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How to Choose a Linear Solver

This guide helps you select the appropriate linear solver for your network matrix computations.

Available Solvers

PowerNetworkMatrices.jl supports three linear solver methods:

  1. KLU (default) - Sparse solver using KLU factorization
  2. Dense - Dense matrix operations
  3. MKLPardiso - Intel's MKL Pardiso solver (Intel systems only)

Choosing the Right Solver

Use KLU When:

  • Working with typical power systems (most cases)
  • System size is medium to large (> 100 buses)
  • You want good performance without special dependencies
  • Running on any platform (Linux, macOS, Windows)

Use PTDF with the default KLU solver:

ptdf_matrix = PTDF(sys)  # KLU is the default
# or explicitly:
ptdf_matrix = PTDF(sys; linear_solver = "KLU")

Use Dense When:

  • System is very small (< 30 buses)
  • You're debugging or validating results
  • Matrix operations are simple and small-scale

Specify the Dense solver explicitly:

ptdf_matrix = PTDF(sys; linear_solver = "Dense")

Use MKLPardiso When:

  • You have Intel processors
  • Running on Linux or Windows (not available on macOS)
  • Maximum performance is critical
  • Working with very large systems (> 1000 buses)

Specify the MKLPardiso solver:

ptdf_matrix = PTDF(sys; linear_solver = "MKLPardiso")

Performance Considerations

System Size

BusesRecommended Solver
< 30Dense or KLU
30-1000KLU
> 1000KLU or MKLPardiso

Platform Availability

SolverLinuxWindowsmacOS
KLU✓✓✓
Dense✓✓✓
MKLPardiso✓✓✗

Switching Solvers

You can easily switch between solvers to compare performance:

using BenchmarkTools

# Benchmark KLU
@btime ptdf_klu = PTDF($sys; linear_solver = "KLU")

# Benchmark Dense
@btime ptdf_dense = PTDF($sys; linear_solver = "Dense")

# Benchmark MKLPardiso (if available)
@btime ptdf_mkl = PTDF($sys; linear_solver = "MKLPardiso")

Troubleshooting

MKLPardiso Not Available

If you get an error when using MKLPardiso:

  1. Verify you're on Linux or Windows (not macOS)
  2. Check that you have Intel processors
  3. Ensure MKL dependencies are installed

Fall back to KLU if MKLPardiso is unavailable.