gemseo_mlearning / adaptive / criteria / standard_deviation

# criterion module¶

Standard deviation of the regression model.

Statistics:

$\sigma[x] = \sqrt{E[(Y(x)-E[Y(x)])^2]}$

Bootstrap estimator:

$\hat{\sigma}[x] = \sqrt{\frac{1}{B-1}\sum_{b=1}^B (Y_b(x)-\widehat{E}[x])^2}$

where $$\widehat{E}[x]= \frac{1}{B}\sum_{b=1}^B Y_b(x)$$.

Standard Deviation of the regression model.

This criterion is scaled by the output range.

# noqa: D205 D212 D415

Parameters:
• algo_distribution (MLRegressorDistribution) – The distribution of a machine learning algorithm.

• **options (MLDataAcquisitionCriterionOptionType) – The acquisition criterion options.

class ApproximationMode(value)

Bases: StrEnum

The approximation derivation modes.

COMPLEX_STEP = 'complex_step'

The complex step method used to approximate the Jacobians by perturbing each variable with a small complex number.

FINITE_DIFFERENCES = 'finite_differences'

The finite differences method used to approximate the Jacobians by perturbing each variable with a small real number.

class ConstraintType(value)

Bases: StrEnum

The type of constraint.

EQ = 'eq'

The type of function for equality constraint.

INEQ = 'ineq'

The type of function for inequality constraint.

class FunctionType(value)

Bases: StrEnum

An enumeration.

EQ = 'eq'
INEQ = 'ineq'
NONE = ''
OBJ = 'obj'
OBS = 'obs'

Check the gradients of the function.

Parameters:
• x_vect (ndarray[Any, dtype[Number]]) – The vector at which the function is checked.

• approximation_mode (ApproximationMode) –

The approximation mode.

By default it is set to “finite_differences”.

• step (float) –

The step for the approximation of the gradients.

By default it is set to 1e-06.

• error_max (float) –

The maximum value of the error.

By default it is set to 1e-08.

Raises:

ValueError – Either if the approximation method is unknown, if the shapes of the analytical and approximated Jacobian matrices are inconsistent or if the analytical gradients are wrong.

Return type:

None

evaluate(x_vect)

Evaluate the function and store the dimension of the output space.

Parameters:

x_vect (ndarray[Any, dtype[Number]]) – The value of the inputs of the function.

Returns:

The value of the output of the function.

Return type:

ndarray[Any, dtype[Number]] | Number

static filt_0(arr, floor_value=1e-06)

Set the non-significant components of a vector to zero.

The component of a vector is non-significant if its absolute value is lower than a threshold.

Parameters:
• arr (ndarray[Any, dtype[Number]]) – The original vector.

• floor_value (float) –

The threshold.

By default it is set to 1e-06.

Returns:

The original vector whose non-significant components have been set at zero.

Return type:
static from_pickle(file_path)

Deserialize a function from a file.

Parameters:

file_path (str | Path) – The path to the file containing the function.

Returns:

The function instance.

Return type:

MDOFunction

classmethod generate_input_names(input_dim, input_names=None)

Generate the names of the inputs of the function.

Parameters:
• input_dim (int) – The dimension of the input space of the function.

• input_names (Sequence[str] | None) – The initial names of the inputs of the function. If there is only one name, e.g. ["var"], use this name as a base name and generate the names of the inputs, e.g. ["var!0", "var!1", "var!2"] if the dimension of the input space is equal to 3. If None, use "x" as a base name and generate the names of the inputs, i.e. ["x!0", "x!1", "x!2"].

Returns:

The names of the inputs of the function.

Return type:

Sequence[str]

get_indexed_name(index)

Return the name of function component.

Parameters:

index (int) – The index of the function component.

Returns:

The name of the function component.

Return type:

str

static init_from_dict_repr(**attributes)

Initialize a new function.

This is typically used for deserialization.

Parameters:

**attributes (Any) – The values of the serializable attributes listed in MDOFunction.DICT_REPR_ATTR.

Returns:

A function initialized from the provided data.

