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**Additional info for (A, B)-Invariant Polyhedral Sets of Linear Discrete-Time Systems**

**Example text**

5 Design of Interfaces for Computational Routines LAPACK95 provides interfaces to all LAPACK computational routines. (See Part III). These interfaces are generic with respect to precision (single or double) and data type (real or complex). In contrast to the driver interfaces, however, they must employ the same argument list as the corresponding LAPACK routines. Thus assumed-shape arrays, automatic allocation of work arrays, and optional arguments are not features of the interfaces to computational routines.

2 Order of Arguments Arguments of an LAPACK95 driver routine appear in the following order: array or scalar arguments containing the input data; some of these may also be used for output data. array or scalar arguments used only for output data. optional arguments. :). On entry, the matrix A. On exit, the factors L and U from the factorization A = PLU; the unit diagonal elements of L are not stored. :) with size(B, 1) = szze(A, 1) or shape (:) with size(B) = size(A, I). On entry, the matrix B. On exit, the solution matrix X.

Originally LAPACK had just the simple and expert drivers described below, and the third driver was added after an improved algorithm was discovered. 2. 5: Driver routines for standard eigenvalue and singular value problems Type of problem SEP NEP SVD Function and storage scheme Real/complex simple driver divide and conquer driver expert driver RRR driver simple driver (packed storage) divide and conquer driver (packed storage) expert driver (packed storage) simple driver (band matrix) divide and conquer driver (band matrix) expert driver (band matrix) simple driver (tridiagonal matrix) divide and conquer driver (tridiagonal matrix) expert driver (tridiagonal matrix) RRR driver (tridiagonal matrix) simple driver for Schur factorization expert driver for Schur factorization simple driver for eigenvalues/vectors expert driver for eigenvalues/vectors simple driver divide and conquer driver LA_SYEV LA_SYEVD LA_SYEVX LA_SYEVR LA_SPEV LA_SPEVD Complex Hermitian LA_HEEV LA_HEEVD LAJIEEVX LA_HEEVR LA_HPEV LA_HPEVD LA_SPEVX LA_SBEV LA_SBEVD LA_HPEVX LA_HBEV LA_HBEVD LA_SBEVX LA_STEV LA_STEVD (real only) LA_STEVX LA_STEVR LAJ3EES LA_GEESX LA_GEEV LA_GEEVX LA_GESVD LA_GESDD LA_HBEVX a simple driver (name ending -GV) computes all the eigenvalues and (optionally) eigenvectors.