
Document for 

    SRRIT - A Fortran subroutine to calculate the dominant invariant
    subspace of a nonsymmetric matrix 

    Z. Bai and G. W. Stewart

Addresses of authors: 

    Zhaojun Bai                  G. W. Stewart
    Department of Mathematics    Department of Computer Science
    University of Kentucky       University of Maryland
    Lexington, KY 40506          College Park, MD 20742
    phone: 606-257-3167          phone:
    email: bai@ms.uky.edu        email: stewart@cs.umd.edu
        
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In the file test.f, it includes the following F77 test routines: 
............................................................................

TEST      test driver routine

SCHECK    test routine for SLAQR3

ATQxxx    matrix-vector multiplication subroutines. They are problem-dependent
          routines, and in general, supplied by user, but the calling sequence
          has to be as described in the subroutine. 

............................................................................
In the source code file srrit.f, it includes the following F77 subroutines: 
............................................................................

SRRIT     main routine,  computes a nested sequence of orthonormal bases for
          the dominant invariant subspaces of a real matrix A of order N.

SRRSTP 	  performs an Schur-Rayleigh-Ritz iteration step.

ORTH   	  orthonormalizes columns of a matrix.

RESID	  computes the each column norm of residual vectors

GROUP 	  finds a cluster of a set of complex numbers.

COND      estimates the infty-norm condition number with respect to inversion
          of an upper Hessenberg matrix.

SLAQR3    computes the Schur factorization of a real upper Hessenberg matrix, 
          the eigenvalues of Schur form appear in descending order of magnitude
          along its diagonal. This subroutine is a variant of LAPACK subroutine
          SLAHQR for computing the Schur decomposition.

SLARAN    generates a random real number from a uniform (0,1) distribution.
          It is in LAPACK test matrix generator suit. 

............................................................................

In addition,  aux.f contains the standard BLAS and LAPACK routines used 
in SRRIT. If BLAS and LAPACK have been installed on your local machines, 
you may replace aux.f by linking to your local BLAS and LAPACK libraries.

On a Unix system, by typing ``make'', it will automatically generate
executive files ``subspiter'' and test the single precision routines.
The output file is ``soutput''.

A real double precision version of SRRIT is also available. The main 
subroutines names are called DSRRIT, DSRRSP, DORTH, DRESID, DGROUP, 
DLAQR3, DCOND, and DLARAN. The rest of routines are from real double
precision BLAS and LAPACK routines. Using the provided makefile, 
the double precision version will be automatically tested. The output 
file is ``doutput''.
 
