Expand description
Spline interpolations
Available splines
- Cubic spline
- Cubic Hermite spline
Spline trait
Methods
Let T: Into<f64> + Copy
fn eval<T>(&self, x: T) -> f64: Evaluate the spline at xfn eval_vec<T>(&self, v: &[T]) -> Vec<f64>: Evaluate spline values for an array vfn polynomial_at<T>(&self, x: T) -> &Polynomial: Get the polynomial at xfn number_of_polynomials(&self) -> usize: Get the number of polynomialsfn get_ranged_polynomials(&self) -> &Vec<(Range<f64>, Polynomial)>: Get the polynomialsfn eval_with_cond<F>(&self, x: f64, cond: F) -> f64: Evaluate the spline at x, with a conditionfn eval_vec_with_cond<F>(&self, v: &[f64], cond: F) -> Vec<f64>: Evaluate spline values for an array v, with a condition
Low-level interface
Members
CubicSpline: Structure for cubic splinefn from_nodes(node_x: &[f64], node_y: &[f64]) -> Self: Create a cubic spline from nodesfn extend_with_nodes(&mut self, node_x: Vec<f64>, node_y: Vec<f64>): Extend the spline with nodes
CubicHermiteSpline: Structure for cubic Hermite splinefn from_nodes_with_slopes(node_x: &[f64], node_y: &[f64], m: &[f64]) -> Self: Create a Cubic Hermite spline from nodes with slopesfn from_nodes(node_x: &[f64], node_y: &[f64], slope_method: SlopeMethod) -> Self: Create a Cubic Hermite spline from nodes with slope estimation methods
SlopeMethod: Enum for slope estimation methodsAkima: Akima’s method to estimate slopes (Akima (1970))Quadratic: Using quadratic interpolation to estimate slopes
Usage
use peroxide::fuga::*;
fn main() {
let x = seq(0, 10, 1);
let y = x.fmap(|t| t.sin());
let cs = CubicSpline::from_nodes(&x, &y);
let cs_akima = CubicHermiteSpline::from_nodes(&x, &y, SlopeMethod::Akima);
let cs_quad = CubicHermiteSpline::from_nodes(&x, &y, SlopeMethod::Quadratic);
cs.polynomial_at(0f64).print();
cs_akima.polynomial_at(0f64).print();
cs_quad.polynomial_at(0f64).print();
// -0.1523x^3 + 0.9937x
// 0.1259x^3 - 0.5127x^2 + 1.2283x
// -0.0000x^3 - 0.3868x^2 + 1.2283x
let new_x = seq(4, 6, 0.1);
let new_y = new_x.fmap(|t| t.sin());
let y_cs = cs.eval_vec(&new_x);
let y_akima = cs_akima.eval_vec(&new_x);
let y_quad = cs_quad.eval_vec(&new_x);
let mut df = DataFrame::new(vec![]);
df.push("x", Series::new(new_x));
df.push("y", Series::new(new_y));
df.push("y_cs", Series::new(y_cs));
df.push("y_akima", Series::new(y_akima));
df.push("y_quad", Series::new(y_quad));
df.print();
// x y y_cs y_akima y_quad
// r[0] 5 -0.9589 -0.9589 -0.9589 -0.9589
// r[1] 5.2 -0.8835 -0.8826 -0.8583 -0.8836
// r[2] 5.4 -0.7728 -0.7706 -0.7360 -0.7629
// r[3] 5.6 -0.6313 -0.6288 -0.5960 -0.6120
// r[4] 5.8 -0.4646 -0.4631 -0.4424 -0.4459
// r[5] 6 -0.2794 -0.2794 -0.2794 -0.2794
}High-level interface
Functions
fn cubic_spline(node_x: &[f64], node_y: &[f64]) -> CubicSpline: Create a cubic spline from nodesfn cubic_hermite_spline(node_x: &[f64], node_y: &[f64], m: &[f64]) -> CubicHermiteSpline: Create a cubic Hermite spline from nodes with slopes
