sellar.py¶
Test objects for the sellar two discipline problem.
From Sellar’s analytic problem.
Sellar, R. S., Batill, S. M., and Renaud, J. E., “Response Surface Based, Concurrent Subspace Optimization for Multidisciplinary System Design,” Proceedings References 79 of the 34th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, January 1996.

class
openmdao.test_suite.components.sellar.
SellarDerivatives
(**kwargs)[source]¶ Bases:
openmdao.core.group.Group
Group containing the Sellar MDA. This version uses the disciplines with derivatives.

__init__
(**kwargs)¶ Set the solvers to nonlinear and linear block Gauss–Seidel by default.
Parameters:  **kwargs : dict
dict of arguments available here and in all descendants of this Group.

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 notyetset 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:  System
The System that was passed in.

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, simul_coloring=None, simul_map=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the constraint variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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 argumentref
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, simul_coloring=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the design variable.
 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 argumentref
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, simul_coloring=None, simul_map=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the objective variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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 driver.
Parameters:  recorder : <BaseRecorder>
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, simul_coloring=None, simul_map=None, 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 argumentref
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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the response variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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 notyetset 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:  <System>
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.

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.

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 subgroups will be included. Otherwise, a graph containing only direct children (both Components and Groups) of this group will be returned.
Returns:  DiGraph
A directed graph containing names of subsystems and their connections.

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.

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:  dict
The constraints defined in the current system.

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

get_linear_vectors
(vec_name='linear')¶ Return the linear inputs, outputs, and residuals vectors.
Parameters:  vec_name : str
Name of the linear righthandside vector. The default is ‘linear’.
Returns:  (inputs, outputs, residuals) : tuple of <Vector> instances
Yields the inputs, outputs, and residuals linear vectors for vec_name.

get_nonlinear_vectors
()¶ Return the inputs, outputs, and residuals vectors.
Returns:  (inputs, outputs, residuals) : tuple of <Vector> instances
Yields the inputs, outputs, and residuals nonlinear vectors.

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:  dict
The objectives defined in the current system.

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

is_active
()¶ Determine if the system is active on this rank.
Returns:  bool
If running under MPI, returns True if this System has a valid communicator. Always returns True if not running under MPI.

jacobian_context
(jac)¶ Context manager that yields the Jacobian assigned to this system in this system’s context.

linear_solver
¶ Get the linear solver for this system.

list_inputs
(values=True, units=False, hierarchical=True, print_arrays=False, 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.
 units : bool, optional
When True, display/return units. 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.
 out_stream : filelike object
Where to send human readable output. Default is sys.stdout. Set to None to suppress.
Returns:  list
list of input names and other optional information about those inputs

list_outputs
(explicit=True, implicit=True, values=True, residuals=False, residuals_tol=None, units=False, shape=False, bounds=False, scaling=False, hierarchical=True, print_arrays=False, 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.
 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.
 out_stream : filelike
Where to send human readable output. Default is sys.stdout. Set to None to suppress.
Returns:  list
list of output names and other optional information about those outputs

ln_solver
¶ Get the linear solver for this system.

metadata
¶ Get the options for this System.

nl_solver
¶ Get the nonlinear solver for this system.

nonlinear_solver
¶ Get the nonlinear solver for this system.

reconfigure
()¶ Perform reconfiguration.
Returns:  bool
If True, reconfiguration is to be performed.

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 jacvec 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 righthandside vectors.
 mode : str
‘fwd’ or ‘rev’.
 scope_out : set or None
Set of absolute output names in the scope of this matvec product. If None, all are in the scope.
 scope_in : set or None
Set of absolute input names in the scope of this matvec 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 righthandside vectors.
 mode : str
‘fwd’ or ‘rev’.
Returns:  boolean
Failure flag; True if failed to converge, False is successful.
 float
relative error.
 float
absolute error.

run_solve_nonlinear
()¶ Compute outputs.
This calls _solve_nonlinear, but with the model assumed to be in an unscaled state.
Returns:  boolean
Failure flag; True if failed to converge, False is successful.
 float
relative error.
 float
absolute error.

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.

setup
()[source]¶ Build this group.
This method should be overidden by your Group’s method. The reason for using this method to add subsystem is to save memory and setup time when using your Group while running under MPI. This avoids the creation of systems that will not be used in the current process.
You may call ‘add_subsystem’ to add systems to this group. You may also issue connections, and set the linear and nonlinear solvers for this group level. You cannot safely change anything on children systems; use the ‘configure’ method instead.
 Available attributes:
 name pathname comm options

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.


class
openmdao.test_suite.components.sellar.
SellarDerivativesConnected
(**kwargs)[source]¶ Bases:
openmdao.core.group.Group
Group containing the Sellar MDA. This version uses the disciplines with derivatives.

__init__
(**kwargs)¶ Set the solvers to nonlinear and linear block Gauss–Seidel by default.
Parameters:  **kwargs : dict
dict of arguments available here and in all descendants of this Group.

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 notyetset 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:  System
The System that was passed in.

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, simul_coloring=None, simul_map=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the constraint variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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 argumentref
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, simul_coloring=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the design variable.
 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 argumentref
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, simul_coloring=None, simul_map=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the objective variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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 driver.
Parameters:  recorder : <BaseRecorder>
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, simul_coloring=None, simul_map=None, 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 argumentref
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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the response variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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 notyetset 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:  <System>
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.

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.

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 subgroups will be included. Otherwise, a graph containing only direct children (both Components and Groups) of this group will be returned.
Returns:  DiGraph
A directed graph containing names of subsystems and their connections.

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.

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:  dict
The constraints defined in the current system.

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

get_linear_vectors
(vec_name='linear')¶ Return the linear inputs, outputs, and residuals vectors.
Parameters:  vec_name : str
Name of the linear righthandside vector. The default is ‘linear’.
Returns:  (inputs, outputs, residuals) : tuple of <Vector> instances
Yields the inputs, outputs, and residuals linear vectors for vec_name.

get_nonlinear_vectors
()¶ Return the inputs, outputs, and residuals vectors.
Returns:  (inputs, outputs, residuals) : tuple of <Vector> instances
Yields the inputs, outputs, and residuals nonlinear vectors.

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:  dict
The objectives defined in the current system.

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

initialize
()¶ Perform any onetime initialization run at instantiation.

is_active
()¶ Determine if the system is active on this rank.
Returns:  bool
If running under MPI, returns True if this System has a valid communicator. Always returns True if not running under MPI.

jacobian_context
(jac)¶ Context manager that yields the Jacobian assigned to this system in this system’s context.

linear_solver
¶ Get the linear solver for this system.

list_inputs
(values=True, units=False, hierarchical=True, print_arrays=False, 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.
 units : bool, optional
When True, display/return units. 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.
 out_stream : filelike object
Where to send human readable output. Default is sys.stdout. Set to None to suppress.
Returns:  list
list of input names and other optional information about those inputs

list_outputs
(explicit=True, implicit=True, values=True, residuals=False, residuals_tol=None, units=False, shape=False, bounds=False, scaling=False, hierarchical=True, print_arrays=False, 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.
 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.
 out_stream : filelike
Where to send human readable output. Default is sys.stdout. Set to None to suppress.
Returns:  list
list of output names and other optional information about those outputs

ln_solver
¶ Get the linear solver for this system.

metadata
¶ Get the options for this System.

nl_solver
¶ Get the nonlinear solver for this system.

nonlinear_solver
¶ Get the nonlinear solver for this system.

reconfigure
()¶ Perform reconfiguration.
Returns:  bool
If True, reconfiguration is to be performed.

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 jacvec 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 righthandside vectors.
 mode : str
‘fwd’ or ‘rev’.
 scope_out : set or None
Set of absolute output names in the scope of this matvec product. If None, all are in the scope.
 scope_in : set or None
Set of absolute input names in the scope of this matvec 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 righthandside vectors.
 mode : str
‘fwd’ or ‘rev’.
Returns:  boolean
Failure flag; True if failed to converge, False is successful.
 float
relative error.
 float
absolute error.

run_solve_nonlinear
()¶ Compute outputs.
This calls _solve_nonlinear, but with the model assumed to be in an unscaled state.
Returns:  boolean
Failure flag; True if failed to converge, False is successful.
 float
relative error.
 float
absolute error.

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.

setup
()[source]¶ Build this group.
This method should be overidden by your Group’s method. The reason for using this method to add subsystem is to save memory and setup time when using your Group while running under MPI. This avoids the creation of systems that will not be used in the current process.
You may call ‘add_subsystem’ to add systems to this group. You may also issue connections, and set the linear and nonlinear solvers for this group level. You cannot safely change anything on children systems; use the ‘configure’ method instead.
 Available attributes:
 name pathname comm options

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.


class
openmdao.test_suite.components.sellar.
SellarDerivativesGrouped
(**kwargs)[source]¶ Bases:
openmdao.core.group.Group
Group containing the Sellar MDA. This version uses the disciplines with derivatives.

__init__
(**kwargs)¶ Set the solvers to nonlinear and linear block Gauss–Seidel by default.
Parameters:  **kwargs : dict
dict of arguments available here and in all descendants of this Group.

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 notyetset 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:  System
The System that was passed in.

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, simul_coloring=None, simul_map=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the constraint variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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 argumentref
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, simul_coloring=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the design variable.
 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 argumentref
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, simul_coloring=None, simul_map=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the objective variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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 driver.
Parameters:  recorder : <BaseRecorder>
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, simul_coloring=None, simul_map=None, 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 argumentref
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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the response variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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 notyetset 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:  <System>
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.

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.

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 subgroups will be included. Otherwise, a graph containing only direct children (both Components and Groups) of this group will be returned.
Returns:  DiGraph
A directed graph containing names of subsystems and their connections.

configure
()[source]¶ 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.

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:  dict
The constraints defined in the current system.

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

get_linear_vectors
(vec_name='linear')¶ Return the linear inputs, outputs, and residuals vectors.
Parameters:  vec_name : str
Name of the linear righthandside vector. The default is ‘linear’.
Returns:  (inputs, outputs, residuals) : tuple of <Vector> instances
Yields the inputs, outputs, and residuals linear vectors for vec_name.

get_nonlinear_vectors
()¶ Return the inputs, outputs, and residuals vectors.
Returns:  (inputs, outputs, residuals) : tuple of <Vector> instances
Yields the inputs, outputs, and residuals nonlinear vectors.

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:  dict
The objectives defined in the current system.

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

is_active
()¶ Determine if the system is active on this rank.
Returns:  bool
If running under MPI, returns True if this System has a valid communicator. Always returns True if not running under MPI.

jacobian_context
(jac)¶ Context manager that yields the Jacobian assigned to this system in this system’s context.

linear_solver
¶ Get the linear solver for this system.

list_inputs
(values=True, units=False, hierarchical=True, print_arrays=False, 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.
 units : bool, optional
When True, display/return units. 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.
 out_stream : filelike object
Where to send human readable output. Default is sys.stdout. Set to None to suppress.
Returns:  list
list of input names and other optional information about those inputs

list_outputs
(explicit=True, implicit=True, values=True, residuals=False, residuals_tol=None, units=False, shape=False, bounds=False, scaling=False, hierarchical=True, print_arrays=False, 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.
 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.
 out_stream : filelike
Where to send human readable output. Default is sys.stdout. Set to None to suppress.
Returns:  list
list of output names and other optional information about those outputs

ln_solver
¶ Get the linear solver for this system.

metadata
¶ Get the options for this System.

nl_solver
¶ Get the nonlinear solver for this system.

nonlinear_solver
¶ Get the nonlinear solver for this system.

reconfigure
()¶ Perform reconfiguration.
Returns:  bool
If True, reconfiguration is to be performed.

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 jacvec 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 righthandside vectors.
 mode : str
‘fwd’ or ‘rev’.
 scope_out : set or None
Set of absolute output names in the scope of this matvec product. If None, all are in the scope.
 scope_in : set or None
Set of absolute input names in the scope of this matvec 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 righthandside vectors.
 mode : str
‘fwd’ or ‘rev’.
Returns:  boolean
Failure flag; True if failed to converge, False is successful.
 float
relative error.
 float
absolute error.

run_solve_nonlinear
()¶ Compute outputs.
This calls _solve_nonlinear, but with the model assumed to be in an unscaled state.
Returns:  boolean
Failure flag; True if failed to converge, False is successful.
 float
relative error.
 float
absolute error.

