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use std::error::Error;
use core::{fmt,cmp::Ordering};
use core::fmt::{Debug, Display};
use indxvec::{Vecops,printing::{GR, UN, YL}};
use crate::{*,algos::*};
impl<T> Error for MedError<T> where T: Sized + Debug + Display {}
impl<T> Display for MedError<T>
where
T: Sized + Debug + Display,
{
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
match self {
MedError::Size(s) => write!(f, "Size of data must be positive: {s}"),
MedError::Nan(s) => write!(f, "Floats must not include NaNs: {s}"),
MedError::Other(s) => write!(f, "Converted from: {s}"),
}
}
}
impl<T> std::fmt::Display for Medians<'_, T>
where
T: Display,
{
fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
match self {
Medians::Odd(m) => {
write!(f, "{YL}odd median: {GR}{}{UN}", *m)
}
Medians::Even((m1, m2)) => {
write!(f, "{YL}even medians: {GR}{} {}{UN}", *m1, *m2)
}
}
}
}
/// Medians of &mut [&f64].
impl Medianf64 for &[f64] {
/// Returns `nan` error when any data item is a NaN, otherwise the median
fn medf_checked(self) -> Result<f64, Me> {
let n = self.len();
match n {
0 => return merror("size", "medf_checked: zero length data"),
1 => return Ok(self[0]),
2 => return Ok((self[0] + self[1]) / 2.0),
_ => (),
};
let mut s = self
.iter()
.map(|x| {
if x.is_nan() {
merror("Nan", "medf_checked: Nan in input!")
} else {
Ok(x)
}
})
.collect::<Result<Vec<&f64>, Me>>()?;
if (n & 1) == 1 {
let oddm = oddmedian_by(&mut s, &mut <f64>::total_cmp);
Ok(*oddm)
} else {
let (&med1, &med2) = evenmedian_by(&mut s, &mut <f64>::total_cmp);
Ok((med1+med2) / 2.0)
}
}
/// Use this when your data does not contain any NaNs.
/// NaNs will not raise an error. However, they will affect the result
/// because of their order positions beyond infinity.
fn medf_unchecked(self) -> f64 {
let n = self.len();
match n {
0 => return 0_f64,
1 => return self[0],
2 => return (self[0] + self[1]) / 2.0,
_ => (),
};
let mut s = self.ref_vec(0..self.len());
if (n & 1) == 1 {
let oddm = oddmedian_by(&mut s, &mut <f64>::total_cmp);
*oddm
} else {
let (&med1, &med2) = evenmedian_by(&mut s, &mut <f64>::total_cmp);
(med1 + med2) / 2.0
}
}
/// Iterative weighted median with accuracy eps
fn medf_weighted(self, ws: Self, eps: f64) -> Result<f64, Me> {
if self.len() != ws.len() {
return merror("size","medf_weighted - data and weights lengths mismatch"); };
if nans(self) {
return merror("Nan","medf_weighted - detected Nan in input"); };
let weights_sum: f64 = ws.iter().sum();
let mut last_median = 0_f64;
for (g,w) in self.iter().zip(ws) { last_median += w*g; };
last_median /= weights_sum; // start iterating from the weighted centre
let mut last_recsum = 0f64;
loop { // iteration till accuracy eps is exceeded
let mut median = 0_f64;
let mut recsum = 0_f64;
for (x,w) in self.iter().zip(ws) {
let mag = (x-last_median).abs();
if mag.is_normal() { // only use this point if its distance from median is > 0.0
let rec = w/(mag.sqrt()); // weight/distance
median += rec*x;
recsum += rec // add separately the reciprocals for final scaling
}
}
if recsum-last_recsum < eps { return Ok(median/recsum); }; // termination test
last_median = median/recsum;
last_recsum = recsum;
}
}
/// Zero mean/median data produced by subtracting the centre,
/// typically the mean or the median.
fn medf_zeroed(self, centre: f64) -> Vec<f64> {
self.iter().map(|&s| s - centre).collect()
}
/// Median correlation = cosine of an angle between two zero median vectors,
/// (where the two data samples are interpreted as n-dimensional vectors).
fn medf_correlation(self, v: Self) -> Result<f64, Me> {
let mut sx2 = 0_f64;
let mut sy2 = 0_f64;
let smedian = self.medf_checked()?;
let vmedian = v.medf_checked()?;
let sxy: f64 = self
.iter()
.zip(v)
.map(|(&xt, &yt)| {
let x = xt - smedian;
let y = yt - vmedian;
sx2 += x * x;
sy2 += y * y;
x * y
})
.sum();
let res = sxy / (sx2 * sy2).sqrt();
if res.is_nan() {
merror("Nan", "medf_correlation: Nan result!")
} else {
Ok(res)
}
}
/// Data dispersion estimator MAD (Median of Absolute Differences).
/// MAD is more stable than standard deviation and more general than quartiles.
/// When argument `centre` is the median, it is the most stable measure of data dispersion.
fn madf(self, centre: f64) -> f64 {
self.iter()
.map(|&s| (s - centre).abs())
.collect::<Vec<f64>>()
.medf_unchecked()
}
}
/// Medians of &[T]
impl<'a, T> Median<'a, T> for &'a [T] {
/// Median of `&[T]` by comparison `c`, quantified to a single f64 by `q`.
/// When T is a primitive type directly convertible to f64, pass in `as f64` for `q`.
/// When f64:From<T> is implemented, pass in `|x| x.into()` for `q`.
/// When T is Ord, use `|a,b| a.cmp(b)` as the comparator closure.
/// In all other cases, use custom closures `c` and `q`.
/// When T is not quantifiable at all, use `median_by` method.
fn qmedian_by(
self,
c: &mut impl FnMut(&T, &T) -> Ordering,
q: impl Fn(&T) -> f64,
) -> Result<f64, Me> {
let n = self.len();
match n {
0 => return merror("size", "qmedian_by: zero length data"),
1 => return Ok(q(&self[0])),
2 => return Ok((q(&self[0]) + q(&self[1])) / 2.0),
_ => (),
};
let mut s = self.ref_vec(0..self.len());
if (n & 1) == 1 {
Ok(q(oddmedian_by(&mut s, c)))
} else {
let (med1, med2) = evenmedian_by(&mut s, c);
Ok((q(med1) + q(med2)) / 2.0)
}
}
/// Median(s) of unquantifiable type by general comparison closure
fn median_by(self, c: &mut impl FnMut(&T, &T) -> Ordering) -> Result<Medians<'a, T>, Me> {
let n = self.len();
match n {
0 => return merror("size", "median_ord: zero length data"),
1 => return Ok(Medians::Odd(&self[0])),
2 => return Ok(Medians::Even((&self[0], &self[1]))),
_ => (),
};
let mut s = self.ref_vec(0..self.len());
if (n & 1) == 1 {
Ok(Medians::Odd(oddmedian_by(&mut s, c)))
} else {
Ok(Medians::Even(evenmedian_by(&mut s, c)))
}
}
/// Zero mean/median data produced by subtracting the centre
fn zeroed(self, centre: f64, q: impl Fn(&T) -> f64) -> Result<Vec<f64>, Me> {
Ok(self.iter().map(|s| q(s) - centre).collect())
}
/// We define median based correlation as cosine of an angle between two
/// zero median vectors (analogously to Pearson's zero mean vectors)
/// # Example
/// ```
/// use medians::{Medianf64,Median};
/// use core::convert::identity;
/// use core::cmp::Ordering::*;
/// let v1 = vec![1_f64,2.,3.,4.,5.,6.,7.,8.,9.,10.,11.,12.,13.,14.];
/// let v2 = vec![14_f64,1.,13.,2.,12.,3.,11.,4.,10.,5.,9.,6.,8.,7.];
/// assert_eq!(v1.medf_correlation(&v2).unwrap(),-0.1076923076923077);
/// assert_eq!(v1.med_correlation(&v2,&mut |a,b| a.total_cmp(b),|&a| identity(a)).unwrap(),-0.1076923076923077);
/// ```
fn med_correlation(
self,
v: Self,
c: &mut impl FnMut(&T, &T) -> Ordering,
q: impl Fn(&T) -> f64,
) -> Result<f64, Me> {
let mut sx2 = 0_f64;
let mut sy2 = 0_f64;
let smedian = self.qmedian_by(c, &q)?;
let vmedian = v.qmedian_by(c, &q)?;
let sxy: f64 = self
.iter()
.zip(v)
.map(|(xt, yt)| {
let x = q(xt) - smedian;
let y = q(yt) - vmedian;
sx2 += x * x;
sy2 += y * y;
x * y
})
.sum();
let res = sxy / (sx2 * sy2).sqrt();
if res.is_nan() {
merror("Nan", "correlation: Nan result!")
} else {
Ok(res)
}
}
/// Data dispersion estimator MAD (Median of Absolute Differences).
/// MAD is more stable than standard deviation and more general than quartiles.
/// When argument `centre` is the median, it is the most stable measure of data dispersion.
fn mad(self, centre: f64, q: impl Fn(&T) -> f64) -> f64 {
self.iter()
.map(|s| (q(s) - centre).abs())
.collect::<Vec<f64>>()
.medf_unchecked()
}
}