qom.solvers.deterministic module

Module to solve deterministic equations of motion.

class qom.solvers.deterministic.HLESolver(system, params: dict, cb_update=None)

Bases: object

Class to solve the Heisenberg-Langevin equations for classical mode amplitudes and quantum quadrature correlations.

Initializes system, params, T, Modes, Corrs, Measures and updater.

Parameters:

  • system (qom.systems.*) – Instance of the system. Requires predefined system methods for certain solver methods.

  • params (dict) –

    Parameters for the solver. Refer to Notes below for all available options. Required options are:

    key

    value

    ’t_min’

    (float) minimum time at which integration starts.

    ’t_max’

    (float) maximum time at which integration stops.

    ’t_dim’

    (int) number of values from 't_max' to 't_min', both inclusive.

  • 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 solver. Default is False.

‘cache’

(bool) option to cache the time series on the disk. Default is True.

‘cache_dir’

(str) directory where the time series is cached. Default is 'cache'.

‘cache_file’

(str) filename of the cached time series. Default is 'V'.

‘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.differential.ODESolver for details of each method. 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.

‘t_min’

(float) minimum time at which integration starts. Default is 0.0.

‘t_max’

(float) maximum time at which integration stops. Default is 1000.0.

‘t_dim’

(int) number of values from 't_max' to 't_min', both inclusive. Default is 10001.

‘t_index_delay’

(int) index of the time to delay for the derived constants and controls. Default is 0.

‘t_index_min’

(float) minimum index of the range of time at which the values are required. If not provided, this is set to 0.

‘t_index_max’

(float) maximum index of the range of time at which the values are required. If not provided, this is set to t_dim - 1.

‘indices’

(list or tuple) indices of the modes as a list, or a tuple of two integers. Default is [0].
desc = 'Heisenberg-Langevin Equations Solver'

Description of the solver.

Type:

str

get_all_corrs()

Method to obtain all the correlations.

Requires predefined system callables get_ivc and func_ode_modes_corrs. Alternatively, if the system inherits qom.systems.base.BaseSystem, get_mode_rates may be defined along with get_A and get_D if correlations are present. Additionally, func_ode_corrs may be defined for dynamical values (refer to the solve method). Refer to qom.systems.base.BaseSystem for their implementations.

Returns:

Corrs – All the correlations calculated at all times.

Return type:

numpy.ndarray

get_all_modes()

Method to obtain all the modes.

Requires predefined system callables get_ivc and func_ode_modes_corrs. Alternatively, if the system inherits qom.systems.base.BaseSystem, get_mode_rates may be defined along with get_A and get_D if correlations are present. Additionally, func_ode_corrs may be defined for dynamical values (refer to the solve method). Refer to qom.systems.base.BaseSystem for their implementations.

Returns:

Modes – All the modes calculated at all times.

Return type:

numpy.ndarray

get_all_modes_corrs()

Method to obtain all the modes and correlations.

Requires predefined system callables get_ivc and func_ode_modes_corrs. Alternatively, if the system inherits qom.systems.base.BaseSystem, get_mode_rates may be defined along with get_A and get_D if correlations are present. Additionally, func_ode_corrs may be defined for dynamical values (refer to the solve method). Refer to qom.systems.base.BaseSystem for their implementations.

Returns:

  • Modes (numpy.ndarray) – All the modes calculated at all times.

  • Corrs (numpy.ndarray) – All the correlations calculated at all times.

get_corr_indices()

Method to obtain the specific correlations in a given range of time.

Returns:

Corrs – Specific correlations in a given range of time.

Return type:

numpy.ndarray

get_corrs()

Method to obtain the dynamics of the correlations in a given range of time.

Requires predefined system callables get_ivc and func_ode_modes_corrs. Alternatively, if the system inherits qom.systems.base.BaseSystem, get_mode_rates may be defined along with get_A and get_D if correlations are present. Additionally, func_ode_corrs may be defined for dynamical values (refer to the solve method). Refer to qom.systems.base.BaseSystem for their implementations.

