Multistep

class pumas.desirability.multistep.MultiStep(params: Dict[str, Any] | None = None)

compute_numeric(x: int | float) → float

Compute the multistep desirability for a numeric input.

Parameters:

x (Union[int, float]) – The numeric input value.

Returns:

The computed desirability value.

Return type:

float

Raises:

• InvalidParameterTypeError – If the input is not a float.

• ParameterValueNotSet – If any required parameter is not set.

compute_ufloat(x: AffineScalarFunc) → AffineScalarFunc

Compute the multistep desirability for an uncertain float input.

Parameters:

x (UFloat) – The uncertain float input value.

Returns:

The computed desirability value with uncertainty.

Return type:

UFloat

Raises:

• InvalidParameterTypeError – If the input is not a UFloat.

• ParameterValueNotSet – If any required parameter is not set.

name: ClassVar[str] = 'multistep'

MultiStep desirability function implementation.

This class implements a multistep desirability function with linear interpolation between defined points. It provides methods to compute the desirability for both numeric and uncertain float inputs.

The multistep function is defined by a set of coordinates (x_i, y_i), where: - x_i represents the input values (independent variable) - y_i represents the corresonding desirability values (dependent variable) - The coordinates are ordered such that x_1 < x_2 < … < x_n - Each y_i must be in the range [0, 1]

Let (x_1, y_1) be the first point and (x_n, y_n) be the last point in the ordered set.

The multistep desirability function D(x) is defined as follows:

\[\begin{split}D(x) = \begin{cases} y_1 & \text{if } x \leq x_1 \\ y_n & \text{if } x \geq x_n \\ y_i + \frac{x - x_i}{x_{i+1} - x_i}(y_{i+1} - y_i) & \text{if } x_i < x < x_{i+1} \end{cases}\end{split}\]

Where:

• For x ≤ x_1, the function returns the desirability of the first point (y_1)

• For x ≥ x_n, the function returns the desirability of the last point (y_n)

• For x_i < x < x_{i+1}, linear interpolation is performed between the two closest points

The interpolation ensures a smooth transition between defined points while maintaining the step-like behavior at the specified coordinates.

Finally, the shift is applied:

\[D_{final}(x) = D(x) \cdot (1 - shift) + shift\]

Parameters:

params (Optional[Dict[str, Any]]) – Initial parameters for the multistep function.

Content of params:

coordinates (Iterable[Tuple[float, float]]): The coordinates defining the multistep function. Each tuple contains (x, y) values. shift (float): Vertical shift of the function, range [0.0, 1.0], default 0.0.

Raises:

• InvalidCoordinateError – If the coordinates list is empty.

• InvalidCoordinateError – If only one coordinate is provided (at least two are required).

• InvalidCoordinateError – If any y-coordinate is not between 0 and 1.

• InvalidCoordinateError – If any coordinate cannot be converted to a valid Point object (internal representation of coordinates).

Usage Example:

>>> from pumas.desirability import desirability_catalogue

>>> desirability_class = desirability_catalogue.get("multistep")

>>> coords = [(0, 0), (1, 0.5), (4, 1)]
>>> params = {"coordinates": coords, "shift": 0.0}
>>> desirability = desirability_class(params=params)
>>> print(desirability.get_parameters_values())
{'coordinates': [(0, 0), (1, 0.5), (4, 1)], 'shift': 0.0}

>>> result = desirability.compute_numeric(x=-1.0)
>>> print(f"{result:.2f}")
0.00

>>> result = desirability.compute_numeric(x=0.5)
>>> print(f"{result:.2f}")
0.25

>>> result = desirability.compute_numeric(x=2.5)
>>> print(f"{result:.2f}")
0.75

>>> result = desirability.compute_numeric(x=5.0)
>>> print(f"{result:.2f}")
1.00

class pumas.desirability.multistep.multistep(x: float | AffineScalarFunc, coordinates: List[Tuple[float, float]], shift: float = 0.0)

Compute the multistep desirability value for a given input.

Parameters:

• x (Union[float, UFloat]) – The input value.

• coordinates (Iterable[Tuple[float, float]]) – The coordinates defining the multistep function.

• shift (float, optional) – Vertical shift of the function. Defaults to 0.0.

Returns:

The computed desirability value.

Return type:

Union[float, UFloat]

class pumas.desirability.multistep.interpolate(x: float | AffineScalarFunc, p1: Point, p2: Point)

Perform linear interpolation between two points.

Parameters:

• x (Union[float, UFloat]) – The x-value to interpolate.

• p1 (Point) – The first point.

• p2 (Point) – The second point.

Returns:

The interpolated y-value.

Return type:

Union[float, UFloat]

Parameter Analysis

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