branin.py¶
Test objects for the singlediscipline Branin (or BraninHoo) problem.
The Branin, or BraninHoo, function has three global minima. The recommended values of a, b, c, r, s and t are: a = 1 b = 5.1/(4pi2), c = 5/pi, r = 6, s = 10 and t = 1/(8pi).
This function is usually evaluated on the square x0 ~ [5, 10], x1 ~ [0, 15].
The global minimum can be found at f(x) = 0.397887

class
openmdao.test_suite.components.branin.
Branin
(**kwargs)[source]¶ Bases:
openmdao.core.explicitcomponent.ExplicitComponent
The Branin test problem. This version is the standard version and contains two continuous parameters.

__init__
(**kwargs)¶ Store some bound methods so we can detect runtime overrides.
Parameters: **kwargs : dict of keyword arguments
available here and in all descendants of this system.

add_constraint
(name, lower=None, upper=None, equals=None, ref=None, ref0=None, adder=None, scaler=None, indices=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, simul_coloring=None, simul_map=None)¶ Add a constraint variable to this system.
Parameters: name : string
Name of the response variable in the system.
lower : float or ndarray, optional
Lower boundary for the variable
upper : float or ndarray, optional
Upper boundary for the variable
equals : float or ndarray, optional
Equality constraint value for the variable
ref : float or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
ref0 : float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
adder : float or ndarray, optional
Value to add to the model value to get the scaled value. Adder is first in precedence.
scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
indices : sequence of int, optional
If variable is an array, these indicate which entries are of interest for this particular response. These may be positive or negative integers.
linear : bool
Set to True if constraint is linear. Default is False.
parallel_deriv_color : string
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
vectorize_derivs : bool
If True, vectorize derivative calculations.
simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the constraint variable.
simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
Notes
The response can be scaled using ref and ref0. The argument
ref0
represents the physical value when the scaled value is 0. The argumentref
represents the physical value when the scaled value is 1.

add_design_var
(name, lower=None, upper=None, ref=None, ref0=None, indices=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, simul_coloring=None)¶ Add a design variable to this system.
Parameters: name : string
Name of the design variable in the system.
lower : float or ndarray, optional
Lower boundary for the param
upper : upper or ndarray, optional
Upper boundary for the param
ref : float or ndarray, optional
Value of design var that scales to 1.0 in the driver.
ref0 : float or ndarray, optional
Value of design var that scales to 0.0 in the driver.
indices : iter of int, optional
If a param is an array, these indicate which entries are of interest for this particular design variable. These may be positive or negative integers.
adder : float or ndarray, optional
Value to add to the model value to get the scaled value. Adder is first in precedence.
scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
parallel_deriv_color : string
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
vectorize_derivs : bool
If True, vectorize derivative calculations.
simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the design variable.
Notes
The response can be scaled using ref and ref0. The argument
ref0
represents the physical value when the scaled value is 0. The argumentref
represents the physical value when the scaled value is 1.

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

add_objective
(name, ref=None, ref0=None, index=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, simul_coloring=None, simul_map=None)¶ Add a response variable to this system.
Parameters: name : string
Name of the response variable in the system.
ref : float or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
ref0 : float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
index : int, optional
If variable is an array, this indicates which entry is of interest for this particular response. This may be a positive or negative integer.
adder : float or ndarray, optional
Value to add to the model value to get the scaled value. Adder is first in precedence.
scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
parallel_deriv_color : string
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
vectorize_derivs : bool
If True, vectorize derivative calculations.
simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the objective variable.
simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).
Notes
The objective can be scaled using scaler and adder, where
\[x_{scaled} = scaler(x + adder)\]or through the use of ref/ref0, which map to scaler and adder through the equations:
\[ \begin{align}\begin{aligned}0 = scaler(ref_0 + adder)\\1 = scaler(ref + adder)\end{aligned}\end{align} \]which results in:
\[ \begin{align}\begin{aligned}adder = ref_0\\scaler = \frac{1}{ref + adder}\end{aligned}\end{align} \]

