pycollocation package¶

Submodules¶

pycollocation.boundary_value_problems module¶

pycollocation.differential_equations module¶

pycollocation.models module¶

pycollocation.orthogonal_polynomials module¶

pycollocation.solvers module¶

Objects imported here will live in the pycollocation.solvers namespace

class pycollocation.solvers.LeastSquaresSolver(basis_functions)[source]¶

Bases: pycollocation.solvers.solvers.Solver

Attributes

basis_functions Functions used to approximate the solution to a boundary value problem.

Methods

solve(basis_kwargs, boundary_points, ...) Solve a boundary value problem using the collocation method.

solve(basis_kwargs, boundary_points, coefs_array, nodes, problem, **solver_options)[source]¶

Solve a boundary value problem using the collocation method.

Parameters:

basis_kwargs : dict

Dictionary of keyword arguments used to build basis functions.

coefs_array : numpy.ndarray

Array of coefficients for basis functions defining the initial condition.

problem : bvp.TwoPointBVPLike

A two-point boundary value problem (BVP) to solve.

solver_options : dict

Dictionary of options to pass to the non-linear equation solver.

class pycollocation.solvers.Solver(basis_functions)[source]¶

Bases: pycollocation.solvers.solvers.SolverLike

Attributes

basis_functions Functions used to approximate the solution to a boundary value problem.

Methods

solve(basis_kwargs, boundary_points, ...) Solve a boundary value problem using the collocation method.

solve(basis_kwargs, boundary_points, coefs_array, nodes, problem, **solver_options)[source]¶

Solve a boundary value problem using the collocation method.

Parameters:

basis_kwargs : dict

Dictionary of keyword arguments used to build basis functions.

coefs_array : numpy.ndarray

Array of coefficients for basis functions defining the initial condition.

problem : bvp.TwoPointBVPLike

A two-point boundary value problem (BVP) to solve.

solver_options : dict

Dictionary of options to pass to the non-linear equation solver.

class pycollocation.solvers.Solution(basis_kwargs, functions, nodes, problem, residual_function, result)[source]¶

Bases: pycollocation.solvers.solutions.SolutionLike

Class representing the solution to a Boundary Value Problem (BVP).

Attributes

`basis_kwargs`
`functions`
`nodes`
`problem`
`residual_function`
`result`

Methods

`evaluate_residual`(points)
`evaluate_solution`(points)
`normalize_residuals`(points)	Normalize residuals by the level of the variable.

evaluate_residual(points)[source]¶

evaluate_solution(points)[source]¶

normalize_residuals(points)[source]¶: Normalize residuals by the level of the variable.

class pycollocation.solvers.SolutionLike[source]¶

Bases: object

Attributes

`basis_kwargs`
`functions`
`nodes`
`problem`
`residual_function`
`result`

basis_kwargs¶

functions¶

nodes¶

problem¶

residual_function¶

result¶

class pycollocation.solvers.SolverLike[source]¶

Bases: object

Class describing the protocol the all SolverLike objects should satisfy.

Notes

Subclasses should implement solve method as described below.

Attributes

basis_functions Functions used to approximate the solution to a boundary value problem.

Methods

solve(basis_kwargs, boundary_points, ...) Solve a boundary value problem using the collocation method.

basis_functions¶

Functions used to approximate the solution to a boundary value problem.

Getter:	Return the current basis functions.
Type:	basis_functions.BasisFunctions

solve(basis_kwargs, boundary_points, coefs_array, nodes, problem, **solver_options)[source]¶

Solve a boundary value problem using the collocation method.

Parameters:

basis_kwargs : dict

Dictionary of keyword arguments used to build basis functions.

coefs_array : numpy.ndarray

Array of coefficients for basis functions defining the initial condition.

problem : bvp.TwoPointBVPLike

A two-point boundary value problem (BVP) to solve.

solver_options : dict

Dictionary of options to pass to the non-linear equation solver.

pycollocation.symbolics module¶

pycollocation.version module¶

pycollocation.visualizers module¶

Module contents¶

Objects imported here will live in the pycollocation namespace