gemseo / algos

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design_space module

Design space.

A design space is used to represent the optimization’s unknowns, a.k.a. the design variables.

A DesignSpace describes this design space at a given state, in terms of names, sizes, types, bounds and current values of the design variables.

Variables can easily be added to the DesignSpace using the DesignSpace.add_variable() method or removed using the DesignSpace.remove_variable() method.

We can also filter the design variables using the DesignSpace.filter() method.

Getters and setters are also available to get or set the value of a given variable property.

Lastly, an instance of DesignSpace can be stored in a txt or HDF file.

class gemseo.algos.design_space.DesignSpace(name='')[source]

Bases: MutableMapping

Description of a design space.

It defines a set of variables from their names, sizes, types and bounds.

In addition, it provides the current values of these variables that can be used as the initial solution of an OptimizationProblem.

A DesignSpace has the same API as a dictionary, e.g. variable = design_space["x"], other_design_space["x"] = design_space["x"], del design_space["x"], for name, value in design_space["x"].items(), …

Parameters:

name (str) –

The name to be given to the design space. If empty, the design space is unnamed.

By default it is set to “”.

class DesignVariable(size=1, var_type=_DesignVariableType.FLOAT, l_b=None, u_b=None, value=None)[source]

Bases: NamedTuple

A design variable.

Create new instance of DesignVariable(size, var_type, l_b, u_b, value)

Parameters:
  • size (int | None) –

    By default it is set to 1.

  • var_type (NDArray[_DesignVariableType] | _DesignVariableType | None) –

    By default it is set to “float”.

  • l_b (ndarray | None)

  • u_b (ndarray | None)

  • value (ndarray | None)

l_b: ndarray | None

Alias for field number 2

size: int | None

Alias for field number 0

u_b: ndarray | None

Alias for field number 3

value: ndarray | None

Alias for field number 4

var_type: NDArray[_DesignVariableType] | _DesignVariableType | None

Alias for field number 1

DesignVariableType

alias of _DesignVariableType

add_variable(name, size=1, var_type=_DesignVariableType.FLOAT, l_b=None, u_b=None, value=None)[source]

Add a variable to the design space.

Parameters:
  • name (str) – The name of the variable.

  • size (int) –

    The size of the variable.

    By default it is set to 1.

  • var_type (DesignVariableType | Sequence[DesignVariableType]) –

    Either the type of the variable or the types of its components.

    By default it is set to “float”.

  • l_b (Number | Iterable[Number] | None) – The lower bound of the variable. If None, use \(-\infty\).

  • u_b (Number | Iterable[Number] | None) – The upper bound of the variable. If None, use \(+\infty\).

  • value (Number | Iterable[Number] | None) – The default value of the variable. If None, do not use a default value.

Raises:

ValueError – Either if the variable already exists or if the size is not a positive integer.

Return type:

None

array_to_dict(x_array)[source]

Convert a design array into a dictionary indexed by the variables names.

Parameters:

x_array (ndarray) – A design value expressed as a NumPy array.

Returns:

The design value expressed as a dictionary of NumPy arrays.

Return type:

dict[str, ndarray]

check()[source]

Check the state of the design space.

Raises:

ValueError – If the design space is empty.

Return type:

None

check_membership(x_vect, variable_names=None)[source]

Check whether the variables satisfy the design space requirements.

Parameters:
  • x_vect (Mapping[str, ndarray] | ndarray) – The values of the variables.

  • variable_names (Sequence[str] | None) – The names of the variables. If None, use the names of the variables of the design space.

Raises:

ValueError – Either if the dimension of the values vector is wrong, if the values are not specified as an array or a dictionary, if the values are outside the bounds of the variables or if the component of an integer variable is not an integer.

Return type:

None

dict_to_array(design_values, variable_names=None)[source]

Convert a mapping of design values into a NumPy array.

Parameters:
  • design_values (Mapping[str, ndarray]) – The mapping of design values.

  • variable_names (Iterable[str] | None) – The design variables to be considered. If None, consider all the design variables.

Returns:

The design values as a NumPy array.

Return type:

ndarray

Notes

The data type of the returned NumPy array is the most general data type of the values of the mapping design_values corresponding to the keys iterable from variables_names.

extend(other)[source]

Extend the design space with another design space.

