Struct ScalarField 

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

A scalar field f: ℝⁿ → ℝ

Represents a function that maps points in n-dimensional space to scalar values.

Examples

use amari_calculus::ScalarField;

// Define f(x, y) = x² + y²
let f = ScalarField::<3, 0, 0>::new(|coords| {
    coords[0].powi(2) + coords[1].powi(2)
});

// Evaluate at (3, 4)
let value = f.evaluate(&[3.0, 4.0, 0.0]);
assert!((value - 25.0).abs() < 1e-10);

Implementations

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

pub fn new(function: fn(&[f64]) -> f64) -> Self

Create a new scalar field from a function

Arguments

• function - Function mapping coordinates to scalar values

Examples

use amari_calculus::ScalarField;

// Quadratic function f(x, y) = x² + y²
let f = ScalarField::<3, 0, 0>::new(|coords| {
    coords[0].powi(2) + coords[1].powi(2)
});

pub fn with_dimension(function: fn(&[f64]) -> f64, dim: usize) -> Self

Create a scalar field with explicit dimension

Useful when the field dimension doesn’t match the algebra dimension.

pub fn evaluate(&self, coords: &[f64]) -> f64

Evaluate the scalar field at a point

Arguments

• coords - Coordinates of the point

Returns

The scalar value at the point

Errors

Returns error if coordinate dimension doesn’t match field dimension

pub fn dimension(&self) -> usize

Get the domain dimension

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

Compute numerical derivative along coordinate axis

Uses centered difference: f’(x) ≈ (f(x+h) - f(x-h)) / (2h)

Arguments

• coords - Point at which to compute derivative
• axis - Coordinate axis index (0 = x, 1 = y, etc.)
• h - Step size (default: 1e-5)

Trait Implementations

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

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

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

Formats the value using the given formatter.