Parameter space¶
The class ParameterSpace¶
Variable space defining both deterministic and uncertain variables.
Overview¶
The ParameterSpace
class describes a set of parameters of interest
which can be either deterministic or uncertain.
This class inherits from DesignSpace
.
Capabilities¶
The DesignSpace.add_variable()
aims to add deterministic variables from:
a variable name,
an optional variable size (default: 1),
an optional variable type (default: float),
an optional lower bound (default: - infinity),
an optional upper bound (default: + infinity),
an optional current value (default: None).
The add_random_variable()
aims to add uncertain
variables (a.k.a. random variables) from:
a variable name,
a distribution name (see
get_available_distributions()
),an optional variable size,
optional distribution parameters (
parameters
set as a tuple of positional arguments forOTDistribution
or a dictionary of keyword arguments forSPDistribution
, or keyword arguments for standard probability distribution such asOTNormalDistribution
andSPNormalDistribution
).
The ParameterSpace
also provides the following methods:
ParameterSpace.compute_samples()
: returns several samples of the uncertain variables,evaluate_cdf()
: evaluate the cumulative density function for the different variables and their differentget_range()
returns the numerical range of the different uncertain parameters,get_support()
: returns the mathematical support of the different uncertain variables,is_uncertain()
: checks if a parameter is uncertain,is_deterministic()
: checks if a parameter is deterministic.
- class gemseo.algos.parameter_space.ParameterSpace(hdf_file=None, copula='independent_copula', name=None)[source]
Parameter space.
- Parameters
- Return type
None
- add_random_variable(name, distribution, size=1, **parameters)[source]
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 ‘SPDistribution’.
size (int) –
The dimension of the random variable.
By default it is set to 1.
**parameters (Union[int, Tuple[str, int, float], Mapping[str, Union[str, int, float]], None, float]) – The parameters of the distribution.
- 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 (VarType) –
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 \(-\infty\).
By default it is set to None.
u_b (float | ndarray | None) –
The upper bound of the variable. If None, use \(+\infty\).
By default it is set to None.
value (float | ndarray | None) –
The default value of the variable. If None, do not use a default value.
By default it is set to None.
- 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 (numpy.ndarray) – A design value expressed as a NumPy array.
- Returns
The design value expressed as a dictionary of NumPy arrays.
- Return type
- 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
- 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)[source]
Sample the random variables and return the realizations.
- Parameters
- 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_to_array(design_values, variable_names=None)
Convert a point as dictionary into an array.
- Parameters
design_values (dict[str, numpy.ndarray]) – The design point to be converted.
variable_names (Optional[Iterable[str]]) –
The variables to be considered. If None, use the variables of the design space.
By default it is set to None.
- Returns
The point as an array.
- Return type
- evaluate_cdf(value, inverse=False)[source]
Evaluate the cumulative density function (or its inverse) of each marginal.
- Parameters
value (dict[str, numpy.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
- export_hdf(file_path, append=False)
Export the design space to an HDF file.
- export_to_txt(output_file, fields=None, header_char='', **table_options)
Export the design space to a text 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.
By default it is set to None.
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 byDesignSpace.get_pretty_table()
.
- Return type
None
- extend(other)
Extend the design space with another design space.
- Parameters
other (gemseo.algos.design_space.DesignSpace) – The design space to be appended to the current one.
- Return type
None
- extract_deterministic_space()[source]
Define a new
DesignSpace
from the deterministic variables only.- Returns
A
DesignSpace
defined by the deterministic variables only.- Return type
- extract_uncertain_space(as_design_space=False)[source]
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 aDesignSpace
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
- filter(keep_variables, copy=False)
Filter the design space to keep a subset of variables.
- Parameters
- Returns
Either the filtered original design space or a copy.
- Raises
ValueError – If the variable is not in the design space.
- Return type
- filter_dim(variable, keep_dimensions)
Filter the design space to keep a subset of dimensions for a variable.
- Parameters
- Returns
The filtered design space.
- Raises
ValueError – If a dimension is unknown.
- Return type
- 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.By default it is set to None.
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
- get_current_value(variable_names=None, complex_to_real=False, as_dict=False, normalize=False)
Return the current design value.