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.

setup
()[source]¶ Build this group.
This method should be overidden by your Group’s method. The reason for using this method to add subsystem is to save memory and setup time when using your Group while running under MPI. This avoids the creation of systems that will not be used in the current process.
You may call ‘add_subsystem’ to add systems to this group. You may also issue connections, and set the linear and nonlinear solvers for this group level. You cannot safely change anything on children systems; use the ‘configure’ method instead.
 Available attributes:
 name pathname comm options

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.


class
openmdao.test_suite.components.sellar.
SellarDis1
(units=None, scaling=None)[source]¶ Bases:
openmdao.core.explicitcomponent.ExplicitComponent
Component containing Discipline 1 – no derivatives version.

__init__
(units=None, scaling=None)[source]¶ Store some bound methods so we can detect runtime overrides.
Parameters:  **kwargs : dict of keyword arguments
Keyword arguments that will be mapped into the Component options.

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, simul_coloring=None, simul_map=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the constraint variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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 argumentref
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, simul_coloring=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the design variable.
 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 argumentref
represents the physical value when the scaled value is 1.

add_input
(name, val=1.0, shape=None, src_indices=None, flat_src_indices=None, units=None, desc='', var_set=0)¶ Add an input variable to the component.
Parameters:  name : str
name of the variable in this component’s namespace.
 val : float or list or tuple or ndarray or Iterable
The initial value of the variable being added in userdefined units. Default is 1.0.
 shape : int or tuple or list or None
Shape of this variable, only required if src_indices not provided and val is not an array. Default is None.
 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. A value of None implies this input depends on all entries of source. Default is None. 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 each entry must be a tuple or list of size equal to the number of dimensions of the source.
 units : str or None
Units in which this input variable will be provided to the component during execution. Default is None, which means it is unitless.
 desc : str
description of the variable
 var_set : hashable object
For advanced users only. ID or color for this variable, relevant for reconfigurability. Default is 0.
Returns:  dict
metadata for added variable

add_objective
(name, ref=None, ref0=None, index=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, simul_coloring=None, simul_map=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the objective variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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_output
(name, val=1.0, shape=None, units=None, res_units=None, desc='', lower=None, upper=None, ref=1.0, ref0=0.0, res_ref=None, var_set=0)¶ Add an output variable to the component.
For ExplicitComponent, res_ref defaults to the value in res unless otherwise specified.
Parameters:  name : str
name of the variable in this component’s namespace.
 val : float or list or tuple or ndarray
The initial value of the variable being added in userdefined units. Default is 1.0.
 shape : int or tuple or list or None
Shape of this variable, only required if val is not an array. Default is None.
 units : str or None
Units in which the output variables will be provided to the component during execution. Default is None, which means it has no units.
 res_units : str or None
Units in which the residuals of this output will be given to the user when requested. Default is None, which means it has no units.
 desc : str
description of the variable.
 lower : float or list or tuple or ndarray or None
lower bound(s) in userdefined units. It can be (1) a float, (2) an array_like consistent with the shape arg (if given), or (3) an array_like matching the shape of val, if val is array_like. A value of None means this output has no lower bound. Default is None.
 upper : float or list or tuple or ndarray or None
upper bound(s) in userdefined units. It can be (1) a float, (2) an array_like consistent with the shape arg (if given), or (3) an array_like matching the shape of val, if val is array_like. A value of None means this output has no upper bound. Default is None.
 ref : float
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 1. Default is 1.
 ref0 : float
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 0. Default is 0.
 res_ref : float
Scaling parameter. The value in the userdefined res_units of this output’s residual when the scaled value is 1. Default is None, which means residual scaling matches output scaling.
 var_set : hashable object
For advanced users only. ID or color for this variable, relevant for reconfigurability. Default is 0.
Returns:  dict
metadata for added variable

add_recorder
(recorder, recurse=False)¶ Add a recorder to the driver.
Parameters:  recorder : <BaseRecorder>
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, simul_coloring=None, simul_map=None, 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 argumentref
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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the response variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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.

check_config
(logger)¶ Perform optional error checks.
Parameters:  logger : object
The object that manages logging output.

compute_jacvec_product
(inputs, d_inputs, d_outputs, mode)¶ Compute jacvector product. The model is assumed to be in an unscaled state.
 If mode is:
‘fwd’: d_inputs > d_outputs
‘rev’: d_outputs > d_inputs
Parameters:  inputs : Vector
unscaled, dimensional input variables read via inputs[key]
 d_inputs : Vector
see inputs; product must be computed only if var_name in d_inputs
 d_outputs : Vector
see outputs; product must be computed only if var_name in d_outputs
 mode : str
either ‘fwd’ or ‘rev’

compute_partials
(inputs, partials)¶ Compute subjacobian parts. The model is assumed to be in an unscaled state.
Parameters:  inputs : Vector
unscaled, dimensional input variables read via inputs[key]
 partials : Jacobian
subjac components written to partials[output_name, input_name]

declare_partials
(of, wrt, dependent=True, rows=None, cols=None, val=None, method='exact', step=None, form=None, step_calc=None)¶ Declare information about this component’s subjacobians.
Parameters:  of : str or list of str
The name of the residual(s) that derivatives are being computed for. May also contain a glob pattern.
 wrt : str or list of str
The name of the variables that derivatives are taken with respect to. This can contain the name of any input or output variable. May also contain a glob pattern.
 dependent : bool(True)
If False, specifies no dependence between the output(s) and the input(s). This is only necessary in the case of a sparse global jacobian, because if ‘dependent=False’ is not specified and declare_partials is not called for a given pair, then a dense matrix of zeros will be allocated in the sparse global jacobian for that pair. In the case of a dense global jacobian it doesn’t matter because the space for a dense subjac will always be allocated for every pair.
 rows : ndarray of int or None
Row indices for each nonzero entry. For sparse subjacobians only.
 cols : ndarray of int or None
Column indices for each nonzero entry. For sparse subjacobians only.
 val : float or ndarray of float or scipy.sparse
Value of subjacobian. If rows and cols are not None, this will contain the values found at each (row, col) location in the subjac.
 method : str
The type of approximation that should be used. Valid options include: ‘fd’: Finite Difference, ‘cs’: Complex Step, ‘exact’: use the component defined analytic derivatives. Default is ‘exact’.
 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.

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:  dict
The constraints defined in the current system.

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

get_linear_vectors
(vec_name='linear')¶ Return the linear inputs, outputs, and residuals vectors.
Parameters:  vec_name : str
Name of the linear righthandside vector. The default is ‘linear’.
Returns:  (inputs, outputs, residuals) : tuple of <Vector> instances
Yields the inputs, outputs, and residuals linear vectors for vec_name.

get_nonlinear_vectors
()¶ Return the inputs, outputs, and residuals vectors.
Returns:  (inputs, outputs, residuals) : tuple of <Vector> instances
Yields the inputs, outputs, and residuals nonlinear vectors.

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:  dict
The objectives defined in the current system.

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

initialize
()¶ Perform any onetime initialization run at instantiation.

is_active
()¶ Determine if the system is active on this rank.
Returns:  bool
If running under MPI, returns True if this System has a valid communicator. Always returns True if not running under MPI.

jacobian_context
(jac)¶ Context manager that yields the Jacobian assigned to this system in this system’s context.

linear_solver
¶ Get the linear solver for this system.

list_inputs
(values=True, units=False, hierarchical=True, print_arrays=False, 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.
 units : bool, optional
When True, display/return units. 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.
 out_stream : filelike object
Where to send human readable output. Default is sys.stdout. Set to None to suppress.
Returns:  list
list of input names and other optional information about those inputs

list_outputs
(explicit=True, implicit=True, values=True, residuals=False, residuals_tol=None, units=False, shape=False, bounds=False, scaling=False, hierarchical=True, print_arrays=False, 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.
 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.
 out_stream : filelike
Where to send human readable output. Default is sys.stdout. Set to None to suppress.
Returns:  list
list of output names and other optional information about those outputs

ln_solver
¶ Get the linear solver for this system.

metadata
¶ Get the options for this System.

nl_solver
¶ Get the nonlinear solver for this system.

nonlinear_solver
¶ Get the nonlinear solver for this system.

reconfigure
()¶ Perform reconfiguration.
Returns:  bool
If True, reconfiguration is to be performed.

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 jacvec 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 righthandside vectors.
 mode : str
‘fwd’ or ‘rev’.
 scope_out : set or None
Set of absolute output names in the scope of this matvec product. If None, all are in the scope.
 scope_in : set or None
Set of absolute input names in the scope of this matvec 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 righthandside vectors.
 mode : str
‘fwd’ or ‘rev’.
Returns:  boolean
Failure flag; True if failed to converge, False is successful.
 float
relative error.
 float
absolute error.

run_solve_nonlinear
()¶ Compute outputs.
This calls _solve_nonlinear, but with the model assumed to be in an unscaled state.
Returns:  boolean
Failure flag; True if failed to converge, False is successful.
 float
relative error.
 float
absolute error.

set_check_partial_options
(wrt, method='fd', form=None, step=None, step_calc=None)¶ Set options that will be used for checking partial derivatives.
Parameters:  wrt : str or list of str
The name or names of the variables that derivatives are taken with respect to. This can contain the name of any input or output variable. May also contain a glob pattern.
 method : str
Method for check: “fd” for finite difference, “cs” for complex step.
 form : str
Finite difference form for check, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.
 step : float
Step size for finite difference check. Leave undeclared to keep unchanged from previous or default value.
 step_calc : str
Type of step calculation for check, can be “abs” for absolute (default) or “rel” for relative. Leave undeclared to keep unchanged from previous or default value.

set_initial_values
()¶ Set all input and output variables to their declared initial values.

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.


class
openmdao.test_suite.components.sellar.
SellarDis1withDerivatives
(units=None, scaling=None)[source]¶ Bases:
openmdao.test_suite.components.sellar.SellarDis1
Component containing Discipline 1 – derivatives version.

__init__
(units=None, scaling=None)¶ Store some bound methods so we can detect runtime overrides.
Parameters:  **kwargs : dict of keyword arguments
Keyword arguments that will be mapped into the Component options.

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, simul_coloring=None, simul_map=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the constraint variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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 argumentref
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, simul_coloring=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the design variable.
 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 argumentref
represents the physical value when the scaled value is 1.

add_input
(name, val=1.0, shape=None, src_indices=None, flat_src_indices=None, units=None, desc='', var_set=0)¶ Add an input variable to the component.
Parameters:  name : str
name of the variable in this component’s namespace.
 val : float or list or tuple or ndarray or Iterable
The initial value of the variable being added in userdefined units. Default is 1.0.
 shape : int or tuple or list or None
Shape of this variable, only required if src_indices not provided and val is not an array. Default is None.
 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. A value of None implies this input depends on all entries of source. Default is None. 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 each entry must be a tuple or list of size equal to the number of dimensions of the source.
 units : str or None
Units in which this input variable will be provided to the component during execution. Default is None, which means it is unitless.
 desc : str
description of the variable
 var_set : hashable object
For advanced users only. ID or color for this variable, relevant for reconfigurability. Default is 0.
Returns:  dict
metadata for added variable

add_objective
(name, ref=None, ref0=None, index=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, simul_coloring=None, simul_map=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the objective variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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_output
(name, val=1.0, shape=None, units=None, res_units=None, desc='', lower=None, upper=None, ref=1.0, ref0=0.0, res_ref=None, var_set=0)¶ Add an output variable to the component.
For ExplicitComponent, res_ref defaults to the value in res unless otherwise specified.
Parameters:  name : str
name of the variable in this component’s namespace.
 val : float or list or tuple or ndarray
The initial value of the variable being added in userdefined units. Default is 1.0.
 shape : int or tuple or list or None
Shape of this variable, only required if val is not an array. Default is None.
 units : str or None
Units in which the output variables will be provided to the component during execution. Default is None, which means it has no units.
 res_units : str or None
Units in which the residuals of this output will be given to the user when requested. Default is None, which means it has no units.
 desc : str
description of the variable.
 lower : float or list or tuple or ndarray or None
lower bound(s) in userdefined units. It can be (1) a float, (2) an array_like consistent with the shape arg (if given), or (3) an array_like matching the shape of val, if val is array_like. A value of None means this output has no lower bound. Default is None.
 upper : float or list or tuple or ndarray or None
upper bound(s) in userdefined units. It can be (1) a float, (2) an array_like consistent with the shape arg (if given), or (3) an array_like matching the shape of val, if val is array_like. A value of None means this output has no upper bound. Default is None.
 ref : float
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 1. Default is 1.
 ref0 : float
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 0. Default is 0.
 res_ref : float
Scaling parameter. The value in the userdefined res_units of this output’s residual when the scaled value is 1. Default is None, which means residual scaling matches output scaling.
 var_set : hashable object
For advanced users only. ID or color for this variable, relevant for reconfigurability. Default is 0.
Returns:  dict
metadata for added variable

add_recorder
(recorder, recurse=False)¶ Add a recorder to the driver.
Parameters:  recorder : <BaseRecorder>
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, simul_coloring=None, simul_map=None, 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 argumentref
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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the response variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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.