Parameters:

other (DesignSpace) – The design space to be appended to the current one.

Return type:

None

filter(keep_variables, copy=False)[source]

Filter the design space to keep a subset of variables.

Parameters:
  • keep_variables (str | Iterable[str]) – The names of the variables to be kept.

  • copy (bool) –

    If True, then a copy of the design space is filtered, otherwise the design space itself is filtered.

    By default it is set to False.

Returns:

Either the filtered original design space or a copy.

Raises:

ValueError – If the variable is not in the design space.

Return type:

DesignSpace

filter_dim(variable, keep_dimensions)[source]

Filter the design space to keep a subset of dimensions for a variable.

Parameters:
  • variable (str) – The name of the variable.

  • keep_dimensions (Iterable[int]) – The dimensions of the variable to be kept, between \(0\) and \(d-1\) where \(d\) is the number of dimensions of the variable.

Returns:

The filtered design space.

Raises:

ValueError – If a dimension is unknown.

Return type:

DesignSpace

classmethod from_csv(file_path, header=None)[source]

Create a design space from a CSV file.

Parameters:
  • file_path (str | Path) – The path to the CSV file.

  • header (Iterable[str] | None) – The names of the fields saved in the file. If None, read them in the file.

Returns:

The design space defined in the file.

Raises:

ValueError – If the file does not contain the minimal variables in its header.

Return type:

DesignSpace

classmethod from_file(file_path, hdf_node_path='', **options)[source]

Create a design space from a file.

Parameters:
  • file_path (str | Path) – The path to the file. If the extension starts with “hdf”, the file will be considered as an HDF file.

  • hdf_node_path (str) –

    The path of the HDF node from which the database should be imported. If empty, the root node is considered.

    By default it is set to “”.

  • **options (Any) – The keyword reading options.

Returns:

The design space defined in the file.

Return type:

DesignSpace

classmethod from_hdf(file_path, hdf_node_path='')[source]

Create a design space from an HDF file.

Parameters:
  • file_path (str | Path) – The path to the HDF file.

  • hdf_node_path (str) –

    The path of the HDF node from which the database should be imported. If empty, the root node is considered.

    By default it is set to “”.

Returns:

The design space defined in the file.

Return type:

DesignSpace

get_active_bounds(x_vec=None, tol=1e-08)[source]

Determine which bound constraints of a design value are active.

Parameters:
  • x_vec (ndarray | None) – The design value at which to check the bounds. If None, use the current design value.

  • tol (float) –

    The tolerance of comparison of a scalar with a bound.

    By default it is set to 1e-08.

Returns:

Whether the components of the lower and upper bound constraints are active, the first returned value representing the lower bounds and the second one the upper bounds, e.g.

(
    {
        "x": array(are_x_lower_bounds_active),
        "y": array(are_y_lower_bounds_active),
    },
    {
        "x": array(are_x_upper_bounds_active),
        "y": array(are_y_upper_bounds_active),
    },
)

where:

are_x_lower_bounds_active = [True, False]
are_x_upper_bounds_active = [False, False]
are_y_lower_bounds_active = [False]
are_y_upper_bounds_active = [True]

Return type:

tuple[dict[str, ndarray], dict[str, ndarray]]

get_current_value(variable_names=None, complex_to_real=False, as_dict=False, normalize=False)[source]

Return the current design value.

If the names of the variables are empty then an empty data is returned.

Parameters:
  • variable_names (Sequence[str] | None) – The names of the design variables. If None, use all the design variables.

  • complex_to_real (bool) –

    Whether to cast complex numbers to real ones.

    By default it is set to False.

  • as_dict (bool) –

    Whether to return the current design value as a dictionary of the form {variable_name: variable_value}.

    By default it is set to False.

  • normalize (bool) –

    Whether to normalize the design values in \([0,1]\) with the bounds of the variables.

    By default it is set to False.

Returns:

The current design value.

Raises:

ValueError – If names in variable_names are not in the design space.

Return type:

ndarray | dict[str, ndarray]

Warning

For performance purposes, get_current_value() does not return a copy of the current value. This means that modifying the returned object will make the DesignSpace inconsistent (the current design value stored as a NumPy array and the current design value stored as a dictionary of NumPy arrays will be different). To modify the returned object without impacting the DesignSpace, you shall copy this object and modify the copy.

