paraboloid_mat_vec.py¶

class
openmdao.test_suite.components.paraboloid_mat_vec.
ParaboloidMatVec
(**kwargs)[source]¶ Bases:
openmdao.test_suite.components.paraboloid.Paraboloid
Use matrixvector product.

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

add_constraint
(self, name, lower=None, upper=None, equals=None, ref=None, ref0=None, adder=None, scaler=None, indices=None, linear=False, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a constraint variable to this system.
 Parameters
 namestring
Name of the response variable in the system.
 lowerfloat or ndarray, optional
Lower boundary for the variable
 upperfloat or ndarray, optional
Upper boundary for the variable
 equalsfloat or ndarray, optional
Equality constraint value for the variable
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 indicessequence of int, optional
If variable is an array, these indicate which entries are of interest for this particular response. These may be positive or negative integers.
 linearbool
Set to True if constraint is linear. Default is False.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
If True, store the linear solution vectors for this variable so they can be used to start the next linear solution with an initial guess equal to the solution from the previous linear solve.
Notes
The response can be scaled using ref and ref0. The argument
ref0
represents the physical value when the scaled value is 0. The argumentref
represents the physical value when the scaled value is 1.

add_design_var
(self, name, lower=None, upper=None, ref=None, ref0=None, indices=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a design variable to this system.
 Parameters
 namestring
Name of the design variable in the system.
 lowerfloat or ndarray, optional
Lower boundary for the param
 upperupper or ndarray, optional
Upper boundary for the param
 reffloat or ndarray, optional
Value of design var that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of design var that scales to 0.0 in the driver.
 indicesiter of int, optional
If a param is an array, these indicate which entries are of interest for this particular design variable. These may be positive or negative integers.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
If True, store the linear solution vectors for this variable so they can be used to start the next linear solution with an initial guess equal to the solution from the previous linear solve.
Notes
The response can be scaled using ref and ref0. The argument
ref0
represents the physical value when the scaled value is 0. The argumentref
represents the physical value when the scaled value is 1.

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

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

add_input
(self, name, val=1.0, shape=None, src_indices=None, flat_src_indices=None, units=None, desc='', tags=None)¶ Add an input variable to the component.
 Parameters
 namestr
name of the variable in this component’s namespace.
 valfloat or list or tuple or ndarray or Iterable
The initial value of the variable being added in userdefined units. Default is 1.0.
 shapeint or tuple or list or None
Shape of this variable, only required if src_indices not provided and val is not an array. Default is None.
 src_indicesint or list of ints or tuple of ints or int ndarray or Iterable or None
The global indices of the source variable to transfer data from. A value of None implies this input depends on all entries of source. Default is None. The shapes of the target and src_indices must match, and form of the entries within is determined by the value of ‘flat_src_indices’.
 flat_src_indicesbool
If True, each entry of src_indices is assumed to be an index into the flattened source. Otherwise each entry must be a tuple or list of size equal to the number of dimensions of the source.
 unitsstr or None
Units in which this input variable will be provided to the component during execution. Default is None, which means it is unitless.
 descstr
description of the variable
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs.
 Returns
 dict
metadata for added variable

add_objective
(self, name, ref=None, ref0=None, index=None, adder=None, scaler=None, parallel_deriv_color=None, vectorize_derivs=False, cache_linear_solution=False)¶ Add a response variable to this system.
 Parameters
 namestring
Name of the response variable in the system.
 reffloat or ndarray, optional
Value of response variable that scales to 1.0 in the driver.
 ref0float or ndarray, optional
Value of response variable that scales to 0.0 in the driver.
 indexint, optional
If variable is an array, this indicates which entry is of interest for this particular response. This may be a positive or negative integer.
 adderfloat or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder is first in precedence. adder and scaler are an alterantive to using ref and ref0.
 scalerfloat or ndarray, optional
value to multiply the model value to get the scaled value for the driver. scaler is second in precedence. adder and scaler are an alterantive to using ref and ref0.
 parallel_deriv_colorstring
If specified, this design var will be grouped for parallel derivative calculations with other variables sharing the same parallel_deriv_color.
 vectorize_derivsbool
If True, vectorize derivative calculations.
 cache_linear_solutionbool
If True, store the linear solution vectors for this variable so they can be used to start the next linear solution with an initial guess equal to the solution from the previous linear solve.
Notes
The objective can be scaled using scaler and adder, where
\[x_{scaled} = scaler(x + adder)\]or through the use of ref/ref0, which map to scaler and adder through the equations:
\[ \begin{align}\begin{aligned}0 = scaler(ref_0 + adder)\\1 = scaler(ref + adder)\end{aligned}\end{align} \]which results in:
\[ \begin{align}\begin{aligned}adder = ref_0\\scaler = \frac{1}{ref + adder}\end{aligned}\end{align} \]

