quasi_newton module¶
A set of quasi Newton algorithm variants for solving MDAs.
- class gemseo.mda.quasi_newton.MDAQuasiNewton(disciplines, max_mda_iter=10, name=None, grammar_type=GrammarType.JSON, method='hybr', use_gradient=False, tolerance=1e-06, linear_solver_tolerance=1e-12, warm_start=False, use_lu_fact=False, coupling_structure=None, linear_solver='DEFAULT', linear_solver_options=None)[source]¶
Bases:
MDARoot
Quasi-Newton solver for MDA.
Quasi-Newton methods include numerous variants ( Broyden, Levenberg-Marquardt <https://en.wikipedia.org/wiki/Levenberg-Marquardt_algorithm> __, …).
The name of the variant should be provided via the
method
parameter of the class.The new iterate is given by:
\[\begin{split}x_{k+1} = x_k - \\rho_k B_k f(x_k)\end{split}\]where \(\\rho_k\) is a coefficient chosen in order to minimize the convergence and \(B_k\) is an approximation of \(Df(x_k)^{-1}\), the inverse of the Jacobian of \(f\) at \(x_k\).
Initialize self. See help(type(self)) for accurate signature.
- Parameters:
disciplines (Sequence[MDODiscipline]) – The disciplines from which to compute the MDA.
max_mda_iter (int) –
The maximum iterations number for the MDA algorithm.
By default it is set to 10.
name (str | None) – The name to be given to the MDA. If
None
, use the name of the class.grammar_type (MDODiscipline.GrammarType) –
The type of the input and output grammars.
By default it is set to “JSONGrammar”.
method (str) –
The name of the method in scipy root finding, among
QUASI_NEWTON_METHODS
.By default it is set to “hybr”.
use_gradient (bool) –
Whether to use the analytic gradient of the discipline.
By default it is set to False.
tolerance (float) –
The tolerance of the iterative direct coupling solver; the norm of the current residuals divided by initial residuals norm shall be lower than the tolerance to stop iterating.
By default it is set to 1e-06.
linear_solver_tolerance (float) –
The tolerance of the linear solver in the adjoint equation.
By default it is set to 1e-12.
warm_start (bool) –
Whether the second iteration and ongoing start from the previous coupling solution.
By default it is set to False.
use_lu_fact (bool) –
Whether to store a LU factorization of the matrix when using adjoint/forward differentiation. to solve faster multiple RHS problem.
By default it is set to False.
coupling_structure (MDOCouplingStructure | None) – The coupling structure to be used by the MDA. If
None
, it is created from disciplines.linear_solver (str) –
The name of the linear solver.
By default it is set to “DEFAULT”.
linear_solver_options (Mapping[str, Any] | None) – The options passed to the linear solver factory.
- Raises:
ValueError – If the method is not a valid quasi-Newton method.
- class ApproximationMode(value)¶
Bases:
StrEnum
The approximation derivation modes.
- CENTERED_DIFFERENCES = 'centered_differences'¶
The centered differences method used to approximate the Jacobians by perturbing each variable with a small real number.
- COMPLEX_STEP = 'complex_step'¶
The complex step method used to approximate the Jacobians by perturbing each variable with a small complex number.
- FINITE_DIFFERENCES = 'finite_differences'¶
The finite differences method used to approximate the Jacobians by perturbing each variable with a small real number.
- class CacheType(value)¶
Bases:
StrEnum
The name of the cache class.
- HDF5 = 'HDF5Cache'¶
- MEMORY_FULL = 'MemoryFullCache'¶
- NONE = ''¶
No cache is used.
- SIMPLE = 'SimpleCache'¶
- class ExecutionStatus(value)¶
Bases:
StrEnum
The execution statuses of a discipline.
- DONE = 'DONE'¶
- FAILED = 'FAILED'¶
- LINEARIZE = 'LINEARIZE'¶
- PENDING = 'PENDING'¶
- RUNNING = 'RUNNING'¶
- VIRTUAL = 'VIRTUAL'¶
- class GrammarType(value)¶
Bases:
StrEnum
The name of the grammar class.
