Crate rebasis 

Linear maps between function bases.

A quantity f(x) = Σ_j f_j B_j(x) is described by coefficients in a Space of Elements. rebasis computes the sparse matrices that take f_j to coefficients or measurements in another space: instrument line shapes (measure), point evaluation (evaluate), L2 projection for regridding (Projection) and penalized least-squares fitting for smooth conservative upsampling and smoothing (Fit).

All inner products are exact for piecewise-polynomial elements (boxes, hats, B-splines, tabulated shapes) and accurate to rounding for the analytic profiles (Profile).

Re-exports

pub use coordinate::CoordinateMap;

pub use covariance::Atoms;

pub use covariance::Covariance1d;

pub use covariance::Family;

pub use covariance::ProductCovariance;

pub use covariance::VarianceProfile;

pub use element::Element;

pub use element::Segment;

pub use element::Shape;

pub use error::Error;

pub use error::Result;

pub use ops::Bounds;

pub use ops::Fit;

pub use ops::Normalization;

pub use ops::Penalty;

pub use ops::Projection;

pub use ops::evaluate;

pub use ops::gram;

pub use ops::inner_products;

pub use ops::measure;

pub use ops::measure_derivative;

pub use profile::Apodization;

pub use profile::FWHM_PER_SIGMA;

pub use profile::MaternOrder;

pub use profile::Parameter;

pub use profile::Profile;

pub use space::Interpolation;

pub use space::Space;

pub use sparse::Csr;

Modules

coordinate

Changes of coordinate: an element defined in u used in x = forward(u).

covariance

Separable stationary covariances, and the exact covariances between weighted averages that optimal estimation needs.

element

Single basis functions (or measurement kernels) on the real line.

error

ops

Linear maps between spaces.

profile

Analytic line-shape profiles: smooth (or piecewise smooth) functions of the offset t from the line center, each normalized to 1 at t = 0.

space

A space is an ordered set of elements: the basis {B_j} that coefficients f_j refer to, or a set of measurement kernels {K_i}.

sparse

Compressed sparse row matrices: the output of every rebasis operation.

special

Special functions for the line-shape profiles.

Structs

BandedCholesky

Enums

Weight

The weight w(x) of the inner product.

Functions

inner

⟨a, b⟩_w. knots is scratch space, reused between calls to avoid allocation.

inner_derivative

∂/∂p ⟨k, b⟩_w for a parameter p of the kernel k. jumps must be k.jumps(p).

integral

∫ φ(x) w(x) dx (w(x₀) for a delta at x₀).

integral_derivative

∂/∂p ∫ k w for a parameter p of the kernel k. jumps must be k.jumps(p).