See also

To modify the current value, please use set_current_value() or set_current_variable().

get_indexed_var_name(variable_name)[source]

Create the names of the components of a variable.

If the size of the variable is equal to 1, this method returns the name of the variable. Otherwise, it concatenates the name of the variable, the separator DesignSpace.SEP and the index of the component.

Parameters:

variable_name (str) – The name of the variable.

Returns:

The names of the components of the variable.

Return type:

str | list[str]

get_indexed_variable_names()[source]

Create the names of the components of all the variables.

If the size of the variable is equal to 1, this method uses its name. Otherwise, it concatenates the name of the variable, the separator DesignSpace.SEP and the index of the component.

Returns:

The name of the components of all the variables.

Return type:

list[str]

get_lower_bound(name)[source]

Return the lower bound of a variable.

Parameters:

name (str) – The name of the variable.

Returns:

The lower bound of the variable (possibly infinite).

Return type:

ndarray | None

get_lower_bounds(variable_names: Sequence[str] | None = None, as_dict: Literal[False] = False) ndarray[source]
get_lower_bounds(variable_names: Sequence[str] | None = None, as_dict: Literal[True] = False) dict[str, ndarray]

Return the lower bounds of design variables.

Parameters:
  • variable_names – The names of the design variables. If None, the lower bounds of all the design variables are returned.

  • as_dict – Whether to return the lower bounds as a dictionary of the form {variable_name: variable_lower_bound}.

Returns:

The lower bounds of the design variables.

get_pretty_table(fields=None, with_index=False, capitalize=False, simplify=False)[source]

Build a tabular view of the design space.

Parameters:
  • fields (Sequence[str] | None) – The name of the fields to be exported. If None, export all the fields.

  • with_index (bool) –

    Whether to show index of names for arrays. This is ignored for scalars.

    By default it is set to False.

  • capitalize (bool) –

    Whether to capitalize the field names and replace "_" by " ".

    By default it is set to False.

  • simplify (bool) –

    Whether to return a simplified tabular view.

    By default it is set to False.

Returns:

A tabular view of the design space.

Return type:

PrettyTable

get_size(name)[source]

Get the size of a variable.

Parameters:

name (str) – The name of the variable.

Returns:

The size of the variable, None if it is not known.

Return type:

int | None

get_type(name)[source]

Return the type of a variable.

Parameters:

name (str) – The name of the variable.

Returns:

The type of the variable, None if it is not known.

Return type:

str | None

get_upper_bound(name)[source]

Return the upper bound of a variable.

Parameters:

name (str) – The name of the variable.

Returns:

The upper bound of the variable (possibly infinite).

Return type:

ndarray | None

get_upper_bounds(variable_names: Sequence[str] | None = None, as_dict: Literal[False] = False) ndarray[source]
get_upper_bounds(variable_names: Sequence[str] | None = None, as_dict: Literal[True] = False) dict[str, ndarray]

Return the upper bounds of design variables.

Parameters:
  • variable_names – The names of the design variables. If None, the upper bounds of all the design variables are returned.

  • as_dict – Whether to return the upper bounds as a dictionary of the form {variable_name: variable_upper_bound}.

Returns:

The upper bounds of the design variables.

get_variables_indexes(variable_names, use_design_space_order=True)[source]

Return the indexes of a design array corresponding to variables names.

Parameters:
  • variable_names (Iterable[str]) – The names of the variables.

  • use_design_space_order (bool) –

    Whether to order the indexes according to the order of the variables names in the design space. Otherwise the indexes will be ordered in the same order as the variables names were required.

    By default it is set to True.

Returns:

The indexes of a design array corresponding to the variables names.

Return type:

NDArray[int]

has_current_value()[source]

Check if each variable has a current value.

Returns:

Whether the current design value is defined for all variables.

Return type:

bool

has_integer_variables()[source]

Check if the design space has at least one integer variable.

Returns:

Whether the design space has at least one integer variable.

Return type:

bool

initialize_missing_current_values()[source]

Initialize the current values of the design variables when missing.

Use:

  • the center of the design space when the lower and upper bounds are finite,

  • the lower bounds when the upper bounds are infinite,

  • the upper bounds when the lower bounds are infinite,

  • zero when the lower and upper bounds are infinite.

