Command Line Interface

Commands

harmonic-measure corners

Compute harmonic measure of corner neighborhoods.

harmonic-measure corners --n 16 --radius 0.1
harmonic-measure corners --n 32 --basepoint 0.5,0.5

Options:

  • --n: Lamé exponent (default: 8)

  • --radius: Corner neighborhood radius (default: 0.1)

  • --basepoint: Interior basepoint as x,y (default: 0,0)

  • --quality: Computation quality: fast, mid, high

harmonic-measure convergence

Test convergence with adaptive refinement.

harmonic-measure convergence --n 32 --quality high

Options:

  • --n: Lamé exponent

  • --quality: Refinement quality level

  • --tol: Convergence tolerance (default: 1e-8)

  • --verbose: Show refinement history

harmonic-measure scaling

Verify the n^{-2} scaling law across multiple exponents.

harmonic-measure scaling --ns 8 12 16 24 32 48 64
harmonic-measure scaling --output scaling.json

Options:

  • --ns: List of Lamé exponents

  • --quality: Quality for each computation

  • --output: Save results to JSON file

  • --plot: Generate log-log plot

harmonic-measure density

Visualize harmonic measure density on the boundary.

harmonic-measure density --n 16 --output density.png
harmonic-measure density --n 32 --basepoint 0.3,0.3 --show

Options:

  • --n: Lamé exponent

  • --basepoint: Interior point (default: origin)

  • --output: Save plot to file

  • --show: Display plot interactively

  • --colormap: Matplotlib colormap name

Examples

Basic Workflow

# 1. Quick convergence check
harmonic-measure convergence --n 16 --quality fast

# 2. Full scaling study
harmonic-measure scaling --ns 8 16 32 64 --quality mid --output results.json

# 3. Visualize density
harmonic-measure density --n 32 --output fig1.png

Research Workflow

# High-accuracy convergence
harmonic-measure convergence --n 48 --quality high --tol 1e-10 --verbose

# Generate publication figure
harmonic-measure scaling --ns 8 12 16 24 32 48 64 96 --quality high --plot --output scaling.pdf