Struct PartialDerivatives 

pub struct PartialDerivatives;

Main partial derivatives interface

Implementations

impl PartialDerivatives

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

Compute mixed partial derivative ∂ⁿf/∂x₁∂x₂…∂xₙ

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::PartialDerivatives;

let x = symbol!(x);
let y = symbol!(y);
let expr = Expression::mul(vec![
    Expression::pow(Expression::symbol(x.clone()), Expression::integer(2)),
    Expression::pow(Expression::symbol(y.clone()), Expression::integer(3))
]);
let mixed = PartialDerivatives::mixed_partial(&expr, vec![x, y]);

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

Compute gradient vector - delegates to specialized module

Examples

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

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 grad = PartialDerivatives::gradient(&expr, vec![x, y]);

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

Compute Hessian matrix - delegates to specialized module

Examples

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

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

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

Compute directional derivative - delegates to specialized module

Examples

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

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 direction = vec![Expression::integer(1), Expression::integer(1)];
let dir_deriv = PartialDerivatives::directional_derivative(&expr, vec![x, y], direction);

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

Compute Jacobian matrix - delegates to specialized module

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

Compute Jacobian determinant - delegates to specialized module

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

Compute divergence - delegates to specialized module

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

Compute curl - delegates to specialized module

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

Compute Laplacian - delegates to specialized module

pub fn is_conservative( vector_field: &[Expression], variables: Vec<Symbol>, ) -> bool

Check if vector field is conservative - delegates to specialized module

pub fn find_potential( vector_field: &[Expression], variables: Vec<Symbol>, ) -> Option<Expression>

Find potential function - delegates to specialized module