This is the set of files related to Expokit, the matrix exponential package. Please report bugs and comments to rbs@maths.uq.edu.au. 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. |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| |||||||||||||||||||||||||||||||| FORTRAN ||||||||||||||||||||||||||||| |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| 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 |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| ||||||||||||||||||||||||||||||| MATLAB ||||||||||||||||||||||||||||||| |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| 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 |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| |||||||||||||||||||||||||||||| PLATFORMS ||||||||||||||||||||||||||||| |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| 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. |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| ||||||||||||||||||||||||||||||| BUGS ||||||||||||||||||||||||||||| |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| 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.