Ecosystem Integration Tutorial

Gradient

Use autodiff/linalg when a scalar function consumes a Luna Flow vector.

let x = @la.Vector::from_array([2.0, 3.0])
let gradient = @linalg.gradient(
  fn(v) { v[0] * v[0] + v[0] * v[1] },
  x,
)

For f(x, y) = x² + xy, the gradient at (2, 3) is [7, 2].

Jacobian

jacobian works for vector-valued functions.

let x = @la.Vector::from_array([2.0, 3.0])
let jacobian = @linalg.jacobian(
  fn(v) { @la.Vector::from_array([v[0] + v[1], v[0] * v[1]]) },
  x,
)

The returned matrix is output-by-input:

[[1, 1],
 [3, 2]]

Polynomial Derivative At A Point

autodiff/poly differentiates a polynomial at a point by evaluating it over Dual[T].

let p = @dense.DensePolynomial::from_coefficients([1.0, 2.0, 1.0])
let (value, derivative) = @poly.value_and_derivative_at(p, 3.0)

For p(x) = x² + 2x + 1, the value is 16 and the derivative is 8.