spheresmooth.smoothing#

This module provides the core functionality for penalized spherical smoothing, equivalent to the exported functions in the R package spheresmooth.

The functions defined here implement the public-facing API of the Python version, while internal mathematical components (loss gradients, penalty gradients, jump operators, Acos utilities, etc.) are delegated to _internal.py.

Main features include:

  • Construction of quantile-based knot locations (knots_quantile)

  • Computation of geodesic loss on the sphere (calculate_loss)

  • Full penalized spline fitting procedure (penalized_linear_spherical_spline)

  • Integration with geometric utilities such as:

    • spherical distance (spherical_dist)

    • exponential map (exp_map)

    • geodesic interpolation (geodesic, geodesic_lower)

    • piecewise geodesic curve construction (piecewise_geodesic)

    • coordinate transformations (spherical/cartesian)

This module works closely with geometry.py and _internal.py, reproducing the piecewise-geodesic smoothing structure of the original R implementation from the spheresmooth package.

Functions

calculate_loss(y, gamma)

Calculate loss based on squared spherical distances between observed values and predicted values on the curve.

knots_quantile(x, dimension[, tiny])

Exact Python replication of R's knots_quantile() with quantile(type = 3).

penalized_linear_spherical_spline(t, y[, ...])

Fully implemented Python version of the R function penalized_linear_spherical_spline().

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