sellar_design_space module¶
The design space for the MDO problem proposed by Sellar et al. in.
Sellar, R., Batill, S., & Renaud, J. (1996). Response surface based, concurrent subspace optimization for multidisciplinary system design. In 34th aerospace sciences meeting and exhibit (p. 714).
- class gemseo.problems.sellar.sellar_design_space.SellarDesignSpace(dtype='complex128')[source]¶
Bases:
gemseo.algos.design_space.DesignSpace
The design space for the MDO problem proposed by Sellar et al (1996).
It is composed of: - \(x_{local}\) belonging to \([0., 10.]\), - \(x_{shared,1}\) belonging to \([-10., 10.]\), - \(x_{shared,2}\) belonging to \([0., 10.]\), - \(y_1\) belonging to \([-100., 100.]\), - \(y_2\) belonging to \([-100., 100.]\).
This design space is initialized with the initial solution:
\(x_{local}=1\),
\(x_{shared,1}=4\),
\(x_{shared,2}=3\),
\(y_1=1\),
\(y_2=1\).
- Parameters
dtype (str) –
The type of the variables defined in the design space.
By default it is set to complex128.
- 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. ¶
- 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
- 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
- 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_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.
- 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
- initialize_missing_current_values()¶
Initialize the current values of the design variables when missing.
Use:
the center of the design space when the lower and upper bounds are finite,
the lower bounds when the upper bounds are infinite,
the upper bounds when the lower bounds are infinite,
zero when the lower and upper bounds are infinite.
- 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)¶
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, out=None)¶
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)¶
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)¶
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)¶
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
- transform_vect(vector, out=None)¶
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, out=None)¶
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)¶
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 ¶
- 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'¶
- dimension: int¶
The total dimension of the space, corresponding to the sum of the sizes of the variables.