Struct HessianOperations 

pub struct HessianOperations;

Hessian matrix operations

Implementations

impl HessianOperations

pub fn compute(expr: &Expression, variables: &[Symbol]) -> Vec<Vec<Expression>>

Compute Hessian matrix

Examples

use mathhook_core::simplify::Simplify;
use mathhook_core::calculus::derivatives::Derivative;
use mathhook_core::{Expression};
use mathhook_core::symbol;
use mathhook_core::calculus::derivatives::HessianOperations;

let x = symbol!(x);
let y = symbol!(y);
let expr = Expression::add(vec![
    Expression::pow(Expression::symbol(x.clone()), Expression::integer(2)),
    Expression::pow(Expression::symbol(y.clone()), Expression::integer(2))
]);
let hessian = HessianOperations::compute(&expr, &[x, y]);

pub fn determinant(expr: &Expression, variables: Vec<Symbol>) -> Expression

Compute Hessian determinant

Examples

use mathhook_core::{Expression, Symbol};
use mathhook_core::symbol;
use mathhook_core::calculus::derivatives::HessianOperations;

let x = symbol!(x);
let y = symbol!(y);
let expr = Expression::add(vec![
    Expression::pow(Expression::symbol(x.clone()), Expression::integer(2)),
    Expression::pow(Expression::symbol(y.clone()), Expression::integer(2))
]);
let det = HessianOperations::determinant(&expr, vec![x, y]);

pub fn is_positive_definite(expr: &Expression, variables: Vec<Symbol>) -> bool

Check if Hessian is positive definite (for optimization)

Examples

use mathhook_core::{Expression};
use mathhook_core::symbol;
use mathhook_core::calculus::derivatives::HessianOperations;

let x = symbol!(x);
let y = symbol!(y);
let expr = Expression::add(vec![
    Expression::pow(Expression::symbol(x.clone()), Expression::integer(2)),
    Expression::pow(Expression::symbol(y.clone()), Expression::integer(2))
]);
let is_pos_def = HessianOperations::is_positive_definite(&expr, vec![x, y]);

pub fn trace(expr: &Expression, variables: Vec<Symbol>) -> Expression

Compute trace of Hessian matrix

Examples

use mathhook_core::{Expression, Symbol};
use mathhook_core::symbol;
use mathhook_core::calculus::derivatives::HessianOperations;

let x = symbol!(x);
let y = symbol!(y);
let expr = Expression::add(vec![
    Expression::mul(vec![Expression::integer(3), Expression::pow(Expression::symbol(x.clone()), Expression::integer(2))]),
    Expression::mul(vec![Expression::integer(5), Expression::pow(Expression::symbol(y.clone()), Expression::integer(2))])
]);
let trace = HessianOperations::trace(&expr, vec![x, y]);