Return type:

None

normalize_grad(g_vect)[source]

Normalize an unnormalized gradient.

This method is based on the chain rule:

\[\frac{df(x)}{dx} = \frac{df(x)}{dx_u}\frac{dx_u}{dx} = \frac{df(x)}{dx_u}\frac{1}{u_b-l_b}\]

where \(x_u = \frac{x-l_b}{u_b-l_b}\) is the normalized input vector, \(x\) is the unnormalized input vector and \(l_b\) and \(u_b\) are the lower and upper bounds of \(x\).

Then, the normalized gradient reads:

\[\frac{df(x)}{dx_u} = (u_b-l_b)\frac{df(x)}{dx}\]

where \(\frac{df(x)}{dx}\) is the unnormalized one.

Parameters:

g_vect (RealOrComplexArrayT) – The gradient to be normalized.

Returns:

The normalized gradient.

Return type:

RealOrComplexArrayT

normalize_vect(x_vect, minus_lb=True, out=None)[source]

Normalize a vector of the design space.

If minus_lb is True:

\[x_u = \frac{x-l_b}{u_b-l_b}\]

where \(l_b\) and \(u_b\) are the lower and upper bounds of \(x\).

Otherwise:

\[x_u = \frac{x}{u_b-l_b}\]

Unbounded variables are not normalized.

Parameters:
  • x_vect (RealOrComplexArrayT) – The values of the design variables.

  • minus_lb (bool) –

    If True, remove the lower bounds at normalization.

    By default it is set to True.

  • out (ndarray | None) – The array to store the normalized vector. If None, create a new array.

Returns:

The normalized vector.

Return type:

RealOrComplexArrayT

project_into_bounds(x_c, normalized=False)[source]

Project a vector onto the bounds, using a simple coordinate wise approach.

Parameters:
  • normalized (bool) –

    If True, then the vector is assumed to be normalized.

    By default it is set to False.

  • x_c (ndarray) – The vector to be projected onto the bounds.

Returns:

The projected vector.

Return type:

ndarray

remove_variable(name)[source]

Remove a variable from the design space.

Parameters:

name (str) – The name of the variable to be removed.

Return type:

None

rename_variable(current_name, new_name)[source]

Rename a variable.

Parameters:
  • current_name (str) – The name of the variable to rename.

  • new_name (str) – The new name of the variable.

Return type:

None

round_vect(x_vect, copy=True)[source]

Round the vector where variables are of integer type.

Parameters:
  • x_vect (ndarray) – The values to be rounded.

  • copy (bool) –

    Whether to round a copy of x_vect.

    By default it is set to True.

Returns:

The rounded values.

Return type:

ndarray

set_current_value(value)[source]

Set the current design value.

Parameters:

value (ndarray | Mapping[str, ndarray] | OptimizationResult) – The value of the current design.

Raises:
Return type:

None

set_current_variable(name, current_value)[source]

Set the current value of a single variable.

Parameters:
  • name (str) – The name of the variable.

  • current_value (ndarray) – The current value of the variable.

Return type:

None

set_lower_bound(name, lower_bound)[source]

Set the lower bound of a variable.

Parameters:
  • name (str) – The name of the variable.

  • lower_bound (ndarray | None) – The value of the lower bound.

Raises:

ValueError – If the variable does not exist.

Return type:

None

set_upper_bound(name, upper_bound)[source]

Set the upper bound of a variable.

Parameters:
  • name (str) – The name of the variable.

  • upper_bound (ndarray | None) – The value of the upper bound.

Raises:

ValueError – If the variable does not exist.

Return type:

None

to_complex()[source]

Cast the current value to complex.

Return type:

None

to_csv(output_file, fields=None, header_char='', **table_options)[source]

Export the design space to a CSV file.

Parameters:
  • output_file (str | Path) – The path to the file.

  • fields (Sequence[str] | None) – The fields to be exported. If None, export all fields.

  • header_char (str) –

    The header character.

    By default it is set to “”.

  • **table_options (Any) – The names and values of additional attributes for the PrettyTable view generated by DesignSpace.get_pretty_table().

Return type:

None

to_file(file_path, **options)[source]

Save the design space.

Parameters:
  • file_path (str | Path) – The file path to save the design space. If the extension starts with “hdf”, the design space will be saved in an HDF file.

