performed by calls to the Basic Linear Algebra
Subprograms (BLAS).
Highly efficient machine-specific implementations of the BLAS are
available for many modern high-performance computers.

contact

lapack@cs.utk.edu

keywords

numerical library; linear algebra; vectorprocessor;
shared memory multiprocessor