LAPACK

LAPACK, the Linear Algebra PACKage, is a software library for numerical computing written in Fortran 77. It provides routines for solving systems of simultaneous linear equations, least-squares solutions of linear systems of equations, eigenvalue problems, Householder transformation to implement QR decomposition on a matrix and singular value problems. Lapack95 uses features of Fortran 95 to simplify the interface of the routines.

LAPACK was designed to run on the then-modern vector computers with shared memory.

It depends on the Basic Linear Algebra Subprograms BLAS and has been extended to run on distributed systems with ScaLAPACK and PLAPACK.

LAPACK has largely superseded the Eigenvalue routines from EISPACK, and the linear equations and linear least-squares problems from LINPACK.

A C++ version of the library, called LAPACK++ has also been launched.

[edit] Naming scheme

Here is a table of Matrix types in the LAPACK naming scheme

Name	Description
BD	Bidiagonal matrix
DI	Diagonal matrix
GB	Band matrix
GE	Matrix (i.e., unsymmetric, in some cases rectangular)
GG	general matrices, generalized problem (i.e., a pair of general matrices)
GT	Tridiagonal Matrix General Matrix
HB	(complex) Hermitian matrix Band matrix
HE	(complex) Hermitian matrix
HG	upper Hessenberg matrix, generalized problem (i.e a Hessenberg and a Triangular matrix)
HP	(complex) Hermitian matrix, Packed storage matrix
HS	upper Hessenberg matrix
OP	(real) Orthogonal matrix, Packed storage matrix
OR	(real) Orthogonal matrix
PB	Symmetric matrix or Hermitian matrix positive definite band
PO	Symmetric matrix or Hermitian matrix positive definite
PP	Symmetric matrix or Hermitian matrix positive definite, Packed storage matrix
PT	Symmetric matrix or Hermitian matrix positive definite Tridiagonal matrix
SB	(real) Symmetric matrix Band matrix
SP	Symmetric matrix, Packed storage matrix
ST	(real) Symmetric matrix Tridiagonal matrix
SY	Symmetric matrix
TB	Triangular matrix Band matrix
TG	triangular matrices, generalized problem (i.e., a pair of triangular matrices)
TP	Triangular matrix, Packed storage matrix
TR	Triangular matrix (or in some cases quasi-triangular)
TZ	Trapezoidal matrix
UN	(complex) Unitary matrix
UP	(complex) Unitary matrix, Packed storage matrix