gesolve(1)

📦 version 2.1.11, in fedora 43, fedora 44, nixos 26.05, nixpkgs unstable

💖 NAME 💖

okay so bestie, this is the manual page for gesolve(1) — a utility command that is literally an eigensolver for generalized eigenvalue problems. No cap. 💅

✨ SYNOPSIS ✨

gesolve matrix_a_filename matrix_b_filename evalues_filename
evectors_filename residuals_filename iters_filename [options]

🌸 DESCRIPTION 🌸

okay so this program inputs the matrix data from matrix_a_filename and 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 — and the number of those 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, all 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, bestie:

🎀 -e eigensolver 🎀

  • -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 🎀

  • -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 🎀

  • -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

🔥 SEE ALSO 🔥

and that's the whole manual page, bestie! It's gesolve(1), from the Man Page source/version, dated 4 Nov 2017. Slay. 💅✨

📦 where this page comes from