Bell

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

compute_numeric(x: int | float) → float

Compute the bell 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 bell 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] = 'bell'

Bell desirability function implementation.

Mathematical Definition:

The bell function is defined as:

\[f(x) = \frac{1}{1 + |\frac{x - center}{width}|^{2 * slope}} * (1 - shift) + shift\]

Where:

• x is the input value.

• width is the width parameter of the bell curve, controls the horizontal spread (width > 0).

• slope is the slope parameter of the bell curve, controls the steepness of the curve’s sides.

• center is the center of the bell curve, indicates the x value at the highest point of the curve (peak).

• invert is a boolean parameter that, if True, inverts the curve.

• shift is the vertical shift applied to the entire curve, ranging from 0 (no shift) to 1 (maximum shift).

Parameters:

params (Optional[Dict[str, Any]]) – Initial parameters for the sigmoid function. Defaults to None.

width

The width parameter of the bell curve, controls the horizontal spread (width > 0).

Type:

float

slope

The slope parameter of the bell curve, controls the steepness of the curve’s sides.

Type:

float

center

The center of the bell curve, indicates the x value at the highest point of the curve (peak).

Type:

float

invert

If True, the curve is inverted, i.e., the desirability decreases as x approaches the center.

Type:

bool

shift

The vertical shift applied to the entire curve, ranging from 0 (no shift) to 1 (maximum shift).

Type:

float

Usage Example:

>>> from pumas.desirability import desirability_catalogue

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

>>> params = {'center': 0.5, 'width': 1.0, 'slope': 2.0, 'invert': False, 'shift': 0.0}
>>> desirability = desirability_class(params=params)
>>> print(desirability.get_parameters_values())
{'center': 0.5, 'width': 1.0, 'slope': 2.0, 'invert': False, 'shift': 0.0}

>>> result = desirability.compute_numeric(x=0.5)
>>> print(f"{result:.2f}")
1.00

>>> result = desirability(x=0.5) # Same as compute_numeric
>>> print(f"{result:.2f}")
1.00

>>> from uncertainties import ufloat
>>> result = desirability.compute_ufloat(x=ufloat(0.5, 0.1))
>>> print(result)
1.0+/-0

class pumas.desirability.bell.bell(x: float | ~uncertainties.core.AffineScalarFunc, width: float, slope: float, center: float, invert: bool = False, shift: float = 0.0, math_module: ~types.ModuleType = <module 'math' from '/home/docs/.asdf/installs/python/3.12.10/lib/python3.12/lib-dynload/math.cpython-312-x86_64-linux-gnu.so'>)

Parameter Analysis

(Source code, png, hires.png, pdf)