Added main file and test file for bisection method

Author: mapcrafter2048

search/bisection.go

@@ -0,0 +1,62 @@
+package search
+
+import (
+	"fmt"
+)
+
+// Package search provides functions for searching and root-finding algorithms.
+//
+// bisection searches for the root of the function f in the interval [a, b].
+// The function f must be continuous and f(a) and f(b) must have different signs.
+// This method uses the bisection algorithm to iteratively narrow down the interval
+// until the root is found within the specified tolerance or the maximum number of
+// iterations is reached.
+//
+// Parameters:
+//   - f: A function that takes a float64 and returns a float64. This is the function
+//     for which we are trying to find the root.
+//   - a: The start of the interval.
+//   - b: The end of the interval.
+//   - tol: The tolerance for the root. The algorithm stops when the interval width
+//     is less than this value.
+//   - maxIter: The maximum number of iterations to perform.
+//
+// Returns:
+//   - float64: The approximate root of the function.
+//   - error: An error is returned if f(a) and f(b) do not have different signs or
+//     if the maximum number of iterations is reached without finding the root.
+//
+// Complexity:
+//   - Worst: O(log((b-a)/tol))
+//   - Average: O(log((b-a)/tol))
+//   - Best: O(1)
+//
+// Example usage:
+//
+//	root, err := bisection(func(x float64) float64 { return math.Pow(x, 3) - x - 2 }, 1, 2, 1e-6, 1000)
+//	if err != nil {
+//	    log.Fatal(err)
+//	}
+//	fmt.Println(root) // Output: 1.521379
+//
+// Reference:
+//   - https://en.wikipedia.org/wiki/Bisection_method
+func bisection(f func(float64) float64, a, b, tol float64, maxIter int) (float64, error) {
+	if f(a)*f(b) >= 0 {
+		return 0, fmt.Errorf("f(a) and f(b) must have different signs")
+	}
+
+	var c float64
+	for i := 0; i < maxIter; i++ {
+		c = (a + b) / 2
+		if f(c) == 0 || (b-a)/2 < tol {
+			return c, nil
+		}
+		if f(c)*f(a) < 0 {
+			b = c
+		} else {
+			a = c
+		}
+	}
+	return c, fmt.Errorf("maximum number of iterations reached")
+}

search/bisection_test.go

@@ -0,0 +1,74 @@
+package search
+
+import (
+	"math"
+	"testing"
+)
+
+func TestBisection(t *testing.T) {
+	tests := []struct {
+		f       func(float64) float64
+		a, b    float64
+		tol     float64
+		maxIter int
+		want    float64
+		wantErr bool
+	}{
+		{
+			f:       func(x float64) float64 { return math.Pow(x, 3) - x - 2 },
+			a:       1,
+			b:       2,
+			tol:     1e-6,
+			maxIter: 1000,
+			want:    1.521380,
+			wantErr: false,
+		},
+		{
+			f:       func(x float64) float64 { return x*x - 4 },
+			a:       0,
+			b:       3,
+			tol:     1e-6,
+			maxIter: 1000,
+			want:    2,
+			wantErr: false,
+		},
+		{
+			f:       func(x float64) float64 { return x - 5 },
+			a:       0,
+			b:       10,
+			tol:     1e-6,
+			maxIter: 1000,
+			want:    5,
+			wantErr: false,
+		},
+		{
+			f:       func(x float64) float64 { return math.Sin(x) },
+			a:       3,
+			b:       4,
+			tol:     1e-6,
+			maxIter: 1000,
+			want:    math.Pi,
+			wantErr: false,
+		},
+		{
+			f:       func(x float64) float64 { return x*x + 1 },
+			a:       -1,
+			b:       1,
+			tol:     1e-6,
+			maxIter: 1000,
+			want:    0,
+			wantErr: true,
+		},
+	}
+
+	for _, tt := range tests {
+		got, err := bisection(tt.f, tt.a, tt.b, tt.tol, tt.maxIter)
+		if (err != nil) != tt.wantErr {
+			t.Errorf("bisection() error = %v, wantErr %v", err, tt.wantErr)
+			continue
+		}
+		if math.Abs(got-tt.want) > tt.tol {
+			t.Errorf("bisection() = %v, want %v", got, tt.want)
+		}
+	}
+}