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 for OTDistribution or a dictionary of keyword arguments for SPDistribution, or keyword arguments for standard probability distribution such as OTNormalDistribution and SPNormalDistribution).

The ParameterSpace also provides the following methods:

• compute_samples(): returns several samples of the uncertain variables,

• evaluate_cdf(): evaluate the cumulative density function for the different variables and their different

• get_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.

Classes:

ParameterSpace([copula])

Parameter space.

class gemseo.algos.parameter_space.ParameterSpace(copula='independent_copula')

Parameter space.

Attributes

• uncertain_variables (List(str)) – The names of the uncertain variables.

• distributions (Dict(str,Distribution)) – The marginal probability distributions of the uncertain variables.

• distribution (ComposedDistribution) – The joint probability distribution of the uncertain variables.

Parameters

copula (str) – A name of copula defining the dependency between random variables.

Return type

None

Methods:

add_random_variable(name, distribution[, size])	Add a random variable from a probability distribution.
add_variable(name[, size, var_type, l_b, …])	Add a variable to the design space.
array_to_dict(x_array)	Split the current point into a dictionary with variables names.
check()	Check the state of the design space.
check_membership(x_vect[, variables_names])	Checks whether the input variables satisfy the design space requirements.
compute_samples([n_samples, as_dict])	Sample the random variables and return the realizations.
dict_to_array(x_dict[, all_vars, all_var_list])	Aggregate a point as dictionary into array.
evaluate_cdf(value[, inverse])	Evaluate the cumulative density function (or its inverse) of each marginal.
export_hdf(file_path[, append])	Export to hdf file.
export_to_txt(output_file[, fields, header_char])	Exports the design space to a text file.
extend(other)	Extend the design space with another design space.
extract_deterministic_space()	Extract the deterministic space.
extract_uncertain_space()	Extract the uncertain space.
filter(keep_variables[, copy])	Filter the design space to keep a sublist of variables.
filter_dim(variable, keep_dimensions)	Filters the design space to keep a sublist of dimensions for a given variable.
get_active_bounds([x_vec, tol])	Determine which bound constraints of the current point are active.
get_current_x([variables_names])	Gets the current point in the design space.
get_current_x_dict()	Get the current point in the design space.
get_current_x_normalized()	Returns the current point normalized.
get_indexed_var_name(variable_name)	Return a list of the variables names with their indices such as.
get_indexed_variables_names()	Return a list of the variables names with their indices such as.
get_lower_bound(name)	Gets the lower bound of a variable.
get_lower_bounds([variables_names])	Generates an array of the variables’ lower bounds.
get_pretty_table([fields])	Builds a PrettyTable object from the design space data.
get_range(variable)	Return the numerical range of a random variable.
get_size(name)	Get the size of a variable Return None if the variable is not known.
get_support(variable)	Return the mathematical support of a random variable.
get_tabular_view([decimals])	Return a tabular view of the parameter space.
get_type(name)	Get the type of a variable Return None if the variable is not known.
get_upper_bound(name)	Gets the upper bound of a variable.
get_upper_bounds([variables_names])	Generates an array of the variables’ upper bounds.
get_variables_indexes(variables_names)	Return the indexes of a design array corresponding to the variables names.
has_current_x()	Tests if current_x is defined.
import_hdf(file_path)	Imports design space from hdf file.
init_from_dataset(dataset[, groups, …])	Initialize the parameter space from a dataset.
is_deterministic(variable)	Check if a variable is deterministic.
is_uncertain(variable)	Check if a variable is uncertain.
normalize_vect(x_vect[, minus_lb, use_dist])	Normalize a vector.
project_into_bounds(x_c[, normalized])	Projects x_c onto the bounds, using a simple coordinate wise approach.
read_from_txt(input_file[, header])	Parses a csv file to read the DesignSpace.
remove_variable(name)	Remove a variable from the probability space.
round_vect(x_vect)	Rounds the vector where variables are of integer type.
set_current_variable(name, current_value)	Set the current value of a single variable.
set_current_x(current_x)	Set the current point.
set_lower_bound(name, lower_bound)	Set a new lower bound for variable name.
set_upper_bound(name, upper_bound)	Set a new upper bound for variable name.
to_complex()	Casts the current value to complex.
unnormalize_vect(x_vect[, minus_lb, …])	Unnormalize an unit vector.

