qom.solvers.differential module

Module to solve ordinary differential equations.

class qom.solvers.differential.ODESolver(func, params: dict, cb_update=None)

Bases: object

Class to solve ordinary differential equations using scipy.integrate.

Initializes solver_methods, func, params, integrator and updater.

Parameters:

  • func (callable) – Function returning the rate equations of the input variables, formatted as func(t, v, c), where t is the time at which the integration is performed, v is a list of variables and c is a list of constants. The output should match the dimension of v.

  • params (dict) – Parameters for the solver. Refer to Notes below for all available options.

  • cb_update (callable, optional) – Callback function to update status and progress, formatted as cb_update(status, progress, reset), where status is a string, progress is a float and reset is a boolean.

Notes

The params dictionary currently supports the following keys:

key

value

‘show_progress’

(bool) option to display the progress of the integration. Default is False.

‘ode_method’

(str) method used to solve the ODEs. Available options are 'BDF', 'DOP853', 'LSODA', 'Radau', 'RK23', 'RK45' (fallback), 'dop853', 'dopri5', 'lsoda', 'vode' and 'zvode' (refer to qom.solvers.ODESolver). Default is 'RK45'.

‘ode_is_stiff’

(bool) option to select whether the integration is a stiff problem or a non-stiff one. Default is False.

‘ode_atol’

(float) absolute tolerance of the integrator. Default is 1e-12.

‘ode_rtol’

(float) relative tolerance of the integrator. Default is 1e-6.
Currently available Python-based methods are:

value

meaning

‘BDF’

backward-differentiation formulas.

‘DOP853’

explicit Runge-Kutta method of order 8(5, 3).

‘LSODA’

Adams/BDF method with automatic stiffness detection and switching.

‘Radau’

implicit Runge-Kutta of Radau IIA family of order 5.

‘RK23’

explicit Runge-Kutta method of order 3(2).

‘RK45’

explicit Runge-Kutta method of order 5(4) (fallback).
Currently available FORTRAN-based are:

value

meaning

‘dop853’

explicit Runge-Kutta method of order 8(5, 3).

‘dopri5’

explicit Runge-Kutta method of order 5(4).

‘lsoda’

real-valued Adams/BDF method with automatic stiffness detection and switching.

‘vode’

real-valued implicit Adams/BDF methods.

‘zvode’

complex-valued implicit Adams/BDF methods.
desc = 'Ordinary Differential Equations Solver'

Description of the solver.

Type:

str

name = 'ODESolver'

Name of the solver.

Type:

str

new_api_methods = ['BDF', 'DOP853', 'LSODA', 'Radau', 'RK23', 'RK45']

New Python-based methods availabile in scipy.integrate.

Type:

list

old_api_methods = ['dop853', 'dopri5', 'lsoda', 'vode', 'zvode']

Old FORTRAN-based methods availabile in scipy.integrate.

Type:

list

set_params(params)

Method to set the solver parameters.

Parameters:

params (dict) – Parameters of the solver.

solve(T, iv, c=None, func_c=None)

Method to obtain the solutions of the ODE at all times.

Parameters:

  • T (numpy.ndarray) – Times at which the values are calculated.

  • iv (numpy.ndarray) – Initial values for the integration.

  • c (numpy.ndarray) – Constants of the integration.

  • func_c (callable, optional) – Function returning the time-dependent constants of the integration, formatted as func_c(i), where i is the i-th step of integration.

Returns:

vs – Values of the variables at all times.

Return type:

numpy.ndarray

solve_new(T, iv, c)

Method to integrate with the new API methods.

Parameters:

  • T (float) – Times at which the values are obtained.

  • iv (numpy.ndarray) – Initial values of the variables.

  • c (numpy.ndarray) – Constants of the integration.

Returns:

vs – Values of the variables.

Return type:

numpy.ndarray

solver_defaults = {'ode_atol': 1e-12, 'ode_is_stiff': False, 'ode_method': 'RK45', 'ode_rtol': 1e-06, 'show_progress': False}

Default parameters of the solver.

Type:

dict