add_output
(name, val=1.0, shape=None, units=None, res_units=None, desc='', lower=None, upper=None, ref=1.0, ref0=0.0, res_ref=None, var_set=0)¶ Add an output variable to the component.
For ExplicitComponent, res_ref defaults to the value in res unless otherwise specified.
Parameters: name : str
name of the variable in this component’s namespace.
val : float or list or tuple or ndarray
The initial value of the variable being added in userdefined units. Default is 1.0.
shape : int or tuple or list or None
Shape of this variable, only required if val is not an array. Default is None.
units : str or None
Units in which the output variables will be provided to the component during execution. Default is None, which means it has no units.
res_units : str or None
Units in which the residuals of this output will be given to the user when requested. Default is None, which means it has no units.
desc : str
description of the variable.
lower : float or list or tuple or ndarray or None
lower bound(s) in userdefined units. It can be (1) a float, (2) an array_like consistent with the shape arg (if given), or (3) an array_like matching the shape of val, if val is array_like. A value of None means this output has no lower bound. Default is None.
upper : float or list or tuple or ndarray or None
upper bound(s) in userdefined units. It can be (1) a float, (2) an array_like consistent with the shape arg (if given), or (3) an array_like matching the shape of val, if val is array_like. A value of None means this output has no upper bound. Default is None.
ref : float
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 1. Default is 1.
ref0 : float
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 0. Default is 0.
res_ref : float
Scaling parameter. The value in the userdefined res_units of this output’s residual when the scaled value is 1. Default is None, which means residual scaling matches output scaling.
var_set : hashable object
For advanced users only. ID or color for this variable, relevant for reconfigurability. Default is 0.
Returns: dict
metadata for added variable

add_recorder
(recorder, recurse=False)¶ Add a recorder to the driver.
Parameters: recorder : <BaseRecorder>
A recorder instance.
recurse : boolean
Flag indicating if the recorder should be added to all the subsystems.

add_response
(name, type_, lower=None, upper=None, equals=None, ref=None, ref0=None, indices=None, index=None, adder=None, scaler=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, simul_coloring=None, simul_map=None)¶ Add a response variable to this system.
The response can be scaled using ref and ref0. The argument
ref0
represents the physical value when the scaled value is 0. The argumentref
represents the physical value when the scaled value is 1.Parameters: name : string
Name of the response variable in the system.
type_ : string
The type of response. Supported values are ‘con’ and ‘obj’
lower : float or ndarray, optional
Lower boundary for the variable
upper : upper or ndarray, optional
Upper boundary for the variable
equals : equals or ndarray, optional
Equality constraint value for the variable
ref : float or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
ref0 : upper or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
indices : sequence of int, optional
If variable is an array, these indicate which entries are of interest for this particular response.
index : int, optional
If variable is an array, this indicates which entry is of interest for this particular response.
adder : float or ndarray, optional
Value to add to the model value to get the scaled value. Adder is first in precedence.
scaler : float or ndarray, optional
value to multiply the model value to get the scaled value. Scaler is second in precedence.
linear : bool
Set to True if constraint is linear. Default is False.
parallel_deriv_color : string
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
vectorize_derivs : bool
If True, vectorize derivative calculations.
simul_coloring : ndarray or list of int
An array or list of integer color values. Must match the size of the response variable.
simul_map : dict
Mapping of this response to each design variable where simultaneous derivs will be used. Each design variable entry is another dict keyed on color, and the values in the color dict are tuples of the form (resp_idxs, color_idxs).

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

compute
(inputs, outputs)[source]¶ Define the function f(xI, xC).
When Branin is used in a mixed integer problem, x0 is integer and x1 is continuous.

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

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

get_constraints
(recurse=True)¶ Get the Constraint settings from this system.
Retrieve the constraint settings for the current system as a dict, keyed by variable name.
Parameters: recurse : bool, optional
If True, recurse through the subsystems and return the path of all constraints relative to the this system.
Returns: dict
The constraints defined in the current system.

get_design_vars
(recurse=True, get_sizes=True)¶ Get the DesignVariable settings from this system.
Retrieve all design variable settings from the system and, if recurse is True, all of its subsystems.
Parameters: recurse : bool
If True, recurse through the subsystems and return the path of all design vars relative to the this system.
get_sizes : bool, optional
If True, compute the size of each response.
Returns: dict
The design variables defined in the current system and, if recurse=True, its subsystems.

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

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

get_objectives
(recurse=True)¶ Get the Objective settings from this system.
Retrieve all objectives settings from the system as a dict, keyed by variable name.
Parameters: recurse : bool, optional
If True, recurse through the subsystems and return the path of all objective relative to the this system.
Returns: dict
The objectives defined in the current system.

get_responses
(recurse=True, get_sizes=True)¶ Get the response variable settings from this system.
Retrieve all response variable settings from the system as a dict, keyed by variable name.
Parameters: recurse : bool, optional
If True, recurse through the subsystems and return the path of all responses relative to the this system.
get_sizes : bool, optional
If True, compute the size of each response.
Returns: dict
The responses defined in the current system and, if recurse=True, its subsystems.