- Parameters
variable_names (Sequence[str] | None) –
The names of the design variables. If
None
, use all the design variables.By default it is set to None.
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
KeyError – If a variable has no current value.
- Return type
- get_indexed_var_name(variable_name)
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.
- get_indexed_variables_names()
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.
- get_lower_bound(name)
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
- get_lower_bounds(variable_names=None)
Generate an array of the variables’ lower bounds.
- Parameters
variable_names (Sequence[str] | None) –
The names of the variables of which the lower bounds are required. If None, use the variables of the design space.
By default it is set to None.
- Returns
The lower bounds of the variables.
- Return type
ndarray
- get_pretty_table(fields=None)
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.
By default it is set to None.
- Returns
A tabular view of the design space.
- Return type
- get_range(variable)[source]
Return the numerical range of a random variable.
- Parameters
variable (str) – The name of the random variable.
- Returns
The range of the components of the random variable.
- Return type
- get_size(name)
Get the size of a variable.
- get_support(variable)[source]
Return the mathematical support of a random variable.
- Parameters
variable (str) – The name of the random variable.
- Returns
The support of the components of the random variable.
- Return type
- get_tabular_view(decimals=2)[source]
Return a tabular view of the parameter space.
This view contains statistical information.
- get_type(name)
Return the type of a variable.
- get_upper_bound(name)
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
- get_upper_bounds(variable_names=None)
Generate an array of the variables’ upper bounds.
- Parameters
variable_names (Sequence[str] | None) –
The names of the variables of which the upper bounds are required. If None, use the variables of the design space.
By default it is set to None.
- Returns
The upper bounds of the variables.
- Return type
ndarray
- get_variables_indexes(variable_names)
Return the indexes of a design array corresponding to the variables names.
- Parameters
variable_names (Iterable[str]) – The names of the variables.
- Returns
The indexes of a design array corresponding to the variables names.
- Return type
- has_current_value()
Check if each variable has a current value.
- Returns
Whether the current design value is defined for all variables.
- Return type
- has_integer_variables()
Check if the design space has at least one integer variable.
- Returns
Whether the design space has at least one integer variable.
- Return type
- import_hdf(file_path)
Import a design space from an HDF file.
- Parameters
file_path (str | Path) – The path to the file containing the description of a design space.
- Return type
None
- static init_from_dataset(dataset, groups=None, uncertain=None, copula='independent_copula')[source]
Initialize the parameter space from a dataset.
- Parameters
dataset (Dataset) – The dataset used for the initialization.
groups (Iterable[str] | None) –
The groups of the dataset to be considered. If None, consider all the groups.
By default it is set to None.
uncertain (Mapping[str, bool] | None) –
Whether the variables should be uncertain or not.
By default it is set to None.
copula (str) –
A name of copula defining the dependency between random variables.
By default it is set to independent_copula.
- Return type
- is_deterministic(variable)[source]
Check if a variable is deterministic.
- is_uncertain(variable)[source]
Check if a variable is uncertain.
- items() a set-like object providing a view on D's items
- keys() a set-like object providing a view on D's keys
- normalize_grad(g_vect)
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 (numpy.ndarray) – The gradient to be normalized.
- Returns
The normalized gradient.
- Return type
- normalize_vect(x_vect, minus_lb=True, use_dist=False, out=None)[source]
Normalize a vector of the parameter space.
If use_dist is True, use the cumulative probability distributions of the random variables to scale the components of the random variables between 0 and 1. Otherwise, use the approach defined in
DesignSpace.normalize_vect()
with minus_lb.For the components of the deterministic variables, use the approach defined in
DesignSpace.normalize_vect()
with minus_lb.- Parameters
x_vect (ndarray) – The values of the design variables.
minus_lb (bool) –
If True, remove the lower bounds at normalization.
By default it is set to True.
use_dist (bool) –
If True, normalize the components of the random variables with their cumulative probability distributions.
By default it is set to False.
out (ndarray | None) –
The array to store the normalized vector. If None, create a new array.
By default it is set to None.
- Returns
The normalized vector.
- Return type
ndarray
- pop(k[, d]) v, remove specified key and return the corresponding value.
If key is not found, d is returned if given, otherwise KeyError is raised.
