Submodules¶

pycollocation.boundary_value_problems module¶

Classes for constructing two-point boundary value problems.

@author : davidrpugh

class pycollocation.boundary_value_problems.BoundaryValueProblem[source]¶

Bases: object

Attributes

boundary_conditions

Boundary conditions for the problem.

boundary_conditions[source]¶

Boundary conditions for the problem.

Getter:	Return the boundary conditions for the problem.
Setter:	Set new boundary conditions for the problem.
Type:	dict

class pycollocation.boundary_value_problems.SymbolicBoundaryValueProblem(boundary_conditions, dependent_vars, independent_var, rhs, params)[source]¶

Bases: pycollocation.boundary_value_problems.BoundaryValueProblem, pycollocation.symbolics.SymbolicBoundaryValueProblemLike, pycollocation.differential_equations.SymbolicDifferentialEquation

Class for representing two-point boundary value problems.

Attributes

boundary_conditions	Boundary conditions for the problem.
dependent_vars	Model dependent variables.
independent_var	Symbolic variable representing the independent variable.
params	Dictionary of model parameters.
rhs	Symbolic representation of the right-hand side of a system of differential/difference equations.

pycollocation.differential_equations module¶

Classes for constructing systems of ordinary differential equations.

@author : davidrpugh

class pycollocation.differential_equations.DifferentialEquation(dependent_vars, independent_var, rhs, params)[source]¶

Bases: pycollocation.models.ModelLike

Attributes

dependent_vars	Model dependent variables.
independent_var	Symbolic variable representing the independent variable.
params	Dictionary of model parameters.
rhs	Symbolic representation of the right-hand side of a system of differential/difference equations.

class pycollocation.differential_equations.SymbolicDifferentialEquation(dependent_vars, independent_var, rhs, params)[source]¶

Bases: pycollocation.differential_equations.DifferentialEquation, pycollocation.symbolics.SymbolicModelLike

Attributes

dependent_vars	Model dependent variables.
independent_var	Symbolic variable representing the independent variable.
params	Dictionary of model parameters.
rhs	Symbolic representation of the right-hand side of a system of differential/difference equations.

pycollocation.models module¶

class pycollocation.models.ModelLike[source]¶

Bases: object

Attributes

dependent_vars	Model dependent variables.
independent_var	Symbolic variable representing the independent variable.
params	Dictionary of model parameters.
rhs	Symbolic representation of the right-hand side of a system of differential/difference equations.

dependent_vars[source]¶

Model dependent variables.

Getter:	Return the model dependent variables.
Type:	list

independent_var[source]¶

Symbolic variable representing the independent variable.

Getter:	Return the symbol representing the independent variable.
Type:	sympy.Symbol

params[source]¶

Dictionary of model parameters.

Getter:	Return the current parameter dictionary.
Setter:	Set a new parameter dictionary.
Type:	dict

rhs[source]¶

Symbolic representation of the right-hand side of a system of differential/difference equations.

Getter:	Return the right-hand side of the system of equations.
Type:	dict

pycollocation.orthogonal_polynomials module¶

Classes for solving models using collocation with orthogonal polynomials as the underlying basis functions.

@author: davidrpugh

class pycollocation.orthogonal_polynomials.OrthogonalPolynomialBasis[source]¶

Bases: object

Class for constucting orthogonal polynomial basis functions.

Attributes

degrees	Degrees used when constructing the orthogonal polynomials.
domain	Domain over which the approximated solution is valid.
kind	Kind of polynomials to use when constructing the approximation.

degrees[source]¶

Degrees used when constructing the orthogonal polynomials.

Getter:	Return the degrees attribute.
Type:	dict

domain[source]¶

Domain over which the approximated solution is valid.

Getter:	Return the domain attribute.
Type:	list

kind[source]¶

Kind of polynomials to use when constructing the approximation.

Getter:	Return the kind of orthogonal polynomials.
Type:	string

class pycollocation.orthogonal_polynomials.OrthogonalPolynomialSolver(model)[source]¶

Bases: pycollocation.orthogonal_polynomials.OrthogonalPolynomialBasis, pycollocation.solvers.Solver

Attributes

coefficients	Coefficients to use when constructing the approximating polynomials.
degrees	Degrees used when constructing the orthogonal polynomials.
derivatives	Derivatives of the approximating basis functions.
domain	Domain over which the approximated solution is valid.
functions	The basis functions used to approximate the solution to the model.
kind	Kind of polynomials to use when constructing the approximation.
model	Symbolic representation of the model to solve.
residual_functions	Residual functions
result	Result object

Methods

solve(kind, coefs_dict, domain[, method])

Solve a boundary value problem using orthogonal collocation.

solve(kind, coefs_dict, domain, method='hybr', **kwargs)[source]¶

Solve a boundary value problem using orthogonal collocation.

pycollocation.solvers module¶

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

Bases: object

Base class for all Solvers.

Attributes

coefficients	Coefficients to use when constructing the approximating polynomials.
derivatives	Derivatives of the approximating basis functions.
functions	The basis functions used to approximate the solution to the model.
model	Symbolic representation of the model to solve.
residual_functions	Residual functions
result	Result object

coefficients[source]¶

Coefficients to use when constructing the approximating polynomials.

