1. Purpose ------- This directory contains example drivers that call ARPACK subroutines __aupd.f and __eupd.f to solve various eigenvalue problems using regular, shift-invert or other special modes (such as Cayley, Bucking etc.) These drivers illustrate how to set various ARPACK parameters to solve different problems in different modes. They provide a guideline on how to use ARPACK's reverse communication interface. The user may modify any one of these drivers, and supply his/her own matrix vector multiplication routine to solve the problem of his/her own interest. These drivers are installed in the following subdirectories. SIMPLE --- simple drivers for beginners. SYM --- drivers for symmetric eigenvalue problems NONSYM --- drivers for nonsymmetric eigenvalue problems COMPLEX --- drivers for eigenvalue problem with complex matrices BAND --- drivers for eigenvalue problem with BANDED matrices SVD --- drivers for computing singular values and vectors of a m by n matrix. 2. Getting started --------------- If you have never used ARPACK before, it might be a good idea to go into the subdirectory SIMPLE, and read one of the simple drivers [s,d]ssimp.f, [s,d]nsimp.f [c,z]nsimp.f first. The documentation explains how to use ARPACK in considerable detail. To run these drivers, you may use the makefile in that directory and issue, for example, "make sssimp", and then execute using "sssimp" The output should look like: _saupd: number of update iterations taken ----------------------------------------- 1 - 1: 5 _saupd: number of "converged" Ritz values ----------------------------------------- 1 - 1: 4 _saupd: final Ritz values ------------------------- 1 - 4: 8.912E+02 9.198E+02 9.198E+02 9.484E+02 _saupd: corresponding error bounds ---------------------------------- 1 - 4: 4.686E-11 1.905E-08 1.050E-10 5.700E-19 ========================================== = Symmetric implicit Arnoldi update code = = Version Number: 2.1 = = Version Date: 11/15/95 = ========================================== = Summary of timing statistics = ========================================== Total number update iterations = 5 Total number of OP*x operations = 78 Total number of B*x operations = 0 Total number of reorthogonalization steps = 78 Total number of iterative refinement steps = 0 Total number of restart steps = 0 Total time in user OP*x operation = 0.066667 Total time in user B*x operation = 0.000000 Total time in Arnoldi update routine = 1.166667 Total time in ssaup2 routine = 1.166667 Total time in basic Arnoldi iteration loop = 0.216667 Total time in reorthogonalization phase = 0.066667 Total time in (re)start vector generation = 0.000000 Total time in trid eigenvalue subproblem = 0.050000 Total time in getting the shifts = 0.000000 Total time in applying the shifts = 0.900000 Total time in convergence testing = 0.000000 Ritz values and relative residuals ---------------------------------- Col 1 Col 2 Row 1: 8.91167E+02 6.95597E-07 Row 2: 9.19781E+02 3.30156E-07 Row 3: 9.19781E+02 4.25717E-07 Row 4: 9.48395E+02 3.20519E-07 _SSIMP ====== Size of the matrix is 100 The number of Ritz values requested is 4 The number of Arnoldi vectors generated (NCV) is 20 What portion of the spectrum: LM The number of converged Ritz values is 4 The number of Implicit Arnoldi update iterations taken is 5 The number of OP*x is 78 The convergence criterion is 5.96046E-08 3. Convention ---------- The naming convention for each driver is explained in the README file in each subdirectory. 4. LAPACK & BLAS routines ---------------------- All ARPACK codes assume the use of LAPACK version 2.0 codes. LAPACK and BLAS routines needed for each driver program are listed at the beginning of the documentation in each driver program.