- JSON = 'JSONGrammar'¶
- PYDANTIC = 'PydanticGrammar'¶
- SIMPLE = 'SimpleGrammar'¶
- SIMPLER = 'SimplerGrammar'¶
- class InitJacobianType(value)¶
Bases:
StrEnum
The way to initialize Jacobian matrices.
- DENSE = 'dense'¶
The Jacobian is initialized as a NumPy ndarray filled in with zeros.
- EMPTY = 'empty'¶
The Jacobian is initialized as an empty NumPy ndarray.
- SPARSE = 'sparse'¶
The Jacobian is initialized as a SciPy CSR array with zero elements.
- class LinearizationMode(value)¶
Bases:
StrEnum
An enumeration.
- ADJOINT = 'adjoint'¶
- AUTO = 'auto'¶
- CENTERED_DIFFERENCES = 'centered_differences'¶
- COMPLEX_STEP = 'complex_step'¶
- DIRECT = 'direct'¶
- FINITE_DIFFERENCES = 'finite_differences'¶
- REVERSE = 'reverse'¶
- class ReExecutionPolicy(value)¶
Bases:
StrEnum
The re-execution policy of a discipline.
- DONE = 'RE_EXEC_DONE'¶
- NEVER = 'RE_EXEC_NEVER'¶
- class ResidualScaling(value)¶
Bases:
LowercaseStrEnum
The scaling method applied to MDA residuals for convergence monitoring.
- INITIAL_RESIDUAL_COMPONENT = 'initial_residual_component'¶
k`-th residual is scaled component-wise. Each component is scaled by the corresponding component of the initial residual (if not null, else it is not scaled). The MDA is considered converged when each component satisfies,
\[\max_i \left| \frac{(R_k)_i}{(R_0)_i} \right| \leq \text{tol}.\]- Type:
The
- Type:
math
- INITIAL_RESIDUAL_NORM = 'initial_residual_norm'¶
k`-th residual vector is scaled by the Euclidean norm of the initial residual (if not null, else it is not scaled). The MDA is considered converged when its Euclidean norm satisfies,
\[\frac{ \|R_k\|_2 }{ \|R_0\|_2 } \leq \text{tol}.\]- Type:
The
- Type:
math
- INITIAL_SUBRESIDUAL_NORM = 'initial_subresidual_norm'¶
k`-th residual vector is scaled discipline-wise. The sub-residual associated wich each discipline is scaled by the Euclidean norm of the initial sub-residual (if not null, else it is not scaled). The MDA is considered converged when the Euclidean norm of each sub-residual satisfies,
\[\max_i \left| \frac{\|r^i_k\|_2}{\|r^i_0\|_2} \right| \leq \text{tol}.\]- Type:
The
- Type:
math
- NO_SCALING = 'no_scaling'¶
The residual vector is not scaled. The MDA is considered converged when its Euclidean norm satisfies,
\[\|R_k\|_2 \leq \text{tol}.\]
- N_COUPLING_VARIABLES = 'n_coupling_variables'¶
k`-th residual vector is scaled using the number of coupling variables. The MDA is considered converged when its Euclidean norm satisfies, .. math:
\frac{ \|R_k\|_2 }{ \sqrt{n_\text{coupl.}} } \leq \text{tol}.
- Type:
The
- Type:
math
- SCALED_INITIAL_RESIDUAL_COMPONENT = 'scaled_initial_residual_component'¶
k`-th residual vector is scaled component-wise and by the number coupling variables. If \(\div\) denotes the component-wise division between two vectors, then the MDA is considered converged when the residual vector satisfies,
\[\frac{1}{\sqrt{n_\text{coupl.}}} \| R_k \div R_0 \|_2 \leq \text{tol}.\]- Type:
The
- Type:
math
- classmethod activate_time_stamps()¶
Activate the time stamps.
For storing start and end times of execution and linearizations.
- Return type:
None
- add_differentiated_inputs(inputs=None)¶
Add the inputs for differentiation.
The inputs that do not represent continuous numbers are filtered out.
