Added: CheckGaussian for partial gaussian checks

gaussian.go

 package gomatrix
 
+import (
+	"math/big"
+)
+
 // GaussianElimination converts the matrix to an echelon form
 //
-// This function applies the gaussian elemination to the matrix in order to
+// This function applies the gaussian elimination to the matrix in order to
 // create an echelon form.
 func (f *F2) GaussianElimination() {
 	// iterate through all possible pivot bits
@@ -125,3 +129,53 @@ func (f *F2) partialDiagonalize(startRow, startCol, stopRow, stopCol int) {
 		}
 	}
 }
+
+// CheckGaussian checks if the given range in the matrix is the identity matrix
+//
+// @param int startRow The row where the check starts
+// @param int startCol The column where the check starts
+// @param int n        The size of the submatrix to check
+//
+// @return bool
+func (f *F2) CheckGaussian(startRow, startCol, n int) bool {
+	counter := 0
+
+	// iterate through the rows
+	for _, row := range f.Rows[startRow:] {
+		// if the counter is reached...
+		if counter == n {
+			// ...break
+			break
+		}
+
+		// create the bitmask for the row
+		bitmask := big.NewInt(0).SetBit(
+			big.NewInt(0),
+			startCol+counter,
+			1,
+		)
+
+		// get the bits to check
+		bitsToCheck := big.NewInt(0).And(
+			row,
+			bitmask,
+		)
+
+		// xor the bits to check with the bitmask
+		shouldBeZero := big.NewInt(0).Xor(
+			bitsToCheck,
+			bitmask,
+		)
+
+		// if the xor'ed result is not zero...
+		if shouldBeZero.Cmp(big.NewInt(0)) != 0 {
+			// ...the check failed
+			return false
+		}
+
+		// increase the counter
+		counter++
+	}
+
+	return true
+}

gaussian_test.go

@@ -90,3 +90,73 @@ func TestPartialGaussianElimination(t *testing.T) {
 		assert.True(t, test.matrixA.IsEqual(test.expectedMatrix))
 	}
 }
+
+func TestCheckGaussian(t *testing.T) {
+	tests := []struct {
+		description    string
+		matrix         *F2
+		startRow       int
+		startCol       int
+		n              int
+		expectedResult bool
+	}{
+		{
+			description: "3x3 identity matrix",
+			matrix: NewF2(3, 3).Set([]*big.Int{
+				big.NewInt(1),
+				big.NewInt(2),
+				big.NewInt(4),
+			}),
+			startRow:       0,
+			startCol:       0,
+			n:              3,
+			expectedResult: true,
+		},
+		{
+			description: "3x3 matrix",
+			matrix: NewF2(3, 3).Set([]*big.Int{
+				big.NewInt(2),
+				big.NewInt(1),
+				big.NewInt(4),
+			}),
+			startRow:       0,
+			startCol:       0,
+			n:              3,
+			expectedResult: false,
+		},
+		{
+			description: "3x3 matrix with lower right identity matrix",
+			matrix: NewF2(3, 3).Set([]*big.Int{
+				big.NewInt(2),
+				big.NewInt(2),
+				big.NewInt(4),
+			}),
+			startRow:       1,
+			startCol:       1,
+			n:              3,
+			expectedResult: true,
+		},
+		{
+			description: "3x3 matrix with upper left identity matrix",
+			matrix: NewF2(3, 3).Set([]*big.Int{
+				big.NewInt(1),
+				big.NewInt(2),
+				big.NewInt(7),
+			}),
+			startRow:       0,
+			startCol:       0,
+			n:              2,
+			expectedResult: true,
+		},
+	}
+
+	for _, test := range tests {
+		result := test.matrix.CheckGaussian(
+			test.startRow,
+			test.startCol,
+			test.n,
+		)
+
+		assert.Equalf(t, test.expectedResult, result, test.description)
+	}
+}