Bisection Method

Schrick-Noah_Project-2.R

@@ -1,4 +1,76 @@
 # Project 2 for the University of Tulsa's CS-7863 Sci-Stat Course
 # Roots and Zeros of Functions
 # Professor: Dr. McKinney, Spring 2023
-# Noah L. Schrick - 1492657
+# Noah L. Schrick - 1492657
+
+## Part 1: Bisection
+findZeroBisect <- function(func, xl, xr, tol, maxsteps=1e6){
+  steps <- 0
+  if (func(xl) * func(xr) >= 0){
+    stop("Bad interval: try again with different endpoints")
+  }
+  
+  repeat{
+    xm <- (xl + xr)/2
+    if(abs(func(xm)) < tol || steps >= maxsteps){
+      break
+    }
+    
+    ifelse(func(xl) * func(xm) > 0, xl<-xm, xr<-xm)
+    steps <- steps + 1
+  }
+  return(c(xm, func(xm), steps))
+}
+
+# Solve 1a
+fun.a <- function(x) {x^2-2}
+fun.a.string <- "x^2-2=0"
+sqrt2.estimate <- findZeroBisect(fun.a.string,1,2,1e-6)
+sqrt2.estimate[1]
+# Plot 1a
+if (!require("ggplot2")) install.packages("ggplot2")
+library(ggplot2)
+ggplot(data.frame(x=seq(1,2,.1)), aes(x)) + 
+  stat_function(fun=fun.a, aes(col=fun.string)) + 
+  geom_hline(aes(yintercept=0, col = "y=0"), show.legend=TRUE)+
+  geom_vline(aes(xintercept=sqrt2.estimate[1], 
+                 col = "bisection estimate"), show.legend=TRUE)+
+  ggtitle("Zero Function") +
+  xlab("x") + ylab("Zero Function") +
+  theme(text = element_text(size=20), plot.title = element_text(hjust = 0.5))
+
+# Solve 1b
+fun.b <- function(x) {-3+x+2*exp(-x)}
+fun.b.string <- "-3+x+2*exp(-x)=0"
+fun.b.estimate.left <- findZeroBisect(fun.b,-2.5,0,1e-6)
+fun.b.estimate.left[1]
+fun.b.estimate.right <- findZeroBisect(fun.b,1,4,1e-6)
+fun.b.estimate.right[1]
+# Plot 1b
+ggplot(data.frame(x=seq(-2.5,5,.1)), aes(x)) + 
+  stat_function(fun=fun.b, aes(col=fun.b.string)) + 
+  geom_hline(aes(yintercept=0, col = "y=0"), show.legend=TRUE)+
+  geom_vline(aes(xintercept=fun.b.estimate.left[1], 
+                 col = "first bisection estimate"), show.legend=TRUE)+
+  geom_vline(aes(xintercept=fun.b.estimate.right[1], 
+                 col = "second bisection estimate"), show.legend=TRUE)+
+  ggtitle("Zero Function") +
+  xlab("x") + ylab("Zero Function") +
+  theme(text = element_text(size=20), plot.title = element_text(hjust = 0.5))
+
+# Solve 1c
+fun.c <- function(x) {x^3-sin(x)^2}
+fun.c.string <- "x^3-sin(x)^2=0"
+fun.c.estimate <- findZeroBisect(fun.c,0.5,1,1e-6)
+fun.c.estimate[1]
+# Plot 1c
+ggplot(data.frame(x=seq(0.5,1,.1)), aes(x)) + 
+  stat_function(fun=fun.c, aes(col=fun.c.string)) + 
+  geom_hline(aes(yintercept=0, col = "y=0"), show.legend=TRUE)+
+  geom_vline(aes(xintercept=fun.c.estimate[1], 
+                 col = "bisection estimate"), show.legend=TRUE)+
+  ggtitle("Zero Function") +
+  xlab("x") + ylab("Zero Function") +
+  theme(text = element_text(size=20), plot.title = element_text(hjust = 0.5))
+
+