rebasis

Linear maps between function bases: instrument line shapes, regridding, projection.

A quantity f(x) = Σ_j f_j B_j(x) is described by coefficients in a Space of elements (boxes, hats, B-splines, delta functions, and line-shape profiles: Gaussian, Lorentzian, Voigt, pseudo-Voigt, super-Gaussian, smoothed box, Fourier-transform spectrometer line shapes with the standard apodizations, and tabulated shapes). rebasis computes the sparse matrices that take f_j to

• the responses of measurement kernels (measure), with exact derivatives with respect to the kernels' parameters (measure_derivative);
• point values (evaluate);
• the best L2 representation in another space (Projection, optionally bounded), for conservative regridding;
• the coefficients of a model fitted to measurements (Fit), for smooth conservative upsampling and smoothing splines.

Elements can be used in another coordinate (Space::mapped, e.g. a line shape given in wavelength against a basis in wavenumber). Inner products are exact for piecewise polynomials and accurate to rounding for the analytic profiles.

The Python package is pyrebasis (import rebasis); documentation at https://usask-arg.github.io/rebasis/.

License: MIT.