Experimental

SpectralKit.Experimental — Module

Experimental functionality. Officially not (yet) part of the API.

A best effort is made to

only change in breaking ways (including integration into the public API) with major or minor releases.
fix issues (users are encouraged to open them)

source

Proposed additions to general API

SpectralKit.Experimental.constant_coefficients — Function

constant_coefficients(basis, y)

Approximate a constant value y on basis.

Formally, return a set of coefficients θ such that linear_combination(basis, θ, x) ≈ y for all x in the domain.

source

modeling setup

          make_model_parameters       ┏━━━━━━━━━━━━━━━━━━━━┓
       ╭──────▷──────╭───────────────▶┃  model_parameters  ┃
       │  ┏━━━━━━━━━━┷━━━━━━━━━━━┓    ┗━━┯━━━━━━━━━━━━━━━━━┛
       │  ┃  model_coefficients  ┃       │
       │  ┃  (model_dimension)   ┃       │
       │  ┗━━━━━━━━━━┯━━━━━━━━━━━┛       │  calculate_derived_quantities   ┏━━━━━━━━━━━━━━━━━━━━━━┓
       │   ╭────▷────╰─────────▷─────────╰──────────────▷─────────────────▶┃  derived_quantities  ┃
       │   │                                                               ┗━━━┯━━━━━━━━━━━━━━━━━━┛
       │   │                                                                   │
       │   │                                                                   │
       │   │                          make_approximation                       │     ┏━━━━━━━━━━━━━━━━━┓
       │   │   ╭────────▷─────────╭────────────▷───────────╭─────▷────╭────▷───╰────▶┃  approximation  ┃
       │   │   │                  │                        │          │              ┗━━━━━━━━━━━━━━━━━┛
       │   │   │                  │                        │  ┏━━━━━━━┷━━━━━━━━━━━━━━━━━━━━━━┓
       │   │   │                  │                        │  ┃  approximation coefficients  ┃
       │   │   │                  │                        │  ┃   (approximation_dimension)  ┃
       │   │   │                  │                        │  ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
  ┏━━━━┷━━━┷━━━┷━━━┓  ┏━━━━━━━━━━━┷━━━━━━━━━━━┓   ┏━━━━━━━━┷━━━━━━━━━━━━━━━━┓
  ┃  model_family  ┃  ┃  approximation_setup  ┃   ┃   approximation_level   ┃
  ┗━━━━━━━┯━━━━━━━━┛  ┗━━━━━━━━━━┯━━━━━━━━━━━━┛   ┃ (approximation_levels)  ┃
          │                      │                ┗━━━━━━━━━━┯━━━━━━━━━━━━━━┛
          │                      │                           │
          │                      │                           │      make_grid        ┏━━━━━━━━┓
          ╰─────────────▷────────╰─────────────▷─────────────╰───────────▷──────────▶┃  grid  ┃
                                                                                     ┗━━━━━━━━┛

augment_coefficients(model_family, approximation_setup, approximation_level, approximation_coefficients)

initial_guess(model_family, approximation_setup) => approximation_level, approximation_coefficients

residuals(model_family, model_parameters, approximation, gridpoint)

vec_residuals(model_family, approximation_level, model_coefficients, approximation_coefficients, gridpoint)