Returns:

Corrs – All the correlations calculated in a given range of time.

Return type:

numpy.ndarray

get_mode_indices()

Method to obtain the specific modes in a given range of time.

Returns:

Modes – Specific modes in a given range of time.

Return type:

numpy.ndarray

get_mode_intensities()

Method to obtain the intensities of specific modes.

Returns:

intensities – The intensities of specific modes.

Return type:

numpy.ndarray

get_modes()

Method to obtain the dynamics of the modes in a given range of time.

Requires predefined system callables get_ivc and func_ode_modes_corrs. Alternatively, if the system inherits qom.systems.base.BaseSystem, get_mode_rates may be defined along with get_A and get_D if correlations are present. Additionally, func_ode_corrs may be defined for dynamical values (refer to the solve method). Refer to qom.systems.base.BaseSystem for their implementations.

Returns:

Modes – All the modes calculated in a given range of time.

Return type:

numpy.ndarray

get_modes_corrs()

Method to obtain the dynamics of the modes and correlations in a given range of time.

Requires predefined system callables get_ivc and func_ode_modes_corrs. Alternatively, if the system inherits qom.systems.base.BaseSystem, get_mode_rates may be defined along with get_A and get_D if correlations are present. Additionally, func_ode_corrs may be defined for dynamical values (refer to the solve method). Refer to qom.systems.base.BaseSystem for their implementations.

Returns:

  • Modes (numpy.ndarray) – All the modes calculated in a given range of time.

  • Corrs (numpy.ndarray) – All the correlations calculated in a given range of time.

get_times()

Method to obtain the times in the given range.

Returns:

T – Times in the given range.

Return type:

numpy.ndarray

name = 'HLESolver'

Name of the solver.

Type:

str

required_params = ['t_min', 't_max', 't_dim']

Required parameters of the solver.

Type:

list

set_params(params)

Method to validate and set the solver parameters, cache options and times.

Parameters:

params (dict) – Parameters of the solver.

set_results(func_ode_modes_corrs, iv_modes, iv_corrs, c, func_ode_corrs)

Method to solve the ODEs and update the results.

Parameters:

  • func_ode_modes_corrs (callable) – Function returning the rate equations of the modes and correlations. If func_ode_corrs parameter is given, this function is treated as the function for the modes only. Refer to qom.systems.base.BaseSystem for their implementations.

  • iv_modes (list or numpy.ndarray) – Initial values for the modes.

  • iv_corrs (list or numpy.ndarray) – Initial values for the correlations.

  • c (list or numpy.ndarray) – Derived constants and controls for the function.

  • func_ode_corrs (callable) – Function returning the rate equations of the correlations.

solve(func_ode_modes_corrs, iv_modes, iv_corrs, c=None, func_ode_corrs=None)

Method to solve the HLEs.

Loads solutions if disk cache is found, else solves and saves the solutions to disk cache.

Parameters:

  • func_ode_modes_corrs (callable) – Function returning the rate equations of the modes and correlations. If func_ode_corrs parameter is given, this function is treated as the function for the modes only. Refer to qom.systems.base.BaseSystem for their implementations.

  • iv_modes (list or numpy.ndarray) – Initial values for the modes.

  • iv_corrs (list or numpy.ndarray) – Initial values for the correlations.

  • c (list or numpy.ndarray) – Derived constants and controls for the function.

  • func_ode_corrs (callable) – Function returning the rate equations of the correlations.

Returns:

results – Results obtained after solving, with keys 'T' and 'V' for times and values.

Return type:

dict

solver_defaults = {'cache': True, 'cache_dir': 'cache', 'cache_file': 'V', 'indices': [0], 'ode_atol': 1e-12, 'ode_is_stiff': False, 'ode_method': 'RK45', 'ode_rtol': 1e-06, 'show_progress': False, 't_dim': 10001, 't_index_delay': 0, 't_index_max': None, 't_index_min': None, 't_max': 1000.0, 't_min': 0.0}

Default parameters of the solver.

