Function integrate 

pub fn integrate<T, F>(
    f: &F,
    a: &[f64],
    b: &[f64],
    gk_order: usize,
    tci_options: TCI2Options,
) -> Result<T>
where
    T: Scalar + TTScalar + Default + MatrixLuciScalar,
    DenseFaerLuKernel: PivotKernel<T>,
    LazyBlockRookKernel: PivotKernel<T>,
    F: Fn(&[f64]) -> T,

Integrate a function over a hypercube [a, b] using TCI and Gauss-Kronrod quadrature.

The integrand is sampled at Gauss-Kronrod nodes in each dimension, and a tensor-train approximation is built via crossinterpolate2. The integral is then computed as a weighted sum of the tensor train.

Arguments

• f – function to integrate, takes a coordinate slice &[f64]
• a – lower bounds for each dimension
• b – upper bounds for each dimension
• gk_order – Gauss-Kronrod quadrature order (15 or 31)
• tci_options – options for the TCI approximation

Returns

The approximate integral value.

Errors

Returns an error if a and b have different lengths, or if gk_order is not 15 or 31.

Examples

use tensor4all_tensorci::integration::integrate;
use tensor4all_tensorci::TCI2Options;

// Integrate (x^2 + y^2) over [0,1]^2 = 2/3
let f = |x: &[f64]| x.iter().map(|&xi| xi * xi).sum::<f64>();
let a = vec![0.0, 0.0];
let b = vec![1.0, 1.0];
let options = TCI2Options { tolerance: 1e-10, ..TCI2Options::default() };

let result: f64 = integrate(&f, &a, &b, 15, options).unwrap();
assert!((result - 2.0 / 3.0).abs() < 1e-8);