stats.rs.html -- source
Description: Source to the Rust file `src/libtest/stats.rs`.
Keywords: rust, rustlang, rust-lang

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    #![allow(missing_docs)]
    #![allow(deprecated)] // Float

    use std::cmp::Ordering::{self, Equal, Greater, Less};
    use std::mem;

    #[cfg(test)]
    mod tests;

    fn local_cmp(x: f64, y: f64) -> Ordering {
        // arbitrarily decide that NaNs are larger than everything.
        if y.is_nan() {
            Less
        } else if x.is_nan() {
            Greater
        } else if x < y {
            Less
        } else if x == y {
            Equal
        } else {
            Greater
        }
    }

    fn local_sort(v: &mut [f64]) {
        v.sort_by(|x: &f64, y: &f64| local_cmp(*x, *y));
    }

    /// Trait that provides simple descriptive statistics on a univariate set of numeric samples.
    pub trait Stats {
        /// Sum of the samples.
        ///
        /// Note: this method sacrifices performance at the altar of accuracy
        /// Depends on IEEE-754 arithmetic guarantees. See proof of correctness at:
        /// ["Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric
        /// Predicates"][paper]
        ///
        /// [paper]: http://www.cs.cmu.edu/~quake-papers/robust-arithmetic.ps
        fn sum(&self) -> f64;

        /// Minimum value of the samples.
        fn min(&self) -> f64;

        /// Maximum value of the samples.
        fn max(&self) -> f64;

        /// Arithmetic mean (average) of the samples: sum divided by sample-count.
        ///
        /// See: <https://en.wikipedia.org/wiki/Arithmetic_mean>
        fn mean(&self) -> f64;

        /// Median of the samples: value separating the lower half of the samples from the higher half.
        /// Equal to `self.percentile(50.0)`.
        ///
        /// See: <https://en.wikipedia.org/wiki/Median>
        fn median(&self) -> f64;

        /// Variance of the samples: bias-corrected mean of the squares of the differences of each
        /// sample from the sample mean. Note that this calculates the _sample variance_ rather than the
        /// population variance, which is assumed to be unknown. It therefore corrects the `(n-1)/n`
        /// bias that would appear if we calculated a population variance, by dividing by `(n-1)` rather
        /// than `n`.
        ///
        /// See: <https://en.wikipedia.org/wiki/Variance>
        fn var(&self) -> f64;

        /// Standard deviation: the square root of the sample variance.
        ///
        /// Note: this is not a robust statistic for non-normal distributions. Prefer the
        /// `median_abs_dev` for unknown distributions.
        ///
        /// See: <https://en.wikipedia.org/wiki/Standard_deviation>
        fn std_dev(&self) -> f64;

        /// Standard deviation as a percent of the mean value. See `std_dev` and `mean`.
        ///
        /// Note: this is not a robust statistic for non-normal distributions. Prefer the
        /// `median_abs_dev_pct` for unknown distributions.
        fn std_dev_pct(&self) -> f64;

        /// Scaled median of the absolute deviations of each sample from the sample median. This is a
        /// robust (distribution-agnostic) estimator of sample variability. Use this in preference to
        /// `std_dev` if you cannot assume your sample is normally distributed. Note that this is scaled
        /// by the constant `1.4826` to allow its use as a consistent estimator for the standard
        /// deviation.
        ///
        /// See: <http://en.wikipedia.org/wiki/Median_absolute_deviation>
        fn median_abs_dev(&self) -> f64;

        /// Median absolute deviation as a percent of the median. See `median_abs_dev` and `median`.
        fn median_abs_dev_pct(&self) -> f64;

        /// Percentile: the value below which `pct` percent of the values in `self` fall. For example,
        /// percentile(95.0) will return the value `v` such that 95% of the samples `s` in `self`
        /// satisfy `s <= v`.
        ///
        /// Calculated by linear interpolation between closest ranks.
        ///
        /// See: <http://en.wikipedia.org/wiki/Percentile>
        fn percentile(&self, pct: f64) -> f64;

        /// Quartiles of the sample: three values that divide the sample into four equal groups, each
        /// with 1/4 of the data. The middle value is the median. See `median` and `percentile`. This
        /// function may calculate the 3 quartiles more efficiently than 3 calls to `percentile`, but
        /// is otherwise equivalent.
        ///
        /// See also: <https://en.wikipedia.org/wiki/Quartile>
        fn quartiles(&self) -> (f64, f64, f64);

        /// Inter-quartile range: the difference between the 25th percentile (1st quartile) and the 75th
        /// percentile (3rd quartile). See `quartiles`.
        ///
        /// See also: <https://en.wikipedia.org/wiki/Interquartile_range>
        fn iqr(&self) -> f64;
    }

    /// Extracted collection of all the summary statistics of a sample set.
    #[derive(Debug, Clone, PartialEq, Copy)]
    #[allow(missing_docs)]
    pub struct Summary {
        pub sum: f64,
        pub min: f64,
        pub max: f64,
        pub mean: f64,
        pub median: f64,
        pub var: f64,
        pub std_dev: f64,
        pub std_dev_pct: f64,
        pub median_abs_dev: f64,
        pub median_abs_dev_pct: f64,
        pub quartiles: (f64, f64, f64),
        pub iqr: f64,
    }

    impl Summary {
        /// Construct a new summary of a sample set.
        pub fn new(samples: &[f64]) -> Summary {
            Summary {
                sum: samples.sum(),
                min: samples.min(),
                max: samples.max(),
                mean: samples.mean(),
                median: samples.median(),
                var: samples.var(),
                std_dev: samples.std_dev(),
                std_dev_pct: samples.std_dev_pct(),
                median_abs_dev: samples.median_abs_dev(),
                median_abs_dev_pct: samples.median_abs_dev_pct(),
                quartiles: samples.quartiles(),
                iqr: samples.iqr(),
            }
        }
    }

