esolve(1)

🌸 NAME 🌸

esolve — eigensolver for standard eigenvalue problems 💖

Welcome to esolve(1), bestie. Section 1 of the manual, Utility Commands energy. It solves eigenvalue problems, that's the whole personality, and it does it so well. 🎀

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✨ SYNOPSIS ✨

esolve matrix_filename evalues_filename evectors_filename residuals_filename iters_filename [options]

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🦋 DESCRIPTION 🦋

okay so here's the tea ☕ — this program takes the matrix data from matrix_filename and solves the standard eigenvalue problem A*x = l*x with whichever solver you picked in options. Then it writes out the number of eigenvalues you asked for — and that count comes from the -ss option — into evalues_filename, plus the associated eigenvectors, residual norms, and numbers of iterations into evectors_filename, residuals_filename, and iters_filename respectively. All of it lands in the extended Matrix Market format (see the Appendix of the Lis User Guide for the full deets). 📝

And for the matrix filename itself? Both the Matrix Market format and the Harwell-Boeing format are supported. Versatile queen. We love that for us. 👑

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💅 OPTIONS 💅

The following options are supported:

• -e eigensolver — pick ur eigensolver, this is the main character of the whole operation ✨

The following options are supported for eigensolver:

• -e {pi|1} — Power
• -e {ii|2} — Inverse
• -e {rqi|3} — Rayleigh Quotient
• -e {cg|4} — CG
• -e {cr|5} — CR
• -e {si|6} — Subspace
  • -ss [1] — the size of the subspace
• -e {li|7} — Lanczos
  • -ss [1] — the size of the subspace
• -e {ai|8} — Arnoldi
  • -ss [1] — the size of the subspace

• -i linear solver — the inner linear solver, aka the supporting cast 🫶

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 glow-up that makes ur linear solver actually behave ✨

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
• -ie [ii] — the inner eigensolver used in Subspace, Lanczos and 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. 📖 (fr fr, it's all in there)

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🚪 EXIT STATUS 🚪

The following exit values are returned:

• 0 — the process is normally terminated ✅ slay
• unspecified — an error occurred 😭 not slay

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👀 SEE ALSO 👀

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

http://www.ssisc.org/lis/

http://math.nist.gov/MatrixMarket/

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and that's the whole page, bestie 🫶 this one's a Man Page, dated 19 Sep 2017, and it lives under esolve(1) — go forth and diagonalize, you absolute icon 👑✨