Struct sparse_interp::ClassicalTraits

pub struct ClassicalTraits<C>(_);

PolyTraits implementation for classical (slow) algorithms.

The underlying algorithms are neither fast nor numerically stable. They should be used only for very small sizes, or for debugging.

• ClassicalTraits::slice_mul() uses a classical quadratic-time algorithm
• ClassicalTraits::mp_eval_slice() simply evaluates each point one at a time, using Horner’s rule. O(num_points * poly_degree) time.
• ClassicalTraits::sparse_interp_slice() uses unstructured linear algebra and classical root finding, with complexity O(sparsity^3).

Trait Implementations

impl<C: Clone> Clone for ClassicalTraits<C>

fn clone(&self) -> ClassicalTraits<C>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<C: Copy> Copy for ClassicalTraits<C>

impl<C: Debug> Debug for ClassicalTraits<C>

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

Formats the value using the given formatter.

impl<C: Default> Default for ClassicalTraits<C>

fn default() -> ClassicalTraits<C>

Returns the “default value” for a type.

impl<C: Eq> Eq for ClassicalTraits<C>

impl<C: PartialEq> PartialEq<ClassicalTraits<C>> for ClassicalTraits<C>

fn eq(&self, other: &ClassicalTraits<C>) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &ClassicalTraits<C>) -> bool

This method tests for !=.

impl<C> PolyTraits for ClassicalTraits<C> where
    C: Clone + Mul<Output = C> + AddAssign,
    DefConv<C, Complex64>: TwoWay<Source = C, Dest = Complex64>, 

type Coeff = C

The type of polynomial coefficients.

type SparseInterpEval = EvalTrait<Self, Complex64>

The evaluation needed for sparse interpolation.

type SparseInterpInfo = (usize, Vec<(usize, Complex64)>, RelativeParams<Complex64, f64>)

An opaque type returned by the pre-processing method Self::sparse_interp_prep().

fn slice_mul(out: &mut [Self::Coeff], lhs: &[Self::Coeff], rhs: &[Self::Coeff])

Multiplies two polynomails (represented by slices) and stores the result in another slice.

fn sparse_interp_prep(
    sparsity: usize,
    expons: impl Iterator<Item = usize>,
    _max_coeff: &Self::Coeff
) -> (<Self::SparseInterpEval as EvalTypes>::EvalInfo, Self::SparseInterpInfo)

Pre-processing for sparse interpolation.

fn sparse_interp_slice(
    evals: &[Complex64],
    info: &Self::SparseInterpInfo
) -> Result<Vec<(usize, Self::Coeff)>>

Sparse interpolation following evaluation.

fn mp_eval_prep<U>(
    pts: impl Iterator<Item = U>
) -> <EvalTrait<Self, U> as EvalTypes>::EvalInfo where
    EvalTrait<Self, U>: EvalTypes<Coeff = Self::Coeff, Eval = U>, 

Pre-processing for multi-point evaluation.

fn mp_eval_slice<U>(
    out: &mut impl Extend<U>,
    coeffs: &[Self::Coeff],
    info: &<EvalTrait<Self, U> as EvalTypes>::EvalInfo
) -> Result<()> where
    EvalTrait<Self, U>: EvalTypes<Coeff = Self::Coeff, Eval = U>, 

Multi-point evaluation.

impl<C> StructuralEq for ClassicalTraits<C>

impl<C> StructuralPartialEq for ClassicalTraits<C>