gemseo / algos

# parameter_space module¶

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:

The ParameterSpace also provides the following methods:

Classes:

 ParameterSpace([hdf_file, copula, name]) Parameter space. RandomVariable(distribution, size, parameters) Create new instance of RandomVariable(distribution, size, parameters)
class gemseo.algos.parameter_space.ParameterSpace(hdf_file=None, copula='independent_copula', name=None)[source]

Parameter space.

uncertain_variables

The names of the uncertain variables.

Type

List(str)

distributions

The marginal probability distributions of the uncertain variables.

Type

Dict(str,Distribution)

distribution

The joint probability distribution of the uncertain variables.

Type

ComposedDistribution

Parameters
• copula (str) –

A name of copula defining the dependency between random variables.

By default it is set to independent_copula.

• hdf_file (Optional[Union[str,Path]]) –

By default it is set to None.

• name (Optional[str]) –

By default it is set to None.

Return type

None

Attributes:

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) Convert the current point into a dictionary indexed by the variables names. Check the state of the design space. check_membership(x_vect[, variables_names]) Check whether the 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]) Convert an point as dictionary into an array. evaluate_cdf(value[, inverse]) Evaluate the cumulative density function (or its inverse) of each marginal. export_hdf(file_path[, append]) Export the design space to an HDF file. export_to_txt(output_file[, fields, header_char]) Export the design space to a text file. extend(other) Extend the design space with another design space. Define a new DesignSpace from the deterministic variables only. extract_uncertain_space([as_design_space]) Define a new DesignSpace from the uncertain variables only. filter(keep_variables[, copy]) Filter the design space to keep a subset of variables. filter_dim(variable, keep_dimensions) Filter the design space to keep a subset of dimensions for a variable. get(k[,d]) get_active_bounds([x_vec, tol]) Determine which bound constraints of the current point are active. get_current_x([variables_names]) Return the current point in the design space. Return the current point in the design space as a dictionary. Return the current point normalized. get_indexed_var_name(variable_name) Create the names of the components of a variable. Create the names of the components of all the variables. Return the lower bound of a variable. get_lower_bounds([variables_names]) Generate an array of the variables' lower bounds. get_pretty_table([fields]) Build a tabular view of the design space. get_range(variable) Return the numerical range of a random variable. get_size(name) Get the size of a variable. 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) Return the type of a variable. Return the upper bound of a variable. get_upper_bounds([variables_names]) Generate an array of the variables' upper bounds. get_variables_indexes(variables_names) Return the indexes of a design array corresponding to the variables names. Check if the current design value is defined for all variables. import_hdf(file_path) Import a design space from an 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_grad(g_vect) Normalize an unnormalized gradient. normalize_vect(x_vect[, minus_lb, use_dist]) Normalize a vector of the parameter space. pop(k[,d]) If key is not found, d is returned if given, otherwise KeyError is raised. as a 2-tuple; but raise KeyError if D is empty. project_into_bounds(x_c[, normalized]) Project a vector onto the bounds, using a simple coordinate wise approach. read_from_txt(input_file[, header]) Create a design space from a text file. Remove a variable from the probability space. round_vect(x_vect) Round 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 the lower bound of a variable. set_upper_bound(name, upper_bound) Set the upper bound of a variable. setdefault(k[,d]) Cast the current value to complex. Convert the parameter space into a DesignSpace. transform_vect(vector) Map a point of the design space to a vector with components in $$[0,1]$$. unnormalize_grad(g_vect) Unnormalize a normalized gradient. unnormalize_vect(x_vect[, minus_lb, ...]) Unnormalize a normalized vector of the parameter space. untransform_vect(vector) Map a vector with components in $$[0,1]$$ to the design space. update([E, ]**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
AVAILABLE_TYPES = [<DesignVariableType.FLOAT: 'float'>, <DesignVariableType.INTEGER: 'integer'>]
DESIGN_SPACE_GROUP = 'design_space'
FLOAT = 'float'
INTEGER = 'integer'
LB_GROUP = 'l_b'
MINIMAL_FIELDS = ['name', 'lower_bound', 'upper_bound']
NAMES_GROUP = 'names'
NAME_GROUP = 'name'
SEP = '!'
SIZE_GROUP = 'size'
TABLE_NAMES = ['name', 'lower_bound', 'value', 'upper_bound', 'type']
UB_GROUP = 'u_b'
VALUE_GROUP = 'value'
VAR_TYPE_GROUP = 'var_type'

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 (Union[str, Sequence[str], gemseo.algos.design_space.DesignVariableType, Sequence[gemseo.algos.design_space.DesignVariableType]]) –

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

By default it is set to FLOAT.

