Trait InterpolateArbitrary 

pub trait InterpolateArbitrary<F: Field>: Matrix<F> {
    // Provided methods
    fn interpolate_arbitrary_point<EF: ExtensionField<F>>(
        &self,
        x_coords: &[F],
        point: EF,
    ) -> Option<Vec<EF>> { ... }
    fn interpolate_arbitrary_with_precomputation<EF: ExtensionField<F>>(
        &self,
        weights: &[F],
        diff_invs: &[EF],
    ) -> Vec<EF> { ... }
    fn recover_coefficients(&self, x_coords: &[F]) -> Option<RowMajorMatrix<F>> { ... }
}

Lagrange interpolation over arbitrary evaluation domains.

General-domain counterpart of the structured-domain trait.

Blanket-implemented for every matrix over a field — just import and call.

Provided Methods

fn interpolate_arbitrary_point<EF: ExtensionField<F>>( &self, x_coords: &[F], point: EF, ) -> Option<Vec<EF>>

Evaluates every column polynomial at point via barycentric interpolation.

Each row holds evaluations at the corresponding domain point.

Performance

O(n^2) weight computation + O(n * width) evaluation.

Returns

• None if any domain points coincide.
• The matching row directly when the target equals a domain point.

fn interpolate_arbitrary_with_precomputation<EF: ExtensionField<F>>( &self, weights: &[F], diff_invs: &[EF], ) -> Vec<EF>

Evaluates every column polynomial at a target point with precomputed data.

Hot path: O(n * width) per call when weights are reused across targets.

Safety

• The evaluation point z must not equal any domain point x_i.
• weights[i] must be the barycentric weight for x_i, i.e. 1 / prod_{j != i} (x_i - x_j).
• diff_invs[i] must be 1 / (z - x_i).

Panics

Debug-panics if the slices differ in length from the matrix height.

fn recover_coefficients(&self, x_coords: &[F]) -> Option<RowMajorMatrix<F>>

Recovers coefficient vectors for every column via batched Newton interpolation.

Each row of self holds evaluations at the corresponding domain point. Returns an n * width matrix where row i holds degree-i coefficients.

Performance

• O(n^2 * width) field operations.
• O(n + width) auxiliary memory, zero allocations inside the main loop.

Returns

None if any domain points coincide.

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety".

Implementors

impl<F: Field, M: Matrix<F>> InterpolateArbitrary<F> for M