/*
* p: position
* q: momentum
* epsilon: step size
*/
leapfrog_step = function(p, q, epsilon, negative_gradient) {
q = math.add(q, math.multiply(epsilon / 2, negative_gradient(p)));
p = math.add(p, math.multiply(epsilon, q));
q = math.add(q, math.multiply(epsilon / 2, negative_gradient(p)));
return ({ position: p, momentum: q });
}
leapfrog = function(steps, epsilon, log_density, gradient_log_density, p_init, q_init) {
const negative_log_density = (x) => math.multiply(-1, log_density(x));
const negative_gradient_log_density = (x) => math.multiply(-1, gradient_log_density(x));
// Calculate initial kinetic and potential energy
const K0 = math.sum(q_init.map((d) => Math.pow(d, 2))) / 2;
const P0 = negative_log_density(p_init);
const K = [K0];
const P = [P0];
const p = [p_init];
const q = [q_init];
// Run leapfrog integrator
for(let step = 1; step < steps; step++) {
// Apply leapfrog integration step to get next values
// for theta, momentum
const next_step = leapfrog_step(p[step - 1], q[step - 1], epsilon, negative_gradient_log_density);
p[step] = next_step.position;
q[step] = next_step.momentum;
// Calculate kinetic and potential energy
K[step] = math.sum(q[step].map((d) => Math.pow(d, 2))) / 2;
P[step] = negative_log_density(p[step]);
}
return ({
K, P,
p,
q,
divergent: P[P.length - 1] > 10000
});
}
Purpose-built for displays of data
Observable is your go-to platform for exploring data and creating expressive data visualizations. Use reactive JavaScript notebooks for prototyping and a collaborative canvas for visual data exploration and dashboard creation.
