1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129

use ndarray::{array, s, Array1, ArrayView, ArrayView1, ArrayViewMut1, Axis};
use num::{
    complex::{Complex64, ComplexFloat},
    Complex, Num, One, Zero,
};

use super::output_type::Zpk;

pub fn bilinear_zpk(mut input: Zpk, fs: f64) -> Zpk {
    println!("z size {} p size {}", input.z.len(), input.p.len());
    let degree = relative_degree(&input);
    let fs2 = fs * 2.0;

    println!("fs - {fs}");
    let z_prod = input.z.map(|a| fs2 - a).product();
    let p_prod = input.p.map(|a| fs2 - a).product();

    input.z.mapv_inplace(|a| (fs2 + a) / (fs2 - a));
    input.p.mapv_inplace(|a| (fs2 + a) / (fs2 - a));
    let zeros = vec![-Complex::one(); degree];
    input.z.append(Axis(0), ArrayView::from(&zeros));
    input.k *= (z_prod / p_prod).re;
    input
}

pub fn relative_degree(input: &Zpk) -> usize {
    input.p.len() - input.z.len()
}

/// Compute polynomial coefficients from zeroes
///
/// # Examples
///
/// ```rust
/// # use sciport_rs::signal::tools::poly;
/// # use num::complex::Complex64;
/// # use ndarray::array;
/// let complex_z = array![ Complex64::new(2.1, 3.2), Complex64::new(1.0, 1.0) ];
///
/// let coeffs = poly((&complex_z).into());
///
/// ```
pub fn poly<T: Num + Copy>(zeroes: ArrayView1<'_, T>) -> Array1<T> {
    let mut coeff = array![T::one()];
    for z in zeroes {
        let mut clone = coeff.clone();
        mul_by_x(&mut coeff);
        mul_by_scalar(clone.view_mut(), *z);
        sub_coeff(coeff.slice_mut(s![1..]), clone)
    }
    coeff
}

fn mul_by_x<T: Num + Clone>(coeff: &mut Array1<T>) {
    coeff.append(Axis(0), (&array![T::zero()]).into()).unwrap();
}

fn mul_by_scalar<T: Num + Copy>(mut coeff: ArrayViewMut1<T>, scalar: T) {
    coeff.map_inplace(move |a| *a = *a * scalar);
}

fn sub_coeff<T: Num + Copy>(mut coeff: ArrayViewMut1<T>, ar: Array1<T>) {
    for (i, c) in coeff.iter_mut().enumerate() {
        *c = *c - ar[i]
    }
}

pub fn polyval<T: Into<Complex<f64>> + Copy, const S: usize>(v: T, coeff: [T; S]) -> Complex<f64> {
    fn polyval<const S: usize>(v: Complex<f64>, coeff: [Complex<f64>; S]) -> Complex<f64> {
        coeff
            .iter()
            .enumerate()
            .fold(Complex64::zero(), |acc, (i, item)| {
                acc + v.powi(i as _) * item
            })
    }

    let tmp: [Complex<f64>; S] = coeff
        .into_iter()
        .map(|a| a.into())
        .collect::<Vec<_>>()
        .try_into()
        .unwrap();
    polyval(v.into(), tmp)
}

pub fn newton(
    f: impl Fn(Complex64) -> Complex64,
    fp: impl Fn(Complex64) -> Complex64,
    mut x0: Complex64,
    tol: f64,
    maxiter: usize,
) -> Complex64 {
    for _ in 0..maxiter {
        let fval = f(x0);

        if fval == 0.0.into() {}

        let fder = fp(x0);
        let newton_step = fval / fder;
        let x = x0 - newton_step;

        if is_close(x, x0, tol) {
            return x;
        }
        x0 = x;
    }

    panic!()
}

fn is_close(x: Complex64, y: Complex64, tol: f64) -> bool {
    let df = x - y;
    let a = df.abs();

    a < tol
}

#[cfg(test)]
mod tests {
    use num::complex::Complex64;

    use crate::special::kve;
    #[test]
    fn test_i() {
        let res = kve(1.0, Complex64::new(-29.5, -88.33333333));
        dbg!(res);
    }
}