latom.odes.odes_2d_group

@authors: Alberto FOSSA’ Giuliana Elena MICELI

Classes

Group(**kwargs)	Class used to group systems together; instantiate or inherit.
ODE2dConstThrust(**kwargs)	ODE2dConstThrust class defines the equations of motion for a two dim.
ODE2dLLO2Apo(**kwargs)	ODE2dLLO2Apo class defines the equations of motion for a two dim.
ODE2dLLO2HEO(**kwargs)	ODE2dLLO2HEO class defines the equations of motion for a two dim.
ODE2dVToff(**kwargs)	ODE2dVToff class defines the equations of motion for a two dim.
ODE2dVarThrust(**kwargs)	ODE2dVarThrust class defines the equations of motion for a two dim.
Polar2AEH(**kwargs)	Polar2AEH class defines the set of equations to derive the a and h from Polar coordinates.
Polar2RApo(**kwargs)	Polar2RApo class defines the set of equations to derive the apoapsis radius from Polar coordinates.
SafeAlt(**kwargs)	SafeAlt class defines the curve representing geographical constraints on the central body surface.
declare_parameter(name[, targets, shape, …])	Class Decorator used to attach ODE parameter metadata to an OpenMDAO system.
declare_state(name, rate_source[, targets, …])	Class Decorator used to attach ODE state metadata to an OpenMDAO system.
declare_time([targets, units, …])	Class Decorator used to attach ODE time metadata to an OpenMDAO system.

class latom.odes.odes_2d_group.ODE2dVToff(**kwargs)

Bases: openmdao.core.group.Group

ODE2dVToff class defines the equations of motion for a two dim. powered trajectory with vertical take-off.

Other Parameters

• time (ndarray) – Represents the time variable of the system [-]

• r (ndarray) – Represents a position along the trajectory. The distance is measured from the center of the central body [-]

• theta (ndarray) – Angle spawn from the starting point of the orbit to the final one [-]

• u (ndarray) – Radial velocity of a point along the trajectory [-]

• v (ndarray) – Tangential velocity of a point along the trajectory [-]

• m (ndarray) – Mass of the space vehicle that performs the trajectory [-]

• alpha (ndarray) – Angle defining the thrust direction [-]

• thrust (ndarray) – Value of the applied thrust force [-]

• w (float) – Value of the exhaust velocity [-]

• num_nodes (int) – Number of nodes where to compute the equations

• GM (float) – Standard gravitational parameter for the central attracting body [-]

• R (float) – Moon radius [-]

• alt_safe (float) – Altitude of the curve representing the geographical constraint [-]

• slope (float) – Slope of the curves defining a geographical constraint [-]

initialize()

Initializes the ODE2dVToff class variables.

setup()

Setup of ODE2dVToff parameters. Declaration of subsystem, input and output.

add(name, subsys, promotes=None)

Add a subsystem (deprecated version of <Group.add_subsystem>).

Parameters

• name (str) – Name of the subsystem being added

• subsys (System) – An instantiated, but not-yet-set up system object.

• promotes (iter of str, optional) – A list of variable names specifying which subsystem variables to ‘promote’ up to this group. This is for backwards compatibility with older versions of OpenMDAO.

Returns

The System that was passed in.

Return type

System

add_constraint(name, lower=None, upper=None, equals=None, ref=None, ref0=None, adder=None, scaler=None, indices=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)

Add a constraint variable to this system.

Parameters

• name (string) – Name of the response variable in the system.

• lower (float or ndarray, optional) – Lower boundary for the variable

• upper (float or ndarray, optional) – Upper boundary for the variable

• equals (float or ndarray, optional) – Equality constraint value for the variable

• ref (float or ndarray, optional) – Value of response variable that scales to 1.0 in the driver.

• ref0 (float or ndarray, optional) – Value of response variable that scales to 0.0 in the driver.

• adder (float or ndarray, optional) – Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.

• scaler (float or ndarray, optional) – value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.

• indices (sequence of int, optional) – If variable is an array, these indicate which entries are of interest for this particular response. These may be positive or negative integers.

• linear (bool) – Set to True if constraint is linear. Default is False.

• parallel_deriv_color (string) – If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.

• vectorize_derivs (bool) – If True, vectorize derivative calculations.

• cache_linear_solution (bool) – If True, store the linear solution vectors for this variable so they can be used to start the next linear solution with an initial guess equal to the solution from the previous linear solve.

Notes

The response can be scaled using ref and ref0. The argument ref0 represents the physical value when the scaled value is 0. The argument ref represents the physical value when the scaled value is 1.

add_design_var(name, lower=None, upper=None, ref=None, ref0=None, indices=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)

Add a design variable to this system.

Parameters

• name (string) – Name of the design variable in the system.

• lower (float or ndarray, optional) – Lower boundary for the param

• upper (upper or ndarray, optional) – Upper boundary for the param

• ref (float or ndarray, optional) – Value of design var that scales to 1.0 in the driver.

• ref0 (float or ndarray, optional) – Value of design var that scales to 0.0 in the driver.

• indices (iter of int, optional) – If a param is an array, these indicate which entries are of interest for this particular design variable. These may be positive or negative integers.

• adder (float or ndarray, optional) – Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.

• scaler (float or ndarray, optional) – value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.

• parallel_deriv_color (string) – If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.

• vectorize_derivs (bool) – If True, vectorize derivative calculations.

• cache_linear_solution (bool) – If True, store the linear solution vectors for this variable so they can be used to start the next linear solution with an initial guess equal to the solution from the previous linear solve.

Notes

The response can be scaled using ref and ref0. The argument ref0 represents the physical value when the scaled value is 0. The argument ref represents the physical value when the scaled value is 1.

add_objective(name, ref=None, ref0=None, index=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)

Add a response variable to this system.

Parameters

• name (string) – Name of the response variable in the system.

• ref (float or ndarray, optional) – Value of response variable that scales to 1.0 in the driver.

• ref0 (float or ndarray, optional) – Value of response variable that scales to 0.0 in the driver.

• index (int, optional) – If variable is an array, this indicates which entry is of interest for this particular response. This may be a positive or negative integer.

• adder (float or ndarray, optional) – Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.

• scaler (float or ndarray, optional) – value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.

• parallel_deriv_color (string) – If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.

• vectorize_derivs (bool) – If True, vectorize derivative calculations.

• cache_linear_solution (bool) – If True, store the linear solution vectors for this variable so they can be used to start the next linear solution with an initial guess equal to the solution from the previous linear solve.

Notes

The objective can be scaled using scaler and adder, where

\[x_{scaled} = scaler(x + adder)\]

or through the use of ref/ref0, which map to scaler and adder through the equations:

\[ \begin{align}\begin{aligned}0 = scaler(ref_0 + adder)\\1 = scaler(ref + adder)\end{aligned}\end{align} \]

which results in:

\[ \begin{align}\begin{aligned}adder = -ref_0\\scaler = \frac{1}{ref + adder}\end{aligned}\end{align} \]

add_recorder(recorder, recurse=False)

Add a recorder to the system.

Parameters

• recorder (<CaseRecorder>) – A recorder instance.

• recurse (boolean) – Flag indicating if the recorder should be added to all the subsystems.

add_response(name, type_, lower=None, upper=None, equals=None, ref=None, ref0=None, indices=None, index=None, adder=None, scaler=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)

Add a response variable to this system.

The response can be scaled using ref and ref0. The argument ref0 represents the physical value when the scaled value is 0. The argument ref represents the physical value when the scaled value is 1.

Parameters

• name (string) – Name of the response variable in the system.

• type_ (string) – The type of response. Supported values are ‘con’ and ‘obj’

• lower (float or ndarray, optional) – Lower boundary for the variable

• upper (upper or ndarray, optional) – Upper boundary for the variable

• equals (equals or ndarray, optional) – Equality constraint value for the variable

• ref (float or ndarray, optional) – Value of response variable that scales to 1.0 in the driver.

• ref0 (upper or ndarray, optional) – Value of response variable that scales to 0.0 in the driver.

• indices (sequence of int, optional) – If variable is an array, these indicate which entries are of interest for this particular response.

• index (int, optional) – If variable is an array, this indicates which entry is of interest for this particular response.

• adder (float or ndarray, optional) – Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.

• scaler (float or ndarray, optional) – value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.

• linear (bool) – Set to True if constraint is linear. Default is False.

