NAME

gesolve - eigensolver for generalized eigenvalue problems

SYNOPSIS

gesolve matrix_a_filename matrix_b_filename evalues_filename evectors_filename residuals_filename iters_filename [options]

DESCRIPTION

This program inputs the matrix data from matrix_a_filename matrix_b_filename, and solves the generalized eigenvalue problem A*x = l*B*x with the solver specified by options. It outputs the specified number of eigenvalues, the number of which is given by option -ss, to evalues_filename and the associated eigenvectors, residual norms, and numbers of iterations to evectors_filename, residuals_filename, and iters_filename respectively in the extended Matrix Market format (see Appendix of Lis User Guide). Both the Matrix Market format and the Harwell-Boeing format are supported for the matrix filenames.

OPTIONS

The following options are supported:

-e eigensolver: The following options are supported for eigensolver:

-e {gpi|9}: Generalized Power
-e {gii|10}: Generalized Inverse
-e {grqi|11}: Generalized Rayleigh Quotient
-e {gcg|12}: Generalized CR
-e {gcr|13}: Generalized CR
-e {gsi|14}: Generalized Subspace

-ss [1]: The size of the subspace

-e {gli|15}: Generalized Lanczos

-ss [1]: The size of the subspace

-e {gai|16}: Generalized Arnoldi

-ss [1]: The size of the subspace

-i linear solver: The following options are supported for inner linear solver:

-i {cg|1}: CG
-i {bicg|2}: BiCG
-i {cgs|3}: CGS
-i {bicgstab|4}: BiCGSTAB
-i {bicgstabl|5}: BiCGSTAB(l)

-ell [2]: The degree l

-i {gpbicg|6}: GPBiCG
-i {tfqmr|7}: TFQMR
-i {orthomin|8}: Orthomin(m)

-restart [40]: The restart value m

-i {gmres|9}: GMRES(m)

-restart [40]: The restart value m

-i {jacobi|10}: Jacobi
-i {gs|11}: Gauss-Seidel
-i {sor|12}: SOR

-omega [1.9]: The relaxation coefficient omega (0<omega<2)

-i {bicgsafe|13}: BiCGSafe
-i {cr|14}: CR
-i {bicr|15}: BiCR
-i {crs|16}: CRS
-i {bicrstab|17}: BiCRSTAB
-i {gpbicr|18}: GPBiCR
-i {bicrsafe|19}: BiCRSafe
-i {fgmres|20}: FGMRES(m)

-restart [40]: The restart value m

-i {idrs|21}: IDR(s)

-irestart [2]: The restart value s

-i {idr1|22}: IDR(1)
-i {minres|23}: MINRES
-i {cocg|24}: COCG
-i {cocr|25}: COCR

-p preconditioner: The following options are supported for preconditioner:

-p {none|0}: None
-p {jacobi|1}: Jacobi
-p {ilu|2}: ILU(k)

-ilu_fill [0]: The fill level k

-p {ssor|3}: SSOR

-ssor_omega [1.0]: The relaxation coefficient omega (0<omega<2)

-p {hybrid|4}: Hybrid

-hybrid_i [sor]: The linear solver

-hybrid_maxiter [25]: The maximum number of the iterations

-hybrid_tol [1.0e-3]: The convergence criterion

-hybrid_omega [1.5]: The relaxation coefficient omega of the SOR (0<omega<2)

-hybrid_ell [2]: The degree l of the BiCGSTAB(l)

-hybrid_restart [40]: The restart values of the GMRES and Orthomin

-p {is|5}: I+S

-is_alpha [1.0]: The parameter alpha of I+alpha*S(m)

-is_m [3]: The parameter m of I+alpha*S(m)

-p {sainv|6}: SAINV

-sainv_drop [0.05]: The drop criterion

-p {saamg|7}: SA-AMG

-saamg_unsym [false]: Select the unsymmetric version (The matrix structure must be symmetric)

-saamg_theta [0.05|0.12]: The drop criterion

-p {iluc|8}: Crout ILU

-iluc_drop [0.05]: The drop criterion

-iluc_rate [5.0]: The ration of maximum fill-in

-p {ilut|9}: ILUT

-ilut_drop [0.05]: The drop criterion

-ilut_rate [5.0]: The ration of maximum fill-in

-adds true: Additive Schwarz

-adds_iter [1]: The number of the iteration

Other Options for eigensolver:

-emaxiter [1000]: The maximum number of the iterations
-etol [1.0e-12]: The convergence criterion
-eprint [0]: The output of the residual history

-eprint {none|0}: None

-eprint {mem|1}: Save the residual history

-eprint {out|2}: Output it to the standard output

-eprint {all|3}: Save the residual history and output it to the standard output

-ige [gii]: The inner eigensolver used in generalized Subspace, generalized Lanczos, and generalized Arnoldi
-shift [0.0]: The amount of the shift
-initx_ones [true]: The behavior of the initial vector x_0

-initx_ones {false|0}: Given values

-initx_ones {true|1}: All values are set to 1

-omp_num_threads [t]: The number of the threads (t represents the maximum number of the threads)
-estorage [0]: The matrix storage format
-estorage_block [2]: The block size of the BSR and BSC formats
-ef [0]: The precision of the eigensolver

-ef {double|0}: Double precision

-ef {quad|1}: Double-double (quadruple) precision

Other options for inner linear solver:

-maxiter [1000]: The maximum number of the iterations
-tol [1.0e-12]: The convergence criterion
-print [0]: The output of the residual history

-print {none|0}: None

-print {mem|1}: Save the residual history

-print {out|2}: Output it to the standard output

-print {all|3}: Save the residual history and output it to the standard output

-scale [0]: The scaling

-scale {none|0}: No scaling

-scale {jacobi|1}: The Jacobi scaling

-scale {symm_diag|2}: The diagonal scaling

-initx_zeros [true]: The behavior of the initial vector x_0

-initx_zero {false|0}: Given values

-initx_zero {true|1}: All values are set to 0

-omp_num_threads [t]: The number of the threads (t represents the maximum number of the threads)
-storage [0]: The matrix storage format
-storage_block [2]: The block size of the BSR and BSC formats
-f [0]: The precision of the linear solver

-f {double|0}: Double precision

-f {quad|1}: Double-double (quadruple) precision

See Lis User Guide for full description.

EXIT STATUS

The following exit values are returned:

0: The process is normally terminated
unspecified: An error occurred

NAME

SYNOPSIS

DESCRIPTION

OPTIONS

EXIT STATUS

SEE ALSO