# three_bar_truss.py¶

3 Bar Truss Problem.

• 3 continuous design variables - Cross sectional area of each bar.

• 3 discrete material choices for each bar. Complete enumeration requires 64 continuous optimization.

The global optima is 3,3,x (x can be anything), with mass = 5.28 kg

class openmdao.test_suite.components.three_bar_truss.ThreeBarTruss(**kwargs)[source]

3 Bar truss problem with 3 continuous design variables and 3 discrete material choices. Material chosen as follows:

1 Aluminum 2 Titanium 3 Steel 4 Nickel

This component calculates the total mass of the truss.

__init__(**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.

abs_name_iter(iotype, local=True, cont=True, discrete=False)

Iterate over absolute variable names for this System.

By setting appropriate values for ‘cont’ and ‘discrete’, yielded variable names can be continuous only, discrete only, or both.

Parameters
iotypestr

Either ‘input’ or ‘output’.

localbool

If True, include only names of local variables. Default is True.

contbool

If True, include names of continuous variables. Default is True.

discretebool

If True, include names of discrete variables. Default is False.

add_constraint(name, lower=None, upper=None, equals=None, ref=None, ref0=None, adder=None, scaler=None, units=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.

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.

unitsstr, optional

Units to convert to before applying scaling.

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 argument ref represents the physical value when the scaled value is 1. The arguments (lower, upper, equals) can not be strings or variable names.

add_design_var(name, lower=None, upper=None, ref=None, ref0=None, indices=None, adder=None, scaler=None, units=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 input

upperupper or ndarray, optional

Upper boundary for the input

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 an input is an array, these indicate which entries are of interest for this particular design variable. These may be positive or negative integers.

unitsstr, optional

Units to convert to before applying scaling.

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 argument ref represents the physical value when the scaled value is 1.

add_discrete_input(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

add_discrete_output(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

add_input(name, val=1.0, shape=None, src_indices=None, flat_src_indices=None, units=None, desc='', tags=None, shape_by_conn=False, copy_shape=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 user-defined 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.

shape_by_connbool

If True, shape this input to match its connected output.

copy_shapestr or None

If a str, that str is the name of a variable. Shape this input to match that of the named variable.

Returns
dict

add_objective(name, ref=None, ref0=None, index=None, units=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.

unitsstr, optional

Units to convert to before applying scaling.

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(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, shape_by_conn=False, copy_shape=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 user-defined 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 user-defined 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 user-defined 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 user-defined units of this output variable when the scaled value is 1. Default is 1.

ref0float

Scaling parameter. The value in the user-defined units of this output variable when the scaled value is 0. Default is 0.

res_reffloat

Scaling parameter. The value in the user-defined 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.

shape_by_connbool

If True, shape this output to match its connected input(s).

copy_shapestr or None

If a str, that str is the name of a variable. Shape this output to match that of the named variable.

Returns
dict

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

Add a response variable to this system.

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

Parameters
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.

unitsstr, optional

Units to convert to before applying scaling.

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(logger)

Perform optional error checks.

Parameters
loggerobject

The object that manages logging output.

cleanup()

Clean up resources prior to exit.

compute(inputs, outputs)[source]

Define the function f(xI, xC).

Here xI is integer and xC is continuous.

compute_jacvec_product(inputs, d_inputs, d_outputs, mode, discrete_inputs=None)

Compute jac-vector 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(inputs, partials, discrete_inputs=None)

Compute sub-jacobian parts. The model is assumed to be in an unscaled state.

Parameters
inputsVector

unscaled, dimensional input variables read via inputs[key]

partialsJacobian

sub-jac components written to partials[output_name, input_name]

discrete_inputsdict or None

If not None, dict containing discrete input values.

convert2units(name, val, units)

Convert the given value to the specified units.

Parameters
namestr

Name of the variable.

valfloat or ndarray of float

The value of the variable.

unitsstr

The units to convert to.

Returns
float or ndarray of float

The value converted to the specified units.

convert_from_units(name, val, units)

Convert the given value from the specified units to those of the named variable.

Parameters
namestr

Name of the variable.

valfloat or ndarray of float

The value of the variable.

unitsstr

The units to convert to.

