Struct PiecewiseLegendrePoly 

pub struct PiecewiseLegendrePoly { /* private fields */ }

A single piecewise Legendre polynomial

Implementations

impl PiecewiseLegendrePoly

pub fn new( data: Mat<f64>, knots: Vec<f64>, l: i32, delta_x: Option<Vec<f64>>, symm: i32, ) -> Result<PiecewiseLegendrePoly, Error>

Create a new PiecewiseLegendrePoly from data and knots

data holds the Legendre coefficients, one column per segment; the nsegments + 1 knots bound the segments. delta_x (the segment widths) is computed from the knots when None. symm is the parity of the polynomial: 1 (even), -1 (odd) or 0 (no definite parity).

Errors

• Error::EmptyInput if data has no row or no column
• Error::InvalidParameter if knots does not have one entry more than data has columns, a knot is not finite, or a segment length knots[i] - knots[i - 1] is not a positive normal double (this includes decreasing knots, NaN, lengths that overflow and subnormal lengths); or if delta_x does not have one entry per segment or differs from the knot spacing e by more than max(1e-10 * |e|, 8 * f64::EPSILON * max(|knots[i]|, |knots[i + 1]|))
• Error::InvalidParameter if symm is not -1, 0 or 1

pub fn symm(&self) -> i32

Get the symmetry parameter

pub fn rescale_domain( &self, new_knots: Vec<f64>, new_delta_x: Option<Vec<f64>>, new_symm: Option<i32>, ) -> Result<PiecewiseLegendrePoly, Error>

Rescale domain: create a new polynomial with the same data but different knots

This is useful for transforming from one domain to another, e.g., from x ∈ [-1, 1] to τ ∈ [0, β].

Arguments

• new_knots - New knot points
• new_delta_x - Optional new segment widths (computed from knots if None)
• new_symm - Optional new symmetry parameter (keeps old if None)

Returns

New polynomial with rescaled domain

Errors

The errors of new for the new knots and widths

pub fn scale_data(&self, factor: f64) -> PiecewiseLegendrePoly

Scale all data values by a constant factor

This is useful for normalizations, e.g., multiplying by √β for Fourier transform preparations.

Arguments

• factor - Scaling factor to multiply all data by

Returns

New polynomial with scaled data

pub fn evaluate(&self, x: f64) -> f64

Evaluate the polynomial at a given point

Panics

Panics if x is outside [xmin, xmax] or NaN; see Self::try_evaluate.

pub fn try_evaluate(&self, x: f64) -> Result<f64, Error>

Self::evaluate returning an error instead of panicking

Errors

Error::OutOfDomain if x is outside [xmin, xmax] or NaN

pub fn evaluate_many(&self, xs: &[f64]) -> Vec<f64>

Evaluate the polynomial at multiple points

Panics

Panics if a point is outside [xmin, xmax] or NaN; see Self::try_evaluate_many.

pub fn try_evaluate_many(&self, xs: &[f64]) -> Result<Vec<f64>, Error>

Self::evaluate_many returning an error instead of panicking

Errors

Error::OutOfDomain for the first point of xs that is outside [xmin, xmax] or NaN; no point is evaluated then

pub fn split(&self, x: f64) -> (usize, f64)

Split x into segment index and normalized x

Panics

Panics if x is outside [xmin, xmax] or NaN; see Self::try_split.

pub fn try_split(&self, x: f64) -> Result<(usize, f64), Error>

Self::split returning an error instead of panicking

Errors

Error::OutOfDomain if x is outside [xmin, xmax] or NaN

pub fn evaluate_legendre_polynomial(&self, x: f64, coeffs: &[f64]) -> f64

Evaluate Legendre polynomial using recurrence relation

pub fn deriv(&self, n: usize) -> PiecewiseLegendrePoly

Compute derivative of the polynomial

The result has polyorder equal to the number of its coefficient rows (at least 1).

pub fn derivs(&self, x: f64) -> Vec<f64>

Compute derivatives at a point x

Returns the values of the derivatives of order 0 to polyorder - 1.

Panics

Panics if x is outside [xmin, xmax] or NaN; see Self::try_derivs.

pub fn try_derivs(&self, x: f64) -> Result<Vec<f64>, Error>

Self::derivs returning an error instead of panicking

Errors

Error::OutOfDomain if x is outside [xmin, xmax] or NaN

pub fn overlap<F>(&self, f: F) -> f64

where F: Fn(f64) -> f64,

Compute overlap integral with a function

pub fn roots(&self) -> Vec<f64>

Find roots of the polynomial using C++ compatible algorithm

pub fn get_xmin(&self) -> f64

pub fn get_xmax(&self) -> f64

pub fn get_l(&self) -> i32

pub fn get_domain(&self) -> (f64, f64)

pub fn get_knots(&self) -> &[f64]

pub fn get_delta_x(&self) -> &[f64]

pub fn get_symm(&self) -> i32

pub fn get_data(&self) -> &Mat<f64>

pub fn get_norms(&self) -> &[f64]

pub fn get_polyorder(&self) -> usize

Trait Implementations

impl Clone for PiecewiseLegendrePoly

fn clone(&self) -> PiecewiseLegendrePoly

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for PiecewiseLegendrePoly

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

Formats the value using the given formatter.