• parallel_deriv_color (string) – If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.

• vectorize_derivs (bool) – If True, vectorize derivative calculations.

• cache_linear_solution (bool) – If True, store the linear solution vectors for this variable so they can be used to start the next linear solution with an initial guess equal to the solution from the previous linear solve.

add_subsystem(name, subsys, promotes=None, promotes_inputs=None, promotes_outputs=None, min_procs=1, max_procs=None, proc_weight=1.0)

Add a subsystem.

Parameters

• name (str) – Name of the subsystem being added

• subsys (<System>) – An instantiated, but not-yet-set up system object.

• promotes (iter of (str or tuple), optional) – A list of variable names specifying which subsystem variables to ‘promote’ up to this group. If an entry is a tuple of the form (old_name, new_name), this will rename the variable in the parent group.

• promotes_inputs (iter of (str or tuple), optional) – A list of input variable names specifying which subsystem input variables to ‘promote’ up to this group. If an entry is a tuple of the form (old_name, new_name), this will rename the variable in the parent group.

• promotes_outputs (iter of (str or tuple), optional) – A list of output variable names specifying which subsystem output variables to ‘promote’ up to this group. If an entry is a tuple of the form (old_name, new_name), this will rename the variable in the parent group.

• min_procs (int) – Minimum number of MPI processes usable by the subsystem. Defaults to 1.

• max_procs (int or None) – Maximum number of MPI processes usable by the subsystem. A value of None (the default) indicates there is no maximum limit.

• proc_weight (float) – Weight given to the subsystem when allocating available MPI processes to all subsystems. Default is 1.0.

Returns

the subsystem that was passed in. This is returned to enable users to instantiate and add a subsystem at the same time, and get the reference back.

Return type

<System>

approx_totals(method='fd', step=None, form=None, step_calc=None)

Approximate derivatives for a Group using the specified approximation method.

Parameters

• method (str) – The type of approximation that should be used. Valid options include: ‘fd’: Finite Difference, ‘cs’: Complex Step

• step (float) – Step size for approximation. Defaults to None, in which case, the approximation method provides its default value.

• form (string) – Form for finite difference, can be ‘forward’, ‘backward’, or ‘central’. Defaults to None, in which case, the approximation method provides its default value.

• step_calc (string) – Step type for finite difference, can be ‘abs’ for absolute’, or ‘rel’ for relative. Defaults to None, in which case, the approximation method provides its default value.

check_config(logger)

Perform optional error checks.

Parameters

logger (object) – The object that manages logging output.

cleanup()

Clean up resources prior to exit.

compute_sys_graph(comps_only=False)

Compute a dependency graph for subsystems in this group.

Variable connection information is stored in each edge of the system graph.

Parameters

comps_only (bool (False)) – If True, return a graph of all components within this group or any of its descendants. No sub-groups will be included. Otherwise, a graph containing only direct children (both Components and Groups) of this group will be returned.

Returns

A directed graph containing names of subsystems and their connections.

Return type

DiGraph

configure()

Configure this group to assign children settings.

This method may optionally be overidden by your Group’s method.

You may only use this method to change settings on your children subsystems. This includes setting solvers in cases where you want to override the defaults.

You can assume that the full hierarchy below your level has been instantiated and has already called its own configure methods.

Available attributes:

name pathname comm options system hieararchy with attribute access

connect(src_name, tgt_name, src_indices=None, flat_src_indices=None)

Connect source src_name to target tgt_name in this namespace.

Parameters

• src_name (str) – name of the source variable to connect

• tgt_name (str or [str, .. ] or (str, ..)) – name of the target variable(s) to connect

• src_indices (int or list of ints or tuple of ints or int ndarray or Iterable or None) – The global indices of the source variable to transfer data from. The shapes of the target and src_indices must match, and form of the entries within is determined by the value of ‘flat_src_indices’.

• flat_src_indices (bool) – If True, each entry of src_indices is assumed to be an index into the flattened source. Otherwise it must be a tuple or list of size equal to the number of dimensions of the source.

declare_coloring(wrt=('*', ), method='fd', form=None, step=None, per_instance=True, num_full_jacs=3, tol=1e-25, orders=None, perturb_size=1e-09, min_improve_pct=5.0, show_summary=True, show_sparsity=False)

Set options for deriv coloring of a set of wrt vars matching the given pattern(s).

Parameters

• wrt (str or list of str) – The name or names of the variables that derivatives are taken with respect to. This can contain input names, output names, or glob patterns.

• method (str) – Method used to compute derivative: “fd” for finite difference, “cs” for complex step.

• form (str) – Finite difference form, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.

• step (float) – Step size for finite difference. Leave undeclared to keep unchanged from previous or default value.

• per_instance (bool) – If True, a separate coloring will be generated for each instance of a given class. Otherwise, only one coloring for a given class will be generated and all instances of that class will use it.

• num_full_jacs (int) – Number of times to repeat partial jacobian computation when computing sparsity.

• tol (float) – Tolerance used to determine if an array entry is nonzero during sparsity determination.

• orders (int) – Number of orders above and below the tolerance to check during the tolerance sweep.

• perturb_size (float) – Size of input/output perturbation during generation of sparsity.

• min_improve_pct (float) – If coloring does not improve (decrease) the number of solves more than the given percentage, coloring will not be used.

• show_summary (bool) – If True, display summary information after generating coloring.

• show_sparsity (bool) – If True, display sparsity with coloring info after generating coloring.

get_approx_coloring_fname()

Return the full pathname to a coloring file.

Parameters

system (System) – The System having its coloring saved or loaded.

Returns

Full pathname of the coloring file.

Return type

str

get_constraints(recurse=True)

Get the Constraint settings from this system.

Retrieve the constraint settings for the current system as a dict, keyed by variable name.

Parameters

recurse (bool, optional) – If True, recurse through the subsystems and return the path of all constraints relative to the this system.

Returns

The constraints defined in the current system.

Return type

dict

get_design_vars(recurse=True, get_sizes=True)

Get the DesignVariable settings from this system.

Retrieve all design variable settings from the system and, if recurse is True, all of its subsystems.

Parameters

• recurse (bool) – If True, recurse through the subsystems and return the path of all design vars relative to the this system.

• get_sizes (bool, optional) – If True, compute the size of each design variable.

Returns

The design variables defined in the current system and, if recurse=True, its subsystems.

Return type

dict

get_linear_vectors(vec_name='linear')

Return the linear inputs, outputs, and residuals vectors.

Parameters

vec_name (str) – Name of the linear right-hand-side vector. The default is ‘linear’.

Returns

(inputs, outputs, residuals) – Yields the inputs, outputs, and residuals linear vectors for vec_name.

Return type

tuple of <Vector> instances

get_nonlinear_vectors()

Return the inputs, outputs, and residuals vectors.

Returns

(inputs, outputs, residuals) – Yields the inputs, outputs, and residuals nonlinear vectors.

Return type

tuple of <Vector> instances

get_objectives(recurse=True)

Get the Objective settings from this system.

Retrieve all objectives settings from the system as a dict, keyed by variable name.

Parameters

recurse (bool, optional) – If True, recurse through the subsystems and return the path of all objective relative to the this system.

Returns

The objectives defined in the current system.

Return type

dict

get_responses(recurse=True, get_sizes=True)

Get the response variable settings from this system.

Retrieve all response variable settings from the system as a dict, keyed by variable name.

Parameters

• recurse (bool, optional) – If True, recurse through the subsystems and return the path of all responses relative to the this system.

• get_sizes (bool, optional) – If True, compute the size of each response.

Returns

The responses defined in the current system and, if recurse=True, its subsystems.

Return type

dict

guess_nonlinear(inputs, outputs, residuals, discrete_inputs=None, discrete_outputs=None)

Provide initial guess for states.

Override this method to set the initial guess for states.

Parameters

• inputs (Vector) – unscaled, dimensional input variables read via inputs[key]

• outputs (Vector) – unscaled, dimensional output variables read via outputs[key]

• residuals (Vector) – unscaled, dimensional residuals written to via residuals[key]

• discrete_inputs (dict or None) – If not None, dict containing discrete input values.

• discrete_outputs (dict or None) – If not None, dict containing discrete output values.

is_active()

Determine if the system is active on this rank.

Returns

If running under MPI, returns True if this System has a valid communicator. Always returns True if not running under MPI.