Returns
float or ndarray of float

The value converted to the specified units.

convert_units(name, val, units_from, units_to)

Wrap the utility convert_units and give a good error message.

Parameters
namestr

Name of the variable.

valfloat or ndarray of float

The value of the variable.

units_fromstr

The units to convert from.

units_tostr

The units to convert to.

Returns
float or ndarray of float

The value converted to the specified units.

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

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

Parameters
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.

min_improve_pctfloat

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

show_summarybool

If True, display summary information after generating coloring.

show_sparsitybool

If True, display sparsity with coloring info after generating coloring.

declare_partials(of, wrt, dependent=True, rows=None, cols=None, val=None, method='exact', step=None, form=None, step_calc=None)

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).

get_approx_coloring_fname()

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(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(recurse=True, get_sizes=True, use_prom_ivc=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.

use_prom_ivcbool

Translate auto_ivc_names to their promoted input names.

Returns
dict

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

get_io_metadata(iotypes=('input', 'output'), metadata_keys=None, includes=None, excludes=None, tags=(), get_remote=False, rank=None, return_rel_names=True)

Retrieve metdata for a filtered list of variables.

Parameters
iotypesstr or iter of str

Will contain either ‘input’, ‘output’, or both. Defaults to both.

Names of metadata entries to be retrieved or None, meaning retrieve all available ‘allprocs’ metadata. If ‘values’ or ‘src_indices’ are required, their keys must be provided explicitly since they are not found in the ‘allprocs’ metadata and must be retrieved from local metadata located in each process.

includesstr, iter of str or None

Collection of glob patterns for pathnames of variables to include. Default is None, which includes all variables.

excludesstr, iter of str or None

Collection of glob patterns for pathnames of variables to exclude. Default is None.

tagsstr or iter 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.

get_remotebool

If True, retrieve variables from other MPI processes as well.

rankint or None

If None, and get_remote is True, retrieve values from all MPI process to all other MPI processes. Otherwise, if get_remote is True, retrieve values from all MPI processes only to the specified rank.

return_rel_namesbool

If True, the names returned will be relative to the scope of this System. Otherwise they will be absolute names.

Returns
dict

A dict of metadata keyed on name, where name is either absolute or relative based on the value of the return_rel_names arg, and metadata is a dict containing entries based on the value of the metadata_keys arg. Every metadata dict will always contain two entries, ‘promoted_name’ and ‘discrete’, to indicate a given variable’s promoted name and whether or not it is discrete.

get_linear_vectors(vec_name='linear')

Return the linear inputs, outputs, and residuals vectors.

Parameters
vec_namestr

Name of the linear right-hand-side 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
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_relevant_vars(desvars, responses, mode)

Find all relevant vars between desvars and responses.

Both vars are assumed to be outputs (either design vars or responses).

Parameters
desvarslist of str

Names of design variables.

responseslist of str

Names of response variables.

modestr

Direction of derivatives, either ‘fwd’ or ‘rev’.

Returns
dict

Dict of ({‘outputs’: dep_outputs, ‘inputs’: dep_inputs, dep_systems) keyed by design vars and responses.

get_responses(recurse=True, get_sizes=True, use_prom_ivc=False)

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.

use_prom_ivcbool

Translate auto_ivc_names to their promoted input names.

Returns
dict

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

get_source(name)

Return the source variable connected to the given named variable.

The name can be a promoted name or an absolute name. If the given variable is an input, the absolute name of the connected source will be returned. If the given variable itself is a source, its own absolute name will be returned.

Parameters
namestr

Absolute or promoted name of the variable.

Returns
str

The absolute name of the source variable.

get_val(name, units=None, indices=None, get_remote=False, rank=None, vec_name='nonlinear', kind=None, flat=False, from_src=True)

Get an output/input/residual 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 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 or None

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. If False, only retrieve the value if it is on the current process, or only the part of the value that’s on the current process for a distributed variable. If None and the variable is remote or distributed, a RuntimeError will be raised.

rankint or None

If not None, only gather the value to this rank.

vec_namestr

Name of the vector to use. Defaults to ‘nonlinear’.

kindstr or None

Kind of variable (‘input’, ‘output’, or ‘residual’). If None, returned value will be either an input or output.

flatbool

If True, return the flattened version of the value.

from_srcbool

If True, retrieve value of an input variable from its connected source.