Usage
use peroxide::fuga::*;
fn main() {
let x = seq(0, 10, 1);
let y = x.fmap(|t| t.sin());
let cs = cubic_spline(&x, &y);
let cs_akima = cubic_hermite_spline(&x, &y, SlopeMethod::Akima);
let cs_quad = cubic_hermite_spline(&x, &y, SlopeMethod::Quadratic);
cs.polynomial_at(0f64).print();
cs_akima.polynomial_at(0f64).print();
cs_quad.polynomial_at(0f64).print();
// -0.1523x^3 + 0.9937x
// 0.1259x^3 - 0.5127x^2 + 1.2283x
// -0.0000x^3 - 0.3868x^2 + 1.2283x
let new_x = seq(4, 6, 0.1);
let new_y = new_x.fmap(|t| t.sin());
let y_cs = cs.eval_vec(&new_x);
let y_akima = cs_akima.eval_vec(&new_x);
let y_quad = cs_quad.eval_vec(&new_x);
let mut df = DataFrame::new(vec![]);
df.push("x", Series::new(new_x));
df.push("y", Series::new(new_y));
df.push("y_cs", Series::new(y_cs));
df.push("y_akima", Series::new(y_akima));
df.push("y_quad", Series::new(y_quad));
df.print();
// x y y_cs y_akima y_quad
// r[0] 5 -0.9589 -0.9589 -0.9589 -0.9589
// r[1] 5.2 -0.8835 -0.8826 -0.8583 -0.8836
// r[2] 5.4 -0.7728 -0.7706 -0.7360 -0.7629
// r[3] 5.6 -0.6313 -0.6288 -0.5960 -0.6120
// r[4] 5.8 -0.4646 -0.4631 -0.4424 -0.4459
// r[5] 6 -0.2794 -0.2794 -0.2794 -0.2794
}Calculus with splines
Usage
use peroxide::fuga::*;
use std::f64::consts::PI;
fn main() {
let x = seq(0, 10, 1);
let y = x.fmap(|t| t.sin());
let cs = cubic_spline(&x, &y);
let cs_akima = cubic_hermite_spline(&x, &y, SlopeMethod::Akima);
let cs_quad = cubic_hermite_spline(&x, &y, SlopeMethod::Quadratic);
println!("============ Polynomial at x=0 ============");
cs.polynomial_at(0f64).print();
cs_akima.polynomial_at(0f64).print();
cs_quad.polynomial_at(0f64).print();
println!("============ Derivative at x=0 ============");
cs.derivative().polynomial_at(0f64).print();
cs_akima.derivative().polynomial_at(0f64).print();
cs_quad.derivative().polynomial_at(0f64).print();
println!("============ Integral at x=0 ============");
cs.integral().polynomial_at(0f64).print();
cs_akima.integral().polynomial_at(0f64).print();
cs_quad.integral().polynomial_at(0f64).print();
println!("============ Integrate from x=0 to x=pi ============");
cs.integrate((0f64, PI)).print();
cs_akima.integrate((0f64, PI)).print();
cs_quad.integrate((0f64, PI)).print();
// ============ Polynomial at x=0 ============
// -0.1523x^3 + 0.9937x
// 0.1259x^3 - 0.5127x^2 + 1.2283x
// -0.0000x^3 - 0.3868x^2 + 1.2283x
// ============ Derivative at x=0 ============
// -0.4568x^2 + 0.9937
// 0.3776x^2 - 1.0254x + 1.2283
// -0.0000x^2 - 0.7736x + 1.2283
// ============ Integral at x=0 ============
// -0.0381x^4 + 0.4969x^2
// 0.0315x^4 - 0.1709x^3 + 0.6141x^2
// -0.0000x^4 - 0.1289x^3 + 0.6141x^2
// ============ Integrate from x=0 to x=pi ============
// 1.9961861265456702
// 2.0049920614062775
// 2.004327391790717
}References
- Gary D. Knott, Interpolating Splines, Birkhäuser Boston, MA, (2000).
Structs
Cubic Spline (Natural)
Enums
Traits
Trait for spline interpolation
Functions
Cubic Spline (Natural)