Getter:	Return the coefficients attribute.
Type:	dict

derivatives[source]¶

Derivatives of the approximating basis functions.

Getter:	Return the derivatives attribute.
Type:	dict

functions[source]¶

The basis functions used to approximate the solution to the model.

Getter:	Return the functions attribute.
Type:	dict

model[source]¶

Symbolic representation of the model to solve.

Getter:	Return the current model.
Setter:	Set a new model to solve.
Type:	models.Model

residual_functions[source]¶

Residual functions

Getter:	Return the current residual functions.

result[source]¶

Result object

Getter:	Return the current result object.
Type:	optimize.Result

pycollocation.symbolics module¶

Classes for constructing symbolic models.

@author : davidrpugh

class pycollocation.symbolics.SymbolicBase[source]¶

Bases: object

class pycollocation.symbolics.SymbolicBoundaryValueProblemLike[source]¶

Bases: pycollocation.symbolics.SymbolicModelLike

class pycollocation.symbolics.SymbolicModelLike[source]¶

Bases: pycollocation.symbolics.SymbolicBase

pycollocation.version module¶

pycollocation.visualizers module¶

Base class for all Visualizer objects.

class pycollocation.visualizers.Visualizer(solver)[source]¶

Bases: object

Base class for all Visualizer objects.

Attributes

interpolation_knots	Interpolation knots to use when computing the solution.
normalized_residuals	Absolute values of the solution residuals normalized by the value of the solution.
residuals	Solution residuals.
result	An instance of the optimize.optimize.OptimizeResult class that stores the raw output of a solvers.Solver object.
solution	Solution to the model represented as a Pandas DataFrame.

interpolation_knots[source]¶

Interpolation knots to use when computing the solution.

Getter:	Return the array of interpolation knots.
Setter:	Set a new array of interpolation knots.
Type:	numpy.ndarray

normalized_residuals[source]¶

Absolute values of the solution residuals normalized by the value of the solution.

Getter:	Return the normalized solution residuals.
Type:	pandas.DataFrame

residuals[source]¶

Solution residuals.

Getter:	Return the solution residuals.
Type:	pandas.DataFrame

result[source]¶

An instance of the optimize.optimize.OptimizeResult class that stores the raw output of a solvers.Solver object.

Getter:	Return the result attribute.
Type:	optimize.optimize.OptimizeResult

solution[source]¶

Solution to the model represented as a Pandas DataFrame.

Getter:	Return the DataFrame representing the current solution.
Type:	pandas.DataFrame

Module contents¶

Objects imported here will live in the pycollocation namespace

class pycollocation.SymbolicBoundaryValueProblem(boundary_conditions, dependent_vars, independent_var, rhs, params)¶

Bases: pycollocation.boundary_value_problems.BoundaryValueProblem, pycollocation.symbolics.SymbolicBoundaryValueProblemLike, pycollocation.differential_equations.SymbolicDifferentialEquation

Class for representing two-point boundary value problems.

Attributes

boundary_conditions	Boundary conditions for the problem.
dependent_vars	Model dependent variables.
independent_var	Symbolic variable representing the independent variable.
params	Dictionary of model parameters.
rhs	Symbolic representation of the right-hand side of a system of differential/difference equations.

class pycollocation.OrthogonalPolynomialSolver(model)¶

Bases: pycollocation.orthogonal_polynomials.OrthogonalPolynomialBasis, pycollocation.solvers.Solver

Attributes

coefficients	Coefficients to use when constructing the approximating polynomials.
degrees	Degrees used when constructing the orthogonal polynomials.
derivatives	Derivatives of the approximating basis functions.
domain	Domain over which the approximated solution is valid.
functions	The basis functions used to approximate the solution to the model.
kind	Kind of polynomials to use when constructing the approximation.
model	Symbolic representation of the model to solve.
residual_functions	Residual functions
result	Result object

Methods

solve(kind, coefs_dict, domain[, method])

Solve a boundary value problem using orthogonal collocation.

solve(kind, coefs_dict, domain, method='hybr', **kwargs)¶

Solve a boundary value problem using orthogonal collocation.

class pycollocation.Visualizer(solver)¶

Bases: object

Base class for all Visualizer objects.

Attributes

interpolation_knots	Interpolation knots to use when computing the solution.
normalized_residuals	Absolute values of the solution residuals normalized by the value of the solution.
residuals	Solution residuals.
result	An instance of the optimize.optimize.OptimizeResult class that stores the raw output of a solvers.Solver object.
solution	Solution to the model represented as a Pandas DataFrame.

interpolation_knots¶

Interpolation knots to use when computing the solution.

Getter:	Return the array of interpolation knots.
Setter:	Set a new array of interpolation knots.
Type:	numpy.ndarray

normalized_residuals¶

Absolute values of the solution residuals normalized by the value of the solution.

Getter:	Return the normalized solution residuals.
Type:	pandas.DataFrame

residuals¶

Solution residuals.

Getter:	Return the solution residuals.
Type:	pandas.DataFrame

result¶

An instance of the optimize.optimize.OptimizeResult class that stores the raw output of a solvers.Solver object.

Getter:	Return the result attribute.
Type:	optimize.optimize.OptimizeResult

solution¶

Solution to the model represented as a Pandas DataFrame.

Getter:	Return the DataFrame representing the current solution.
Type:	pandas.DataFrame