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utils.rs
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utils.rs
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use crate::structure::matrix::*;
use crate::structure::ad::*;
use crate::structure::ad::AD::*;
use crate::util::non_macro::{cat, zeros};
/// Jacobian Matrix
///
/// # Description
/// : Exact jacobian matrix using Automatic Differenitation
///
/// # Type
/// `(F, &Vec<f64>) -> Matrix where F: Fn(&Vec<AD>) -> Vec<AD>`
///
/// # Examples
/// ```
/// #[macro_use]
/// extern crate peroxide;
/// use peroxide::fuga::*;
///
/// fn main() {
/// let x = c!(1, 1);
/// let j = jacobian(f, &x);
/// j.print();
///
/// // c[0] c[1]
/// // r[0] 1 -1
/// // r[1] 1 2
/// }
///
/// fn f(xs: &Vec<AD>) -> Vec<AD> {
/// let x = xs[0];
/// let y = xs[1];
///
/// vec![
/// x - y,
/// x + 2.*y,
/// ]
/// }
/// ```
#[allow(non_snake_case)]
pub fn jacobian<F: Fn(&Vec<AD>) -> Vec<AD>>(f: F, x: &Vec<f64>) -> Matrix {
let l = x.len();
let mut x_ad: Vec<AD> = x.iter().map(|&x| AD1(x, 0f64)).collect();
let l2 = f(&x_ad).len();
let mut J = zeros(l2, l);
for i in 0 .. l {
x_ad[i][1] = 1f64;
let slopes: Vec<f64> = f(&x_ad).iter().map(|ad| ad.dx()).collect();
J.subs_col(i, &slopes);
x_ad[i][1] = 0f64;
}
J
}
///// Hessian Matrix
//#[allow(non_snake_case)]
//pub fn hessian<F: Fn(&Vec<AD>) -> AD>(f: F, x: &Vec<f64>) -> Matrix {
// let l = x.len();
// let mut x_ad: Vec<AD> = x.iter().map(|&x| AD2(x, 0f64, 0f64)).collect();
//
// let mut H = zeros(l, l);
//
// for i in 0 .. l {
// for j in 0 .. l {
// }
// }
//
// unimplemented!()
//}
//#[allow(non_snake_case)]
//pub fn jacobian_ad<F: Fn(&Vec<AD>) -> Vec<AD>>(f: F, x: &Vec<AD>) -> Vec<Vec<AD>> {
// let l = x.len();
// let mut x_ad: Vec<AD> = x.clone().into_iter().map(|mut t| {
// t.iter_mut().skip(1).for_each(|k| *k = 0f64);
// t
// }).collect();
// let l2 = f(&x_ad).len();
//
// let mut JT: Vec<Vec<AD>> = vec![vec![AD0(0f64); l2]; l];
//
// for i in 0 .. l {
// x_ad[i][1] = 1f64;
// let ads = f(&x_ad);
// JT[i] = ads;
// x_ad[i][1] = 0f64;
// }
// JT
//}
/// TriDiagonal Matrix Algorithm (TDMA)
///
/// # Description
///
/// Solve tri-diagonal matrix system efficiently (O(n))
/// ```bash
/// |b0 c0 | |x0| |y0|
/// |a1 b1 c1 | |x1| |y1|
/// | a2 b2 c2 | |x2| = |y2|
/// | ... | |..| |..|
/// | am bm| |xm| |ym|
/// ```
///
/// # Caution
///
/// You should apply boundary condition yourself
pub fn tdma(a_input: Vec<f64>, b_input: Vec<f64>, c_input: Vec<f64>, y_input: Vec<f64>) -> Matrix {
let n = b_input.len();
assert_eq!(a_input.len(), n - 1);
assert_eq!(c_input.len(), n - 1);
assert_eq!(y_input.len(), n);
let a = cat(0f64, &a_input);
let mut b = b_input.clone();
let c = {
let mut c_temp = c_input.clone();
c_temp.push(0f64);
c_temp.clone()
};
let mut y = y_input.clone();
// Forward substitution
let mut w = vec![0f64; n];
for i in 1..n {
w[i] = a[i] / b[i - 1];
b[i] = b[i] - w[i] * c[i - 1];
y[i] = y[i] - w[i] * y[i - 1];
}
// Backward substitution
let mut x = vec![0f64; n];
x[n - 1] = y[n - 1] / b[n - 1];
for i in (0..n - 1).rev() {
x[i] = (y[i] - c[i] * x[i + 1]) / b[i];
}
x.into()
}