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

add
(self, name, subsys, promotes=None)¶ Add a subsystem (deprecated version of <Group.add_subsystem>).
 Parameters
 namestr
Name of the subsystem being added
 subsysSystem
An instantiated, but notyetset up system object.
 promotesiter 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
(self, name, lower=None, upper=None, equals=None, ref=None, ref0=None, adder=None, scaler=None, indices=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a constraint variable to this system.
 Parameters
 namestring
Name of the response variable in the system.
 lowerfloat or ndarray, optional
Lower boundary for the variable
 upperfloat or ndarray, optional
Upper boundary for the variable
 equalsfloat or ndarray, optional
Equality constraint value for the variable
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 indicessequence 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.
 linearbool
Set to True if constraint is linear. Default is False.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, name, lower=None, upper=None, ref=None, ref0=None, indices=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a design variable to this system.
 Parameters
 namestring
Name of the design variable in the system.
 lowerfloat or ndarray, optional
Lower boundary for the param
 upperupper or ndarray, optional
Upper boundary for the param
 reffloat or ndarray, optional
Value of design var that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of design var that scales to 0.0 in the driver.
 indicesiter 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.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, name, ref=None, ref0=None, index=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a response variable to this system.
 Parameters
 namestring
Name of the response variable in the system.
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 indexint, 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.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, recorder, recurse=False)¶ Add a recorder to the system.
 Parameters
 recorder<CaseRecorder>
A recorder instance.
 recurseboolean
Flag indicating if the recorder should be added to all the subsystems.

add_response
(self, name, type_, lower=None, upper=None, equals=None, ref=None, ref0=None, indices=None, index=None, adder=None, scaler=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a response variable to this system.
The response can be scaled using ref and ref0. The argument
ref0
represents the physical value when the scaled value is 0. The argumentref
represents the physical value when the scaled value is 1. Parameters
 namestring
Name of the response variable in the system.
 type_string
The type of response. Supported values are ‘con’ and ‘obj’
 lowerfloat or ndarray, optional
Lower boundary for the variable
 upperupper or ndarray, optional
Upper boundary for the variable
 equalsequals or ndarray, optional
Equality constraint value for the variable
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0upper or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 indicessequence of int, optional
If variable is an array, these indicate which entries are of interest for this particular response.
 indexint, optional
If variable is an array, this indicates which entry is of interest for this particular response.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 linearbool
Set to True if constraint is linear. Default is False.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, name, subsys, promotes=None, promotes_inputs=None, promotes_outputs=None, min_procs=1, max_procs=None, proc_weight=1.0)¶ Add a subsystem.
 Parameters
 namestr
Name of the subsystem being added
 subsys<System>
An instantiated, but notyetset up system object.
 promotesiter 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_inputsiter 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_outputsiter 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_procsint
Minimum number of MPI processes usable by the subsystem. Defaults to 1.
 max_procsint or None
Maximum number of MPI processes usable by the subsystem. A value of None (the default) indicates there is no maximum limit.
 proc_weightfloat
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
(self, method='fd', step=None, form=None, step_calc=None)¶ Approximate derivatives for a Group using the specified approximation method.
 Parameters
 methodstr
The type of approximation that should be used. Valid options include: ‘fd’: Finite Difference, ‘cs’: Complex Step
 stepfloat
Step size for approximation. Defaults to None, in which case, the approximation method provides its default value.
 formstring
Form for finite difference, can be ‘forward’, ‘backward’, or ‘central’. Defaults to None, in which case, the approximation method provides its default value.
 step_calcstring
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
(self, logger)¶ Perform optional error checks.
 Parameters
 loggerobject
The object that manages logging output.

cleanup
(self)¶ Clean up resources prior to exit.

compute_sys_graph
(self, 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_onlybool (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
(self)¶ 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
(self, src_name, tgt_name, src_indices=None, flat_src_indices=None)¶ Connect source src_name to target tgt_name in this namespace.
 Parameters
 src_namestr
name of the source variable to connect
 tgt_namestr or [str, … ] or (str, …)
name of the target variable(s) to connect
 src_indicesint 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_indicesbool
If True, each entry of src_indices is assumed to be an index into the flattened source. Otherwise it must be a tuple or list of size equal to the number of dimensions of the source.

declare_coloring
(self, wrt=('*', ), method='fd', form=None, step=None, per_instance=False, num_full_jacs=3, tol=1e25, orders=None, perturb_size=1e09, show_summary=True, show_sparsity=False)¶ Set options for deriv coloring of a set of wrt vars matching the given pattern(s).
 Parameters
 wrtstr or list of str
The name or names of the variables that derivatives are taken with respect to. This can contain input names, output names, or glob patterns.
 methodstr
Method used to compute derivative: “fd” for finite difference, “cs” for complex step.
 formstr
Finite difference form, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.
 stepfloat
Step size for finite difference. Leave undeclared to keep unchanged from previous or default value.
 per_instancebool
If True, a separate coloring will be generated for each instance of a given class. Otherwise, only one coloring for a given class will be generated and all instances of that class will use it.
 num_full_jacsint
Number of times to repeat partial jacobian computation when computing sparsity.
 tolfloat
Tolerance used to determine if an array entry is nonzero during sparsity determination.
 ordersint
Number of orders above and below the tolerance to check during the tolerance sweep.
 perturb_sizefloat
Size of input/output perturbation during generation of sparsity.
 show_summarybool
If True, display summary information after generating coloring.
 show_sparsitybool
If True, display sparsity with coloring info after generating coloring.

get_approx_coloring_fname
(self)¶ Return the full pathname to a coloring file.
 Parameters
 systemSystem
The System having its coloring saved or loaded.
 Returns
 str
Full pathname of the coloring file.

get_constraints
(self, 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
 recursebool, 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
(self, 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
 recursebool
If True, recurse through the subsystems and return the path of all design vars relative to the this system.
 get_sizesbool, optional
If True, compute the size of each design variable.
 Returns
 dict
The design variables defined in the current system and, if recurse=True, its subsystems.

get_linear_vectors
(self, vec_name='linear')¶ Return the linear inputs, outputs, and residuals vectors.
 Parameters
 vec_namestr
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
(self)¶ 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
(self, recurse=True)¶ Get the Objective settings from this system.
Retrieve all objectives settings from the system as a dict, keyed by variable name.
 Parameters
 recursebool, 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
(self, 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
 recursebool, optional
If True, recurse through the subsystems and return the path of all responses relative to the this system.
 get_sizesbool, 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
(self, inputs, outputs, residuals, discrete_inputs=None, discrete_outputs=None)¶ Provide initial guess for states.
Override this method to set the initial guess for states.
 Parameters
 inputsVector
unscaled, dimensional input variables read via inputs[key]
 outputsVector
unscaled, dimensional output variables read via outputs[key]
 residualsVector
unscaled, dimensional residuals written to via residuals[key]
 discrete_inputsdict or None
If not None, dict containing discrete input values.
 discrete_outputsdict or None
If not None, dict containing discrete output values.

is_active
(self)¶ 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.

property
linear_solver
¶ Get the linear solver for this system.

list_inputs
(self, values=True, prom_name=False, units=False, shape=False, hierarchical=True, print_arrays=False, tags=None, out_stream=<object object at 0x7f1bddbe81f0>)¶ 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
 valuesbool, optional
When True, display/return input values. Default is True.
 prom_namebool, optional
When True, display/return the promoted name of the variable. Default is False.
 unitsbool, optional
When True, display/return units. Default is False.
 shapebool, optional
When True, display/return the shape of the value. Default is False.
 hierarchicalbool, optional
When True, human readable output shows variables in hierarchical format.
 print_arraysbool, 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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed. Only inputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.
 out_streamfilelike 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
(self, explicit=True, implicit=True, values=True, prom_name=False, residuals=False, residuals_tol=None, units=False, shape=False, bounds=False, scaling=False, hierarchical=True, print_arrays=False, tags=None, out_stream=<object object at 0x7f1bddbe81f0>)¶ 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
 explicitbool, optional
include outputs from explicit components. Default is True.
 implicitbool, optional
include outputs from implicit components. Default is True.
 valuesbool, optional
When True, display/return output values. Default is True.
 prom_namebool, optional
When True, display/return the promoted name of the variable. Default is False.
 residualsbool, optional
When True, display/return residual values. Default is False.
 residuals_tolfloat, 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.
 unitsbool, optional
When True, display/return units. Default is False.
 shapebool, optional
When True, display/return the shape of the value. Default is False.
 boundsbool, optional
When True, display/return bounds (lower and upper). Default is False.
 scalingbool, optional
When True, display/return scaling (ref, ref0, and res_ref). Default is False.
 hierarchicalbool, optional
When True, human readable output shows variables in hierarchical format.
 print_arraysbool, 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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed. Only outputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.
 out_streamfilelike
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

property
ln_solver
¶ Get the linear solver for this system.

property
metadata
¶ Get the options for this System.

property
msginfo
¶ Our instance pathname, if available, or our class name. For use in error messages.
 Returns
 str
Either our instance pathname or class name.

property
nl_solver
¶ Get the nonlinear solver for this system.

property
nonlinear_solver
¶ Get the nonlinear solver for this system.

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

record_iteration
(self)¶ Record an iteration of the current System.

resetup
(self, setup_mode='full')¶ Public wrapper for _setup that reconfigures after an initial setup has been performed.
 Parameters
 setup_modestr
Must be one of ‘full’, ‘reconf’, or ‘update’.

run_apply_linear
(self, 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.
 modestr
‘fwd’ or ‘rev’.
 scope_outset or None
Set of absolute output names in the scope of this matvec product. If None, all are in the scope.
 scope_inset or None
Set of absolute input names in the scope of this matvec product. If None, all are in the scope.

run_apply_nonlinear
(self)¶ Compute residuals.
This calls _apply_nonlinear, but with the model assumed to be in an unscaled state.

run_linearize
(self, sub_do_ln=True)¶ Compute jacobian / factorization.
This calls _linearize, but with the model assumed to be in an unscaled state.
 Parameters
 sub_do_lnboolean
Flag indicating if the children should call linearize on their linear solvers.

run_solve_linear
(self, 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.
 modestr
‘fwd’ or ‘rev’.

run_solve_nonlinear
(self)¶ Compute outputs.
This calls _solve_nonlinear, but with the model assumed to be in an unscaled state.

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

set_order
(self, new_order)¶ Specify a new execution order for this system.
 Parameters
 new_orderlist of str
List of system names in desired new execution order.

setup
(self)[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
(self, include_self=False, recurse=True, typ=None)¶ Yield a generator of local subsystems of this system.
 Parameters
 include_selfbool
If True, include this system in the iteration.
 recursebool
If True, iterate over the whole tree under this system.
 typtype
If not None, only yield Systems that match that are instances of the given type.

use_fixed_coloring
(self, coloring=<object object at 0x7f1bde39daf0>, recurse=True)¶ Use a precomputed coloring for this System.
 Parameters
 coloringstr
A coloring filename. If no arg is passed, filename will be determined automatically.
 recursebool
If True, set fixed coloring in all subsystems that declare a coloring. Ignored if a specific coloring is passed in.


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

add
(self, name, subsys, promotes=None)¶ Add a subsystem (deprecated version of <Group.add_subsystem>).
 Parameters
 namestr
Name of the subsystem being added
 subsysSystem
An instantiated, but notyetset up system object.
 promotesiter 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
(self, name, lower=None, upper=None, equals=None, ref=None, ref0=None, adder=None, scaler=None, indices=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a constraint variable to this system.
 Parameters
 namestring
Name of the response variable in the system.
 lowerfloat or ndarray, optional
Lower boundary for the variable
 upperfloat or ndarray, optional
Upper boundary for the variable
 equalsfloat or ndarray, optional
Equality constraint value for the variable
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 indicessequence 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.
 linearbool
Set to True if constraint is linear. Default is False.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, name, lower=None, upper=None, ref=None, ref0=None, indices=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a design variable to this system.
 Parameters
 namestring
Name of the design variable in the system.
 lowerfloat or ndarray, optional
Lower boundary for the param
 upperupper or ndarray, optional
Upper boundary for the param
 reffloat or ndarray, optional
Value of design var that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of design var that scales to 0.0 in the driver.
 indicesiter 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.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, name, ref=None, ref0=None, index=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a response variable to this system.
 Parameters
 namestring
Name of the response variable in the system.
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 indexint, 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.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, recorder, recurse=False)¶ Add a recorder to the system.
 Parameters
 recorder<CaseRecorder>
A recorder instance.
 recurseboolean
Flag indicating if the recorder should be added to all the subsystems.

add_response
(self, name, type_, lower=None, upper=None, equals=None, ref=None, ref0=None, indices=None, index=None, adder=None, scaler=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a response variable to this system.
The response can be scaled using ref and ref0. The argument
ref0
represents the physical value when the scaled value is 0. The argumentref
represents the physical value when the scaled value is 1. Parameters
 namestring
Name of the response variable in the system.
 type_string
The type of response. Supported values are ‘con’ and ‘obj’
 lowerfloat or ndarray, optional
Lower boundary for the variable
 upperupper or ndarray, optional
Upper boundary for the variable
 equalsequals or ndarray, optional
Equality constraint value for the variable
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0upper or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 indicessequence of int, optional
If variable is an array, these indicate which entries are of interest for this particular response.
 indexint, optional
If variable is an array, this indicates which entry is of interest for this particular response.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 linearbool
Set to True if constraint is linear. Default is False.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, name, subsys, promotes=None, promotes_inputs=None, promotes_outputs=None, min_procs=1, max_procs=None, proc_weight=1.0)¶ Add a subsystem.
 Parameters
 namestr
Name of the subsystem being added
 subsys<System>
An instantiated, but notyetset up system object.
 promotesiter 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_inputsiter 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_outputsiter 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_procsint
Minimum number of MPI processes usable by the subsystem. Defaults to 1.
 max_procsint or None
Maximum number of MPI processes usable by the subsystem. A value of None (the default) indicates there is no maximum limit.
 proc_weightfloat
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
(self, method='fd', step=None, form=None, step_calc=None)¶ Approximate derivatives for a Group using the specified approximation method.
 Parameters
 methodstr
The type of approximation that should be used. Valid options include: ‘fd’: Finite Difference, ‘cs’: Complex Step
 stepfloat
Step size for approximation. Defaults to None, in which case, the approximation method provides its default value.
 formstring
Form for finite difference, can be ‘forward’, ‘backward’, or ‘central’. Defaults to None, in which case, the approximation method provides its default value.
 step_calcstring
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
(self, logger)¶ Perform optional error checks.
 Parameters
 loggerobject
The object that manages logging output.

cleanup
(self)¶ Clean up resources prior to exit.

compute_sys_graph
(self, 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_onlybool (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
(self)¶ 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
(self, src_name, tgt_name, src_indices=None, flat_src_indices=None)¶ Connect source src_name to target tgt_name in this namespace.
 Parameters
 src_namestr
name of the source variable to connect
 tgt_namestr or [str, … ] or (str, …)
name of the target variable(s) to connect
 src_indicesint 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_indicesbool
If True, each entry of src_indices is assumed to be an index into the flattened source. Otherwise it must be a tuple or list of size equal to the number of dimensions of the source.

declare_coloring
(self, wrt=('*', ), method='fd', form=None, step=None, per_instance=False, num_full_jacs=3, tol=1e25, orders=None, perturb_size=1e09, show_summary=True, show_sparsity=False)¶ Set options for deriv coloring of a set of wrt vars matching the given pattern(s).
 Parameters
 wrtstr or list of str
The name or names of the variables that derivatives are taken with respect to. This can contain input names, output names, or glob patterns.
 methodstr
Method used to compute derivative: “fd” for finite difference, “cs” for complex step.
 formstr
Finite difference form, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.
 stepfloat
Step size for finite difference. Leave undeclared to keep unchanged from previous or default value.
 per_instancebool
If True, a separate coloring will be generated for each instance of a given class. Otherwise, only one coloring for a given class will be generated and all instances of that class will use it.
 num_full_jacsint
Number of times to repeat partial jacobian computation when computing sparsity.
 tolfloat
Tolerance used to determine if an array entry is nonzero during sparsity determination.
 ordersint
Number of orders above and below the tolerance to check during the tolerance sweep.
 perturb_sizefloat
Size of input/output perturbation during generation of sparsity.
 show_summarybool
If True, display summary information after generating coloring.
 show_sparsitybool
If True, display sparsity with coloring info after generating coloring.

get_approx_coloring_fname
(self)¶ Return the full pathname to a coloring file.
 Parameters
 systemSystem
The System having its coloring saved or loaded.
 Returns
 str
Full pathname of the coloring file.

get_constraints
(self, 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
 recursebool, 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
(self, 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
 recursebool
If True, recurse through the subsystems and return the path of all design vars relative to the this system.
 get_sizesbool, optional
If True, compute the size of each design variable.
 Returns
 dict
The design variables defined in the current system and, if recurse=True, its subsystems.

get_linear_vectors
(self, vec_name='linear')¶ Return the linear inputs, outputs, and residuals vectors.
 Parameters
 vec_namestr
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
(self)¶ 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
(self, recurse=True)¶ Get the Objective settings from this system.
Retrieve all objectives settings from the system as a dict, keyed by variable name.
 Parameters
 recursebool, 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
(self, 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
 recursebool, optional
If True, recurse through the subsystems and return the path of all responses relative to the this system.
 get_sizesbool, 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
(self, inputs, outputs, residuals, discrete_inputs=None, discrete_outputs=None)¶ Provide initial guess for states.
Override this method to set the initial guess for states.
 Parameters
 inputsVector
unscaled, dimensional input variables read via inputs[key]
 outputsVector
unscaled, dimensional output variables read via outputs[key]
 residualsVector
unscaled, dimensional residuals written to via residuals[key]
 discrete_inputsdict or None
If not None, dict containing discrete input values.
 discrete_outputsdict or None
If not None, dict containing discrete output values.

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

is_active
(self)¶ 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.

property
linear_solver
¶ Get the linear solver for this system.

list_inputs
(self, values=True, prom_name=False, units=False, shape=False, hierarchical=True, print_arrays=False, tags=None, out_stream=<object object at 0x7f1bddbe81f0>)¶ 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
 valuesbool, optional
When True, display/return input values. Default is True.
 prom_namebool, optional
When True, display/return the promoted name of the variable. Default is False.
 unitsbool, optional
When True, display/return units. Default is False.
 shapebool, optional
When True, display/return the shape of the value. Default is False.
 hierarchicalbool, optional
When True, human readable output shows variables in hierarchical format.
 print_arraysbool, 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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed. Only inputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.
 out_streamfilelike 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
(self, explicit=True, implicit=True, values=True, prom_name=False, residuals=False, residuals_tol=None, units=False, shape=False, bounds=False, scaling=False, hierarchical=True, print_arrays=False, tags=None, out_stream=<object object at 0x7f1bddbe81f0>)¶ 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
 explicitbool, optional
include outputs from explicit components. Default is True.
 implicitbool, optional
include outputs from implicit components. Default is True.
 valuesbool, optional
When True, display/return output values. Default is True.
 prom_namebool, optional
When True, display/return the promoted name of the variable. Default is False.
 residualsbool, optional
When True, display/return residual values. Default is False.
 residuals_tolfloat, 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.
 unitsbool, optional
When True, display/return units. Default is False.
 shapebool, optional
When True, display/return the shape of the value. Default is False.
 boundsbool, optional
When True, display/return bounds (lower and upper). Default is False.
 scalingbool, optional
When True, display/return scaling (ref, ref0, and res_ref). Default is False.
 hierarchicalbool, optional
When True, human readable output shows variables in hierarchical format.
 print_arraysbool, 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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed. Only outputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.
 out_streamfilelike
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

property
ln_solver
¶ Get the linear solver for this system.

property
metadata
¶ Get the options for this System.

property
msginfo
¶ Our instance pathname, if available, or our class name. For use in error messages.
 Returns
 str
Either our instance pathname or class name.

property
nl_solver
¶ Get the nonlinear solver for this system.

property
nonlinear_solver
¶ Get the nonlinear solver for this system.

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

record_iteration
(self)¶ Record an iteration of the current System.

resetup
(self, setup_mode='full')¶ Public wrapper for _setup that reconfigures after an initial setup has been performed.
 Parameters
 setup_modestr
Must be one of ‘full’, ‘reconf’, or ‘update’.

run_apply_linear
(self, 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.
 modestr
‘fwd’ or ‘rev’.
 scope_outset or None
Set of absolute output names in the scope of this matvec product. If None, all are in the scope.
 scope_inset or None
Set of absolute input names in the scope of this matvec product. If None, all are in the scope.

run_apply_nonlinear
(self)¶ Compute residuals.
This calls _apply_nonlinear, but with the model assumed to be in an unscaled state.

run_linearize
(self, sub_do_ln=True)¶ Compute jacobian / factorization.
This calls _linearize, but with the model assumed to be in an unscaled state.
 Parameters
 sub_do_lnboolean
Flag indicating if the children should call linearize on their linear solvers.

run_solve_linear
(self, 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.
 modestr
‘fwd’ or ‘rev’.

run_solve_nonlinear
(self)¶ Compute outputs.
This calls _solve_nonlinear, but with the model assumed to be in an unscaled state.

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

set_order
(self, new_order)¶ Specify a new execution order for this system.
 Parameters
 new_orderlist of str
List of system names in desired new execution order.

setup
(self)[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
(self, include_self=False, recurse=True, typ=None)¶ Yield a generator of local subsystems of this system.
 Parameters
 include_selfbool
If True, include this system in the iteration.
 recursebool
If True, iterate over the whole tree under this system.
 typtype
If not None, only yield Systems that match that are instances of the given type.

use_fixed_coloring
(self, coloring=<object object at 0x7f1bde39daf0>, recurse=True)¶ Use a precomputed coloring for this System.
 Parameters
 coloringstr
A coloring filename. If no arg is passed, filename will be determined automatically.
 recursebool
If True, set fixed coloring in all subsystems that declare a coloring. Ignored if a specific coloring is passed in.


