This software is intended for the solution of nonlinear eigenvalue problems
of the type
  
   [ K - lambda*M + i*sum( f_k(lambda)*W_k ) ]*x = 0

where k=1,2,...,NT, i = sqrt(-1), and K, M, W_k are real matrices. Pade 
approximants are used for the construction of an equivalent linear 
eigenvalue problem, which is then solved with ARPACK and SuperLU 
(shift-and-invert mode). With the exception of ARPACK (and
residuals), all computations are performed in real arithmetic.

The software has been customized to solve the problem

   [ K- lambda*M +
         i*sqrt(lambda-(sigma_1)^2)*W_1 +
         i*sqrt(lambda-(sigma_2)^2)*W_2 ]*x = 0

which appears in the study of linear accelerator cavities.

Directories:

  DATA: test cases
  INPUT: input files (parameters for the test cases)  
  INSTALL: installation specifics 
  SRC: source files

Input files:

  Each input file should contain, in this order:

  file where the matrix K   will be read from
  file where the matrix M   will be read from
  file where the matrix W_1 will be read from
  file where the matrix W_2 will be read from
  sigma_1
  sigma_2
  sigma_P (expansion point of Pade approximants)
  sigma (translation of origin, not necessarily equal to sigma_P)
  p_1 (order of the polynomials in the rational function associated to W_1)
  p_2 (order of the polynomials in the rational function associated to W_2)
  number of eigenpairs to be computed

Installation:

  The program has been compiled/tested with the gnu and intel compilers. Specifics 
  are given in INSTALL, e.g. make.inc.gcc and make.inc.icc. One of those files 
  needs to be copied into make.inc, and modified to point to the installations 
  of LAPACK, BLAS, SuperLU and ARPACK.

Testing:
   
  Once succesfully compiled, one can do 

     main_PAL.x < INPUT/input_a.dat 

  to check the integrity of the installation. 

Assumptions/restrictions:

- The matrix K, M, W_k are stored in COO format, with indices starting
  at 1 (adjustmens to 0 are done internally).
- K and M must have the same sparse pattern. 
- Low-rank approximations for W_k are computed with LAPACK's dgeqp3/dorgqr; 
  a cutoff is used to determine the rank of W_k. (To be implemented: a
  more robust strategy to determine the rank of W.) 
- Currently, sigma=sigma_P and p_1=p_2