LAPACK (Linear Algebra PACKage) is a software library for numerical linear algebra. It provides routines for solving systems of linear equations and linear least squares, eigenvalue problems, and singular value decomposition. It also includes routines to implement the associated matrix factorizations such as LU, QR, Cholesky and Schur decomposition. LAPACK was originally written in FORTRAN 77, but moved to Fortran 90 in version 3.2 (2008).[1] The routines handle both real and complex matrices in both single and double precision.
LAPACK can be seen as the successor to the linear equations and linear least-squares routines of LINPACK and the eigenvalue routines of EISPACK. LINPACK was designed to run on the then-modern vector computers with shared memory. LAPACK, in contrast, was designed to effectively exploit the caches on modern cache-based architectures, and thus can run orders of magnitude faster than LINPACK on such machines, given a well-tuned BLAS implementation. LAPACK has also been extended to run on distributed-memory systems in later packages such as ScaLAPACK and PLAPACK.
LAPACK is licensed under a three-clause BSD style license, a permissive free software license with few restrictions.
Naming scheme
Subroutines in LAPACK have a characteristic naming convention which makes the identifiers short but rather obscure. This was necessary as the first Fortran standards only supported identifiers up to six characters long, so the names had to be shortened to fit into this limit.
A LAPACK subroutine name is in the form pmmaaa, where:
p is a one-letter code denoting the type of numerical constants used. S, D stand for real floating point arithmetic respectively in single and double precision, while C and Z stand for complex arithmetic with respectively single and double precision. The newer version, LAPACK95, uses generic subroutines in order to overcome the need to explicitly specify the data type.mm is a two-letter code denoting the kind of matrix expected by the algorithm. The codes for the different kind of matrices are reported below; the actual data are stored in a different format depending on the specific kind; e.g., when the code DI is given, the subroutine expects a vector of length n containing the elements on the diagonal, while when the code GE is given, the subroutine expects an n×n array containing the entries of the matrix.aaa is a one- to three-letter code describing the actual algorithm implemented in the subroutine, e.g. SV denotes a subroutine to solve linear system, while R denotes a rank-1 update.
For example, the subroutine to solve a linear system with a general (non-structured) matrix using real double-precision arithmetic is called DGESV.
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 |
Details on this scheme can be found in the Naming scheme section in LAPACK Users' Guide.
Use with other programming languages
Many programming environments today support the use of libraries with C binding. The LAPACK routines can be used like C functions if a few restrictions are observed.
Several alternative language bindings are also available:
See also
References
Further reading
- Anderson, E.; Bai, Z.; Bischof, C.; Blackford, S.; Demmel, J.; Dongarra, J.; Du Croz, J.; Greenbaum, A.; Hammarling, S.; McKenney, A.; Sorensen, D. (1999). LAPACK Users' Guide (Third ed.). Philadelphia, PA: Society for Industrial and Applied Mathematics. ISBN 0-89871-447-8.
External links
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