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

add
(self, name, subsys, promotes=None)¶ Add a subsystem (deprecated version of <Group.add_subsystem>).
 Parameters
 namestr
Name of the subsystem being added
 subsysSystem
An instantiated, but notyetset up system object.
 promotesiter 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
(self, name, lower=None, upper=None, equals=None, ref=None, ref0=None, adder=None, scaler=None, indices=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a constraint variable to this system.
 Parameters
 namestring
Name of the response variable in the system.
 lowerfloat or ndarray, optional
Lower boundary for the variable
 upperfloat or ndarray, optional
Upper boundary for the variable
 equalsfloat or ndarray, optional
Equality constraint value for the variable
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 indicessequence 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.
 linearbool
Set to True if constraint is linear. Default is False.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, name, lower=None, upper=None, ref=None, ref0=None, indices=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a design variable to this system.
 Parameters
 namestring
Name of the design variable in the system.
 lowerfloat or ndarray, optional
Lower boundary for the param
 upperupper or ndarray, optional
Upper boundary for the param
 reffloat or ndarray, optional
Value of design var that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of design var that scales to 0.0 in the driver.
 indicesiter 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.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, name, ref=None, ref0=None, index=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a response variable to this system.
 Parameters
 namestring
Name of the response variable in the system.
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 indexint, 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.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, recorder, recurse=False)¶ Add a recorder to the system.
 Parameters
 recorder<CaseRecorder>
A recorder instance.
 recurseboolean
Flag indicating if the recorder should be added to all the subsystems.

add_response
(self, name, type_, lower=None, upper=None, equals=None, ref=None, ref0=None, indices=None, index=None, adder=None, scaler=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a response variable to this system.
The response can be scaled using ref and ref0. The argument
ref0
represents the physical value when the scaled value is 0. The argumentref
represents the physical value when the scaled value is 1. Parameters
 namestring
Name of the response variable in the system.
 type_string
The type of response. Supported values are ‘con’ and ‘obj’
 lowerfloat or ndarray, optional
Lower boundary for the variable
 upperupper or ndarray, optional
Upper boundary for the variable
 equalsequals or ndarray, optional
Equality constraint value for the variable
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0upper or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 indicessequence of int, optional
If variable is an array, these indicate which entries are of interest for this particular response.
 indexint, optional
If variable is an array, this indicates which entry is of interest for this particular response.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 linearbool
Set to True if constraint is linear. Default is False.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, name, subsys, promotes=None, promotes_inputs=None, promotes_outputs=None, min_procs=1, max_procs=None, proc_weight=1.0)¶ Add a subsystem.
 Parameters
 namestr
Name of the subsystem being added
 subsys<System>
An instantiated, but notyetset up system object.
 promotesiter 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_inputsiter 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_outputsiter 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_procsint
Minimum number of MPI processes usable by the subsystem. Defaults to 1.
 max_procsint or None
Maximum number of MPI processes usable by the subsystem. A value of None (the default) indicates there is no maximum limit.
 proc_weightfloat
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
(self, method='fd', step=None, form=None, step_calc=None)¶ Approximate derivatives for a Group using the specified approximation method.
 Parameters
 methodstr
The type of approximation that should be used. Valid options include: ‘fd’: Finite Difference, ‘cs’: Complex Step
 stepfloat
Step size for approximation. Defaults to None, in which case, the approximation method provides its default value.
 formstring
Form for finite difference, can be ‘forward’, ‘backward’, or ‘central’. Defaults to None, in which case, the approximation method provides its default value.
 step_calcstring
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
(self, logger)¶ Perform optional error checks.
 Parameters
 loggerobject
The object that manages logging output.

cleanup
(self)¶ Clean up resources prior to exit.

compute_sys_graph
(self, 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_onlybool (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
(self)[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
(self, src_name, tgt_name, src_indices=None, flat_src_indices=None)¶ Connect source src_name to target tgt_name in this namespace.
 Parameters
 src_namestr
name of the source variable to connect
 tgt_namestr or [str, … ] or (str, …)
name of the target variable(s) to connect
 src_indicesint 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_indicesbool
If True, each entry of src_indices is assumed to be an index into the flattened source. Otherwise it must be a tuple or list of size equal to the number of dimensions of the source.

declare_coloring
(self, wrt=('*', ), method='fd', form=None, step=None, per_instance=False, num_full_jacs=3, tol=1e25, orders=None, perturb_size=1e09, show_summary=True, show_sparsity=False)¶ Set options for deriv coloring of a set of wrt vars matching the given pattern(s).
 Parameters
 wrtstr or list of str
The name or names of the variables that derivatives are taken with respect to. This can contain input names, output names, or glob patterns.
 methodstr
Method used to compute derivative: “fd” for finite difference, “cs” for complex step.
 formstr
Finite difference form, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.
 stepfloat
Step size for finite difference. Leave undeclared to keep unchanged from previous or default value.
 per_instancebool
If True, a separate coloring will be generated for each instance of a given class. Otherwise, only one coloring for a given class will be generated and all instances of that class will use it.
 num_full_jacsint
Number of times to repeat partial jacobian computation when computing sparsity.
 tolfloat
Tolerance used to determine if an array entry is nonzero during sparsity determination.
 ordersint
Number of orders above and below the tolerance to check during the tolerance sweep.
 perturb_sizefloat
Size of input/output perturbation during generation of sparsity.
 show_summarybool
If True, display summary information after generating coloring.
 show_sparsitybool
If True, display sparsity with coloring info after generating coloring.

get_approx_coloring_fname
(self)¶ Return the full pathname to a coloring file.
 Parameters
 systemSystem
The System having its coloring saved or loaded.
 Returns
 str
Full pathname of the coloring file.

get_constraints
(self, 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
 recursebool, 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
(self, 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
 recursebool
If True, recurse through the subsystems and return the path of all design vars relative to the this system.
 get_sizesbool, optional
If True, compute the size of each design variable.
 Returns
 dict
The design variables defined in the current system and, if recurse=True, its subsystems.

get_linear_vectors
(self, vec_name='linear')¶ Return the linear inputs, outputs, and residuals vectors.
 Parameters
 vec_namestr
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
(self)¶ 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
(self, recurse=True)¶ Get the Objective settings from this system.
Retrieve all objectives settings from the system as a dict, keyed by variable name.
 Parameters
 recursebool, 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
(self, 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
 recursebool, optional
If True, recurse through the subsystems and return the path of all responses relative to the this system.
 get_sizesbool, 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
(self, inputs, outputs, residuals, discrete_inputs=None, discrete_outputs=None)¶ Provide initial guess for states.
Override this method to set the initial guess for states.
 Parameters
 inputsVector
unscaled, dimensional input variables read via inputs[key]
 outputsVector
unscaled, dimensional output variables read via outputs[key]
 residualsVector
unscaled, dimensional residuals written to via residuals[key]
 discrete_inputsdict or None
If not None, dict containing discrete input values.
 discrete_outputsdict or None
If not None, dict containing discrete output values.

is_active
(self)¶ 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.

property
linear_solver
¶ Get the linear solver for this system.

list_inputs
(self, values=True, prom_name=False, units=False, shape=False, hierarchical=True, print_arrays=False, tags=None, out_stream=<object object at 0x7f1bddbe81f0>)¶ 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
 valuesbool, optional
When True, display/return input values. Default is True.
 prom_namebool, optional
When True, display/return the promoted name of the variable. Default is False.
 unitsbool, optional
When True, display/return units. Default is False.
 shapebool, optional
When True, display/return the shape of the value. Default is False.
 hierarchicalbool, optional
When True, human readable output shows variables in hierarchical format.
 print_arraysbool, 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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed. Only inputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.
 out_streamfilelike 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
(self, explicit=True, implicit=True, values=True, prom_name=False, residuals=False, residuals_tol=None, units=False, shape=False, bounds=False, scaling=False, hierarchical=True, print_arrays=False, tags=None, out_stream=<object object at 0x7f1bddbe81f0>)¶ 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
 explicitbool, optional
include outputs from explicit components. Default is True.
 implicitbool, optional
include outputs from implicit components. Default is True.
 valuesbool, optional
When True, display/return output values. Default is True.
 prom_namebool, optional
When True, display/return the promoted name of the variable. Default is False.
 residualsbool, optional
When True, display/return residual values. Default is False.
 residuals_tolfloat, 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.
 unitsbool, optional
When True, display/return units. Default is False.
 shapebool, optional
When True, display/return the shape of the value. Default is False.
 boundsbool, optional
When True, display/return bounds (lower and upper). Default is False.
 scalingbool, optional
When True, display/return scaling (ref, ref0, and res_ref). Default is False.
 hierarchicalbool, optional
When True, human readable output shows variables in hierarchical format.
 print_arraysbool, 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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed. Only outputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.
 out_streamfilelike
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

property
ln_solver
¶ Get the linear solver for this system.

property
metadata
¶ Get the options for this System.

property
msginfo
¶ Our instance pathname, if available, or our class name. For use in error messages.
 Returns
 str
Either our instance pathname or class name.

property
nl_solver
¶ Get the nonlinear solver for this system.

property
nonlinear_solver
¶ Get the nonlinear solver for this system.

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

record_iteration
(self)¶ Record an iteration of the current System.

resetup
(self, setup_mode='full')¶ Public wrapper for _setup that reconfigures after an initial setup has been performed.
 Parameters
 setup_modestr
Must be one of ‘full’, ‘reconf’, or ‘update’.

run_apply_linear
(self, 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.
 modestr
‘fwd’ or ‘rev’.
 scope_outset or None
Set of absolute output names in the scope of this matvec product. If None, all are in the scope.
 scope_inset or None
Set of absolute input names in the scope of this matvec product. If None, all are in the scope.

run_apply_nonlinear
(self)¶ Compute residuals.
This calls _apply_nonlinear, but with the model assumed to be in an unscaled state.

run_linearize
(self, sub_do_ln=True)¶ Compute jacobian / factorization.
This calls _linearize, but with the model assumed to be in an unscaled state.
 Parameters
 sub_do_lnboolean
Flag indicating if the children should call linearize on their linear solvers.

run_solve_linear
(self, 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.
 modestr
‘fwd’ or ‘rev’.

run_solve_nonlinear
(self)¶ Compute outputs.
This calls _solve_nonlinear, but with the model assumed to be in an unscaled state.

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

set_order
(self, new_order)¶ Specify a new execution order for this system.
 Parameters
 new_orderlist of str
List of system names in desired new execution order.

setup
(self)[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
(self, include_self=False, recurse=True, typ=None)¶ Yield a generator of local subsystems of this system.
 Parameters
 include_selfbool
If True, include this system in the iteration.
 recursebool
If True, iterate over the whole tree under this system.
 typtype
If not None, only yield Systems that match that are instances of the given type.

use_fixed_coloring
(self, coloring=<object object at 0x7f1bde39daf0>, recurse=True)¶ Use a precomputed coloring for this System.
 Parameters
 coloringstr
A coloring filename. If no arg is passed, filename will be determined automatically.
 recursebool
If True, set fixed coloring in all subsystems that declare a coloring. Ignored if a specific coloring is passed in.


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

add_constraint
(self, name, lower=None, upper=None, equals=None, ref=None, ref0=None, adder=None, scaler=None, indices=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a constraint variable to this system.
 Parameters
 namestring
Name of the response variable in the system.
 lowerfloat or ndarray, optional
Lower boundary for the variable
 upperfloat or ndarray, optional
Upper boundary for the variable
 equalsfloat or ndarray, optional
Equality constraint value for the variable
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 indicessequence 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.
 linearbool
Set to True if constraint is linear. Default is False.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, name, lower=None, upper=None, ref=None, ref0=None, indices=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a design variable to this system.
 Parameters
 namestring
Name of the design variable in the system.
 lowerfloat or ndarray, optional
Lower boundary for the param
 upperupper or ndarray, optional
Upper boundary for the param
 reffloat or ndarray, optional
Value of design var that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of design var that scales to 0.0 in the driver.
 indicesiter 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.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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_discrete_input
(self, name, val, desc='', tags=None)¶ Add a discrete input variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 vala picklable object
The initial value of the variable being added.
 descstr
description of the variable
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_discrete_output
(self, name, val, desc='', tags=None)¶ Add an output variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 vala picklable object
The initial value of the variable being added.
 descstr
description of the variable.
 tagsstr or list of strs or set of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_input
(self, name, val=1.0, shape=None, src_indices=None, flat_src_indices=None, units=None, desc='', tags=None)¶ Add an input variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 valfloat or list or tuple or ndarray or Iterable
The initial value of the variable being added in userdefined units. Default is 1.0.
 shapeint 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_indicesint 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_indicesbool
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.
 unitsstr or None
Units in which this input variable will be provided to the component during execution. Default is None, which means it is unitless.
 descstr
description of the variable
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_objective
(self, name, ref=None, ref0=None, index=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a response variable to this system.
 Parameters
 namestring
Name of the response variable in the system.
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 indexint, 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.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, 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, tags=None)¶ Add an output variable to the component.
For ExplicitComponent, res_ref defaults to the value in res unless otherwise specified.
 Parameters
 namestr
name of the variable in this component’s namespace.
 valfloat or list or tuple or ndarray
The initial value of the variable being added in userdefined units. Default is 1.0.
 shapeint or tuple or list or None
Shape of this variable, only required if val is not an array. Default is None.
 unitsstr 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_unitsstr 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.
 descstr
description of the variable.
 lowerfloat 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.
 upperfloat 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.
 reffloat
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 1. Default is 1.
 ref0float
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 0. Default is 0.
 res_reffloat
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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs and also when listing results from case recorders.
 Returns
 dict
metadata for added variable

add_recorder
(self, recorder, recurse=False)¶ Add a recorder to the system.
 Parameters
 recorder<CaseRecorder>
A recorder instance.
 recurseboolean
Flag indicating if the recorder should be added to all the subsystems.

add_response
(self, name, type_, lower=None, upper=None, equals=None, ref=None, ref0=None, indices=None, index=None, adder=None, scaler=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a response variable to this system.
The response can be scaled using ref and ref0. The argument
ref0
represents the physical value when the scaled value is 0. The argumentref
represents the physical value when the scaled value is 1. Parameters
 namestring
Name of the response variable in the system.
 type_string
The type of response. Supported values are ‘con’ and ‘obj’
 lowerfloat or ndarray, optional
Lower boundary for the variable
 upperupper or ndarray, optional
Upper boundary for the variable
 equalsequals or ndarray, optional
Equality constraint value for the variable
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0upper or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 indicessequence of int, optional
If variable is an array, these indicate which entries are of interest for this particular response.
 indexint, optional
If variable is an array, this indicates which entry is of interest for this particular response.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 linearbool
Set to True if constraint is linear. Default is False.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, logger)¶ Perform optional error checks.
 Parameters
 loggerobject
The object that manages logging output.

cleanup
(self)¶ Clean up resources prior to exit.

compute_jacvec_product
(self, inputs, d_inputs, d_outputs, mode, discrete_inputs=None)¶ 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
 inputsVector
unscaled, dimensional input variables read via inputs[key]
 d_inputsVector
see inputs; product must be computed only if var_name in d_inputs
 d_outputsVector
see outputs; product must be computed only if var_name in d_outputs
 modestr
either ‘fwd’ or ‘rev’
 discrete_inputsdict or None
If not None, dict containing discrete input values.

compute_partials
(self, inputs, partials, discrete_inputs=None)¶ Compute subjacobian parts. The model is assumed to be in an unscaled state.
 Parameters
 inputsVector
unscaled, dimensional input variables read via inputs[key]
 partialsJacobian
subjac components written to partials[output_name, input_name]
 discrete_inputsdict or None
If not None, dict containing discrete input values.

declare_coloring
(self, wrt=('*', ), method='fd', form=None, step=None, per_instance=False, num_full_jacs=3, tol=1e25, orders=None, perturb_size=1e09, show_summary=True, show_sparsity=False)¶ Set options for deriv coloring of a set of wrt vars matching the given pattern(s).
 Parameters
 wrtstr or list of str
The name or names of the variables that derivatives are taken with respect to. This can contain input names, output names, or glob patterns.
 methodstr
Method used to compute derivative: “fd” for finite difference, “cs” for complex step.
 formstr
Finite difference form, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.
 stepfloat
Step size for finite difference. Leave undeclared to keep unchanged from previous or default value.
 per_instancebool
If True, a separate coloring will be generated for each instance of a given class. Otherwise, only one coloring for a given class will be generated and all instances of that class will use it.
 num_full_jacsint
Number of times to repeat partial jacobian computation when computing sparsity.
 tolfloat
Tolerance used to determine if an array entry is nonzero during sparsity determination.
 ordersint
Number of orders above and below the tolerance to check during the tolerance sweep.
 perturb_sizefloat
Size of input/output perturbation during generation of sparsity.
 show_summarybool
If True, display summary information after generating coloring.
 show_sparsitybool
If True, display sparsity with coloring info after generating coloring.

declare_partials
(self, 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
 ofstr or list of str
The name of the residual(s) that derivatives are being computed for. May also contain a glob pattern.
 wrtstr 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.
 dependentbool(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.
 rowsndarray of int or None
Row indices for each nonzero entry. For sparse subjacobians only.
 colsndarray of int or None
Column indices for each nonzero entry. For sparse subjacobians only.
 valfloat 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.
 methodstr
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’.
 stepfloat
Step size for approximation. Defaults to None, in which case the approximation method provides its default value.
 formstring
Form for finite difference, can be ‘forward’, ‘backward’, or ‘central’. Defaults to None, in which case the approximation method provides its default value.
 step_calcstring
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.
 Returns
 dict
Metadata dict for the specified partial(s).

property
distributed
¶ Provide ‘distributed’ property for backwards compatibility.
 Returns
 bool
reference to the ‘distributed’ option.

get_approx_coloring_fname
(self)¶ Return the full pathname to a coloring file.
 Parameters
 systemSystem
The System having its coloring saved or loaded.
 Returns
 str
Full pathname of the coloring file.

get_constraints
(self, 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
 recursebool, 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
(self, 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
 recursebool
If True, recurse through the subsystems and return the path of all design vars relative to the this system.
 get_sizesbool, optional
If True, compute the size of each design variable.
 Returns
 dict
The design variables defined in the current system and, if recurse=True, its subsystems.

get_linear_vectors
(self, vec_name='linear')¶ Return the linear inputs, outputs, and residuals vectors.
 Parameters
 vec_namestr
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
(self)¶ 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
(self, recurse=True)¶ Get the Objective settings from this system.
Retrieve all objectives settings from the system as a dict, keyed by variable name.
 Parameters
 recursebool, 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
(self, 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
 recursebool, optional
If True, recurse through the subsystems and return the path of all responses relative to the this system.
 get_sizesbool, 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
(self)¶ Perform any onetime initialization run at instantiation.

is_active
(self)¶ 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.

property
linear_solver
¶ Get the linear solver for this system.

list_inputs
(self, values=True, prom_name=False, units=False, shape=False, hierarchical=True, print_arrays=False, tags=None, out_stream=<object object at 0x7f1bddbe81f0>)¶ 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
 valuesbool, optional
When True, display/return input values. Default is True.
 prom_namebool, optional
When True, display/return the promoted name of the variable. Default is False.
 unitsbool, optional
When True, display/return units. Default is False.
 shapebool, optional
When True, display/return the shape of the value. Default is False.
 hierarchicalbool, optional
When True, human readable output shows variables in hierarchical format.
 print_arraysbool, 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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed. Only inputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.
 out_streamfilelike 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
(self, explicit=True, implicit=True, values=True, prom_name=False, residuals=False, residuals_tol=None, units=False, shape=False, bounds=False, scaling=False, hierarchical=True, print_arrays=False, tags=None, out_stream=<object object at 0x7f1bddbe81f0>)¶ 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
 explicitbool, optional
include outputs from explicit components. Default is True.
 implicitbool, optional
include outputs from implicit components. Default is True.
 valuesbool, optional
When True, display/return output values. Default is True.
 prom_namebool, optional
When True, display/return the promoted name of the variable. Default is False.
 residualsbool, optional
When True, display/return residual values. Default is False.
 residuals_tolfloat, 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.
 unitsbool, optional
When True, display/return units. Default is False.
 shapebool, optional
When True, display/return the shape of the value. Default is False.
 boundsbool, optional
When True, display/return bounds (lower and upper). Default is False.
 scalingbool, optional
When True, display/return scaling (ref, ref0, and res_ref). Default is False.
 hierarchicalbool, optional
When True, human readable output shows variables in hierarchical format.
 print_arraysbool, 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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed. Only outputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.
 out_streamfilelike
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

property
ln_solver
¶ Get the linear solver for this system.

property
metadata
¶ Get the options for this System.

property
msginfo
¶ Our instance pathname, if available, or our class name. For use in error messages.
 Returns
 str
Either our instance pathname or class name.

property
nl_solver
¶ Get the nonlinear solver for this system.

property
nonlinear_solver
¶ Get the nonlinear solver for this system.

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

record_iteration
(self)¶ Record an iteration of the current System.

resetup
(self, setup_mode='full')¶ Public wrapper for _setup that reconfigures after an initial setup has been performed.
 Parameters
 setup_modestr
Must be one of ‘full’, ‘reconf’, or ‘update’.

run_apply_linear
(self, 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.
 modestr
‘fwd’ or ‘rev’.
 scope_outset or None
Set of absolute output names in the scope of this matvec product. If None, all are in the scope.
 scope_inset or None
Set of absolute input names in the scope of this matvec product. If None, all are in the scope.

run_apply_nonlinear
(self)¶ Compute residuals.
This calls _apply_nonlinear, but with the model assumed to be in an unscaled state.

run_linearize
(self, sub_do_ln=True)¶ Compute jacobian / factorization.
This calls _linearize, but with the model assumed to be in an unscaled state.
 Parameters
 sub_do_lnboolean
Flag indicating if the children should call linearize on their linear solvers.

run_solve_linear
(self, 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.
 modestr
‘fwd’ or ‘rev’.

run_solve_nonlinear
(self)¶ Compute outputs.
This calls _solve_nonlinear, but with the model assumed to be in an unscaled state.

set_check_partial_options
(self, wrt, method='fd', form=None, step=None, step_calc=None, directional=False)¶ Set options that will be used for checking partial derivatives.
 Parameters
 wrtstr 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.
 methodstr
Method for check: “fd” for finite difference, “cs” for complex step.
 formstr
Finite difference form for check, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.
 stepfloat
Step size for finite difference check. Leave undeclared to keep unchanged from previous or default value.
 step_calcstr
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.
 directionalbool
Set to True to perform a single directional derivative for each vector variable in the pattern named in wrt.