Return type

bool

property linear_solver

Get the linear solver for this system.

list_inputs(values=True, prom_name=False, units=False, shape=False, hierarchical=True, print_arrays=False, tags=None, includes=None, excludes=None, out_stream=<object object>)

Return and optionally log a list of input names and other optional information.

If the model is parallel, only the local variables are returned to the process. Also optionally logs the information to a user defined output stream. If the model is parallel, the rank 0 process logs information about all variables across all processes.

Parameters

• values (bool, optional) – When True, display/return input values. Default is True.

• prom_name (bool, optional) – When True, display/return the promoted name of the variable. Default is False.

• units (bool, optional) – When True, display/return units. Default is False.

• shape (bool, optional) – When True, display/return the shape of the value. Default is False.

• hierarchical (bool, optional) – When True, human readable output shows variables in hierarchical format.

• print_arrays (bool, optional) – When False, in the columnar display, just display norm of any ndarrays with size > 1. The norm is surrounded by vertical bars to indicate that it is a norm. When True, also display full values of the ndarray below the row. Format is affected by the values set with numpy.set_printoptions Default is False.

• tags (str or list of strs) – User defined tags that can be used to filter what gets listed. Only inputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.

• includes (None or list_like) – List of glob patterns for pathnames to include in the check. Default is None, which includes all components in the model.

• excludes (None or list_like) – List of glob patterns for pathnames to exclude from the check. Default is None, which excludes nothing.

• out_stream (file-like object) – Where to send human readable output. Default is sys.stdout. Set to None to suppress.

Returns

list of input names and other optional information about those inputs

Return type

list

list_outputs(explicit=True, implicit=True, values=True, prom_name=False, residuals=False, residuals_tol=None, units=False, shape=False, bounds=False, scaling=False, hierarchical=True, print_arrays=False, tags=None, includes=None, excludes=None, out_stream=<object object>)

Return and optionally log a list of output names and other optional information.

If the model is parallel, only the local variables are returned to the process. Also optionally logs the information to a user defined output stream. If the model is parallel, the rank 0 process logs information about all variables across all processes.

Parameters

• explicit (bool, optional) – include outputs from explicit components. Default is True.

• implicit (bool, optional) – include outputs from implicit components. Default is True.

• values (bool, optional) – When True, display/return output values. Default is True.

• prom_name (bool, optional) – When True, display/return the promoted name of the variable. Default is False.

• residuals (bool, optional) – When True, display/return residual values. Default is False.

• residuals_tol (float, optional) – If set, limits the output of list_outputs to only variables where the norm of the resids array is greater than the given ‘residuals_tol’. Default is None.

• units (bool, optional) – When True, display/return units. Default is False.

• shape (bool, optional) – When True, display/return the shape of the value. Default is False.

• bounds (bool, optional) – When True, display/return bounds (lower and upper). Default is False.

• scaling (bool, optional) – When True, display/return scaling (ref, ref0, and res_ref). Default is False.

• hierarchical (bool, optional) – When True, human readable output shows variables in hierarchical format.

• print_arrays (bool, optional) – When False, in the columnar display, just display norm of any ndarrays with size > 1. The norm is surrounded by vertical bars to indicate that it is a norm. When True, also display full values of the ndarray below the row. Format is affected by the values set with numpy.set_printoptions Default is False.

• tags (str or list of strs) – User defined tags that can be used to filter what gets listed. Only outputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.

• includes (None or list_like) – List of glob patterns for pathnames to include in the check. Default is None, which includes all components in the model.

• excludes (None or list_like) – List of glob patterns for pathnames to exclude from the check. Default is None, which excludes nothing.

• out_stream (file-like) – Where to send human readable output. Default is sys.stdout. Set to None to suppress.

Returns

list of output names and other optional information about those outputs

Return type

list

property ln_solver

Get the linear solver for this system.

property metadata

Get the options for this System.

property msginfo

Our instance pathname, if available, or our class name. For use in error messages.

Returns

Either our instance pathname or class name.

Return type

str

property nl_solver

Get the nonlinear solver for this system.

property nonlinear_solver

Get the nonlinear solver for this system.

ode_options = <dymos.ode_options.ODEOptions object>

reconfigure()

Perform reconfiguration.

Returns

If True, reconfiguration is to be performed.

Return type

bool

record_iteration()

Record an iteration of the current System.

resetup(setup_mode='full')

Public wrapper for _setup that reconfigures after an initial setup has been performed.

Parameters

setup_mode (str) – Must be one of ‘full’, ‘reconf’, or ‘update’.

run_apply_linear(vec_names, mode, scope_out=None, scope_in=None)

Compute jac-vec product.

This calls _apply_linear, but with the model assumed to be in an unscaled state.

Parameters

• vec_names ([str, ..]) – list of names of the right-hand-side vectors.

• mode (str) – ‘fwd’ or ‘rev’.

• scope_out (set or None) – Set of absolute output names in the scope of this mat-vec product. If None, all are in the scope.

• scope_in (set or None) – Set of absolute input names in the scope of this mat-vec product. If None, all are in the scope.

run_apply_nonlinear()

Compute residuals.

This calls _apply_nonlinear, but with the model assumed to be in an unscaled state.

run_linearize(sub_do_ln=True)

Compute jacobian / factorization.

This calls _linearize, but with the model assumed to be in an unscaled state.

Parameters

sub_do_ln (boolean) – Flag indicating if the children should call linearize on their linear solvers.

run_solve_linear(vec_names, mode)

Apply inverse jac product.

This calls _solve_linear, but with the model assumed to be in an unscaled state.

Parameters

• vec_names ([str, ..]) – list of names of the right-hand-side vectors.

• mode (str) – ‘fwd’ or ‘rev’.

run_solve_nonlinear()

Compute outputs.

This calls _solve_nonlinear, but with the model assumed to be in an unscaled state.

set_initial_values()

Set all input and output variables to their declared initial values.

set_order(new_order)

Specify a new execution order for this system.

Parameters

new_order (list of str) – List of system names in desired new execution order.

system_iter(include_self=False, recurse=True, typ=None)

Yield a generator of local subsystems of this system.

Parameters

• include_self (bool) – If True, include this system in the iteration.

• recurse (bool) – If True, iterate over the whole tree under this system.

• typ (type) – If not None, only yield Systems that match that are instances of the given type.

use_fixed_coloring(coloring=<object object>, recurse=True)

Use a precomputed coloring for this System.

Parameters

• coloring (str) – A coloring filename. If no arg is passed, filename will be determined automatically.

• recurse (bool) – If True, set fixed coloring in all subsystems that declare a coloring. Ignored if a specific coloring is passed in.

class latom.odes.odes_2d_group.ODE2dLLO2Apo(**kwargs)

Bases: openmdao.core.group.Group

ODE2dLLO2Apo class defines the equations of motion for a two dim. powered trajectory to leave the intial LLO and enter a ballistic arc with apoapsis radius equal to ra.

Other Parameters

• time (ndarray) – Represents the time variable of the system [-]

• r (ndarray) – Represents a position along the trajectory. The distance is measured from the center of the central body [-]

• theta (ndarray) – Angle spawn from the starting point of the orbit to the final one [-]

• u (ndarray) – Radial velocity of a point along the trajectory [-]

• v (ndarray) – Tangential velocity of a point along the trajectory [-]

• m (ndarray) – Mass of the space vehicle that performs the trajectory [-]

• alpha (ndarray) – Angle defining the thrust direction [-]

• thrust (ndarray) – Value of the applied thrust force [-]

• w (float) – Value of the exhaust velocity [-]

• num_nodes (int) – Number of nodes where to compute the equations

• GM (float) – Standard gravitational parameter for the central attracting body [-]

• T (float) – Value of the constant thrust force [-]

• ra (float) – Value of the apoapsis radius [-]

initialize()

Initializes the ODE2dLLO2Apo class variables.

setup()

Setup of ODE2dLLO2Apo parameters. Declaration of subsystem, input and output.

add(name, subsys, promotes=None)

Add a subsystem (deprecated version of <Group.add_subsystem>).

Parameters

• name (str) – Name of the subsystem being added

• subsys (System) – An instantiated, but not-yet-set up system object.

• promotes (iter of str, optional) – A list of variable names specifying which subsystem variables to ‘promote’ up to this group. This is for backwards compatibility with older versions of OpenMDAO.

Returns

The System that was passed in.

