quad_implicit.py

quad_implicit.py#

class openmdao.test_suite.components.quad_implicit.QuadraticComp(**kwargs)[source]

Bases: ImplicitComponent

A Simple Implicit Component representing a Quadratic Equation.

R(a, b, c, x) = ax^2 + bx + c

Solution via Quadratic Formula: x = (-b + sqrt(b^2 - 4ac)) / 2a

__init__(**kwargs)

Store some bound methods so we can detect runtime overrides.

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

Iterate over absolute variable names and their metadata 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.

Yields:

str, dict

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.

Yields:

str

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, cache_linear_solution=False, flat_indices=False, alias=None)

Add a constraint variable to this system.

Parameters:

namestr
Name of the response variable in the system.

lowerfloat or ndarray, optional
Lower boundary for the variable.

upperfloat or ndarray, optional
Upper boundary for the variable.

equalsfloat or ndarray, optional
Equality constraint value for the variable.

reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.

ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.

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

scalerfloat or ndarray, optional
Value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alternative 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_colorstr
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.

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.

flat_indicesbool
If True, interpret specified indices as being indices into a flat source array.

aliasstr
Alias for this response. Necessary when adding multiple constraints on different indices or slices of a single 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 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, cache_linear_solution=False, flat_indices=False)

Add a design variable to this system.

Parameters:

namestr
Promoted 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.

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

scalerfloat or ndarray, optional
Value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.

unitsstr, optional
Units to convert to before applying scaling.

parallel_deriv_colorstr
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.

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.

flat_indicesbool
If True, interpret specified indices as being indices into a flat source array.

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
Metadata for added variable.

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
Metadata for added variable.

add_input(name, val=1.0, shape=None, units=None, desc='', tags=None, shape_by_conn=False, copy_shape=None, compute_shape=None, require_connection=False, distributed=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 val is not an array. Default is None.

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.

compute_shapefunction
A function taking a dict arg containing names and shapes of this component’s outputs and returning the shape of this input.

require_connectionbool
If True and this input is not a design variable, it must be connected to an output.

distributedbool
If True, this variable is a distributed variable, so it can have different sizes/values across MPI processes.

Returns:

dict
Metadata for added variable.

add_objective(name, ref=None, ref0=None, index=None, units=None, adder=None, scaler=None, parallel_deriv_color=None, cache_linear_solution=False, flat_indices=False, alias=None)

Add a response variable to this system.

Parameters:

namestr
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.

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

scalerfloat or ndarray, optional
Value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.

parallel_deriv_colorstr
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.

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.

flat_indicesbool
If True, interpret specified indices as being indices into a flat source array.

aliasstr
Alias for this response. Necessary when adding multiple objectives on different indices or slices of a single variable.

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, **kwargs)

Add an output variable to the component.

Parameters:

namestr
Name of the variable in this component’s namespace.

valfloat or list or tuple or ndarray
The initial value of the variable being added in user-defined units. Default is 1.0.

**kwargsdict
Keyword args to store. The value corresponding to each key is a dict containing the metadata for the input name that matches that key.

Returns:

dict
Metadata for added variable.

add_recorder(recorder, recurse=False)

Add a recorder to the system.

Parameters:

recorder<CaseRecorder>
A recorder instance.

recursebool
Flag indicating if the recorder should be added to all the subsystems.

add_residual(name, shape=(1,), units=None, desc='', ref=None)

Add a residual variable to the component.

Note that the total size of the residual vector must match the total size of the outputs vector for this component.

Parameters:

namestr
Name of the residual in this component’s namespace.

shapeint or tuple
Shape of this residual.

unitsstr or None
Units in which this residual will be given to the user when requested. Default is None, which means it has no units.

descstr
Description of the residual.

reffloat or ndarray or None
Scaling parameter. The value in the user-defined units of this residual when the scaled value is 1. Default is 1.

Returns:

dict
Metadata for the added residual.

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, cache_linear_solution=False, flat_indices=None, alias=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 argument ref represents the physical value when the scaled value is 1.

Parameters:

namestr
Promoted name of the response variable in the system.

type_str
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.

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

scalerfloat or ndarray, optional
Value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.

linearbool
Set to True if constraint is linear. Default is False.

parallel_deriv_colorstr
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.

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.

flat_indicesbool
If True, interpret specified indices as being indices into a flat source array.

aliasstr or None
Alias for this response. Necessary when adding multiple responses on different indices of the same variable.

apply_linear(inputs, outputs, d_inputs, d_outputs, d_residuals, mode)

Compute jac-vector product. The model is assumed to be in an unscaled state.

