add statistics module

provides some basic statistics functions (sum, mean, etc.)
and a function to return the parameters of the linear regression of
two variables

implemented using num_traits to be more flexible for the types

Signed-off-by: Dominik Csapak <d.csapak@proxmox.com>

Cargo.toml

@@ -30,6 +30,7 @@ lazy_static = "1.4"
 libc = "0.2"
 log = "0.4"
 nix = "0.16"
+num-traits = "0.2"
 once_cell = "1.3.1"
 openssl = "0.10"
 pam = "0.7"

src/api2.rs

@@ -5,6 +5,7 @@ pub mod config;
 pub mod node;
 pub mod reader;
 mod subscription;
+pub mod status;
 pub mod types;
 pub mod version;
 pub mod pull;

src/tools.rs

@@ -30,6 +30,7 @@ pub mod lru_cache;
 pub mod runtime;
 pub mod ticket;
 pub mod timer;
+pub mod statistics;
 pub mod systemd;
 
 mod wrapped_reader_stream;

src/tools/statistics.rs

@@ -0,0 +1,123 @@
+//! Helpers for common statistics tasks
+use num_traits::NumAssignRef;
+use num_traits::cast::ToPrimitive;
+
+/// Calculates the sum of a list of numbers
+/// ```
+/// # use proxmox_backup::tools::statistics::sum;
+/// # use num_traits::cast::ToPrimitive;
+///
+/// assert_eq!(sum(&[0,1,2,3,4,5]), 15);
+/// assert_eq!(sum(&[-1,1,-2,2]), 0);
+/// assert!((sum(&[0.0, 0.1,0.2]).to_f64().unwrap() - 0.3).abs() < 0.001);
+/// assert!((sum(&[0.0, -0.1,0.2]).to_f64().unwrap() - 0.1).abs() < 0.001);
+/// ```
+pub fn sum<T>(list: &[T]) -> T
+where
+    T: NumAssignRef + ToPrimitive
+{
+    let mut sum = T::zero();
+    for num in list {
+        sum += num;
+    }
+    sum
+}
+
+/// Calculates the mean of a variable x
+/// ```
+/// # use proxmox_backup::tools::statistics::mean;
+///
+/// assert!((mean(&[0,1,2,3,4,5]).unwrap() - 2.5).abs() < 0.001);
+/// assert_eq!(mean::<u64>(&[]), None)
+/// ```
+pub fn mean<T>(list: &[T]) -> Option<f64>
+where
+    T: NumAssignRef + ToPrimitive
+{
+    let len = list.len();
+    if len == 0 {
+        return None
+    }
+    Some(sum(list).to_f64()?/(list.len() as f64))
+}
+
+/// Calculates the variance of a variable x
+/// ```
+/// # use proxmox_backup::tools::statistics::variance;
+///
+/// assert!((variance(&[1,2,3,4]).unwrap() - 1.25).abs() < 0.001);
+/// assert_eq!(variance::<u64>(&[]), None)
+/// ```
+pub fn variance<T>(list: &[T]) -> Option<f64>
+where
+    T: NumAssignRef + ToPrimitive
+{
+    covariance(list, list)
+}
+
+/// Calculates the (non-corrected) covariance of two variables x,y
+pub fn covariance<X, Y> (x: &[X], y: &[Y]) -> Option<f64>
+where
+    X: NumAssignRef + ToPrimitive,
+    Y: NumAssignRef + ToPrimitive,
+{
+    let len_x = x.len();
+    let len_y = y.len();
+    if len_x == 0 || len_y == 0 || len_x != len_y {
+        return None
+    }
+
+    let mean_x = mean(x)?;
+    let mean_y = mean(y)?;
+
+    let covariance = sum(&(0..len_x).map(|i| {
+        let x = x[i].to_f64().unwrap_or(0.0);
+        let y = y[i].to_f64().unwrap_or(0.0);
+        (x - mean_x)*(y - mean_y)
+    }).collect::<Vec<f64>>());
+
+    Some(covariance/(len_x as f64))
+}
+
+/// Returns the factors (a,b) of a linear regression y = a + bx
+/// for the variables [x,y] or None if the lists are not the same length
+/// ```
+/// # use proxmox_backup::tools::statistics::linear_regression;
+///
+/// let x = &[0,1,2,3,4];
+/// let y = &[-4,-2,0,2,4];
+/// let (a,b) = linear_regression(x,y).unwrap();
+/// assert!((a - -4.0).abs() < 0.001);
+/// assert!((b - 2.0).abs() < 0.001);
+/// ```
+pub fn linear_regression<X, Y> (x: &[X], y: &[Y]) -> Option<(f64, f64)>
+where
+    X: NumAssignRef + ToPrimitive,
+    Y: NumAssignRef + ToPrimitive
+{
+    let len_x = x.len();
+    let len_y = y.len();
+    if len_x == 0 || len_y == 0 || len_x != len_y {
+        return None
+    }
+
+    let mean_x = mean(x)?;
+    let mean_y = mean(y)?;
+
+    let mut covariance = 0.0;
+    let mut variance = 0.0;
+
+    for i in 0..len_x {
+        let x = x[i].to_f64()?;
+        let y = y[i].to_f64()?;
+
+        let x_mean_x = x - mean_x;
+
+        covariance += x_mean_x*(y - mean_y);
+        variance += x_mean_x * x_mean_x;
+    }
+
+    let beta = covariance/variance;
+    let alpha = mean_y - beta*mean_x;
+    Some((alpha,beta))
+}