Return type

System

add_constraint(name, lower=None, upper=None, equals=None, ref=None, ref0=None, adder=None, scaler=None, indices=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)

Add a constraint variable to this system.

Parameters

• name (string) – Name of the response variable in the system.

• lower (float or ndarray, optional) – Lower boundary for the variable

• upper (float or ndarray, optional) – Upper boundary for the variable

• equals (float or ndarray, optional) – Equality constraint value for the variable

• ref (float or ndarray, optional) – Value of response variable that scales to 1.0 in the driver.

• ref0 (float or ndarray, optional) – Value of response variable that scales to 0.0 in the driver.

• adder (float or ndarray, optional) – Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.

• scaler (float or ndarray, optional) – value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.

• indices (sequence of int, optional) – If variable is an array, these indicate which entries are of interest for this particular response. These may be positive or negative integers.

• linear (bool) – Set to True if constraint is linear. Default is False.

• parallel_deriv_color (string) – If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.

• vectorize_derivs (bool) – If True, vectorize derivative calculations.

• cache_linear_solution (bool) – If True, store the linear solution vectors for this variable so they can be used to start the next linear solution with an initial guess equal to the solution from the previous linear solve.

Notes

The response can be scaled using ref and ref0. The argument ref0 represents the physical value when the scaled value is 0. The argument ref represents the physical value when the scaled value is 1.

add_design_var(name, lower=None, upper=None, ref=None, ref0=None, indices=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)

Add a design variable to this system.

Parameters

• name (string) – Name of the design variable in the system.

• lower (float or ndarray, optional) – Lower boundary for the param

• upper (upper or ndarray, optional) – Upper boundary for the param

• ref (float or ndarray, optional) – Value of design var that scales to 1.0 in the driver.

• ref0 (float or ndarray, optional) – Value of design var that scales to 0.0 in the driver.

• indices (iter of int, optional) – If a param is an array, these indicate which entries are of interest for this particular design variable. These may be positive or negative integers.

• adder (float or ndarray, optional) – Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.

• scaler (float or ndarray, optional) – value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.

• parallel_deriv_color (string) – If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.

• vectorize_derivs (bool) – If True, vectorize derivative calculations.

• cache_linear_solution (bool) – If True, store the linear solution vectors for this variable so they can be used to start the next linear solution with an initial guess equal to the solution from the previous linear solve.

Notes

The response can be scaled using ref and ref0. The argument ref0 represents the physical value when the scaled value is 0. The argument ref represents the physical value when the scaled value is 1.

add_objective(name, ref=None, ref0=None, index=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)

Add a response variable to this system.

Parameters

• name (string) – Name of the response variable in the system.

• ref (float or ndarray, optional) – Value of response variable that scales to 1.0 in the driver.

• ref0 (float or ndarray, optional) – Value of response variable that scales to 0.0 in the driver.

• index (int, optional) – If variable is an array, this indicates which entry is of interest for this particular response. This may be a positive or negative integer.

• adder (float or ndarray, optional) – Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.

• scaler (float or ndarray, optional) – value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.

• parallel_deriv_color (string) – If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.

• vectorize_derivs (bool) – If True, vectorize derivative calculations.

• cache_linear_solution (bool) – If True, store the linear solution vectors for this variable so they can be used to start the next linear solution with an initial guess equal to the solution from the previous linear solve.

Notes

The objective can be scaled using scaler and adder, where

\[x_{scaled} = scaler(x + adder)\]

or through the use of ref/ref0, which map to scaler and adder through the equations:

\[ \begin{align}\begin{aligned}0 = scaler(ref_0 + adder)\\1 = scaler(ref + adder)\end{aligned}\end{align} \]

which results in:

\[ \begin{align}\begin{aligned}adder = -ref_0\\scaler = \frac{1}{ref + adder}\end{aligned}\end{align} \]

add_recorder(recorder, recurse=False)

Add a recorder to the system.

Parameters

• recorder (<CaseRecorder>) – A recorder instance.

• recurse (boolean) – Flag indicating if the recorder should be added to all the subsystems.

add_response(name, type_, lower=None, upper=None, equals=None, ref=None, ref0=None, indices=None, index=None, adder=None, scaler=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)

Add a response variable to this system.

The response can be scaled using ref and ref0. The argument ref0 represents the physical value when the scaled value is 0. The argument ref represents the physical value when the scaled value is 1.

Parameters

• name (string) – Name of the response variable in the system.

• type_ (string) – The type of response. Supported values are ‘con’ and ‘obj’

• lower (float or ndarray, optional) – Lower boundary for the variable

• upper (upper or ndarray, optional) – Upper boundary for the variable

• equals (equals or ndarray, optional) – Equality constraint value for the variable

• ref (float or ndarray, optional) – Value of response variable that scales to 1.0 in the driver.

• ref0 (upper or ndarray, optional) – Value of response variable that scales to 0.0 in the driver.

• indices (sequence of int, optional) – If variable is an array, these indicate which entries are of interest for this particular response.

• index (int, optional) – If variable is an array, this indicates which entry is of interest for this particular response.

• adder (float or ndarray, optional) – Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.

• scaler (float or ndarray, optional) – value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.

• linear (bool) – Set to True if constraint is linear. Default is False.

• parallel_deriv_color (string) – If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.

• vectorize_derivs (bool) – If True, vectorize derivative calculations.

• cache_linear_solution (bool) – If True, store the linear solution vectors for this variable so they can be used to start the next linear solution with an initial guess equal to the solution from the previous linear solve.

add_subsystem(name, subsys, promotes=None, promotes_inputs=None, promotes_outputs=None, min_procs=1, max_procs=None, proc_weight=1.0)

Add a subsystem.

Parameters

• name (str) – Name of the subsystem being added

• subsys (<System>) – An instantiated, but not-yet-set up system object.

• promotes (iter of (str or tuple), optional) – A list of variable names specifying which subsystem variables to ‘promote’ up to this group. If an entry is a tuple of the form (old_name, new_name), this will rename the variable in the parent group.

• promotes_inputs (iter of (str or tuple), optional) – A list of input variable names specifying which subsystem input variables to ‘promote’ up to this group. If an entry is a tuple of the form (old_name, new_name), this will rename the variable in the parent group.

• promotes_outputs (iter of (str or tuple), optional) – A list of output variable names specifying which subsystem output variables to ‘promote’ up to this group. If an entry is a tuple of the form (old_name, new_name), this will rename the variable in the parent group.

• min_procs (int) – Minimum number of MPI processes usable by the subsystem. Defaults to 1.

• max_procs (int or None) – Maximum number of MPI processes usable by the subsystem. A value of None (the default) indicates there is no maximum limit.

• proc_weight (float) – Weight given to the subsystem when allocating available MPI processes to all subsystems. Default is 1.0.

Returns

the subsystem that was passed in. This is returned to enable users to instantiate and add a subsystem at the same time, and get the reference back.

Return type

<System>

approx_totals(method='fd', step=None, form=None, step_calc=None)

Approximate derivatives for a Group using the specified approximation method.

Parameters

• method (str) – The type of approximation that should be used. Valid options include: ‘fd’: Finite Difference, ‘cs’: Complex Step

• step (float) – Step size for approximation. Defaults to None, in which case, the approximation method provides its default value.

• form (string) – Form for finite difference, can be ‘forward’, ‘backward’, or ‘central’. Defaults to None, in which case, the approximation method provides its default value.

• step_calc (string) – Step type for finite difference, can be ‘abs’ for absolute’, or ‘rel’ for relative. Defaults to None, in which case, the approximation method provides its default value.

check_config(logger)

Perform optional error checks.

Parameters

logger (object) – The object that manages logging output.

cleanup()

Clean up resources prior to exit.

compute_sys_graph(comps_only=False)

Compute a dependency graph for subsystems in this group.

Variable connection information is stored in each edge of the system graph.

Parameters

comps_only (bool (False)) – If True, return a graph of all components within this group or any of its descendants. No sub-groups will be included. Otherwise, a graph containing only direct children (both Components and Groups) of this group will be returned.

Returns

A directed graph containing names of subsystems and their connections.

Return type

DiGraph

configure()

Configure this group to assign children settings.

This method may optionally be overidden by your Group’s method.

You may only use this method to change settings on your children subsystems. This includes setting solvers in cases where you want to override the defaults.

You can assume that the full hierarchy below your level has been instantiated and has already called its own configure methods.