• l_b (Optional[Union[float, numpy.ndarray]]) –

The lower bound of the variable. If None, use $$-\infty$$.

By default it is set to None.

• u_b (Optional[Union[float, numpy.ndarray]]) –

The upper bound of the variable. If None, use $$+\infty$$.

By default it is set to None.

• value (Optional[Union[float, numpy.ndarray]]) –

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 the current point into a dictionary indexed by the variables names.

Parameters

x_array (numpy.ndarray) – The current point.

Returns

The dictionary version of the current point.

Return type

Dict[str, numpy.ndarray]

check()

Check the state of the design space.

Raises

ValueError – If the design space is empty.

Return type

None

check_membership(x_vect, variables_names=None)

Check whether the variables satisfy the design space requirements.

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

• variables_names (Optional[Sequence[str]]) –

The names of the variables. If None, use the names of the variables of the design space.

By default it is set to None.

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 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
• 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

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)

Convert an point as dictionary into an array.

Parameters
• x_dict (Dict[str, numpy.ndarray]) – The point to be converted.

• all_vars (bool) –

If True, all the variables to be considered shall be in the provided point.

By default it is set to True.

• all_var_list (Optional[Sequence[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

numpy.ndarray

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

Dict[str, numpy.ndarray]

export_hdf(file_path, append=False)

Export the design space to an HDF file.

Parameters
• file_path (Union[str, pathlib.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.

Return type

None

Export the design space to a text file.

Parameters
• output_file (Union[str,Path],) – The path to the file.

• fields (Optional[Sequence[str]]) –

The fields to be exported. If None, export all fields.

By default it is set to None.

By default it is set to .

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

gemseo.algos.design_space.DesignSpace

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 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
filter(keep_variables, copy=False)

Filter the design space to keep a subset of variables.

Parameters
• keep_variables (Union[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

gemseo.algos.design_space.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

gemseo.algos.design_space.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 the current point are active.

Parameters
• x_vec (Optional[numpy.ndarray]) –

The point at which to check the bounds. If None, use the current point.

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

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

get_current_x(variables_names=None)

Return the current point in the design space.

Parameters

variables_names (Optional[Iterable[str]]) –

The names of the required variables. If None, use the names of the variables of the design space.

By default it is set to None.

Raises

KeyError – If a variable has no current value.

Return type

numpy.ndarray

get_current_x_dict()

Return the current point in the design space as a dictionary.

Returns

The current point in the design space as a dictionary, whose keys are the names of the variables and values are the values of the variables.

Return type

Dict[str, numpy.ndarray]

get_current_x_normalized()

Return the current point normalized.

Returns

The current point as an array normalized by the bounds of the variables.

Returns

If the current point cannot be normalized.

Return type

KeyError

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 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

Union[str, List[str]]

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 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)

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

numpy.ndarray

get_lower_bounds(variables_names=None)

Generate an array of the variables’ lower bounds.

Parameters

variables_names (Optional[Sequence[str]]) –

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

numpy.ndarray

get_pretty_table(fields=None)

Build a tabular view of the design space.

Parameters

fields (Optional[Sequence[str]]) –

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

gemseo.third_party.prettytable.prettytable.PrettyTable

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

List[numpy.ndarray]

get_size(name)

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

Optional[int]

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

List[numpy.ndarray]

get_tabular_view(decimals=2)[source]

Return a tabular view of the parameter space.

This view contains statistical information.

Parameters

decimals (int) –

The number of decimals to print.

By default it is set to 2.

Returns

The tabular view.