Type:

dict

class qom.solvers.deterministic.LLESolver(system, params: dict, cb_update=None)

Bases: object

Method to solve the Lugiato-Lefever equation (LLE) for classical mode amplitudes using the split-step Fourier method.

Initializes system, params, T, Modes and updater.

Parameters:

  • system (qom.systems.*) – Instance of the system. Requires predefined system methods for certain solver methods.

  • params (dict) –

    Parameters for the solver. Refer to Notes below for all available options. Required options are:

    key

    value

    ’t_min’

    (float) minimum time at which the method starts.

    ’t_max’

    (float) maximum time at which the method stops.

    ’t_dim’

    (int) number of values from 't_max' to 't_min', both inclusive.

  • 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 solver. Default is False.

‘t_min’

(float) minimum time at which integration starts. Default is 0.0.

‘t_max’

(float) maximum time at which integration stops. Default is 1000.0.

‘t_dim’

(int) number of values from 't_max' to 't_min', both inclusive. Default is 10001.

‘indices’

(list or tuple) indices of the modes as a list. Default is [0].
desc = 'Lugiato-Lefever Equation Solver'

Description of the solver.

Type:

str

get_all_modes()

Method to obtain all the modes.

Requires predefined system callables get_ivc, get_coeffs_dispersion, get_nonlinearities and get_sources. Refer to qom.systems.base.BaseSystem for their implementations.

Returns:

Modes – All the modes calculated at all times.

Return type:

numpy.ndarray

get_mode_indices()

Method to obtain the specific modes in a given range of time.

Returns:

Modes – Specific modes in a given range of time.

Return type:

numpy.ndarray

get_mode_intensities()

Method to obtain the intensities of specific modes.

Returns:

intensities – The intensities of specific modes.

Return type:

numpy.ndarray

name = 'LLESolver'

Name of the solver.

Type:

str

required_params = ['t_min', 't_max', 't_dim']

Required parameters of the solver.

Type:

list

set_params(params)

Method to validate and set the solver parameters and times.

Parameters:

params (dict) – Parameters of the solver.

solver_defaults = {'indices': [0], 'show_progress': False, 't_dim': 10001, 't_max': 1000.0, 't_min': 0.0}

Default parameters of the solver.

Type:

dict

class qom.solvers.deterministic.NLSESolver(system, params: dict, cb_update=None)

Bases: object

Method to solve the non-linear Schrodinger equation (NLSE) using the split-step Fourier method.

Initializes system, params, T, Modes and updater.

Parameters:

  • system (qom.systems.*) – Instance of the system. Requires predefined system methods for certain solver methods.

  • params (dict) –

    Parameters for the solver. Refer to Notes below for all available options.Required options are:

    key

    value

    ’t_min’

    (float) minimum time at which the method starts.

    ’t_max’

    (float) maximum time at which the method stops.

    ’t_dim’

    (int) number of values from 't_max' to 't_min', both inclusive.

  • 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 solver. Default is False.

‘update_betas’

(bool) option to use the mechanical mode rates. Requires either one of the predefined system methods get_beta_rates (priority) or get_betas (fallback). Refer to qom.systems.base.BaseSystem for their implementations. Default is False.

‘use_sources’

(bool) option to use the source terms. Requires the predefined system method get_sources. Refer to qom.systems.base.BaseSystem for its implementation. Default is True.

‘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.differential.ODESolver for details of each method. 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.

‘t_min’

(float) minimum time at which integration starts. Default is 0.0.

‘t_max’

(float) maximum time at which integration stops. Default is 1000.0.

‘t_dim’

(int) number of values from 't_max' to 't_min', both inclusive. Default is 10001.

‘t_div’

(int) number of further divisions in each time step, both inclusive. Default is 1.

‘indices’

(list or tuple) indices of the modes as a list. Default is [0].
desc = 'Non-linear Schrodinger Equation Solver'

Description of the solver.

Type:

str

get_all_modes()

Method to obtain all the modes.

Requires predefined system callables get_ivc, get_coeffs_dispersion and get_nonlinearities. Either one of the callables get_beta_rates or get_betas may also be defined to update the mechanical mode rates. Additionally get_sources may be defined to include source terms. Refer to qom.systems.base.BaseSystem for their implementations.