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

system_iter
(self, include_self=False, recurse=True, typ=None)¶ Yield a generator of local subsystems of this system.
 Parameters
 include_selfbool
If True, include this system in the iteration.
 recursebool
If True, iterate over the whole tree under this system.
 typtype
If not None, only yield Systems that match that are instances of the given type.

use_fixed_coloring
(self, coloring=<object object at 0x7f1bde39daf0>, recurse=True)¶ Use a precomputed coloring for this System.
 Parameters
 coloringstr
A coloring filename. If no arg is passed, filename will be determined automatically.
 recursebool
If True, set fixed coloring in all subsystems that declare a coloring. Ignored if a specific coloring is passed in.


class
openmdao.test_suite.components.sellar.
SellarDis1CS
(units=None, scaling=None)[source]¶ Bases:
openmdao.test_suite.components.sellar.SellarDis1
Component containing Discipline 1 – complex step version.

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

add_constraint
(self, name, lower=None, upper=None, equals=None, ref=None, ref0=None, adder=None, scaler=None, indices=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a constraint variable to this system.
 Parameters
 namestring
Name of the response variable in the system.
 lowerfloat or ndarray, optional
Lower boundary for the variable
 upperfloat or ndarray, optional
Upper boundary for the variable
 equalsfloat or ndarray, optional
Equality constraint value for the variable
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 indicessequence 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.
 linearbool
Set to True if constraint is linear. Default is False.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, name, lower=None, upper=None, ref=None, ref0=None, indices=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a design variable to this system.
 Parameters
 namestring
Name of the design variable in the system.
 lowerfloat or ndarray, optional
Lower boundary for the param
 upperupper or ndarray, optional
Upper boundary for the param
 reffloat or ndarray, optional
Value of design var that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of design var that scales to 0.0 in the driver.
 indicesiter 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.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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_discrete_input
(self, name, val, desc='', tags=None)¶ Add a discrete input variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 vala picklable object
The initial value of the variable being added.
 descstr
description of the variable
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_discrete_output
(self, name, val, desc='', tags=None)¶ Add an output variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 vala picklable object
The initial value of the variable being added.
 descstr
description of the variable.
 tagsstr or list of strs or set of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_input
(self, name, val=1.0, shape=None, src_indices=None, flat_src_indices=None, units=None, desc='', tags=None)¶ Add an input variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 valfloat or list or tuple or ndarray or Iterable
The initial value of the variable being added in userdefined units. Default is 1.0.
 shapeint 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_indicesint 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_indicesbool
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.
 unitsstr or None
Units in which this input variable will be provided to the component during execution. Default is None, which means it is unitless.
 descstr
description of the variable
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_objective
(self, name, ref=None, ref0=None, index=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a response variable to this system.
 Parameters
 namestring
Name of the response variable in the system.
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 indexint, 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.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, 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, tags=None)¶ Add an output variable to the component.
For ExplicitComponent, res_ref defaults to the value in res unless otherwise specified.
 Parameters
 namestr
name of the variable in this component’s namespace.
 valfloat or list or tuple or ndarray
The initial value of the variable being added in userdefined units. Default is 1.0.
 shapeint or tuple or list or None
Shape of this variable, only required if val is not an array. Default is None.
 unitsstr 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_unitsstr 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.
 descstr
description of the variable.
 lowerfloat 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.
 upperfloat 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.
 reffloat
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 1. Default is 1.
 ref0float
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 0. Default is 0.
 res_reffloat
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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs and also when listing results from case recorders.
 Returns
 dict
metadata for added variable

add_recorder
(self, recorder, recurse=False)¶ Add a recorder to the system.
 Parameters
 recorder<CaseRecorder>
A recorder instance.
 recurseboolean
Flag indicating if the recorder should be added to all the subsystems.

add_response
(self, name, type_, lower=None, upper=None, equals=None, ref=None, ref0=None, indices=None, index=None, adder=None, scaler=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a response variable to this system.
The response can be scaled using ref and ref0. The argument
ref0
represents the physical value when the scaled value is 0. The argumentref
represents the physical value when the scaled value is 1. Parameters
 namestring
Name of the response variable in the system.
 type_string
The type of response. Supported values are ‘con’ and ‘obj’
 lowerfloat or ndarray, optional
Lower boundary for the variable
 upperupper or ndarray, optional
Upper boundary for the variable
 equalsequals or ndarray, optional
Equality constraint value for the variable
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0upper or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 indicessequence of int, optional
If variable is an array, these indicate which entries are of interest for this particular response.
 indexint, optional
If variable is an array, this indicates which entry is of interest for this particular response.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 linearbool
Set to True if constraint is linear. Default is False.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, logger)¶ Perform optional error checks.
 Parameters
 loggerobject
The object that manages logging output.

cleanup
(self)¶ Clean up resources prior to exit.

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

compute_jacvec_product
(self, inputs, d_inputs, d_outputs, mode, discrete_inputs=None)¶ 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
 inputsVector
unscaled, dimensional input variables read via inputs[key]
 d_inputsVector
see inputs; product must be computed only if var_name in d_inputs
 d_outputsVector
see outputs; product must be computed only if var_name in d_outputs
 modestr
either ‘fwd’ or ‘rev’
 discrete_inputsdict or None
If not None, dict containing discrete input values.

compute_partials
(self, inputs, partials, discrete_inputs=None)¶ Compute subjacobian parts. The model is assumed to be in an unscaled state.
 Parameters
 inputsVector
unscaled, dimensional input variables read via inputs[key]
 partialsJacobian
subjac components written to partials[output_name, input_name]
 discrete_inputsdict or None
If not None, dict containing discrete input values.

declare_coloring
(self, wrt=('*', ), method='fd', form=None, step=None, per_instance=False, num_full_jacs=3, tol=1e25, orders=None, perturb_size=1e09, show_summary=True, show_sparsity=False)¶ Set options for deriv coloring of a set of wrt vars matching the given pattern(s).
 Parameters
 wrtstr or list of str
The name or names of the variables that derivatives are taken with respect to. This can contain input names, output names, or glob patterns.
 methodstr
Method used to compute derivative: “fd” for finite difference, “cs” for complex step.
 formstr
Finite difference form, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.
 stepfloat
Step size for finite difference. Leave undeclared to keep unchanged from previous or default value.
 per_instancebool
If True, a separate coloring will be generated for each instance of a given class. Otherwise, only one coloring for a given class will be generated and all instances of that class will use it.
 num_full_jacsint
Number of times to repeat partial jacobian computation when computing sparsity.
 tolfloat
Tolerance used to determine if an array entry is nonzero during sparsity determination.
 ordersint
Number of orders above and below the tolerance to check during the tolerance sweep.
 perturb_sizefloat
Size of input/output perturbation during generation of sparsity.
 show_summarybool
If True, display summary information after generating coloring.
 show_sparsitybool
If True, display sparsity with coloring info after generating coloring.

declare_partials
(self, 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
 ofstr or list of str
The name of the residual(s) that derivatives are being computed for. May also contain a glob pattern.
 wrtstr 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.
 dependentbool(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.
 rowsndarray of int or None
Row indices for each nonzero entry. For sparse subjacobians only.
 colsndarray of int or None
Column indices for each nonzero entry. For sparse subjacobians only.
 valfloat 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.
 methodstr
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’.
 stepfloat
Step size for approximation. Defaults to None, in which case the approximation method provides its default value.
 formstring
Form for finite difference, can be ‘forward’, ‘backward’, or ‘central’. Defaults to None, in which case the approximation method provides its default value.
 step_calcstring
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.
 Returns
 dict
Metadata dict for the specified partial(s).

property
distributed
¶ Provide ‘distributed’ property for backwards compatibility.
 Returns
 bool
reference to the ‘distributed’ option.

get_approx_coloring_fname
(self)¶ Return the full pathname to a coloring file.
 Parameters
 systemSystem
The System having its coloring saved or loaded.
 Returns
 str
Full pathname of the coloring file.

get_constraints
(self, 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
 recursebool, 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
(self, 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
 recursebool
If True, recurse through the subsystems and return the path of all design vars relative to the this system.
 get_sizesbool, optional
If True, compute the size of each design variable.
 Returns
 dict
The design variables defined in the current system and, if recurse=True, its subsystems.

get_linear_vectors
(self, vec_name='linear')¶ Return the linear inputs, outputs, and residuals vectors.
 Parameters
 vec_namestr
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
(self)¶ 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
(self, recurse=True)¶ Get the Objective settings from this system.
Retrieve all objectives settings from the system as a dict, keyed by variable name.
 Parameters
 recursebool, 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
(self, 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
 recursebool, optional
If True, recurse through the subsystems and return the path of all responses relative to the this system.
 get_sizesbool, 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
(self)¶ Perform any onetime initialization run at instantiation.

is_active
(self)¶ 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.

property
linear_solver
¶ Get the linear solver for this system.

list_inputs
(self, values=True, prom_name=False, units=False, shape=False, hierarchical=True, print_arrays=False, tags=None, out_stream=<object object at 0x7f1bddbe81f0>)¶ 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
 valuesbool, optional
When True, display/return input values. Default is True.
 prom_namebool, optional
When True, display/return the promoted name of the variable. Default is False.
 unitsbool, optional
When True, display/return units. Default is False.
 shapebool, optional
When True, display/return the shape of the value. Default is False.
 hierarchicalbool, optional
When True, human readable output shows variables in hierarchical format.
 print_arraysbool, 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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed. Only inputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.
 out_streamfilelike 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
(self, explicit=True, implicit=True, values=True, prom_name=False, residuals=False, residuals_tol=None, units=False, shape=False, bounds=False, scaling=False, hierarchical=True, print_arrays=False, tags=None, out_stream=<object object at 0x7f1bddbe81f0>)¶ 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
 explicitbool, optional
include outputs from explicit components. Default is True.
 implicitbool, optional
include outputs from implicit components. Default is True.
 valuesbool, optional
When True, display/return output values. Default is True.
 prom_namebool, optional
When True, display/return the promoted name of the variable. Default is False.
 residualsbool, optional
When True, display/return residual values. Default is False.
 residuals_tolfloat, 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.
 unitsbool, optional
When True, display/return units. Default is False.
 shapebool, optional
When True, display/return the shape of the value. Default is False.
 boundsbool, optional
When True, display/return bounds (lower and upper). Default is False.
 scalingbool, optional
When True, display/return scaling (ref, ref0, and res_ref). Default is False.
 hierarchicalbool, optional
When True, human readable output shows variables in hierarchical format.
 print_arraysbool, 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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed. Only outputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.
 out_streamfilelike
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

property
ln_solver
¶ Get the linear solver for this system.

property
metadata
¶ Get the options for this System.

property
msginfo
¶ Our instance pathname, if available, or our class name. For use in error messages.
 Returns
 str
Either our instance pathname or class name.

property
nl_solver
¶ Get the nonlinear solver for this system.

property
nonlinear_solver
¶ Get the nonlinear solver for this system.

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

record_iteration
(self)¶ Record an iteration of the current System.

resetup
(self, setup_mode='full')¶ Public wrapper for _setup that reconfigures after an initial setup has been performed.
 Parameters
 setup_modestr
Must be one of ‘full’, ‘reconf’, or ‘update’.

run_apply_linear
(self, 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.
 modestr
‘fwd’ or ‘rev’.
 scope_outset or None
Set of absolute output names in the scope of this matvec product. If None, all are in the scope.
 scope_inset or None
Set of absolute input names in the scope of this matvec product. If None, all are in the scope.

run_apply_nonlinear
(self)¶ Compute residuals.
This calls _apply_nonlinear, but with the model assumed to be in an unscaled state.

run_linearize
(self, sub_do_ln=True)¶ Compute jacobian / factorization.
This calls _linearize, but with the model assumed to be in an unscaled state.
 Parameters
 sub_do_lnboolean
Flag indicating if the children should call linearize on their linear solvers.

run_solve_linear
(self, 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.
 modestr
‘fwd’ or ‘rev’.

run_solve_nonlinear
(self)¶ Compute outputs.
This calls _solve_nonlinear, but with the model assumed to be in an unscaled state.

set_check_partial_options
(self, wrt, method='fd', form=None, step=None, step_calc=None, directional=False)¶ Set options that will be used for checking partial derivatives.
 Parameters
 wrtstr 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.
 methodstr
Method for check: “fd” for finite difference, “cs” for complex step.
 formstr
Finite difference form for check, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.
 stepfloat
Step size for finite difference check. Leave undeclared to keep unchanged from previous or default value.
 step_calcstr
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.
 directionalbool
Set to True to perform a single directional derivative for each vector variable in the pattern named in wrt.

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

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

system_iter
(self, include_self=False, recurse=True, typ=None)¶ Yield a generator of local subsystems of this system.
 Parameters
 include_selfbool
If True, include this system in the iteration.
 recursebool
If True, iterate over the whole tree under this system.
 typtype
If not None, only yield Systems that match that are instances of the given type.

use_fixed_coloring
(self, coloring=<object object at 0x7f1bde39daf0>, recurse=True)¶ Use a precomputed coloring for this System.
 Parameters
 coloringstr
A coloring filename. If no arg is passed, filename will be determined automatically.
 recursebool
If True, set fixed coloring in all subsystems that declare a coloring. Ignored if a specific coloring is passed in.


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

add_constraint
(self, name, lower=None, upper=None, equals=None, ref=None, ref0=None, adder=None, scaler=None, indices=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a constraint variable to this system.
 Parameters
 namestring
Name of the response variable in the system.
 lowerfloat or ndarray, optional
Lower boundary for the variable
 upperfloat or ndarray, optional
Upper boundary for the variable
 equalsfloat or ndarray, optional
Equality constraint value for the variable
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 indicessequence 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.
 linearbool
Set to True if constraint is linear. Default is False.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, name, lower=None, upper=None, ref=None, ref0=None, indices=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a design variable to this system.
 Parameters
 namestring
Name of the design variable in the system.
 lowerfloat or ndarray, optional
Lower boundary for the param
 upperupper or ndarray, optional
Upper boundary for the param
 reffloat or ndarray, optional
Value of design var that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of design var that scales to 0.0 in the driver.
 indicesiter 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.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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_discrete_input
(self, name, val, desc='', tags=None)¶ Add a discrete input variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 vala picklable object
The initial value of the variable being added.
 descstr
description of the variable
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_discrete_output
(self, name, val, desc='', tags=None)¶ Add an output variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 vala picklable object
The initial value of the variable being added.
 descstr
description of the variable.
 tagsstr or list of strs or set of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_input
(self, name, val=1.0, shape=None, src_indices=None, flat_src_indices=None, units=None, desc='', tags=None)¶ Add an input variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 valfloat or list or tuple or ndarray or Iterable
The initial value of the variable being added in userdefined units. Default is 1.0.
 shapeint 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_indicesint 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_indicesbool
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.
 unitsstr or None
Units in which this input variable will be provided to the component during execution. Default is None, which means it is unitless.
 descstr
description of the variable
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_objective
(self, name, ref=None, ref0=None, index=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a response variable to this system.
 Parameters
 namestring
Name of the response variable in the system.
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 indexint, 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.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, 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, tags=None)¶ Add an output variable to the component.
For ExplicitComponent, res_ref defaults to the value in res unless otherwise specified.
 Parameters
 namestr
name of the variable in this component’s namespace.
 valfloat or list or tuple or ndarray
The initial value of the variable being added in userdefined units. Default is 1.0.
 shapeint or tuple or list or None
Shape of this variable, only required if val is not an array. Default is None.
 unitsstr 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_unitsstr 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.
 descstr
description of the variable.
 lowerfloat 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.
 upperfloat 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.
 reffloat
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 1. Default is 1.
 ref0float
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 0. Default is 0.
 res_reffloat
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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs and also when listing results from case recorders.
 Returns
 dict
metadata for added variable

add_recorder
(self, recorder, recurse=False)¶ Add a recorder to the system.
 Parameters
 recorder<CaseRecorder>
A recorder instance.
 recurseboolean
Flag indicating if the recorder should be added to all the subsystems.

add_response
(self, name, type_, lower=None, upper=None, equals=None, ref=None, ref0=None, indices=None, index=None, adder=None, scaler=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a response variable to this system.
The response can be scaled using ref and ref0. The argument
ref0
represents the physical value when the scaled value is 0. The argumentref
represents the physical value when the scaled value is 1. Parameters
 namestring
Name of the response variable in the system.
 type_string
The type of response. Supported values are ‘con’ and ‘obj’
 lowerfloat or ndarray, optional
Lower boundary for the variable
 upperupper or ndarray, optional
Upper boundary for the variable
 equalsequals or ndarray, optional
Equality constraint value for the variable
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0upper or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 indicessequence of int, optional
If variable is an array, these indicate which entries are of interest for this particular response.
 indexint, optional
If variable is an array, this indicates which entry is of interest for this particular response.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 linearbool
Set to True if constraint is linear. Default is False.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, logger)¶ Perform optional error checks.
 Parameters
 loggerobject
The object that manages logging output.

cleanup
(self)¶ Clean up resources prior to exit.

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

compute_jacvec_product
(self, inputs, d_inputs, d_outputs, mode, discrete_inputs=None)¶ 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
 inputsVector
unscaled, dimensional input variables read via inputs[key]
 d_inputsVector
see inputs; product must be computed only if var_name in d_inputs
 d_outputsVector
see outputs; product must be computed only if var_name in d_outputs
 modestr
either ‘fwd’ or ‘rev’
 discrete_inputsdict or None
If not None, dict containing discrete input values.

declare_coloring
(self, wrt=('*', ), method='fd', form=None, step=None, per_instance=False, num_full_jacs=3, tol=1e25, orders=None, perturb_size=1e09, show_summary=True, show_sparsity=False)¶ Set options for deriv coloring of a set of wrt vars matching the given pattern(s).
 Parameters
 wrtstr or list of str
The name or names of the variables that derivatives are taken with respect to. This can contain input names, output names, or glob patterns.
 methodstr
Method used to compute derivative: “fd” for finite difference, “cs” for complex step.
 formstr
Finite difference form, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.
 stepfloat
Step size for finite difference. Leave undeclared to keep unchanged from previous or default value.
 per_instancebool
If True, a separate coloring will be generated for each instance of a given class. Otherwise, only one coloring for a given class will be generated and all instances of that class will use it.
 num_full_jacsint
Number of times to repeat partial jacobian computation when computing sparsity.
 tolfloat
Tolerance used to determine if an array entry is nonzero during sparsity determination.
 ordersint
Number of orders above and below the tolerance to check during the tolerance sweep.
 perturb_sizefloat
Size of input/output perturbation during generation of sparsity.
 show_summarybool
If True, display summary information after generating coloring.
 show_sparsitybool
If True, display sparsity with coloring info after generating coloring.

declare_partials
(self, 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
 ofstr or list of str
The name of the residual(s) that derivatives are being computed for. May also contain a glob pattern.
 wrtstr 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.
 dependentbool(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.
 rowsndarray of int or None
Row indices for each nonzero entry. For sparse subjacobians only.
 colsndarray of int or None
Column indices for each nonzero entry. For sparse subjacobians only.
 valfloat 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.
 methodstr
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’.
 stepfloat
Step size for approximation. Defaults to None, in which case the approximation method provides its default value.
 formstring
Form for finite difference, can be ‘forward’, ‘backward’, or ‘central’. Defaults to None, in which case the approximation method provides its default value.
 step_calcstring
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.
 Returns
 dict
Metadata dict for the specified partial(s).

property
distributed
¶ Provide ‘distributed’ property for backwards compatibility.
 Returns
 bool
reference to the ‘distributed’ option.

get_approx_coloring_fname
(self)¶ Return the full pathname to a coloring file.
 Parameters
 systemSystem
The System having its coloring saved or loaded.
 Returns
 str
Full pathname of the coloring file.

get_constraints
(self, 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
 recursebool, 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
(self, 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
 recursebool
If True, recurse through the subsystems and return the path of all design vars relative to the this system.
 get_sizesbool, optional
If True, compute the size of each design variable.
 Returns
 dict
The design variables defined in the current system and, if recurse=True, its subsystems.

get_linear_vectors
(self, vec_name='linear')¶ Return the linear inputs, outputs, and residuals vectors.
 Parameters
 vec_namestr
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
(self)¶ 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
(self, recurse=True)¶ Get the Objective settings from this system.
Retrieve all objectives settings from the system as a dict, keyed by variable name.
 Parameters
 recursebool, 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
(self, 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
 recursebool, optional
If True, recurse through the subsystems and return the path of all responses relative to the this system.
 get_sizesbool, 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
(self)¶ Perform any onetime initialization run at instantiation.

is_active
(self)¶ 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.

property
linear_solver
¶ Get the linear solver for this system.

list_inputs
(self, values=True, prom_name=False, units=False, shape=False, hierarchical=True, print_arrays=False, tags=None, out_stream=<object object at 0x7f1bddbe81f0>)¶ 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
 valuesbool, optional
When True, display/return input values. Default is True.
 prom_namebool, optional
When True, display/return the promoted name of the variable. Default is False.
 unitsbool, optional
When True, display/return units. Default is False.
 shapebool, optional
When True, display/return the shape of the value. Default is False.
 hierarchicalbool, optional
When True, human readable output shows variables in hierarchical format.
 print_arraysbool, 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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed. Only inputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.
 out_streamfilelike 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
(self, explicit=True, implicit=True, values=True, prom_name=False, residuals=False, residuals_tol=None, units=False, shape=False, bounds=False, scaling=False, hierarchical=True, print_arrays=False, tags=None, out_stream=<object object at 0x7f1bddbe81f0>)¶ 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
 explicitbool, optional
include outputs from explicit components. Default is True.
 implicitbool, optional
include outputs from implicit components. Default is True.
 valuesbool, optional
When True, display/return output values. Default is True.
 prom_namebool, optional
When True, display/return the promoted name of the variable. Default is False.
 residualsbool, optional
When True, display/return residual values. Default is False.
 residuals_tolfloat, 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.
 unitsbool, optional
When True, display/return units. Default is False.
 shapebool, optional
When True, display/return the shape of the value. Default is False.
 boundsbool, optional
When True, display/return bounds (lower and upper). Default is False.
 scalingbool, optional
When True, display/return scaling (ref, ref0, and res_ref). Default is False.
 hierarchicalbool, optional
When True, human readable output shows variables in hierarchical format.
 print_arraysbool, 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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed. Only outputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.
 out_streamfilelike
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

property
ln_solver
¶ Get the linear solver for this system.

property
metadata
¶ Get the options for this System.

property
msginfo
¶ Our instance pathname, if available, or our class name. For use in error messages.
 Returns
 str
Either our instance pathname or class name.

property
nl_solver
¶ Get the nonlinear solver for this system.

property
nonlinear_solver
¶ Get the nonlinear solver for this system.

