This is the set of files related to Expokit, the matrix exponential
package. Please report bugs and comments to [email protected].

This version dated: Oct 7, 1997
URL:  http://www.maths.uq.edu.au/expokit

Notes:
======
1. w(t) = exp(t*A)v is the analytic solution of the homogeneous 
   ODE problem:
               w'(t) = Aw(t),  w(0) = v

2. w(t) = exp(t*A)*v + t*phi(t*A)u, where phi(z) = (exp(z)-1)/z,
   is the analytic solution of the nonhomogeneous ODE problem:
               w'(t) = Aw(t) + u,  w(0) = v

------------------------------------------------------------------------

expokit.tar.gz       complete expokit package, current release
------------------------------------------------------------------------

Otherwise...

expodoc.ps  description of the methods used in the package
README      this file
Makefile    Fortran makefile
expokit.f   all-in-one file, i.e., concatenation of all .f files, 
            except BLAS, LAPACK and the aid and driver routines.
            Hence a minimal Fortran trial would include:
            Makefile, expokit.f, blas.f, lapack.f, mataid.f, 
            and one of the drivers.


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||||||||||||||||||||||||||||||||  FORTRAN  |||||||||||||||||||||||||||||
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REAL      COMPLEX
=======================================================================|
                          SMALL DENSE ROUTINES

dgpadm.f  zgpadm.f   exp(t*A) in full using irreducible Pade, A general
dspadm.f  zhpadm.f   exp(t*A) in full using Pade, A symmetric/Hermitian
dgchbv.f  zgchbv.f   exp(t*A)*v using Chebyshev, A general
dschbv.f             exp(t*A)*v using Chebyshev, A symmetric
dnchbv.f  znchbv.f   exp(t*A)*v using Chebyshev, A upper Hessenberg

blas.f               minimal substitute to BLAS
lapack.f             minimal substitute to LAPACK

=======================================================================|
                           LARGE SPARSE ROUTINES

dmexpv.f             exp(t*A)*v using Krylov, A is a Markov matrix
dgexpv.f  zgexpv.f   exp(t*A)*v using Krylov, A general
dsexpv.f  zhexpv.f   exp(t*A)*v using Krylov, A symmetric/Hermitian
dgphiv.f  zgphiv.f   exp(t*A)*v + t*phi(t*A)*u using Krylov, A general
dsphiv.f  zhphiv.f   exp(t*A)*v + t*phi(t*A)*u using Krylov, A sym/Hem

dgcnvr.f  zgcnvr.f   convert a sparse format into another one
dgmatv.f  zgmatv.f   matrix-vector utilities
loadhb.f             load and converts a Harwell-Boeing matrix

mataid.f             concatenation of the files above (i.e., __cnvr.f, 
                     __matv.f, and loadhb.f) 

=======================================================================|
                             SAMPLE DRIVERS

sample_d.f           dense example
sample_g.f           general example
sample_z.f           Complex example
sample_b.f           forward-backward example
sample_m.f           Markov example
sample_p.f           phi example

clock.f              utility timer function - MUST BE SET BY THE USER
		     
c1024.crs.gz         Markov chains matrix used in sample_m.f
gr3030.gz            Harwell-Boeing matrix used in sample_b.f
orani678.gz          Harwell-Boeing matrix used in sample_g.f/_p.f
bcspwr10.gz          Harwell-Boeing pattern used in sample_z.f

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chbv.m               Chebyshev algorithm for w = exp(t*A)v
padm.m               irreducible Pade algorithm for exp(t*A)
phiv.m               Krylov algorithm for w = exp(t*A)*v + t*phi(t*A)u
expv.m               Krylov algorithm for w = exp(t*A)*v
mexpv.m              Markov algorithm for w = exp(t*A)*v
		     
mat2ccs.m            save matrix into an ascii file under CCS format
mat2coo.m            save matrix into an ascii file under COO format
mat2crs.m            save matrix into an ascii file under CRS format
		     
loadccs.m            load matrix from a file under CCS format
loadcoo.m            load matrix from a file under COO format
loadcrs.m            load matrix from a file under CRS format
		     
example.m            sample program illustrating the use of _expv.m


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The drivers have been successfully tested on the following platforms:

SUN 
-------------------------------
       SPARC workstation

IBM
--------------------------------
       RS/6000 workstation
       SP2 (one node)

SGI
--------------------------------
       Indy workstation
       Power Challenge (one node)


Others? Please notify.


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|||||||||||||||||||||||||||||||    BUGS    |||||||||||||||||||||||||||||
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On some systems, the compilation of Expokit will generate a warning
message about an incompatibility of type in the call of DNCHBV. This is
due to the fact that a real array is used as argument where a complex 
array is expected. This is an artefact to avoid an otherwise idle
complex array in the calling routine. Thus it is not a bug as such 
and no side-effects arise. There is a notice about this in the header 
of DNCHBV.