Available attributes:

name pathname comm options system hieararchy with attribute access

connect(src_name, tgt_name, src_indices=None, flat_src_indices=None)

Connect source src_name to target tgt_name in this namespace.

Parameters

• src_name (str) – name of the source variable to connect

• tgt_name (str or [str, .. ] or (str, ..)) – name of the target variable(s) to connect

• src_indices (int or list of ints or tuple of ints or int ndarray or Iterable or None) – The global indices of the source variable to transfer data from. The shapes of the target and src_indices must match, and form of the entries within is determined by the value of ‘flat_src_indices’.

• flat_src_indices (bool) – If True, each entry of src_indices is assumed to be an index into the flattened source. Otherwise it must be a tuple or list of size equal to the number of dimensions of the source.

declare_coloring(wrt=('*', ), method='fd', form=None, step=None, per_instance=True, num_full_jacs=3, tol=1e-25, orders=None, perturb_size=1e-09, min_improve_pct=5.0, show_summary=True, show_sparsity=False)

Set options for deriv coloring of a set of wrt vars matching the given pattern(s).

Parameters

• wrt (str or list of str) – The name or names of the variables that derivatives are taken with respect to. This can contain input names, output names, or glob patterns.

• method (str) – Method used to compute derivative: “fd” for finite difference, “cs” for complex step.

• form (str) – Finite difference form, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.

• step (float) – Step size for finite difference. Leave undeclared to keep unchanged from previous or default value.

• per_instance (bool) – If True, a separate coloring will be generated for each instance of a given class. Otherwise, only one coloring for a given class will be generated and all instances of that class will use it.

• num_full_jacs (int) – Number of times to repeat partial jacobian computation when computing sparsity.

• tol (float) – Tolerance used to determine if an array entry is nonzero during sparsity determination.

• orders (int) – Number of orders above and below the tolerance to check during the tolerance sweep.

• perturb_size (float) – Size of input/output perturbation during generation of sparsity.

• min_improve_pct (float) – If coloring does not improve (decrease) the number of solves more than the given percentage, coloring will not be used.

• show_summary (bool) – If True, display summary information after generating coloring.

• show_sparsity (bool) – If True, display sparsity with coloring info after generating coloring.

get_approx_coloring_fname()

Return the full pathname to a coloring file.

Parameters

system (System) – The System having its coloring saved or loaded.

Returns

Full pathname of the coloring file.

Return type

str

get_constraints(recurse=True)

Get the Constraint settings from this system.

Retrieve the constraint settings for the current system as a dict, keyed by variable name.

Parameters

recurse (bool, optional) – If True, recurse through the subsystems and return the path of all constraints relative to the this system.

Returns

The constraints defined in the current system.

Return type

dict

get_design_vars(recurse=True, get_sizes=True)

Get the DesignVariable settings from this system.

Retrieve all design variable settings from the system and, if recurse is True, all of its subsystems.

Parameters

• recurse (bool) – If True, recurse through the subsystems and return the path of all design vars relative to the this system.

• get_sizes (bool, optional) – If True, compute the size of each design variable.

Returns

The design variables defined in the current system and, if recurse=True, its subsystems.

Return type

dict

get_linear_vectors(vec_name='linear')

Return the linear inputs, outputs, and residuals vectors.

Parameters

vec_name (str) – Name of the linear right-hand-side vector. The default is ‘linear’.

Returns

(inputs, outputs, residuals) – Yields the inputs, outputs, and residuals linear vectors for vec_name.

Return type

tuple of <Vector> instances

get_nonlinear_vectors()

Return the inputs, outputs, and residuals vectors.

Returns

(inputs, outputs, residuals) – Yields the inputs, outputs, and residuals nonlinear vectors.

Return type

tuple of <Vector> instances

get_objectives(recurse=True)

Get the Objective settings from this system.

Retrieve all objectives settings from the system as a dict, keyed by variable name.

Parameters

recurse (bool, optional) – If True, recurse through the subsystems and return the path of all objective relative to the this system.

Returns

The objectives defined in the current system.

Return type

dict

get_responses(recurse=True, get_sizes=True)

Get the response variable settings from this system.

Retrieve all response variable settings from the system as a dict, keyed by variable name.

Parameters

• recurse (bool, optional) – If True, recurse through the subsystems and return the path of all responses relative to the this system.

• get_sizes (bool, optional) – If True, compute the size of each response.

Returns

The responses defined in the current system and, if recurse=True, its subsystems.

Return type

dict

guess_nonlinear(inputs, outputs, residuals, discrete_inputs=None, discrete_outputs=None)

Provide initial guess for states.

Override this method to set the initial guess for states.

Parameters

• inputs (Vector) – unscaled, dimensional input variables read via inputs[key]

• outputs (Vector) – unscaled, dimensional output variables read via outputs[key]

• residuals (Vector) – unscaled, dimensional residuals written to via residuals[key]

• discrete_inputs (dict or None) – If not None, dict containing discrete input values.

• discrete_outputs (dict or None) – If not None, dict containing discrete output values.

is_active()

Determine if the system is active on this rank.

Returns

If running under MPI, returns True if this System has a valid communicator. Always returns True if not running under MPI.

Return type

bool

property linear_solver

Get the linear solver for this system.

list_inputs(values=True, prom_name=False, units=False, shape=False, hierarchical=True, print_arrays=False, tags=None, includes=None, excludes=None, out_stream=<object object>)

Return and optionally log a list of input names and other optional information.

If the model is parallel, only the local variables are returned to the process. Also optionally logs the information to a user defined output stream. If the model is parallel, the rank 0 process logs information about all variables across all processes.

Parameters

• values (bool, optional) – When True, display/return input values. Default is True.

• prom_name (bool, optional) – When True, display/return the promoted name of the variable. Default is False.

• units (bool, optional) – When True, display/return units. Default is False.

• shape (bool, optional) – When True, display/return the shape of the value. Default is False.

• hierarchical (bool, optional) – When True, human readable output shows variables in hierarchical format.

• print_arrays (bool, optional) – When False, in the columnar display, just display norm of any ndarrays with size > 1. The norm is surrounded by vertical bars to indicate that it is a norm. When True, also display full values of the ndarray below the row. Format is affected by the values set with numpy.set_printoptions Default is False.

• tags (str or list of strs) – User defined tags that can be used to filter what gets listed. Only inputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.

• includes (None or list_like) – List of glob patterns for pathnames to include in the check. Default is None, which includes all components in the model.

• excludes (None or list_like) – List of glob patterns for pathnames to exclude from the check. Default is None, which excludes nothing.

• out_stream (file-like object) – Where to send human readable output. Default is sys.stdout. Set to None to suppress.

Returns

list of input names and other optional information about those inputs

Return type

list

list_outputs(explicit=True, implicit=True, values=True, prom_name=False, residuals=False, residuals_tol=None, units=False, shape=False, bounds=False, scaling=False, hierarchical=True, print_arrays=False, tags=None, includes=None, excludes=None, out_stream=<object object>)

Return and optionally log a list of output names and other optional information.

If the model is parallel, only the local variables are returned to the process. Also optionally logs the information to a user defined output stream. If the model is parallel, the rank 0 process logs information about all variables across all processes.

Parameters

• explicit (bool, optional) – include outputs from explicit components. Default is True.

• implicit (bool, optional) – include outputs from implicit components. Default is True.

• values (bool, optional) – When True, display/return output values. Default is True.

• prom_name (bool, optional) – When True, display/return the promoted name of the variable. Default is False.

• residuals (bool, optional) – When True, display/return residual values. Default is False.

• residuals_tol (float, optional) – If set, limits the output of list_outputs to only variables where the norm of the resids array is greater than the given ‘residuals_tol’. Default is None.

• units (bool, optional) – When True, display/return units. Default is False.

• shape (bool, optional) – When True, display/return the shape of the value. Default is False.

• bounds (bool, optional) – When True, display/return bounds (lower and upper). Default is False.

• scaling (bool, optional) – When True, display/return scaling (ref, ref0, and res_ref). Default is False.

• hierarchical (bool, optional) – When True, human readable output shows variables in hierarchical format.

• print_arrays (bool, optional) – When False, in the columnar display, just display norm of any ndarrays with size > 1. The norm is surrounded by vertical bars to indicate that it is a norm. When True, also display full values of the ndarray below the row. Format is affected by the values set with numpy.set_printoptions Default is False.

