Naming Conventions

      IMPLICIT COMPLEX (C)

      IMPLICIT DOUBLE PRECISION (D)

      IMPLICIT INTEGER (I-N)

      IMPLICIT DOUBLE COMPLEX (Z)

      CHARACTER BALANC, COMPZ, DIAG, EQUED, FACT, HOWMNY, JOB,  

     $          JOBSV, JOBU, JOBVL, JOBVR, JOBVT, NORM, SENSE,  

     $          SORTEV, TRANSA, UPLO

      LOGICAL BWORK3, SELECT

The first letter of a subroutine name identifies the type of the result. The second and third letters identify the form of the output matrix and its mode of storage in an array. The legal forms are shown below:

BD	bidiagonal
GB	general in banded storage
GE	general
GG	general matrix, generalized problem
GT	general tridiagonal
HB	Hermitian in banded storage
HE	Hermitian
HG	upper Hessenberg matrix, generalized problem
HP	Hermitian in packed storage
HS	upper Hessenberg
OP	orthogonal matrix in packed storage
OR	orthogonal matrix
PB	symmetric (or Hermitian) positive definite in banded storage
PO	symmetric (or Hermitian) positive definite
PP	symmetric (or Hermitian) positive definite in packed storage
PT	symmetric (or Hermitian) tridiagonal positive definite
SB	symmetric in banded storage
SP	symmetric in packed storage
ST	symmetric tridiagonal
SY	symmetric
TB	triangular in banded storage
TG	triangular matrix, generalized problem
TP	triangular in packed storage
TR	triangular
TZ	upper trapezoidal
UN	unitary
UP	unitary in packed storage

The remaining letters identify the operation that the subroutine performs. The legal operations are shown below. Not all operations shown below can be applied to all types of matrices shown above.

BAK	back transform eigenvectors of a balanced matrix
BAL	balance a matrix to attempt to improve subsequence eigenvalue / eigenvector computation
BRD	reduce a matrix to bidiagonal form
CON	estimate the condition number
EBZ	compute eigenvalues via bisection
EIN	compute eigenvectors via inverse iteration
EQR	compute eigenvalues and eigenvectors
EQU	compute equilibration scale factors
ERF	compute eigenvalues via QR
ES	compute eigenvalues and Schur factorization
ESX	compute eigenvalues, Schur factorization, and various condition numbers
EV	compute eigenvalues and eigenvectors
EVC	compute eigenvectors of a quasi-triangular matrix
EVX	compute eigenvalues, eigenvectors, condition numbers with high accuracy
EXC	move a 1×1 or 2×2 block on the diagonal of a matrix in Schur canonical form to another place
GBR	generate U and V after reduction of A to bidiagonal form
GHR	generate a matrix after reduction to upper Hessenberg form
GLQ	generate Q from elementary reflectors computed during an LQ factorization
GQL	generate Q from elementary reflectors computed during a QL factorization
GQR	generate Q from elementary reflectors computed during a QR factorization
GRQ	generate Q from elementary reflectors computed during an RQ factorization
GST	reduce a matrix for a generalized eigenproblem to a matrix for a standard eigenproblem
GTR	generate Q from elementary reflectors computed during a reduction to tridiagonal form
GV	solve generalized eigenproblem
HRD	reduce to upper Hessenberg form
LQF	LQ factorization
LS	solve a linear least squares problem using QR or LQ factorization
LSS	solve a linear least squares problem using the singular value decomposition
LSX	solve a linear least squares problem using complete orthogonal factorization
MBR	multiply a matrix by U and V after reduction of A to bidiagonal form
MHR	multiply a matrix by Q using elementary reflectors computed during a Hessenberg reduction
MLQ	multiply a matrix by Q using elementary reflectors computed during an LQ factorization
MQL	multiply a matrix by Q using elementary reflectors computed during a QL factorization
MQR	multiply a matrix by Q using elementary reflectors computed during a QR factorization
MRQ	multiply a matrix by Q using elementary reflectors computed during an RQ factorization
MTR	multiply a matrix by Q using elementary reflectors computed during a tridiagonal reduction
QLF	QL factorization
QPF	QR factorization with column pivoting
QRF	QR factorization
RFS	refine the solution to a linear system
RQF	RQ factorization
SEN	move a set of eigenvalues of a matrix in Schur form and compute various condition numbers
SNA	compute condition numbers for a matrix in Schur canonical form
SQR	compute singular values of a bidiagonal matrix
SV	solve a linear system, non-expert driver
SV	solve a linear system, expert driver
SVD	singular value decomposition
SYL	solve the Sylvester equation AX ± XB = C
TRD	reduce a matrix to real symmetric tridiagonal form
TRF	factor a matrix
TRI	compute inverse of a matrix
TRS	solve a triangular or LU-factored system

To specify the group of subroutines that perform the same operation but are of different types, this manual uses a lowercase x. For example, xGESV refers to the subroutines DGESV, SGESV, ZGESV, and CGESV. This same convention is used for arguments: xA refers to the arguments DA, SA, ZA, and CA.