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

record_iteration
(self)¶ Record an iteration of the current System.

resetup
(self, setup_mode='full')¶ Public wrapper for _setup that reconfigures after an initial setup has been performed.
 Parameters
 setup_modestr
Must be one of ‘full’, ‘reconf’, or ‘update’.

run_apply_linear
(self, 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.
 modestr
‘fwd’ or ‘rev’.
 scope_outset or None
Set of absolute output names in the scope of this matvec product. If None, all are in the scope.
 scope_inset or None
Set of absolute input names in the scope of this matvec product. If None, all are in the scope.

run_apply_nonlinear
(self)¶ Compute residuals.
This calls _apply_nonlinear, but with the model assumed to be in an unscaled state.

run_linearize
(self, sub_do_ln=True)¶ Compute jacobian / factorization.
This calls _linearize, but with the model assumed to be in an unscaled state.
 Parameters
 sub_do_lnboolean
Flag indicating if the children should call linearize on their linear solvers.

run_solve_linear
(self, 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.
 modestr
‘fwd’ or ‘rev’.

run_solve_nonlinear
(self)¶ Compute outputs.
This calls _solve_nonlinear, but with the model assumed to be in an unscaled state.

set_check_partial_options
(self, wrt, method='fd', form=None, step=None, step_calc=None, directional=False)¶ Set options that will be used for checking partial derivatives.
 Parameters
 wrtstr 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.
 methodstr
Method for check: “fd” for finite difference, “cs” for complex step.
 formstr
Finite difference form for check, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.
 stepfloat
Step size for finite difference check. Leave undeclared to keep unchanged from previous or default value.
 step_calcstr
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.
 directionalbool
Set to True to perform a single directional derivative for each vector variable in the pattern named in wrt.

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

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

system_iter
(self, include_self=False, recurse=True, typ=None)¶ Yield a generator of local subsystems of this system.
 Parameters
 include_selfbool
If True, include this system in the iteration.
 recursebool
If True, iterate over the whole tree under this system.
 typtype
If not None, only yield Systems that match that are instances of the given type.

use_fixed_coloring
(self, coloring=<object object at 0x7f1bde39daf0>, recurse=True)¶ Use a precomputed coloring for this System.
 Parameters
 coloringstr
A coloring filename. If no arg is passed, filename will be determined automatically.
 recursebool
If True, set fixed coloring in all subsystems that declare a coloring. Ignored if a specific coloring is passed in.


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

add_constraint
(self, name, lower=None, upper=None, equals=None, ref=None, ref0=None, adder=None, scaler=None, indices=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a constraint variable to this system.
 Parameters
 namestring
Name of the response variable in the system.
 lowerfloat or ndarray, optional
Lower boundary for the variable
 upperfloat or ndarray, optional
Upper boundary for the variable
 equalsfloat or ndarray, optional
Equality constraint value for the variable
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 indicessequence 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.
 linearbool
Set to True if constraint is linear. Default is False.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, name, lower=None, upper=None, ref=None, ref0=None, indices=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a design variable to this system.
 Parameters
 namestring
Name of the design variable in the system.
 lowerfloat or ndarray, optional
Lower boundary for the param
 upperupper or ndarray, optional
Upper boundary for the param
 reffloat or ndarray, optional
Value of design var that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of design var that scales to 0.0 in the driver.
 indicesiter 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.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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_discrete_input
(self, name, val, desc='', tags=None)¶ Add a discrete input variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 vala picklable object
The initial value of the variable being added.
 descstr
description of the variable
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_discrete_output
(self, name, val, desc='', tags=None)¶ Add an output variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 vala picklable object
The initial value of the variable being added.
 descstr
description of the variable.
 tagsstr or list of strs or set of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_input
(self, name, val=1.0, shape=None, src_indices=None, flat_src_indices=None, units=None, desc='', tags=None)¶ Add an input variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 valfloat or list or tuple or ndarray or Iterable
The initial value of the variable being added in userdefined units. Default is 1.0.
 shapeint 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_indicesint 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_indicesbool
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.
 unitsstr or None
Units in which this input variable will be provided to the component during execution. Default is None, which means it is unitless.
 descstr
description of the variable
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_objective
(self, name, ref=None, ref0=None, index=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a response variable to this system.
 Parameters
 namestring
Name of the response variable in the system.
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 indexint, 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.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, 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, tags=None)¶ Add an output variable to the component.
For ExplicitComponent, res_ref defaults to the value in res unless otherwise specified.
 Parameters
 namestr
name of the variable in this component’s namespace.
 valfloat or list or tuple or ndarray
The initial value of the variable being added in userdefined units. Default is 1.0.
 shapeint or tuple or list or None
Shape of this variable, only required if val is not an array. Default is None.
 unitsstr 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_unitsstr 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.
 descstr
description of the variable.
 lowerfloat 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.
 upperfloat 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.
 reffloat
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 1. Default is 1.
 ref0float
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 0. Default is 0.
 res_reffloat
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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs and also when listing results from case recorders.
 Returns
 dict
metadata for added variable

add_recorder
(self, recorder, recurse=False)¶ Add a recorder to the system.
 Parameters
 recorder<CaseRecorder>
A recorder instance.
 recurseboolean
Flag indicating if the recorder should be added to all the subsystems.

add_response
(self, name, type_, lower=None, upper=None, equals=None, ref=None, ref0=None, indices=None, index=None, adder=None, scaler=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a response variable to this system.
The response can be scaled using ref and ref0. The argument
ref0
represents the physical value when the scaled value is 0. The argumentref
represents the physical value when the scaled value is 1. Parameters
 namestring
Name of the response variable in the system.
 type_string
The type of response. Supported values are ‘con’ and ‘obj’
 lowerfloat or ndarray, optional
Lower boundary for the variable
 upperupper or ndarray, optional
Upper boundary for the variable
 equalsequals or ndarray, optional
Equality constraint value for the variable
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0upper or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 indicessequence of int, optional
If variable is an array, these indicate which entries are of interest for this particular response.
 indexint, optional
If variable is an array, this indicates which entry is of interest for this particular response.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 linearbool
Set to True if constraint is linear. Default is False.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, logger)¶ Perform optional error checks.
 Parameters
 loggerobject
The object that manages logging output.

cleanup
(self)¶ Clean up resources prior to exit.

compute_jacvec_product
(self, inputs, d_inputs, d_outputs, mode, discrete_inputs=None)¶ 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
 inputsVector
unscaled, dimensional input variables read via inputs[key]
 d_inputsVector
see inputs; product must be computed only if var_name in d_inputs
 d_outputsVector
see outputs; product must be computed only if var_name in d_outputs
 modestr
either ‘fwd’ or ‘rev’
 discrete_inputsdict or None
If not None, dict containing discrete input values.

compute_partials
(self, inputs, partials, discrete_inputs=None)¶ Compute subjacobian parts. The model is assumed to be in an unscaled state.
 Parameters
 inputsVector
unscaled, dimensional input variables read via inputs[key]
 partialsJacobian
subjac components written to partials[output_name, input_name]
 discrete_inputsdict or None
If not None, dict containing discrete input values.

declare_coloring
(self, wrt=('*', ), method='fd', form=None, step=None, per_instance=False, num_full_jacs=3, tol=1e25, orders=None, perturb_size=1e09, show_summary=True, show_sparsity=False)¶ Set options for deriv coloring of a set of wrt vars matching the given pattern(s).
 Parameters
 wrtstr or list of str
The name or names of the variables that derivatives are taken with respect to. This can contain input names, output names, or glob patterns.
 methodstr
Method used to compute derivative: “fd” for finite difference, “cs” for complex step.
 formstr
Finite difference form, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.
 stepfloat
Step size for finite difference. Leave undeclared to keep unchanged from previous or default value.
 per_instancebool
If True, a separate coloring will be generated for each instance of a given class. Otherwise, only one coloring for a given class will be generated and all instances of that class will use it.
 num_full_jacsint
Number of times to repeat partial jacobian computation when computing sparsity.
 tolfloat
Tolerance used to determine if an array entry is nonzero during sparsity determination.
 ordersint
Number of orders above and below the tolerance to check during the tolerance sweep.
 perturb_sizefloat
Size of input/output perturbation during generation of sparsity.
 show_summarybool
If True, display summary information after generating coloring.
 show_sparsitybool
If True, display sparsity with coloring info after generating coloring.

declare_partials
(self, 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
 ofstr or list of str
The name of the residual(s) that derivatives are being computed for. May also contain a glob pattern.
 wrtstr 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.
 dependentbool(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.
 rowsndarray of int or None
Row indices for each nonzero entry. For sparse subjacobians only.
 colsndarray of int or None
Column indices for each nonzero entry. For sparse subjacobians only.
 valfloat 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.
 methodstr
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’.
 stepfloat
Step size for approximation. Defaults to None, in which case the approximation method provides its default value.
 formstring
Form for finite difference, can be ‘forward’, ‘backward’, or ‘central’. Defaults to None, in which case the approximation method provides its default value.
 step_calcstring
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.
 Returns
 dict
Metadata dict for the specified partial(s).

property
distributed
¶ Provide ‘distributed’ property for backwards compatibility.
 Returns
 bool
reference to the ‘distributed’ option.

get_approx_coloring_fname
(self)¶ Return the full pathname to a coloring file.
 Parameters
 systemSystem
The System having its coloring saved or loaded.
 Returns
 str
Full pathname of the coloring file.

get_constraints
(self, 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
 recursebool, 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
(self, 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
 recursebool
If True, recurse through the subsystems and return the path of all design vars relative to the this system.
 get_sizesbool, optional
If True, compute the size of each design variable.
 Returns
 dict
The design variables defined in the current system and, if recurse=True, its subsystems.

get_linear_vectors
(self, vec_name='linear')¶ Return the linear inputs, outputs, and residuals vectors.
 Parameters
 vec_namestr
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
(self)¶ 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
(self, recurse=True)¶ Get the Objective settings from this system.
Retrieve all objectives settings from the system as a dict, keyed by variable name.
 Parameters
 recursebool, 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
(self, 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
 recursebool, optional
If True, recurse through the subsystems and return the path of all responses relative to the this system.
 get_sizesbool, 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
(self)¶ Perform any onetime initialization run at instantiation.

is_active
(self)¶ 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.

property
linear_solver
¶ Get the linear solver for this system.

list_inputs
(self, values=True, prom_name=False, units=False, shape=False, hierarchical=True, print_arrays=False, tags=None, out_stream=<object object at 0x7f1bddbe81f0>)¶ 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
 valuesbool, optional
When True, display/return input values. Default is True.
 prom_namebool, optional
When True, display/return the promoted name of the variable. Default is False.
 unitsbool, optional
When True, display/return units. Default is False.
 shapebool, optional
When True, display/return the shape of the value. Default is False.
 hierarchicalbool, optional
When True, human readable output shows variables in hierarchical format.
 print_arraysbool, 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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed. Only inputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.
 out_streamfilelike 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
(self, explicit=True, implicit=True, values=True, prom_name=False, residuals=False, residuals_tol=None, units=False, shape=False, bounds=False, scaling=False, hierarchical=True, print_arrays=False, tags=None, out_stream=<object object at 0x7f1bddbe81f0>)¶ 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
 explicitbool, optional
include outputs from explicit components. Default is True.
 implicitbool, optional
include outputs from implicit components. Default is True.
 valuesbool, optional
When True, display/return output values. Default is True.
 prom_namebool, optional
When True, display/return the promoted name of the variable. Default is False.
 residualsbool, optional
When True, display/return residual values. Default is False.
 residuals_tolfloat, 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.
 unitsbool, optional
When True, display/return units. Default is False.
 shapebool, optional
When True, display/return the shape of the value. Default is False.
 boundsbool, optional
When True, display/return bounds (lower and upper). Default is False.
 scalingbool, optional
When True, display/return scaling (ref, ref0, and res_ref). Default is False.
 hierarchicalbool, optional
When True, human readable output shows variables in hierarchical format.
 print_arraysbool, 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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed. Only outputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.
 out_streamfilelike
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

property
ln_solver
¶ Get the linear solver for this system.

property
metadata
¶ Get the options for this System.

property
msginfo
¶ Our instance pathname, if available, or our class name. For use in error messages.
 Returns
 str
Either our instance pathname or class name.

property
nl_solver
¶ Get the nonlinear solver for this system.

property
nonlinear_solver
¶ Get the nonlinear solver for this system.

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

record_iteration
(self)¶ Record an iteration of the current System.

resetup
(self, setup_mode='full')¶ Public wrapper for _setup that reconfigures after an initial setup has been performed.
 Parameters
 setup_modestr
Must be one of ‘full’, ‘reconf’, or ‘update’.

run_apply_linear
(self, 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.
 modestr
‘fwd’ or ‘rev’.
 scope_outset or None
Set of absolute output names in the scope of this matvec product. If None, all are in the scope.
 scope_inset or None
Set of absolute input names in the scope of this matvec product. If None, all are in the scope.

run_apply_nonlinear
(self)¶ Compute residuals.
This calls _apply_nonlinear, but with the model assumed to be in an unscaled state.

run_linearize
(self, sub_do_ln=True)¶ Compute jacobian / factorization.
This calls _linearize, but with the model assumed to be in an unscaled state.
 Parameters
 sub_do_lnboolean
Flag indicating if the children should call linearize on their linear solvers.

run_solve_linear
(self, 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.
 modestr
‘fwd’ or ‘rev’.

run_solve_nonlinear
(self)¶ Compute outputs.
This calls _solve_nonlinear, but with the model assumed to be in an unscaled state.

set_check_partial_options
(self, wrt, method='fd', form=None, step=None, step_calc=None, directional=False)¶ Set options that will be used for checking partial derivatives.
 Parameters
 wrtstr 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.
 methodstr
Method for check: “fd” for finite difference, “cs” for complex step.
 formstr
Finite difference form for check, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.
 stepfloat
Step size for finite difference check. Leave undeclared to keep unchanged from previous or default value.
 step_calcstr
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.
 directionalbool
Set to True to perform a single directional derivative for each vector variable in the pattern named in wrt.

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

system_iter
(self, include_self=False, recurse=True, typ=None)¶ Yield a generator of local subsystems of this system.
 Parameters
 include_selfbool
If True, include this system in the iteration.
 recursebool
If True, iterate over the whole tree under this system.
 typtype
If not None, only yield Systems that match that are instances of the given type.

use_fixed_coloring
(self, coloring=<object object at 0x7f1bde39daf0>, recurse=True)¶ Use a precomputed coloring for this System.
 Parameters
 coloringstr
A coloring filename. If no arg is passed, filename will be determined automatically.
 recursebool
If True, set fixed coloring in all subsystems that declare a coloring. Ignored if a specific coloring is passed in.


class
openmdao.test_suite.components.sellar.
SellarDis2CS
(units=None, scaling=None)[source]¶ Bases:
openmdao.test_suite.components.sellar.SellarDis2
Component containing Discipline 2 – complex step version.

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

add_constraint
(self, name, lower=None, upper=None, equals=None, ref=None, ref0=None, adder=None, scaler=None, indices=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a constraint variable to this system.
 Parameters
 namestring
Name of the response variable in the system.
 lowerfloat or ndarray, optional
Lower boundary for the variable
 upperfloat or ndarray, optional
Upper boundary for the variable
 equalsfloat or ndarray, optional
Equality constraint value for the variable
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 indicessequence 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.
 linearbool
Set to True if constraint is linear. Default is False.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, name, lower=None, upper=None, ref=None, ref0=None, indices=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a design variable to this system.
 Parameters
 namestring
Name of the design variable in the system.
 lowerfloat or ndarray, optional
Lower boundary for the param
 upperupper or ndarray, optional
Upper boundary for the param
 reffloat or ndarray, optional
Value of design var that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of design var that scales to 0.0 in the driver.
 indicesiter 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.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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_discrete_input
(self, name, val, desc='', tags=None)¶ Add a discrete input variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 vala picklable object
The initial value of the variable being added.
 descstr
description of the variable
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_discrete_output
(self, name, val, desc='', tags=None)¶ Add an output variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 vala picklable object
The initial value of the variable being added.
 descstr
description of the variable.
 tagsstr or list of strs or set of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_input
(self, name, val=1.0, shape=None, src_indices=None, flat_src_indices=None, units=None, desc='', tags=None)¶ Add an input variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 valfloat or list or tuple or ndarray or Iterable
The initial value of the variable being added in userdefined units. Default is 1.0.
 shapeint 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_indicesint 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_indicesbool
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.
 unitsstr or None
Units in which this input variable will be provided to the component during execution. Default is None, which means it is unitless.
 descstr
description of the variable
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_objective
(self, name, ref=None, ref0=None, index=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a response variable to this system.
 Parameters
 namestring
Name of the response variable in the system.
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 indexint, 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.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, 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, tags=None)¶ Add an output variable to the component.
For ExplicitComponent, res_ref defaults to the value in res unless otherwise specified.
 Parameters
 namestr
name of the variable in this component’s namespace.
 valfloat or list or tuple or ndarray
The initial value of the variable being added in userdefined units. Default is 1.0.
 shapeint or tuple or list or None
Shape of this variable, only required if val is not an array. Default is None.
 unitsstr 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_unitsstr 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.
 descstr
description of the variable.
 lowerfloat 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.
 upperfloat 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.
 reffloat
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 1. Default is 1.
 ref0float
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 0. Default is 0.
 res_reffloat
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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs and also when listing results from case recorders.
 Returns
 dict
metadata for added variable

add_recorder
(self, recorder, recurse=False)¶ Add a recorder to the system.
 Parameters
 recorder<CaseRecorder>
A recorder instance.
 recurseboolean
Flag indicating if the recorder should be added to all the subsystems.

add_response
(self, name, type_, lower=None, upper=None, equals=None, ref=None, ref0=None, indices=None, index=None, adder=None, scaler=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a response variable to this system.
The response can be scaled using ref and ref0. The argument
ref0
represents the physical value when the scaled value is 0. The argumentref
represents the physical value when the scaled value is 1. Parameters
 namestring
Name of the response variable in the system.
 type_string
The type of response. Supported values are ‘con’ and ‘obj’
 lowerfloat or ndarray, optional
Lower boundary for the variable
 upperupper or ndarray, optional
Upper boundary for the variable
 equalsequals or ndarray, optional
Equality constraint value for the variable
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0upper or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 indicessequence of int, optional
If variable is an array, these indicate which entries are of interest for this particular response.
 indexint, optional
If variable is an array, this indicates which entry is of interest for this particular response.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 linearbool
Set to True if constraint is linear. Default is False.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, logger)¶ Perform optional error checks.
 Parameters
 loggerobject
The object that manages logging output.

cleanup
(self)¶ Clean up resources prior to exit.

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

compute_jacvec_product
(self, inputs, d_inputs, d_outputs, mode, discrete_inputs=None)¶ 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
 inputsVector
unscaled, dimensional input variables read via inputs[key]
 d_inputsVector
see inputs; product must be computed only if var_name in d_inputs
 d_outputsVector
see outputs; product must be computed only if var_name in d_outputs
 modestr
either ‘fwd’ or ‘rev’
 discrete_inputsdict or None
If not None, dict containing discrete input values.

compute_partials
(self, inputs, partials, discrete_inputs=None)¶ Compute subjacobian parts. The model is assumed to be in an unscaled state.
 Parameters
 inputsVector
unscaled, dimensional input variables read via inputs[key]
 partialsJacobian
subjac components written to partials[output_name, input_name]
 discrete_inputsdict or None
If not None, dict containing discrete input values.

declare_coloring
(self, wrt=('*', ), method='fd', form=None, step=None, per_instance=False, num_full_jacs=3, tol=1e25, orders=None, perturb_size=1e09, show_summary=True, show_sparsity=False)¶ Set options for deriv coloring of a set of wrt vars matching the given pattern(s).
 Parameters
 wrtstr or list of str
The name or names of the variables that derivatives are taken with respect to. This can contain input names, output names, or glob patterns.
 methodstr
Method used to compute derivative: “fd” for finite difference, “cs” for complex step.
 formstr
Finite difference form, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.
 stepfloat
Step size for finite difference. Leave undeclared to keep unchanged from previous or default value.
 per_instancebool
If True, a separate coloring will be generated for each instance of a given class. Otherwise, only one coloring for a given class will be generated and all instances of that class will use it.
 num_full_jacsint
Number of times to repeat partial jacobian computation when computing sparsity.
 tolfloat
Tolerance used to determine if an array entry is nonzero during sparsity determination.
 ordersint
Number of orders above and below the tolerance to check during the tolerance sweep.
 perturb_sizefloat
Size of input/output perturbation during generation of sparsity.
 show_summarybool
If True, display summary information after generating coloring.
 show_sparsitybool
If True, display sparsity with coloring info after generating coloring.

declare_partials
(self, 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
 ofstr or list of str
The name of the residual(s) that derivatives are being computed for. May also contain a glob pattern.
 wrtstr 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.
 dependentbool(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.
 rowsndarray of int or None
Row indices for each nonzero entry. For sparse subjacobians only.
 colsndarray of int or None
Column indices for each nonzero entry. For sparse subjacobians only.
 valfloat 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.
 methodstr
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’.
 stepfloat
Step size for approximation. Defaults to None, in which case the approximation method provides its default value.
 formstring
Form for finite difference, can be ‘forward’, ‘backward’, or ‘central’. Defaults to None, in which case the approximation method provides its default value.
 step_calcstring
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.
 Returns
 dict
Metadata dict for the specified partial(s).

property
distributed
¶ Provide ‘distributed’ property for backwards compatibility.
 Returns
 bool
reference to the ‘distributed’ option.

get_approx_coloring_fname
(self)¶ Return the full pathname to a coloring file.
 Parameters
 systemSystem
The System having its coloring saved or loaded.
 Returns
 str
Full pathname of the coloring file.

get_constraints
(self, 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
 recursebool, 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
(self, 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
 recursebool
If True, recurse through the subsystems and return the path of all design vars relative to the this system.
 get_sizesbool, optional
If True, compute the size of each design variable.
 Returns
 dict
The design variables defined in the current system and, if recurse=True, its subsystems.

get_linear_vectors
(self, vec_name='linear')¶ Return the linear inputs, outputs, and residuals vectors.
 Parameters
 vec_namestr
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
(self)¶ 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
(self, recurse=True)¶ Get the Objective settings from this system.
Retrieve all objectives settings from the system as a dict, keyed by variable name.
 Parameters
 recursebool, 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
(self, 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
 recursebool, optional
If True, recurse through the subsystems and return the path of all responses relative to the this system.
 get_sizesbool, 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
(self)¶ Perform any onetime initialization run at instantiation.

is_active
(self)¶ 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.

property
linear_solver
¶ Get the linear solver for this system.

list_inputs
(self, values=True, prom_name=False, units=False, shape=False, hierarchical=True, print_arrays=False, tags=None, out_stream=<object object at 0x7f1bddbe81f0>)¶ 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
 valuesbool, optional
When True, display/return input values. Default is True.
 prom_namebool, optional
When True, display/return the promoted name of the variable. Default is False.
 unitsbool, optional
When True, display/return units. Default is False.
 shapebool, optional
When True, display/return the shape of the value. Default is False.
 hierarchicalbool, optional
When True, human readable output shows variables in hierarchical format.
 print_arraysbool, 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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed. Only inputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.
 out_streamfilelike 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
(self, explicit=True, implicit=True, values=True, prom_name=False, residuals=False, residuals_tol=None, units=False, shape=False, bounds=False, scaling=False, hierarchical=True, print_arrays=False, tags=None, out_stream=<object object at 0x7f1bddbe81f0>)¶ 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
 explicitbool, optional
include outputs from explicit components. Default is True.
 implicitbool, optional
include outputs from implicit components. Default is True.
 valuesbool, optional
When True, display/return output values. Default is True.
 prom_namebool, optional
When True, display/return the promoted name of the variable. Default is False.
 residualsbool, optional
When True, display/return residual values. Default is False.
 residuals_tolfloat, 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.
 unitsbool, optional
When True, display/return units. Default is False.
 shapebool, optional
When True, display/return the shape of the value. Default is False.
 boundsbool, optional
When True, display/return bounds (lower and upper). Default is False.
 scalingbool, optional
When True, display/return scaling (ref, ref0, and res_ref). Default is False.
 hierarchicalbool, optional
When True, human readable output shows variables in hierarchical format.
 print_arraysbool, 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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed. Only outputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.
 out_streamfilelike
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

property
ln_solver
¶ Get the linear solver for this system.

property
metadata
¶ Get the options for this System.

property
msginfo
¶ Our instance pathname, if available, or our class name. For use in error messages.
 Returns
 str
Either our instance pathname or class name.

property
nl_solver
¶ Get the nonlinear solver for this system.

property
nonlinear_solver
¶ Get the nonlinear solver for this system.

