User guide

The user guide explains how to use PETAL2D reliably and how to interpret its outputs. The formal derivations live in the Theory. The API signatures live in the API reference.

• Inputs, coordinates, and centering
  • Callable fields
  • Sampled Cartesian fields
  • Expansion origin
  • rmax and safe_rmax
• Choosing parameters
  • Radial resolution: Nr
  • Angular resolution: Ntheta
  • Angular truncation: recon_err_tol
  • Maximum angular index: m_abs_max
  • Interpolation: interp_method
  • Radial cutoff diagnostics
• Interpreting results
  • Full spectrum versus retained spectrum
  • Radial coefficients rho[m]
  • Mode power
  • selected_pairs
  • Reconstruction error
  • domain_consistency
  • Cutoff radii
• Applications and interpretation patterns
  • Complex wavefunctions and angular momentum
  • Atomic-orbital and Wannier character
  • Local crystal symmetry
  • Densities and scalar observables
  • Complex order parameters and vortices
  • Photonic, phononic, acoustic, and PDE modes
  • Scientific imaging and morphology
  • When PETAL2D is the wrong tool
• Plotting
  • Harmonic spectrum and radial profiles
  • Original versus reconstruction
  • Saving figures
• Numerical considerations and failure modes
  • Exact mathematics versus numerical implementation
  • Radial quadrature
  • Angular aliasing
  • Interpolation leakage
  • Centering sensitivity
  • Multiple localized objects
  • Complex fields
  • What PETAL2D does not currently support