check_config
(logger)¶ Perform optional error checks.
Parameters:  logger : object
The object that manages logging output.

compute
(inputs, outputs)¶ Evaluates the equation y1 = z1**2 + z2 + x1  0.2*y2

compute_jacvec_product
(inputs, d_inputs, d_outputs, mode)¶ Compute jacvector product. The model is assumed to be in an unscaled state.
 If mode is:
‘fwd’: d_inputs > d_outputs
‘rev’: d_outputs > d_inputs
Parameters:  inputs : Vector
unscaled, dimensional input variables read via inputs[key]
 d_inputs : Vector
see inputs; product must be computed only if var_name in d_inputs
 d_outputs : Vector
see outputs; product must be computed only if var_name in d_outputs
 mode : str
either ‘fwd’ or ‘rev’

declare_partials
(of, wrt, dependent=True, rows=None, cols=None, val=None, method='exact', step=None, form=None, step_calc=None)¶ Declare information about this component’s subjacobians.
Parameters:  of : str or list of str
The name of the residual(s) that derivatives are being computed for. May also contain a glob pattern.
 wrt : str or list of str
The name of the variables that derivatives are taken with respect to. This can contain the name of any input or output variable. May also contain a glob pattern.
 dependent : bool(True)
If False, specifies no dependence between the output(s) and the input(s). This is only necessary in the case of a sparse global jacobian, because if ‘dependent=False’ is not specified and declare_partials is not called for a given pair, then a dense matrix of zeros will be allocated in the sparse global jacobian for that pair. In the case of a dense global jacobian it doesn’t matter because the space for a dense subjac will always be allocated for every pair.
 rows : ndarray of int or None
Row indices for each nonzero entry. For sparse subjacobians only.
 cols : ndarray of int or None
Column indices for each nonzero entry. For sparse subjacobians only.
 val : float or ndarray of float or scipy.sparse
Value of subjacobian. If rows and cols are not None, this will contain the values found at each (row, col) location in the subjac.
 method : str
The type of approximation that should be used. Valid options include: ‘fd’: Finite Difference, ‘cs’: Complex Step, ‘exact’: use the component defined analytic derivatives. Default is ‘exact’.
 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.

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:  dict
The constraints defined in the current system.

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

get_linear_vectors
(vec_name='linear')¶ Return the linear inputs, outputs, and residuals vectors.
Parameters:  vec_name : str
Name of the linear righthandside vector. The default is ‘linear’.
Returns:  (inputs, outputs, residuals) : tuple of <Vector> instances
Yields the inputs, outputs, and residuals linear vectors for vec_name.

get_nonlinear_vectors
()¶ Return the inputs, outputs, and residuals vectors.
Returns:  (inputs, outputs, residuals) : tuple of <Vector> instances
Yields the inputs, outputs, and residuals nonlinear vectors.

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:  dict
The objectives defined in the current system.

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

initialize
()¶ Perform any onetime initialization run at instantiation.

is_active
()¶ Determine if the system is active on this rank.
Returns:  bool
If running under MPI, returns True if this System has a valid communicator. Always returns True if not running under MPI.

jacobian_context
(jac)¶ Context manager that yields the Jacobian assigned to this system in this system’s context.

linear_solver
¶ Get the linear solver for this system.

list_inputs
(values=True, units=False, hierarchical=True, print_arrays=False, 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.
 units : bool, optional
When True, display/return units. 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.
 out_stream : filelike object
Where to send human readable output. Default is sys.stdout. Set to None to suppress.
Returns:  list
list of input names and other optional information about those inputs

list_outputs
(explicit=True, implicit=True, values=True, residuals=False, residuals_tol=None, units=False, shape=False, bounds=False, scaling=False, hierarchical=True, print_arrays=False, 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.
 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.
 out_stream : filelike
Where to send human readable output. Default is sys.stdout. Set to None to suppress.
Returns:  list
list of output names and other optional information about those outputs

ln_solver
¶ Get the linear solver for this system.

metadata
¶ Get the options for this System.

nl_solver
¶ Get the nonlinear solver for this system.

nonlinear_solver
¶ Get the nonlinear solver for this system.

reconfigure
()¶ Perform reconfiguration.
Returns:  bool
If True, reconfiguration is to be performed.

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 jacvec 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 righthandside vectors.
 mode : str
‘fwd’ or ‘rev’.
 scope_out : set or None
Set of absolute output names in the scope of this matvec product. If None, all are in the scope.
 scope_in : set or None
Set of absolute input names in the scope of this matvec 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 righthandside vectors.
 mode : str
‘fwd’ or ‘rev’.
Returns:  boolean
Failure flag; True if failed to converge, False is successful.
 float
relative error.
 float
absolute error.

run_solve_nonlinear
()¶ Compute outputs.
This calls _solve_nonlinear, but with the model assumed to be in an unscaled state.
Returns:  boolean
Failure flag; True if failed to converge, False is successful.
 float
relative error.
 float
absolute error.

set_check_partial_options
(wrt, method='fd', form=None, step=None, step_calc=None)¶ Set options that will be used for checking partial derivatives.
Parameters:  wrt : str or list of str
The name or names of the variables that derivatives are taken with respect to. This can contain the name of any input or output variable. May also contain a glob pattern.
 method : str
Method for check: “fd” for finite difference, “cs” for complex step.
 form : str
Finite difference form for check, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.
 step : float
Step size for finite difference check. Leave undeclared to keep unchanged from previous or default value.
 step_calc : str
Type of step calculation for check, can be “abs” for absolute (default) or “rel” for relative. Leave undeclared to keep unchanged from previous or default value.

set_initial_values
()¶ Set all input and output variables to their declared initial values.

setup
()¶ Declare inputs and outputs.
 Available attributes:
 name pathname comm options

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.


class
openmdao.test_suite.components.sellar.
SellarDis2
(units=None, scaling=None)[source]¶ Bases:
openmdao.core.explicitcomponent.ExplicitComponent
Component containing Discipline 2 – no derivatives version.

__init__
(units=None, scaling=None)[source]¶ Store some bound methods so we can detect runtime overrides.
Parameters:  **kwargs : dict of keyword arguments
Keyword arguments that will be mapped into the Component options.

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, simul_coloring=None, simul_map=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the constraint variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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 argumentref
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, simul_coloring=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the design variable.
 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 argumentref
represents the physical value when the scaled value is 1.

add_input
(name, val=1.0, shape=None, src_indices=None, flat_src_indices=None, units=None, desc='', var_set=0)¶ Add an input variable to the component.
Parameters:  name : str
name of the variable in this component’s namespace.
 val : float or list or tuple or ndarray or Iterable
The initial value of the variable being added in userdefined units. Default is 1.0.
 shape : int or tuple or list or None
Shape of this variable, only required if src_indices not provided and val is not an array. Default is None.
 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. A value of None implies this input depends on all entries of source. Default is None. 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 each entry must be a tuple or list of size equal to the number of dimensions of the source.
 units : str or None
Units in which this input variable will be provided to the component during execution. Default is None, which means it is unitless.
 desc : str
description of the variable
 var_set : hashable object
For advanced users only. ID or color for this variable, relevant for reconfigurability. Default is 0.
Returns:  dict
metadata for added variable

add_objective
(name, ref=None, ref0=None, index=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, simul_coloring=None, simul_map=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the objective variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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_output
(name, val=1.0, shape=None, units=None, res_units=None, desc='', lower=None, upper=None, ref=1.0, ref0=0.0, res_ref=None, var_set=0)¶ Add an output variable to the component.
For ExplicitComponent, res_ref defaults to the value in res unless otherwise specified.
Parameters:  name : str
name of the variable in this component’s namespace.
 val : float or list or tuple or ndarray
The initial value of the variable being added in userdefined units. Default is 1.0.
 shape : int or tuple or list or None
Shape of this variable, only required if val is not an array. Default is None.
 units : str or None
Units in which the output variables will be provided to the component during execution. Default is None, which means it has no units.
 res_units : str or None
Units in which the residuals of this output will be given to the user when requested. Default is None, which means it has no units.
 desc : str
description of the variable.
 lower : float or list or tuple or ndarray or None
lower bound(s) in userdefined units. It can be (1) a float, (2) an array_like consistent with the shape arg (if given), or (3) an array_like matching the shape of val, if val is array_like. A value of None means this output has no lower bound. Default is None.
 upper : float or list or tuple or ndarray or None
upper bound(s) in userdefined units. It can be (1) a float, (2) an array_like consistent with the shape arg (if given), or (3) an array_like matching the shape of val, if val is array_like. A value of None means this output has no upper bound. Default is None.
 ref : float
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 1. Default is 1.
 ref0 : float
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 0. Default is 0.
 res_ref : float
Scaling parameter. The value in the userdefined res_units of this output’s residual when the scaled value is 1. Default is None, which means residual scaling matches output scaling.
 var_set : hashable object
For advanced users only. ID or color for this variable, relevant for reconfigurability. Default is 0.
Returns:  dict
metadata for added variable

add_recorder
(recorder, recurse=False)¶ Add a recorder to the driver.
Parameters:  recorder : <BaseRecorder>
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, simul_coloring=None, simul_map=None, 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 argumentref
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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the response variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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.

check_config
(logger)¶ Perform optional error checks.
Parameters:  logger : object
The object that manages logging output.

compute_jacvec_product
(inputs, d_inputs, d_outputs, mode)¶ Compute jacvector product. The model is assumed to be in an unscaled state.
 If mode is:
‘fwd’: d_inputs > d_outputs
‘rev’: d_outputs > d_inputs
Parameters:  inputs : Vector
unscaled, dimensional input variables read via inputs[key]
 d_inputs : Vector
see inputs; product must be computed only if var_name in d_inputs
 d_outputs : Vector
see outputs; product must be computed only if var_name in d_outputs
 mode : str
either ‘fwd’ or ‘rev’

compute_partials
(inputs, partials)¶ Compute subjacobian parts. The model is assumed to be in an unscaled state.
Parameters:  inputs : Vector
unscaled, dimensional input variables read via inputs[key]
 partials : Jacobian
subjac components written to partials[output_name, input_name]

declare_partials
(of, wrt, dependent=True, rows=None, cols=None, val=None, method='exact', step=None, form=None, step_calc=None)¶ Declare information about this component’s subjacobians.
Parameters:  of : str or list of str
The name of the residual(s) that derivatives are being computed for. May also contain a glob pattern.
 wrt : str or list of str
The name of the variables that derivatives are taken with respect to. This can contain the name of any input or output variable. May also contain a glob pattern.
 dependent : bool(True)
If False, specifies no dependence between the output(s) and the input(s). This is only necessary in the case of a sparse global jacobian, because if ‘dependent=False’ is not specified and declare_partials is not called for a given pair, then a dense matrix of zeros will be allocated in the sparse global jacobian for that pair. In the case of a dense global jacobian it doesn’t matter because the space for a dense subjac will always be allocated for every pair.
 rows : ndarray of int or None
Row indices for each nonzero entry. For sparse subjacobians only.
 cols : ndarray of int or None
Column indices for each nonzero entry. For sparse subjacobians only.
 val : float or ndarray of float or scipy.sparse
Value of subjacobian. If rows and cols are not None, this will contain the values found at each (row, col) location in the subjac.
 method : str
The type of approximation that should be used. Valid options include: ‘fd’: Finite Difference, ‘cs’: Complex Step, ‘exact’: use the component defined analytic derivatives. Default is ‘exact’.
 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.

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:  dict
The constraints defined in the current system.

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

get_linear_vectors
(vec_name='linear')¶ Return the linear inputs, outputs, and residuals vectors.
Parameters:  vec_name : str
Name of the linear righthandside vector. The default is ‘linear’.
Returns:  (inputs, outputs, residuals) : tuple of <Vector> instances
Yields the inputs, outputs, and residuals linear vectors for vec_name.

get_nonlinear_vectors
()¶ Return the inputs, outputs, and residuals vectors.
Returns:  (inputs, outputs, residuals) : tuple of <Vector> instances
Yields the inputs, outputs, and residuals nonlinear vectors.

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:  dict
The objectives defined in the current system.