  • **options – The keyword reading options.

Return type:

None

to_hdf(file_path, append=False, hdf_node_path='')[source]

Export the design space to an HDF file.

Parameters:
  • file_path (str | Path) – The path to the file to export the design space.

  • append (bool) –

    If True, appends the data in the file.

    By default it is set to False.

  • hdf_node_path (str) –

    The path of the HDF node in which the design space should be exported. If empty, the root node is considered.

    By default it is set to “”.

Return type:

None

transform_vect(vector, out=None)[source]

Map a point of the design space to a vector with components in \([0,1]\).

Parameters:
  • vector (ndarray) – A point of the design space.

  • out (ndarray | None) – The array to store the transformed vector. If None, create a new array.

Returns:

A vector with components in \([0,1]\).

Return type:

ndarray

unnormalize_grad(g_vect)[source]

Unnormalize a normalized gradient.

This method is based on the chain rule:

\[\frac{df(x)}{dx} = \frac{df(x)}{dx_u}\frac{dx_u}{dx} = \frac{df(x)}{dx_u}\frac{1}{u_b-l_b}\]

where \(x_u = \frac{x-l_b}{u_b-l_b}\) is the normalized input vector, \(x\) is the unnormalized input vector, \(\frac{df(x)}{dx_u}\) is the unnormalized gradient \(\frac{df(x)}{dx}\) is the normalized one, and \(l_b\) and \(u_b\) are the lower and upper bounds of \(x\).

Parameters:

g_vect (RealOrComplexArrayT) – The gradient to be unnormalized.

Returns:

The unnormalized gradient.

Return type:

RealOrComplexArrayT

unnormalize_vect(x_vect, minus_lb=True, no_check=False, out=None)[source]

Unnormalize a normalized vector of the design space.

If minus_lb is True:

\[x = x_u(u_b-l_b) + l_b\]

where \(x_u\) is the normalized input vector, \(x\) is the unnormalized input vector and \(l_b\) and \(u_b\) are the lower and upper bounds of \(x\).

Otherwise:

\[x = x_u(u_b-l_b)\]
Parameters:
  • x_vect (RealOrComplexArrayT) – The values of the design variables.

  • minus_lb (bool) –

    Whether to remove the lower bounds at normalization.

    By default it is set to True.

  • no_check (bool) –

    Whether to check if the components are in \([0,1]\).

    By default it is set to False.

  • out (ndarray | None) – The array to store the unnormalized vector. If None, create a new array.

Returns:

The unnormalized vector.

Return type:

RealOrComplexArrayT

untransform_vect(vector, no_check=False, out=None)[source]

Map a vector with components in \([0,1]\) to the design space.

Parameters:
  • vector (ndarray) – A vector with components in \([0,1]\).

  • no_check (bool) –

    Whether to check if the components are in \([0,1]\).

    By default it is set to False.

  • out (ndarray | None) – The array to store the untransformed vector. If None, create a new array.

Returns:

A point of the variables space.

Return type:

ndarray

DESIGN_SPACE_GROUP = 'design_space'
LB_GROUP = 'l_b'
MINIMAL_FIELDS: ClassVar[list[str]] = ['name', 'lower_bound', 'upper_bound']
NAMES_GROUP = 'names'
NAME_GROUP = 'name'
SEP = '!'
SIZE_GROUP = 'size'
TABLE_NAMES: ClassVar[list[str]] = ['name', 'lower_bound', 'value', 'upper_bound', 'type']
UB_GROUP = 'u_b'
VALUE_GROUP = 'value'
VARIABLE_TYPES_TO_DTYPES: Final[dict[str, str]] = {_DesignVariableType.FLOAT: 'float64', _DesignVariableType.INTEGER: 'int32'}

One NumPy dtype per design variable type.

VAR_TYPE_GROUP = 'var_type'
dimension: int

The total dimension of the space, corresponding to the sum of the sizes of the variables.

name: str | None

The name of the space.

property names_to_indices: dict[str, range]

The names bound to the indices.

normalize: dict[str, ndarray]

The normalization policies of the variables components indexed by the variables names; if True, the component can be normalized.

variable_names: list[str]

The names of the variables.

variable_sizes: dict[str, int]

The sizes of the variables.

variable_types: dict[str, ndarray]

The types of the variables components, which can be any DesignSpace.DesignVariableType.

