Struct SigmoidModel

pub struct SigmoidModel;

Provides a sigmoid (logistic) influence model with a configurable growth phase.

f(x) = L / (1 + e^(-k * (x - x0)))

You do not set k or x0 directly. Instead you describe the shape of the curve using five intuitive parameters, and the model derives k and x0 from them:

• L : the maximum output the curve can ever reach
• alpha : what fraction of L marks the start of the growth phase (e.g. 0.1 = 10%)
• beta : what fraction of L marks the end of the growth phase (e.g. 0.9 = 90%)
• x_alpha : the input value where output first reaches alpha * L
• x_beta : the input value where output reaches beta * L

From those, the model computes:

• w = x_beta - x_alpha (growth width)
• k = [ ln(beta / (1 - beta)) - ln(alpha / (1 - alpha)) ] / w (growth rate)
• x0 = x_alpha - (1 / k) * ln(alpha / (1 - alpha)) (midpoint)

Signed Arithmetic

Even when the context FixedPoint is unsigned, all intermediate steps (logit, k, x0, the exponent) are computed in concrete FixedI128 via FixedSignedCast. This is necessary because logit(alpha) is negative for any alpha < 0.5, and the exponent -k * (x - x0) is negative for all x > x0. Unsigned arithmetic would silently clamp both to zero, producing a completely wrong curve.

Precision Note

The ln -> k -> x0 -> exp chain accumulates a small amount of rounding error across four fixed-point operations. The practical effect is that x0 lands fractionally above its exact value, shifting the curve slightly to the right. At the definition points x_alpha and x_beta the logit cancels cleanly and the output is exact. At all other points including the midpoint, the output may be 1 integer unit below the ideal value – for example, f(x_beta) may yield 89 instead of 90 when L = 100.

• Exact: f(80) = 90.000000000
• Fixed-point: f(80) = 89.999999... -> truncates to 89

This is expected and inconsequential for integer influence scores.

Guard Conditions (returns zero)

• alpha <= 0 or alpha >= 1
• beta <= 0 or beta >= 1
• x_beta <= x_alpha (degenerate or inverted growth window)
• k == 0 (flat curve, midpoint is undefined)

Trait Implementations

impl Debug for SigmoidModel

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Default for SigmoidModel

fn default() -> SigmoidModel

Returns the “default value” for a type.

impl<FixedPoint, Input> PurePluginModel<Input, SigmoidModelConfig<FixedPoint>, Input> for SigmoidModel

where Input: IntegerToFixed + FixedForInteger<FixedPoint = FixedPoint> + Zero, FixedPoint: FixedPointNumber + FixedSignedCast<Signed = FixedI128>,

fn compute( &self, input: Input, context: &SigmoidModelConfig<FixedPoint>, ) -> Input

Computes the model’s output for a given immutable input and context.