Attributes:

deterministic_variables

The deterministic variables.

add_random_variable(name, distribution, size=1, **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 ‘SPDistribution’.

• size (int) – The dimension of the random variable.

• **parameters – The parameters of the distribution.

• parameters (Union[int, Tuple[str, int, float], Mapping[str, Union[str, int, float]], None, float]) –

Return type

None

add_variable(name, size=1, var_type='float', l_b=None, u_b=None, value=None)

Add a variable to the design space.

Parameters

• name – param size: (Default value = 1)

• var_type – Default value = FLOAT)

• l_b – Default value = None)

• u_b – Default value = None)

• value – Default value = None)

• size – (Default value = 1)

array_to_dict(x_array)

Split the current point into a dictionary with variables names.

Parameters

x_array – x array to be converted to a dict of array

check()

Check the state of the design space.

check_membership(x_vect, variables_names=None)

Checks whether the input variables satisfy the design space requirements.

Parameters

• x_vect (dict or array) – design variables

• variables_names – names of the variables to be checked

compute_samples(n_samples=1, as_dict=False)

Sample the random variables and return the realizations.

Parameters

• n_samples (int) – A number of samples.

• as_dict (bool) – The type of the returned object. If True, return a dictionary. Otherwise, return an array.

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

Union[Dict[str, numpy.ndarray], numpy.ndarray]

property deterministic_variables

The deterministic variables.

dict_to_array(x_dict, all_vars=True, all_var_list=None)

Aggregate a point as dictionary into array.

Parameters

• x_dict – point as dictionary

• all_vars – if True, all variables shall be in x_dict

• all_var_list – list of whole set of variables, if None, use self.variables_names

evaluate_cdf(value, inverse=False)

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.

Returns

A dictionary where the keys are the names of the random variables

and the values are the evaluations.

Return type

Dict[str, numpy.ndarray]

export_hdf(file_path, append=False)

Export to hdf file.

Parameters

• file_path – path to file to write

• append – if True, appends the data in the file

export_to_txt(output_file, fields=None, header_char='', **table_options)

Exports the design space to a text file.

Parameters

• output_file – output file path

• fields – list of fields to export, by default all

extend(other)

Extend the design space with another design space.

Parameters

other (DesignSpace) – design space to be appended

extract_deterministic_space()

Extract the deterministic space.

Returns

The deterministic space.

Return type

gemseo.algos.parameter_space.ParameterSpace

extract_uncertain_space()

Extract the uncertain space.

Returns

The uncertain space.

Return type

gemseo.algos.parameter_space.ParameterSpace

filter(keep_variables, copy=False)

Filter the design space to keep a sublist of variables.

Parameters

• keep_variables (str of list(str)) – the list of variables to keep

• copy (bool) – if True then a copy of the design space is filtered, otherwise the design space itself is filtered

Returns

the filtered design space (or a copy)

Return type

DesignSpace

filter_dim(variable, keep_dimensions)

Filters the design space to keep a sublist of dimensions for a given variable.

Parameters

• variable – the variable

• keep_dimensions – the list of dimension to keep

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

Determine which bound constraints of the current point are active.

Parameters

• x_vec – the point at which we check the bounds

• tol – tolerance of comparison of a scalar with a bound (Default value = 1e-8)

get_current_x(variables_names=None)

Gets the current point in the design space.

Parameters

variables_names (list(str)) – names of the required variables, optional

Returns

the x vector as array

Return type

ndarray

get_current_x_dict()

Get the current point in the design space.

Returns

the x vector as a dict, keys are the variable names values are the variable vales as np array

get_current_x_normalized()

Returns the current point normalized.

Returns

the x vector as array normalized by the bounds

get_indexed_var_name(variable_name)

Return a list of the variables names with their indices such as.

[x!0,x!1,y,z!0,z!1]

Parameters

variable_name (str) – name of the variable

Returns

names of the variable components

Return type

list(str)

get_indexed_variables_names()

Return a list of the variables names with their indices such as.

[x!0,x!1,y,z!0,z!1]

Returns

names of all the variables components

Return type

list(str)

get_lower_bound(name)

Gets the lower bound of a variable.

Parameters

name – variable name

Returns

variable lower bound (possibly infinite)

get_lower_bounds(variables_names=None)

Generates an array of the variables’ lower bounds.