Examples using DesignSpace

Example for exterior penalty applied to the Sobieski test case.

Example for exterior penalty applied to the Sobieski test case.

Parameter space

Parameter space

Comparing sensitivity indices

Comparing sensitivity indices

Correlation analysis

Correlation analysis

Morris analysis

Morris analysis

Sobol’ analysis

Sobol' analysis

Empirical estimation of statistics

Empirical estimation of statistics

Analytical test case # 2

Analytical test case # 2

Analytical test case # 3

Analytical test case # 3

Examples for constraint aggregation

Examples for constraint aggregation

Pareto front on the Binh and Korn problem using a BiLevel formulation

Pareto front on the Binh and Korn problem using a BiLevel formulation

Create a DOE Scenario

Create a DOE Scenario

Create an MDO Scenario

Create an MDO Scenario

Gantt Chart

Gantt Chart

Store observables

Store observables

A from scratch example on the Sellar problem

A from scratch example on the Sellar problem

Application: Sobieski’s Super-Sonic Business Jet (MDO)

Application: Sobieski's Super-Sonic Business Jet (MDO)

GEMSEO in 10 minutes

GEMSEO in 10 minutes

MDO formulations for a toy example in aerostructure

MDO formulations for a toy example in aerostructure

Design space

Design space

Post-processing

Post-processing

Sample several disciplines

Sample several disciplines

Scenario

Scenario

Multistart optimization

Multistart optimization

Diagonal design of experiments

Diagonal design of experiments

Scalable diagonal discipline

Scalable diagonal discipline

Scalable problem

Scalable problem

BiLevel-based DOE on the Sobieski SSBJ test case

BiLevel-based DOE on the Sobieski SSBJ test case

BiLevel-based MDO on the Sobieski SSBJ test case

BiLevel-based MDO on the Sobieski SSBJ test case

IDF-based MDO on the Sobieski SSBJ test case

IDF-based MDO on the Sobieski SSBJ test case

MDF-based DOE on the Sobieski SSBJ test case

MDF-based DOE on the Sobieski SSBJ test case

MDF-based MDO on the Sobieski SSBJ test case.

MDF-based MDO on the Sobieski SSBJ test case.

Change the seed of a DOE

Change the seed of a DOE

Simple disciplinary DOE example on the Sobieski SSBJ test case

Simple disciplinary DOE example on the Sobieski SSBJ test case

Use a design of experiments from a file

Use a design of experiments from a file

Use a design of experiments from an array

Use a design of experiments from an array

Create a surrogate discipline

Create a surrogate discipline

Plug a surrogate discipline in a Scenario

Plug a surrogate discipline in a Scenario

Calibration of a polynomial regression

Calibration of a polynomial regression

Machine learning algorithm selection example

Machine learning algorithm selection example

API

API

GP regression

GP regression

Linear regression

Linear regression

PCE regression

PCE regression

Polynomial regression

Polynomial regression

RBF regression

RBF regression

Random forest regression

Random forest regression

Save and Load

Save and Load

Scaling

Scaling

Solve a 2D L-shape topology optimization problem

Solve a 2D L-shape topology optimization problem

Solve a 2D MBB topology optimization problem

Solve a 2D MBB topology optimization problem

Solve a 2D short cantilever topology optimization problem

Solve a 2D short cantilever topology optimization problem

DesignSpace creation and manipulation

DesignSpace creation and manipulation

DesignSpace import and export from disk

DesignSpace import and export from disk

Parameter space

Parameter space

Basic history

Basic history

Constraints history

Constraints history

Correlations

Correlations

Gradient Sensitivity

Gradient Sensitivity

Objective and constraints history

Objective and constraints history

Optimization History View

Optimization History View

Parallel coordinates

Parallel coordinates

Pareto front

Pareto front

Quadratic approximations

Quadratic approximations

Radar chart

Radar chart

Robustness

Robustness

Scatter plot matrix

Scatter plot matrix

Self-Organizing Map

Self-Organizing Map

Variables influence

Variables influence

Examples using _DesignVariableType

Examples for constraint aggregation

Examples for constraint aggregation

Use a design of experiments from a file

Use a design of experiments from a file

Use a design of experiments from an array

Use a design of experiments from an array