Math on statili

Activation Functions

Mon, 01 Jan 0001 00:00:00 +0000

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# sigmoid function

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sigmoid(z: number): number

Sigmoid (logistic) activation function: σ(z) = 1 / (1 + e⁻ᶻ).

Maps any real-valued input to the open interval (0, 1), making it suitable for modelling probabilities. The function is smooth and differentiable everywhere, which is why it is used in gradient-based optimisation (e.g. logistic regression, neural networks).

Descriptive Statistics

Mon, 01 Jan 0001 00:00:00 +0000

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# covariance function

packages/math/src/descriptive.ts:300

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covariance(xs: number[], ys: number[]): number

Returns the sample covariance between two equal-length arrays xs and ys (divided by n − 1).

Covariance measures the joint variability of two variables — a positive value means they tend to increase together; a negative value means one tends to decrease as the other increases.

Distribution

Mon, 01 Jan 0001 00:00:00 +0000

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# logGamma function

packages/math/src/distribution.ts:41

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logGamma(x: number): number

Natural logarithm of the gamma function, ln Γ(x), via the Lanczos approximation.

Γ(x) overflows a double for x greater than about 171, so the log form is used throughout — every consumer here needs ratios of gamma functions, which become differences of logs and stay in range.

Linear Algebra

Mon, 01 Jan 0001 00:00:00 +0000

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# gaussianElimination function

packages/math/src/linalg.ts:40

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gaussianElimination(input: number[][], order: number): number[]

Solves the linear system Ax = b via Gaussian elimination with partial pivoting.

The augmented matrix [A | b] is passed as input: an n × (n+1) matrix where the first n columns represent A and the last column represents b. The function operates on a deep copy and does not mutate its input.

Numeric Utilities

Mon, 01 Jan 0001 00:00:00 +0000

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# clamp function

packages/math/src/numeric.ts:70

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clamp(lo: number, hi: number, value: number): number

Clamps value to the closed interval [lo, hi].

Useful when mapping statistical outputs (e.g. probabilities, normalised scores) to a bounded domain before rendering.

Parameters

Name	Type	Description
lo	number	Lower bound (inclusive).
hi	number	Upper bound (inclusive).
value	number	The value to clamp.

Returns

number

lo if value < lo, hi if value > hi, otherwise value.

Example

clamp(0, 1, -0.3)  // 0
clamp(0, 1, 1.7)   // 1
clamp(0, 1, 0.5)   // 0.5

// Partial application — create a unit-clamp helper
const unitClamp = clamp(0, 1);
unitClamp(sigmoid(-100))  // 0 (not quite, but clamped to 0)

# isFiniteNumber function

packages/math/src/numeric.ts:46

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isFiniteNumber(value: unknown): boolean

Returns true when value is a finite, non-NaN number (i.e., safe for arithmetic). Rejects NaN, Infinity, -Infinity, null, and undefined.

Replaces the inline isValid guard scattered across @statili/stats regression methods.

Parameters

Name	Type	Description
value	unknown	Any value to test.

Returns

boolean

true if value is a finite number, false otherwise.

Example

isFiniteNumber(3.14)      // true
isFiniteNumber(NaN)       // false
isFiniteNumber(Infinity)  // false
isFiniteNumber(null)      // false

# lerp function

packages/math/src/numeric.ts:95

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lerp(a: number, b: number, t: number): number

Linearly interpolates between a and b by factor t.

t = 0 returns a
t = 1 returns b
t = 0.5 returns the midpoint
Values outside [0, 1] extrapolate beyond the endpoints

Handy for generating evenly-spaced prediction points along a regression curve or animating transitions between two chart states.