Parameters

variables_names – names of the variables of which the lower bounds are required

get_pretty_table(fields=None)

Builds a PrettyTable object from the design space data.

Parameters

fields – list of fields to export, by default all

Returns

the pretty table object

get_range(variable)

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

List[numpy.ndarray]

get_size(name)

Get the size of a variable Return None if the variable is not known.

Parameters

name – name of the variable

get_support(variable)

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

List[numpy.ndarray]

get_tabular_view(decimals=2)

Return a tabular view of the parameter space.

This view contains statistical information.

Parameters

decimals (int) – The number of decimals to print.

Returns

The tabular view.

Return type

str

get_type(name)

Get the type of a variable Return None if the variable is not known.

Parameters

name – name of the variable

get_upper_bound(name)

Gets the upper bound of a variable.

Parameters

name – variable name

Returns

variable upper bound (possibly infinite)

get_upper_bounds(variables_names=None)

Generates an array of the variables’ upper bounds.

Parameters

variables_names – names of the variables of which the upper bounds are required

get_variables_indexes(variables_names)

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

Parameters

variables_names (list(str)) – names of the variables

Returns

indexes of a design array corresponding to the variables names

Return type

ndarray

has_current_x()

Tests if current_x is defined.

Returns

True if current_x is defined

import_hdf(file_path)

Imports design space from hdf file.

Parameters

file_path –

static init_from_dataset(dataset, groups=None, uncertain=None, copula='independent_copula')

Initialize the parameter space from a dataset.

Parameters

• dataset (Dataset) – The dataset used for the initialization.

• groups (Optional[Iterable[str]]) – The groups of the dataset to be considered. If None, consider all the groups.

• uncertain (Optional[Mapping[str,bool]]) – Whether the variables should be uncertain or not.

• copula (str) – A name of copula defining the dependency between random variables.

Return type

ParameterSpace

is_deterministic(variable)

Check if a variable is deterministic.

Parameters

variable (str) – The name of the variable.

Returns

True is the variable is deterministic.

Return type

bool

is_uncertain(variable)

Check if a variable is uncertain.

Parameters

variable (str) – The name of the variable.

Returns

True is the variable is uncertain.

Return type

bool

normalize_vect(x_vect, minus_lb=True, use_dist=False)

Normalize a vector.

Parameters

• x_vect (numpy.ndarray) – The vector to normalize.

• minus_lb (bool) – The type of normalization. If True, remove lower bounds at normalization.

• no_check – The data checker. If True, do not check that values are in [0,1].

• use_dist (bool) – The statistical scaling. If True, rescale wrt the statistical law.

Returns

The normalized vector.

Return type

numpy.ndarray

project_into_bounds(x_c, normalized=False)

Projects x_c onto the bounds, using a simple coordinate wise approach.

Parameters

• normalized (bool) – if True then the vector is assumed to be normalized

• x_c – x vector (np array)

Returns

projected x_c

static read_from_txt(input_file, header=None)

Parses a csv file to read the DesignSpace.

Parameters

• input_file – returns: s: the design space

• header – fields list, or by default, read in the file

Returns

the design space

remove_variable(name)

Remove a variable from the probability space.

Parameters

name (str) – The name of the variable.

Return type

None

round_vect(x_vect)

Rounds the vector where variables are of integer type.

Parameters

x_vect – design variables to round

set_current_variable(name, current_value)

Set the current value of a single variable.

Parameters

• name – name of the variable

• current_value – current value of the variable

set_current_x(current_x)

Set the current point.

Parameters

current_x – the current design vector

set_lower_bound(name, lower_bound)

Set a new lower bound for variable name.

Parameters

• name – name of the variable

• lower_bound – lower bound

set_upper_bound(name, upper_bound)

Set a new upper bound for variable name.

Parameters

• name – name of the variable

• upper_bound – upper bound

to_complex()

Casts the current value to complex.

unnormalize_vect(x_vect, minus_lb=True, no_check=False, use_dist=True)

Unnormalize an unit vector.

Parameters

• x_vect (numpy.ndarray) – The unit vector to unnormalize.

• minus_lb (bool) – The type of normalization. If True, remove lower bounds at normalization.

• no_check (bool) – The data checker. If True, do not check that values are in [0,1].

• use_dist (bool) – The statistical scaling. If True, rescale wrt the statistical law.

Returns

The unnormalized vector.

Return type

numpy.ndarray

Examples

Parameter space