- Parameters:
inputs (Iterable[str] | None) – The input variables against which to differentiate the outputs. If
None
, all the inputs of the discipline are used.- Raises:
ValueError – When ``inputs `` are not in the input grammar.
- Return type:
None
- add_differentiated_outputs(outputs=None)¶
Add the outputs for differentiation.
The outputs that do not represent continuous numbers are filtered out.
- Parameters:
outputs (Iterable[str] | None) – The output variables to be differentiated. If
None
, all the outputs of the discipline are used.- Raises:
ValueError – When ``outputs `` are not in the output grammar.
- Return type:
None
- add_namespace_to_input(name, namespace)¶
Add a namespace prefix to an existing input grammar element.
The updated input grammar element name will be
namespace
+namespaces_separator
+name
.
- add_namespace_to_output(name, namespace)¶
Add a namespace prefix to an existing output grammar element.
The updated output grammar element name will be
namespace
+namespaces_separator
+name
.
- add_status_observer(obs)¶
Add an observer for the status.
Add an observer for the status to be notified when self changes of status.
- Parameters:
obs (Any) – The observer to add.
- Return type:
None
- auto_get_grammar_file(is_input=True, name=None, comp_dir=None)¶
Use a naming convention to associate a grammar file to the discipline.
Search in the directory
comp_dir
for either an input grammar file namedname + "_input.json"
or an output grammar file namedname + "_output.json"
.- Parameters:
is_input (bool) –
Whether to search for an input or output grammar file.
By default it is set to True.
name (str | None) – The name to be searched in the file names. If
None
, use the name of the discipline class.comp_dir (str | Path | None) – The directory in which to search the grammar file. If
None
, use theGRAMMAR_DIRECTORY
if any, or the directory of the discipline class module.
- Returns:
The grammar file path.
- Return type:
Path
- check_input_data(input_data, raise_exception=True)¶
Check the input data validity.
- check_jacobian(input_data=None, derr_approx=ApproximationMode.FINITE_DIFFERENCES, step=1e-07, threshold=1e-08, linearization_mode='auto', inputs=None, outputs=None, parallel=False, n_processes=2, use_threading=False, wait_time_between_fork=0, auto_set_step=False, plot_result=False, file_path='jacobian_errors.pdf', show=False, fig_size_x=10, fig_size_y=10, reference_jacobian_path=None, save_reference_jacobian=False, indices=None)¶
Check if the analytical Jacobian is correct with respect to a reference one.
If reference_jacobian_path is not None and save_reference_jacobian is True, compute the reference Jacobian with the approximation method and save it in reference_jacobian_path.
If reference_jacobian_path is not None and save_reference_jacobian is False, do not compute the reference Jacobian but read it from reference_jacobian_path.
If reference_jacobian_path is None, compute the reference Jacobian without saving it.
- Parameters:
input_data (Mapping[str, ndarray] | None) – The input values. If
None
, use the default input values.derr_approx (MDODiscipline.ApproximationMode) –
The derivative approximation method.
By default it is set to “finite_differences”.
step (float) –
The step for finite differences or complex step differentiation methods.
By default it is set to 1e-07.
threshold (float) –
The acceptance threshold for the Jacobian error.
By default it is set to 1e-08.
linearization_mode (str) –
The mode of linearization, either “direct”, “adjoint” or “auto” switch depending on dimensions of inputs and outputs.
By default it is set to “auto”.
inputs (Iterable[str] | None) – The names of the inputs with respect to which to differentiate. If
None
, use the inputs of the MDA.outputs (Iterable[str] | None) – The outputs to differentiate. If
None
, use all the outputs of the MDA.parallel (bool) –
Whether to execute the MDA in parallel.
By default it is set to False.
n_processes (int) –
The maximum simultaneous number of threads, if
use_threading
is True, or processes otherwise, used to parallelize the execution.By default it is set to 2.
use_threading (bool) –
Whether to use threads instead of processes to parallelize the execution; multiprocessing will copy (serialize) all the disciplines, while threading will share all the memory. This is important to note if you want to execute the same discipline multiple times, you shall use multiprocessing.