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

initialize
()¶ Perform any onetime initialization run at instantiation.

is_active
()¶ Determine if the system is active on this rank.
Returns:  bool
If running under MPI, returns True if this System has a valid communicator. Always returns True if not running under MPI.

jacobian_context
(jac)¶ Context manager that yields the Jacobian assigned to this system in this system’s context.

linear_solver
¶ Get the linear solver for this system.

list_inputs
(values=True, units=False, hierarchical=True, print_arrays=False, 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.
 units : bool, optional
When True, display/return units. 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.
 out_stream : filelike object
Where to send human readable output. Default is sys.stdout. Set to None to suppress.
Returns:  list
list of input names and other optional information about those inputs

list_outputs
(explicit=True, implicit=True, values=True, residuals=False, residuals_tol=None, units=False, shape=False, bounds=False, scaling=False, hierarchical=True, print_arrays=False, 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.
 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.
 out_stream : filelike
Where to send human readable output. Default is sys.stdout. Set to None to suppress.
Returns:  list
list of output names and other optional information about those outputs

ln_solver
¶ Get the linear solver for this system.

metadata
¶ Get the options for this System.

nl_solver
¶ Get the nonlinear solver for this system.

nonlinear_solver
¶ Get the nonlinear solver for this system.

reconfigure
()¶ Perform reconfiguration.
Returns:  bool
If True, reconfiguration is to be performed.

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 jacvec 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 righthandside vectors.
 mode : str
‘fwd’ or ‘rev’.
 scope_out : set or None
Set of absolute output names in the scope of this matvec product. If None, all are in the scope.
 scope_in : set or None
Set of absolute input names in the scope of this matvec 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 righthandside vectors.
 mode : str
‘fwd’ or ‘rev’.
Returns:  boolean
Failure flag; True if failed to converge, False is successful.
 float
relative error.
 float
absolute error.

run_solve_nonlinear
()¶ Compute outputs.
This calls _solve_nonlinear, but with the model assumed to be in an unscaled state.
Returns:  boolean
Failure flag; True if failed to converge, False is successful.
 float
relative error.
 float
absolute error.

set_check_partial_options
(wrt, method='fd', form=None, step=None, step_calc=None)¶ Set options that will be used for checking partial derivatives.
Parameters:  wrt : str or list of str
The name or names of the variables that derivatives are taken with respect to. This can contain the name of any input or output variable. May also contain a glob pattern.
 method : str
Method for check: “fd” for finite difference, “cs” for complex step.
 form : str
Finite difference form for check, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.
 step : float
Step size for finite difference check. Leave undeclared to keep unchanged from previous or default value.
 step_calc : str
Type of step calculation for check, can be “abs” for absolute (default) or “rel” for relative. Leave undeclared to keep unchanged from previous or default value.

set_initial_values
()¶ Set all input and output variables to their declared initial values.

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.


class
openmdao.test_suite.components.sellar.
SellarDis2withDerivatives
(units=None, scaling=None)[source]¶ Bases:
openmdao.test_suite.components.sellar.SellarDis2
Component containing Discipline 2 – derivatives version.

__init__
(units=None, scaling=None)¶ Store some bound methods so we can detect runtime overrides.
Parameters:  **kwargs : dict of keyword arguments
Keyword arguments that will be mapped into the Component options.

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, simul_coloring=None, simul_map=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the constraint variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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 argumentref
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, simul_coloring=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the design variable.
 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 argumentref
represents the physical value when the scaled value is 1.

add_input
(name, val=1.0, shape=None, src_indices=None, flat_src_indices=None, units=None, desc='', var_set=0)¶ Add an input variable to the component.
Parameters:  name : str
name of the variable in this component’s namespace.
 val : float or list or tuple or ndarray or Iterable
The initial value of the variable being added in userdefined units. Default is 1.0.
 shape : int or tuple or list or None
Shape of this variable, only required if src_indices not provided and val is not an array. Default is None.
 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. A value of None implies this input depends on all entries of source. Default is None. 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 each entry must be a tuple or list of size equal to the number of dimensions of the source.
 units : str or None
Units in which this input variable will be provided to the component during execution. Default is None, which means it is unitless.
 desc : str
description of the variable
 var_set : hashable object
For advanced users only. ID or color for this variable, relevant for reconfigurability. Default is 0.
Returns:  dict
metadata for added variable

add_objective
(name, ref=None, ref0=None, index=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, simul_coloring=None, simul_map=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the objective variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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_output
(name, val=1.0, shape=None, units=None, res_units=None, desc='', lower=None, upper=None, ref=1.0, ref0=0.0, res_ref=None, var_set=0)¶ Add an output variable to the component.
For ExplicitComponent, res_ref defaults to the value in res unless otherwise specified.
Parameters:  name : str
name of the variable in this component’s namespace.
 val : float or list or tuple or ndarray
The initial value of the variable being added in userdefined units. Default is 1.0.
 shape : int or tuple or list or None
Shape of this variable, only required if val is not an array. Default is None.
 units : str or None
Units in which the output variables will be provided to the component during execution. Default is None, which means it has no units.
 res_units : str or None
Units in which the residuals of this output will be given to the user when requested. Default is None, which means it has no units.
 desc : str
description of the variable.
 lower : float or list or tuple or ndarray or None
lower bound(s) in userdefined units. It can be (1) a float, (2) an array_like consistent with the shape arg (if given), or (3) an array_like matching the shape of val, if val is array_like. A value of None means this output has no lower bound. Default is None.
 upper : float or list or tuple or ndarray or None
upper bound(s) in userdefined units. It can be (1) a float, (2) an array_like consistent with the shape arg (if given), or (3) an array_like matching the shape of val, if val is array_like. A value of None means this output has no upper bound. Default is None.
 ref : float
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 1. Default is 1.
 ref0 : float
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 0. Default is 0.
 res_ref : float
Scaling parameter. The value in the userdefined res_units of this output’s residual when the scaled value is 1. Default is None, which means residual scaling matches output scaling.
 var_set : hashable object
For advanced users only. ID or color for this variable, relevant for reconfigurability. Default is 0.
Returns:  dict
metadata for added variable

add_recorder
(recorder, recurse=False)¶ Add a recorder to the driver.
Parameters:  recorder : <BaseRecorder>
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, simul_coloring=None, simul_map=None, 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 argumentref
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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the response variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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.

check_config
(logger)¶ Perform optional error checks.
Parameters:  logger : object
The object that manages logging output.

compute
(inputs, outputs)¶ Evaluates the equation y2 = y1**(.5) + z1 + z2

compute_jacvec_product
(inputs, d_inputs, d_outputs, mode)¶ Compute jacvector product. The model is assumed to be in an unscaled state.
 If mode is:
‘fwd’: d_inputs > d_outputs
‘rev’: d_outputs > d_inputs
Parameters:  inputs : Vector
unscaled, dimensional input variables read via inputs[key]
 d_inputs : Vector
see inputs; product must be computed only if var_name in d_inputs
 d_outputs : Vector
see outputs; product must be computed only if var_name in d_outputs
 mode : str
either ‘fwd’ or ‘rev’

declare_partials
(of, wrt, dependent=True, rows=None, cols=None, val=None, method='exact', step=None, form=None, step_calc=None)¶ Declare information about this component’s subjacobians.
Parameters:  of : str or list of str
The name of the residual(s) that derivatives are being computed for. May also contain a glob pattern.
 wrt : str or list of str
The name of the variables that derivatives are taken with respect to. This can contain the name of any input or output variable. May also contain a glob pattern.
 dependent : bool(True)
If False, specifies no dependence between the output(s) and the input(s). This is only necessary in the case of a sparse global jacobian, because if ‘dependent=False’ is not specified and declare_partials is not called for a given pair, then a dense matrix of zeros will be allocated in the sparse global jacobian for that pair. In the case of a dense global jacobian it doesn’t matter because the space for a dense subjac will always be allocated for every pair.
 rows : ndarray of int or None
Row indices for each nonzero entry. For sparse subjacobians only.
 cols : ndarray of int or None
Column indices for each nonzero entry. For sparse subjacobians only.
 val : float or ndarray of float or scipy.sparse
Value of subjacobian. If rows and cols are not None, this will contain the values found at each (row, col) location in the subjac.
 method : str
The type of approximation that should be used. Valid options include: ‘fd’: Finite Difference, ‘cs’: Complex Step, ‘exact’: use the component defined analytic derivatives. Default is ‘exact’.
 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.

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:  dict
The constraints defined in the current system.

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

get_linear_vectors
(vec_name='linear')¶ Return the linear inputs, outputs, and residuals vectors.
Parameters:  vec_name : str
Name of the linear righthandside vector. The default is ‘linear’.
Returns:  (inputs, outputs, residuals) : tuple of <Vector> instances
Yields the inputs, outputs, and residuals linear vectors for vec_name.

get_nonlinear_vectors
()¶ Return the inputs, outputs, and residuals vectors.
Returns:  (inputs, outputs, residuals) : tuple of <Vector> instances
Yields the inputs, outputs, and residuals nonlinear vectors.

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:  dict
The objectives defined in the current system.

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

initialize
()¶ Perform any onetime initialization run at instantiation.

is_active
()¶ Determine if the system is active on this rank.
Returns:  bool
If running under MPI, returns True if this System has a valid communicator. Always returns True if not running under MPI.

jacobian_context
(jac)¶ Context manager that yields the Jacobian assigned to this system in this system’s context.

linear_solver
¶ Get the linear solver for this system.

list_inputs
(values=True, units=False, hierarchical=True, print_arrays=False, 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.
 units : bool, optional
When True, display/return units. 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.
 out_stream : filelike object
Where to send human readable output. Default is sys.stdout. Set to None to suppress.
Returns:  list
list of input names and other optional information about those inputs

list_outputs
(explicit=True, implicit=True, values=True, residuals=False, residuals_tol=None, units=False, shape=False, bounds=False, scaling=False, hierarchical=True, print_arrays=False, 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.
 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.
 out_stream : filelike
Where to send human readable output. Default is sys.stdout. Set to None to suppress.
Returns:  list
list of output names and other optional information about those outputs

ln_solver
¶ Get the linear solver for this system.

metadata
¶ Get the options for this System.

nl_solver
¶ Get the nonlinear solver for this system.

nonlinear_solver
¶ Get the nonlinear solver for this system.

reconfigure
()¶ Perform reconfiguration.
Returns:  bool
If True, reconfiguration is to be performed.

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 jacvec 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 righthandside vectors.
 mode : str
‘fwd’ or ‘rev’.
 scope_out : set or None
Set of absolute output names in the scope of this matvec product. If None, all are in the scope.
 scope_in : set or None
Set of absolute input names in the scope of this matvec 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 righthandside vectors.
 mode : str
‘fwd’ or ‘rev’.
Returns:  boolean
Failure flag; True if failed to converge, False is successful.
 float
relative error.
 float
absolute error.

run_solve_nonlinear
()¶ Compute outputs.
This calls _solve_nonlinear, but with the model assumed to be in an unscaled state.
Returns:  boolean
Failure flag; True if failed to converge, False is successful.
 float
relative error.
 float
absolute error.

set_check_partial_options
(wrt, method='fd', form=None, step=None, step_calc=None)¶ Set options that will be used for checking partial derivatives.
Parameters:  wrt : str or list of str
The name or names of the variables that derivatives are taken with respect to. This can contain the name of any input or output variable. May also contain a glob pattern.
 method : str
Method for check: “fd” for finite difference, “cs” for complex step.
 form : str
Finite difference form for check, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.
 step : float
Step size for finite difference check. Leave undeclared to keep unchanged from previous or default value.
 step_calc : str
Type of step calculation for check, can be “abs” for absolute (default) or “rel” for relative. Leave undeclared to keep unchanged from previous or default value.

set_initial_values
()¶ Set all input and output variables to their declared initial values.

setup
()¶ Declare inputs and outputs.
 Available attributes:
 name pathname comm options

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.


class
openmdao.test_suite.components.sellar.
SellarImplicitDis1
(units=None, scaling=None)[source]¶ Bases:
openmdao.core.implicitcomponent.ImplicitComponent
Component containing Discipline 1 – no derivatives version.

__init__
(units=None, scaling=None)[source]¶ Store some bound methods so we can detect runtime overrides.
Parameters:  **kwargs : dict of keyword arguments
Keyword arguments that will be mapped into the Component options.

