polycal

Trait PolynomialSeries

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pub trait PolynomialSeries<E: PartialOrd + Scalar<Real = E>>: Clone + Sized {
    // Required methods
    fn roots(&self) -> Result<Vec<E>, ChebyshevError>;
    fn evaluate(&self, t: E) -> E;
    fn first_derivative(&self) -> Self;
    fn degree(&self) -> usize;
    fn domain(&self) -> Range<E>;
    fn null(domain: Range<E>) -> Self;

    // Provided methods
    fn derivative(&self, count: usize) -> Self { ... }
    fn roots_in_window(&self, window: Range<E>) -> Result<bool, ChebyshevError> { ... }
    fn evaluate_unscaled(&self, x: E) -> E { ... }
    fn number_of_coefficients(&self) -> usize { ... }
    fn is_monotonic(&self) -> Result<bool, ChebyshevError> { ... }
}
Expand description

All the necessary methods for a polynomial series

Required Methods§

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fn roots(&self) -> Result<Vec<E>, ChebyshevError>

Finds all roots of the polynomial

§Errors
  • If there is an error building the companion matrix
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fn evaluate(&self, t: E) -> E

Evaluate the polynomial using an input value t which is scaled to the domain of the polynomial.

Polynomials are scaled to the domain [-1, +1]. The true unscaled limits [a, b] are stored on creation based on the input calibration data. This function evaluates the polynomial assuming the input value t has already been rescaled from [a, b] to [-1,1]

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fn first_derivative(&self) -> Self

Take a single order derivative of the polynomial series

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fn degree(&self) -> usize

Returns the degree of the polynomial

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fn domain(&self) -> Range<E>

The domain is the physical range of independent values used to create the polynomial.

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fn null(domain: Range<E>) -> Self

Returns the null polynomial, which is the zero-polynomial defined on the same range and window as the original

Provided Methods§

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fn derivative(&self, count: usize) -> Self

Calculate the count order derivative of the polynomial

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fn roots_in_window(&self, window: Range<E>) -> Result<bool, ChebyshevError>

Finds all roots of the polynomial which lie in window

§Errors
  • If there is an error building the companion matrix
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fn evaluate_unscaled(&self, x: E) -> E

Evaluate the polynomial using the true input value x

Polynomials are scaled to the domain [-1, +1]. The true unscaled limits [a, b] are stored on creation based on the input calibration data. This function evaluates the polynomial assuming the input value x is in [a, b], rescaling it to [-1, +1] before calling the internal evaluation method

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fn number_of_coefficients(&self) -> usize

The number of independent coefficients of the polynomial, which is the degree of the polynomial plus one for the scalar offset

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fn is_monotonic(&self) -> Result<bool, ChebyshevError>

Returns true if the polynomial is monotonic

The monotonicity of the polynomial can be checked by analysis of the first derivative. If the first derivative has no roots in the domain of the polynomial, then the polynomial is monotonic, and if not it is.

§Errors
  • If there is an error calculating the roots of the polynomial, or building the companion matrix

Dyn Compatibility§

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementors§