hpcg_kernel(1)

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

💖 hpcg_kernel 💖 — the NAME section, bestie

so this page is for hpcg_kernel — the high performance conjugate gradient kernel benchmark ✨ (it lives in section 1 of the Utility Commands manual, in case you were wondering 🫶)

🌈 SYNOPSIS 🌈

hpcg_kernel matrix_type solution_filename rhistory_filename [options]

💅 DESCRIPTION 💅

okay so here's the vibe: this program solves the linear equation Ax = b using an additive Schwarz, symmetric Gauss-Seidel preconditioned conjugate gradient solver. the coefficient matrix A of size lmn comes from a discretized three dimensional Poisson's equation, using the twenty-seven point central difference scheme — iconic, honestly. the coefficient matrix gets stored in the storage format you pick with matrix_type, and the solver is whatever you pick with options. 🎀

it drops the solution into solution_filename in the extended Matrix Market format, and the residual history into rhistory_filename in the PLAIN format (peep the Appendix of the Lis User Guide for that one). the right-hand side vector is set such that the values of the elements of the solution are 1. and the values l, m and n? those are the numbers of grid points in each dimension. no cap. 💅

✨ OVERRIDE OPTIONS ✨

the following options are supported, bestie — take notes 📝

  • -i linear solver — pick your linear solver. here's the whole menu:
    • -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, and it's gotta be 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 — and now the preconditioner, the other main character:
    • -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, still gotta be 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 (heads up: 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 🫶

  • -maxiter [1000] — the maximum number of the iterations
  • -tol [1.0e-12] — the convergence criterion
  • -print [0] — the display of the residual history
    • -print {none|0} — None
    • -print {mem|1} — Save the residual history
    • -print {out|2} — Display the residual history
    • -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. 📖 (fr fr, go read it if you want the whole lore)

💀 EXIT STATUS 💀

the following exit values are returned:

  1. 0 — the process is normally terminated 🥳
  2. unspecified — an error occurred 😭

👑 SEE ALSO 👑

lis(3), lsolve(1), esolve(1), hpcg_spmvtest(1), spmvtest1(1), spmvtest2(1), spmvtest2b(1), spmvtest3(1), spmvtest3b(1), spmvtest4(1), spmvtest5(1)

and that's the whole page, bestie 💖 this lil' Man Page came out on 14 Sep 2017, filed under hpcg_kernel(1) — go slay some sparse linear systems, you got this ✨🎀🦋

📦 where this page comes from