Returns
object

The value of the requested output/input variable.

get_var_meta(name, key)

Parameters
namestr

Variable name (promoted, relative, or absolute) in the root system’s namespace.

keystr

Key into the metadata dict for the given variable.

Returns
object

The value stored under key in the metadata dictionary for the named variable.

initialize()

Perform any one-time 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.

property linear_solver

Get the linear solver for this system.

list_inputs(values=True, prom_name=False, units=False, shape=False, global_shape=False, desc=False, hierarchical=True, print_arrays=False, tags=None, includes=None, excludes=None, all_procs=False, out_stream=DEFAULT_OUT_STREAM)

Write a list of input names and other optional information to a specified stream.

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.

global_shapebool, optional

When True, display/return the global shape of the value. Default is False.

descbool, optional

When True, display/return description. 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.

includesNone or iter of str

Collection of glob patterns for pathnames of variables to include. Default is None, which includes all input variables.

excludesNone or iter of str

Collection of glob patterns for pathnames of variables to exclude. Default is None.

all_procsbool, optional

When True, display output on all ranks. Default is False, which will display output only from rank 0.

out_streamfile-like object

Where to send human readable output. Default is sys.stdout. Set to None to suppress.

Returns

List of input names and other optional information about those inputs.

list_outputs(explicit=True, implicit=True, values=True, prom_name=False, residuals=False, residuals_tol=None, units=False, shape=False, global_shape=False, bounds=False, scaling=False, desc=False, hierarchical=True, print_arrays=False, tags=None, includes=None, excludes=None, all_procs=False, list_autoivcs=False, out_stream=DEFAULT_OUT_STREAM)

Write a list of output names and other optional information to a specified stream.

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 output values. Default is True.

prom_namebool, optional

When True, display the promoted name of the variable. Default is False.

residualsbool, optional

When True, display 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 units. Default is False.

shapebool, optional

When True, display/return the shape of the value. Default is False.

global_shapebool, optional

When True, display/return the global 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.

descbool, optional

When True, display/return description. 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.

includesNone or iter of str

Collection of glob patterns for pathnames of variables to include. Default is None, which includes all output variables.

excludesNone or iter of str

Collection of glob patterns for pathnames of variables to exclude. Default is None.

all_procsbool, optional

When True, display output on all processors. Default is False.

list_autoivcsbool

If True, include auto_ivc outputs in the listing. Defaults to False.

out_streamfile-like

Where to send human readable output. Default is sys.stdout. Set to None to suppress.

Returns

List of output names and other optional information about those outputs.

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 nonlinear_solver

Get the nonlinear solver for this system.

record_iteration()

Record an iteration of the current System.

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

Compute jac-vec product.

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

Parameters
vec_names[str, …]

list of names of the right-hand-side vectors.

modestr

‘fwd’ or ‘rev’.

scope_outset or None

Set of absolute output names in the scope of this mat-vec product. If None, all are in the scope.

scope_inset or None

Set of absolute input names in the scope of this mat-vec product. If None, all are in the scope.

run_apply_nonlinear()

Compute residuals.

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

run_linearize(sub_do_ln=True)

Compute jacobian / factorization.

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

Parameters
sub_do_lnboolean

Flag indicating if the children should call linearize on their linear solvers.

run_solve_linear(vec_names, mode)

Apply inverse jac product.

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

Parameters
vec_names[str, …]

list of names of the right-hand-side vectors.

modestr

‘fwd’ or ‘rev’.

run_solve_nonlinear()

Compute outputs.

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

set_check_partial_options(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()

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

set_solver_print(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.

setup()[source]

Declare inputs and outputs.

Available attributes:

name pathname comm options

setup_partials()[source]

Declare partials.