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, simul_coloring=None, simul_map=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the constraint variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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 argumentref
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, simul_coloring=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the design variable.
 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 argumentref
represents the physical value when the scaled value is 1.

add_input
(name, val=1.0, shape=None, src_indices=None, flat_src_indices=None, units=None, desc='', var_set=0)¶ Add an input variable to the component.
Parameters:  name : str
name of the variable in this component’s namespace.
 val : float or list or tuple or ndarray or Iterable
The initial value of the variable being added in userdefined units. Default is 1.0.
 shape : int or tuple or list or None
Shape of this variable, only required if src_indices not provided and val is not an array. Default is None.
 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. A value of None implies this input depends on all entries of source. Default is None. 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 each entry must be a tuple or list of size equal to the number of dimensions of the source.
 units : str or None
Units in which this input variable will be provided to the component during execution. Default is None, which means it is unitless.
 desc : str
description of the variable
 var_set : hashable object
For advanced users only. ID or color for this variable, relevant for reconfigurability. Default is 0.
Returns:  dict
metadata for added variable

add_objective
(name, ref=None, ref0=None, index=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, simul_coloring=None, simul_map=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the objective variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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_output
(name, val=1.0, shape=None, units=None, res_units=None, desc='', lower=None, upper=None, ref=1.0, ref0=0.0, res_ref=1.0, var_set=0)¶ Add an output variable to the component.
Parameters:  name : str
name of the variable in this component’s namespace.
 val : float or list or tuple or ndarray
The initial value of the variable being added in userdefined units. Default is 1.0.
 shape : int or tuple or list or None
Shape of this variable, only required if val is not an array. Default is None.
 units : str or None
Units in which the output variables will be provided to the component during execution. Default is None, which means it has no units.
 res_units : str or None
Units in which the residuals of this output will be given to the user when requested. Default is None, which means it has no units.
 desc : str
description of the variable.
 lower : float or list or tuple or ndarray or Iterable or None
lower bound(s) in userdefined units. It can be (1) a float, (2) an array_like consistent with the shape arg (if given), or (3) an array_like matching the shape of val, if val is array_like. A value of None means this output has no lower bound. Default is None.
 upper : float or list or tuple or ndarray or or Iterable None
upper bound(s) in userdefined units. It can be (1) a float, (2) an array_like consistent with the shape arg (if given), or (3) an array_like matching the shape of val, if val is array_like. A value of None means this output has no upper bound. Default is None.
 ref : float or ndarray
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 1. Default is 1.
 ref0 : float or ndarray
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 0. Default is 0.
 res_ref : float or ndarray
Scaling parameter. The value in the userdefined res_units of this output’s residual when the scaled value is 1. Default is 1.
 var_set : hashable object
For advanced users only. ID or color for this variable, relevant for reconfigurability. Default is 0.
Returns:  dict
metadata for added variable

add_recorder
(recorder, recurse=False)¶ Add a recorder to the driver.
Parameters:  recorder : <BaseRecorder>
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, simul_coloring=None, simul_map=None, 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 argumentref
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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the response variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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.

apply_linear
(inputs, outputs, d_inputs, d_outputs, d_residuals, mode)¶ Compute jacvector product. The model is assumed to be in an unscaled state.
 If mode is:
‘fwd’: (d_inputs, d_outputs) > d_residuals
‘rev’: d_residuals > (d_inputs, d_outputs)
Parameters:  inputs : Vector
unscaled, dimensional input variables read via inputs[key]
 outputs : Vector
unscaled, dimensional output variables read via outputs[key]
 d_inputs : Vector
see inputs; product must be computed only if var_name in d_inputs
 d_outputs : Vector
see outputs; product must be computed only if var_name in d_outputs
 d_residuals : Vector
see outputs
 mode : str
either ‘fwd’ or ‘rev’

apply_nonlinear
(inputs, outputs, resids)[source]¶ Evaluates the equation y1 = z1**2 + z2 + x1  0.2*y2

check_config
(logger)¶ Perform optional error checks.
Parameters:  logger : object
The object that manages logging output.

declare_partials
(of, wrt, dependent=True, rows=None, cols=None, val=None, method='exact', step=None, form=None, step_calc=None)¶ Declare information about this component’s subjacobians.
Parameters:  of : str or list of str
The name of the residual(s) that derivatives are being computed for. May also contain a glob pattern.
 wrt : str or list of str
The name of the variables that derivatives are taken with respect to. This can contain the name of any input or output variable. May also contain a glob pattern.
 dependent : bool(True)
If False, specifies no dependence between the output(s) and the input(s). This is only necessary in the case of a sparse global jacobian, because if ‘dependent=False’ is not specified and declare_partials is not called for a given pair, then a dense matrix of zeros will be allocated in the sparse global jacobian for that pair. In the case of a dense global jacobian it doesn’t matter because the space for a dense subjac will always be allocated for every pair.
 rows : ndarray of int or None
Row indices for each nonzero entry. For sparse subjacobians only.
 cols : ndarray of int or None
Column indices for each nonzero entry. For sparse subjacobians only.
 val : float or ndarray of float or scipy.sparse
Value of subjacobian. If rows and cols are not None, this will contain the values found at each (row, col) location in the subjac.
 method : str
The type of approximation that should be used. Valid options include: ‘fd’: Finite Difference, ‘cs’: Complex Step, ‘exact’: use the component defined analytic derivatives. Default is ‘exact’.
 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.

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:  dict
The constraints defined in the current system.

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

get_linear_vectors
(vec_name='linear')¶ Return the linear inputs, outputs, and residuals vectors.
Parameters:  vec_name : str
Name of the linear righthandside vector. The default is ‘linear’.
Returns:  (inputs, outputs, residuals) : tuple of <Vector> instances
Yields the inputs, outputs, and residuals linear vectors for vec_name.

get_nonlinear_vectors
()¶ Return the inputs, outputs, and residuals vectors.
Returns:  (inputs, outputs, residuals) : tuple of <Vector> instances
Yields the inputs, outputs, and residuals nonlinear vectors.

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:  dict
The objectives defined in the current system.

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

guess_nonlinear
(inputs, outputs, residuals)¶ 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]

initialize
()¶ Perform any onetime initialization run at instantiation.

is_active
()¶ Determine if the system is active on this rank.
Returns:  bool
If running under MPI, returns True if this System has a valid communicator. Always returns True if not running under MPI.

jacobian_context
(jac)¶ Context manager that yields the Jacobian assigned to this system in this system’s context.

linear_solver
¶ Get the linear solver for this system.

list_inputs
(values=True, units=False, hierarchical=True, print_arrays=False, 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.
 units : bool, optional
When True, display/return units. 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.
 out_stream : filelike object
Where to send human readable output. Default is sys.stdout. Set to None to suppress.
Returns:  list
list of input names and other optional information about those inputs

list_outputs
(explicit=True, implicit=True, values=True, residuals=False, residuals_tol=None, units=False, shape=False, bounds=False, scaling=False, hierarchical=True, print_arrays=False, 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.
 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.
 out_stream : filelike
Where to send human readable output. Default is sys.stdout. Set to None to suppress.
Returns:  list
list of output names and other optional information about those outputs

ln_solver
¶ Get the linear solver for this system.

metadata
¶ Get the options for this System.

nl_solver
¶ Get the nonlinear solver for this system.

nonlinear_solver
¶ Get the nonlinear solver for this system.

reconfigure
()¶ Perform reconfiguration.
Returns:  bool
If True, reconfiguration is to be performed.

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 jacvec 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 righthandside vectors.
 mode : str
‘fwd’ or ‘rev’.
 scope_out : set or None
Set of absolute output names in the scope of this matvec product. If None, all are in the scope.
 scope_in : set or None
Set of absolute input names in the scope of this matvec 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 righthandside vectors.
 mode : str
‘fwd’ or ‘rev’.
Returns:  boolean
Failure flag; True if failed to converge, False is successful.
 float
relative error.
 float
absolute error.

run_solve_nonlinear
()¶ Compute outputs.
This calls _solve_nonlinear, but with the model assumed to be in an unscaled state.
Returns:  boolean
Failure flag; True if failed to converge, False is successful.
 float
relative error.
 float
absolute error.

set_check_partial_options
(wrt, method='fd', form=None, step=None, step_calc=None)¶ Set options that will be used for checking partial derivatives.
Parameters:  wrt : str or list of str
The name or names of the variables that derivatives are taken with respect to. This can contain the name of any input or output variable. May also contain a glob pattern.
 method : str
Method for check: “fd” for finite difference, “cs” for complex step.
 form : str
Finite difference form for check, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.
 step : float
Step size for finite difference check. Leave undeclared to keep unchanged from previous or default value.
 step_calc : str
Type of step calculation for check, can be “abs” for absolute (default) or “rel” for relative. Leave undeclared to keep unchanged from previous or default value.

set_initial_values
()¶ Set all input and output variables to their declared initial values.

solve_linear
(d_outputs, d_residuals, mode)¶ Apply inverse jac product. The model is assumed to be in an unscaled state.
 If mode is:
‘fwd’: d_residuals > d_outputs
‘rev’: d_outputs > d_residuals
Note: this is not the linear solution for the implicit component. We use identity so that simple implicit components can function in a preconditioner under linear gaussseidel. To correctly solve this component, you should slot a solver in linear_solver or override this method.
Parameters:  d_outputs : Vector
unscaled, dimensional quantities read via d_outputs[key]
 d_residuals : Vector
unscaled, dimensional quantities read via d_residuals[key]
 mode : str
either ‘fwd’ or ‘rev’
Returns:  None or bool or (bool, float, float)
The bool is the failure flag; and the two floats are absolute and relative error.

solve_nonlinear
(inputs, outputs)¶ Compute outputs given inputs. The model is assumed to be in an unscaled state.
Parameters:  inputs : Vector
unscaled, dimensional input variables read via inputs[key]
 outputs : Vector
unscaled, dimensional output variables read via outputs[key]
Returns:  None or bool or (bool, float, float)
The bool is the failure flag; and the two floats are absolute and relative error.

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.


class
openmdao.test_suite.components.sellar.
SellarImplicitDis2
(units=None, scaling=None)[source]¶ Bases:
openmdao.core.implicitcomponent.ImplicitComponent
Component containing Discipline 2 – implicit version.

__init__
(units=None, scaling=None)[source]¶ Store some bound methods so we can detect runtime overrides.
Parameters:  **kwargs : dict of keyword arguments
Keyword arguments that will be mapped into the Component options.

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, simul_coloring=None, simul_map=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the constraint variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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 argumentref
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, simul_coloring=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the design variable.
 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 argumentref
represents the physical value when the scaled value is 1.

add_input
(name, val=1.0, shape=None, src_indices=None, flat_src_indices=None, units=None, desc='', var_set=0)¶ Add an input variable to the component.
Parameters:  name : str
name of the variable in this component’s namespace.
 val : float or list or tuple or ndarray or Iterable
The initial value of the variable being added in userdefined units. Default is 1.0.
 shape : int or tuple or list or None
Shape of this variable, only required if src_indices not provided and val is not an array. Default is None.
 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. A value of None implies this input depends on all entries of source. Default is None. 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 each entry must be a tuple or list of size equal to the number of dimensions of the source.
 units : str or None
Units in which this input variable will be provided to the component during execution. Default is None, which means it is unitless.
 desc : str
description of the variable
 var_set : hashable object
For advanced users only. ID or color for this variable, relevant for reconfigurability. Default is 0.
Returns:  dict
metadata for added variable

add_objective
(name, ref=None, ref0=None, index=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, simul_coloring=None, simul_map=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the objective variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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_output
(name, val=1.0, shape=None, units=None, res_units=None, desc='', lower=None, upper=None, ref=1.0, ref0=0.0, res_ref=1.0, var_set=0)¶ Add an output variable to the component.
Parameters:  name : str
name of the variable in this component’s namespace.
 val : float or list or tuple or ndarray
The initial value of the variable being added in userdefined units. Default is 1.0.
 shape : int or tuple or list or None
Shape of this variable, only required if val is not an array. Default is None.
 units : str or None
Units in which the output variables will be provided to the component during execution. Default is None, which means it has no units.
 res_units : str or None
Units in which the residuals of this output will be given to the user when requested. Default is None, which means it has no units.
 desc : str
description of the variable.
 lower : float or list or tuple or ndarray or Iterable or None
lower bound(s) in userdefined units. It can be (1) a float, (2) an array_like consistent with the shape arg (if given), or (3) an array_like matching the shape of val, if val is array_like. A value of None means this output has no lower bound. Default is None.
 upper : float or list or tuple or ndarray or or Iterable None
upper bound(s) in userdefined units. It can be (1) a float, (2) an array_like consistent with the shape arg (if given), or (3) an array_like matching the shape of val, if val is array_like. A value of None means this output has no upper bound. Default is None.
 ref : float or ndarray
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 1. Default is 1.
 ref0 : float or ndarray
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 0. Default is 0.
 res_ref : float or ndarray
Scaling parameter. The value in the userdefined res_units of this output’s residual when the scaled value is 1. Default is 1.
 var_set : hashable object
For advanced users only. ID or color for this variable, relevant for reconfigurability. Default is 0.
Returns:  dict
metadata for added variable

add_recorder
(recorder, recurse=False)¶ Add a recorder to the driver.
Parameters:  recorder : <BaseRecorder>
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, simul_coloring=None, simul_map=None, 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 argumentref
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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the response variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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.

