Struct JacobianDeterminant 

pub struct JacobianDeterminant;

Jacobian determinant operations

Implementations

impl JacobianDeterminant

pub fn compute(functions: &[Expression], variables: &[Symbol]) -> Expression

Compute Jacobian determinant

Examples

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

let x = symbol!(x);
let y = symbol!(y);
let functions = vec![
    Expression::mul(vec![Expression::symbol(x.clone()), Expression::symbol(y.clone())]),
    Expression::add(vec![Expression::symbol(x.clone()), Expression::symbol(y.clone())])
];
let variables = vec![x, y];
let jac_det = JacobianDeterminant::compute(&functions, &variables);

pub fn absolute(functions: &[Expression], variables: &[Symbol]) -> Expression

Compute absolute value of Jacobian determinant (for coordinate transformations)

Examples

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

let r = symbol!(r);
let theta = symbol!(theta);
let functions = vec![
    Expression::mul(vec![
        Expression::symbol(r.clone()),
        Expression::function("cos", vec![Expression::symbol(theta.clone())])
    ]),
    Expression::mul(vec![
        Expression::symbol(r.clone()),
        Expression::function("sin", vec![Expression::symbol(theta.clone())])
    ])
];
let variables = vec![r, theta];
let abs_jac_det = JacobianDeterminant::absolute(&functions, &variables);

pub fn is_singular(functions: &[Expression], variables: &[Symbol]) -> bool

Check if Jacobian is singular (determinant = 0)

Examples

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

let x = symbol!(x);
let y = symbol!(y);
let functions = vec![
    Expression::symbol(x.clone()),
    Expression::symbol(x.clone())  // Linearly dependent
];
let variables = vec![x, y];
let is_singular = JacobianDeterminant::is_singular(&functions, &variables);

pub fn condition_estimate( functions: &[Expression], variables: &[Symbol], ) -> Expression

Compute condition number estimate (for numerical stability analysis)

Examples

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

let x = symbol!(x);
let y = symbol!(y);
let functions = vec![
    Expression::add(vec![Expression::symbol(x.clone()), Expression::symbol(y.clone())]),
    Expression::add(vec![
        Expression::symbol(x.clone()),
        Expression::mul(vec![
            Expression::mul(vec![
                Expression::integer(1),
                Expression::pow(Expression::integer(1000), Expression::integer(-1))
            ]),
            Expression::symbol(y.clone())
        ])
    ])
];
let variables = vec![x, y];
let condition = JacobianDeterminant::condition_estimate(&functions, &variables);