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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.
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