apply_linear
(inputs, outputs, d_inputs, d_outputs, d_residuals, mode)¶ Compute jacvector product. The model is assumed to be in an unscaled state.
 If mode is:
‘fwd’: (d_inputs, d_outputs) > d_residuals
‘rev’: d_residuals > (d_inputs, d_outputs)
Parameters:  inputs : Vector
unscaled, dimensional input variables read via inputs[key]
 outputs : Vector
unscaled, dimensional output variables read via outputs[key]
 d_inputs : Vector
see inputs; product must be computed only if var_name in d_inputs
 d_outputs : Vector
see outputs; product must be computed only if var_name in d_outputs
 d_residuals : Vector
see outputs
 mode : str
either ‘fwd’ or ‘rev’

check_config
(logger)¶ Perform optional error checks.
Parameters:  logger : object
The object that manages logging output.

declare_partials
(of, wrt, dependent=True, rows=None, cols=None, val=None, method='exact', step=None, form=None, step_calc=None)¶ Declare information about this component’s subjacobians.
Parameters:  of : str or list of str
The name of the residual(s) that derivatives are being computed for. May also contain a glob pattern.
 wrt : str or list of str
The name of the variables that derivatives are taken with respect to. This can contain the name of any input or output variable. May also contain a glob pattern.
 dependent : bool(True)
If False, specifies no dependence between the output(s) and the input(s). This is only necessary in the case of a sparse global jacobian, because if ‘dependent=False’ is not specified and declare_partials is not called for a given pair, then a dense matrix of zeros will be allocated in the sparse global jacobian for that pair. In the case of a dense global jacobian it doesn’t matter because the space for a dense subjac will always be allocated for every pair.
 rows : ndarray of int or None
Row indices for each nonzero entry. For sparse subjacobians only.
 cols : ndarray of int or None
Column indices for each nonzero entry. For sparse subjacobians only.
 val : float or ndarray of float or scipy.sparse
Value of subjacobian. If rows and cols are not None, this will contain the values found at each (row, col) location in the subjac.
 method : str
The type of approximation that should be used. Valid options include: ‘fd’: Finite Difference, ‘cs’: Complex Step, ‘exact’: use the component defined analytic derivatives. Default is ‘exact’.
 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.

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:  dict
The constraints defined in the current system.

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

get_linear_vectors
(vec_name='linear')¶ Return the linear inputs, outputs, and residuals vectors.
Parameters:  vec_name : str
Name of the linear righthandside vector. The default is ‘linear’.
Returns:  (inputs, outputs, residuals) : tuple of <Vector> instances
Yields the inputs, outputs, and residuals linear vectors for vec_name.

get_nonlinear_vectors
()¶ Return the inputs, outputs, and residuals vectors.
Returns:  (inputs, outputs, residuals) : tuple of <Vector> instances
Yields the inputs, outputs, and residuals nonlinear vectors.

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:  dict
The objectives defined in the current system.

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

guess_nonlinear
(inputs, outputs, residuals)¶ 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]

initialize
()¶ Perform any onetime initialization run at instantiation.

is_active
()¶ Determine if the system is active on this rank.
Returns:  bool
If running under MPI, returns True if this System has a valid communicator. Always returns True if not running under MPI.

jacobian_context
(jac)¶ Context manager that yields the Jacobian assigned to this system in this system’s context.

linear_solver
¶ Get the linear solver for this system.

list_inputs
(values=True, units=False, hierarchical=True, print_arrays=False, 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.
 units : bool, optional
When True, display/return units. 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.
 out_stream : filelike object
Where to send human readable output. Default is sys.stdout. Set to None to suppress.
Returns:  list
list of input names and other optional information about those inputs

list_outputs
(explicit=True, implicit=True, values=True, residuals=False, residuals_tol=None, units=False, shape=False, bounds=False, scaling=False, hierarchical=True, print_arrays=False, 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.
 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.
 out_stream : filelike
Where to send human readable output. Default is sys.stdout. Set to None to suppress.
Returns:  list
list of output names and other optional information about those outputs

ln_solver
¶ Get the linear solver for this system.

metadata
¶ Get the options for this System.

nl_solver
¶ Get the nonlinear solver for this system.

nonlinear_solver
¶ Get the nonlinear solver for this system.

reconfigure
()¶ Perform reconfiguration.
Returns:  bool
If True, reconfiguration is to be performed.

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 jacvec 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 righthandside vectors.
 mode : str
‘fwd’ or ‘rev’.
 scope_out : set or None
Set of absolute output names in the scope of this matvec product. If None, all are in the scope.
 scope_in : set or None
Set of absolute input names in the scope of this matvec 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 righthandside vectors.
 mode : str
‘fwd’ or ‘rev’.
Returns:  boolean
Failure flag; True if failed to converge, False is successful.
 float
relative error.
 float
absolute error.

run_solve_nonlinear
()¶ Compute outputs.
This calls _solve_nonlinear, but with the model assumed to be in an unscaled state.
Returns:  boolean
Failure flag; True if failed to converge, False is successful.
 float
relative error.
 float
absolute error.

set_check_partial_options
(wrt, method='fd', form=None, step=None, step_calc=None)¶ Set options that will be used for checking partial derivatives.
Parameters:  wrt : str or list of str
The name or names of the variables that derivatives are taken with respect to. This can contain the name of any input or output variable. May also contain a glob pattern.
 method : str
Method for check: “fd” for finite difference, “cs” for complex step.
 form : str
Finite difference form for check, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.
 step : float
Step size for finite difference check. Leave undeclared to keep unchanged from previous or default value.
 step_calc : str
Type of step calculation for check, can be “abs” for absolute (default) or “rel” for relative. Leave undeclared to keep unchanged from previous or default value.

set_initial_values
()¶ Set all input and output variables to their declared initial values.

solve_linear
(d_outputs, d_residuals, mode)¶ Apply inverse jac product. The model is assumed to be in an unscaled state.
 If mode is:
‘fwd’: d_residuals > d_outputs
‘rev’: d_outputs > d_residuals
Note: this is not the linear solution for the implicit component. We use identity so that simple implicit components can function in a preconditioner under linear gaussseidel. To correctly solve this component, you should slot a solver in linear_solver or override this method.
Parameters:  d_outputs : Vector
unscaled, dimensional quantities read via d_outputs[key]
 d_residuals : Vector
unscaled, dimensional quantities read via d_residuals[key]
 mode : str
either ‘fwd’ or ‘rev’
Returns:  None or bool or (bool, float, float)
The bool is the failure flag; and the two floats are absolute and relative error.

solve_nonlinear
(inputs, outputs)¶ Compute outputs given inputs. The model is assumed to be in an unscaled state.
Parameters:  inputs : Vector
unscaled, dimensional input variables read via inputs[key]
 outputs : Vector
unscaled, dimensional output variables read via outputs[key]
Returns:  None or bool or (bool, float, float)
The bool is the failure flag; and the two floats are absolute and relative error.

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.


class
openmdao.test_suite.components.sellar.
SellarNoDerivatives
(**kwargs)[source]¶ Bases:
openmdao.core.group.Group
Group containing the Sellar MDA. This version uses the disciplines without derivatives.

__init__
(**kwargs)¶ Set the solvers to nonlinear and linear block Gauss–Seidel by default.
Parameters:  **kwargs : dict
dict of arguments available here and in all descendants of this Group.

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 notyetset 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:  System
The System that was passed in.

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, simul_coloring=None, simul_map=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the constraint variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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 argumentref
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, simul_coloring=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the design variable.
 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 argumentref
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, simul_coloring=None, simul_map=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the objective variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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 driver.
Parameters:  recorder : <BaseRecorder>
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, simul_coloring=None, simul_map=None, 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 argumentref
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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the response variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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 notyetset 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:  <System>
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.

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.

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 subgroups will be included. Otherwise, a graph containing only direct children (both Components and Groups) of this group will be returned.
Returns:  DiGraph
A directed graph containing names of subsystems and their connections.

configure
()[source]¶ 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.

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:  dict
The constraints defined in the current system.

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

get_linear_vectors
(vec_name='linear')¶ Return the linear inputs, outputs, and residuals vectors.
Parameters:  vec_name : str
Name of the linear righthandside vector. The default is ‘linear’.
Returns:  (inputs, outputs, residuals) : tuple of <Vector> instances
Yields the inputs, outputs, and residuals linear vectors for vec_name.

get_nonlinear_vectors
()¶ Return the inputs, outputs, and residuals vectors.
Returns:  (inputs, outputs, residuals) : tuple of <Vector> instances
Yields the inputs, outputs, and residuals nonlinear vectors.

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:  dict
The objectives defined in the current system.

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

is_active
()¶ Determine if the system is active on this rank.
Returns:  bool
If running under MPI, returns True if this System has a valid communicator. Always returns True if not running under MPI.

jacobian_context
(jac)¶ Context manager that yields the Jacobian assigned to this system in this system’s context.

linear_solver
¶ Get the linear solver for this system.

list_inputs
(values=True, units=False, hierarchical=True, print_arrays=False, 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.
 units : bool, optional
When True, display/return units. 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.
 out_stream : filelike object
Where to send human readable output. Default is sys.stdout. Set to None to suppress.
Returns:  list
list of input names and other optional information about those inputs

list_outputs
(explicit=True, implicit=True, values=True, residuals=False, residuals_tol=None, units=False, shape=False, bounds=False, scaling=False, hierarchical=True, print_arrays=False, 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.
 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.
 out_stream : filelike
Where to send human readable output. Default is sys.stdout. Set to None to suppress.
Returns:  list
list of output names and other optional information about those outputs

ln_solver
¶ Get the linear solver for this system.

metadata
¶ Get the options for this System.

nl_solver
¶ Get the nonlinear solver for this system.

nonlinear_solver
¶ Get the nonlinear solver for this system.

reconfigure
()¶ Perform reconfiguration.
Returns:  bool
If True, reconfiguration is to be performed.

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 jacvec 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 righthandside vectors.
 mode : str
‘fwd’ or ‘rev’.
 scope_out : set or None
Set of absolute output names in the scope of this matvec product. If None, all are in the scope.
 scope_in : set or None
Set of absolute input names in the scope of this matvec 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 righthandside vectors.
 mode : str
‘fwd’ or ‘rev’.
Returns:  boolean
Failure flag; True if failed to converge, False is successful.
 float
relative error.
 float
absolute error.

run_solve_nonlinear
()¶ Compute outputs.
This calls _solve_nonlinear, but with the model assumed to be in an unscaled state.
Returns:  boolean
Failure flag; True if failed to converge, False is successful.
 float
relative error.
 float
absolute error.

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.

setup
()[source]¶ Build this group.
This method should be overidden by your Group’s method. The reason for using this method to add subsystem is to save memory and setup time when using your Group while running under MPI. This avoids the creation of systems that will not be used in the current process.
You may call ‘add_subsystem’ to add systems to this group. You may also issue connections, and set the linear and nonlinear solvers for this group level. You cannot safely change anything on children systems; use the ‘configure’ method instead.
 Available attributes:
 name pathname comm options

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.


class
openmdao.test_suite.components.sellar.
SellarProblem
(model_class=<class 'openmdao.test_suite.components.sellar.SellarDerivatives'>, **kwargs)[source]¶ Bases:
openmdao.core.problem.Problem
The Sellar problem with configurable model class.

__getitem__
(name)¶ Get an output/input variable.
Parameters:  name : str
Promoted or relative variable name in the root system’s namespace.
Returns:  float or ndarray
the requested output/input variable.

__init__
(model_class=<class 'openmdao.test_suite.components.sellar.SellarDerivatives'>, **kwargs)[source]¶ Initialize attributes.
Parameters:  model : <System> or None
Pointer to the toplevel <System> object (root node in the tree).
 comm : MPI.Comm or <FakeComm> or None
The global communicator.
 use_ref_vector : bool
If True, allocate vectors to store ref. values.
 root : <System> or None
Deprecated kwarg for model.

