Editing LAPACK (section)

==Naming scheme==
Subroutines in LAPACK have a naming convention which makes the identifiers very compact. 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.<ref name="LAPACK User Manual" />{{rp|at=[https://www.netlib.org/lapack/lug/node24.html "Naming Scheme"]}}

A LAPACK subroutine name is in the form <code>pmmaaa</code>, where:

* <code>p</code> is a one-letter code denoting the type of numerical constants used. <code>S</code>, <code>D</code> stand for real [[floating-point arithmetic]] respectively in single and double precision, while <code>C</code> and <code>Z</code> stand for [[complex number|complex arithmetic]] with respectively single and double precision. The newer version, LAPACK95, uses [[generic function|generic]] subroutines in order to overcome the need to explicitly specify the data type.
* <code>mm</code> 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 <code>DI</code> is given, the subroutine expects a vector of length <code>n</code> containing the elements on the diagonal, while when the code <code>GE</code> is given, the subroutine expects an {{math|''n''×''n''}} array containing the entries of the matrix.
* <code>aaa</code> is a one- to three-letter code describing the actual algorithm implemented in the subroutine, e.g. <code>SV</code> denotes a subroutine to solve [[linear system]], while <code>R</code> 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 <code>DGESV</code>.<ref name="LAPACK User Manual" />{{Rp|at=[https://www.netlib.org/lapack/lug/node26.html "Linear Equations"]}}

{|class="wikitable"
|+ Matrix types in the LAPACK naming scheme
|-
! Name
! Description
|-
| BD
| [[bidiagonal matrix]]
|-
| DI
| [[diagonal matrix]]
|-
| GB
| general [[band matrix]]
|-
| GE
| general [[matrix (mathematics)|matrix]] (i.e., [[symmetric matrix|unsymmetric]], in some cases rectangular)
|-
| GG
| general matrices, generalized problem (i.e., a pair of general matrices)
|-
| GT
| general [[tridiagonal matrix]]
|-
| HB
| ([[Complex number|complex]]) [[Hermitian matrix|Hermitian]] [[band matrix]]
|-
| HE
| ([[Complex number|complex]]) [[Hermitian matrix]]
|-
| HG
| [[upper Hessenberg matrix]], generalized problem (i.e. a Hessenberg and a [[triangular matrix]])
|-
| HP
| ([[Complex number|complex]]) [[Hermitian matrix|Hermitian]], [[packed storage matrix]]
|-
| HS
| [[upper Hessenberg matrix]]
|-
| OP
| ([[Real number|real]]) [[orthogonal matrix]], [[packed storage matrix]]
|-
| OR
| ([[Real number|real]]) [[orthogonal matrix]]
|-
| PB
| [[symmetric matrix]] or [[Hermitian matrix]] [[positive definite matrix|positive definite]] band
|-
| PO
| [[symmetric matrix]] or [[Hermitian matrix]] [[positive definite matrix|positive definite]]
|-
| PP
| [[symmetric matrix]] or [[Hermitian matrix]] [[positive definite matrix|positive definite]], [[packed storage matrix]]
|-
| PT
| [[symmetric matrix]] or [[Hermitian matrix]] [[positive definite matrix|positive definite]] [[tridiagonal matrix]]
|-
| SB
| ([[Real number|real]]) [[symmetric matrix|symmetric]] [[band matrix]]
|-
| SP
| [[Symmetric matrix|symmetric]], [[packed storage matrix]]
|-
| ST
| ([[Real number|real]]) [[symmetric matrix]] [[tridiagonal matrix]]
|-
| SY
| [[symmetric matrix]]
|-
| TB
| [[Triangular matrix|triangular]] [[band matrix]]
|-
| TG
| [[Triangular matrix|triangular matrices]], generalized problem (i.e., a pair of [[triangular matrix|triangular matrices]])
|-
| TP
| [[Triangular matrix|triangular]], [[packed storage matrix]]
|-
| TR
| [[triangular matrix]] (or in some cases quasi-triangular)
|-
| TZ
| [[trapezoidal matrix]]
|-
| UN
| ([[Complex number|complex]]) [[unitary matrix]]
|-
| UP
| ([[Complex number|complex]]) [[unitary matrix|unitary]], [[packed storage matrix]]
|}