    impl Stats for [f64] {
        // FIXME #11059 handle NaN, inf and overflow
        fn sum(&self) -> f64 {
            let mut partials = vec![];

            for &x in self {
                let mut x = x;
                let mut j = 0;
                // This inner loop applies `hi`/`lo` summation to each
                // partial so that the list of partial sums remains exact.
                for i in 0..partials.len() {
                    let mut y: f64 = partials[i];
                    if x.abs() < y.abs() {
                        mem::swap(&mut x, &mut y);
                    }
                    // Rounded `x+y` is stored in `hi` with round-off stored in
                    // `lo`. Together `hi+lo` are exactly equal to `x+y`.
                    let hi = x + y;
                    let lo = y - (hi - x);
                    if lo != 0.0 {
                        partials[j] = lo;
                        j += 1;
                    }
                    x = hi;
                }
                if j >= partials.len() {
                    partials.push(x);
                } else {
                    partials[j] = x;
                    partials.truncate(j + 1);
                }
            }
            let zero: f64 = 0.0;
            partials.iter().fold(zero, |p, q| p + *q)
        }

        fn min(&self) -> f64 {
            assert!(!self.is_empty());
            self.iter().fold(self[0], |p, q| p.min(*q))
        }

        fn max(&self) -> f64 {
            assert!(!self.is_empty());
            self.iter().fold(self[0], |p, q| p.max(*q))
        }

        fn mean(&self) -> f64 {
            assert!(!self.is_empty());
            self.sum() / (self.len() as f64)
        }

        fn median(&self) -> f64 {
            self.percentile(50_f64)
        }

        fn var(&self) -> f64 {
            if self.len() < 2 {
                0.0
            } else {
                let mean = self.mean();
                let mut v: f64 = 0.0;
                for s in self {
                    let x = *s - mean;
                    v = v + x * x;
                }
                // N.B., this is _supposed to be_ len-1, not len. If you
                // change it back to len, you will be calculating a
                // population variance, not a sample variance.
                let denom = (self.len() - 1) as f64;
                v / denom
            }
        }

        fn std_dev(&self) -> f64 {
            self.var().sqrt()
        }

        fn std_dev_pct(&self) -> f64 {
            let hundred = 100_f64;
            (self.std_dev() / self.mean()) * hundred
        }

        fn median_abs_dev(&self) -> f64 {
            let med = self.median();
            let abs_devs: Vec<f64> = self.iter().map(|&v| (med - v).abs()).collect();
            // This constant is derived by smarter statistics brains than me, but it is
            // consistent with how R and other packages treat the MAD.
            let number = 1.4826;
            abs_devs.median() * number
        }

        fn median_abs_dev_pct(&self) -> f64 {
            let hundred = 100_f64;
            (self.median_abs_dev() / self.median()) * hundred
        }

        fn percentile(&self, pct: f64) -> f64 {
            let mut tmp = self.to_vec();
            local_sort(&mut tmp);
            percentile_of_sorted(&tmp, pct)
        }

        fn quartiles(&self) -> (f64, f64, f64) {
            let mut tmp = self.to_vec();
            local_sort(&mut tmp);
            let first = 25_f64;
            let a = percentile_of_sorted(&tmp, first);
            let second = 50_f64;
            let b = percentile_of_sorted(&tmp, second);
            let third = 75_f64;
            let c = percentile_of_sorted(&tmp, third);
            (a, b, c)
        }

        fn iqr(&self) -> f64 {
            let (a, _, c) = self.quartiles();
            c - a
        }
    }

    // Helper function: extract a value representing the `pct` percentile of a sorted sample-set, using
    // linear interpolation. If samples are not sorted, return nonsensical value.
    fn percentile_of_sorted(sorted_samples: &[f64], pct: f64) -> f64 {
        assert!(!sorted_samples.is_empty());
        if sorted_samples.len() == 1 {
            return sorted_samples[0];
        }
        let zero: f64 = 0.0;
        assert!(zero <= pct);
        let hundred = 100_f64;
        assert!(pct <= hundred);
        if pct == hundred {
            return sorted_samples[sorted_samples.len() - 1];
        }
        let length = (sorted_samples.len() - 1) as f64;
        let rank = (pct / hundred) * length;
        let lrank = rank.floor();
        let d = rank - lrank;
        let n = lrank as usize;
        let lo = sorted_samples[n];
        let hi = sorted_samples[n + 1];
        lo + (hi - lo) * d
    }

    /// Winsorize a set of samples, replacing values above the `100-pct` percentile
    /// and below the `pct` percentile with those percentiles themselves. This is a
    /// way of minimizing the effect of outliers, at the cost of biasing the sample.
    /// It differs from trimming in that it does not change the number of samples,
    /// just changes the values of those that are outliers.
    ///
    /// See: <http://en.wikipedia.org/wiki/Winsorising>
    pub fn winsorize(samples: &mut [f64], pct: f64) {
        let mut tmp = samples.to_vec();
        local_sort(&mut tmp);
        let lo = percentile_of_sorted(&tmp, pct);
        let hundred = 100_f64;
        let hi = percentile_of_sorted(&tmp, hundred - pct);
        for samp in samples {
            if *samp > hi {
                *samp = hi
            } else if *samp < lo {
                *samp = lo
            }
        }
    }