diff options
| author | Benjamin Culkin <bjculkin@mix.wvu.edu> | 2018-04-09 15:42:35 -0700 |
|---|---|---|
| committer | Benjamin Culkin <bjculkin@mix.wvu.edu> | 2018-04-09 15:42:35 -0700 |
| commit | 88fc0b666c58334009bc274105ea0d2b90edf75d (patch) | |
| tree | 7af54f97dd1e75873984069dbbf3e73ebe4e2893 /CSMath/src/bisection/PreBisection.java | |
Initial commit
Diffstat (limited to 'CSMath/src/bisection/PreBisection.java')
| -rw-r--r-- | CSMath/src/bisection/PreBisection.java | 74 |
1 files changed, 74 insertions, 0 deletions
diff --git a/CSMath/src/bisection/PreBisection.java b/CSMath/src/bisection/PreBisection.java new file mode 100644 index 0000000..39bbd60 --- /dev/null +++ b/CSMath/src/bisection/PreBisection.java @@ -0,0 +1,74 @@ +package bisection;
+/*
+ * Benjamin Culkin
+ * 1/16/2018
+ * CS 479
+ * Bisection
+ *
+ * Use the bisection method to find bracketed roots of arbitrary real-valued functions.
+ */
+import java.util.function.DoubleUnaryOperator;
+
+public class PreBisection {
+ public static void main(String[] args) {
+ // The functions we're approximating a root for
+ DoubleUnaryOperator functionA = x -> Math.cos(x) - x;
+
+ DoubleUnaryOperator functionB = x -> {
+ double valA = Math.pow(x, 5);
+ double valB = 3 * Math.pow(x, 4);
+ double valC = 4 * Math.pow(x, 3);
+
+ return valA - valB + valC - 1;
+ };
+
+ DoubleUnaryOperator functionC = x -> (x * x) - 3;
+
+ // The approximated roots
+ double answerA = bisect(functionA, 0, 1, 0.0001);
+ double answerB = bisect(functionB, 0, 1, 0.0001);
+ double answerC = bisect(functionC, 1, 2, 0.0000001);
+
+ // Print out the answers + their function
+ System.out.printf("x = cos(x) => %.4f\n", answerA);
+ System.out.printf("x^5 - 3x^4 + 4x^2 - 1 => %.4f\n", answerB);
+ System.out.printf("x^2 - 3 => %.7f\n", answerC);
+ }
+
+ // Calculate the number of iterations to approximate to a specified tolerance
+ private static double iterCount(double a, double b, double tol) {
+ double inside = Math.log((b - a) / tol);
+
+ return Math.ceil(inside / Math.log(2));
+ }
+
+ // Calculate a root for an equation by the bisection method
+ private static double bisect(DoubleUnaryOperator func, double a, double b, double tol) {
+ // Calculate the number of iterations
+ double N = iterCount(a, b, tol);
+
+ double val = 0.0;
+
+ // Set our values
+ double newa = a;
+ double newb = b;
+ double newc = (a + b) / 2;
+
+ // Continue onwards until we get the approximation to within the right tolerance
+ for (int i = 0; i < N; i++) {
+ newc = (newa + newb) / 2;
+
+ val = func.applyAsDouble(newc);
+
+ // Pick the right direction to bisect in
+ if (func.applyAsDouble(newa) * val < 0) {
+ newb = newc;
+ } else {
+ newa = newc;
+ }
+ }
+
+ // Return the right value
+ return newc;
+ }
+}
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