Struct StateDerivatives 

pub struct StateDerivatives<const N: usize> {
    pub grad: [f64; N],
    pub hessian: [f64; N],
    pub hessian_full: [[f64; N]; N],
    pub fwd: [f64; N],
    pub bwd: [f64; N],
}

Derivatives of the value function at a state.

• grad[i] is the centered first derivative dV/dx_i.
• hessian[i] is the diagonal second derivative d^2V/dx_i^2.
• hessian_full[i][j] is the symmetric mixed second derivative d^2V/dx_i dx_j; its diagonal hessian_full[i][i] equals hessian[i].
• fwd[i] is the forward difference (V(x + h_i e_i) - V(x)) / h_i.
• bwd[i] is the backward difference (V(x) - V(x - h_i e_i)) / h_i.

Continuous controls consume grad/hessian (and hessian_full when their noise is correlated across coordinates); jump controls (e.g. market making on a discrete inventory) consume fwd/bwd. The diagonal hessian and the full matrix are kept consistent: constructors that take only a diagonal fill hessian_full with zeros off the diagonal.

Fields

grad: [f64; N]

hessian: [f64; N]

hessian_full: [[f64; N]; N]

fwd: [f64; N]

bwd: [f64; N]

Implementations

impl<const N: usize> StateDerivatives<N>

pub fn new(grad: [f64; N], hessian: [f64; N]) -> Self

Construct a derivative bundle from first and diagonal second derivatives, with zero directional differences and zero off-diagonal Hessian.

Examples

use solver::models::control::StateDerivatives;
let d = StateDerivatives::new([0.1], [-0.02]);
assert_eq!(d.grad, [0.1]);
assert_eq!(d.hessian, [-0.02]);
assert_eq!(d.fwd, [0.0]);
assert_eq!(d.hessian_full, [[-0.02]]);

pub fn with_directional( grad: [f64; N], hessian: [f64; N], fwd: [f64; N], bwd: [f64; N], ) -> Self

Construct a derivative bundle from all four components, with zero off-diagonal Hessian.

pub fn with_full_hessian( grad: [f64; N], hessian_full: [[f64; N]; N], fwd: [f64; N], bwd: [f64; N], ) -> Self

Construct a derivative bundle with an explicit full symmetric Hessian.

hessian_full[i][j] must equal hessian_full[j][i]; the diagonal is taken from hessian_full[i][i] and the hessian diagonal is kept in sync.

Examples

use solver::models::control::StateDerivatives;
let d = StateDerivatives::<2>::with_full_hessian(
    [1.0, 2.0],
    [[0.5, 0.25], [0.25, -0.5]],
    [3.0, 4.0],
    [5.0, 6.0],
);
assert_eq!(d.hessian, [0.5, -0.5]);
assert_eq!(d.hessian_full[0][1], 0.25);
assert_eq!(d.hessian_full[1][0], 0.25);

Trait Implementations

impl<const N: usize> Clone for StateDerivatives<N>

fn clone(&self) -> StateDerivatives<N>

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<const N: usize> Copy for StateDerivatives<N>

impl<const N: usize> Debug for StateDerivatives<N>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.