arima 0.3.0

use core::ops::{Neg, Sub};
use num::{Float, Num};
use std::ops::{Add, AddAssign};

/// Returns a n-tau vector containing the time series lagged by tau.
///
/// # Arguments
///
/// * `&x` - Reference to input vector slice of length n.
/// * `tau` - Lag.
///
/// # Returns
///
/// * Output vector of length n-tau.
///
/// # Example
///
/// ```
/// use arima::util;
/// let x = [-4, -9, 20, 23, -18, 6];
/// assert_eq!(util::lag(&x, 2), &[20, 23, -18, 6]);
/// ```
pub fn lag<T: Num + Copy>(x: &[T], tau: u32) -> Vec<T> {
    let mut y: Vec<T> = Vec::new();
    assert!(tau < x.len() as u32);
    for a in x.iter().skip(tau as usize) {
        y.push(*a);
    }
    y
}

/// Returns a n-1 vector containing the pairwise difference x_t - x_t-1.
///
/// # Arguments
///
/// * `&x` - Reference to input vector slice of length n.
/// * `d` - Number of differences to be taken.
///
/// # Returns
///
/// * Output vector of length n-1.
///
/// # Example
///
/// ```
/// use arima::util;
/// let x = [1, 2, 3];
/// assert_eq!(util::diff(&x, 1), &[1, 1])
/// ```
pub fn diff<T: Num + Copy + Neg<Output = T> + Sub>(x: &[T], d: usize) -> Vec<T> {
    let mut y: Vec<T> = x.to_vec();
    let len = y.len();
    for s in 0..d {
        for i in 1..len - s {
            // we iterate backwards through the vector to avoid cloning
            y[len - i] = y[len - i] - y[len - i - 1];
        }
    }
    y.drain(0..d);
    y
}

/// Returns a n-1 vector containing the pairwise difference of log(x_t) - log(x_t-1).
///
/// # Arguments
///
/// * `&x` - Reference to input vector slice of length n.
///
/// # Returns
///
/// * Output vector of length n-1.
///
/// # Example
///
/// ```
/// use arima::util;
/// let x = [1.0, 4.0, 6.0];
/// let y = util::diff_log(&x);
/// assert!(y[0] - 1.3862944 < 1.0e-7);
/// assert!(y[1] - 0.4054651 < 1.0e-7);
/// ```
pub fn diff_log<T: Float>(x: &[T]) -> Vec<T> {
    let mut y: Vec<T> = x.to_vec();
    let len = y.len();

    y[len - 1] = y[len - 1].ln();
    for i in 1..len {
        // we iterate backwards through the vector to avoid re-calculation of ln()
        y[len - i - 1] = y[len - i - 1].ln();
        y[len - i] = y[len - i] - y[len - i - 1];
    }
    y.drain(0..1);
    y
}

/// Calculate the cumulative sum of a vector.
///
/// # Arguments
///
/// * `&x` - Reference to input vector slice of length n.
///
/// # Returns
///
/// * Output vector of length n containing the cumulated values.
///
/// # Example
///
/// ```
/// use arima::util;
/// let x = [1, 2, 3];
/// assert_eq!(util::cumsum(&x), &[1, 3, 6]);
/// ```
pub fn cumsum<T: Num + Add + AddAssign + Copy + From<u8>>(x: &[T]) -> Vec<T> {
    let mut y: Vec<T> = Vec::new();
    if x.len() < 2 {
        y.push(From::from(0));
        return y;
    }
    y.push(x[0]);
    for i in 1..x.len() {
        y.push(y[i - 1] + x[i]);
    }
    y
}

/// Calculate the inverse difference of a vector.
///
/// # Arguments
///
/// * `&x` - Reference to input vector slice of length n.
/// * `d` - How often the inverse differences should be applied.
///
/// # Returns
///
/// * Output vector of length n+d containing the inversed values. The first d values are zero.
///
/// # Example
///
/// ```
/// use arima::util;
/// let x = [1, 1, 1, 1, 1];
/// let y = util::diffinv(&x, 1);
/// assert_eq!(y, &[0, 1, 2, 3, 4, 5]);
///
/// let z = util::diff(&y, 1);
/// assert_eq!(z, x);
/// ```
pub fn diffinv<T: Num + Add + AddAssign + Copy + From<u8>>(x: &[T], d: usize) -> Vec<T> {
    let zero = From::from(0);

    // x vector with d leading zeros
    let mut cum: Vec<T> = [&vec![zero; d], x].concat().to_vec();

    // build cumulative sum d times
    for _ in 0..d {
        cum = cumsum(&cum);
    }
    cum
}

/// Calculate the mean of a vector.
///
/// # Arguments
///
/// * `&x` - Vector of length n to calculate the mean for.
///
/// # Returns
///
/// * Output vector containing the mean sum(x)/.
///
/// # Example
///
/// ```
/// use arima::util;
/// let x = [2, 3, 4, 5, 6];
/// let y = util::mean(&x);
/// assert_eq!(y, 4);
/// ```
pub fn mean<T: Num + Copy + Add<T, Output = T> + From<i32>>(x: &[T]) -> T {
    let zero: T = From::from(0_i32);
    let n: T = From::from(x.len() as i32);
    x.iter().fold(zero, |sum, &item| sum + item) / n
}

/// Center vector, i.e. remove the mean from each element. Returns a tuple containing the
/// centered vector and the mean.
///
/// # Arguments
///
/// * `&x` - Vector of length n to be centered.
///
/// # Returns
///
/// * Tuple of (y, mean) where y is the centered vector and mean is the mean.
///
/// # Example
///
/// ```
/// use arima::util;
/// let x = [2, 3, 4, 5, 6];
/// let (y, m) = util::center(&x);
/// assert_eq!(y, [-2, -1, 0, 1, 2]);
/// assert_eq!(m, 4);
/// ```
pub fn center<T: Num + Copy + Add + AddAssign + Copy + From<i32>>(x: &[T]) -> (Vec<T>, T) {
    let m = mean(x);
    (x.iter().map(|&x| x - m).collect(), m)
}