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

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

jacobian
¶ Get the Jacobian object assigned to this system (or None if unassigned).

jacobian_context
(*args, **kwds)¶ Context manager that yields the Jacobian assigned to this system in this system’s context.

linear_solver
¶ Get the linear solver for this system.

list_inputs
(values=True, units=False, hierarchical=True, print_arrays=False, out_stream=<object object>)¶ Return and optionally log a list of input names and other optional information.
If the model is parallel, only the local variables are returned to the process. Also optionally logs the information to a user defined output stream. If the model is parallel, the rank 0 process logs information about all variables across all processes.
Parameters: values : bool, optional
When True, display/return input values. Default is True.
units : bool, optional
When True, display/return units. Default is False.
hierarchical : bool, optional
When True, human readable output shows variables in hierarchical format.
print_arrays : bool, optional
When False, in the columnar display, just display norm of any ndarrays with size > 1. The norm is surrounded by vertical bars to indicate that it is a norm. When True, also display full values of the ndarray below the row. Format is affected by the values set with numpy.set_printoptions Default is False.
out_stream : filelike object
Where to send human readable output. Default is sys.stdout. Set to None to suppress.
Returns: list
list of input names and other optional information about those inputs

list_outputs
(explicit=True, implicit=True, values=True, residuals=False, residuals_tol=None, units=False, shape=False, bounds=False, scaling=False, hierarchical=True, print_arrays=False, out_stream=<object object>)¶ Return and optionally log a list of output names and other optional information.
If the model is parallel, only the local variables are returned to the process. Also optionally logs the information to a user defined output stream. If the model is parallel, the rank 0 process logs information about all variables across all processes.
Parameters: explicit : bool, optional
include outputs from explicit components. Default is True.
implicit : bool, optional
include outputs from implicit components. Default is True.
values : bool, optional
When True, display/return output values. Default is True.
residuals : bool, optional
When True, display/return residual values. Default is False.
residuals_tol : float, optional
If set, limits the output of list_outputs to only variables where the norm of the resids array is greater than the given ‘residuals_tol’. Default is None.
units : bool, optional
When True, display/return units. Default is False.
shape : bool, optional
When True, display/return the shape of the value. Default is False.
bounds : bool, optional
When True, display/return bounds (lower and upper). Default is False.
scaling : bool, optional
When True, display/return scaling (ref, ref0, and res_ref). Default is False.
hierarchical : bool, optional
When True, human readable output shows variables in hierarchical format.
print_arrays : bool, optional
When False, in the columnar display, just display norm of any ndarrays with size > 1. The norm is surrounded by vertical bars to indicate that it is a norm. When True, also display full values of the ndarray below the row. Format is affected by the values set with numpy.set_printoptions Default is False.
out_stream : filelike
Where to send human readable output. Default is sys.stdout. Set to None to suppress.
Returns: list
list of output names and other optional information about those outputs

ln_solver
¶ Get the linear solver for this system.

nl_solver
¶ Get the nonlinear solver for this system.

nonlinear_solver
¶ Get the nonlinear solver for this system.

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

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

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

run_apply_linear
(vec_names, mode, scope_out=None, scope_in=None)¶ Compute jacvec product.
This calls _apply_linear, but with the model assumed to be in an unscaled state.
Parameters: vec_names : [str, ...]
list of names of the righthandside vectors.
mode : str
‘fwd’ or ‘rev’.
scope_out : set or None
Set of absolute output names in the scope of this matvec product. If None, all are in the scope.
scope_in : set or None
Set of absolute input names in the scope of this matvec product. If None, all are in the scope.

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

run_linearize
(do_nl=True, do_ln=True)¶ Compute jacobian / factorization.
This calls _linearize, but with the model assumed to be in an unscaled state.
Parameters: do_nl : boolean
Flag indicating if the nonlinear solver should be linearized.
do_ln : boolean
Flag indicating if the linear solver should be linearized.

run_solve_linear
(vec_names, mode)¶ Apply inverse jac product.
This calls _solve_linear, but with the model assumed to be in an unscaled state.
Parameters: vec_names : [str, ...]
list of names of the righthandside vectors.
mode : str
‘fwd’ or ‘rev’.
Returns: boolean
Failure flag; True if failed to converge, False is successful.
float
relative error.
float
absolute error.

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

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

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

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