Struct VectorField 

pub struct VectorField<const P: usize, const Q: usize, const R: usize> { /* private fields */ }

A vector field F: ℝⁿ → Cl(p,q,r)_1 (grade-1 multivectors)

Represents a function that maps points in n-dimensional space to vectors (grade-1 multivectors).

Examples

use amari_calculus::{VectorField, vector_from_slice};

// Define F(x, y, z) = (x, y, z) - radial vector field
let f = VectorField::<3, 0, 0>::new(|coords| {
    vector_from_slice(&[coords[0], coords[1], coords[2]])
});

// Evaluate at (1, 2, 3)
let value = f.evaluate(&[1.0, 2.0, 3.0]);

Implementations

impl<const P: usize, const Q: usize, const R: usize> VectorField<P, Q, R>

pub fn new(function: fn(&[f64]) -> Multivector<P, Q, R>) -> Self

Create a new vector field from a function

Arguments

• function - Function mapping coordinates to vectors

Examples

use amari_calculus::{VectorField, vector_from_slice};

// Rotation field F(x, y) = (-y, x, 0)
let f = VectorField::<3, 0, 0>::new(|coords| {
    vector_from_slice(&[-coords[1], coords[0], 0.0])
});

pub fn with_dimension( function: fn(&[f64]) -> Multivector<P, Q, R>, dim: usize, ) -> Self

Create a vector field with explicit dimension

pub fn evaluate(&self, coords: &[f64]) -> Multivector<P, Q, R>

Evaluate the vector field at a point

Arguments

• coords - Coordinates of the point

Returns

The vector value at the point

pub fn dimension(&self) -> usize

Get the domain dimension

pub fn partial_derivative( &self, coords: &[f64], axis: usize, h: f64, ) -> CalculusResult<Multivector<P, Q, R>>

Compute numerical derivative of vector field component along coordinate axis

Arguments

• coords - Point at which to compute derivative
• axis - Coordinate axis index
• h - Step size (default: 1e-5)

Trait Implementations

impl<const P: usize, const Q: usize, const R: usize> Clone for VectorField<P, Q, R>

fn clone(&self) -> VectorField<P, Q, R>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<const P: usize, const Q: usize, const R: usize> Debug for VectorField<P, Q, R>

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

Formats the value using the given formatter.