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Table of contents

• ROUTINE-ABSTRACTS
• GENERAL-INFORMATION
• NAMING-CONVENTIONS

ROUTINE-ABSTRACTS

 These menu nodes are keyed to the first letter of LAPACK subroutine names.

• blas: .
• c: .
• d: .
• i: .
• l: .
• s: .
• x: .
• z: .

GENERAL-INFORMATION

 LAPACK is a FORTRAN program system for solving linear equations for
 matrices which fit entirely in core.  Separate versions are available
 for data of type REAL, DOUBLE PRECISION, COMPLEX, and double
 precision complex (COMPLEX*16).

 On UNIX, the LAPACK library may be accessed with -llapack, like this

	f77 -o foo foo.f -llapack

 On-line help can be viewed in node LAPACK in the Emacs info system.

 Complete documentation may be found in the book "LAPACK User's Guide"
 by E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. Du
 Croz, A. Greenbaum, S.  Hammarling, A. McKenney, S. Ostrouchov and D.
 Sorenson, published in 1992 by the Society for Industrial and Applied
 Mathematics (SIAM), 33 South 17th Street, Philadelpha, PA 19103, Tel:
 (215) 564-2929, ISBN 0-89871-294-7, Library of Congress catalog
 number QA76.73.F25 L36 1992, xv + 235 pages.

 LAPACK has been very extensively tested on a wide variety of machines
 and is written completely in Standard FORTRAN 77.  NO changes are
 required to run it on any machine supporting Standard FORTRAN 77.
 LAPACK is in the public domain, and may be freely redistributed.

NAMING-CONVENTIONS

 A subroutine naming convention is employed in which each subroutine
 name is a coded specification of the computation done by that
 subroutine.  All names consist of five or six letters in the form
 TXXYYY.  The first letter, T, indicates the matrix data type.
 Standard FORTRAN allows the use of three such types:

        S       REAL
        D       DOUBLE PRECISION
        C       COMPLEX

 In addition, some FORTRAN systems allow a double precision complex
 type:

        Z       COMPLEX*16

 The next two letters, XX, indicate the form of the matrix or its
 decomposition:

 	BD	bidiagonal
        GB      general band
        GE      general (i.e. unsymmetric, in some cases rectangular)
 	GG	generalized matrices, generalized problems (i.e. a pair
 		of general matrices)
        GT      general tridiagonal
	HB 	(complex) Hermitian band
 	HE	(complex) Hermitian
 	HG	upper Hessenberg matrix, generalized problem (i.e. a
		Hessenberg and a triangular matrix)
        HP      (complex) Hermitian, packed storage
 	HS	upper Hessenberg
 	OP	(real) orthogonal, packed storage
 	OR	(real) orthogonal
        PB      symmetric or Hermitian positive definite band
        PO      symmetric or Hermitian positive definite
        PP      symmetric or Hermitian positive definite, packed storage
        PT      symmetric or Hermitian positive definite tridiagonal
 	SB	(real) symmetric band
        SP      symmetric indefinite, packed storage
 	ST	(real) symmetric tridiagonal
 	SY	symmetric
 	TB	triangular band
 	TG	triangular matrices, generalized problem (i.e. a pair
		of triangular matrices)
 	TP	triangular, packed storage
        TR      triangular (or in some cases quasi-triangular)
 	TZ	trapezoidal
	UN	(complex) unitary
	UP	(complex) unitary, packed storage

 The final three letters, YYY, indicate the computation done by a
 particular subroutine:

	TRF	factorize
	TRS	use the factorization (or the matrix A itself if it is
		triangular) to solve AX = B by forward or backward
		substitution
	CON	estimate the reciprocal of the condition number
	RFS	compute bounds on the error in the computerd solution
		and refined the solution to reduce backward error
	TRI	use the factorization (or the matrix A itself if it is
		triangular) to compute A**(-1)
	EQU	compute scaling factors to equilibrate A