feat: add determinant implementation for matrix (#732)

* feat: add determinant implementation for matrix

Added the Determinant method for the Matrix struct under math/matrix.
This method returns the determinant of the matrix.

* fix: determinant spelling and linting

Fixed the spelling error in determinant.go.
Fixed ineffectual error assignment in determinant_test.go.

* test: add test for matrix determinant

Added a test case for single-element matrix.

---------

Co-authored-by: Rak Laptudirm <rak@laptudirm.com>

Author: Carter907

math/matrix/determinant.go

@@ -0,0 +1,59 @@
+// determinant.go
+// description: This method finds the determinant of a matrix.
+// details: For a theoretical explanation as for what the determinant
+// represents, see the [Wikipedia Article](https://en.wikipedia.org/wiki/Determinant)
+// author [Carter907](https://github.com/Carter907)
+// see determinant_test.go
+
+package matrix
+
+import (
+	"errors"
+)
+
+// Calculates the determinant of the matrix.
+// This method only works for square matrices (e.i. matrices with equal rows and columns).
+func (mat Matrix[T]) Determinant() (T, error) {
+
+	var determinant T = 0
+	var elements = mat.elements
+	if mat.rows != mat.columns {
+
+		return 0, errors.New("Matrix rows and columns must equal in order to find the determinant.")
+	}
+
+	// Specify base cases for different sized matrices.
+	switch mat.rows {
+	case 1:
+		return elements[0][0], nil
+	case 2:
+		return elements[0][0]*elements[1][1] - elements[1][0]*elements[0][1], nil
+	default:
+		for i := 0; i < mat.rows; i++ {
+
+			var initialValue T = 0
+			minor := New(mat.rows-1, mat.columns-1, initialValue)
+			// Fill the contents of minor excluding the 0th row and the ith column.
+			for j, minor_i := 1, 0; j < mat.rows && minor_i < minor.rows; j, minor_i = j+1, minor_i+1 {
+				for k, minor_j := 0, 0; k < mat.rows && minor_j < minor.rows; k, minor_j = k+1, minor_j+1 {
+					if k != i {
+						minor.elements[minor_i][minor_j] = elements[j][k]
+					} else {
+						minor_j-- // Decrement the column of minor to account for skipping the ith column of the matrix.
+					}
+				}
+			}
+
+			if i%2 == 0 {
+				minor_det, _ := minor.Determinant()
+
+				determinant += elements[0][i] * minor_det
+			} else {
+				minor_det, _ := minor.Determinant()
+
+				determinant += elements[0][i] * minor_det
+			}
+		}
+		return determinant, nil
+	}
+}

math/matrix/determinant_test.go

@@ -0,0 +1,142 @@
+package matrix_test
+
+import (
+	"errors"
+	"math"
+	"math/rand"
+	"testing"
+
+	"github.com/TheAlgorithms/Go/math/matrix"
+)
+
+// Test different matrix contents
+func TestMatrixDeterminant(t *testing.T) {
+	// Find Determinant of a 2 by 2 matrix.
+	matrix1, err := matrix.NewFromElements([][]int{
+		{3, 8},
+		{4, 6},
+	})
+	if err != nil {
+		t.Fatalf("Error creating 3 by 3 matrix: %v", err)
+	}
+	determinant, err := matrix1.Determinant()
+	if err != nil {
+		t.Fatalf("Error returned from 3 by 3 matrix: %v", err)
+	}
+	if determinant != -14 {
+		t.Fatalf("Determinant returned for a 3 by 3 matrix was %d; wanted -14", determinant)
+	}
+
+	// Find Dertminant of a 1 by 1 matrix
+	expectedValue := rand.Intn(math.MaxInt)
+	matrix2, err := matrix.NewFromElements([][]int{
+		{expectedValue},
+	})
+	if err != nil {
+		t.Fatalf("Error creating 1 by 1 matrix: %v", err)
+	}
+	determinant, err = matrix2.Determinant()
+	if err != nil {
+		t.Fatalf("Error returned from 1 by 1 matrix: %v", err)
+	}
+	if determinant != expectedValue {
+		t.Fatalf("Determinant returned for a 1 by 1 matrix was %d; wanted %d", determinant, expectedValue)
+	}
+
+}
+
+func TestEmptyMatrix(t *testing.T) {
+	emptyElements := [][]int{}
+	matrix, err := matrix.NewFromElements(emptyElements)
+
+	if err != nil {
+		t.Fatalf("Error creating Matrix with empty elements: %v", err)
+	}
+
+	determinant, err := matrix.Determinant()
+
+	if err != nil {
+		t.Fatalf("Determinant returned an error for empty matrix: %v", err)
+	}
+
+	// Check that 0 is returned from an empty matrix.
+	expectedValue := 0
+	if determinant != expectedValue {
+		t.Errorf("Determinant returned from empty matrix was %d; wanted %d", determinant, expectedValue)
+	}
+
+}
+
+func TestNonSquareMatrix(t *testing.T) {
+	// Creating non-square matrix for testing.
+	initialValue := 0
+	initialRows := 4
+	initialCols := 2
+
+	nonSquareMatrix := matrix.New(initialRows, initialCols, initialValue)
+
+	determinant, err := nonSquareMatrix.Determinant()
+	// Check if non square matrix returns an error.
+	if err == nil {
+		t.Fatalf("No error was returned for a non-square matrix")
+	}
+
+	// Check if the correct error was returned.
+	expectedError := errors.New("Matrix rows and columns must equal in order to find the determinant.")
+
+	if err.Error() != expectedError.Error() {
+		t.Errorf("Error returned from non-square matrix was \n\"%v\"; \nwanted \n\"%v\"", err, expectedError)
+	}
+
+	// Check if the determinant of the non-square matrix is 0.
+	if determinant != 0 {
+		t.Errorf("Determinant of non-square matrix was not 0 but was %d", determinant)
+	}
+
+}
+
+// Test matrix returned from matrix.New
+func TestDefaultMatrix(t *testing.T) {
+	initialValue := 0
+	initialRows := 3
+	initialCols := 3
+	defaultMatrix := matrix.New(initialRows, initialCols, initialValue)
+
+	determinant, err := defaultMatrix.Determinant()
+
+	if err != nil {
+		t.Fatalf("Error finding the determinant of 3 by 3 default matrix: %v.", err)
+	}
+	expectedValue := 0
+	if determinant != expectedValue {
+		t.Errorf("Determinant of the default matrix with an initial value 0 was %d; wanted %d.", initialValue, expectedValue)
+	}
+}
+
+// Benchmark a 3 by 3 matrix for computational throughput
+func BenchmarkSmallMatrixDeterminant(b *testing.B) {
+	// Create a 3 by 3 matrix for benchmarking
+	rows := 3
+	columns := 3
+	initialValue := 0
+	matrix := matrix.New(rows, columns, initialValue)
+
+	for i := 0; i < b.N; i++ {
+		_, _ = matrix.Determinant()
+	}
+}
+
+// Benchmark a 10 by 10 matrix for computational throughput.
+func BenchmarkMatrixDeterminant(b *testing.B) {
+	// Create a 10 by 10 matrix for benchmarking
+	rows := 10
+	columns := 10
+	initialValue := 0
+	matrix := matrix.New(rows, columns, initialValue)
+
+	b.ResetTimer()
+
+	for i := 0; i < b.N; i++ {
+		_, _ = matrix.Determinant()
+	}
+}