gemseo / problems / scalable / parametric

scalable_design_space module¶

The design space for the scalable problem.

class gemseo.problems.scalable.parametric.scalable_design_space.ScalableDesignSpace(discipline_settings=((1, 1), (1, 1)), d_0=1, names_to_default_values=mappingproxy({}), add_uncertain_variables=False)[source]¶

Bases: ParameterSpace

The design space for the scalable problem.

It is the space in which the design and coupling variables vary. For all the variables, the lower bound is 0, the upper bound is 1 and the default value is 0.5.

Parameters:

discipline_settings (Iterable[ScalableDisciplineSettings]) –
The configurations of the different disciplines. If None, use a single discipline with default ScalableDisciplineSettings.

By default it is set to (ScalableDisciplineSettings(d_i=1, p_i=1), ScalableDisciplineSettings(d_i=1, p_i=1)).
d_0 (int) –
The size of the shared design variable \(x_0\).

By default it is set to 1.
names_to_default_values (Mapping[str, NDArray[float]]) –
The default values of the variables.

By default it is set to {}.
add_uncertain_variables (bool) –
Whether to add the uncertain variables impacting the coupling variables as \(y_{i,j}:=y_{i,j}+\epsilon_{i,j}\) where \(\epsilon_{i,j}\) are independent and identically distributed standard Gaussian variables.

By default it is set to False.

Notes

The lengths of n_local and n_coupling must be equal and correspond to the number of scalable disciplines. n_local[i] (resp. n_coupling[i]) is the number of local design variables (resp. coupling variables) of the i-th scalable discipline.

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

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) –

count(value, /)¶

Return number of occurrences of value.

index(value, start=0, stop=9223372036854775807, /)¶

Return first index of value.

Raises ValueError if the value is not present.

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_random_variable(name, distribution, size=1, interfaced_distribution='', interfaced_distribution_parameters=(), **parameters)¶

Add a random variable from a probability distribution.

Parameters:

name (str) – The name of the random variable.
distribution (str) – The name of a class implementing a probability distribution, e.g. "OTUniformDistribution" or "SPUniformDistribution", or an interface to a library of probability distributions, e.g. "OTDistribution" or "SPDistribution".
size (int) –
The dimension of the random variable. The parameters of the distribution are shared by all the components of the random variable.

By default it is set to 1.
interfaced_distribution (str) –
The name of the distribution in the library of probability distributions when distribution is the name of a class implementing an interface to this library.

By default it is set to “”.
interfaced_distribution_parameters (tuple[Any] | Mapping[str, Any]) –
The parameters of the distribution in the library of probability distributions when distribution is the name of a class implementing an interface to this library; if empty, use the default ones.

By default it is set to ().
**parameters (Any) – The parameters of the distribution; otherwise, use the default ones.

Return type:

None

Warning

The probability distributions must have the same DISTRIBUTION_FAMILY_ID. For instance, one cannot mix a random variable distributed as an OTUniformDistribution with identifier "OT" and a random variable distributed as a SPNormalDistribution with identifier "SP".

add_random_vector(name, distribution, size=0, interfaced_distribution='', interfaced_distribution_parameters=(), **parameters)¶

Add a d-length random vector from a probability distribution.

Warning

The probability distributions must have the same DISTRIBUTION_FAMILY_ID. For instance, one cannot mix a random vector using a OTUniformDistribution with identifier "OT" and a random vector using a SPNormalDistribution with identifier "SP".

Parameters:

name (str) – The name of the random vector.
distribution (str) – The name of a class implementing a probability distribution, e.g. "OTUniformDistribution" or "SPUniformDistribution", or an interface to a library of probability distributions, e.g. "OTDistribution" or "SPDistribution".
size (int) –
The length d of the random vector. If 0, deduce it from the parameters.

By default it is set to 0.
interfaced_distribution (str) –
The name of the distribution in the library of probability distributions when distribution is the name of a class implementing an interface to this library.

By default it is set to “”.
interfaced_distribution_parameters (tuple[list[Any]] | Mapping[str, list[Any]]) –
The parameters of the distribution in the library of probability distributions when distribution is the name of a class implementing an interface to this library. The values of the data structure (mapping or tuple) must be set either as [p_1,...,p_d] (one value per component of the random vector) or as [p] (one value for all the components) If empty, use the default ones.

By default it is set to ().
**parameters (list[Any]) – The parameters of the distribution, either as [p_1,...,p_d] (one value per component of the random vector) or as [p] (one value for all the components); otherwise, use the default ones.

Raises:

ValueError – When mixing probability distributions from different families, e.g. an OTDistribution and a SPDistribution or when the lengths of the distribution parameter collections are not consistent.

Return type:

None

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

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 (float | ndarray | None) – The lower bound of the variable. If None, use \(-\infty\).
u_b (float | ndarray | None) – The upper bound of the variable. If None, use \(+\infty\).
value (float | ndarray | 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)¶

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]

build_composed_distribution(copula=None)¶

Build the joint probability distribution.

Parameters:: copula (Any | None) – A copula distribution defining the dependency structure between random variables; if None, consider an independent copula.
Return type:: None

check()¶

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)¶

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

clear() → None. Remove all items from D.¶

compute_samples(n_samples=1, as_dict=False)¶

Sample the random variables and return the realizations.

Parameters:

n_samples (int) –
A number of samples.

By default it is set to 1.
as_dict (bool) –
The type of the returned object. If True, return a dictionary. Otherwise, return an array.

By default it is set to False.

Returns:

The realizations of the random variables, either stored in an array or in a dictionary whose values are the names of the random variables and the values are the evaluations.

Return type:

dict[str, ndarray] | ndarray

dict_to_array(design_values, variable_names=None)¶

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.

evaluate_cdf(value, inverse=False)¶

Evaluate the cumulative density function (or its inverse) of each marginal.

Parameters:

value (dict[str, ndarray]) – The values of the uncertain variables passed as a dictionary whose keys are the names of the variables.
inverse (bool) –
The type of function to evaluate. If True, compute the cumulative density function. Otherwise, compute the inverse cumulative density function.

By default it is set to False.

Returns:

A dictionary where the keys are the names of the random variables and the values are the evaluations.

Return type:

dict[str, ndarray]

extend(other)¶

Extend the design space with another design space.

Parameters:: other (DesignSpace) – The design space to be appended to the current one.
Return type:: None

extract_deterministic_space()¶

Define a new DesignSpace from the deterministic variables only.

Returns:: A DesignSpace defined by the deterministic variables only.
Return type:: DesignSpace

extract_uncertain_space(as_design_space=False)¶

Define a new DesignSpace from the uncertain variables only.

Parameters:

as_design_space (bool) –

If False, return a ParameterSpace containing the original uncertain variables as is; otherwise, return a DesignSpace where the original uncertain variables are made deterministic. In that case, the bounds of a deterministic variable correspond to the limits of the support of the original probability distribution and the current value correspond to its mean.

By default it is set to False.

Returns:

A ParameterSpace defined by the uncertain variables only.

Return type:

DesignSpace | ParameterSpace

filter(keep_variables, copy=False)¶

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)¶

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)¶

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)¶

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='')¶

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(k[, d]) → D[k] if k in D, else d. d defaults to None.¶

get_active_bounds(x_vec=None, tol=1e-08)¶

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)¶

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.