add_output
(self, name, val=1.0, shape=None, units=None, res_units=None, desc='', lower=None, upper=None, ref=1.0, ref0=0.0, res_ref=None, tags=None)¶ Add an output variable to the component.
For ExplicitComponent, res_ref defaults to the value in res unless otherwise specified.
 Parameters
 namestr
name of the variable in this component’s namespace.
 valfloat or list or tuple or ndarray
The initial value of the variable being added in userdefined units. Default is 1.0.
 shapeint or tuple or list or None
Shape of this variable, only required if val is not an array. Default is None.
 unitsstr or None
Units in which the output variables will be provided to the component during execution. Default is None, which means it has no units.
 res_unitsstr or None
Units in which the residuals of this output will be given to the user when requested. Default is None, which means it has no units.
 descstr
description of the variable.
 lowerfloat or list or tuple or ndarray or None
lower bound(s) in userdefined units. It can be (1) a float, (2) an array_like consistent with the shape arg (if given), or (3) an array_like matching the shape of val, if val is array_like. A value of None means this output has no lower bound. Default is None.
 upperfloat or list or tuple or ndarray or None
upper bound(s) in userdefined units. It can be (1) a float, (2) an array_like consistent with the shape arg (if given), or (3) an array_like matching the shape of val, if val is array_like. A value of None means this output has no upper bound. Default is None.
 reffloat
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 1. Default is 1.
 ref0float
Scaling parameter. The value in the userdefined units of this output variable when the scaled value is 0. Default is 0.
 res_reffloat
Scaling parameter. The value in the userdefined res_units of this output’s residual when the scaled value is 1. Default is None, which means residual scaling matches output scaling.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed when calling list_inputs and list_outputs and also when listing results from case recorders.
 Returns
 dict
metadata for added variable

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

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

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

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

compute
(self, inputs, outputs)¶ f(x,y) = (x3)^2 + xy + (y+4)^2  3
Optimal solution (minimum): x = 6.6667; y = 7.3333

compute_jacvec_product
(self, inputs, dinputs, doutputs, mode)[source]¶ Returns the product of the incoming vector with the Jacobian.

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

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

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

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

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

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

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

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

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

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

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

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

property
linear_solver
¶ Get the linear solver for this system.

list_inputs
(self, values=True, prom_name=False, units=False, shape=False, hierarchical=True, print_arrays=False, tags=None, out_stream=<object object at 0x7f6401d061e0>)¶ Return and optionally log a list of input names and other optional information.
If the model is parallel, only the local variables are returned to the process. Also optionally logs the information to a user defined output stream. If the model is parallel, the rank 0 process logs information about all variables across all processes.
 Parameters
 valuesbool, optional
When True, display/return input values. Default is True.
 prom_namebool, optional
When True, display/return the promoted name of the variable. Default is False.
 unitsbool, optional
When True, display/return units. Default is False.
 shapebool, optional
When True, display/return the shape of the value. Default is False.
 hierarchicalbool, optional
When True, human readable output shows variables in hierarchical format.
 print_arraysbool, optional
When False, in the columnar display, just display norm of any ndarrays with size > 1. The norm is surrounded by vertical bars to indicate that it is a norm. When True, also display full values of the ndarray below the row. Format is affected by the values set with numpy.set_printoptions Default is False.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed. Only inputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.
 out_streamfilelike object
Where to send human readable output. Default is sys.stdout. Set to None to suppress.
 Returns
 list
list of input names and other optional information about those inputs

list_outputs
(self, explicit=True, implicit=True, values=True, prom_name=False, residuals=False, residuals_tol=None, units=False, shape=False, bounds=False, scaling=False, hierarchical=True, print_arrays=False, tags=None, out_stream=<object object at 0x7f6401d061e0>)¶ Return and optionally log a list of output names and other optional information.
If the model is parallel, only the local variables are returned to the process. Also optionally logs the information to a user defined output stream. If the model is parallel, the rank 0 process logs information about all variables across all processes.
 Parameters
 explicitbool, optional
include outputs from explicit components. Default is True.
 implicitbool, optional
include outputs from implicit components. Default is True.
 valuesbool, optional
When True, display/return output values. Default is True.
 prom_namebool, optional
When True, display/return the promoted name of the variable. Default is False.
 residualsbool, optional
When True, display/return residual values. Default is False.
 residuals_tolfloat, optional
If set, limits the output of list_outputs to only variables where the norm of the resids array is greater than the given ‘residuals_tol’. Default is None.
 unitsbool, optional
When True, display/return units. Default is False.
 shapebool, optional
When True, display/return the shape of the value. Default is False.
 boundsbool, optional
When True, display/return bounds (lower and upper). Default is False.
 scalingbool, optional
When True, display/return scaling (ref, ref0, and res_ref). Default is False.
 hierarchicalbool, optional
When True, human readable output shows variables in hierarchical format.
 print_arraysbool, optional
When False, in the columnar display, just display norm of any ndarrays with size > 1. The norm is surrounded by vertical bars to indicate that it is a norm. When True, also display full values of the ndarray below the row. Format is affected by the values set with numpy.set_printoptions Default is False.
 tagsstr or list of strs
User defined tags that can be used to filter what gets listed. Only outputs with the given tags will be listed. Default is None, which means there will be no filtering based on tags.
 out_streamfilelike
Where to send human readable output. Default is sys.stdout. Set to None to suppress.
 Returns
 list
list of output names and other optional information about those outputs

property
ln_solver
¶ Get the linear solver for this system.

property
metadata
¶ Get the options for this System.

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

property
nl_solver
¶ Get the nonlinear solver for this system.

property
nonlinear_solver
¶ Get the nonlinear solver for this system.

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

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

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

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

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

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

run_solve_linear
(self, vec_names, mode)¶ Apply inverse jac product.
This calls _solve_linear, but with the model assumed to be in an unscaled state.
 Parameters
 vec_names[str, …]
list of names of the righthandside vectors.
 modestr
‘fwd’ or ‘rev’.

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

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

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

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

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

use_fixed_coloring
(self, coloring=<object object at 0x7f640240aad0>, 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.