__setitem__
(name, value)¶ Set an output/input variable.
Parameters:  name : str
Promoted or relative variable name in the root system’s namespace.
 value : float or ndarray or list
value to set this variable to.

check_partials
(out_stream=<object object>, includes=None, excludes=None, compact_print=False, abs_err_tol=1e06, rel_err_tol=1e06, method='fd', step=1e06, form='forward', step_calc='abs', force_dense=True, show_only_incorrect=False)¶ Check partial derivatives comprehensively for all components in your model.
Parameters:  out_stream : filelike object
Where to send human readable output. By default it goes to stdout. Set to None to suppress.
 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.
 compact_print : bool
Set to True to just print the essentials, one line per unknownparam pair.
 abs_err_tol : float
Threshold value for absolute error. Errors about this value will have a ‘*’ displayed next to them in output, making them easy to search for. Default is 1.0E6.
 rel_err_tol : float
Threshold value for relative error. Errors about this value will have a ‘*’ displayed next to them in output, making them easy to search for. Note at times there may be a significant relative error due to a minor absolute error. Default is 1.0E6.
 method : str
Method, ‘fd’ for finite difference or ‘cs’ for complex step. Default is ‘fd’.
 step : float
Step size for approximation. Default is the default value of step for the ‘fd’ method.
 form : string
Form for finite difference, can be ‘forward’, ‘backward’, or ‘central’. Default is the default value of step for the ‘fd’ method.
 step_calc : string
Step type for finite difference, can be ‘abs’ for absolute’, or ‘rel’ for relative. Default is the default value of step for the ‘fd’ method.
 force_dense : bool
If True, analytic derivatives will be coerced into arrays. Default is True.
 show_only_incorrect : bool, optional
Set to True if output should print only the subjacs found to be incorrect.
Returns:  dict of dicts of dicts
 First key:
is the component name;
 Second key:
is the (output, input) tuple of strings;
 Third key:
is one of [‘rel error’, ‘abs error’, ‘magnitude’, ‘J_fd’, ‘J_fwd’, ‘J_rev’];
 For ‘rel error’, ‘abs error’, ‘magnitude’ the value is: A tuple containing norms for
forward  fd, adjoint  fd, forward  adjoint.
 For ‘J_fd’, ‘J_fwd’, ‘J_rev’ the value is: A numpy array representing the computed
Jacobian for the three different methods of computation.

check_totals
(of=None, wrt=None, out_stream=<object object>, compact_print=False, driver_scaling=False, abs_err_tol=1e06, rel_err_tol=1e06, method='fd', step=1e06, form='forward', step_calc='abs')¶ Check total derivatives for the model vs. finite difference.
Parameters:  of : list of variable name strings or None
Variables whose derivatives will be computed. Default is None, which uses the driver’s objectives and constraints.
 wrt : list of variable name strings or None
Variables with respect to which the derivatives will be computed. Default is None, which uses the driver’s desvars.
 out_stream : filelike object
Where to send human readable output. By default it goes to stdout. Set to None to suppress.
 compact_print : bool
Set to True to just print the essentials, one line per unknownparam pair.
 driver_scaling : bool
Set to True to scale derivative values by the quantities specified when the desvars and responses were added. Default if False, which is unscaled.
 abs_err_tol : float
Threshold value for absolute error. Errors about this value will have a ‘*’ displayed next to them in output, making them easy to search for. Default is 1.0E6.
 rel_err_tol : float
Threshold value for relative error. Errors about this value will have a ‘*’ displayed next to them in output, making them easy to search for. Note at times there may be a significant relative error due to a minor absolute error. Default is 1.0E6.
 method : str
Method, ‘fd’ for finite difference or ‘cs’ for complex step. Default is ‘fd’
 step : float
Step size for approximation. Default is 1e6.
 form : string
Form for finite difference, can be ‘forward’, ‘backward’, or ‘central’. Default ‘forward’.
 step_calc : string
Step type for finite difference, can be ‘abs’ for absolute’, or ‘rel’ for relative. Default is ‘abs’.
Returns:  Dict of Dicts of Tuples of Floats
 First key:
is the (output, input) tuple of strings;
 Second key:
is one of [‘rel error’, ‘abs error’, ‘magnitude’, ‘fdstep’];
 For ‘rel error’, ‘abs error’, ‘magnitude’ the value is: A tuple containing norms for
forward  fd, adjoint  fd, forward  adjoint.

cleanup
()¶ Clean up resources prior to exit.

compute_totals
(of=None, wrt=None, return_format='flat_dict', debug_print=False, driver_scaling=False)¶ Compute derivatives of desired quantities with respect to desired inputs.
Parameters:  of : list of variable name strings or None
Variables whose derivatives will be computed. Default is None, which uses the driver’s objectives and constraints.
 wrt : list of variable name strings or None
Variables with respect to which the derivatives will be computed. Default is None, which uses the driver’s desvars.
 return_format : string
Format to return the derivatives. Can be either ‘dict’ or ‘flat_dict’. Default is a ‘flat_dict’, which returns them in a dictionary whose keys are tuples of form (of, wrt).
 debug_print : bool
Set to True to print out some debug information during linear solve.
 driver_scaling : bool
Set to True to scale derivative values by the quantities specified when the desvars and responses were added. Default if False, which is unscaled.
Returns:  derivs : object
Derivatives in form requested by ‘return_format’.

final_setup
()¶ Perform final setup phase on problem in preparation for run.
This is the second phase of setup, and is done automatically at the start of run_driver and run_model. At the beginning of final_setup, we have a model hierarchy with defined variables, solvers, case_recorders, and derivative settings. During this phase, the vectors are created and populated, the drivers and solvers are initialized, and the recorders are started, and the rest of the framework is prepared for execution.

get_val
(name, units=None, indices=None)¶ Get an output/input variable.
Function is used if you want to specify display units.
Parameters:  name : str
Promoted or relative variable name in the root system’s namespace.
 units : str, optional
Units to convert to before upon return.
 indices : int or list of ints or tuple of ints or int ndarray or Iterable or None, optional
Indices or slice to return.
Returns:  float or ndarray
The requested output/input variable.

list_problem_vars
(show_promoted_name=True, print_arrays=False, desvar_opts=[], cons_opts=[], objs_opts=[])¶ Print all design variables and responses (objectives and constraints).
Parameters:  show_promoted_name : bool
If True, then show the promoted names of the variables.
 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.
 desvar_opts : list of str
List of optional columns to be displayed in the desvars table. Allowed values are: [‘lower’, ‘upper’, ‘ref’, ‘ref0’, ‘indices’, ‘adder’, ‘scaler’, ‘parallel_deriv_color’, ‘vectorize_derivs’, ‘simul_coloring’, ‘cache_linear_solution’]
 cons_opts : list of str
List of optional columns to be displayed in the cons table. Allowed values are: [‘lower’, ‘upper’, ‘equals’, ‘ref’, ‘ref0’, ‘indices’, ‘index’, ‘adder’, ‘scaler’, ‘linear’, ‘parallel_deriv_color’, ‘vectorize_derivs’, ‘simul_coloring’, ‘simul_map’, ‘cache_linear_solution’]
 objs_opts : list of str
List of optional columns to be displayed in the objs table. Allowed values are: [‘ref’, ‘ref0’, ‘indices’, ‘adder’, ‘scaler’, ‘parallel_deriv_color’, ‘vectorize_derivs’, ‘simul_deriv_color’, ‘simul_map’, ‘cache_linear_solution’]

load_case
(case)¶ Pull all input and output variables from a case into the model.
Parameters:  case : Case object
A Case from a CaseRecorder file.

root
¶ Provide ‘root’ property for backwards compatibility.
Returns:  <Group>
reference to the ‘model’ property.

run
()¶ Backward compatible call for run_driver.
Returns:  boolean
Failure flag; True if failed to converge, False is successful.

run_driver
(case_prefix=None, reset_iter_counts=True)¶ Run the driver on the model.
Parameters:  case_prefix : str or None
Prefix to prepend to coordinates when recording.
 reset_iter_counts : bool
If True and model has been run previously, reset all iteration counters.
Returns:  boolean
Failure flag; True if failed to converge, False is successful.

run_model
(case_prefix=None, reset_iter_counts=True)¶ Run the model by calling the root system’s solve_nonlinear.
Parameters:  case_prefix : str or None
Prefix to prepend to coordinates when recording.
 reset_iter_counts : bool
If True and model has been run previously, reset all iteration counters.
Returns:  boolean
Failure flag; True if failed to converge, False is successful.
 float
relative error.
 float
absolute error.

run_once
()¶ Backward compatible call for run_model.
Returns:  boolean
Failure flag; True if failed to converge, False is successful.
 float
relative error.
 float
absolute error.

set_solver_print
(level=2, depth=1e+99, type_='all')¶ Control printing for solvers and subsolvers in the model.
Parameters:  level : int
iprint level. Set to 2 to print residuals each iteration; set to 1 to print just the iteration totals; set to 0 to disable all printing except for failures, and set to 1 to disable all printing including failures.
 depth : int
How deep to recurse. For example, you can set this to 0 if you only want to print the top level linear and nonlinear solver messages. Default prints everything.
 type_ : str
Type of solver to set: ‘LN’ for linear, ‘NL’ for nonlinear, or ‘all’ for all.

set_val
(name, value, units=None, indices=None)¶ Set an output/input variable.
Function is used if you want to set a value using a different unit.
Parameters:  name : str
Promoted or relative variable name in the root system’s namespace.
 value : float or ndarray or list
Value to set this variable to.
 units : str, optional
Units that value is defined in.
 indices : int or list of ints or tuple of ints or int ndarray or Iterable or None, optional
Indices or slice to set to specified value.

setup
(vector_class=None, check=False, logger=None, mode='rev', force_alloc_complex=False, distributed_vector_class=<class 'openmdao.vectors.petsc_vector.PETScVector'>, local_vector_class=<class 'openmdao.vectors.default_vector.DefaultVector'>)¶ Set up the model hierarchy.
When setup is called, the model hierarchy is assembled, the processors are allocated (for MPI), and variables and connections are all assigned. This method traverses down the model hierarchy to call setup on each subsystem, and then traverses up te model hierarchy to call configure on each subsystem.
Parameters:  vector_class : type
Reference to an actual <Vector> class; not an instance. This is deprecated. Use distributed_vector_class instead.
 check : boolean
whether to run config check after setup is complete.
 logger : object
Object for logging config checks if check is True.
 mode : string
Derivatives calculation mode, ‘fwd’ for forward, and ‘rev’ for reverse (adjoint). Default is ‘rev’.
 force_alloc_complex : bool
Force allocation of imaginary part in nonlinear vectors. OpenMDAO can generally detect when you need to do this, but in some cases (e.g., complex step is used after a reconfiguration) you may need to set this to True.
 distributed_vector_class : type
Reference to the <Vector> class or factory function used to instantiate vectors and associated transfers involved in interprocess communication.
 local_vector_class : type
Reference to the <Vector> class or factory function used to instantiate vectors and associated transfers involved in intraprocess communication.
Returns:  self : <Problem>
this enables the user to instantiate and setup in one line.


class
openmdao.test_suite.components.sellar.
SellarStateConnection
(**kwargs)[source]¶ Bases:
openmdao.core.group.Group
Group containing the Sellar MDA. This version uses the disciplines with derivatives.

__init__
(**kwargs)¶ Set the solvers to nonlinear and linear block Gauss–Seidel by default.
Parameters:  **kwargs : dict
dict of arguments available here and in all descendants of this Group.

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 notyetset 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:  System
The System that was passed in.

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, simul_coloring=None, simul_map=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the constraint variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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 argumentref
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, simul_coloring=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the design variable.
 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 argumentref
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, simul_coloring=None, simul_map=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the objective variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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 driver.
Parameters:  recorder : <BaseRecorder>
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, simul_coloring=None, simul_map=None, 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 argumentref
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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the response variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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 notyetset 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:  <System>
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.

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.

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 subgroups will be included. Otherwise, a graph containing only direct children (both Components and Groups) of this group will be returned.
Returns:  DiGraph
A directed graph containing names of subsystems and their connections.

configure
()[source]¶ 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.

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:  dict
The constraints defined in the current system.

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

get_linear_vectors
(vec_name='linear')¶ Return the linear inputs, outputs, and residuals vectors.
Parameters:  vec_name : str
Name of the linear righthandside vector. The default is ‘linear’.
Returns:  (inputs, outputs, residuals) : tuple of <Vector> instances
Yields the inputs, outputs, and residuals linear vectors for vec_name.

get_nonlinear_vectors
()¶ Return the inputs, outputs, and residuals vectors.
Returns:  (inputs, outputs, residuals) : tuple of <Vector> instances
Yields the inputs, outputs, and residuals nonlinear vectors.

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:  dict
The objectives defined in the current system.