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

record_iteration
(self)¶ Record an iteration of the current System.

resetup
(self, setup_mode='full')¶ Public wrapper for _setup that reconfigures after an initial setup has been performed.
 Parameters
 setup_modestr
Must be one of ‘full’, ‘reconf’, or ‘update’.

run_apply_linear
(self, 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.
 modestr
‘fwd’ or ‘rev’.
 scope_outset or None
Set of absolute output names in the scope of this matvec product. If None, all are in the scope.
 scope_inset or None
Set of absolute input names in the scope of this matvec product. If None, all are in the scope.

run_apply_nonlinear
(self)¶ Compute residuals.
This calls _apply_nonlinear, but with the model assumed to be in an unscaled state.

run_linearize
(self, sub_do_ln=True)¶ Compute jacobian / factorization.
This calls _linearize, but with the model assumed to be in an unscaled state.
 Parameters
 sub_do_lnboolean
Flag indicating if the children should call linearize on their linear solvers.

run_solve_linear
(self, 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.
 modestr
‘fwd’ or ‘rev’.

run_solve_nonlinear
(self)¶ Compute outputs.
This calls _solve_nonlinear, but with the model assumed to be in an unscaled state.

set_check_partial_options
(self, wrt, method='fd', form=None, step=None, step_calc=None, directional=False)¶ Set options that will be used for checking partial derivatives.
 Parameters
 wrtstr 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.
 methodstr
Method for check: “fd” for finite difference, “cs” for complex step.
 formstr
Finite difference form for check, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.
 stepfloat
Step size for finite difference check. Leave undeclared to keep unchanged from previous or default value.
 step_calcstr
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.
 directionalbool
Set to True to perform a single directional derivative for each vector variable in the pattern named in wrt.

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

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

system_iter
(self, include_self=False, recurse=True, typ=None)¶ Yield a generator of local subsystems of this system.
 Parameters
 include_selfbool
If True, include this system in the iteration.
 recursebool
If True, iterate over the whole tree under this system.
 typtype
If not None, only yield Systems that match that are instances of the given type.

use_fixed_coloring
(self, coloring=<object object at 0x7f1bde39daf0>, recurse=True)¶ Use a precomputed coloring for this System.
 Parameters
 coloringstr
A coloring filename. If no arg is passed, filename will be determined automatically.
 recursebool
If True, set fixed coloring in all subsystems that declare a coloring. Ignored if a specific coloring is passed in.


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

add_constraint
(self, name, lower=None, upper=None, equals=None, ref=None, ref0=None, adder=None, scaler=None, indices=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a constraint variable to this system.
 Parameters
 namestring
Name of the response variable in the system.
 lowerfloat or ndarray, optional
Lower boundary for the variable
 upperfloat or ndarray, optional
Upper boundary for the variable
 equalsfloat or ndarray, optional
Equality constraint value for the variable
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 indicessequence 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.
 linearbool
Set to True if constraint is linear. Default is False.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, name, lower=None, upper=None, ref=None, ref0=None, indices=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a design variable to this system.
 Parameters
 namestring
Name of the design variable in the system.
 lowerfloat or ndarray, optional
Lower boundary for the param
 upperupper or ndarray, optional
Upper boundary for the param
 reffloat or ndarray, optional
Value of design var that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of design var that scales to 0.0 in the driver.
 indicesiter 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.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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_discrete_input
(self, name, val, desc='', tags=None)¶ Add a discrete input variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 vala picklable object
The initial value of the variable being added.
 descstr
description of the variable
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_discrete_output
(self, name, val, desc='', tags=None)¶ Add an output variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 vala picklable object
The initial value of the variable being added.
 descstr
description of the variable.
 tagsstr or list of strs or set of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_input
(self, name, val=1.0, shape=None, src_indices=None, flat_src_indices=None, units=None, desc='', tags=None)¶ Add an input variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 valfloat or list or tuple or ndarray or Iterable
The initial value of the variable being added in userdefined units. Default is 1.0.
 shapeint 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_indicesint 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_indicesbool
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.
 unitsstr or None
Units in which this input variable will be provided to the component during execution. Default is None, which means it is unitless.
 descstr
description of the variable
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_objective
(self, name, ref=None, ref0=None, index=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a response variable to this system.
 Parameters
 namestring
Name of the response variable in the system.
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 indexint, 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.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, 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, tags=None)¶ Add an output variable to the component.
For ExplicitComponent, res_ref defaults to the value in res unless otherwise specified.
 Parameters
 namestr
name of the variable in this component’s namespace.
 valfloat or list or tuple or ndarray
The initial value of the variable being added in userdefined units. Default is 1.0.
 shapeint or tuple or list or None
Shape of this variable, only required if val is not an array. Default is None.
 unitsstr 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_unitsstr 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.
 descstr
description of the variable.
 lowerfloat 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.
 upperfloat 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.
 reffloat
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 1. Default is 1.
 ref0float
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 0. Default is 0.
 res_reffloat
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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs and also when listing results from case recorders.
 Returns
 dict
metadata for added variable

add_recorder
(self, recorder, recurse=False)¶ Add a recorder to the system.
 Parameters
 recorder<CaseRecorder>
A recorder instance.
 recurseboolean
Flag indicating if the recorder should be added to all the subsystems.

add_response
(self, name, type_, lower=None, upper=None, equals=None, ref=None, ref0=None, indices=None, index=None, adder=None, scaler=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a response variable to this system.
The response can be scaled using ref and ref0. The argument
ref0
represents the physical value when the scaled value is 0. The argumentref
represents the physical value when the scaled value is 1. Parameters
 namestring
Name of the response variable in the system.
 type_string
The type of response. Supported values are ‘con’ and ‘obj’
 lowerfloat or ndarray, optional
Lower boundary for the variable
 upperupper or ndarray, optional
Upper boundary for the variable
 equalsequals or ndarray, optional
Equality constraint value for the variable
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0upper or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 indicessequence of int, optional
If variable is an array, these indicate which entries are of interest for this particular response.
 indexint, optional
If variable is an array, this indicates which entry is of interest for this particular response.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 linearbool
Set to True if constraint is linear. Default is False.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, logger)¶ Perform optional error checks.
 Parameters
 loggerobject
The object that manages logging output.

cleanup
(self)¶ Clean up resources prior to exit.

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

compute_jacvec_product
(self, inputs, d_inputs, d_outputs, mode, discrete_inputs=None)¶ 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
 inputsVector
unscaled, dimensional input variables read via inputs[key]
 d_inputsVector
see inputs; product must be computed only if var_name in d_inputs
 d_outputsVector
see outputs; product must be computed only if var_name in d_outputs
 modestr
either ‘fwd’ or ‘rev’
 discrete_inputsdict or None
If not None, dict containing discrete input values.

declare_coloring
(self, wrt=('*', ), method='fd', form=None, step=None, per_instance=False, num_full_jacs=3, tol=1e25, orders=None, perturb_size=1e09, show_summary=True, show_sparsity=False)¶ Set options for deriv coloring of a set of wrt vars matching the given pattern(s).
 Parameters
 wrtstr or list of str
The name or names of the variables that derivatives are taken with respect to. This can contain input names, output names, or glob patterns.
 methodstr
Method used to compute derivative: “fd” for finite difference, “cs” for complex step.
 formstr
Finite difference form, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.
 stepfloat
Step size for finite difference. Leave undeclared to keep unchanged from previous or default value.
 per_instancebool
If True, a separate coloring will be generated for each instance of a given class. Otherwise, only one coloring for a given class will be generated and all instances of that class will use it.
 num_full_jacsint
Number of times to repeat partial jacobian computation when computing sparsity.
 tolfloat
Tolerance used to determine if an array entry is nonzero during sparsity determination.
 ordersint
Number of orders above and below the tolerance to check during the tolerance sweep.
 perturb_sizefloat
Size of input/output perturbation during generation of sparsity.
 show_summarybool
If True, display summary information after generating coloring.
 show_sparsitybool
If True, display sparsity with coloring info after generating coloring.

declare_partials
(self, 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
 ofstr or list of str
The name of the residual(s) that derivatives are being computed for. May also contain a glob pattern.
 wrtstr 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.
 dependentbool(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.
 rowsndarray of int or None
Row indices for each nonzero entry. For sparse subjacobians only.
 colsndarray of int or None
Column indices for each nonzero entry. For sparse subjacobians only.
 valfloat 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.
 methodstr
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’.
 stepfloat
Step size for approximation. Defaults to None, in which case the approximation method provides its default value.
 formstring
Form for finite difference, can be ‘forward’, ‘backward’, or ‘central’. Defaults to None, in which case the approximation method provides its default value.
 step_calcstring
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.
 Returns
 dict
Metadata dict for the specified partial(s).

property
distributed
¶ Provide ‘distributed’ property for backwards compatibility.
 Returns
 bool
reference to the ‘distributed’ option.

get_approx_coloring_fname
(self)¶ Return the full pathname to a coloring file.
 Parameters
 systemSystem
The System having its coloring saved or loaded.
 Returns
 str
Full pathname of the coloring file.

get_constraints
(self, 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
 recursebool, 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
(self, 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
 recursebool
If True, recurse through the subsystems and return the path of all design vars relative to the this system.
 get_sizesbool, optional
If True, compute the size of each design variable.
 Returns
 dict
The design variables defined in the current system and, if recurse=True, its subsystems.

get_linear_vectors
(self, vec_name='linear')¶ Return the linear inputs, outputs, and residuals vectors.
 Parameters
 vec_namestr
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
(self)¶ 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
(self, recurse=True)¶ Get the Objective settings from this system.
Retrieve all objectives settings from the system as a dict, keyed by variable name.
 Parameters
 recursebool, 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
(self, 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
 recursebool, optional
If True, recurse through the subsystems and return the path of all responses relative to the this system.
 get_sizesbool, 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
(self)¶ Perform any onetime initialization run at instantiation.

is_active
(self)¶ 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.

property
linear_solver
¶ Get the linear solver for this system.

list_inputs
(self, values=True, prom_name=False, units=False, shape=False, hierarchical=True, print_arrays=False, tags=None, out_stream=<object object at 0x7f1bddbe81f0>)¶ 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
 valuesbool, optional
When True, display/return input values. Default is True.
 prom_namebool, optional
When True, display/return the promoted name of the variable. Default is False.
 unitsbool, optional
When True, display/return units. Default is False.
 shapebool, optional
When True, display/return the shape of the value. Default is False.
 hierarchicalbool, optional
When True, human readable output shows variables in hierarchical format.
 print_arraysbool, 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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed. Only inputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.
 out_streamfilelike 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
(self, explicit=True, implicit=True, values=True, prom_name=False, residuals=False, residuals_tol=None, units=False, shape=False, bounds=False, scaling=False, hierarchical=True, print_arrays=False, tags=None, out_stream=<object object at 0x7f1bddbe81f0>)¶ 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
 explicitbool, optional
include outputs from explicit components. Default is True.
 implicitbool, optional
include outputs from implicit components. Default is True.
 valuesbool, optional
When True, display/return output values. Default is True.
 prom_namebool, optional
When True, display/return the promoted name of the variable. Default is False.
 residualsbool, optional
When True, display/return residual values. Default is False.
 residuals_tolfloat, 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.
 unitsbool, optional
When True, display/return units. Default is False.
 shapebool, optional
When True, display/return the shape of the value. Default is False.
 boundsbool, optional
When True, display/return bounds (lower and upper). Default is False.
 scalingbool, optional
When True, display/return scaling (ref, ref0, and res_ref). Default is False.
 hierarchicalbool, optional
When True, human readable output shows variables in hierarchical format.
 print_arraysbool, 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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed. Only outputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.
 out_streamfilelike
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

property
ln_solver
¶ Get the linear solver for this system.

property
metadata
¶ Get the options for this System.

property
msginfo
¶ Our instance pathname, if available, or our class name. For use in error messages.
 Returns
 str
Either our instance pathname or class name.

property
nl_solver
¶ Get the nonlinear solver for this system.

property
nonlinear_solver
¶ Get the nonlinear solver for this system.

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

record_iteration
(self)¶ Record an iteration of the current System.

resetup
(self, setup_mode='full')¶ Public wrapper for _setup that reconfigures after an initial setup has been performed.
 Parameters
 setup_modestr
Must be one of ‘full’, ‘reconf’, or ‘update’.

run_apply_linear
(self, 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.
 modestr
‘fwd’ or ‘rev’.
 scope_outset or None
Set of absolute output names in the scope of this matvec product. If None, all are in the scope.
 scope_inset or None
Set of absolute input names in the scope of this matvec product. If None, all are in the scope.

run_apply_nonlinear
(self)¶ Compute residuals.
This calls _apply_nonlinear, but with the model assumed to be in an unscaled state.

run_linearize
(self, sub_do_ln=True)¶ Compute jacobian / factorization.
This calls _linearize, but with the model assumed to be in an unscaled state.
 Parameters
 sub_do_lnboolean
Flag indicating if the children should call linearize on their linear solvers.

run_solve_linear
(self, 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.
 modestr
‘fwd’ or ‘rev’.

run_solve_nonlinear
(self)¶ Compute outputs.
This calls _solve_nonlinear, but with the model assumed to be in an unscaled state.

set_check_partial_options
(self, wrt, method='fd', form=None, step=None, step_calc=None, directional=False)¶ Set options that will be used for checking partial derivatives.
 Parameters
 wrtstr 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.
 methodstr
Method for check: “fd” for finite difference, “cs” for complex step.
 formstr
Finite difference form for check, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.
 stepfloat
Step size for finite difference check. Leave undeclared to keep unchanged from previous or default value.
 step_calcstr
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.
 directionalbool
Set to True to perform a single directional derivative for each vector variable in the pattern named in wrt.

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

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

system_iter
(self, include_self=False, recurse=True, typ=None)¶ Yield a generator of local subsystems of this system.
 Parameters
 include_selfbool
If True, include this system in the iteration.
 recursebool
If True, iterate over the whole tree under this system.
 typtype
If not None, only yield Systems that match that are instances of the given type.

use_fixed_coloring
(self, coloring=<object object at 0x7f1bde39daf0>, recurse=True)¶ Use a precomputed coloring for this System.
 Parameters
 coloringstr
A coloring filename. If no arg is passed, filename will be determined automatically.
 recursebool
If True, set fixed coloring in all subsystems that declare a coloring. Ignored if a specific coloring is passed in.


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

add_constraint
(self, name, lower=None, upper=None, equals=None, ref=None, ref0=None, adder=None, scaler=None, indices=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a constraint variable to this system.
 Parameters
 namestring
Name of the response variable in the system.
 lowerfloat or ndarray, optional
Lower boundary for the variable
 upperfloat or ndarray, optional
Upper boundary for the variable
 equalsfloat or ndarray, optional
Equality constraint value for the variable
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 indicessequence 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.
 linearbool
Set to True if constraint is linear. Default is False.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, name, lower=None, upper=None, ref=None, ref0=None, indices=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a design variable to this system.
 Parameters
 namestring
Name of the design variable in the system.
 lowerfloat or ndarray, optional
Lower boundary for the param
 upperupper or ndarray, optional
Upper boundary for the param
 reffloat or ndarray, optional
Value of design var that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of design var that scales to 0.0 in the driver.
 indicesiter 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.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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_discrete_input
(self, name, val, desc='', tags=None)¶ Add a discrete input variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 vala picklable object
The initial value of the variable being added.
 descstr
description of the variable
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_discrete_output
(self, name, val, desc='', tags=None)¶ Add an output variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 vala picklable object
The initial value of the variable being added.
 descstr
description of the variable.
 tagsstr or list of strs or set of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_input
(self, name, val=1.0, shape=None, src_indices=None, flat_src_indices=None, units=None, desc='', tags=None)¶ Add an input variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 valfloat or list or tuple or ndarray or Iterable
The initial value of the variable being added in userdefined units. Default is 1.0.
 shapeint 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_indicesint 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_indicesbool
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.
 unitsstr or None
Units in which this input variable will be provided to the component during execution. Default is None, which means it is unitless.
 descstr
description of the variable
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_objective
(self, name, ref=None, ref0=None, index=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a response variable to this system.
 Parameters
 namestring
Name of the response variable in the system.
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 indexint, 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.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, 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, tags=None)¶ Add an output variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 valfloat or list or tuple or ndarray
The initial value of the variable being added in userdefined units. Default is 1.0.
 shapeint or tuple or list or None
Shape of this variable, only required if val is not an array. Default is None.
 unitsstr 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_unitsstr 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.
 descstr
description of the variable.
 lowerfloat 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.
 upperfloat 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.
 reffloat or ndarray
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 1. Default is 1.
 ref0float or ndarray
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 0. Default is 0.
 res_reffloat 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.
 tagsstr or list of strs or set of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_recorder
(self, recorder, recurse=False)¶ Add a recorder to the system.
 Parameters
 recorder<CaseRecorder>
A recorder instance.
 recurseboolean
Flag indicating if the recorder should be added to all the subsystems.

add_response
(self, name, type_, lower=None, upper=None, equals=None, ref=None, ref0=None, indices=None, index=None, adder=None, scaler=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a response variable to this system.
The response can be scaled using ref and ref0. The argument
ref0
represents the physical value when the scaled value is 0. The argumentref
represents the physical value when the scaled value is 1. Parameters
 namestring
Name of the response variable in the system.
 type_string
The type of response. Supported values are ‘con’ and ‘obj’
 lowerfloat or ndarray, optional
Lower boundary for the variable
 upperupper or ndarray, optional
Upper boundary for the variable
 equalsequals or ndarray, optional
Equality constraint value for the variable
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0upper or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 indicessequence of int, optional
If variable is an array, these indicate which entries are of interest for this particular response.
 indexint, optional
If variable is an array, this indicates which entry is of interest for this particular response.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 linearbool
Set to True if constraint is linear. Default is False.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, 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
 inputsVector
unscaled, dimensional input variables read via inputs[key]
 outputsVector
unscaled, dimensional output variables read via outputs[key]
 d_inputsVector
see inputs; product must be computed only if var_name in d_inputs
 d_outputsVector
see outputs; product must be computed only if var_name in d_outputs
 d_residualsVector
see outputs
 modestr
either ‘fwd’ or ‘rev’

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

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

cleanup
(self)¶ Clean up resources prior to exit.

declare_coloring
(self, wrt=('*', ), method='fd', form=None, step=None, per_instance=False, num_full_jacs=3, tol=1e25, orders=None, perturb_size=1e09, show_summary=True, show_sparsity=False)¶ Set options for deriv coloring of a set of wrt vars matching the given pattern(s).
 Parameters
 wrtstr or list of str
The name or names of the variables that derivatives are taken with respect to. This can contain input names, output names, or glob patterns.
 methodstr
Method used to compute derivative: “fd” for finite difference, “cs” for complex step.
 formstr
Finite difference form, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.
 stepfloat
Step size for finite difference. Leave undeclared to keep unchanged from previous or default value.
 per_instancebool
If True, a separate coloring will be generated for each instance of a given class. Otherwise, only one coloring for a given class will be generated and all instances of that class will use it.
 num_full_jacsint
Number of times to repeat partial jacobian computation when computing sparsity.
 tolfloat
Tolerance used to determine if an array entry is nonzero during sparsity determination.
 ordersint
Number of orders above and below the tolerance to check during the tolerance sweep.
 perturb_sizefloat
Size of input/output perturbation during generation of sparsity.
 show_summarybool
If True, display summary information after generating coloring.
 show_sparsitybool
If True, display sparsity with coloring info after generating coloring.

declare_partials
(self, 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
 ofstr or list of str
The name of the residual(s) that derivatives are being computed for. May also contain a glob pattern.
 wrtstr 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.
 dependentbool(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.
 rowsndarray of int or None
Row indices for each nonzero entry. For sparse subjacobians only.
 colsndarray of int or None
Column indices for each nonzero entry. For sparse subjacobians only.
 valfloat 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.
 methodstr
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’.
 stepfloat
Step size for approximation. Defaults to None, in which case the approximation method provides its default value.
 formstring
Form for finite difference, can be ‘forward’, ‘backward’, or ‘central’. Defaults to None, in which case the approximation method provides its default value.
 step_calcstring
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.
 Returns
 dict
Metadata dict for the specified partial(s).

property
distributed
¶ Provide ‘distributed’ property for backwards compatibility.
 Returns
 bool
reference to the ‘distributed’ option.

get_approx_coloring_fname
(self)¶ Return the full pathname to a coloring file.
 Parameters
 systemSystem
The System having its coloring saved or loaded.
 Returns
 str
Full pathname of the coloring file.

get_constraints
(self, 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
 recursebool, 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
(self, 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
 recursebool
If True, recurse through the subsystems and return the path of all design vars relative to the this system.
 get_sizesbool, optional
If True, compute the size of each design variable.
 Returns
 dict
The design variables defined in the current system and, if recurse=True, its subsystems.

get_linear_vectors
(self, vec_name='linear')¶ Return the linear inputs, outputs, and residuals vectors.
 Parameters
 vec_namestr
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
(self)¶ 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
(self, recurse=True)¶ Get the Objective settings from this system.
Retrieve all objectives settings from the system as a dict, keyed by variable name.
 Parameters
 recursebool, 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
(self, 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
 recursebool, optional
If True, recurse through the subsystems and return the path of all responses relative to the this system.
 get_sizesbool, 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
(self, inputs, outputs, residuals, discrete_inputs=None, discrete_outputs=None)¶ Provide initial guess for states.
Override this method to set the initial guess for states.
 Parameters
 inputsVector
unscaled, dimensional input variables read via inputs[key]
 outputsVector
unscaled, dimensional output variables read via outputs[key]
 residualsVector
unscaled, dimensional residuals written to via residuals[key]
 discrete_inputsdict or None
If not None, dict containing discrete input values.
 discrete_outputsdict or None
If not None, dict containing discrete output values.

