vsh-tools 0.1.0

Vector Spherical Harmonics analysis tools (rotation, glide, quadrupole)

Vector Spherical Harmonics (VSH) analysis toolkit

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A modern Python package for vector spherical harmonics (VSH) analysis — primarily for astrometric and celestial reference frame studies (e.g., Gaia, VLBI).

Reference: Mignard & Klioner (2012), A&A 547, A59 doi:10.1051/0004-6361/201219927

Package structure

vsh_tools/
 ├── basis.py           # scalar & vector spherical harmonic bases
 ├── bootstrap.py       # bootstrap confidence estimation
 ├── diagnostics.py     # goodness-of-fit, residual diagnostics
 ├── fit.py             # LSQ fitting interface (vsh_fit)
 ├── glide.py           # glide decomposition, GA-related utilities
 ├── legacy.py          # consolidated older workflow
 ├── linalg.py          # linear algebra helpers
 ├── metrics.py         # stats & chi² computations
 ├── outliers.py        # outlier clipping
 ├── power.py           # power spectrum and significance
 ├── rgq.py             # rotation–glide–quadrupole functions
 ├── scalar_basis.py    # scalar spherical harmonics
 ├── significance.py    # significance of harmonics
 ├── stats.py           # statistical utilities
 └── transforms.py      # conversions between parameter representations

Quick test

import numpy as np
from vsh_tools.fit import vsh_fit
from vsh_tools.rgq import vsh_func

# true params: (g1,g2,g3,r1,r2,r3)
p_true = np.array([30, 24, 12, 20, 30, 15])
ra  = np.deg2rad(np.linspace(0, 360, 1000))
dec = np.deg2rad(np.linspace(-90, 90, 1000))

dra, ddec = vsh_func(ra, dec, p_true, l_max=1)
dra_err = ddec_err = np.ones_like(dra)

out = vsh_fit(dra, ddec, dra_err, ddec_err, np.rad2deg(ra), np.rad2deg(dec),
              l_max=1, pos_in_rad=False, fit_type="full")
print(out["pmt"])  # estimated coefficients

For any questions and comments, please contact me at [e-mail].