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LAPACK - Definition and Overview |
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Linear Algebra PACKage (LAPACK). LAPACK is written in Fortran 77 and 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_(mathematics) and singular value problems. Lapack95 (http://www.netlib.org/lapack95/) uses features of Fortran 95 to simplify the interface of the routines.
LAPACK is designed to run on modern high performance vector computers and used shared memory.
It depends on the Basic Linear Algebra Subprograms BLAS and has been extended to run on distributed systems with ScaLAPACK
LAPACK has largly superceeded the Eigenvalue routines from EISPACK, and the linear equations and linear least-squares problems from LINPACK.
Here is a table Matrix types in the LAPACK naming scheme
| Name
| Description
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| BD
| Bidiagonal matrix
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| DI
| Diagonal matrix
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| GB
| Band matrix
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| GE
| Matrix (i.e., unsymmetric, in some
cases rectangular)
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| GG
| general matrices , generalized problem (i.e., a pair of general matrices)
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| GT
| Tridiagonal Matrix General Matrix
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| HB
| (complex) Hermitian matrix Band matrix
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| HE
| (complex) Hermitian matrix
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| HG
| upper Hessenberg matrix, generalized problem (i.e a Hessenberg and a Triangular matrix)
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| HP
| (complex) Hermitian matrix, Packed Storage matrix
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| HS
| upper Hessenberg matrix
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| OP
| (real) Orthogonal matrix, Packed Storage matrix
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| OR
| (real) Orthogonal matrix
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| PB
| Symmetric matrix or Hermitian matrix positive definite band
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| PO
| Symmetric matrix or Hermitian matrix positive definite
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| PP
| Symmetric matrix or Hermitian matrix positive definite, Packed Storage matrix
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| PT
| Symmetric matrix or Hermitian matrix positive definite Tridiagonal matrix
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| SB
| (real) Symmetric matrix Band matrix
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| SP
| Symmetric matrix, Packed Storage matrix
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| ST
| (real) Symmetric matrix Tridiagonal matrix
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| SY
| Symmetric matrix
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| TB
| Triangular matrix Band matrix
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| TG
| triangular matrices, generalized problem (i.e., a pair of triangular matrices)
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| TP
| Triangular matrix, Packed Storage matrix
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| TR
| Triangular matrix (or in some cases quasi-triangular)
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| TZ
| Trapezoidal matrix
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| UN
| (complex) Unitary matrix
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| UP
| (complex) Unitary matrix, Packed Storage matrix
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External links
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Example Usage of LAPACK |
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eurodollari: CULAという実装で可能ではないかと RT @conflex: 絶対値的には魅力十分なんですよね．．．LAPACKフルサポートしてくれたかなぁ．．．10万×10万行列の固有値問題を解たいんですよ． RT 最新型のTeslaは倍精度でも630GFlops出ますよ |
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conflex: 絶対値的には魅力十分なんですよね．．．LAPACKフルサポートしてくれたかなぁ．．．10万×10万行列の固有値問題を解たいんですよ． RT @eurodollari: 最新型のTeslaは倍精度でも630GFlops出ますよ |
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asaijo: Ubuntuにinkscapeを入れたら、BLASとLAPACKを要求されて驚いた。Numpyが使ってるんだな。 |
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