If mode is:
‘fwd’: (d_inputs, d_outputs) |-> d_residuals

‘rev’: d_residuals |-> (d_inputs, d_outputs)

Parameters:

inputsVector
Unscaled, dimensional input variables read via inputs[key].

outputsVector
Unscaled, dimensional output variables read via outputs[key].

d_inputsVector
See inputs; product must be computed only if var_name in d_inputs.

d_outputsVector
See outputs; product must be computed only if var_name in d_outputs.

d_residualsVector
See outputs.

modestr
Either ‘fwd’ or ‘rev’.

apply_nonlinear(inputs, outputs, residuals)[source]

Compute residuals given inputs and outputs.

The model is assumed to be in an unscaled state.

Parameters:

inputsVector
Unscaled, dimensional input variables read via inputs[key].

outputsVector
Unscaled, dimensional output variables read via outputs[key].

residualsVector
Unscaled, dimensional residuals written to via residuals[key].

discrete_inputsdict or None
If not None, dict containing discrete input values.

discrete_outputsdict or None
If not None, dict containing discrete output values.

best_partial_deriv_direction()

Return the best direction for partial deriv calculations based on input and output sizes.

Returns:

str
The best direction for derivative calculations, ‘fwd’ or ‘rev’.

check_config(logger)

Perform optional error checks.

Parameters:

loggerobject
The object that manages logging output.

check_subjac_sparsity()

Check the declared sparsity of the sub-jacobians vs. the computed sparsity.

property checking

Return True if check_partials or check_totals is executing.

Returns:

bool
True if we’re running within check_partials or check_totals.

cleanup()

Clean up resources prior to exit.

property comm

Return the MPI communicator object for the system.

Returns:

MPI.Comm
MPI communicator object.

comm_info_iter()

Yield comm size for this system and all subsystems.

Yields:

tuple
A tuple of the form (abs_name, comm_size).

compute_sparsity()

Compute the sparsity of the partial jacobian.

Returns:

coo_matrix
The sparsity matrix.

dict
Metadata about the sparsity computation.

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, minimum_step=None)

Declare information about this component’s subjacobians.

Parameters:

ofstr or iter of str
The name of the residual(s) that derivatives are being computed for. May also contain a glob pattern.

wrtstr or iter 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.

formstr
Form for finite difference, can be ‘forward’, ‘backward’, or ‘central’. Defaults to None, in which case the approximation method provides its default value.

step_calcstr
Step type for computing the size of the finite difference step. It can be ‘abs’ for absolute, ‘rel_avg’ for a size relative to the absolute value of the vector input, or ‘rel_element’ for a size relative to each value in the vector input. In addition, it can be ‘rel_legacy’ for a size relative to the norm of the vector. For backwards compatibilty, it can be ‘rel’, which is now equivalent to ‘rel_avg’. Defaults to None, in which case the approximation method provides its default value.

minimum_stepfloat
Minimum step size allowed when using one of the relative step_calc options.

Returns:

dict
Metadata dict for the specified partial(s).

dist_size_iter(io, top_comm)

Yield names and distributed ranges of all local and remote variables in this system.

Parameters:

iostr
Either ‘input’ or ‘output’.

top_commMPI.Comm or None
The top-level MPI communicator.

Yields:

tuple
A tuple of the form ((abs_name, rank), start, end).

get_coloring_fname(mode)

Return the full pathname to a coloring file.

Parameters:

modestr
The type of coloring file desired. Must be either ‘input’ or ‘output’.

Returns:

pathlib.Path
Full pathname of the coloring file.

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

get_sizesbool, optional
If True, compute the size of each constraint.

use_prom_ivcbool
Translate ivc names to their promoted input names.

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 of a group 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
Use promoted names for inputs, else convert to absolute source 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, is_indep_var=None, is_design_var=None, tags=None, get_remote=False, rank=None, return_rel_names=True)

Retrieve metadata for a filtered list of variables.

Parameters:

iotypesstr or iter of str
Will contain either ‘input’, ‘output’, or both. Defaults to both.

metadata_keysiter of str or None
Names of metadata entries to be retrieved or None, meaning retrieve all available ‘allprocs’ metadata. If ‘val’ 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.

is_indep_varbool or None
If None (the default), do no additional filtering of the inputs. If True, list only inputs connected to an output tagged openmdao:indep_var. If False, list only inputs _not_ connected to outputs tagged openmdao:indep_var.

is_design_varbool or None
If None (the default), do no additional filtering of the inputs. If True, list only inputs connected to outputs that are driver design variables. If False, list only inputs _not_ connected to outputs that are driver design variables.

