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//! Linear regression //! //! `linreg` calculates linear regressions for two dimensional measurements, also known as //! [simple linear regression](https://en.wikipedia.org/wiki/Simple_linear_regression). //! //! Base for all calculations of linear regression is the simple model found in //! https://en.wikipedia.org/wiki/Ordinary_least_squares#Simple_linear_regression_model. //! //! ## Example use //! //! ```rust //! use linreg::{linear_regression, linear_regression_of}; //! //! // Example 1: x and y values stored in two different vectors //! let xs: Vec<f64> = vec![1.0, 2.0, 3.0, 4.0, 5.0]; //! let ys: Vec<f64> = vec![2.0, 4.0, 5.0, 4.0, 5.0]; //! //! assert_eq!(Ok((0.6, 2.2)), linear_regression(&xs, &ys)); //! //! //! // Example 2: x and y values stored as tuples //! let tuples: Vec<(f32, f32)> = vec![(1.0, 2.0), //! (2.0, 4.0), //! (3.0, 5.0), //! (4.0, 4.0), //! (5.0, 5.0)]; //! //! assert_eq!(Ok((0.6, 2.2)), linear_regression_of(&tuples)); //! //! //! // Example 3: directly operating on integer (converted to float as required) //! let xs: Vec<u8> = vec![1, 2, 3, 4, 5]; //! let ys: Vec<u8> = vec![2, 4, 5, 4, 5]; //! //! assert_eq!(Ok((0.6, 2.2)), linear_regression(&xs, &ys)); //! ``` #![no_std] extern crate num_traits; use num_traits::float::FloatCore; #[cfg(test)] #[macro_use] extern crate std; use core::iter::Iterator; use core::iter::Sum; use displaydoc::Display; /// The kinds of errors that can occur when calculating a linear regression. #[derive(Copy, Clone, Display, Debug, PartialEq)] pub enum Error { /// The slope is too steep to represent, approaching infinity. TooSteep, /// Failed to calculate mean. /// /// This means the input was empty or had too many elements. Mean, /// Lengths of the inputs are different. InputLenDif, /// Can't compute linear regression of zero elements NoElements, } /// Single-pass simple linear regression. /// /// Similar to `lin_reg`, but does not require a mean value to be computed in advance and thus /// does not require a second pass over the input data. /// /// Returns `Ok((slope, intercept))` of the regression line. /// /// # Errors /// /// Errors if the number of elements is too large to be represented as `F` or /// the slope is too steep to represent, approaching infinity. pub fn lin_reg_imprecise<I, F>(xys: I) -> Result<(F, F), Error> where F: FloatCore, I: Iterator<Item = (F, F)>, { details::lin_reg_imprecise_components(xys)?.finish() } /// A module containing the building parts of the main API. /// You can use these if you want to have more control over the linear regression mod details { use super::Error; use num_traits::float::FloatCore; /// Low level linear regression primitive for pushing values instead of fetching them /// from an iterator #[derive(Debug)] pub struct Accumulator<F: FloatCore> { x_mean: F, y_mean: F, x_mul_y_mean: F, x_squared_mean: F, n: usize, } impl<F: FloatCore> Default for Accumulator<F> { fn default() -> Self { Self::new() } } impl<F: FloatCore> Accumulator<F> { pub fn new() -> Self { Self { x_mean: F::zero(), y_mean: F::zero(), x_mul_y_mean: F::zero(), x_squared_mean: F::zero(), n: 0, } } pub fn push(&mut self, x: F, y: F) { self.x_mean = self.x_mean + x; self.y_mean = self.y_mean + y; self.x_mul_y_mean = self.x_mul_y_mean + x * y; self.x_squared_mean = self.x_squared_mean + x * x; self.n += 1; } pub fn normalize(&mut self) -> Result<(), Error> { match self.n { 1 => return Ok(()), 0 => return Err(Error::NoElements), _ => {} } let n = F::from(self.n).ok_or(Error::Mean)?; self.n = 1; self.x_mean = self.x_mean / n; self.y_mean = self.y_mean / n; self.x_mul_y_mean = self.x_mul_y_mean / n; self.x_squared_mean = self.x_squared_mean / n; Ok(()) } pub fn parts(mut self) -> Result<(F, F, F, F), Error> { self.normalize()?; let Self { x_mean, y_mean, x_mul_y_mean, x_squared_mean, .. } = self; Ok((x_mean, y_mean, x_mul_y_mean, x_squared_mean)) } pub fn finish(self) -> Result<(F, F), Error> { let (x_mean, y_mean, x_mul_y_mean, x_squared_mean) = self.parts()?; let slope = (x_mul_y_mean - x_mean * y_mean) / (x_squared_mean - x_mean * x_mean); let intercept = y_mean - slope * x_mean; if slope.is_nan() { return Err(Error::TooSteep); } Ok((slope, intercept)) } } pub fn lin_reg_imprecise_components<I, F>(xys: I) -> Result<Accumulator<F>, Error> where F: FloatCore, I: Iterator<Item = (F, F)>, { let mut acc = Accumulator::new(); for (x, y) in xys { acc.push(x, y); } acc.normalize()?; Ok(acc) } } /// Calculates a linear regression with a known mean. /// /// Lower-level linear regression function. Assumes that `x_mean` and `y_mean` /// have already been calculated. Returns `Error::DivByZero` if /// /// * the slope is too steep to represent, approaching infinity. /// /// Since there is a mean, this function assumes that `xs` and `ys` are both non-empty. /// /// Returns `Ok((slope, intercept))` of the regression line. pub fn lin_reg<I, F>(xys: I, x_mean: F, y_mean: F) -> Result<(F, F), Error> where I: Iterator<Item = (F, F)>, F: FloatCore, { // SUM (x-mean(x))^2 let mut xxm2 = F::zero(); // SUM (x-mean(x)) (y-mean(y)) let mut xmym2 = F::zero(); for (x, y) in xys { xxm2 = xxm2 + (x - x_mean) * (x - x_mean); xmym2 = xmym2 + (x - x_mean) * (y - y_mean); } let slope = xmym2 / xxm2; // we check for divide-by-zero after the fact if slope.is_nan() { return Err(Error::TooSteep); } let intercept = y_mean - slope * x_mean; Ok((slope, intercept)) } /// Two-pass simple linear regression from slices. /// /// Calculates the linear regression from two slices, one for x- and one for y-values, by /// calculating the mean and then calling `lin_reg`. /// /// Returns `Ok(slope, intercept)` of the regression line. /// /// # Errors /// /// Returns an error if /// /// * `xs` and `ys` differ in length /// * `xs` or `ys` are empty /// * the slope is too steep to represent, approaching infinity /// * the number of elements cannot be represented as an `F` /// pub fn linear_regression<X, Y, F>(xs: &[X], ys: &[Y]) -> Result<(F, F), Error> where X: Clone + Into<F>, Y: Clone + Into<F>, F: FloatCore + Sum, { if xs.len() != ys.len() { return Err(Error::InputLenDif); } if xs.is_empty() { return Err(Error::Mean); } let x_sum: F = xs.iter().cloned().map(Into::into).sum(); let n = F::from(xs.len()).ok_or(Error::Mean)?; let x_mean = x_sum / n; let y_sum: F = ys.iter().cloned().map(Into::into).sum(); let y_mean = y_sum / n; lin_reg( xs.iter() .map(|i| i.clone().into()) .zip(ys.iter().map(|i| i.clone().into())), x_mean, y_mean, ) } /// Two-pass linear regression from tuples. /// /// Calculates the linear regression from a slice of tuple values by first calculating the mean /// before calling `lin_reg`. /// /// Returns `Ok(slope, intercept)` of the regression line. /// /// # Errors /// /// Returns an error if /// /// * `xys` is empty /// * the slope is too steep to represent, approaching infinity /// * the number of elements cannot be represented as an `F` pub fn linear_regression_of<X, Y, F>(xys: &[(X, Y)]) -> Result<(F, F), Error> where X: Clone + Into<F>, Y: Clone + Into<F>, F: FloatCore, { if xys.is_empty() { return Err(Error::Mean); } // We're handrolling the mean computation here, because our generic implementation can't handle tuples. // If we ran the generic impl on each tuple field, that would be very cache inefficient let n = F::from(xys.len()).ok_or(Error::Mean)?; let (x_sum, y_sum) = xys .iter() .cloned() .fold((F::zero(), F::zero()), |(sx, sy), (x, y)| { (sx + x.into(), sy + y.into()) }); let x_mean = x_sum / n; let y_mean = y_sum / n; lin_reg( xys.iter() .map(|(x, y)| (x.clone().into(), y.clone().into())), x_mean, y_mean, ) } #[cfg(test)] mod tests { use std::vec::Vec; use super::*; #[test] fn float_slices_regression() { let xs: Vec<f64> = vec![1.0, 2.0, 3.0, 4.0, 5.0]; let ys: Vec<f64> = vec![2.0, 4.0, 5.0, 4.0, 5.0]; assert_eq!(Ok((0.6, 2.2)), linear_regression(&xs, &ys)); } #[test] fn lin_reg_imprecises_vs_linreg() { let xs: Vec<f64> = vec![1.0, 2.0, 3.0, 4.0, 5.0]; let ys: Vec<f64> = vec![2.0, 4.0, 5.0, 4.0, 5.0]; let (x1, y1) = lin_reg_imprecise(xs.iter().cloned().zip(ys.iter().cloned())).unwrap(); let (x2, y2): (f64, f64) = linear_regression(&xs, &ys).unwrap(); assert!(f64::abs(x1 - x2) < 0.00001); assert!(f64::abs(y1 - y2) < 0.00001); } #[test] fn int_slices_regression() { let xs: Vec<u8> = vec![1, 2, 3, 4, 5]; let ys: Vec<u8> = vec![2, 4, 5, 4, 5]; assert_eq!(Ok((0.6, 2.2)), linear_regression(&xs, &ys)); } #[test] fn float_tuples_regression() { let tuples: Vec<(f32, f32)> = vec![(1.0, 2.0), (2.0, 4.0), (3.0, 5.0), (4.0, 4.0), (5.0, 5.0)]; assert_eq!(Ok((0.6, 2.2)), linear_regression_of(&tuples)); } #[test] fn int_tuples_regression() { let tuples: Vec<(u32, u32)> = vec![(1, 2), (2, 4), (3, 5), (4, 4), (5, 5)]; assert_eq!(Ok((0.6, 2.2)), linear_regression_of(&tuples)); } }