Returns:

Modes – All the modes calculated at all times.

Return type:

numpy.ndarray

get_mode_indices()

Method to obtain the specific modes in a given range of time.

Returns:

Modes – Specific modes in a given range of time.

Return type:

numpy.ndarray

get_mode_intensities()

Method to obtain the intensities of specific modes.

Returns:

intensities – The intensities of each mode.

Return type:

numpy.ndarray

name = 'NLSESolver'

Name of the solver.

Type:

str

required_params = ['t_min', 't_max', 't_dim']

Required parameters of the solver.

Type:

list

set_params(params)

Method to validate and set the solver parameters and times.

Parameters:

params (dict) – Parameters of the solver.

solver_defaults = {'indices': [0], 'ode_atol': 1e-12, 'ode_is_stiff': False, 'ode_method': 'RK45', 'ode_rtol': 1e-06, 'show_progress': False, 't_dim': 10001, 't_div': 1, 't_max': 1000.0, 't_min': 0.0, 'update_betas': True, 'use_sources': False}

Default parameters of the solver.

Type:

dict

class qom.solvers.deterministic.SSHLESolver(system, params: dict, cb_update=None)

Bases: object

Class to solve the steady state Heisenberg-Langevin equations for classical mode amplitudes and quantum quadrature correlations.

Initializes system, params, Modes, Corrs, As, Ds, Measures and updater.

Parameters:

  • system (qom.systems.*) – Instance of the system. Requires predefined system methods for certain solver methods.

  • 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 solver. Default is False.

‘indices’

(list or tuple) indices of the modes as a list or tuple of two integers. Default is [0].

‘use_system_method’

(bool) option to use the system method get_modes_steady_state to obtain the steady state mode amplitudes. Requires the predefined system method get_coeffs_N_o if the system method implements get_mean_optical_occupancies. Default is True.
desc = 'Steady State Heisenberg-Langevin Equations Solver'

Description of the solver.

Type:

str

get_As()

Method to obtain the steady state drift matrices.

Returns:

As – Drift matrices calculated at steady-state.

Return type:

numpy.ndarray

get_Ds()

Method to obtain the steady state noise matrices.

Returns:

Ds – Noise matrices calculated at steady-state.

Return type:

numpy.ndarray

get_corr_indices()

Method to obtain the steady states of specific correlations.

Returns:

corrs – Specific correlations calculated at steady-state.

Return type:

numpy.ndarray

get_corrs()

Method to obtain the steady state correlations.

Returns:

Corrs – Correlations calculated at steady-state.

Return type:

numpy.ndarray

get_mode_indices()

Method to obtain the steady states of specific modes.

Returns:

modes – Specific modes calculated at steady-state.

Return type:

numpy.ndarray

get_mode_intensities()

Method to obtain the intensities of specific modes.

Returns:

intensities – The intensities of specific modes.

Return type:

numpy.ndarray

get_modes()

Method to obtain the steady state modes.

Returns:

Modes – Modes calculated at steady-state.

Return type:

numpy.ndarray

get_modes_corrs()

Method to obtain the steady states of the modes and correlations.

Requires system method predefined system callables get_ivc. To calculate the modes, either get_modes_steady_state or get_mode_rates should be defined. Priority is given to get_modes_steady_state. The correlations are calculated by solving the Lyapunov equation. For this, the get_A and get_D methods should be defined along with the method required to calculate the modes.

Returns:

  • Modes (numpy.ndarray) – Modes calculated at steady-state.

  • Corrs (numpy.ndarray) – Correlations calculated at steady-state.

name = 'SSHLESolver'

Name of the solver.

Type:

str

required_params = []

Required parameters of the solver.

Type:

list

set_params(params)

Method to validate and set the solver parameters.

Parameters:

params (dict) – Parameters of the solver.

solver_defaults = {'indices': [0], 'show_progress': False, 'use_system_method': True}

Default parameters of the solver.

Type:

dict