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, ‘prom_name’ and ‘discrete’, to indicate a given variable’s promoted name and whether or not it is discrete.

get_linear_vectors()

Return the linear inputs, outputs, and residuals vectors.

Returns:

(inputs, outputs, residuals): tuple of <Vector> instances
Yields the linear inputs, outputs, and residuals vectors.

get_nonlinear_vectors()

Return the inputs, outputs, and residuals vectors.

Returns:

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

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

get_sizesbool, optional
If True, compute the size of each objective.

use_prom_ivcbool
Translate ivc names to their promoted input names.

Returns:

dict
The objectives defined in the current system.

get_outputs_dir(*subdirs, mkdir=True)

Get the path under which all output files of this system are to be placed.

Parameters:

*subdirsstr
Subdirectories nested under the relevant problem output directory. To create {prob_output_dir}/a/b one would pass system.get_outputs_dir(‘a’, ‘b’).

mkdirbool
If True, attempt to create this directory if it does not exist.

Returns:

pathlib.Path
The path of the outputs directory for the problem.

get_promotions(inprom=None, outprom=None)

Return all promotions for the given promoted variable(s).

In other words, how and where did promotions occur to convert absolute variable names into the given promoted name(s) at the current System level.

Parameters:

inpromstr or None
The promoted input variable name.

outpromstr or None
The promoted output variable name.

Returns:

dict
Dictionary keyed on system pathname containing input and/or output promotion lists for each System where promotions occurred to produce the given promoted variable(s).

get_reports_dir()

Get the path to the directory where the report files should go.

If it doesn’t exist, it will be created.

Returns:

str
The path to the directory where reports should be written.

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 either absolute variable name, promoted name, or alias name, depending on the value of use_prom_ivc and whether the original key was a promoted output, promoted input, or an alias.

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 ivc names to their promoted input names.

Returns:

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

get_self_statics()

Override this in derived classes if compute_primal references static values.

Do NOT include self._discrete_inputs in the returned tuple. Include things like self.options[‘opt_name’], etc., that are used in compute_primal but are assumed to be constant during derivative computation.

Return value MUST be a tuple. Don’t forget the trailing comma if tuple has only one item. Return value MUST be hashable.

The order of these values doesn’t matter. They are only checked (by computing their hash) to see if they have changed since the last time compute_primal was jitted, and if so, compute_primal will be re-jitted.

Returns:

tuple
Tuple containing all static values required by compute_primal.

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_dup_info(name, io)

Return information about how the given variable is duplicated across MPI processes.

Parameters:

namestr
Name of the variable.

iostr
Either ‘input’ or ‘output’.

Returns:

tuple
A tuple of the form (is_duplicated, num_zeros, is_distributed).

get_var_sizes(name, io)

Return the sizes of the given variable on all procs.

Parameters:

namestr
Name of the variable.

iostr
Either ‘input’ or ‘output’.

Returns:

ndarray
Array of sizes of the variable on all procs.

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

Provide initial guess for states.

Override this method to set the initial guess for states.

Parameters:

inputsVector
Unscaled, dimensional input variables read via inputs[key].

outputsVector
Unscaled, dimensional output variables read via outputs[key].

residualsVector
Unscaled, dimensional residuals written to via residuals[key].

discrete_inputsdict or None
If not None, dict containing discrete input values.

discrete_outputsdict or None
If not None, dict containing discrete output values.

initialize()

Perform any one-time initialization run at instantiation.

is_explicit()

Return True if this is an explicit component.

Returns:

bool
True if this is an explicit component.

property linear_solver

Get the linear solver for this system.

linearize(inputs, outputs, partials)[source]

Compute sub-jacobian parts and any applicable matrix factorizations.

The model is assumed to be in an unscaled state.

Parameters:

inputsVector
Unscaled, dimensional input variables read via inputs[key].

outputsVector
Unscaled, dimensional output variables read via outputs[key].

jacobianJacobian
Sub-jac components written to jacobian[output_name, input_name].

discrete_inputsdict or None
If not None, dict containing discrete input values.

discrete_outputsdict or None
If not None, dict containing discrete output values.

list_inputs(val=True, prom_name=True, units=False, shape=False, global_shape=False, desc=False, hierarchical=True, print_arrays=False, tags=None, print_tags=False, includes=None, excludes=None, is_indep_var=None, is_design_var=None, all_procs=False, out_stream=DEFAULT_OUT_STREAM, print_min=False, print_max=False, return_format='list')

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

Parameters:

valbool, 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 True.

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.

print_tagsbool
When true, display tags in the columnar display.

