Module weighted 

Weighted least squares optimization

This module provides weighted least squares methods where each residual can have a different weight, allowing for handling heteroscedastic data (data with varying variance).

Example

use scirs2_core::ndarray::{array, Array1, Array2};
use scirs2_optimize::least_squares::weighted::{weighted_least_squares, WeightedOptions};

// Define a function that returns the residuals
fn residual(x: &[f64], data: &[f64]) -> Array1<f64> {
    let n = data.len() / 2;
    let t_values = &data[0..n];
    let y_values = &data[n..];
     
    let mut res = Array1::zeros(n);
    for i in 0..n {
        res[i] = y_values[i] - (x[0] + x[1] * t_values[i]);
    }
    res
}

// Define the Jacobian
fn jacobian(x: &[f64], data: &[f64]) -> Array2<f64> {
    let n = data.len() / 2;
    let t_values = &data[0..n];
     
    let mut jac = Array2::zeros((n, 2));
    for i in 0..n {
        jac[[i, 0]] = -1.0;
        jac[[i, 1]] = -t_values[i];
    }
    jac
}

// Create data
let data = array![0.0, 1.0, 2.0, 3.0, 4.0, 0.1, 0.9, 2.1, 2.9, 4.1];

// Define weights (higher weight = more importance)
let weights = array![1.0, 1.0, 1.0, 10.0, 10.0]; // Last two points have more weight

// Initial guess
let x0 = array![0.0, 0.0];

// Solve using weighted least squares
let result = weighted_least_squares(
    residual,
    &x0,
    &weights,
    Some(jacobian),
    &data,
    None
)?;

assert!(result.success);

Structs

WeightedOptions

Options for weighted least squares optimization

Functions

weighted_least_squares

Solve a weighted least squares problem