Struct ManifoldIntegrator 

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

Integrator for scalar and multivector fields on manifolds

Uses adaptive quadrature and measure-theoretic methods for accurate integration.

Implementations

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

pub fn new() -> Self

Create new manifold integrator

Examples

use amari_calculus::ManifoldIntegrator;

let integrator = ManifoldIntegrator::<3, 0, 0>::new();

pub fn with_tolerance(self, tolerance: f64) -> Self

Set tolerance for adaptive integration

pub fn integrate_scalar_1d( &self, f: &ScalarField<P, Q, R>, a: f64, b: f64, n: usize, ) -> f64

Integrate scalar field over 1D interval [a, b]

Uses adaptive Simpson’s rule for accurate integration.

Arguments

• f - Scalar field to integrate
• a - Lower bound
• b - Upper bound
• n - Number of subdivisions (must be even)

Returns

Approximation of ∫_a^b f(x) dx

Examples

use amari_calculus::{ScalarField, ManifoldIntegrator};

// f(x) = x²
let f = ScalarField::<3, 0, 0>::with_dimension(
    |coords| coords[0].powi(2),
    1
);

let integrator = ManifoldIntegrator::<3, 0, 0>::new();

// ∫_0^1 x² dx = 1/3
let result = integrator.integrate_scalar_1d(&f, 0.0, 1.0, 100);
assert!((result - 1.0/3.0).abs() < 1e-4);

pub fn integrate_scalar_2d( &self, f: &ScalarField<P, Q, R>, x_range: (f64, f64), y_range: (f64, f64), n: usize, ) -> f64

Integrate scalar field over 2D rectangular domain [x_min, x_max] × [y_min, y_max]

Arguments

• f - Scalar field to integrate
• x_range - (x_min, x_max) bounds
• y_range - (y_min, y_max) bounds
• n - Number of subdivisions per dimension

Returns

Approximation of ∫∫_R f(x,y) dx dy

Examples

use amari_calculus::{ScalarField, ManifoldIntegrator};

// f(x, y) = x*y
let f = ScalarField::<3, 0, 0>::with_dimension(
    |coords| coords[0] * coords[1],
    2
);

let integrator = ManifoldIntegrator::<3, 0, 0>::new();

// ∫_0^1 ∫_0^1 x*y dx dy = 1/4
let result = integrator.integrate_scalar_2d(&f, (0.0, 1.0), (0.0, 1.0), 50);
assert!((result - 0.25).abs() < 1e-4);

pub fn integrate_scalar_3d( &self, f: &ScalarField<P, Q, R>, x_range: (f64, f64), y_range: (f64, f64), z_range: (f64, f64), n: usize, ) -> f64

Integrate scalar field over 3D rectangular domain

Arguments

• f - Scalar field to integrate
• x_range - (x_min, x_max) bounds
• y_range - (y_min, y_max) bounds
• z_range - (z_min, z_max) bounds
• n - Number of subdivisions per dimension

Returns

Approximation of ∫∫∫_V f(x,y,z) dx dy dz

pub fn verify_fundamental_theorem_2d( &self, f: &VectorField<P, Q, R>, x_range: (f64, f64), y_range: (f64, f64), n: usize, ) -> (f64, f64)

Verify the fundamental theorem of geometric calculus: ∫V (∇F) dV = ∮∂V F dS

For a 2D rectangular domain, this reduces to checking: ∫∫R div(F) dx dy = ∮∂R F·n ds

where n is the outward normal to the boundary.

Trait Implementations

impl<const P: usize, const Q: usize, const R: usize> Default for ManifoldIntegrator<P, Q, R>

fn default() -> Self

Returns the “default value” for a type.