This is meant to be overridden by component classes. All partials should be declared here since this is called after all size/shape information is known for all variables.

system_iter(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(coloring=<object object>, 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.three_bar_truss.ThreeBarTrussVector(**kwargs)[source]

3 Bar truss problem with 3 continuous design variables and 3 discrete material choices. Material chosen as follows:

1 Aluminum 2 Titanium 3 Steel 4 Nickel

This component calculates the total mass of the truss.

This version places all areas in a single vector and all materials in a single vector for test purporses.

__init__(**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.

abs_name_iter(iotype, local=True, cont=True, discrete=False)

Iterate over absolute variable names for this System.

By setting appropriate values for ‘cont’ and ‘discrete’, yielded variable names can be continuous only, discrete only, or both.

Parameters
iotypestr

Either ‘input’ or ‘output’.

localbool

If True, include only names of local variables. Default is True.

contbool

If True, include names of continuous variables. Default is True.

discretebool

If True, include names of discrete variables. Default is False.

add_constraint(name, lower=None, upper=None, equals=None, ref=None, ref0=None, adder=None, scaler=None, units=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.

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.

unitsstr, optional

Units to convert to before applying scaling.

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 argument ref represents the physical value when the scaled value is 1. The arguments (lower, upper, equals) can not be strings or variable names.

add_design_var(name, lower=None, upper=None, ref=None, ref0=None, indices=None, adder=None, scaler=None, units=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 input

upperupper or ndarray, optional

Upper boundary for the input

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 an input is an array, these indicate which entries are of interest for this particular design variable. These may be positive or negative integers.

unitsstr, optional

Units to convert to before applying scaling.

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 argument ref represents the physical value when the scaled value is 1.

add_discrete_input(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

add_discrete_output(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

add_input(name, val=1.0, shape=None, src_indices=None, flat_src_indices=None, units=None, desc='', tags=None, shape_by_conn=False, copy_shape=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 user-defined 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.

shape_by_connbool

If True, shape this input to match its connected output.

copy_shapestr or None

If a str, that str is the name of a variable. Shape this input to match that of the named variable.

Returns
dict

add_objective(name, ref=None, ref0=None, index=None, units=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.

unitsstr, optional

Units to convert to before applying scaling.

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(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, shape_by_conn=False, copy_shape=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 user-defined 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 user-defined 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 user-defined 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 user-defined units of this output variable when the scaled value is 1. Default is 1.

ref0float

Scaling parameter. The value in the user-defined units of this output variable when the scaled value is 0. Default is 0.

res_reffloat

Scaling parameter. The value in the user-defined 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.

shape_by_connbool

If True, shape this output to match its connected input(s).

copy_shapestr or None

If a str, that str is the name of a variable. Shape this output to match that of the named variable.

Returns
dict

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

Add a response variable to this system.

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

Parameters
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.

unitsstr, optional

Units to convert to before applying scaling.

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(logger)

Perform optional error checks.

Parameters
loggerobject

The object that manages logging output.

cleanup()

Clean up resources prior to exit.

compute(inputs, outputs)[source]

Define the function f(xI, xC) Here xI is integer and xC is continuous

compute_jacvec_product(inputs, d_inputs, d_outputs, mode, discrete_inputs=None)

Compute jac-vector 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(inputs, partials, discrete_inputs=None)

Compute sub-jacobian parts. The model is assumed to be in an unscaled state.

Parameters
inputsVector

unscaled, dimensional input variables read via inputs[key]

partialsJacobian

sub-jac components written to partials[output_name, input_name]

discrete_inputsdict or None

If not None, dict containing discrete input values.

convert2units(name, val, units)

Convert the given value to the specified units.

Parameters
namestr

Name of the variable.

valfloat or ndarray of float

The value of the variable.

unitsstr

The units to convert to.

Returns
float or ndarray of float

The value converted to the specified units.

convert_from_units(name, val, units)

Convert the given value from the specified units to those of the named variable.

Parameters
namestr

Name of the variable.

valfloat or ndarray of float

The value of the variable.

unitsstr

The units to convert to.

Returns
float or ndarray of float

The value converted to the specified units.

convert_units(name, val, units_from, units_to)

Wrap the utility convert_units and give a good error message.

Parameters
namestr

Name of the variable.

valfloat or ndarray of float

The value of the variable.

units_fromstr

The units to convert from.

units_tostr

The units to convert to.

