import { Matrix } from '../main.js';
import { JacobianFunction } from '../types/types.js';
/**
 * Calculates the Jacobian matrix of a given Jacobian function.
 *
 * The function calculates how small perturbations in each input variable affect all output variables,
 * using a second-order accurate central difference approximation.
 *
 * In orbital mechanics applications, this matrix is essential for solving complex problems like
 * orbit transfers, trajectory optimization, and precise orbital determination.
 * @param f The Jacobian function.
 * @param m The number of rows in the Jacobian matrix.
 * @param x0 The initial values of the variables.
 * @param step The step size for numerical differentiation (default: 1e-5).
 * @returns The Jacobian matrix.
 */
export declare const jacobian: (f: JacobianFunction, m: number, x0: Float64Array, step?: number) => Matrix;