By default it is set to False.
wait_time_between_fork (int) –
The time waited between two forks of the process / thread.
By default it is set to 0.
auto_set_step (bool) –
Whether to compute the optimal step for a forward first order finite differences gradient approximation.
By default it is set to False.
plot_result (bool) –
Whether to plot the result of the validation comparing the exact and approximated Jacobians.
By default it is set to False.
file_path (str | Path) –
The path to the output file if plot_result is True.
By default it is set to “jacobian_errors.pdf”.
show (bool) –
Whether to open the figure.
By default it is set to False.
fig_size_x (float) –
The x size of the figure in inches.
By default it is set to 10.
fig_size_y (float) –
The y size of the figure in inches.
By default it is set to 10.
reference_jacobian_path (None | Path | str) – The path of the reference Jacobian file.
save_reference_jacobian (bool) –
Whether to save the reference Jacobian.
By default it is set to False.
indices (Iterable[int] | None) – The indices of the inputs and outputs for the different sub-Jacobian matrices, formatted as
{variable_name: variable_components}
wherevariable_components
can be either an integer, e.g. 2 a sequence of integers, e.g. [0, 3], a slice, e.g. slice(0,3), the ellipsis symbol (…) or None, which is the same as ellipsis. If a variable name is missing, consider all its components. IfNone
, consider all the components of all theinputs
andoutputs
.
- Returns:
Whether the passed Jacobian is correct.
- Return type:
- check_output_data(raise_exception=True)¶
Check the output data validity.
- Parameters:
raise_exception (bool) –
Whether to raise an exception when the data is invalid.
By default it is set to True.
- Return type:
None
- classmethod deactivate_time_stamps()¶
Deactivate the time stamps.
For storing start and end times of execution and linearizations.
- Return type:
None
- execute(input_data=None)¶
Execute the discipline.
This method executes the discipline:
Adds the default inputs to the
input_data
if some inputs are not defined in input_data but exist inMDODiscipline.default_inputs
.Checks whether the last execution of the discipline was called with identical inputs, i.e. cached in
MDODiscipline.cache
; if so, directly returnsself.cache.get_output_cache(inputs)
.Caches the inputs.
Checks the input data against
MDODiscipline.input_grammar
.If
MDODiscipline.data_processor
is not None, runs the preprocessor.Updates the status to
MDODiscipline.ExecutionStatus.RUNNING
.Calls the
MDODiscipline._run()
method, that shall be defined.If
MDODiscipline.data_processor
is not None, runs the postprocessor.Checks the output data.
Caches the outputs.
Updates the status to
MDODiscipline.ExecutionStatus.DONE
orMDODiscipline.ExecutionStatus.FAILED
.Updates summed execution time.
- Parameters:
input_data (Mapping[str, Any] | None) – The input data needed to execute the discipline according to the discipline input grammar. If
None
, use theMDODiscipline.default_inputs
.- Returns:
The discipline local data after execution.
- Return type:
- execute_all_disciplines(input_local_data, update_local_data=True)¶
Execute all disciplines.
- static from_pickle(file_path)¶
Deserialize a discipline from a file.
- Parameters:
file_path (str | Path) – The path to the file containing the discipline.
- Returns:
The discipline instance.
- Return type:
- get_all_inputs()¶
Return the local input data.
The order is given by
MDODiscipline.get_input_data_names()
.- Returns:
The local input data.
- Return type:
Iterator[Any]
- get_all_outputs()¶
Return the local output data.
The order is given by
MDODiscipline.get_output_data_names()
.- Returns:
The local output data.
- Return type:
Iterator[Any]
- get_current_resolved_variables_vector()¶
Return the vector of resolved variables (couplings and state variables).
- Return type:
- static get_data_list_from_dict(keys, data_dict)¶
Filter the dict from a list of keys or a single key.
If keys is a string, then the method return the value associated to the key. If keys is a list of strings, then the method returns a generator of value corresponding to the keys which can be iterated.