Returns
float or ndarray of float

The value converted to the specified units.

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

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

Parameters
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.

min_improve_pctfloat

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

show_summarybool

If True, display summary information after generating coloring.

show_sparsitybool

If True, display sparsity with coloring info after generating coloring.

declare_partials(of, wrt, dependent=True, rows=None, cols=None, val=None, method='exact', step=None, form=None, step_calc=None)

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).

get_approx_coloring_fname()

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(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(recurse=True, get_sizes=True, use_prom_ivc=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.

use_prom_ivcbool

Translate auto_ivc_names to their promoted input names.

Returns
dict

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

get_io_metadata(iotypes=('input', 'output'), metadata_keys=None, includes=None, excludes=None, tags=(), get_remote=False, rank=None, return_rel_names=True)

Retrieve metdata for a filtered list of variables.

Parameters
iotypesstr or iter of str

Will contain either ‘input’, ‘output’, or both. Defaults to both.

Names of metadata entries to be retrieved or None, meaning retrieve all available ‘allprocs’ metadata. If ‘values’ or ‘src_indices’ are required, their keys must be provided explicitly since they are not found in the ‘allprocs’ metadata and must be retrieved from local metadata located in each process.

includesstr, iter of str or None

Collection of glob patterns for pathnames of variables to include. Default is None, which includes all variables.

excludesstr, iter of str or None

Collection of glob patterns for pathnames of variables to exclude. Default is None.

tagsstr or iter 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.

get_remotebool

If True, retrieve variables from other MPI processes as well.

rankint or None

If None, and get_remote is True, retrieve values from all MPI process to all other MPI processes. Otherwise, if get_remote is True, retrieve values from all MPI processes only to the specified rank.

return_rel_namesbool

If True, the names returned will be relative to the scope of this System. Otherwise they will be absolute names.

Returns
dict

A dict of metadata keyed on name, where name is either absolute or relative based on the value of the return_rel_names arg, and metadata is a dict containing entries based on the value of the metadata_keys arg. Every metadata dict will always contain two entries, ‘promoted_name’ and ‘discrete’, to indicate a given variable’s promoted name and whether or not it is discrete.

get_linear_vectors(vec_name='linear')

Return the linear inputs, outputs, and residuals vectors.

Parameters
vec_namestr

Name of the linear right-hand-side 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
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_relevant_vars(desvars, responses, mode)

Find all relevant vars between desvars and responses.

Both vars are assumed to be outputs (either design vars or responses).

Parameters
desvarslist of str

Names of design variables.

responseslist of str

Names of response variables.

modestr

Direction of derivatives, either ‘fwd’ or ‘rev’.

Returns
dict

Dict of ({‘outputs’: dep_outputs, ‘inputs’: dep_inputs, dep_systems) keyed by design vars and responses.

get_responses(recurse=True, get_sizes=True, use_prom_ivc=False)

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.

use_prom_ivcbool

Translate auto_ivc_names to their promoted input names.

Returns
dict

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

get_source(name)

Return the source variable connected to the given named variable.

The name can be a promoted name or an absolute name. If the given variable is an input, the absolute name of the connected source will be returned. If the given variable itself is a source, its own absolute name will be returned.

Parameters
namestr

Absolute or promoted name of the variable.

Returns
str

The absolute name of the source variable.

get_val(name, units=None, indices=None, get_remote=False, rank=None, vec_name='nonlinear', kind=None, flat=False, from_src=True)

Get an output/input/residual 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 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 or None

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. If False, only retrieve the value if it is on the current process, or only the part of the value that’s on the current process for a distributed variable. If None and the variable is remote or distributed, a RuntimeError will be raised.

rankint or None

If not None, only gather the value to this rank.

vec_namestr

Name of the vector to use. Defaults to ‘nonlinear’.

kindstr or None

Kind of variable (‘input’, ‘output’, or ‘residual’). If None, returned value will be either an input or output.

flatbool

If True, return the flattened version of the value.

from_srcbool

If True, retrieve value of an input variable from its connected source.