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

excludesNone, str, or iter of str
Collection of glob patterns for pathnames of variables to exclude. Default is None.

is_indep_varbool or None
If None (the default), do no additional filtering of the inputs. If True, list only inputs connected to an output tagged openmdao:indep_var. If False, list only inputs _not_ connected to outputs tagged openmdao:indep_var.

is_design_varbool or None
If None (the default), do no additional filtering of the inputs. If True, list only inputs connected to outputs that are driver design variables. If False, list only inputs _not_ connected to outputs that are driver design variables.

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.

print_minbool
When true, if the input value is an array, print its smallest value.

print_maxbool
When true, if the input value is an array, print its largest value.

return_formatstr
Indicates the desired format of the return value. Can have value of ‘list’ or ‘dict’. If ‘list’, the return value is a list of (name, metadata) tuples. if ‘dict’, the return value is a dictionary mapping {name: metadata}.

Returns:

list of (name, metadata) or dict of {name: metadata}
List or dict of input names and other optional information about those inputs.

list_outputs(explicit=True, implicit=True, val=True, prom_name=True, 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, print_tags=False, includes=None, excludes=None, is_indep_var=None, is_design_var=None, all_procs=False, list_autoivcs=False, out_stream=DEFAULT_OUT_STREAM, print_min=False, print_max=False, return_format='list')

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.

valbool, optional
When True, display output values. Default is True.

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

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.

print_tagsbool
When true, display tags in the columnar display.

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

excludesNone, str, or iter of str
Collection of glob patterns for pathnames of variables to exclude. Default is None.

is_indep_varbool or None
If None (the default), do no additional filtering of the inputs. If True, list only outputs tagged openmdao:indep_var. If False, list only outputs that are _not_ tagged openmdao:indep_var.

is_design_varbool or None
If None (the default), do no additional filtering of the inputs. If True, list only inputs connected to outputs that are driver design variables. If False, list only inputs _not_ connected to outputs that are driver design variables.

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.

print_minbool
When true, if the output value is an array, print its smallest value.

print_maxbool
When true, if the output value is an array, print its largest value.

return_formatstr
Indicates the desired format of the return value. Can have value of ‘list’ or ‘dict’. If ‘list’, the return value is a list of (name, metadata) tuples. if ‘dict’, the return value is a dictionary mapping {name: metadata}.

Returns:

list of (name, metadata) or dict of {name: metadata}
List or dict of output names and other optional information about those outputs.

list_vars(val=True, prom_name=True, residuals=False, residuals_tol=None, units=False, shape=False, global_shape=False, bounds=False, scaling=False, desc=False, print_arrays=False, tags=None, print_tags=False, includes=None, excludes=None, is_indep_var=None, is_design_var=None, all_procs=False, list_autoivcs=False, out_stream=DEFAULT_OUT_STREAM, print_min=False, print_max=False, return_format='list')

Write a list of inputs and outputs sorted by component in execution order.

Parameters:

valbool, optional
When True, display output values. Default is True.

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

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.

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.

print_tagsbool
When true, display tags in the columnar display.

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

excludesNone, str, or iter of str
Collection of glob patterns for pathnames of variables to exclude. Default is None.

is_indep_varbool or None
If None (the default), do no additional filtering of the inputs. If True, list only outputs tagged openmdao:indep_var. If False, list only outputs that are _not_ tagged openmdao:indep_var.

is_design_varbool or None
If None (the default), do no additional filtering of the inputs. If True, list only inputs connected to outputs that are driver design variables. If False, list only inputs _not_ connected to outputs that are driver design variables.

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.

print_minbool
When true, if the output value is an array, print its smallest value.

print_maxbool
When true, if the output value is an array, print its largest value.

return_formatstr
Indicates the desired format of the return value. Can have value of ‘list’ or ‘dict’. If ‘list’, the return value is a list of (name, metadata) tuples. if ‘dict’, the return value is a dictionary mapping {name: metadata}.

Returns:

list of (name, metadata) or dict of {name: metadata}
List or dict of output names and other optional information about those outputs.

load_case(case)

Pull all input and output variables from a Case into this System.

Override this method if the System requires special handling when loading a case.

Parameters:

caseCase or dict
A Case from a CaseReader, or a dictionary with key ‘inputs’ mapped to the output of problem.model.list_inputs and key ‘outputs’ mapped to the output of prob.model.list_outputs. Both list_inputs and list_outputs should be called with prom_name=True and return_format=’dict’.

load_model_options()

Load the relevant model options from Problem._metadata[‘model_options’].

This method examines each path filter and corresponding options in self._problem_meta[‘model_options’]. If this System’s pathname matches the given path filter, it will assume the value for each given option which it possesses.

local_range_iter(io)

Yield names and local ranges of all local variables in this system.