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

is_active
(self)¶ 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.

property
linear_solver
¶ Get the linear solver for this system.

list_inputs
(self, values=True, prom_name=False, units=False, shape=False, hierarchical=True, print_arrays=False, tags=None, out_stream=<object object at 0x7f1bddbe81f0>)¶ 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
 valuesbool, optional
When True, display/return input values. Default is True.
 prom_namebool, optional
When True, display/return the promoted name of the variable. Default is False.
 unitsbool, optional
When True, display/return units. Default is False.
 shapebool, optional
When True, display/return the shape of the value. Default is False.
 hierarchicalbool, optional
When True, human readable output shows variables in hierarchical format.
 print_arraysbool, 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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed. Only inputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.
 out_streamfilelike 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
(self, explicit=True, implicit=True, values=True, prom_name=False, residuals=False, residuals_tol=None, units=False, shape=False, bounds=False, scaling=False, hierarchical=True, print_arrays=False, tags=None, out_stream=<object object at 0x7f1bddbe81f0>)¶ 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
 explicitbool, optional
include outputs from explicit components. Default is True.
 implicitbool, optional
include outputs from implicit components. Default is True.
 valuesbool, optional
When True, display/return output values. Default is True.
 prom_namebool, optional
When True, display/return the promoted name of the variable. Default is False.
 residualsbool, optional
When True, display/return residual values. Default is False.
 residuals_tolfloat, 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.
 unitsbool, optional
When True, display/return units. Default is False.
 shapebool, optional
When True, display/return the shape of the value. Default is False.
 boundsbool, optional
When True, display/return bounds (lower and upper). Default is False.
 scalingbool, optional
When True, display/return scaling (ref, ref0, and res_ref). Default is False.
 hierarchicalbool, optional
When True, human readable output shows variables in hierarchical format.
 print_arraysbool, 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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed. Only outputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.
 out_streamfilelike
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

property
ln_solver
¶ Get the linear solver for this system.

property
metadata
¶ Get the options for this System.

property
msginfo
¶ Our instance pathname, if available, or our class name. For use in error messages.
 Returns
 str
Either our instance pathname or class name.

property
nl_solver
¶ Get the nonlinear solver for this system.

property
nonlinear_solver
¶ Get the nonlinear solver for this system.

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

record_iteration
(self)¶ Record an iteration of the current System.

resetup
(self, setup_mode='full')¶ Public wrapper for _setup that reconfigures after an initial setup has been performed.
 Parameters
 setup_modestr
Must be one of ‘full’, ‘reconf’, or ‘update’.

run_apply_linear
(self, 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.
 modestr
‘fwd’ or ‘rev’.
 scope_outset or None
Set of absolute output names in the scope of this matvec product. If None, all are in the scope.
 scope_inset or None
Set of absolute input names in the scope of this matvec product. If None, all are in the scope.

run_apply_nonlinear
(self)¶ Compute residuals.
This calls _apply_nonlinear, but with the model assumed to be in an unscaled state.

run_linearize
(self, sub_do_ln=True)¶ Compute jacobian / factorization.
This calls _linearize, but with the model assumed to be in an unscaled state.
 Parameters
 sub_do_lnboolean
Flag indicating if the children should call linearize on their linear solvers.

run_solve_linear
(self, 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.
 modestr
‘fwd’ or ‘rev’.

run_solve_nonlinear
(self)¶ Compute outputs.
This calls _solve_nonlinear, but with the model assumed to be in an unscaled state.

set_check_partial_options
(self, wrt, method='fd', form=None, step=None, step_calc=None, directional=False)¶ Set options that will be used for checking partial derivatives.
 Parameters
 wrtstr 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.
 methodstr
Method for check: “fd” for finite difference, “cs” for complex step.
 formstr
Finite difference form for check, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.
 stepfloat
Step size for finite difference check. Leave undeclared to keep unchanged from previous or default value.
 step_calcstr
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.
 directionalbool
Set to True to perform a single directional derivative for each vector variable in the pattern named in wrt.

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

solve_linear
(self, 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_outputsVector
unscaled, dimensional quantities read via d_outputs[key]
 d_residualsVector
unscaled, dimensional quantities read via d_residuals[key]
 modestr
either ‘fwd’ or ‘rev’

solve_nonlinear
(self, inputs, outputs)¶ Compute outputs given inputs. The model is assumed to be in an unscaled state.
 Parameters
 inputsVector
unscaled, dimensional input variables read via inputs[key]
 outputsVector
unscaled, dimensional output variables read via outputs[key]

system_iter
(self, include_self=False, recurse=True, typ=None)¶ Yield a generator of local subsystems of this system.
 Parameters
 include_selfbool
If True, include this system in the iteration.
 recursebool
If True, iterate over the whole tree under this system.
 typtype
If not None, only yield Systems that match that are instances of the given type.

use_fixed_coloring
(self, coloring=<object object at 0x7f1bde39daf0>, recurse=True)¶ Use a precomputed coloring for this System.
 Parameters
 coloringstr
A coloring filename. If no arg is passed, filename will be determined automatically.
 recursebool
If True, set fixed coloring in all subsystems that declare a coloring. Ignored if a specific coloring is passed in.


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

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

add_constraint
(self, name, lower=None, upper=None, equals=None, ref=None, ref0=None, adder=None, scaler=None, indices=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a constraint variable to this system.
 Parameters
 namestring
Name of the response variable in the system.
 lowerfloat or ndarray, optional
Lower boundary for the variable
 upperfloat or ndarray, optional
Upper boundary for the variable
 equalsfloat or ndarray, optional
Equality constraint value for the variable
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 indicessequence 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.
 linearbool
Set to True if constraint is linear. Default is False.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, name, lower=None, upper=None, ref=None, ref0=None, indices=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a design variable to this system.
 Parameters
 namestring
Name of the design variable in the system.
 lowerfloat or ndarray, optional
Lower boundary for the param
 upperupper or ndarray, optional
Upper boundary for the param
 reffloat or ndarray, optional
Value of design var that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of design var that scales to 0.0 in the driver.
 indicesiter 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.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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_discrete_input
(self, name, val, desc='', tags=None)¶ Add a discrete input variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 vala picklable object
The initial value of the variable being added.
 descstr
description of the variable
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_discrete_output
(self, name, val, desc='', tags=None)¶ Add an output variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 vala picklable object
The initial value of the variable being added.
 descstr
description of the variable.
 tagsstr or list of strs or set of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_input
(self, name, val=1.0, shape=None, src_indices=None, flat_src_indices=None, units=None, desc='', tags=None)¶ Add an input variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 valfloat or list or tuple or ndarray or Iterable
The initial value of the variable being added in userdefined units. Default is 1.0.
 shapeint 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_indicesint 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_indicesbool
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.
 unitsstr or None
Units in which this input variable will be provided to the component during execution. Default is None, which means it is unitless.
 descstr
description of the variable
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_objective
(self, name, ref=None, ref0=None, index=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a response variable to this system.
 Parameters
 namestring
Name of the response variable in the system.
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 indexint, 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.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, 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, tags=None)¶ Add an output variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 valfloat or list or tuple or ndarray
The initial value of the variable being added in userdefined units. Default is 1.0.
 shapeint or tuple or list or None
Shape of this variable, only required if val is not an array. Default is None.
 unitsstr 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_unitsstr 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.
 descstr
description of the variable.
 lowerfloat 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.
 upperfloat 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.
 reffloat or ndarray
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 1. Default is 1.
 ref0float or ndarray
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 0. Default is 0.
 res_reffloat 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.
 tagsstr or list of strs or set of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_recorder
(self, recorder, recurse=False)¶ Add a recorder to the system.
 Parameters
 recorder<CaseRecorder>
A recorder instance.
 recurseboolean
Flag indicating if the recorder should be added to all the subsystems.

add_response
(self, name, type_, lower=None, upper=None, equals=None, ref=None, ref0=None, indices=None, index=None, adder=None, scaler=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a response variable to this system.
The response can be scaled using ref and ref0. The argument
ref0
represents the physical value when the scaled value is 0. The argumentref
represents the physical value when the scaled value is 1. Parameters
 namestring
Name of the response variable in the system.
 type_string
The type of response. Supported values are ‘con’ and ‘obj’
 lowerfloat or ndarray, optional
Lower boundary for the variable
 upperupper or ndarray, optional
Upper boundary for the variable
 equalsequals or ndarray, optional
Equality constraint value for the variable
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0upper or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 indicessequence of int, optional
If variable is an array, these indicate which entries are of interest for this particular response.
 indexint, optional
If variable is an array, this indicates which entry is of interest for this particular response.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 linearbool
Set to True if constraint is linear. Default is False.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, 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
 inputsVector
unscaled, dimensional input variables read via inputs[key]
 outputsVector
unscaled, dimensional output variables read via outputs[key]
 d_inputsVector
see inputs; product must be computed only if var_name in d_inputs
 d_outputsVector
see outputs; product must be computed only if var_name in d_outputs
 d_residualsVector
see outputs
 modestr
either ‘fwd’ or ‘rev’

apply_nonlinear
(self, inputs, outputs, resids)[source]¶ Evaluates the equation y2 = y1**(.5) + z1 + z2

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

cleanup
(self)¶ Clean up resources prior to exit.

declare_coloring
(self, wrt=('*', ), method='fd', form=None, step=None, per_instance=False, num_full_jacs=3, tol=1e25, orders=None, perturb_size=1e09, show_summary=True, show_sparsity=False)¶ Set options for deriv coloring of a set of wrt vars matching the given pattern(s).
 Parameters
 wrtstr or list of str
The name or names of the variables that derivatives are taken with respect to. This can contain input names, output names, or glob patterns.
 methodstr
Method used to compute derivative: “fd” for finite difference, “cs” for complex step.
 formstr
Finite difference form, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.
 stepfloat
Step size for finite difference. Leave undeclared to keep unchanged from previous or default value.
 per_instancebool
If True, a separate coloring will be generated for each instance of a given class. Otherwise, only one coloring for a given class will be generated and all instances of that class will use it.
 num_full_jacsint
Number of times to repeat partial jacobian computation when computing sparsity.
 tolfloat
Tolerance used to determine if an array entry is nonzero during sparsity determination.
 ordersint
Number of orders above and below the tolerance to check during the tolerance sweep.
 perturb_sizefloat
Size of input/output perturbation during generation of sparsity.
 show_summarybool
If True, display summary information after generating coloring.
 show_sparsitybool
If True, display sparsity with coloring info after generating coloring.

declare_partials
(self, 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
 ofstr or list of str
The name of the residual(s) that derivatives are being computed for. May also contain a glob pattern.
 wrtstr 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.
 dependentbool(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.
 rowsndarray of int or None
Row indices for each nonzero entry. For sparse subjacobians only.
 colsndarray of int or None
Column indices for each nonzero entry. For sparse subjacobians only.
 valfloat 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.
 methodstr
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’.
 stepfloat
Step size for approximation. Defaults to None, in which case the approximation method provides its default value.
 formstring
Form for finite difference, can be ‘forward’, ‘backward’, or ‘central’. Defaults to None, in which case the approximation method provides its default value.
 step_calcstring
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.
 Returns
 dict
Metadata dict for the specified partial(s).

property
distributed
¶ Provide ‘distributed’ property for backwards compatibility.
 Returns
 bool
reference to the ‘distributed’ option.

get_approx_coloring_fname
(self)¶ Return the full pathname to a coloring file.
 Parameters
 systemSystem
The System having its coloring saved or loaded.
 Returns
 str
Full pathname of the coloring file.

get_constraints
(self, 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
 recursebool, 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
(self, 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
 recursebool
If True, recurse through the subsystems and return the path of all design vars relative to the this system.
 get_sizesbool, optional
If True, compute the size of each design variable.
 Returns
 dict
The design variables defined in the current system and, if recurse=True, its subsystems.

get_linear_vectors
(self, vec_name='linear')¶ Return the linear inputs, outputs, and residuals vectors.
 Parameters
 vec_namestr
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
(self)¶ 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
(self, recurse=True)¶ Get the Objective settings from this system.
Retrieve all objectives settings from the system as a dict, keyed by variable name.
 Parameters
 recursebool, 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
(self, 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
 recursebool, optional
If True, recurse through the subsystems and return the path of all responses relative to the this system.
 get_sizesbool, 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
(self, inputs, outputs, residuals, discrete_inputs=None, discrete_outputs=None)¶ Provide initial guess for states.
Override this method to set the initial guess for states.
 Parameters
 inputsVector
unscaled, dimensional input variables read via inputs[key]
 outputsVector
unscaled, dimensional output variables read via outputs[key]
 residualsVector
unscaled, dimensional residuals written to via residuals[key]
 discrete_inputsdict or None
If not None, dict containing discrete input values.
 discrete_outputsdict or None
If not None, dict containing discrete output values.

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

is_active
(self)¶ 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.

property
linear_solver
¶ Get the linear solver for this system.

list_inputs
(self, values=True, prom_name=False, units=False, shape=False, hierarchical=True, print_arrays=False, tags=None, out_stream=<object object at 0x7f1bddbe81f0>)¶ 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
 valuesbool, optional
When True, display/return input values. Default is True.
 prom_namebool, optional
When True, display/return the promoted name of the variable. Default is False.
 unitsbool, optional
When True, display/return units. Default is False.
 shapebool, optional
When True, display/return the shape of the value. Default is False.
 hierarchicalbool, optional
When True, human readable output shows variables in hierarchical format.
 print_arraysbool, 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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed. Only inputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.
 out_streamfilelike 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
(self, explicit=True, implicit=True, values=True, prom_name=False, residuals=False, residuals_tol=None, units=False, shape=False, bounds=False, scaling=False, hierarchical=True, print_arrays=False, tags=None, out_stream=<object object at 0x7f1bddbe81f0>)¶ 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
 explicitbool, optional
include outputs from explicit components. Default is True.
 implicitbool, optional
include outputs from implicit components. Default is True.
 valuesbool, optional
When True, display/return output values. Default is True.
 prom_namebool, optional
When True, display/return the promoted name of the variable. Default is False.
 residualsbool, optional
When True, display/return residual values. Default is False.
 residuals_tolfloat, 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.
 unitsbool, optional
When True, display/return units. Default is False.
 shapebool, optional
When True, display/return the shape of the value. Default is False.
 boundsbool, optional
When True, display/return bounds (lower and upper). Default is False.
 scalingbool, optional
When True, display/return scaling (ref, ref0, and res_ref). Default is False.
 hierarchicalbool, optional
When True, human readable output shows variables in hierarchical format.
 print_arraysbool, 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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed. Only outputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.
 out_streamfilelike
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

property
ln_solver
¶ Get the linear solver for this system.

property
metadata
¶ Get the options for this System.

property
msginfo
¶ Our instance pathname, if available, or our class name. For use in error messages.
 Returns
 str
Either our instance pathname or class name.

property
nl_solver
¶ Get the nonlinear solver for this system.

property
nonlinear_solver
¶ Get the nonlinear solver for this system.

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

record_iteration
(self)¶ Record an iteration of the current System.

resetup
(self, setup_mode='full')¶ Public wrapper for _setup that reconfigures after an initial setup has been performed.
 Parameters
 setup_modestr
Must be one of ‘full’, ‘reconf’, or ‘update’.

run_apply_linear
(self, 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.
 modestr
‘fwd’ or ‘rev’.
 scope_outset or None
Set of absolute output names in the scope of this matvec product. If None, all are in the scope.
 scope_inset or None
Set of absolute input names in the scope of this matvec product. If None, all are in the scope.

run_apply_nonlinear
(self)¶ Compute residuals.
This calls _apply_nonlinear, but with the model assumed to be in an unscaled state.

run_linearize
(self, sub_do_ln=True)¶ Compute jacobian / factorization.
This calls _linearize, but with the model assumed to be in an unscaled state.
 Parameters
 sub_do_lnboolean
Flag indicating if the children should call linearize on their linear solvers.

run_solve_linear
(self, 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.
 modestr
‘fwd’ or ‘rev’.

run_solve_nonlinear
(self)¶ Compute outputs.
This calls _solve_nonlinear, but with the model assumed to be in an unscaled state.

set_check_partial_options
(self, wrt, method='fd', form=None, step=None, step_calc=None, directional=False)¶ Set options that will be used for checking partial derivatives.
 Parameters
 wrtstr 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.
 methodstr
Method for check: “fd” for finite difference, “cs” for complex step.
 formstr
Finite difference form for check, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.
 stepfloat
Step size for finite difference check. Leave undeclared to keep unchanged from previous or default value.
 step_calcstr
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.
 directionalbool
Set to True to perform a single directional derivative for each vector variable in the pattern named in wrt.

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

solve_linear
(self, 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_outputsVector
unscaled, dimensional quantities read via d_outputs[key]
 d_residualsVector
unscaled, dimensional quantities read via d_residuals[key]
 modestr
either ‘fwd’ or ‘rev’

solve_nonlinear
(self, inputs, outputs)¶ Compute outputs given inputs. The model is assumed to be in an unscaled state.
 Parameters
 inputsVector
unscaled, dimensional input variables read via inputs[key]
 outputsVector
unscaled, dimensional output variables read via outputs[key]

system_iter
(self, include_self=False, recurse=True, typ=None)¶ Yield a generator of local subsystems of this system.
 Parameters
 include_selfbool
If True, include this system in the iteration.
 recursebool
If True, iterate over the whole tree under this system.
 typtype
If not None, only yield Systems that match that are instances of the given type.

use_fixed_coloring
(self, coloring=<object object at 0x7f1bde39daf0>, recurse=True)¶ Use a precomputed coloring for this System.
 Parameters
 coloringstr
A coloring filename. If no arg is passed, filename will be determined automatically.
 recursebool
If True, set fixed coloring in all subsystems that declare a coloring. Ignored if a specific coloring is passed in.


