ootk/dist/utils/jacobian.js

Orbital Object Toolkit including Multiple Propagators, Initial Orbit Determination, and Maneuver Calculations.

import { array2d, Matrix, Vector } from '../main.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 const jacobian = (f, m, x0, step = 0.00001) => {
    const n = x0.length;
    const j = array2d(m, n, 0);
    const h = 0.5 * step;
    for (let k = 0; k < n; k++) {
        const xp = x0.slice();
        xp[k] += h;
        const fp = new Vector(f(xp));
        const xm = x0.slice();
        xm[k] -= h;
        const fm = new Vector(f(xm));
        const cd = fp.subtract(fm).scale(1 / step);
        for (let i = 0; i < m; i++) {
            j[i][k] = cd.elements[i];
        }
    }
    return new Matrix(j);
};
//# sourceMappingURL=jacobian.js.map