- get_disciplines_in_dataflow_chain()¶
Return the disciplines that must be shown as blocks in the XDSM.
By default, only the discipline itself is shown. This function can be differently implemented for any type of inherited discipline.
- Returns:
The disciplines shown in the XDSM chain.
- Return type:
- get_expected_dataflow()¶
Return the expected data exchange sequence.
This method is used for the XDSM representation.
The default expected data exchange sequence is an empty list.
See also
MDOFormulation.get_expected_dataflow
- Returns:
The data exchange arcs.
- Return type:
- get_expected_workflow()¶
Return the expected execution sequence.
This method is used for the XDSM representation.
The default expected execution sequence is the execution of the discipline itself.
See also
MDOFormulation.get_expected_workflow
- Returns:
The expected execution sequence.
- Return type:
- get_input_data(with_namespaces=True)¶
Return the local input data as a dictionary.
- get_input_data_names(with_namespaces=True)¶
Return the names of the input variables.
- get_input_output_data_names(with_namespaces=True)¶
Return the names of the input and output variables.
- get_inputs_asarray()¶
Return the local output data as a large NumPy array.
The order is the one of
MDODiscipline.get_all_outputs()
.- Returns:
The local output data.
- Return type:
- get_inputs_by_name(data_names)¶
Return the local data associated with input variables.
- Parameters:
data_names (Iterable[str]) – The names of the input variables.
- Returns:
The local data for the given input variables.
- Raises:
ValueError – When a variable is not an input of the discipline.
- Return type:
Iterator[Any]
- get_local_data_by_name(data_names)¶
Return the local data of the discipline associated with variables names.
- Parameters:
data_names (Iterable[str]) – The names of the variables.
- Returns:
The local data associated with the variables names.
- Raises:
ValueError – When a name is not a discipline input name.
- Return type:
Iterator[Any]
- get_output_data(with_namespaces=True)¶
Return the local output data as a dictionary.
- get_output_data_names(with_namespaces=True)¶
Return the names of the output variables.
- get_outputs_asarray()¶
Return the local input data as a large NumPy array.
The order is the one of
MDODiscipline.get_all_inputs()
.- Returns:
The local input data.
- Return type:
- get_outputs_by_name(data_names)¶
Return the local data associated with output variables.
- Parameters:
data_names (Iterable[str]) – The names of the output variables.
- Returns:
The local data for the given output variables.
- Raises:
ValueError – When a variable is not an output of the discipline.
- Return type:
Iterator[Any]
- get_sub_disciplines(recursive=False)¶
Determine the sub-disciplines.
This method lists the sub-disciplines’ disciplines. It will list up to one level of disciplines contained inside another one unless the
recursive
argument is set toTrue
.- Parameters:
recursive (bool) –
If
True
, the method will look inside any discipline that has other disciplines inside until it reaches a discipline without sub-disciplines, in this case the return value will not include any discipline that has sub-disciplines. IfFalse
, the method will list up to one level of disciplines contained inside another one, in this case the return value may include disciplines that contain sub-disciplines.By default it is set to False.
- Returns:
The sub-disciplines.
- Return type:
- is_all_inputs_existing(data_names)¶
Test if several variables are discipline inputs.
- is_all_outputs_existing(data_names)¶
Test if several variables are discipline outputs.
- is_input_existing(data_name)¶
Test if a variable is a discipline input.
- is_output_existing(data_name)¶
Test if a variable is a discipline output.
- linearize(input_data=None, compute_all_jacobians=False, execute=True)¶
Compute the Jacobians of some outputs with respect to some inputs.
- Parameters:
input_data (Mapping[str, Any] | None) – The input data for which to compute the Jacobian. If
None
, use theMDODiscipline.default_inputs
.compute_all_jacobians (bool) –
Whether to compute the Jacobians of all the output with respect to all the inputs. Otherwise, set the input variables against which to differentiate the output ones with
add_differentiated_inputs()
and set these output variables to differentiate withadd_differentiated_outputs()
.By default it is set to False.
execute (bool) –
Whether to start by executing the discipline with the input data for which to compute the Jacobian; this allows to ensure that the discipline was executed with the right input data; it can be almost free if the corresponding output data have been stored in the
cache
.By default it is set to True.
