Added Secant method.

src/main.rs

@@ -29,8 +29,10 @@ fn main() {
     let x_newton = univariate_solvers::newton_solve(&(fct as fn(f64) -> f64), &(dfct as fn(f64) -> f64), x0, tol, max_iter);
     let x_newton_num: f64 = univariate_solvers::newton_solve_num(&(fct as fn(f64) -> f64), x0, tol, dx_num, max_iter);
     let x_bisection : f64 = univariate_solvers::bisection_solve(&(fct as fn(f64) -> f64), -5.0, 1.0, tol).unwrap();
-    println!("Mathematica           : x = {}", x_mathematica);
-    println!("Newton's method       : x = {}", x_newton);
-    println!("Newton's method (num) : x = {}", x_newton_num);
-    println!("Bisection             : x = {}", x_bisection);
+    let x_secant : f64 = univariate_solvers::secant_solve(&(fct as fn(f64) -> f64), -1.0, 1.0, tol, max_iter);
+    println!("Mathematica           : x = {}\tf(x) = {}", x_mathematica, fct(x_mathematica));
+    println!("Newton's method       : x = {}\tf(x) = {}", x_newton, fct(x_newton));
+    println!("Newton's method (num) : x = {}\tf(x) = {}", x_newton_num, fct(x_newton_num));
+    println!("Bisection             : x = {}\tf(x) = {}", x_bisection, fct(x_bisection));
+    println!("Secant method         : x = {}\tf(x) = {}", x_secant, fct(x_secant));
 }

src/univariate_solvers.rs

@@ -47,6 +47,13 @@ where F : Fn(f64) -> f64
 // ------------------------ Bracketing methods ------------------------
 // --------------------------------------------------------------------
 
+/// @brief Bisection method for solving a function f(x) = 0
+/// @param f function to solve
+/// @param a left bracket
+/// @param b right bracket
+/// @param tol tolerance
+/// @return solution
+/// @note The interval [a, b] must bracket the root, meaning f(a) and f(b) must be of a different sign.
 pub fn bisection_solve<F>(f : F, mut a : f64, mut b : f64, tol : f64) -> Result<f64, &'static str>
 where F : Fn(f64) -> f64
 {
@@ -70,3 +77,34 @@ where F : Fn(f64) -> f64
     }
     return Result::Ok((a + b)/2.0);
 }
+
+/// @brief Secant method for solving a function f(x) = 0
+/// @param f function to solve
+/// @param a left bracket
+/// @param b right bracket
+/// @param tol tolerance
+/// @param max_iter maximum number of iterations
+/// @return solution
+/// @note The interval [a, b] does not have to bracket the root.
+/// @note The secant method is not guaranteed to converge.
+pub fn secant_solve<F>(f : F, mut a : f64, mut b : f64, tol : f64, max_iter : u32) -> f64
+where F : Fn(f64) -> f64
+{
+    let mut c: f64 = (a + b)/2.0;
+    let mut fa: f64 = f(a);
+    let mut fb: f64 = f(b);
+    let mut fc: f64;
+    for _iter in 0..max_iter {
+        // c is x[n], a is x[n-1], b is x[n-2]
+        c = a - fa*(a - b)/(fa - fb);
+        fc = f(c);
+        b = a;
+        fb = fa;
+        a = c;
+        fa = fc;
+        if (b - a).abs() < tol {
+            break;
+        }
+    }
+    return c;
+}