Added rust implementation of gaussian elimination (#183)

* Created matrix struct

* Added row swapping method

* The gaussian elimination part works now
but back substitution is completely broken

* Fixed back propagation

* Fixed vector initialization and max finding

* Changed getter and setter to index trait

* Fixed a few typos and unneeded complexities

* Cleaned up a bit and added an argument to the matrix constructor

Author: Jess3Jane

chapters/matrix_methods/gaussian_elimination/code/rust/gaussian_elimination.rs

@@ -0,0 +1,106 @@
+// submitted by jess 3jane
+
+use std::cmp::min;
+use std::ops::{Index, IndexMut};
+
+pub struct Matrix {
+    rows: usize,
+    cols: usize,
+    data: Vec<f64>,
+}
+
+impl Matrix {
+    fn new(rows: usize, cols: usize, data: &[f64]) -> Matrix {
+        Matrix {
+            rows,
+            cols,
+            data: data.to_vec(),
+        }
+    }
+
+    fn swap_rows(&mut self, a: usize, b: usize) {
+        for col in 0..self.cols {
+            self.data.swap(a * self.cols + col, b * self.cols + col);
+        }
+    }
+}
+
+impl Index<(usize, usize)> for Matrix {
+    type Output = f64;
+    fn index(&self, (row, col): (usize, usize)) -> &f64 {
+        &self.data[row * self.cols + col]
+    }
+}
+
+impl IndexMut<(usize, usize)> for Matrix {
+    fn index_mut(&mut self, (row, col): (usize, usize)) -> &mut f64 {
+        &mut self.data[row * self.cols + col]
+    }
+}
+
+fn gaussian_elimination(a: &mut Matrix) {
+    for k in 0..min(a.cols, a.rows) {
+        // Step 1: find the maximum element for this column
+        let mut max_row = k;
+        let mut max_value = a[(k, k)].abs();
+        for row in (k + 1)..a.rows {
+            if max_value < a[(row, k)].abs() {
+                max_value = a[(row, k)].abs();
+                max_row = row;
+            }
+        }
+
+        // Check to make sure the matrix is good
+        if a[(max_row, k)] == 0.0 {
+            println!("Matrix is singular, aborting");
+            return;
+        }
+
+        // Step 2: swap the row with the highest value for this kumn to the top
+        a.swap_rows(k, max_row);
+
+        // Loop over all remaining rows
+        for i in k + 1..a.rows {
+            // Step 3: find the fraction
+            let fraction = a[(i, k)] / a[(k, k)];
+
+            // Loop through all columns for that row
+            for j in (k + 1)..a.cols {
+                // Step 4: re-evaluate each element
+                a[(i, j)] -= a[(k, j)] * fraction;
+            }
+
+            // Step 5: set lower elements to 0
+            a[(i, k)] = 0.0;
+        }
+    }
+}
+
+fn back_substitution(a: &Matrix) -> Vec<f64> {
+    let mut soln = vec![0.0; a.rows];
+
+    soln[a.rows - 1] = a[(a.rows - 1, a.cols - 1)] / a[(a.rows - 1, a.cols - 2)];
+
+    for i in (0..a.rows - 1).rev() {
+        let mut sum = 0.0;
+        for j in (i..a.rows).rev() {
+            sum += soln[j] * a[(i, j)];
+        }
+        soln[i] = (a[(i, a.cols - 1)] - sum) / a[(i, i)];
+    }
+
+    soln
+}
+
+fn main() {
+    // The example matrix from the text
+    let mut a = Matrix::new(
+        3,
+        4,
+        &vec![2.0, 3.0, 4.0, 6.0, 1.0, 2.0, 3.0, 4.0, 3.0, -4.0, 0.0, 10.0],
+    );
+
+    gaussian_elimination(&mut a);
+    let soln = back_substitution(&a);
+    println!("Solution: {:?}", soln);
+}

chapters/matrix_methods/gaussian_elimination/gaussian_elimination.md

@@ -281,6 +281,8 @@ The full code can be seen here:
 {% method %}
 {% sample lang="jl" %}
 [import, lang:"julia"](code/julia/gaussian_elimination.jl)
+{% sample lang="rs" %}
+[import, lang:"rust"](code/rust/gaussian_elimination.rs)
 {% endmethod %}