gemseo / algos

design_space module

Design space.

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

Classes:

DesignSpace([hdf_file, name])

Description of a design space.

DesignVariable(size, var_type, l_b, u_b, value)

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

DesignVariableType(value)

A type of design variable.

class gemseo.algos.design_space.DesignSpace(hdf_file=None, name=None)[source]

Bases: collections.abc.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(), …

name

The name of the space.

Type

Optional[str]

variables_names

The names of the variables.

Type

List[str]

dimension

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

Type

int

variables_sizes

The sizes of the variables.

Type

Dict[str,int]

variables_types

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

Type

Dict[str,ndarray]

normalize

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

Type

Dict[str,ndarray]

Parameters
  • hdf_file (str | Path | None) –

    The path to the file containing the description of an initial design space. If None, start with an empty design space.

    By default it is set to None.

  • name (str | None) –

    The name to be given to the design space, None if the design space is unnamed.

    By default it is set to None.

Return type

None

Attributes:

AVAILABLE_TYPES

DESIGN_SPACE_GROUP

FLOAT

INTEGER

LB_GROUP

MINIMAL_FIELDS

NAMES_GROUP

NAME_GROUP

SEP

SIZE_GROUP

TABLE_NAMES

UB_GROUP

VALUE_GROUP

VAR_TYPE_GROUP

Methods:

add_variable(name[, size, var_type, l_b, ...])

Add a variable to the design space.

array_to_dict(x_array)

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

check()

Check the state of the design space.

check_membership(x_vect[, variable_names])

Check whether the variables satisfy the design space requirements.

clear()

dict_to_array(design_values[, variable_names])

Convert a point as dictionary into an array.

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.

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 a design value are active.

get_current_value([variable_names, ...])

Return the current design value.

get_indexed_var_name(variable_name)

Create the names of the components of a variable.

get_indexed_variables_names()

Create the names of the components of all the variables.

get_lower_bound(name)

Return the lower bound of a variable.

get_lower_bounds([variable_names])

Generate an array of the variables' lower bounds.

get_pretty_table([fields])

Build a tabular view of the design space.

get_size(name)

Get the size of a variable.

get_type(name)

Return the type of a variable.

get_upper_bound(name)

Return the upper bound of a variable.

get_upper_bounds([variable_names])

Generate an array of the variables' upper bounds.

get_variables_indexes(variable_names)

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

has_current_value()

Check if each variable has a current value.

has_integer_variables()

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

import_hdf(file_path)

Import a design space from an HDF file.

items()

keys()

normalize_grad(g_vect)

Normalize an unnormalized gradient.

normalize_vect(x_vect[, minus_lb, out])

Normalize a vector of the design space.

pop(k[,d])

If key is not found, d is returned if given, otherwise KeyError is raised.

popitem()

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_variable(name)

Remove a variable from the design space.

rename_variable(current_name, new_name)

Rename a variable.

round_vect(x_vect[, copy])

Round the vector where variables are of integer type.

set_current_value(value)

Set the current dseign value.

set_current_variable(name, current_value)

Set the current value of a single variable.

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])

to_complex()

Cast the current value to complex.

transform_vect(vector[, out])

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 design space.

untransform_vect(vector[, no_check, out])

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

values()

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_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 (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)[source]

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

dict[str, numpy.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.

    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 not an integer.

Return type

None

clear() None.  Remove all items from D.
dict_to_array(design_values, variable_names=None)[source]

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

numpy.ndarray

export_hdf(file_path, append=False)[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.

Return type

None

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

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 by DesignSpace.get_pretty_table().

Return type

None

extend(other)[source]

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

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

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)[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.

    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, 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.

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

ndarray | dict[str, ndarray]

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_variables_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

numpy.ndarray

get_lower_bounds(variable_names=None)[source]

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)[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.

By default it is set to None.

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

numpy.ndarray

get_upper_bounds(variable_names=None)[source]

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)[source]

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

numpy.ndarray

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

import_hdf(file_path)[source]

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

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

Returns

The normalized gradient.

Return type

numpy.ndarray

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 (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.

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

Returns

The projected vector.

Return type

numpy.ndarray

static read_from_txt(input_file, header=None)[source]

Create a design space from a text file.

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

  • header (Iterable[str] | None) –

    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

DesignSpace

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 (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

numpy.ndarray

set_current_value(value)[source]

Set the current dseign 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 (numpy.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 (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)[source]

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()[source]

Cast the current value to complex.

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.

    By default it is set to None.

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 (numpy.ndarray) – The gradient to be unnormalized.

Returns

The unnormalized gradient.

Return type

numpy.ndarray

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 (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.

  • 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
class gemseo.algos.design_space.DesignVariable(size, var_type, l_b, u_b, value)

Bases: tuple

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

Methods:

count(value, /)

Return number of occurrences of value.

index(value[, start, stop])

Return first index of value.

Attributes:

l_b

Alias for field number 2

size

Alias for field number 0

u_b

Alias for field number 3

value

Alias for field number 4

var_type

Alias for field number 1

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

Alias for field number 2

size

Alias for field number 0

u_b

Alias for field number 3

value

Alias for field number 4

var_type

Alias for field number 1

class gemseo.algos.design_space.DesignVariableType(value)[source]

Bases: gemseo.utils.base_enum.BaseEnum

A type of design variable.

Attributes:

FLOAT

INTEGER

FLOAT = 'float'
INTEGER = 'integer'