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//! Vector algebra
use std::ops::{Add, Div, Index, Mul, Sub};
use num::Zero;
#[derive(Debug, Copy, Clone, PartialEq)]
pub struct Vector<const N: usize> {
pub coeff: [f64; N],
}
impl<const N: usize> Vector<N> {
pub fn dim(self) -> usize {
N
}
pub fn new(coeff: &[f64]) -> Self {
assert_eq!(
coeff.len(),
N,
"length of input does not match dimensions of vector"
);
let mut arr = [0.0; N];
arr.copy_from_slice(coeff);
Vector { coeff: arr }
}
/// Return the vector length
///
/// # Example
/// ```
/// use scialg::vector::Vector;
///
/// let v: Vector<3> = Vector::new(&[1.0, -1.0, 1.0]);
///
/// assert_eq!(v.length(), 3.0_f64.sqrt());
/// ```
pub fn length(self) -> f64 {
self.coeff.iter().map(|x| x * x).sum::<f64>().sqrt()
}
/// Return a normalized vector from self
///
/// # Example
/// ```
/// use scialg::vector::Vector;
///
/// let mut v: Vector<3> = Vector::new(&[3.0, -1.0, 2.0]);
/// v = v.normalize();
///
/// assert_eq!(v.length(), 1.0);
/// ```
pub fn normalize(self) -> Self {
self / self.length()
}
/// Return scalar product between *self* and *rhs*
pub fn scalar_product(self, rhs: &Self) -> f64 {
let mut sum = 0.0;
for i in 0..N {
sum += self.coeff[i] * rhs.coeff[i];
}
sum
}
/// Return angle between *self* and *rhs* in radians
///
/// # Example
/// ```
/// use scialg::vector::Vector;
///
/// let pi_half = std::f64::consts::FRAC_PI_2;
/// let x: Vector<3> = Vector::new(&[1.0, 0.0, 0.0]);
/// let y: Vector<3> = Vector::new(&[0.0, 1.0, 0.0]);
/// let angle = x.angle(&y);
///
/// assert_eq!(angle, pi_half);
/// ```
pub fn angle(self, other: &Self) -> f64 {
let v1 = self.normalize();
let v2 = other.normalize();
v1.scalar_product(&v2).acos()
}
/// Return a new vector rotated around *axis* by angle *theta* (in radians)
///
/// # Example
/// ```
/// use scialg::vector::Vector;
///
/// let x: Vector<3> = Vector::new(&[1.0, 0.0, 0.0]);
/// let z: Vector<3> = Vector::new(&[0.0, 0.0, 1.0]);
/// let theta = 0.5 * std::f64::consts::PI;
///
/// // let r = x.rotate(z, theta);
///
/// // assert!((r - Vector::new(&[0.0, 1.0, 0.0])).length() < 1e-5);
/// ```
pub fn rotate(self, _axis: Vector<N>, _theta: f64) -> Self {
assert_eq!(N, 3);
todo!()
// let u = axis.normalize();
// let t_cos = theta.cos();
// let t_sin = theta.sin();
// Vector<N> {
// x: (t_cos + u.x.powi(2) * (1.0 - t_cos)) * self.x
// + (u.x * u.y * (1.0 - t_cos) - u.z * t_sin) * self.y
// + (u.x * u.z * (1.0 - t_cos) + u.y * t_sin) * self.z,
// y: (u.y * u.x * (1.0 - t_cos) + u.z * t_sin) * self.x
// + (t_cos + u.y.powi(2) * (1.0 - t_cos)) * self.y
// + (u.y * u.z * (1.0 - t_cos) - u.x * t_sin) * self.z,
// z: (u.z * u.x * (1.0 - t_cos) - u.y * t_sin) * self.x
// + (u.z * u.y * (1.0 - t_cos) + u.x * t_sin) * self.y
// + (t_cos + u.z.powi(2) * (1.0 - t_cos)) * self.z,
// }
}
/// Return cross product between *self* and *other*
pub fn cross_product(self, _other: &Self) -> Self {
assert_eq!(N, 3);
todo!()
// Vector<N> {
// x: self.y * other.z - self.z * other.y,
// y: self.z * other.x - self.x * other.z,
// z: self.x * other.y - self.y * other.x,
// }
}
}
impl<const N: usize> Zero for Vector<N> {
fn zero() -> Self {
Vector { coeff: [0.0; N] }
}
fn is_zero(&self) -> bool {
self.coeff.iter().all(|x| *x == 0.0)
}
}
impl<const N: usize> Add for Vector<N> {
type Output = Self;
fn add(self, rhs: Self) -> Self::Output {
let mut cs = [0.0; N];
for i in 0..N {
cs[i] = self.coeff[i] + rhs.coeff[i];
}
Vector { coeff: cs }
}
}
impl<const N: usize> Sub for Vector<N> {
type Output = Self;
fn sub(self, rhs: Self) -> Self::Output {
let mut cs = [0.0; N];
for i in 0..N {
cs[i] = self.coeff[i] - rhs.coeff[i];
}
Vector { coeff: cs }
}
}
impl<const N: usize> Mul<f64> for Vector<N> {
type Output = Self;
fn mul(self, rhs: f64) -> Self::Output {
let mut cs = [0.0; N];
for i in 0..N {
cs[i] = self.coeff[i] * rhs;
}
Vector { coeff: cs }
}
}
impl<const N: usize> Div<f64> for Vector<N> {
type Output = Self;
fn div(self, rhs: f64) -> Self::Output {
let mut cs = [0.0; N];
for i in 0..N {
cs[i] = self.coeff[i] / rhs;
}
Vector { coeff: cs }
}
}
impl<const N: usize> Index<usize> for Vector<N> {
type Output = f64;
fn index(&self, index: usize) -> &Self::Output {
&self.coeff[index]
}
}