- Returns:
The Jacobian of the discipline shaped as
{output_name: {input_name: jacobian_array}}
wherejacobian_array[i, j]
is the partial derivative ofoutput_name[i]
with respect toinput_name[j]
.- Raises:
ValueError – When either the inputs for which to differentiate the outputs or the outputs to differentiate are missing.
- Return type:
- linearize_all_disciplines(input_data, execute=True)¶
Linearize all disciplines.
- Parameters:
input_data (Mapping[str, NDArray]) – The input data to be passed to the disciplines.
execute (bool) –
Whether to start by executing the discipline with the input data for which to compute the Jacobian; this allows to ensure that the discipline was executed with the right input data; it can be almost free if the corresponding output data have been stored in the
cache
.By default it is set to True.
- Return type:
None
- notify_status_observers()¶
Notify all status observers that the status has changed.
- Return type:
None
- plot_residual_history(show=False, save=True, n_iterations=None, logscale=None, filename='', fig_size=None)¶
Generate a plot of the residual history.
The first iteration of each new execution is marked with a red dot.
- Parameters:
show (bool) –
Whether to display the plot on screen.
By default it is set to False.
save (bool) –
Whether to save the plot as a PDF file.
By default it is set to True.
n_iterations (int | None) – The number of iterations on the x axis. If
None
, use all the iterations.logscale (tuple[int, int] | None) – The limits of the y axis. If
None
, do not change the limits of the y axis.filename (Path | str) –
The name of the file to save the figure. If empty, use “{mda.name}_residual_history.pdf”.
By default it is set to “”.
fig_size (FigSizeType | None) – The width and height of the figure in inches, e.g. (w, h).
- Returns:
The figure, to be customized if not closed.
- Return type:
Figure
- remove_status_observer(obs)¶
Remove an observer for the status.
- Parameters:
obs (Any) – The observer to remove.
- Return type:
None
- reset_disciplines_statuses()¶
Reset all the statuses of the disciplines.
- Return type:
None
- reset_statuses_for_run()¶
Set all the statuses to
MDODiscipline.ExecutionStatus.PENDING
.- Raises:
ValueError – When the discipline cannot be run because of its status.
- Return type:
None
- set_cache_policy(cache_type=CacheType.SIMPLE, cache_tolerance=0.0, cache_hdf_file=None, cache_hdf_node_path=None, is_memory_shared=True)¶
Set the type of cache to use and the tolerance level.
This method defines when the output data have to be cached according to the distance between the corresponding input data and the input data already cached for which output data are also cached.
The cache can be either a
SimpleCache
recording the last execution or a cache storing all executions, e.g.MemoryFullCache
andHDF5Cache
. Caching data can be either in-memory, e.g.SimpleCache
andMemoryFullCache
, or on the disk, e.g.HDF5Cache
.The attribute
CacheFactory.caches
provides the available caches types.- Parameters:
cache_type (CacheType) –
The type of cache.
By default it is set to “SimpleCache”.
cache_tolerance (float) –
The maximum relative norm of the difference between two input arrays to consider that two input arrays are equal.
By default it is set to 0.0.
cache_hdf_file (str | Path | None) – The path to the HDF file to store the data; this argument is mandatory when the
MDODiscipline.CacheType.HDF5
policy is used.cache_hdf_node_path (str | None) – The name of the HDF file node to store the discipline data, possibly passed as a path
root_name/.../group_name/.../node_name
. IfNone
,MDODiscipline.name
is used.is_memory_shared (bool) –
Whether to store the data with a shared memory dictionary, which makes the cache compatible with multiprocessing.
By default it is set to True.
- Return type:
None
- set_disciplines_statuses(status)¶
Set the sub-disciplines statuses.
To be implemented in subclasses.
- Parameters:
status (str) – The status.