Returns
object

The value of the requested output/input variable.

get_var_meta(name, key)

Parameters
namestr

Variable name (promoted, relative, or absolute) in the root system’s namespace.

keystr

Key into the metadata dict for the given variable.

Returns
object

The value stored under key in the metadata dictionary for the named variable.

initialize()

Perform any one-time 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.

property linear_solver

Get the linear solver for this system.

list_inputs(values=True, prom_name=False, units=False, shape=False, global_shape=False, desc=False, hierarchical=True, print_arrays=False, tags=None, includes=None, excludes=None, all_procs=False, out_stream=DEFAULT_OUT_STREAM)

Write a list of input names and other optional information to a specified stream.

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.

global_shapebool, optional

When True, display/return the global shape of the value. Default is False.

descbool, optional

When True, display/return description. 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.

includesNone or iter of str

Collection of glob patterns for pathnames of variables to include. Default is None, which includes all input variables.

excludesNone or iter of str

Collection of glob patterns for pathnames of variables to exclude. Default is None.

all_procsbool, optional

When True, display output on all ranks. Default is False, which will display output only from rank 0.

out_streamfile-like object

Where to send human readable output. Default is sys.stdout. Set to None to suppress.

Returns

List of input names and other optional information about those inputs.

list_outputs(explicit=True, implicit=True, values=True, prom_name=False, residuals=False, residuals_tol=None, units=False, shape=False, global_shape=False, bounds=False, scaling=False, desc=False, hierarchical=True, print_arrays=False, tags=None, includes=None, excludes=None, all_procs=False, list_autoivcs=False, out_stream=DEFAULT_OUT_STREAM)

Write a list of output names and other optional information to a specified stream.

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 output values. Default is True.

prom_namebool, optional

When True, display the promoted name of the variable. Default is False.

residualsbool, optional

When True, display 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 units. Default is False.

shapebool, optional

When True, display/return the shape of the value. Default is False.

global_shapebool, optional

When True, display/return the global 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.

descbool, optional

When True, display/return description. 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.

includesNone or iter of str

Collection of glob patterns for pathnames of variables to include. Default is None, which includes all output variables.

excludesNone or iter of str

Collection of glob patterns for pathnames of variables to exclude. Default is None.

all_procsbool, optional

When True, display output on all processors. Default is False.

list_autoivcsbool

If True, include auto_ivc outputs in the listing. Defaults to False.

out_streamfile-like

Where to send human readable output. Default is sys.stdout. Set to None to suppress.

Returns

List of output names and other optional information about those outputs.

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 nonlinear_solver

Get the nonlinear solver for this system.

record_iteration()

Record an iteration of the current System.

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

Compute jac-vec product.

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

Parameters
vec_names[str, …]

list of names of the right-hand-side vectors.

modestr

‘fwd’ or ‘rev’.

scope_outset or None

Set of absolute output names in the scope of this mat-vec product. If None, all are in the scope.

scope_inset or None

Set of absolute input names in the scope of this mat-vec product. If None, all are in the scope.

run_apply_nonlinear()

Compute residuals.

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

run_linearize(sub_do_ln=True)

Compute jacobian / factorization.

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

Parameters
sub_do_lnboolean

Flag indicating if the children should call linearize on their linear solvers.

run_solve_linear(vec_names, mode)

Apply inverse jac product.

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

Parameters
vec_names[str, …]

list of names of the right-hand-side vectors.

modestr

‘fwd’ or ‘rev’.

run_solve_nonlinear()

Compute outputs.

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

set_check_partial_options(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()

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

set_solver_print(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.

setup()[source]

Declare inputs and outputs.

Available attributes:

name pathname comm options

setup_partials()[source]

Declare partials.

This is meant to be overridden by component classes. All partials should be declared here since this is called after all size/shape information is known for all variables.

system_iter(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(coloring=<object object>, 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.

openmdao.test_suite.components.three_bar_truss.stress_calc(A, E)[source]

Calculate stress in a 3-bar truss given area and Young’s modulus.

Parameters
Afloat or ndarray

Area of the bar.

Efloat or ndarray

Young’s Modules of the bar.

Returns
float or ndarray

Stress in the bar.