From 232f470ce1d7ed445ec4a053b79b17cda857f405 Mon Sep 17 00:00:00 2001
From: Simon Gardling <titaniumtown@gmail.com>
Date: Wed, 9 Mar 2022 21:15:12 -0500
Subject: [PATCH] roots

---
 TODO.md                |  4 ++--
 src/function.rs        | 28 ++++++++++++++++++++++++++++
 src/function_output.rs | 12 ++++++++++++
 3 files changed, 42 insertions(+), 2 deletions(-)

diff --git a/TODO.md b/TODO.md
index 833eb29..6b829de 100644
--- a/TODO.md
+++ b/TODO.md
@@ -8,10 +8,10 @@
     - Non `y=` functions.
 3. Smart display of graph
     - Display of intersections between functions
-    - Display of roots
 4. Fix integral line
 5. re-add euler's number (well it works if you use capital e like `E^x`)
 6. allow constants in min/max integral input (like pi or euler's number)
 7. sliding values for functions (like a user-interactable slider that adjusts a variable in the function, like desmos)
 8. Keybinds
-9. nth derivative support (again)
\ No newline at end of file
+9. nth derivative support (again)
+10. add configs for toggling display of roots and extrema
\ No newline at end of file
diff --git a/src/function.rs b/src/function.rs
index 90c1783..33ddf16 100644
--- a/src/function.rs
+++ b/src/function.rs
@@ -276,6 +276,33 @@ impl FunctionEntry {
         self
     }
 
+    // Finds roots
+    fn roots(&mut self) {
+        let mut root_list: Vec<Value> = Vec::new();
+        let mut last_ele: Option<Value> = None;
+        for ele in self.output.back.as_ref().unwrap().iter() {
+            if last_ele.is_none() {
+                last_ele = Some(*ele);
+                continue;
+            }
+
+            if last_ele.unwrap().y.signum() != ele.y.signum() {
+                // Do 10 iterations of newton's method, should be more than accurate
+                let x = {
+                    let mut x1: f64 = last_ele.unwrap().x;
+                    for _ in 0..10 {
+                        x1 = last_ele.unwrap().x
+                            - (self.function.get(x1) / self.function.derivative(x1))
+                    }
+                    x1
+                };
+                root_list.push(Value::new(x, self.function.get(x)));
+            }
+            last_ele = Some(*ele);
+        }
+        self.output.roots = Some(root_list);
+    }
+
     // Finds extrema
     fn extrema(&mut self) {
         let mut extrama_list: Vec<Value> = Vec::new();
@@ -309,6 +336,7 @@ impl FunctionEntry {
         self.output.integral = integral;
         self.output.derivative = derivative;
         self.extrema();
+        self.roots();
 
         self.output.display(
             plot_ui,
diff --git a/src/function_output.rs b/src/function_output.rs
index 33e34c6..3f0c2a5 100644
--- a/src/function_output.rs
+++ b/src/function_output.rs
@@ -14,6 +14,7 @@ pub struct FunctionOutput {
     pub(crate) integral: Option<(Vec<Bar>, f64)>,
     pub(crate) derivative: Option<Vec<Value>>,
     pub(crate) extrema: Option<Vec<Value>>,
+    pub(crate) roots: Option<Vec<Value>>,
 }
 
 impl FunctionOutput {
@@ -23,6 +24,7 @@ impl FunctionOutput {
             integral: None,
             derivative: None,
             extrema: None,
+            roots: None,
         }
     }
 
@@ -31,6 +33,7 @@ impl FunctionOutput {
         self.integral = None;
         self.derivative = None;
         self.extrema = None;
+        self.roots = None;
     }
 
     pub fn invalidate_back(&mut self) { self.back = None; }
@@ -68,6 +71,15 @@ impl FunctionOutput {
             );
         }
 
+        if let Some(roots_data) = self.roots.clone() {
+            plot_ui.points(
+                Points::new(Values::from_values(roots_data))
+                    .color(Color32::LIGHT_BLUE)
+                    .name("Root")
+                    .radius(5.0),
+            );
+        }
+
         if let Some(integral_data) = self.integral.clone() {
             plot_ui.bar_chart(
                 BarChart::new(integral_data.0)