- Return type:
None
- set_jacobian_approximation(jac_approx_type=ApproximationMode.FINITE_DIFFERENCES, jax_approx_step=1e-07, jac_approx_n_processes=1, jac_approx_use_threading=False, jac_approx_wait_time=0)¶
Set the Jacobian approximation method.
Sets the linearization mode to approx_method, sets the parameters of the approximation for further use when calling
MDODiscipline.linearize()
.- Parameters:
jac_approx_type (ApproximationMode) –
The approximation method, either “complex_step” or “finite_differences”.
By default it is set to “finite_differences”.
jax_approx_step (float) –
The differentiation step.
By default it is set to 1e-07.
jac_approx_n_processes (int) –
The maximum simultaneous number of threads, if
jac_approx_use_threading
is True, or processes otherwise, used to parallelize the execution.By default it is set to 1.
jac_approx_use_threading (bool) –
Whether to use threads instead of processes to parallelize the execution; multiprocessing will copy (serialize) all the disciplines, while threading will share all the memory This is important to note if you want to execute the same discipline multiple times, you shall use multiprocessing.
By default it is set to False.
jac_approx_wait_time (float) –
The time waited between two forks of the process / thread.
By default it is set to 0.
- Return type:
None
- set_linear_relationships(outputs=(), inputs=())¶
Set linear relationships between discipline inputs and outputs.
- Parameters:
outputs (Iterable[str]) –
The discipline output(s) in a linear relation with the input(s). If empty, all discipline outputs are considered.
By default it is set to ().
inputs (Iterable[str]) –
The discipline input(s) in a linear relation with the output(s). If empty, all discipline inputs are considered.
By default it is set to ().
- Return type:
None
- set_optimal_fd_step(outputs=None, inputs=None, compute_all_jacobians=False, print_errors=False, numerical_error=2.220446049250313e-16)¶
Compute the optimal finite-difference step.
Compute the optimal step for a forward first order finite differences gradient approximation. Requires a first evaluation of the perturbed functions values. The optimal step is reached when the truncation error (cut in the Taylor development), and the numerical cancellation errors (round-off when doing f(x+step)-f(x)) are approximately equal.
Warning
This calls the discipline execution twice per input variables.
See also
https://en.wikipedia.org/wiki/Numerical_differentiation and “Numerical Algorithms and Digital Representation”, Knut Morken , Chapter 11, “Numerical Differentiation”
- Parameters:
inputs (Iterable[str] | None) – The inputs wrt which the outputs are linearized. If
None
, use theMDODiscipline._differentiated_inputs
.outputs (Iterable[str] | None) – The outputs to be linearized. If
None
, use theMDODiscipline._differentiated_outputs
.compute_all_jacobians (bool) –
Whether to compute the Jacobians of all the output with respect to all the inputs. Otherwise, set the input variables against which to differentiate the output ones with
add_differentiated_inputs()
and set these output variables to differentiate withadd_differentiated_outputs()
.By default it is set to False.
print_errors (bool) –
Whether to display the estimated errors.
By default it is set to False.
numerical_error (float) –
The numerical error associated to the calculation of f. By default, this is the machine epsilon (appx 1e-16), but can be higher when the calculation of f requires a numerical resolution.
By default it is set to 2.220446049250313e-16.
- Returns:
The estimated errors of truncation and cancellation error.
- Raises:
ValueError – When the Jacobian approximation method has not been set.
- Return type:
ndarray
- store_local_data(**kwargs)¶
Store discipline data in local data.
- Parameters:
**kwargs (Any) – The data to be stored in
MDODiscipline.local_data
.- Return type:
None
- to_pickle(file_path)¶
Serialize the discipline and store it in a file.
- Parameters:
file_path (str | Path) – The path to the file to store the discipline.
- Return type:
None
- ANDERSON = 'anderson'¶
- BROYDEN1 = 'broyden1'¶
- BROYDEN2 = 'broyden2'¶
- DF_SANE = 'df-sane'¶
- DIAG_BROYDEN = 'diagbroyden'¶
- EXCITING_MIXING = 'excitingmixing'¶
- GRAMMAR_DIRECTORY: ClassVar[str | None] = None¶
The directory in which to search for the grammar files if not the class one.