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

is_active
()¶ Determine if the system is active on this rank.
Returns:  bool
If running under MPI, returns True if this System has a valid communicator. Always returns True if not running under MPI.

jacobian_context
(jac)¶ Context manager that yields the Jacobian assigned to this system in this system’s context.

linear_solver
¶ Get the linear solver for this system.

list_inputs
(values=True, units=False, hierarchical=True, print_arrays=False, 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.
 units : bool, optional
When True, display/return units. 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.
 out_stream : filelike object
Where to send human readable output. Default is sys.stdout. Set to None to suppress.
Returns:  list
list of input names and other optional information about those inputs

list_outputs
(explicit=True, implicit=True, values=True, residuals=False, residuals_tol=None, units=False, shape=False, bounds=False, scaling=False, hierarchical=True, print_arrays=False, 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.
 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.
 out_stream : filelike
Where to send human readable output. Default is sys.stdout. Set to None to suppress.
Returns:  list
list of output names and other optional information about those outputs

ln_solver
¶ Get the linear solver for this system.

metadata
¶ Get the options for this System.

nl_solver
¶ Get the nonlinear solver for this system.

nonlinear_solver
¶ Get the nonlinear solver for this system.

reconfigure
()¶ Perform reconfiguration.
Returns:  bool
If True, reconfiguration is to be performed.

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 jacvec 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 righthandside vectors.
 mode : str
‘fwd’ or ‘rev’.
 scope_out : set or None
Set of absolute output names in the scope of this matvec product. If None, all are in the scope.
 scope_in : set or None
Set of absolute input names in the scope of this matvec 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 righthandside vectors.
 mode : str
‘fwd’ or ‘rev’.
Returns:  boolean
Failure flag; True if failed to converge, False is successful.
 float
relative error.
 float
absolute error.

run_solve_nonlinear
()¶ Compute outputs.
This calls _solve_nonlinear, but with the model assumed to be in an unscaled state.
Returns:  boolean
Failure flag; True if failed to converge, False is successful.
 float
relative error.
 float
absolute error.

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.

setup
()[source]¶ Build this group.
This method should be overidden by your Group’s method. The reason for using this method to add subsystem is to save memory and setup time when using your Group while running under MPI. This avoids the creation of systems that will not be used in the current process.
You may call ‘add_subsystem’ to add systems to this group. You may also issue connections, and set the linear and nonlinear solvers for this group level. You cannot safely change anything on children systems; use the ‘configure’ method instead.
 Available attributes:
 name pathname comm options

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.


class
openmdao.test_suite.components.sellar.
StateConnection
(**kwargs)[source]¶ Bases:
openmdao.core.implicitcomponent.ImplicitComponent
Define connection with an explicit equation.

__init__
(**kwargs)¶ Store some bound methods so we can detect runtime overrides.
Parameters:  **kwargs : dict of keyword arguments
Keyword arguments that will be mapped into the Component options.

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, simul_coloring=None, simul_map=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the constraint variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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 argumentref
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, simul_coloring=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the design variable.
 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 argumentref
represents the physical value when the scaled value is 1.

add_input
(name, val=1.0, shape=None, src_indices=None, flat_src_indices=None, units=None, desc='', var_set=0)¶ Add an input variable to the component.
Parameters:  name : str
name of the variable in this component’s namespace.
 val : float or list or tuple or ndarray or Iterable
The initial value of the variable being added in userdefined units. Default is 1.0.
 shape : int or tuple or list or None
Shape of this variable, only required if src_indices not provided and val is not an array. Default is None.
 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. A value of None implies this input depends on all entries of source. Default is None. 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 each entry must be a tuple or list of size equal to the number of dimensions of the source.
 units : str or None
Units in which this input variable will be provided to the component during execution. Default is None, which means it is unitless.
 desc : str
description of the variable
 var_set : hashable object
For advanced users only. ID or color for this variable, relevant for reconfigurability. Default is 0.
Returns:  dict
metadata for added variable

add_objective
(name, ref=None, ref0=None, index=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, simul_coloring=None, simul_map=None, 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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the objective variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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_output
(name, val=1.0, shape=None, units=None, res_units=None, desc='', lower=None, upper=None, ref=1.0, ref0=0.0, res_ref=1.0, var_set=0)¶ Add an output variable to the component.
Parameters:  name : str
name of the variable in this component’s namespace.
 val : float or list or tuple or ndarray
The initial value of the variable being added in userdefined units. Default is 1.0.
 shape : int or tuple or list or None
Shape of this variable, only required if val is not an array. Default is None.
 units : str or None
Units in which the output variables will be provided to the component during execution. Default is None, which means it has no units.
 res_units : str or None
Units in which the residuals of this output will be given to the user when requested. Default is None, which means it has no units.
 desc : str
description of the variable.
 lower : float or list or tuple or ndarray or Iterable or None
lower bound(s) in userdefined units. It can be (1) a float, (2) an array_like consistent with the shape arg (if given), or (3) an array_like matching the shape of val, if val is array_like. A value of None means this output has no lower bound. Default is None.
 upper : float or list or tuple or ndarray or or Iterable None
upper bound(s) in userdefined units. It can be (1) a float, (2) an array_like consistent with the shape arg (if given), or (3) an array_like matching the shape of val, if val is array_like. A value of None means this output has no upper bound. Default is None.
 ref : float or ndarray
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 1. Default is 1.
 ref0 : float or ndarray
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 0. Default is 0.
 res_ref : float or ndarray
Scaling parameter. The value in the userdefined res_units of this output’s residual when the scaled value is 1. Default is 1.
 var_set : hashable object
For advanced users only. ID or color for this variable, relevant for reconfigurability. Default is 0.
Returns:  dict
metadata for added variable

add_recorder
(recorder, recurse=False)¶ Add a recorder to the driver.
Parameters:  recorder : <BaseRecorder>
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, simul_coloring=None, simul_map=None, 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 argumentref
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. Adder is first in precedence.
 scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
 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.
 simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the response variable.
 simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
 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.

apply_linear
(inputs, outputs, d_inputs, d_outputs, d_residuals, mode)¶ Compute jacvector product. The model is assumed to be in an unscaled state.
 If mode is:
‘fwd’: (d_inputs, d_outputs) > d_residuals
‘rev’: d_residuals > (d_inputs, d_outputs)
Parameters:  inputs : Vector
unscaled, dimensional input variables read via inputs[key]
 outputs : Vector
unscaled, dimensional output variables read via outputs[key]
 d_inputs : Vector
see inputs; product must be computed only if var_name in d_inputs
 d_outputs : Vector
see outputs; product must be computed only if var_name in d_outputs
 d_residuals : Vector
see outputs
 mode : str
either ‘fwd’ or ‘rev’

check_config
(logger)¶ Perform optional error checks.
Parameters:  logger : object
The object that manages logging output.

declare_partials
(of, wrt, dependent=True, rows=None, cols=None, val=None, method='exact', step=None, form=None, step_calc=None)¶ Declare information about this component’s subjacobians.
Parameters:  of : str or list of str
The name of the residual(s) that derivatives are being computed for. May also contain a glob pattern.
 wrt : str or list of str
The name of the variables that derivatives are taken with respect to. This can contain the name of any input or output variable. May also contain a glob pattern.
 dependent : bool(True)
If False, specifies no dependence between the output(s) and the input(s). This is only necessary in the case of a sparse global jacobian, because if ‘dependent=False’ is not specified and declare_partials is not called for a given pair, then a dense matrix of zeros will be allocated in the sparse global jacobian for that pair. In the case of a dense global jacobian it doesn’t matter because the space for a dense subjac will always be allocated for every pair.
 rows : ndarray of int or None
Row indices for each nonzero entry. For sparse subjacobians only.
 cols : ndarray of int or None
Column indices for each nonzero entry. For sparse subjacobians only.
 val : float or ndarray of float or scipy.sparse
Value of subjacobian. If rows and cols are not None, this will contain the values found at each (row, col) location in the subjac.
 method : str
The type of approximation that should be used. Valid options include: ‘fd’: Finite Difference, ‘cs’: Complex Step, ‘exact’: use the component defined analytic derivatives. Default is ‘exact’.
 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.

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:  dict
The constraints defined in the current system.

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

get_linear_vectors
(vec_name='linear')¶ Return the linear inputs, outputs, and residuals vectors.
Parameters:  vec_name : str
Name of the linear righthandside vector. The default is ‘linear’.
Returns:  (inputs, outputs, residuals) : tuple of <Vector> instances
Yields the inputs, outputs, and residuals linear vectors for vec_name.

get_nonlinear_vectors
()¶ Return the inputs, outputs, and residuals vectors.
Returns:  (inputs, outputs, residuals) : tuple of <Vector> instances
Yields the inputs, outputs, and residuals nonlinear vectors.

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:  dict
The objectives defined in the current system.

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

guess_nonlinear
(inputs, outputs, residuals)¶ 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]

initialize
()¶ Perform any onetime initialization run at instantiation.

is_active
()¶ Determine if the system is active on this rank.
Returns:  bool
If running under MPI, returns True if this System has a valid communicator. Always returns True if not running under MPI.

jacobian_context
(jac)¶ Context manager that yields the Jacobian assigned to this system in this system’s context.

linear_solver
¶ Get the linear solver for this system.

list_inputs
(values=True, units=False, hierarchical=True, print_arrays=False, 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.
 units : bool, optional
When True, display/return units. 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.
 out_stream : filelike object
Where to send human readable output. Default is sys.stdout. Set to None to suppress.
Returns:  list
list of input names and other optional information about those inputs

list_outputs
(explicit=True, implicit=True, values=True, residuals=False, residuals_tol=None, units=False, shape=False, bounds=False, scaling=False, hierarchical=True, print_arrays=False, 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.
 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.
 out_stream : filelike
Where to send human readable output. Default is sys.stdout. Set to None to suppress.
Returns:  list
list of output names and other optional information about those outputs

ln_solver
¶ Get the linear solver for this system.

metadata
¶ Get the options for this System.

nl_solver
¶ Get the nonlinear solver for this system.

nonlinear_solver
¶ Get the nonlinear solver for this system.

reconfigure
()¶ Perform reconfiguration.
Returns:  bool
If True, reconfiguration is to be performed.

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 jacvec 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 righthandside vectors.
 mode : str
‘fwd’ or ‘rev’.
 scope_out : set or None
Set of absolute output names in the scope of this matvec product. If None, all are in the scope.
 scope_in : set or None
Set of absolute input names in the scope of this matvec 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 righthandside vectors.
 mode : str
‘fwd’ or ‘rev’.
Returns:  boolean
Failure flag; True if failed to converge, False is successful.
 float
relative error.
 float
absolute error.

run_solve_nonlinear
()¶ Compute outputs.
This calls _solve_nonlinear, but with the model assumed to be in an unscaled state.
Returns:  boolean
Failure flag; True if failed to converge, False is successful.
 float
relative error.
 float
absolute error.

set_check_partial_options
(wrt, method='fd', form=None, step=None, step_calc=None)¶ Set options that will be used for checking partial derivatives.
Parameters:  wrt : str or list of str
The name or names of the variables that derivatives are taken with respect to. This can contain the name of any input or output variable. May also contain a glob pattern.
 method : str
Method for check: “fd” for finite difference, “cs” for complex step.
 form : str
Finite difference form for check, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.
 step : float
Step size for finite difference check. Leave undeclared to keep unchanged from previous or default value.
 step_calc : str
Type of step calculation for check, can be “abs” for absolute (default) or “rel” for relative. Leave undeclared to keep unchanged from previous or default value.

set_initial_values
()¶ Set all input and output variables to their declared initial values.

solve_linear
(d_outputs, d_residuals, mode)¶ Apply inverse jac product. The model is assumed to be in an unscaled state.
 If mode is:
‘fwd’: d_residuals > d_outputs
‘rev’: d_outputs > d_residuals
Note: this is not the linear solution for the implicit component. We use identity so that simple implicit components can function in a preconditioner under linear gaussseidel. To correctly solve this component, you should slot a solver in linear_solver or override this method.
Parameters:  d_outputs : Vector
unscaled, dimensional quantities read via d_outputs[key]
 d_residuals : Vector
unscaled, dimensional quantities read via d_residuals[key]
 mode : str
either ‘fwd’ or ‘rev’
Returns:  None or bool or (bool, float, float)
The bool is the failure flag; and the two floats are absolute and relative error.

solve_nonlinear
(inputs, outputs)¶ Compute outputs given inputs. The model is assumed to be in an unscaled state.
Parameters:  inputs : Vector
unscaled, dimensional input variables read via inputs[key]
 outputs : Vector
unscaled, dimensional output variables read via outputs[key]
Returns:  None or bool or (bool, float, float)
The bool is the failure flag; and the two floats are absolute and relative error.

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.