• tags (str or list of strs) – User defined tags that can be used to filter what gets listed. Only outputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.

• includes (None or list_like) – List of glob patterns for pathnames to include in the check. Default is None, which includes all components in the model.

• excludes (None or list_like) – List of glob patterns for pathnames to exclude from the check. Default is None, which excludes nothing.

• out_stream (file-like) – Where to send human readable output. Default is sys.stdout. Set to None to suppress.

Returns

list of output names and other optional information about those outputs

Return type

list

property ln_solver

Get the linear solver for this system.

property metadata

Get the options for this System.

property msginfo

Our instance pathname, if available, or our class name. For use in error messages.

Returns

Either our instance pathname or class name.

Return type

str

property nl_solver

Get the nonlinear solver for this system.

property nonlinear_solver

Get the nonlinear solver for this system.

ode_options = <dymos.ode_options.ODEOptions object>

reconfigure()

Perform reconfiguration.

Returns

If True, reconfiguration is to be performed.

Return type

bool

record_iteration()

Record an iteration of the current System.

resetup(setup_mode='full')

Public wrapper for _setup that reconfigures after an initial setup has been performed.

Parameters

setup_mode (str) – Must be one of ‘full’, ‘reconf’, or ‘update’.

run_apply_linear(vec_names, mode, scope_out=None, scope_in=None)

Compute jac-vec product.

This calls _apply_linear, but with the model assumed to be in an unscaled state.

Parameters

• vec_names ([str, ..]) – list of names of the right-hand-side vectors.

• mode (str) – ‘fwd’ or ‘rev’.

• scope_out (set or None) – Set of absolute output names in the scope of this mat-vec product. If None, all are in the scope.

• scope_in (set or None) – Set of absolute input names in the scope of this mat-vec product. If None, all are in the scope.

run_apply_nonlinear()

Compute residuals.

This calls _apply_nonlinear, but with the model assumed to be in an unscaled state.

run_linearize(sub_do_ln=True)

Compute jacobian / factorization.

This calls _linearize, but with the model assumed to be in an unscaled state.

Parameters

sub_do_ln (boolean) – Flag indicating if the children should call linearize on their linear solvers.

run_solve_linear(vec_names, mode)

Apply inverse jac product.

This calls _solve_linear, but with the model assumed to be in an unscaled state.

Parameters

• vec_names ([str, ..]) – list of names of the right-hand-side vectors.

• mode (str) – ‘fwd’ or ‘rev’.

run_solve_nonlinear()

Compute outputs.

This calls _solve_nonlinear, but with the model assumed to be in an unscaled state.

set_initial_values()

Set all input and output variables to their declared initial values.

set_order(new_order)

Specify a new execution order for this system.

Parameters

new_order (list of str) – List of system names in desired new execution order.

system_iter(include_self=False, recurse=True, typ=None)

Yield a generator of local subsystems of this system.

Parameters

• include_self (bool) – If True, include this system in the iteration.

• recurse (bool) – If True, iterate over the whole tree under this system.

• typ (type) – If not None, only yield Systems that match that are instances of the given type.

use_fixed_coloring(coloring=<object object>, recurse=True)

Use a precomputed coloring for this System.

Parameters

• coloring (str) – A coloring filename. If no arg is passed, filename will be determined automatically.

• recurse (bool) – If True, set fixed coloring in all subsystems that declare a coloring. Ignored if a specific coloring is passed in.

class latom.odes.odes_2d_group.ODE2dLLO2HEO(**kwargs)

Bases: openmdao.core.group.Group

ODE2dLLO2HEO class defines the equations of motion for a two dim. powered trajectory from LLO to HEO.

Other Parameters

• time (ndarray) – Represents the time variable of the system [-]

• r (ndarray) – Represents a position along the trajectory. The distance is measured from the center of the central body [-]

• theta (ndarray) – Angle spawn from the starting point of the orbit to the final one [-]

• u (ndarray) – Radial velocity of a point along the trajectory [-]

• v (ndarray) – Tangential velocity of a point along the trajectory [-]

• m (ndarray) – Mass of the space vehicle that performs the trajectory [-]

• alpha (ndarray) – Angle defining the thrust direction [-]

• thrust (ndarray) – Value of the applied thrust force [-]

• w (float) – Value of the exhaust velocity [-]

• num_nodes (int) – Number of nodes where to compute the equations

• GM (float) – Standard gravitational parameter for the central attracting body [-]

• T (float) – Value of the constant thrust force [-]

initialize()

Initializes the ODE2dLLO2HEO class variables.

setup()

Setup of ODE2dLLO2HEO parameters. Declaration of subsystem, input and output.

add(name, subsys, promotes=None)

Add a subsystem (deprecated version of <Group.add_subsystem>).

Parameters

• name (str) – Name of the subsystem being added

• subsys (System) – An instantiated, but not-yet-set up system object.

• promotes (iter of str, optional) – A list of variable names specifying which subsystem variables to ‘promote’ up to this group. This is for backwards compatibility with older versions of OpenMDAO.

Returns

The System that was passed in.

Return type

System

add_constraint(name, lower=None, upper=None, equals=None, ref=None, ref0=None, adder=None, scaler=None, indices=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)

Add a constraint variable to this system.

Parameters

• name (string) – Name of the response variable in the system.

• lower (float or ndarray, optional) – Lower boundary for the variable

• upper (float or ndarray, optional) – Upper boundary for the variable

• equals (float or ndarray, optional) – Equality constraint value for the variable

• ref (float or ndarray, optional) – Value of response variable that scales to 1.0 in the driver.

• ref0 (float or ndarray, optional) – Value of response variable that scales to 0.0 in the driver.

• adder (float or ndarray, optional) – Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.

• scaler (float or ndarray, optional) – value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.

• indices (sequence of int, optional) – If variable is an array, these indicate which entries are of interest for this particular response. These may be positive or negative integers.

• linear (bool) – Set to True if constraint is linear. Default is False.

• parallel_deriv_color (string) – If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.

• vectorize_derivs (bool) – If True, vectorize derivative calculations.

• cache_linear_solution (bool) – If True, store the linear solution vectors for this variable so they can be used to start the next linear solution with an initial guess equal to the solution from the previous linear solve.

Notes

The response can be scaled using ref and ref0. The argument ref0 represents the physical value when the scaled value is 0. The argument ref represents the physical value when the scaled value is 1.

add_design_var(name, lower=None, upper=None, ref=None, ref0=None, indices=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)

Add a design variable to this system.

Parameters

• name (string) – Name of the design variable in the system.

• lower (float or ndarray, optional) – Lower boundary for the param

• upper (upper or ndarray, optional) – Upper boundary for the param

• ref (float or ndarray, optional) – Value of design var that scales to 1.0 in the driver.

• ref0 (float or ndarray, optional) – Value of design var that scales to 0.0 in the driver.

• indices (iter of int, optional) – If a param is an array, these indicate which entries are of interest for this particular design variable. These may be positive or negative integers.

• adder (float or ndarray, optional) – Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.

• scaler (float or ndarray, optional) – value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.

• parallel_deriv_color (string) – If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.

• vectorize_derivs (bool) – If True, vectorize derivative calculations.

• cache_linear_solution (bool) – If True, store the linear solution vectors for this variable so they can be used to start the next linear solution with an initial guess equal to the solution from the previous linear solve.

Notes

The response can be scaled using ref and ref0. The argument ref0 represents the physical value when the scaled value is 0. The argument ref represents the physical value when the scaled value is 1.

add_objective(name, ref=None, ref0=None, index=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)

Add a response variable to this system.

Parameters

• name (string) – Name of the response variable in the system.

• ref (float or ndarray, optional) – Value of response variable that scales to 1.0 in the driver.

• ref0 (float or ndarray, optional) – Value of response variable that scales to 0.0 in the driver.

• index (int, optional) – If variable is an array, this indicates which entry is of interest for this particular response. This may be a positive or negative integer.

• adder (float or ndarray, optional) – Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.

• scaler (float or ndarray, optional) – value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.

• parallel_deriv_color (string) – If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.

• vectorize_derivs (bool) – If True, vectorize derivative calculations.

• cache_linear_solution (bool) – If True, store the linear solution vectors for this variable so they can be used to start the next linear solution with an initial guess equal to the solution from the previous linear solve.