Return type

str

get_type(name)

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

Optional[str]

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

numpy.ndarray

get_upper_bounds(variables_names=None)

Generate an array of the variables’ upper bounds.

Parameters

variables_names (Optional[Sequence[str]]) –

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

numpy.ndarray

get_variables_indexes(variables_names)

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

Parameters

variables_names (Iterable[str]) – The names of the variables.

Returns

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

Return type

numpy.ndarray

has_current_x()

Check if the current design value is defined for all variables.

Returns

Whether the current design value is defined for all variables.

Return type

bool

import_hdf(file_path)

Import a design space from an HDF file.

Parameters

file_path (Union[str, pathlib.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 (Optional[Iterable[str]]) –

The groups of the dataset to be considered. If None, consider all the groups.

By default it is set to None.

• uncertain (Optional[Mapping[str,bool]]) –

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

ParameterSpace

is_deterministic(variable)[source]

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)[source]

Check if a variable is uncertain.

Parameters

variable (str) – The name of the variable.

Returns

True is the variable is uncertain.

Return type

bool

items() a set-like object providing a view on D's items
keys() a set-like object providing a view on D's keys

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 $$x$$.

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

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

Parameters

g_vect (numpy.ndarray) – The gradient to be normalized.

Returns

Return type

numpy.ndarray

normalize_vect(x_vect, minus_lb=True, use_dist=False)[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 (numpy.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.

Returns

The normalized vector.

Return type

numpy.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

numpy.ndarray

Create a design space from a text file.

Parameters
• input_file (Union[str, pathlib.Path]) – The path to the file.

The names of the fields saved in the file. If None, read them in the file.

By default it is set to None.

Returns

The design space read from the file.

Raises

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

Return type

gemseo.algos.design_space.DesignSpace

remove_variable(name)[source]

Remove a variable from the probability space.

Parameters

name (str) – The name of the variable.

Return type

None

round_vect(x_vect)

Round the vector where variables are of integer type.

Parameters

x_vect (numpy.ndarray) – The values to be rounded.

Returns

The rounded values values.

Raises

ValueError – If the values is not a one- or two-dimensional

Return type

numpy.ndarray

set_current_variable(name, current_value)

Set the current value of a single variable.

Parameters
• name – The name of the variable.

• current_value – The current value of the variable.

set_current_x(current_x)

Set the current point.

Parameters

current_x (Union[numpy.ndarray, Mapping[str, numpy.ndarray], gemseo.algos.opt_result.OptimizationResult]) – The value of the current point.

Raises
• ValueError – If the value has a wrong dimension.

• TypeError – If the current point is neither a mapping of NumPy arrays, a NumPy array nor an OptimizationResult.

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

gemseo.algos.design_space.DesignSpace

transform_vect(vector)[source]

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

Parameters

vector (numpy.ndarray) – A point of the design space.

Returns

A vector with components in $$[0,1]$$.

Return type

numpy.ndarray

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

Return type

numpy.ndarray

unnormalize_vect(x_vect, minus_lb=True, no_check=False, use_dist=False)[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 in DesignSpace.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 (numpy.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.

• no_check (bool) –

If True, do not check that the values are in [0,1].

By default it is set to False.

• use_dist (bool) –

If True, unnormalize the components of the random variables with their inverse cumulative probability distributions.

By default it is set to False.

Returns

The unnormalized vector.

Return type

numpy.ndarray

untransform_vect(vector)[source]

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

Parameters

vector (numpy.ndarray) – A vector with components in $$[0,1]$$.

Returns

A point of the variables space.

Return type

numpy.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
class gemseo.algos.parameter_space.RandomVariable(distribution, size, parameters)

Bases: tuple

Create new instance of RandomVariable(distribution, size, parameters)

Methods:

 count(value, /) Return number of occurrences of value. index(value[, start, stop]) Return first index of value.

Attributes:

 distribution Alias for field number 0 parameters Alias for field number 2 size Alias for field number 1
count(value, /)

Return number of occurrences of value.

distribution

Alias for field number 0

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

Return first index of value.

Raises ValueError if the value is not present.

parameters

Alias for field number 2

size

Alias for field number 1