/**
 * Numerical helpers shared by the mixture-model estimators.
 *
 * Everything here is dependency-free plain math so the fitted state of the
 * estimators stays serializable (no function-valued fields are ever stored).
 */
/** Machine epsilon for float64 (same constant sklearn uses as `np.finfo(float64).eps`). */
export declare const EPS = 2.220446049250313e-16;
/** Numerically stable log(sum(exp(values))). */
export declare function logsumexp(values: number[]): number;
/**
 * Cholesky decomposition of a symmetric positive-definite matrix.
 * Returns the lower-triangular factor L with A = L·Lᵀ.
 */
export declare function cholesky(a: number[][]): number[][];
/** Solve L·x = b for lower-triangular L (forward substitution). */
export declare function solveLowerTriangular(L: number[][], b: number[]): number[];
/** Inverse of a symmetric positive-definite matrix via its Cholesky factor. */
export declare function spdInverse(a: number[][]): number[][];
/** log Γ(x) via the Lanczos approximation (reflection formula for x < 0.5). */
export declare function logGamma(x: number): number;
/**
 * Digamma function ψ(x) for x > 0: the recurrence ψ(x) = ψ(x+1) − 1/x lifts the
 * argument above 10, then the asymptotic series
 * ψ(x) ≈ ln x − 1/(2x) − 1/(12x²) + 1/(120x⁴) − 1/(252x⁶) + 1/(240x⁸) − 1/(132x¹⁰)
 * is accurate to well below 1e-13.
 */
export declare function digamma(x: number): number;
/** log Β(a, b) = log Γ(a) + log Γ(b) − log Γ(a + b). */
export declare function betaln(a: number, b: number): number;