Notes

The objective can be scaled using scaler and adder, where

\[x_{scaled} = scaler(x + adder)\]

or through the use of ref/ref0, which map to scaler and adder through the equations:

\[ \begin{align}\begin{aligned}0 = scaler(ref_0 + adder)\\1 = scaler(ref + adder)\end{aligned}\end{align} \]

which results in:

\[ \begin{align}\begin{aligned}adder = -ref_0\\scaler = \frac{1}{ref + adder}\end{aligned}\end{align} \]

add_recorder(recorder, recurse=False)

Add a recorder to the system.

Parameters

• recorder (<CaseRecorder>) – A recorder instance.

• recurse (boolean) – Flag indicating if the recorder should be added to all the subsystems.

add_response(name, type_, lower=None, upper=None, equals=None, ref=None, ref0=None, indices=None, index=None, adder=None, scaler=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)

Add a response variable to this system.

The response can be scaled using ref and ref0. The argument ref0 represents the physical value when the scaled value is 0. The argument ref represents the physical value when the scaled value is 1.

Parameters

• name (string) – Name of the response variable in the system.

• type_ (string) – The type of response. Supported values are ‘con’ and ‘obj’

• lower (float or ndarray, optional) – Lower boundary for the variable

• upper (upper or ndarray, optional) – Upper boundary for the variable

• equals (equals or ndarray, optional) – Equality constraint value for the variable

• ref (float or ndarray, optional) – Value of response variable that scales to 1.0 in the driver.

• ref0 (upper or ndarray, optional) – Value of response variable that scales to 0.0 in the driver.

• indices (sequence of int, optional) – If variable is an array, these indicate which entries are of interest for this particular response.

• index (int, optional) – If variable is an array, this indicates which entry is of interest for this particular response.

• adder (float or ndarray, optional) – Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.

• scaler (float or ndarray, optional) – value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.

• linear (bool) – Set to True if constraint is linear. Default is False.

• parallel_deriv_color (string) – If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.

• vectorize_derivs (bool) – If True, vectorize derivative calculations.

• cache_linear_solution (bool) – If True, store the linear solution vectors for this variable so they can be used to start the next linear solution with an initial guess equal to the solution from the previous linear solve.

add_subsystem(name, subsys, promotes=None, promotes_inputs=None, promotes_outputs=None, min_procs=1, max_procs=None, proc_weight=1.0)

Add a subsystem.

Parameters

• name (str) – Name of the subsystem being added

• subsys (<System>) – An instantiated, but not-yet-set up system object.

• promotes (iter of (str or tuple), optional) – A list of variable names specifying which subsystem variables to ‘promote’ up to this group. If an entry is a tuple of the form (old_name, new_name), this will rename the variable in the parent group.

• promotes_inputs (iter of (str or tuple), optional) – A list of input variable names specifying which subsystem input variables to ‘promote’ up to this group. If an entry is a tuple of the form (old_name, new_name), this will rename the variable in the parent group.

• promotes_outputs (iter of (str or tuple), optional) – A list of output variable names specifying which subsystem output variables to ‘promote’ up to this group. If an entry is a tuple of the form (old_name, new_name), this will rename the variable in the parent group.

• min_procs (int) – Minimum number of MPI processes usable by the subsystem. Defaults to 1.

• max_procs (int or None) – Maximum number of MPI processes usable by the subsystem. A value of None (the default) indicates there is no maximum limit.

• proc_weight (float) – Weight given to the subsystem when allocating available MPI processes to all subsystems. Default is 1.0.

Returns

the subsystem that was passed in. This is returned to enable users to instantiate and add a subsystem at the same time, and get the reference back.

Return type

<System>

approx_totals(method='fd', step=None, form=None, step_calc=None)

Approximate derivatives for a Group using the specified approximation method.

Parameters

• method (str) – The type of approximation that should be used. Valid options include: ‘fd’: Finite Difference, ‘cs’: Complex Step

• step (float) – Step size for approximation. Defaults to None, in which case, the approximation method provides its default value.

• form (string) – Form for finite difference, can be ‘forward’, ‘backward’, or ‘central’. Defaults to None, in which case, the approximation method provides its default value.

• step_calc (string) – Step type for finite difference, can be ‘abs’ for absolute’, or ‘rel’ for relative. Defaults to None, in which case, the approximation method provides its default value.

check_config(logger)

Perform optional error checks.

Parameters

logger (object) – The object that manages logging output.

cleanup()

Clean up resources prior to exit.

compute_sys_graph(comps_only=False)

Compute a dependency graph for subsystems in this group.

Variable connection information is stored in each edge of the system graph.

Parameters

comps_only (bool (False)) – If True, return a graph of all components within this group or any of its descendants. No sub-groups will be included. Otherwise, a graph containing only direct children (both Components and Groups) of this group will be returned.

Returns

A directed graph containing names of subsystems and their connections.

Return type

DiGraph

configure()

Configure this group to assign children settings.

This method may optionally be overidden by your Group’s method.

You may only use this method to change settings on your children subsystems. This includes setting solvers in cases where you want to override the defaults.

You can assume that the full hierarchy below your level has been instantiated and has already called its own configure methods.

Available attributes:

name pathname comm options system hieararchy with attribute access

connect(src_name, tgt_name, src_indices=None, flat_src_indices=None)

Connect source src_name to target tgt_name in this namespace.

Parameters

• src_name (str) – name of the source variable to connect

• tgt_name (str or [str, .. ] or (str, ..)) – name of the target variable(s) to connect

• src_indices (int or list of ints or tuple of ints or int ndarray or Iterable or None) – The global indices of the source variable to transfer data from. The shapes of the target and src_indices must match, and form of the entries within is determined by the value of ‘flat_src_indices’.

• flat_src_indices (bool) – If True, each entry of src_indices is assumed to be an index into the flattened source. Otherwise it must be a tuple or list of size equal to the number of dimensions of the source.

declare_coloring(wrt=('*', ), method='fd', form=None, step=None, per_instance=True, num_full_jacs=3, tol=1e-25, orders=None, perturb_size=1e-09, min_improve_pct=5.0, show_summary=True, show_sparsity=False)

Set options for deriv coloring of a set of wrt vars matching the given pattern(s).

Parameters

• wrt (str or list of str) – The name or names of the variables that derivatives are taken with respect to. This can contain input names, output names, or glob patterns.

• method (str) – Method used to compute derivative: “fd” for finite difference, “cs” for complex step.

• form (str) – Finite difference form, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.

• step (float) – Step size for finite difference. Leave undeclared to keep unchanged from previous or default value.

• per_instance (bool) – If True, a separate coloring will be generated for each instance of a given class. Otherwise, only one coloring for a given class will be generated and all instances of that class will use it.

• num_full_jacs (int) – Number of times to repeat partial jacobian computation when computing sparsity.

• tol (float) – Tolerance used to determine if an array entry is nonzero during sparsity determination.

• orders (int) – Number of orders above and below the tolerance to check during the tolerance sweep.

• perturb_size (float) – Size of input/output perturbation during generation of sparsity.

• min_improve_pct (float) – If coloring does not improve (decrease) the number of solves more than the given percentage, coloring will not be used.

• show_summary (bool) – If True, display summary information after generating coloring.

• show_sparsity (bool) – If True, display sparsity with coloring info after generating coloring.

get_approx_coloring_fname()

Return the full pathname to a coloring file.

Parameters

system (System) – The System having its coloring saved or loaded.

Returns

Full pathname of the coloring file.

Return type

str

get_constraints(recurse=True)

Get the Constraint settings from this system.

Retrieve the constraint settings for the current system as a dict, keyed by variable name.

Parameters

recurse (bool, optional) – If True, recurse through the subsystems and return the path of all constraints relative to the this system.

Returns

The constraints defined in the current system.

Return type

dict

get_design_vars(recurse=True, get_sizes=True)

Get the DesignVariable settings from this system.

Retrieve all design variable settings from the system and, if recurse is True, all of its subsystems.

Parameters

• recurse (bool) – If True, recurse through the subsystems and return the path of all design vars relative to the this system.

• get_sizes (bool, optional) – If True, compute the size of each design variable.

Returns

The design variables defined in the current system and, if recurse=True, its subsystems.

Return type

dict

get_linear_vectors(vec_name='linear')

Return the linear inputs, outputs, and residuals vectors.

Parameters

vec_name (str) – Name of the linear right-hand-side vector. The default is ‘linear’.