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

add
(self, name, subsys, promotes=None)¶ Add a subsystem (deprecated version of <Group.add_subsystem>).
 Parameters
 namestr
Name of the subsystem being added
 subsysSystem
An instantiated, but notyetset up system object.
 promotesiter 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
(self, name, lower=None, upper=None, equals=None, ref=None, ref0=None, adder=None, scaler=None, indices=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a constraint variable to this system.
 Parameters
 namestring
Name of the response variable in the system.
 lowerfloat or ndarray, optional
Lower boundary for the variable
 upperfloat or ndarray, optional
Upper boundary for the variable
 equalsfloat or ndarray, optional
Equality constraint value for the variable
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 indicessequence 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.
 linearbool
Set to True if constraint is linear. Default is False.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, name, lower=None, upper=None, ref=None, ref0=None, indices=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a design variable to this system.
 Parameters
 namestring
Name of the design variable in the system.
 lowerfloat or ndarray, optional
Lower boundary for the param
 upperupper or ndarray, optional
Upper boundary for the param
 reffloat or ndarray, optional
Value of design var that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of design var that scales to 0.0 in the driver.
 indicesiter 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.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, name, ref=None, ref0=None, index=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a response variable to this system.
 Parameters
 namestring
Name of the response variable in the system.
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 indexint, 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.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, recorder, recurse=False)¶ Add a recorder to the system.
 Parameters
 recorder<CaseRecorder>
A recorder instance.
 recurseboolean
Flag indicating if the recorder should be added to all the subsystems.

add_response
(self, name, type_, lower=None, upper=None, equals=None, ref=None, ref0=None, indices=None, index=None, adder=None, scaler=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a response variable to this system.
The response can be scaled using ref and ref0. The argument
ref0
represents the physical value when the scaled value is 0. The argumentref
represents the physical value when the scaled value is 1. Parameters
 namestring
Name of the response variable in the system.
 type_string
The type of response. Supported values are ‘con’ and ‘obj’
 lowerfloat or ndarray, optional
Lower boundary for the variable
 upperupper or ndarray, optional
Upper boundary for the variable
 equalsequals or ndarray, optional
Equality constraint value for the variable
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0upper or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 indicessequence of int, optional
If variable is an array, these indicate which entries are of interest for this particular response.
 indexint, optional
If variable is an array, this indicates which entry is of interest for this particular response.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 linearbool
Set to True if constraint is linear. Default is False.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, name, subsys, promotes=None, promotes_inputs=None, promotes_outputs=None, min_procs=1, max_procs=None, proc_weight=1.0)¶ Add a subsystem.
 Parameters
 namestr
Name of the subsystem being added
 subsys<System>
An instantiated, but notyetset up system object.
 promotesiter 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_inputsiter 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_outputsiter 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_procsint
Minimum number of MPI processes usable by the subsystem. Defaults to 1.
 max_procsint or None
Maximum number of MPI processes usable by the subsystem. A value of None (the default) indicates there is no maximum limit.
 proc_weightfloat
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
(self, method='fd', step=None, form=None, step_calc=None)¶ Approximate derivatives for a Group using the specified approximation method.
 Parameters
 methodstr
The type of approximation that should be used. Valid options include: ‘fd’: Finite Difference, ‘cs’: Complex Step
 stepfloat
Step size for approximation. Defaults to None, in which case, the approximation method provides its default value.
 formstring
Form for finite difference, can be ‘forward’, ‘backward’, or ‘central’. Defaults to None, in which case, the approximation method provides its default value.
 step_calcstring
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
(self, logger)¶ Perform optional error checks.
 Parameters
 loggerobject
The object that manages logging output.

cleanup
(self)¶ Clean up resources prior to exit.

compute_sys_graph
(self, 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_onlybool (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
(self)[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
(self, src_name, tgt_name, src_indices=None, flat_src_indices=None)¶ Connect source src_name to target tgt_name in this namespace.
 Parameters
 src_namestr
name of the source variable to connect
 tgt_namestr or [str, … ] or (str, …)
name of the target variable(s) to connect
 src_indicesint 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_indicesbool
If True, each entry of src_indices is assumed to be an index into the flattened source. Otherwise it must be a tuple or list of size equal to the number of dimensions of the source.

declare_coloring
(self, wrt=('*', ), method='fd', form=None, step=None, per_instance=False, num_full_jacs=3, tol=1e25, orders=None, perturb_size=1e09, show_summary=True, show_sparsity=False)¶ Set options for deriv coloring of a set of wrt vars matching the given pattern(s).
 Parameters
 wrtstr or list of str
The name or names of the variables that derivatives are taken with respect to. This can contain input names, output names, or glob patterns.
 methodstr
Method used to compute derivative: “fd” for finite difference, “cs” for complex step.
 formstr
Finite difference form, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.
 stepfloat
Step size for finite difference. Leave undeclared to keep unchanged from previous or default value.
 per_instancebool
If True, a separate coloring will be generated for each instance of a given class. Otherwise, only one coloring for a given class will be generated and all instances of that class will use it.
 num_full_jacsint
Number of times to repeat partial jacobian computation when computing sparsity.
 tolfloat
Tolerance used to determine if an array entry is nonzero during sparsity determination.
 ordersint
Number of orders above and below the tolerance to check during the tolerance sweep.
 perturb_sizefloat
Size of input/output perturbation during generation of sparsity.
 show_summarybool
If True, display summary information after generating coloring.
 show_sparsitybool
If True, display sparsity with coloring info after generating coloring.

get_approx_coloring_fname
(self)¶ Return the full pathname to a coloring file.
 Parameters
 systemSystem
The System having its coloring saved or loaded.
 Returns
 str
Full pathname of the coloring file.

get_constraints
(self, 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
 recursebool, 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
(self, 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
 recursebool
If True, recurse through the subsystems and return the path of all design vars relative to the this system.
 get_sizesbool, optional
If True, compute the size of each design variable.
 Returns
 dict
The design variables defined in the current system and, if recurse=True, its subsystems.

get_linear_vectors
(self, vec_name='linear')¶ Return the linear inputs, outputs, and residuals vectors.
 Parameters
 vec_namestr
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
(self)¶ 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
(self, recurse=True)¶ Get the Objective settings from this system.
Retrieve all objectives settings from the system as a dict, keyed by variable name.
 Parameters
 recursebool, 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
(self, 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
 recursebool, optional
If True, recurse through the subsystems and return the path of all responses relative to the this system.
 get_sizesbool, 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
(self, inputs, outputs, residuals, discrete_inputs=None, discrete_outputs=None)¶ Provide initial guess for states.
Override this method to set the initial guess for states.
 Parameters
 inputsVector
unscaled, dimensional input variables read via inputs[key]
 outputsVector
unscaled, dimensional output variables read via outputs[key]
 residualsVector
unscaled, dimensional residuals written to via residuals[key]
 discrete_inputsdict or None
If not None, dict containing discrete input values.
 discrete_outputsdict or None
If not None, dict containing discrete output values.

is_active
(self)¶ 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.

property
linear_solver
¶ Get the linear solver for this system.

list_inputs
(self, values=True, prom_name=False, units=False, shape=False, hierarchical=True, print_arrays=False, tags=None, out_stream=<object object at 0x7f1bddbe81f0>)¶ 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
 valuesbool, optional
When True, display/return input values. Default is True.
 prom_namebool, optional
When True, display/return the promoted name of the variable. Default is False.
 unitsbool, optional
When True, display/return units. Default is False.
 shapebool, optional
When True, display/return the shape of the value. Default is False.
 hierarchicalbool, optional
When True, human readable output shows variables in hierarchical format.
 print_arraysbool, 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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed. Only inputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.
 out_streamfilelike 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
(self, explicit=True, implicit=True, values=True, prom_name=False, residuals=False, residuals_tol=None, units=False, shape=False, bounds=False, scaling=False, hierarchical=True, print_arrays=False, tags=None, out_stream=<object object at 0x7f1bddbe81f0>)¶ 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
 explicitbool, optional
include outputs from explicit components. Default is True.
 implicitbool, optional
include outputs from implicit components. Default is True.
 valuesbool, optional
When True, display/return output values. Default is True.
 prom_namebool, optional
When True, display/return the promoted name of the variable. Default is False.
 residualsbool, optional
When True, display/return residual values. Default is False.
 residuals_tolfloat, 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.
 unitsbool, optional
When True, display/return units. Default is False.
 shapebool, optional
When True, display/return the shape of the value. Default is False.
 boundsbool, optional
When True, display/return bounds (lower and upper). Default is False.
 scalingbool, optional
When True, display/return scaling (ref, ref0, and res_ref). Default is False.
 hierarchicalbool, optional
When True, human readable output shows variables in hierarchical format.
 print_arraysbool, 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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed. Only outputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.
 out_streamfilelike
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

property
ln_solver
¶ Get the linear solver for this system.

property
metadata
¶ Get the options for this System.

property
msginfo
¶ Our instance pathname, if available, or our class name. For use in error messages.
 Returns
 str
Either our instance pathname or class name.

property
nl_solver
¶ Get the nonlinear solver for this system.

property
nonlinear_solver
¶ Get the nonlinear solver for this system.

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

record_iteration
(self)¶ Record an iteration of the current System.

resetup
(self, setup_mode='full')¶ Public wrapper for _setup that reconfigures after an initial setup has been performed.
 Parameters
 setup_modestr
Must be one of ‘full’, ‘reconf’, or ‘update’.

run_apply_linear
(self, 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.
 modestr
‘fwd’ or ‘rev’.
 scope_outset or None
Set of absolute output names in the scope of this matvec product. If None, all are in the scope.
 scope_inset or None
Set of absolute input names in the scope of this matvec product. If None, all are in the scope.

run_apply_nonlinear
(self)¶ Compute residuals.
This calls _apply_nonlinear, but with the model assumed to be in an unscaled state.

run_linearize
(self, sub_do_ln=True)¶ Compute jacobian / factorization.
This calls _linearize, but with the model assumed to be in an unscaled state.
 Parameters
 sub_do_lnboolean
Flag indicating if the children should call linearize on their linear solvers.

run_solve_linear
(self, 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.
 modestr
‘fwd’ or ‘rev’.

run_solve_nonlinear
(self)¶ Compute outputs.
This calls _solve_nonlinear, but with the model assumed to be in an unscaled state.

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

set_order
(self, new_order)¶ Specify a new execution order for this system.
 Parameters
 new_orderlist of str
List of system names in desired new execution order.

setup
(self)[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
(self, include_self=False, recurse=True, typ=None)¶ Yield a generator of local subsystems of this system.
 Parameters
 include_selfbool
If True, include this system in the iteration.
 recursebool
If True, iterate over the whole tree under this system.
 typtype
If not None, only yield Systems that match that are instances of the given type.

use_fixed_coloring
(self, coloring=<object object at 0x7f1bde39daf0>, recurse=True)¶ Use a precomputed coloring for this System.
 Parameters
 coloringstr
A coloring filename. If no arg is passed, filename will be determined automatically.
 recursebool
If True, set fixed coloring in all subsystems that declare a coloring. Ignored if a specific coloring is passed in.


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__
(self, name)¶ Get an output/input variable.
 Parameters
 namestr
Promoted or relative variable name in the root system’s namespace.
 Returns
 float or ndarray or any python object
the requested output/input variable.

__init__
(self, model_class=<class 'openmdao.test_suite.components.sellar.SellarDerivatives'>, **kwargs)[source]¶ Initialize attributes.
 Parameters
 model<System> or None
The toplevel <System>. If not specified, an empty <Group> will be created.
 driver<Driver> or None
The driver for the problem. If not specified, a simple “Run Once” driver will be used.
 commMPI.Comm or <FakeComm> or None
The global communicator.
 root<System> or None
Deprecated kwarg for model.
 **optionsnamed args
All remaining named args are converted to options.

__setitem__
(self, name, value)¶ Set an output/input variable.
 Parameters
 namestr
Promoted or relative variable name in the root system’s namespace.
 valuefloat or ndarray or any python object
value to set this variable to.

add_recorder
(self, recorder)¶ Add a recorder to the problem.
 Parameters
 recorderCaseRecorder
A recorder instance.

check_config
(self, logger=None, checks=None, out_file='openmdao_checks.out')¶ Perform optional error checks on a Problem.
 Parameters
 loggerobject
Logging object.
 checkslist of str or None
List of specific checks to be performed.
 out_filestr or None
If not None, output will be written to this file in addition to stdout.

check_partials
(self, out_stream=<object object at 0x7f1bd6b42600>, includes=None, excludes=None, compact_print=False, abs_err_tol=1e06, rel_err_tol=1e06, method='fd', step=None, form='forward', step_calc='abs', force_dense=True, show_only_incorrect=False)¶ Check partial derivatives comprehensively for all components in your model.
 Parameters
 out_streamfilelike object
Where to send human readable output. By default it goes to stdout. Set to None to suppress.
 includesNone or list_like
List of glob patterns for pathnames to include in the check. Default is None, which includes all components in the model.
 excludesNone or list_like
List of glob patterns for pathnames to exclude from the check. Default is None, which excludes nothing.
 compact_printbool
Set to True to just print the essentials, one line per unknownparam pair.
 abs_err_tolfloat
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_tolfloat
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.
 methodstr
Method, ‘fd’ for finite difference or ‘cs’ for complex step. Default is ‘fd’.
 stepfloat
Step size for approximation. Default is None, which means 1e6 for ‘fd’ and 1e40 for ‘cs’.
 formstring
Form for finite difference, can be ‘forward’, ‘backward’, or ‘central’. Default ‘forward’.
 step_calcstring
Step type for finite difference, can be ‘abs’ for absolute’, or ‘rel’ for relative. Default is ‘abs’.
 force_densebool
If True, analytic derivatives will be coerced into arrays. Default is True.
 show_only_incorrectbool, 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
(self, of=None, wrt=None, out_stream=<object object at 0x7f1bd6b42600>, compact_print=False, driver_scaling=False, abs_err_tol=1e06, rel_err_tol=1e06, method='fd', step=None, form=None, step_calc='abs')¶ Check total derivatives for the model vs. finite difference.
 Parameters
 oflist of variable name strings or None
Variables whose derivatives will be computed. Default is None, which uses the driver’s objectives and constraints.
 wrtlist 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_streamfilelike object
Where to send human readable output. By default it goes to stdout. Set to None to suppress.
 compact_printbool
Set to True to just print the essentials, one line per unknownparam pair.
 driver_scalingbool
When True, return derivatives that are scaled according to either the adder and scaler or the ref and ref0 values that were specified when add_design_var, add_objective, and add_constraint were called on the model. Default is False, which is unscaled.
 abs_err_tolfloat
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_tolfloat
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.
 methodstr
Method, ‘fd’ for finite difference or ‘cs’ for complex step. Default is ‘fd’
 stepfloat
Step size for approximation. Default is None, which means 1e6 for ‘fd’ and 1e40 for ‘cs’.
 formstring
Form for finite difference, can be ‘forward’, ‘backward’, or ‘central’. Default None, which defaults to ‘forward’ for FD.
 step_calcstring
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
(self)¶ Clean up resources prior to exit.

compute_totals
(self, 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
 oflist of variable name strings or None
Variables whose derivatives will be computed. Default is None, which uses the driver’s objectives and constraints.
 wrtlist 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_formatstring
Format to return the derivatives. Can be ‘dict’, ‘flat_dict’, or ‘array’. Default is a ‘flat_dict’, which returns them in a dictionary whose keys are tuples of form (of, wrt).
 debug_printbool
Set to True to print out some debug information during linear solve.
 driver_scalingbool
When True, return derivatives that are scaled according to either the adder and scaler or the ref and ref0 values that were specified when add_design_var, add_objective, and add_constraint were called on the model. Default is False, which is unscaled.
 Returns
 derivsobject
Derivatives in form requested by ‘return_format’.

final_setup
(self)¶ 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
(self, name, units=None, indices=None, get_remote=False)¶ Get an output/input variable.
Function is used if you want to specify display units.
 Parameters
 namestr
Promoted or relative variable name in the root system’s namespace.
 unitsstr, optional
Units to convert to before upon return.
 indicesint or list of ints or tuple of ints or int ndarray or Iterable or None, optional
Indices or slice to return.
 get_remotebool
If True, retrieve the value even if it is on a remote process. Note that if the variable is remote on ANY process, this function must be called on EVERY process in the Problem’s MPI communicator.
 Returns
 float or ndarray
The requested output/input variable.

is_local
(self, name)¶ Return True if the named variable or system is local to the current process.
 Parameters
 namestr
Name of a variable or system.
 Returns
 bool
True if the named system or variable is local to this process.

list_problem_vars
(self, 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_namebool
If True, then show the promoted names of the variables.
 print_arraysbool, 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_optslist 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’, ‘cache_linear_solution’]
 cons_optslist 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’, ‘cache_linear_solution’]
 objs_optslist 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’, ‘cache_linear_solution’]

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

record_iteration
(self, case_name)¶ Record the variables at the Problem level.
 Parameters
 case_namestr
Name used to identify this Problem case.

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

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

run_driver
(self, case_prefix=None, reset_iter_counts=True)¶ Run the driver on the model.
 Parameters
 case_prefixstr or None
Prefix to prepend to coordinates when recording.
 reset_iter_countsbool
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
(self, case_prefix=None, reset_iter_counts=True)¶ Run the model by calling the root system’s solve_nonlinear.
 Parameters
 case_prefixstr or None
Prefix to prepend to coordinates when recording.
 reset_iter_countsbool
If True and model has been run previously, reset all iteration counters.

run_once
(self)¶ Backward compatible call for run_model.

set_solver_print
(self, level=2, depth=1e+99, type_='all')¶ Control printing for solvers and subsolvers in the model.
 Parameters
 levelint
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.
 depthint
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
(self, 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
 namestr
Promoted or relative variable name in the root system’s namespace.
 valuefloat or ndarray or list
Value to set this variable to.
 unitsstr, optional
Units that value is defined in.
 indicesint 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
(self, vector_class=None, check=False, logger=None, mode='auto', force_alloc_complex=False, distributed_vector_class=<class 'openmdao.vectors.petsc_vector.PETScVector'>, local_vector_class=<class 'openmdao.vectors.default_vector.DefaultVector'>, derivatives=True)¶ 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 the model hierarchy to call configure on each subsystem.
 Parameters
 vector_classtype
Reference to an actual <Vector> class; not an instance. This is deprecated. Use distributed_vector_class instead.
 checkboolean
whether to run config check after setup is complete.
 loggerobject
Object for logging config checks if check is True.
 modestring
Derivatives calculation mode, ‘fwd’ for forward, and ‘rev’ for reverse (adjoint). Default is ‘auto’, which will pick ‘fwd’ or ‘rev’ based on the direction resulting in the smallest number of linear solves required to compute derivatives.
 force_alloc_complexbool
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_classtype
Reference to the <Vector> class or factory function used to instantiate vectors and associated transfers involved in interprocess communication.
 local_vector_classtype
Reference to the <Vector> class or factory function used to instantiate vectors and associated transfers involved in intraprocess communication.
 derivativesbool
If True, perform any memory allocations necessary for derivative computation.
 Returns
 self<Problem>
this enables the user to instantiate and setup in one line.


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

__getitem__
(self, name)¶ Get an output/input variable.
 Parameters
 namestr
Promoted or relative variable name in the root system’s namespace.
 Returns
 float or ndarray or any python object
the requested output/input variable.

__init__
(self, model_class=<class 'openmdao.test_suite.components.sellar.SellarDerivatives'>, **kwargs)[source]¶ Initialize attributes.
 Parameters
 model<System> or None
The toplevel <System>. If not specified, an empty <Group> will be created.
 driver<Driver> or None
The driver for the problem. If not specified, a simple “Run Once” driver will be used.
 commMPI.Comm or <FakeComm> or None
The global communicator.
 root<System> or None
Deprecated kwarg for model.
 **optionsnamed args
All remaining named args are converted to options.

__setitem__
(self, name, value)¶ Set an output/input variable.
 Parameters
 namestr
Promoted or relative variable name in the root system’s namespace.
 valuefloat or ndarray or any python object
value to set this variable to.

add_recorder
(self, recorder)¶ Add a recorder to the problem.
 Parameters
 recorderCaseRecorder
A recorder instance.

check_config
(self, logger=None, checks=None, out_file='openmdao_checks.out')¶ Perform optional error checks on a Problem.
 Parameters
 loggerobject
Logging object.
 checkslist of str or None
List of specific checks to be performed.
 out_filestr or None
If not None, output will be written to this file in addition to stdout.

check_partials
(self, out_stream=<object object at 0x7f1bd6b42600>, includes=None, excludes=None, compact_print=False, abs_err_tol=1e06, rel_err_tol=1e06, method='fd', step=None, form='forward', step_calc='abs', force_dense=True, show_only_incorrect=False)¶ Check partial derivatives comprehensively for all components in your model.
 Parameters
 out_streamfilelike object
Where to send human readable output. By default it goes to stdout. Set to None to suppress.
 includesNone or list_like
List of glob patterns for pathnames to include in the check. Default is None, which includes all components in the model.
 excludesNone or list_like
List of glob patterns for pathnames to exclude from the check. Default is None, which excludes nothing.
 compact_printbool
Set to True to just print the essentials, one line per unknownparam pair.
 abs_err_tolfloat
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_tolfloat
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.
 methodstr
Method, ‘fd’ for finite difference or ‘cs’ for complex step. Default is ‘fd’.
 stepfloat
Step size for approximation. Default is None, which means 1e6 for ‘fd’ and 1e40 for ‘cs’.
 formstring
Form for finite difference, can be ‘forward’, ‘backward’, or ‘central’. Default ‘forward’.
 step_calcstring
Step type for finite difference, can be ‘abs’ for absolute’, or ‘rel’ for relative. Default is ‘abs’.
 force_densebool
If True, analytic derivatives will be coerced into arrays. Default is True.
 show_only_incorrectbool, 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
(self, of=None, wrt=None, out_stream=<object object at 0x7f1bd6b42600>, compact_print=False, driver_scaling=False, abs_err_tol=1e06, rel_err_tol=1e06, method='fd', step=None, form=None, step_calc='abs')¶ Check total derivatives for the model vs. finite difference.
 Parameters
 oflist of variable name strings or None
Variables whose derivatives will be computed. Default is None, which uses the driver’s objectives and constraints.
 wrtlist 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_streamfilelike object
Where to send human readable output. By default it goes to stdout. Set to None to suppress.
 compact_printbool
Set to True to just print the essentials, one line per unknownparam pair.
 driver_scalingbool
When True, return derivatives that are scaled according to either the adder and scaler or the ref and ref0 values that were specified when add_design_var, add_objective, and add_constraint were called on the model. Default is False, which is unscaled.
 abs_err_tolfloat
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_tolfloat
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.
 methodstr
Method, ‘fd’ for finite difference or ‘cs’ for complex step. Default is ‘fd’
 stepfloat
Step size for approximation. Default is None, which means 1e6 for ‘fd’ and 1e40 for ‘cs’.
 formstring
Form for finite difference, can be ‘forward’, ‘backward’, or ‘central’. Default None, which defaults to ‘forward’ for FD.
 step_calcstring
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
(self)¶ Clean up resources prior to exit.

compute_totals
(self, 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
 oflist of variable name strings or None
Variables whose derivatives will be computed. Default is None, which uses the driver’s objectives and constraints.
 wrtlist 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_formatstring
Format to return the derivatives. Can be ‘dict’, ‘flat_dict’, or ‘array’. Default is a ‘flat_dict’, which returns them in a dictionary whose keys are tuples of form (of, wrt).
 debug_printbool
Set to True to print out some debug information during linear solve.
 driver_scalingbool
When True, return derivatives that are scaled according to either the adder and scaler or the ref and ref0 values that were specified when add_design_var, add_objective, and add_constraint were called on the model. Default is False, which is unscaled.
 Returns
 derivsobject
Derivatives in form requested by ‘return_format’.

final_setup
(self)¶ 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
(self, name, units=None, indices=None, get_remote=False)¶ Get an output/input variable.
Function is used if you want to specify display units.
 Parameters
 namestr
Promoted or relative variable name in the root system’s namespace.
 unitsstr, optional
Units to convert to before upon return.
 indicesint or list of ints or tuple of ints or int ndarray or Iterable or None, optional
Indices or slice to return.
 get_remotebool
If True, retrieve the value even if it is on a remote process. Note that if the variable is remote on ANY process, this function must be called on EVERY process in the Problem’s MPI communicator.
 Returns
 float or ndarray
The requested output/input variable.

is_local
(self, name)¶ Return True if the named variable or system is local to the current process.
 Parameters
 namestr
Name of a variable or system.
 Returns
 bool
True if the named system or variable is local to this process.

list_problem_vars
(self, 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_namebool
If True, then show the promoted names of the variables.
 print_arraysbool, 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_optslist 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’, ‘cache_linear_solution’]
 cons_optslist 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’, ‘cache_linear_solution’]
 objs_optslist 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’, ‘cache_linear_solution’]

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

record_iteration
(self, case_name)¶ Record the variables at the Problem level.
 Parameters
 case_namestr
Name used to identify this Problem case.

