Basis module

Compute integrals and dot products of functional bases.

pyrotor.basis.compute_basis_features(basis, basis_features, basis_dimension, derivative)

Format integrals and dot products of basis elements (and their derivatives) for the optimisation problem.

Inputs:

• basis: string

  Name of the functional basis

• basis_features: dict

  Contain information on the basis for each state

• basis_dimension: dict

  Give the number of basis functions for each state

• derivative: boolean

  Take into account or not derivatives of states

Outputs:

• integral: ndarray

  Array containing the integrals over an interval

• dot_product: ndarray

  Matrix containing the dot products

pyrotor.basis.compute_bspline_dot_product_derivatives(basis_features, basis_dimension)

Compute dot products of B-splines and their derivatives.

Input:

• basis_features: dict

  Contain information on the basis for each state

• basis_dimension: dict

  Give the number of basis functions for each state

Outputs:

• dot_product_12: ndarray

  Array containing the dot products of Legendre polynomials with their derivatives

• dot_product_22: ndarray

  Array containing the dot products of Legendre polynomials derivatives

pyrotor.basis.compute_bspline_integral_derivatives(basis_dimension)

Compute integrals of B-splines.

Input:

• basis_dimension: dict

  Give the number of basis functions for each state

Output:

• integral_deriv: ndarray

  Array containing the integrals over an interval

pyrotor.basis.compute_bspline_integral_dot_product(basis_features, basis_dimension)

Compute integrals and dot products of B-splines.

Input:

• basis_features: dict

  Contain information on the basis for each state

• basis_dimension: dict

  Give the number of basis functions for each state

Outputs:

• integral: ndarray

  Array containing the integrals over an interval

• dot_product: ndarray

  Matrix containing the dot products

pyrotor.basis.compute_legendre_dot_product_derivatives(basis_dimension)

Compute dot products of Legendre polynomials and their derivatives.

Input:

• basis_dimension: dict

  Give the number of basis functions for each state

Outputs:

• dot_product_12: ndarray

  Array containing the dot products of Legendre polynomials with their derivatives

• dot_product_22: ndarray

  Array containing the dot products of Legendre polynomials derivatives

pyrotor.basis.compute_legendre_integral_derivatives(basis_dimension)

Compute integrals of Legendre polynomials derivatives.

Input:

• basis_dimension: dict

  Give the number of basis functions for each state

Output:

• integral_deriv: ndarray

  Array containing the integrals over an interval

pyrotor.basis.compute_legendre_integral_dot_product(basis_dimension)

Compute integrals and dot products of Legendre polynomials.

Input:

• basis_dimension: dict

  Give the number of basis functions for each state

Outputs:

• integral: ndarray

  Array containing the integrals over an interval

• dot_product: ndarray

  Matrix containing the dot products