Returns

(inputs, outputs, residuals) – Yields the inputs, outputs, and residuals linear vectors for vec_name.

Return type

tuple of <Vector> instances

get_nonlinear_vectors()

Return the inputs, outputs, and residuals vectors.

Returns

(inputs, outputs, residuals) – Yields the inputs, outputs, and residuals nonlinear vectors.

Return type

tuple of <Vector> instances

get_objectives(recurse=True)

Get the Objective settings from this system.

Retrieve all objectives settings from the system as a dict, keyed by variable name.

Parameters

recurse (bool, optional) – If True, recurse through the subsystems and return the path of all objective relative to the this system.

Returns

The objectives defined in the current system.

Return type

dict

get_responses(recurse=True, get_sizes=True)

Get the response variable settings from this system.

Retrieve all response variable settings from the system as a dict, keyed by variable name.

Parameters

• recurse (bool, optional) – If True, recurse through the subsystems and return the path of all responses relative to the this system.

• get_sizes (bool, optional) – If True, compute the size of each response.

Returns

The responses defined in the current system and, if recurse=True, its subsystems.

Return type

dict

guess_nonlinear(inputs, outputs, residuals, discrete_inputs=None, discrete_outputs=None)

Provide initial guess for states.

Override this method to set the initial guess for states.

Parameters

• inputs (Vector) – unscaled, dimensional input variables read via inputs[key]

• outputs (Vector) – unscaled, dimensional output variables read via outputs[key]

• residuals (Vector) – unscaled, dimensional residuals written to via residuals[key]

• discrete_inputs (dict or None) – If not None, dict containing discrete input values.

• discrete_outputs (dict or None) – If not None, dict containing discrete output values.

is_active()

Determine if the system is active on this rank.

Returns

If running under MPI, returns True if this System has a valid communicator. Always returns True if not running under MPI.

Return type

bool

property linear_solver

Get the linear solver for this system.

list_inputs(values=True, prom_name=False, units=False, shape=False, hierarchical=True, print_arrays=False, tags=None, includes=None, excludes=None, out_stream=<object object>)

Return and optionally log a list of input names and other optional information.

If the model is parallel, only the local variables are returned to the process. Also optionally logs the information to a user defined output stream. If the model is parallel, the rank 0 process logs information about all variables across all processes.

Parameters

• values (bool, optional) – When True, display/return input values. Default is True.

• prom_name (bool, optional) – When True, display/return the promoted name of the variable. Default is False.

• units (bool, optional) – When True, display/return units. Default is False.

• shape (bool, optional) – When True, display/return the shape of the value. Default is False.

• hierarchical (bool, optional) – When True, human readable output shows variables in hierarchical format.

• print_arrays (bool, optional) – When False, in the columnar display, just display norm of any ndarrays with size > 1. The norm is surrounded by vertical bars to indicate that it is a norm. When True, also display full values of the ndarray below the row. Format is affected by the values set with numpy.set_printoptions Default is False.

• tags (str or list of strs) – User defined tags that can be used to filter what gets listed. Only inputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.

• includes (None or list_like) – List of glob patterns for pathnames to include in the check. Default is None, which includes all components in the model.

• excludes (None or list_like) – List of glob patterns for pathnames to exclude from the check. Default is None, which excludes nothing.

• out_stream (file-like object) – Where to send human readable output. Default is sys.stdout. Set to None to suppress.

Returns

list of input names and other optional information about those inputs

Return type

list

list_outputs(explicit=True, implicit=True, values=True, prom_name=False, residuals=False, residuals_tol=None, units=False, shape=False, bounds=False, scaling=False, hierarchical=True, print_arrays=False, tags=None, includes=None, excludes=None, out_stream=<object object>)

Return and optionally log a list of output names and other optional information.

If the model is parallel, only the local variables are returned to the process. Also optionally logs the information to a user defined output stream. If the model is parallel, the rank 0 process logs information about all variables across all processes.

Parameters

• explicit (bool, optional) – include outputs from explicit components. Default is True.

• implicit (bool, optional) – include outputs from implicit components. Default is True.

• values (bool, optional) – When True, display/return output values. Default is True.

• prom_name (bool, optional) – When True, display/return the promoted name of the variable. Default is False.

• residuals (bool, optional) – When True, display/return residual values. Default is False.

• residuals_tol (float, optional) – If set, limits the output of list_outputs to only variables where the norm of the resids array is greater than the given ‘residuals_tol’. Default is None.

• units (bool, optional) – When True, display/return units. Default is False.

• shape (bool, optional) – When True, display/return the shape of the value. Default is False.

• bounds (bool, optional) – When True, display/return bounds (lower and upper). Default is False.

• scaling (bool, optional) – When True, display/return scaling (ref, ref0, and res_ref). Default is False.

• hierarchical (bool, optional) – When True, human readable output shows variables in hierarchical format.

• print_arrays (bool, optional) – When False, in the columnar display, just display norm of any ndarrays with size > 1. The norm is surrounded by vertical bars to indicate that it is a norm. When True, also display full values of the ndarray below the row. Format is affected by the values set with numpy.set_printoptions Default is False.

• tags (str or list of strs) – User defined tags that can be used to filter what gets listed. Only outputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.

• includes (None or list_like) – List of glob patterns for pathnames to include in the check. Default is None, which includes all components in the model.

• excludes (None or list_like) – List of glob patterns for pathnames to exclude from the check. Default is None, which excludes nothing.

• out_stream (file-like) – Where to send human readable output. Default is sys.stdout. Set to None to suppress.

Returns

list of output names and other optional information about those outputs

Return type

list

property ln_solver

Get the linear solver for this system.

property metadata

Get the options for this System.

property msginfo

Our instance pathname, if available, or our class name. For use in error messages.

Returns

Either our instance pathname or class name.

Return type

str

property nl_solver

Get the nonlinear solver for this system.

property nonlinear_solver

Get the nonlinear solver for this system.

ode_options = <dymos.ode_options.ODEOptions object>

reconfigure()

Perform reconfiguration.

Returns

If True, reconfiguration is to be performed.

Return type

bool

record_iteration()

Record an iteration of the current System.

resetup(setup_mode='full')

Public wrapper for _setup that reconfigures after an initial setup has been performed.

Parameters

setup_mode (str) – Must be one of ‘full’, ‘reconf’, or ‘update’.

run_apply_linear(vec_names, mode, scope_out=None, scope_in=None)

Compute jac-vec product.

This calls _apply_linear, but with the model assumed to be in an unscaled state.

Parameters

• vec_names ([str, ..]) – list of names of the right-hand-side vectors.

• mode (str) – ‘fwd’ or ‘rev’.

• scope_out (set or None) – Set of absolute output names in the scope of this mat-vec product. If None, all are in the scope.

• scope_in (set or None) – Set of absolute input names in the scope of this mat-vec product. If None, all are in the scope.

run_apply_nonlinear()

Compute residuals.

This calls _apply_nonlinear, but with the model assumed to be in an unscaled state.

run_linearize(sub_do_ln=True)

Compute jacobian / factorization.

This calls _linearize, but with the model assumed to be in an unscaled state.

Parameters

sub_do_ln (boolean) – Flag indicating if the children should call linearize on their linear solvers.

run_solve_linear(vec_names, mode)

Apply inverse jac product.

This calls _solve_linear, but with the model assumed to be in an unscaled state.

Parameters

• vec_names ([str, ..]) – list of names of the right-hand-side vectors.

• mode (str) – ‘fwd’ or ‘rev’.

run_solve_nonlinear()

Compute outputs.

This calls _solve_nonlinear, but with the model assumed to be in an unscaled state.

set_initial_values()

Set all input and output variables to their declared initial values.

set_order(new_order)

Specify a new execution order for this system.

Parameters

new_order (list of str) – List of system names in desired new execution order.

system_iter(include_self=False, recurse=True, typ=None)

Yield a generator of local subsystems of this system.

Parameters

• include_self (bool) – If True, include this system in the iteration.

• recurse (bool) – If True, iterate over the whole tree under this system.

• typ (type) – If not None, only yield Systems that match that are instances of the given type.

use_fixed_coloring(coloring=<object object>, recurse=True)

Use a precomputed coloring for this System.

Parameters

• coloring (str) – A coloring filename. If no arg is passed, filename will be determined automatically.

• recurse (bool) – If True, set fixed coloring in all subsystems that declare a coloring. Ignored if a specific coloring is passed in.