Parameters:

iostr
Either ‘input’ or ‘output’.

Yields:

tuple
A tuple of the form (abs_name, start, end).

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(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:

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

run_solve_linear(mode)

Apply inverse jac product.

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

Parameters:

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, minimum_step=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
Step type for computing the size of the finite difference step. It can be ‘abs’ for absolute, ‘rel_avg’ for a size relative to the absolute value of the vector input, or ‘rel_element’ for a size relative to each value in the vector input. In addition, it can be ‘rel_legacy’ for a size relative to the norm of the vector. For backwards compatibilty, it can be ‘rel’, which is now equivalent to ‘rel_avg’. Defaults to None, in which case the approximation method provides its default value..

minimum_stepfloat
Minimum step size allowed when using one of the relative step_calc options.

directionalbool
Set to True to perform a single directional derivative for each vector variable in the pattern named in wrt.

set_constraint_options(name, ref=UNDEFINED, ref0=UNDEFINED, equals=UNDEFINED, lower=UNDEFINED, upper=UNDEFINED, adder=UNDEFINED, scaler=UNDEFINED, alias=UNDEFINED)

Set options for constraints in the model.

Can be used to set options that were set using add_constraint.

Parameters:

namestr
Name of the response variable in the system, or alias if given.

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.

equalsfloat or ndarray, optional
Equality constraint value for the variable.

lowerfloat or ndarray, optional
Lower boundary for the variable.

upperfloat or ndarray, optional
Upper boundary for the variable.

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

scalerfloat or ndarray, optional
Value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.

aliasstr, optional
Alias for this response. Necessary when adding multiple constraints on different indices or slices of a single variable.

set_design_var_options(name, lower=UNDEFINED, upper=UNDEFINED, scaler=UNDEFINED, adder=UNDEFINED, ref=UNDEFINED, ref0=UNDEFINED)

Set options for design vars in the model.

Can be used to set the options outside of setting them when calling add_design_var

Parameters:

namestr
Name of the variable in this system’s namespace.

lowerfloat or ndarray, optional
Lower boundary for the input.

upperupper or ndarray, optional
Upper boundary for the input.

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.

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

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.

set_objective_options(name, ref=UNDEFINED, ref0=UNDEFINED, adder=UNDEFINED, scaler=UNDEFINED, alias=UNDEFINED)

Set options for objectives in the model.

Can be used to set options after they have been set by add_objective.

Parameters:

namestr
Name of the response variable in the system, or alias if given.

reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.

ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.

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

scalerfloat or ndarray, optional
Value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.

aliasstr
Alias for this response. Used to disambiguate variable names when adding multiple objectives on different indices or slices of a single variable. Deprecated.

set_output_solver_options(name, lower=UNDEFINED, upper=UNDEFINED, ref=UNDEFINED, ref0=UNDEFINED, res_ref=UNDEFINED)

Set solver output options.

Allows the user to set output solver options after the output has been defined and metadata set using the add_ouput method.

Parameters:

namestr
Name of the variable in this system’s namespace.

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.

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.

set_val(name, val, units=None, indices=None)

Set an input or output variable.

Parameters:

namestr
Promoted or relative variable name in the system’s namespace.

valobject
Value to assign to this variable.

unitsstr, optional
Units of the value.

indicesint or list of ints or tuple of ints or int ndarray or Iterable or None, optional
Indices or slice to set.

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.

setup_residuals()

User hook for adding named residuals to this component.

solve_linear(d_outputs, d_residuals, mode)

Apply inverse jac product. The model is assumed to be in an unscaled state.

If mode is:
‘fwd’: d_residuals |-> d_outputs

‘rev’: d_outputs |-> d_residuals

Note : this is not the linear solution for the implicit component. We use identity so that simple implicit components can function in a preconditioner under linear gauss-seidel. To correctly solve this component, you should slot a solver in linear_solver or override this method.

Parameters:

d_outputsVector
Unscaled, dimensional quantities read via d_outputs[key].

d_residualsVector
Unscaled, dimensional quantities read via d_residuals[key].

modestr
Either ‘fwd’ or ‘rev’.

solve_nonlinear(inputs, outputs)[source]

Compute outputs given inputs. The model is assumed to be in an unscaled state.

Parameters:

inputsVector
Unscaled, dimensional input variables read via inputs[key].

outputsVector
Unscaled, dimensional output variables read via outputs[key].

system_iter(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.

Yields:

type or None

property under_approx

Return True if under complex step or finite difference.

Returns:

bool
True if under CS or FD.

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.