80-digit chiral transfer matrices

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Reference
80-digit chiral transfer matrices
Kind
precision: the same mathematics in mpmath at 60–80 digits, written separately in src/pystratify/references.py and benchmarks/mp_reference.py: proves the numerics, not the formulation
Calculated
chiral T-matrix, layer solutions
Agreement
1e-11
A chiral shell (κ = 0.05 + 0.01i) on a 40 nm core in water, 690 nm: the T-matrix against 80-digit transfer matrices The helicity blocks of the host T-matrix: direct 4×4 transfer matrices in 80-digit arithmetic (mp_reference.py) against PyStratify's scaled recursion in double precision, as the elements fall over many decades.
51015202530354010⁻¹³⁷10⁻¹²⁰10⁻¹⁰³10⁻⁸⁶10⁻⁶⁹10⁻⁵²10⁻³⁵10⁻¹⁸10⁻¹order ℓ|T|
|T₊₊|, PyStratify |T₋₋|, PyStratify |T₊₋|, PyStratify |T₊₊|, 80 digits |T₋₋|, 80 digits |T₊₋|, 80 digits
Hover to read values.
  • largest |T − T₈₀| / max |T₈₀|: 7.71×10⁻¹⁶
  • PyStratify the lines, the reference the circles

Run it yourself: sphere_checks.py · test_chiral.py · figures.py · SPHERE_CHECKS.md on GitHub, PyStratify 97e52a9