pycollocation package¶
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.
- 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
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
- 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.
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
pycollocation.symbolics module¶
Classes for constructing symbolic models.
@author : davidrpugh
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
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