- HYBRID = 'hybr'¶
- KRYLOV = 'krylov'¶
- LEVENBERG_MARQUARDT = 'lm'¶
- LINEAR_MIXING = 'linearmixing'¶
- QUASI_NEWTON_METHODS: ClassVar[list[str]] = ['hybr', 'lm', 'broyden1', 'broyden2', 'anderson', 'linearmixing', 'diagbroyden', 'excitingmixing', 'krylov', 'df-sane']¶
- property acceleration_method: AccelerationMethod¶
The acceleration method.
- activate_counters: ClassVar[bool] = True¶
Whether to activate the counters (execution time, calls and linearizations).
- activate_input_data_check: ClassVar[bool] = True¶
Whether to check the input data respect the input grammar.
- activate_output_data_check: ClassVar[bool] = True¶
Whether to check the output data respect the output grammar.
- assembly: JacobianAssembly¶
- cache: AbstractCache | None¶
The cache containing one or several executions of the discipline according to the cache policy.
- property cache_tol: float¶
The cache input tolerance.
This is the tolerance for equality of the inputs in the cache. If norm(stored_input_data-input_data) <= cache_tol * norm(stored_input_data), the cached data for
stored_input_data
is returned when callingself.execute(input_data)
.- Raises:
ValueError – When the discipline does not have a cache.
- coupling_structure: MDOCouplingStructure¶
The coupling structure to be used by the MDA.
- data_processor: DataProcessor¶
A tool to pre- and post-process discipline data.
- property default_outputs: Defaults¶
The default outputs used when
virtual_execution
isTrue
.
- property disciplines: list[MDODiscipline]¶
The sub-disciplines, if any.
- property exec_time: float | None¶
The cumulated execution time of the discipline.
This property is multiprocessing safe.
- Raises:
RuntimeError – When the discipline counters are disabled.
- property grammar_type: GrammarType¶
The type of grammar to be used for inputs and outputs declaration.
- input_grammar: BaseGrammar¶
The input grammar.
- jac: MutableMapping[str, MutableMapping[str, ndarray | csr_array | JacobianOperator]]¶
The Jacobians of the outputs wrt inputs.
The structure is
{output: {input: matrix}}
.
- property linear_relationships: Mapping[str, Iterable[str]]¶
The linear relationships between inputs and outputs.
- property linearization_mode: LinearizationMode¶
The linearization mode among
MDODiscipline.LinearizationMode
.- Raises:
ValueError – When the linearization mode is unknown.
- property local_data: DisciplineData¶
The current input and output data.
- matrix_type: JacobianAssembly.JacobianType¶
The type of the matrix.
- property n_calls: int | None¶
The number of times the discipline was executed.
This property is multiprocessing safe.
- Raises:
RuntimeError – When the discipline counters are disabled.
- property n_calls_linearize: int | None¶
The number of times the discipline was linearized.
This property is multiprocessing safe.
- Raises:
RuntimeError – When the discipline counters are disabled.
- n_processes: int¶
The maximum number of simultaneous threads, if
use_threading
is True, or processes otherwise, used to parallelize the execution.
- output_grammar: BaseGrammar¶
The output grammar.
- re_exec_policy: ReExecutionPolicy¶
The policy to re-execute the same discipline.
- residual_variables: dict[str, str]¶
The output variables mapping to their inputs, to be considered as residuals; they shall be equal to zero.
- scaling: ResidualScaling¶
The scaling method applied to MDA residuals for convergence monitoring.
- property status: ExecutionStatus¶
The status of the discipline.
The status aims at monitoring the process and give the user a simplified view on the state (the process state = execution or linearize or done) of the disciplines. The core part of the execution is _run, the core part of linearize is _compute_jacobian or approximate jacobian computation.
- time_stamps: ClassVar[dict[str, float] | None] = None¶
The mapping from discipline name to their execution time.
- virtual_execution: ClassVar[bool] = False¶
Whether to skip the
_run()
method during execution and return thedefault_outputs
, whatever the inputs.