Miscellaneous Examples

December 8, 2022 ยท View on GitHub

This directory contains examples and tests for the frontend routines, i.e. solving equations with general coefficient matrices. The examples are used as test codes as well. All examples feature the --help command line options to view the actual parameters that can be used to adjust the example,

The following miscellaneous codes are available:

  • benchmark_eigenvalue_reorder: Check the influence of sorted eigenvalues on the performance of the solvers with local aligned copies for the generalized Sylvester equation.
  • benchmark_dag: Benchmark the level-3 and the DAG solver for the generalized Sylvester Equation.
  • benchmark_recsy: Benchmark the standard RECSY and the parallel RECSY implementation. This is only available if the examples are compiled with RECSY support. Otherwise, this is not build.
  • benchmark_row_columnwise: Benchmark the influence of the row- and column- wise computation of the solution for the generalized Sylvester equation.

Generalized Lyapunov Solvers

The following codes are solvers for the generalized Lyapunov equation that can read the coefficient matrices from a MATLAB (v7.3) file. The following datasets have to exist in the MATLAB file:

  • A: co Miscellaneous Examples ======================

This directory contains examples and tests for the frontend routines, i.e. solving equations with general coefficient matrices. The examples are used as test codes as well. All examples feature the --help command line options to view the actual parameters that can be used to adjust the example,

The following miscellaneous codes are available:

  • benchmark_eigenvalue_reorder: Check the influence of sorted eigenvalues on the performance of the solvers with local aligned copies for the generalized Sylvester equation.
  • benchmark_dag: Benchmark the level-3 and the DAG solver for the generalized Sylvester Equation.
  • benchmark_recsy: Benchmark the standard RECSY and the parallel RECSY implementation. This is only available if the examples are compiled with RECSY support. Otherwise, this is not build.
  • benchmark_row_columnwise: Benchmark the influence of the row- and column- wise computation of the solution for the generalized Sylvester equation.

Generalized Lyapunov Solvers

The following codes are solvers for the generalized Lyapunov equation that can read the coefficient matrices from a MATLAB (v7.3) file. The following datasets have to exist in the MATLAB file:

  • A: coefficient matrix A
  • B: coefficient matrix B
  • ASCHUR: generalized Schur form of A
  • BSCHUR: generalized Schur form of B
  • Q: left-hand side transformation matrix for the generalized Schur form
  • Z: right-hand side transformation matrix for the generalized Schur form
  • TIMES: vector of length two containing the WALL and the CPU time required to compute the generalized Schur decomposition.

All codes are executes via:

 examples inputfile.mat

The following examples exist:

  • solve_slicot_glyap: Solve the generalized Lyapunov equation with SLICOT.
  • solve_mepack_glyap: Solve the generalized Lyapunov equation with MEPACK.
  • solve_refine_glyap: Solve the generalized Lyapunov equation with iterative refinement.

effcient matrix A

  • B: coeffcient matrix B
  • ASCHUR: generalized Schur form of A
  • BSCHUR: generalized Schur form of B
  • Q: left-hand side transformation matrix for the generalized Schur form
  • Z: right-hand side transformation matrix for the generalized Schur form
  • TIMES: vector of length two containing the WALL and the CPU time required to compute the generalized Schur decomposition.

All codes are executes via:

 examples inputfile.mat

The following examples exist:

  • solve_slicot_glyap: Solve the generalized Lyapunov equation with SLICOT.
  • solve_mepack_glyap: Solve the generalized Lyapunov equation with MEPACK.
  • solve_refine_glyap: Solve the generalized Lyapunov equation with iterative refinement.