Raises:

ValueError – If the name of an argument is not in MDOFunction.DICT_REPR_ATTR.

Return type:

MDOFunction

is_constraint()

Check if the function is a constraint.

The type of a constraint function is either ‘eq’ or ‘ineq’.

Returns:

Whether the function is a constraint.

Return type:

bool

offset(value)

Add an offset value to the function.

Parameters:

value (ndarray[Any, dtype[Number]] | Number) – The offset value.

Returns:

The offset function.

Return type:

MDOFunction

static rel_err(a_vect, b_vect, error_max)

Compute the 2-norm of the difference between two vectors.

Normalize it with the 2-norm of the reference vector if the latter is greater than the maximal error.

Parameters:
Returns:

The difference between two vectors, normalized if required.

Return type:

float

set_pt_from_database(database, design_space, normalize=False, jac=True, x_tolerance=1e-10)

Set the original function and Jacobian function from a database.

For a given input vector, the method MDOFunction.func() will return either the output vector stored in the database if the input vector is present or None. The same for the method MDOFunction.jac().

Parameters:
• database (Database) – The database to read.

• design_space (DesignSpace) – The design space used for normalization.

• normalize (bool) –

If True, the values of the inputs are unnormalized before call.

By default it is set to False.

• jac (bool) –

If True, a Jacobian pointer is also generated.

By default it is set to True.

• x_tolerance (float) –

The tolerance on the distance between inputs.

By default it is set to 1e-10.

Return type:

None

to_dict()

Create a dictionary representation of the function.

This is used for serialization. The pointers to the functions are removed.

Returns:

Some attributes of the function indexed by their names. See MDOFunction.DICT_REPR_ATTR.

Return type:

dict[str, str | int | list[str]]

to_pickle(file_path)

Serialize the function and store it in a file.

Parameters:

file_path (str | Path) – The path to the file to store the function.

Return type:

None

COEFF_FORMAT_1D: str = '{:.2e}'

The format to be applied to a number when represented in a vector.

COEFF_FORMAT_ND: str = '{: .2e}'

The format to be applied to a number when represented in a matrix.

DEFAULT_BASE_INPUT_NAME: str = 'x'

The default base name for the inputs.

DICT_REPR_ATTR: list[str] = ['name', 'f_type', 'expr', 'input_names', 'dim', 'special_repr', 'output_names']

The names of the attributes to be serialized.

INDEX_PREFIX: str = '!'

The character used to separate a name base and a prefix, e.g. "x!1.

MAXIMIZE: ClassVar[bool] = True
activate_counters: ClassVar[bool] = True

Whether to count the number of function evaluations.

algo_distribution: MLRegressorDistribution

The distribution of a machine learning algorithm assessor.

property default_repr: str

The default string representation of the function.

property dim: int

The dimension of the output space of the function.

property expects_normalized_inputs: bool

Whether the functions expect normalized inputs or not.

property expr: str

The expression of the function, e.g. “2*x”.

force_real: bool

Whether to cast the results to real value.

property func: Callable[[ndarray[Any, dtype[Number]]], ndarray[Any, dtype[Number]] | Number]

The function to be evaluated from a given input vector.

has_default_name: bool

Whether the name has been set with a default value.

property has_jac: bool

Check if the function has an implemented Jacobian function.

Returns:

Whether the function has an implemented Jacobian function.

property input_names: list[str]

The names of the inputs of the function.

Use a copy of the original names.

property jac: Callable[[ndarray[Any, dtype[Number]]], ndarray[Any, dtype[Number]]]

The Jacobian function to be evaluated from a given input vector.

last_eval: OutputType | None

The value of the function output at the last evaluation.

None if it has not yet been evaluated.

property n_calls: int

The number of times the function has been evaluated.

This count is both multiprocess- and multithread-safe, thanks to the locking process used by MDOFunction.evaluate().

property name: str

The name of the function.

property original_name: str

The original name of the function.

property output_names: list[str]

The names of the outputs of the function.

Use a copy of the original names.

output_range: float

The output range.

special_repr: str