- popitem() (k, v), remove and return some (key, value) pair
as a 2-tuple; but raise KeyError if D is empty.
- project_into_bounds(x_c, normalized=False)
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 (numpy.ndarray) – The vector to be projected onto the bounds.
- Returns
The projected vector.
- Return type
- static read_from_txt(input_file, header=None)
Create a design space from a text file.
- Parameters
- Returns
The design space read from the file.
- Raises
ValueError – If the file does not contain the minimal variables in its header.
- Return type
- remove_variable(name)[source]
Remove a variable from the probability space.
- Parameters
name (str) – The name of the variable.
- Return type
None
- rename_variable(current_name, new_name)[source]
Rename a variable.
- round_vect(x_vect, copy=True)
Round the vector where variables are of integer type.
- Parameters
x_vect (numpy.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
- set_current_value(value)
Set the current design value.
- Parameters
value (ndarray | Mapping[str, ndarray] | OptimizationResult) – The value of the current design.
- Raises
ValueError – If the value has a wrong dimension.
TypeError – If the value is neither a mapping of NumPy arrays, a NumPy array nor an
OptimizationResult
.
- Return type
None
- set_current_variable(name, current_value)
Set the current value of a single variable.
- Parameters
name (str) – The name of the variable.
current_value (numpy.ndarray) – The current value of the variable.
- Return type
None
- set_lower_bound(name, lower_bound)
Set the lower bound of a variable.
- Parameters
name (str) – The name of the variable.
lower_bound (numpy.ndarray) – The value of the lower bound.
- Raises
ValueError – If the variable does not exist.
- Return type
None
- set_upper_bound(name, upper_bound)
Set the upper bound of a variable.
- Parameters
name (str) – The name of the variable.
upper_bound (numpy.ndarray) – The value of the upper bound.
- Raises
ValueError – If the variable does not exist.
- Return type
None
- setdefault(k[, d]) D.get(k,d), also set D[k]=d if k not in D
- to_complex()
Cast the current value to complex.
- Return type
None
- to_design_space()[source]
Convert the parameter space into a
DesignSpace
.The original deterministic variables are kept as is while 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.
- Returns
A
DesignSpace
where all original variables are made deterministic.- Return type
- 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.
By default it is set to None.
- Returns
A vector with components in \([0,1]\).
- Return type
ndarray
- unnormalize_grad(g_vect)
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 (numpy.ndarray) – The gradient to be unnormalized.
- Returns
The unnormalized gradient.
- Return type
- unnormalize_vect(x_vect, minus_lb=True, no_check=False, use_dist=False, out=None)[source]
Unnormalize a normalized vector of the parameter space.
If
use_dist
is True, use the inverse cumulative probability distributions of the random variables to unscale the components of the random variables. Otherwise, use the approach defined inDesignSpace.unnormalize_vect()
with minus_lb and no_check.For the components of the deterministic variables, use the approach defined in
DesignSpace.unnormalize_vect()
with minus_lb and no_check.- Parameters
x_vect (ndarray) – 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.
use_dist (bool) –
Whether to unnormalize the components of the random variables with their inverse cumulative probability distributions.
By default it is set to False.
out (ndarray | None) –
The array to store the unnormalized vector. If None, create a new array.
By default it is set to None.
- Returns
The unnormalized vector.
- Return type
ndarray
- 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.
By default it is set to None.
- Returns
A point of the variables space.
- Return type
ndarray
- update([E, ]**F) None. Update D from mapping/iterable E and F.
If E present and has a .keys() method, does: for k in E: D[k] = E[k] If E present and lacks .keys() method, does: for (k, v) in E: D[k] = v In either case, this is followed by: for k, v in F.items(): D[k] = v
- values() an object providing a view on D's values
- distribution: ComposedDistribution
The joint probability distribution of the uncertain variables.
- distributions: dict[str, Distribution]
The marginal probability distributions of the uncertain variables.
- class gemseo.algos.parameter_space.RandomVariable(distribution, size, parameters)
Create new instance of RandomVariable(distribution, size, parameters)
- 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.
- distribution
Alias for field number 0
- parameters
Alias for field number 2
- size
Alias for field number 1