From 67b7f4d58981cdfa288d3ec5c404df87c7616126 Mon Sep 17 00:00:00 2001
From: Dorival Pedroso <dorival.pedroso@gmail.com>
Date: Mon, 31 Jul 2023 18:47:35 +1000
Subject: [PATCH] Impl linear_fitting

---
 russell_lab/src/lib.rs            |   2 +
 russell_lab/src/linear_fitting.rs | 109 ++++++++++++++++++++++++++++++
 2 files changed, 111 insertions(+)
 create mode 100644 russell_lab/src/linear_fitting.rs

diff --git a/russell_lab/src/lib.rs b/russell_lab/src/lib.rs
index 38e85a7d..ae957c7f 100644
--- a/russell_lab/src/lib.rs
+++ b/russell_lab/src/lib.rs
@@ -39,6 +39,7 @@ mod constants;
 mod enums;
 mod formatters;
 mod generators;
+mod linear_fitting;
 pub mod math;
 mod matrix;
 mod matvec;
@@ -54,6 +55,7 @@ use crate::constants::*;
 pub use crate::enums::*;
 pub use crate::formatters::*;
 pub use crate::generators::*;
+pub use crate::linear_fitting::*;
 pub use crate::matrix::*;
 pub use crate::matvec::*;
 pub use crate::read_table::*;
diff --git a/russell_lab/src/linear_fitting.rs b/russell_lab/src/linear_fitting.rs
new file mode 100644
index 00000000..7468f6cb
--- /dev/null
+++ b/russell_lab/src/linear_fitting.rs
@@ -0,0 +1,109 @@
+use crate::{StrError, Vector};
+
+/// Calculates the parameters of a linear model using least squares fitting
+///
+/// # Input
+///
+/// `x` -- the X-data vector with dimension n
+/// `y` -- the Y-data vector with dimension n
+/// `pass_through_zero` -- compute the parameters such that the line passes through zero (c = 0)
+///
+/// # Output
+///
+/// * `(c, m)` -- the y(x=0)=c intersect and the slope m
+///
+/// NOTE: this function returns `(0.0, f64::INFINITY)` in two situations:
+///
+/// * If `pass_through_zero == True` and `sum(X) == 0`
+/// * If `pass_through_zero == False` and the line is vertical (null denominator)
+pub fn linear_fitting(x: &Vector, y: &Vector, pass_through_zero: bool) -> Result<(f64, f64), StrError> {
+    // dimension
+    let nn = x.dim();
+    if y.dim() != nn {
+        return Err("vectors must have the same dimension");
+    }
+
+    // sums
+    let mut sum_x = 0.0;
+    let mut sum_y = 0.0;
+    let mut sum_xy = 0.0;
+    let mut sum_xx = 0.0;
+    for i in 0..nn {
+        sum_x += x[i];
+        sum_y += y[i];
+        sum_xy += x[i] * y[i];
+        sum_xx += x[i] * x[i];
+    }
+
+    // calculate parameters
+    let c;
+    let m;
+    let n = nn as f64;
+    if pass_through_zero {
+        if sum_xx == 0.0 {
+            return Ok((0.0, f64::INFINITY));
+        }
+        c = 0.0;
+        m = sum_xy / sum_xx;
+    } else {
+        let den = sum_x * sum_x - n * sum_xx;
+        println!("den = {}", den);
+        if den == 0.0 {
+            return Ok((0.0, f64::INFINITY));
+        }
+        c = (sum_x * sum_xy - sum_xx * sum_y) / den;
+        m = (sum_x * sum_y - n * sum_xy) / den;
+    }
+
+    // results
+    Ok((c, m))
+}
+
+////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+
+#[cfg(test)]
+mod tests {
+    use super::linear_fitting;
+    use crate::Vector;
+    use russell_chk::approx_eq;
+
+    #[test]
+    fn linear_fitting_handles_errors() {
+        let x = Vector::from(&[1.0, 2.0]);
+        let y = Vector::from(&[6.0, 5.0, 7.0, 10.0]);
+        assert_eq!(
+            linear_fitting(&x, &y, false).err(),
+            Some("vectors must have the same dimension")
+        );
+    }
+
+    #[test]
+    fn linear_fitting_works() {
+        let x = Vector::from(&[1.0, 2.0, 3.0, 4.0]);
+        let y = Vector::from(&[6.0, 5.0, 7.0, 10.0]);
+
+        let (c, m) = linear_fitting(&x, &y, false).unwrap();
+        assert_eq!(c, 3.5);
+        assert_eq!(m, 1.4);
+
+        let (c, m) = linear_fitting(&x, &y, true).unwrap();
+        assert_eq!(c, 0.0);
+        approx_eq(m, 2.566666666666667, 1e-16);
+    }
+
+    #[test]
+    fn linear_fitting_handles_division_by_zero() {
+        let x = Vector::from(&[1.0, 1.0, 1.0, 1.0]);
+        let y = Vector::from(&[1.0, 2.0, 3.0, 4.0]);
+
+        let (c, m) = linear_fitting(&x, &y, false).unwrap();
+        assert_eq!(c, 0.0);
+        assert_eq!(m, f64::INFINITY);
+
+        let x = Vector::from(&[0.0, 0.0, 0.0, 0.0]);
+        let y = Vector::from(&[1.0, 2.0, 3.0, 4.0]);
+        let (c, m) = linear_fitting(&x, &y, true).unwrap();
+        assert_eq!(c, 0.0);
+        assert_eq!(m, f64::INFINITY);
+    }
+}