Naming Conventions

The types of all arguments follow the notation in Dongarra's original paper as shown below:

 ``` IMPLICIT COMPLEX (C) ``` ``` IMPLICIT DOUBLE PRECISION (D) ``` ``` IMPLICIT INTEGER (I-N) ``` ``` IMPLICIT REAL*16 (Q) ``` ``` IMPLICIT REAL (S) ``` ``` IMPLICIT DOUBLE COMPLEX (Z) ``` ``` CHARACTER UPLO, TRANSA, DIAG ```

The first letter of a subroutine name identifies the type of the result. The next two letters indicate the form of matrix involved. The possible forms are:

 GB General in banded storage GE General HB Hermitian in banded storage HE Hermitian HP Hermitian in packed storage SB Symmetric in banded storage SP Symmetric in packed storage SY Symmetric TB Triangular in banded storage TP Triangular in packed storage TR Triangular

The fourth and fifth letters indicate the operation that the subroutine performs:

 MV Matrix-vector product R Rank-one update R2 Rank-two update SV Solve a triangular system of linear equations

To specify the group of subroutines that perform the same operation but are of different types, this manual uses a lowercase x. For example, xGEMV refers to the subroutines DGEMV, SGEMV, ZGEMV, and CGEMV. This same convention is used for arguments: xA refers to the arguments DA, SA, ZA, and CA.

A-1 denotes the inverse of the square matrix stored in the array A. Whenever the symbol A-1 appears it is assumed that the numerical inverse of A exists. AT denotes the transpose of A and AH denotes the conjugate transpose of A for a complex A.