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

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

run_driver
(self, case_prefix=None, reset_iter_counts=True)¶ Run the driver on the model.
 Parameters
 case_prefixstr or None
Prefix to prepend to coordinates when recording.
 reset_iter_countsbool
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
(self, case_prefix=None, reset_iter_counts=True)¶ Run the model by calling the root system’s solve_nonlinear.
 Parameters
 case_prefixstr or None
Prefix to prepend to coordinates when recording.
 reset_iter_countsbool
If True and model has been run previously, reset all iteration counters.

run_once
(self)¶ Backward compatible call for run_model.

set_solver_print
(self, level=2, depth=1e+99, type_='all')¶ Control printing for solvers and subsolvers in the model.
 Parameters
 levelint
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.
 depthint
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
(self, 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
 namestr
Promoted or relative variable name in the root system’s namespace.
 valuefloat or ndarray or list
Value to set this variable to.
 unitsstr, optional
Units that value is defined in.
 indicesint 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
(self, vector_class=None, check=False, logger=None, mode='auto', force_alloc_complex=False, distributed_vector_class=<class 'openmdao.vectors.petsc_vector.PETScVector'>, local_vector_class=<class 'openmdao.vectors.default_vector.DefaultVector'>, derivatives=True)¶ 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 the model hierarchy to call configure on each subsystem.
 Parameters
 vector_classtype
Reference to an actual <Vector> class; not an instance. This is deprecated. Use distributed_vector_class instead.
 checkboolean
whether to run config check after setup is complete.
 loggerobject
Object for logging config checks if check is True.
 modestring
Derivatives calculation mode, ‘fwd’ for forward, and ‘rev’ for reverse (adjoint). Default is ‘auto’, which will pick ‘fwd’ or ‘rev’ based on the direction resulting in the smallest number of linear solves required to compute derivatives.
 force_alloc_complexbool
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_classtype
Reference to the <Vector> class or factory function used to instantiate vectors and associated transfers involved in interprocess communication.
 local_vector_classtype
Reference to the <Vector> class or factory function used to instantiate vectors and associated transfers involved in intraprocess communication.
 derivativesbool
If True, perform any memory allocations necessary for derivative computation.
 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__
(self, **kwargs)¶ Set the solvers to nonlinear and linear block Gauss–Seidel by default.
 Parameters
 **kwargsdict
dict of arguments available here and in all descendants of this Group.

add
(self, name, subsys, promotes=None)¶ Add a subsystem (deprecated version of <Group.add_subsystem>).
 Parameters
 namestr
Name of the subsystem being added
 subsysSystem
An instantiated, but notyetset up system object.
 promotesiter 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
(self, name, lower=None, upper=None, equals=None, ref=None, ref0=None, adder=None, scaler=None, indices=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a constraint variable to this system.
 Parameters
 namestring
Name of the response variable in the system.
 lowerfloat or ndarray, optional
Lower boundary for the variable
 upperfloat or ndarray, optional
Upper boundary for the variable
 equalsfloat or ndarray, optional
Equality constraint value for the variable
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 indicessequence 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.
 linearbool
Set to True if constraint is linear. Default is False.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, name, lower=None, upper=None, ref=None, ref0=None, indices=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a design variable to this system.
 Parameters
 namestring
Name of the design variable in the system.
 lowerfloat or ndarray, optional
Lower boundary for the param
 upperupper or ndarray, optional
Upper boundary for the param
 reffloat or ndarray, optional
Value of design var that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of design var that scales to 0.0 in the driver.
 indicesiter 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.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, name, ref=None, ref0=None, index=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a response variable to this system.
 Parameters
 namestring
Name of the response variable in the system.
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 indexint, 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.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, recorder, recurse=False)¶ Add a recorder to the system.
 Parameters
 recorder<CaseRecorder>
A recorder instance.
 recurseboolean
Flag indicating if the recorder should be added to all the subsystems.

add_response
(self, name, type_, lower=None, upper=None, equals=None, ref=None, ref0=None, indices=None, index=None, adder=None, scaler=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a response variable to this system.
The response can be scaled using ref and ref0. The argument
ref0
represents the physical value when the scaled value is 0. The argumentref
represents the physical value when the scaled value is 1. Parameters
 namestring
Name of the response variable in the system.
 type_string
The type of response. Supported values are ‘con’ and ‘obj’
 lowerfloat or ndarray, optional
Lower boundary for the variable
 upperupper or ndarray, optional
Upper boundary for the variable
 equalsequals or ndarray, optional
Equality constraint value for the variable
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0upper or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 indicessequence of int, optional
If variable is an array, these indicate which entries are of interest for this particular response.
 indexint, optional
If variable is an array, this indicates which entry is of interest for this particular response.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 linearbool
Set to True if constraint is linear. Default is False.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, name, subsys, promotes=None, promotes_inputs=None, promotes_outputs=None, min_procs=1, max_procs=None, proc_weight=1.0)¶ Add a subsystem.
 Parameters
 namestr
Name of the subsystem being added
 subsys<System>
An instantiated, but notyetset up system object.
 promotesiter 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_inputsiter 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_outputsiter 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_procsint
Minimum number of MPI processes usable by the subsystem. Defaults to 1.
 max_procsint or None
Maximum number of MPI processes usable by the subsystem. A value of None (the default) indicates there is no maximum limit.
 proc_weightfloat
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
(self, method='fd', step=None, form=None, step_calc=None)¶ Approximate derivatives for a Group using the specified approximation method.
 Parameters
 methodstr
The type of approximation that should be used. Valid options include: ‘fd’: Finite Difference, ‘cs’: Complex Step
 stepfloat
Step size for approximation. Defaults to None, in which case, the approximation method provides its default value.
 formstring
Form for finite difference, can be ‘forward’, ‘backward’, or ‘central’. Defaults to None, in which case, the approximation method provides its default value.
 step_calcstring
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
(self, logger)¶ Perform optional error checks.
 Parameters
 loggerobject
The object that manages logging output.

cleanup
(self)¶ Clean up resources prior to exit.

compute_sys_graph
(self, 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_onlybool (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
(self)[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
(self, src_name, tgt_name, src_indices=None, flat_src_indices=None)¶ Connect source src_name to target tgt_name in this namespace.
 Parameters
 src_namestr
name of the source variable to connect
 tgt_namestr or [str, … ] or (str, …)
name of the target variable(s) to connect
 src_indicesint 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_indicesbool
If True, each entry of src_indices is assumed to be an index into the flattened source. Otherwise it must be a tuple or list of size equal to the number of dimensions of the source.

declare_coloring
(self, wrt=('*', ), method='fd', form=None, step=None, per_instance=False, num_full_jacs=3, tol=1e25, orders=None, perturb_size=1e09, show_summary=True, show_sparsity=False)¶ Set options for deriv coloring of a set of wrt vars matching the given pattern(s).
 Parameters
 wrtstr or list of str
The name or names of the variables that derivatives are taken with respect to. This can contain input names, output names, or glob patterns.
 methodstr
Method used to compute derivative: “fd” for finite difference, “cs” for complex step.
 formstr
Finite difference form, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.
 stepfloat
Step size for finite difference. Leave undeclared to keep unchanged from previous or default value.
 per_instancebool
If True, a separate coloring will be generated for each instance of a given class. Otherwise, only one coloring for a given class will be generated and all instances of that class will use it.
 num_full_jacsint
Number of times to repeat partial jacobian computation when computing sparsity.
 tolfloat
Tolerance used to determine if an array entry is nonzero during sparsity determination.
 ordersint
Number of orders above and below the tolerance to check during the tolerance sweep.
 perturb_sizefloat
Size of input/output perturbation during generation of sparsity.
 show_summarybool
If True, display summary information after generating coloring.
 show_sparsitybool
If True, display sparsity with coloring info after generating coloring.

get_approx_coloring_fname
(self)¶ Return the full pathname to a coloring file.
 Parameters
 systemSystem
The System having its coloring saved or loaded.
 Returns
 str
Full pathname of the coloring file.

get_constraints
(self, 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
 recursebool, 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
(self, 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
 recursebool
If True, recurse through the subsystems and return the path of all design vars relative to the this system.
 get_sizesbool, optional
If True, compute the size of each design variable.
 Returns
 dict
The design variables defined in the current system and, if recurse=True, its subsystems.

get_linear_vectors
(self, vec_name='linear')¶ Return the linear inputs, outputs, and residuals vectors.
 Parameters
 vec_namestr
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
(self)¶ 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
(self, recurse=True)¶ Get the Objective settings from this system.
Retrieve all objectives settings from the system as a dict, keyed by variable name.
 Parameters
 recursebool, 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
(self, 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
 recursebool, optional
If True, recurse through the subsystems and return the path of all responses relative to the this system.
 get_sizesbool, 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
(self, inputs, outputs, residuals, discrete_inputs=None, discrete_outputs=None)¶ Provide initial guess for states.
Override this method to set the initial guess for states.
 Parameters
 inputsVector
unscaled, dimensional input variables read via inputs[key]
 outputsVector
unscaled, dimensional output variables read via outputs[key]
 residualsVector
unscaled, dimensional residuals written to via residuals[key]
 discrete_inputsdict or None
If not None, dict containing discrete input values.
 discrete_outputsdict or None
If not None, dict containing discrete output values.

is_active
(self)¶ 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.

property
linear_solver
¶ Get the linear solver for this system.

list_inputs
(self, values=True, prom_name=False, units=False, shape=False, hierarchical=True, print_arrays=False, tags=None, out_stream=<object object at 0x7f1bddbe81f0>)¶ 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
 valuesbool, optional
When True, display/return input values. Default is True.
 prom_namebool, optional
When True, display/return the promoted name of the variable. Default is False.
 unitsbool, optional
When True, display/return units. Default is False.
 shapebool, optional
When True, display/return the shape of the value. Default is False.
 hierarchicalbool, optional
When True, human readable output shows variables in hierarchical format.
 print_arraysbool, 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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed. Only inputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.
 out_streamfilelike 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
(self, explicit=True, implicit=True, values=True, prom_name=False, residuals=False, residuals_tol=None, units=False, shape=False, bounds=False, scaling=False, hierarchical=True, print_arrays=False, tags=None, out_stream=<object object at 0x7f1bddbe81f0>)¶ 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
 explicitbool, optional
include outputs from explicit components. Default is True.
 implicitbool, optional
include outputs from implicit components. Default is True.
 valuesbool, optional
When True, display/return output values. Default is True.
 prom_namebool, optional
When True, display/return the promoted name of the variable. Default is False.
 residualsbool, optional
When True, display/return residual values. Default is False.
 residuals_tolfloat, 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.
 unitsbool, optional
When True, display/return units. Default is False.
 shapebool, optional
When True, display/return the shape of the value. Default is False.
 boundsbool, optional
When True, display/return bounds (lower and upper). Default is False.
 scalingbool, optional
When True, display/return scaling (ref, ref0, and res_ref). Default is False.
 hierarchicalbool, optional
When True, human readable output shows variables in hierarchical format.
 print_arraysbool, 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.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed. Only outputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.
 out_streamfilelike
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

property
ln_solver
¶ Get the linear solver for this system.

property
metadata
¶ Get the options for this System.

property
msginfo
¶ Our instance pathname, if available, or our class name. For use in error messages.
 Returns
 str
Either our instance pathname or class name.

property
nl_solver
¶ Get the nonlinear solver for this system.

property
nonlinear_solver
¶ Get the nonlinear solver for this system.

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

record_iteration
(self)¶ Record an iteration of the current System.

resetup
(self, setup_mode='full')¶ Public wrapper for _setup that reconfigures after an initial setup has been performed.
 Parameters
 setup_modestr
Must be one of ‘full’, ‘reconf’, or ‘update’.

run_apply_linear
(self, 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.
 modestr
‘fwd’ or ‘rev’.
 scope_outset or None
Set of absolute output names in the scope of this matvec product. If None, all are in the scope.
 scope_inset or None
Set of absolute input names in the scope of this matvec product. If None, all are in the scope.

run_apply_nonlinear
(self)¶ Compute residuals.
This calls _apply_nonlinear, but with the model assumed to be in an unscaled state.

run_linearize
(self, sub_do_ln=True)¶ Compute jacobian / factorization.
This calls _linearize, but with the model assumed to be in an unscaled state.
 Parameters
 sub_do_lnboolean
Flag indicating if the children should call linearize on their linear solvers.

run_solve_linear
(self, 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.
 modestr
‘fwd’ or ‘rev’.

run_solve_nonlinear
(self)¶ Compute outputs.
This calls _solve_nonlinear, but with the model assumed to be in an unscaled state.

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

set_order
(self, new_order)¶ Specify a new execution order for this system.
 Parameters
 new_orderlist of str
List of system names in desired new execution order.

setup
(self)[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
(self, include_self=False, recurse=True, typ=None)¶ Yield a generator of local subsystems of this system.
 Parameters
 include_selfbool
If True, include this system in the iteration.
 recursebool
If True, iterate over the whole tree under this system.
 typtype
If not None, only yield Systems that match that are instances of the given type.

use_fixed_coloring
(self, coloring=<object object at 0x7f1bde39daf0>, recurse=True)¶ Use a precomputed coloring for this System.
 Parameters
 coloringstr
A coloring filename. If no arg is passed, filename will be determined automatically.
 recursebool
If True, set fixed coloring in all subsystems that declare a coloring. Ignored if a specific coloring is passed in.


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

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

add_constraint
(self, name, lower=None, upper=None, equals=None, ref=None, ref0=None, adder=None, scaler=None, indices=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a constraint variable to this system.
 Parameters
 namestring
Name of the response variable in the system.
 lowerfloat or ndarray, optional
Lower boundary for the variable
 upperfloat or ndarray, optional
Upper boundary for the variable
 equalsfloat or ndarray, optional
Equality constraint value for the variable
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 indicessequence 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.
 linearbool
Set to True if constraint is linear. Default is False.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, name, lower=None, upper=None, ref=None, ref0=None, indices=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a design variable to this system.
 Parameters
 namestring
Name of the design variable in the system.
 lowerfloat or ndarray, optional
Lower boundary for the param
 upperupper or ndarray, optional
Upper boundary for the param
 reffloat or ndarray, optional
Value of design var that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of design var that scales to 0.0 in the driver.
 indicesiter 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.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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_discrete_input
(self, name, val, desc='', tags=None)¶ Add a discrete input variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 vala picklable object
The initial value of the variable being added.
 descstr
description of the variable
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_discrete_output
(self, name, val, desc='', tags=None)¶ Add an output variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 vala picklable object
The initial value of the variable being added.
 descstr
description of the variable.
 tagsstr or list of strs or set of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_input
(self, name, val=1.0, shape=None, src_indices=None, flat_src_indices=None, units=None, desc='', tags=None)¶ Add an input variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 valfloat or list or tuple or ndarray or Iterable
The initial value of the variable being added in userdefined units. Default is 1.0.
 shapeint 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_indicesint 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_indicesbool
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.
 unitsstr or None
Units in which this input variable will be provided to the component during execution. Default is None, which means it is unitless.
 descstr
description of the variable
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_objective
(self, name, ref=None, ref0=None, index=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a response variable to this system.
 Parameters
 namestring
Name of the response variable in the system.
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 indexint, 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.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, 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, tags=None)¶ Add an output variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 valfloat or list or tuple or ndarray
The initial value of the variable being added in userdefined units. Default is 1.0.
 shapeint or tuple or list or None
Shape of this variable, only required if val is not an array. Default is None.
 unitsstr 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_unitsstr 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.
 descstr
description of the variable.
 lowerfloat 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.
 upperfloat 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.
 reffloat or ndarray
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 1. Default is 1.
 ref0float or ndarray
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 0. Default is 0.
 res_reffloat 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.
 tagsstr or list of strs or set of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_recorder
(self, recorder, recurse=False)¶ Add a recorder to the system.
 Parameters
 recorder<CaseRecorder>
A recorder instance.
 recurseboolean
Flag indicating if the recorder should be added to all the subsystems.

add_response
(self, name, type_, lower=None, upper=None, equals=None, ref=None, ref0=None, indices=None, index=None, adder=None, scaler=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a response variable to this system.
The response can be scaled using ref and ref0. The argument
ref0
represents the physical value when the scaled value is 0. The argumentref
represents the physical value when the scaled value is 1. Parameters
 namestring
Name of the response variable in the system.
 type_string
The type of response. Supported values are ‘con’ and ‘obj’
 lowerfloat or ndarray, optional
Lower boundary for the variable
 upperupper or ndarray, optional
Upper boundary for the variable
 equalsequals or ndarray, optional
Equality constraint value for the variable
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0upper or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 indicessequence of int, optional
If variable is an array, these indicate which entries are of interest for this particular response.
 indexint, optional
If variable is an array, this indicates which entry is of interest for this particular response.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 linearbool
Set to True if constraint is linear. Default is False.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
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
(self, 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
 inputsVector
unscaled, dimensional input variables read via inputs[key]
 outputsVector
unscaled, dimensional output variables read via outputs[key]
 d_inputsVector
see inputs; product must be computed only if var_name in d_inputs
 d_outputsVector
see outputs; product must be computed only if var_name in d_outputs
 d_residualsVector
see outputs
 modestr
either ‘fwd’ or ‘rev’

apply_nonlinear
(self, inputs, outputs, residuals)[source]¶ Don’t solve; just calculate the residual.

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

cleanup
(self)¶ Clean up resources prior to exit.

declare_coloring
(self, wrt=('*', ), method='fd', form=None, step=None, per_instance=False, num_full_jacs=3, tol=1e25, orders=None, perturb_size=1e09, show_summary=True, show_sparsity=False)¶ Set options for deriv coloring of a set of wrt vars matching the given pattern(s).
 Parameters
 wrtstr or list of str
The name or names of the variables that derivatives are taken with respect to. This can contain input names, output names, or glob patterns.
 methodstr
Method used to compute derivative: “fd” for finite difference, “cs” for complex step.
 formstr
Finite difference form, can be “forward”, “central”, or “backward”. Leave undeclared to keep unchanged from previous or default value.
 stepfloat
Step size for finite difference. Leave undeclared to keep unchanged from previous or default value.
 per_instancebool
If True, a separate coloring will be generated for each instance of a given class. Otherwise, only one coloring for a given class will be generated and all instances of that class will use it.
 num_full_jacsint
Number of times to repeat partial jacobian computation when computing sparsity.
 tolfloat
Tolerance used to determine if an array entry is nonzero during sparsity determination.
 ordersint
Number of orders above and below the tolerance to check during the tolerance sweep.
 perturb_sizefloat
Size of input/output perturbation during generation of sparsity.
 show_summarybool
If True, display summary information after generating coloring.
 show_sparsitybool
If True, display sparsity with coloring info after generating coloring.

declare_partials
(self, 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
 ofstr or list of str
The name of the residual(s) that derivatives are being computed for. May also contain a glob pattern.
 wrtstr 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.
 dependentbool(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.
 rowsndarray of int or None
Row indices for each nonzero entry. For sparse subjacobians only.
 colsndarray of int or None
Column indices for each nonzero entry. For sparse subjacobians only.
 valfloat 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.
 methodstr
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’.
 stepfloat
Step size for approximation. Defaults to None, in which case the approximation method provides its default value.
 formstring
Form for finite difference, can be ‘forward’, ‘backward’, or ‘central’. Defaults to None, in which case the approximation method provides its default value.
 step_calcstring
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.
 Returns
 dict
Metadata dict for the specified partial(s).

property
distributed
¶ Provide ‘distributed’ property for backwards compatibility.
 Returns
 bool
reference to the ‘distributed’ option.

get_approx_coloring_fname
(self)¶ Return the full pathname to a coloring file.
 Parameters
 systemSystem
The System having its coloring saved or loaded.
 Returns
 str
Full pathname of the coloring file.

get_constraints
(self, 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
 recursebool, 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
(self, 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
 recursebool
If True, recurse through the subsystems and return the path of all design vars relative to the this system.
 get_sizesbool, optional
If True, compute the size of each design variable.
 Returns
 dict
The design variables defined in the current system and, if recurse=True, its subsystems.

get_linear_vectors
(self, vec_name='linear')¶ Return the linear inputs, outputs, and residuals vectors.
 Parameters
 vec_namestr
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
(self)¶ 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
(self, recurse=True)¶ Get the Objective settings from this system.
Retrieve all objectives settings from the system as a dict, keyed by variable name.
 Parameters
 recursebool, 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
(self, 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
 recursebool, optional
If True, recurse through the subsystems and return the path of all responses relative to the this system.
 get_sizesbool, 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
(self, inputs, outputs, residuals, discrete_inputs=None, discrete_outputs=None)¶ Provide initial guess for states.
Override this method to set the initial guess for states.
 Parameters
 inputsVector
unscaled, dimensional input variables read via inputs[key]
 outputsVector
unscaled, dimensional output variables read via outputs[key]
 residualsVector
unscaled, dimensional residuals written to via residuals[key]
 discrete_inputsdict or None
If not None, dict containing discrete input values.
 discrete_outputsdict or None
If not None, dict containing discrete output values.

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

is_active
(self)¶ 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.

property
linear_solver
¶ Get the linear solver for this system.

list_inputs
(self, values=True, prom_name=False, units=False, shape=False, hierarchical=True, print_arrays=False, tags=None, out_stream=<object object at 0x7f1bddbe81f0>)¶ 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
 valuesbool, optional
When True, display/return input values. Default is True.
 prom_namebool, optional
When True, display/return the promoted name of the variable. Default is False.
 unitsbool, optional
When True, display/return units. Default is False.
 shapebool, optional
When True, display/return the shape of the value. Default is False.
 hierarchicalbool, optional
When True, human readable output shows variables in hierarchical format.
 print_arraysbool, 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.
