From af0572cc87144b6e74824e565474f43634eece1a Mon Sep 17 00:00:00 2001
From: Robert Altner <robert-altner@t-online.de>
Date: Thu, 24 Jan 2019 21:06:46 +0100
Subject: [PATCH] Added way to check if matrix is orthogonal

---
 Matrix/Matrix.hpp | 35 +++++++++++++++++++++++++++++++++++
 Matrix/main.cpp   |  7 +++++--
 2 files changed, 40 insertions(+), 2 deletions(-)

diff --git a/Matrix/Matrix.hpp b/Matrix/Matrix.hpp
index bebdad5..a64edfb 100644
--- a/Matrix/Matrix.hpp
+++ b/Matrix/Matrix.hpp
@@ -44,6 +44,7 @@ public:
 
 	bool IsInvertable();
 	bool IsSquare();
+	bool IsOrthogonal();
 
 
 	// Transformation / arithmetic functions
@@ -80,6 +81,8 @@ public:
 	Matrix operator*(const Matrix& other);
 	void operator*=(const Matrix& other);
 
+	bool operator==(const Matrix& other);
+
 	friend std::ostream& operator<<(std::ostream& stream, const Matrix& other);
 private:
 	doubleMatrix m_matrix;
@@ -226,6 +229,19 @@ bool Matrix::IsSquare()
 	return m_rows == m_cols;
 }
 
+////////////////////////////////////////////////////
+/// \brief Returns wether the matrix is orthogonal
+///
+////////////////////////////////////////////////////
+bool Matrix::IsOrthogonal()
+{
+	if (!IsSquare())
+		return false;
+
+	return ((*this * _transpose(*this)) == Identity(m_rows));
+}
+
+
 
 ////////////////////////////////////////////////////
 /// \brief Prints the whole matrix to the console
@@ -699,6 +715,25 @@ void Matrix::operator*=(const Matrix& other)
 }
 
 
+bool Matrix::operator==(const Matrix& other)
+{
+	DimensionsFitting(*this, other);
+
+	bool equal = true;
+
+	for (int row = 0; row < m_rows; row++) {
+		for (int col = 0; col < m_cols; col++) {
+			if (m_matrix[row][col] == other.GetNumber(row, col)) {
+				equal = false;
+				break;
+			}
+		}
+	}
+
+	return equal;
+}
+
+
 std::ostream& operator<<(std::ostream& stream, const Matrix& other)
 {
 	for (uint row = 0; row < other.m_rows; row++)
diff --git a/Matrix/main.cpp b/Matrix/main.cpp
index 02d3560..8b058a1 100644
--- a/Matrix/main.cpp
+++ b/Matrix/main.cpp
@@ -20,8 +20,7 @@ int main(int argc, char** argv)
 	myMatrix.SetNumber(2, 1, 0);
 	myMatrix.SetNumber(2, 2, 1);
 
-	Matrix inverse = myMatrix;
-	inverse.Invert();
+	Matrix inverse = Invert(myMatrix);
 	
 
 	std::cout << myMatrix << std::endl;
@@ -30,6 +29,10 @@ int main(int argc, char** argv)
 
 	std::cout << mul(myMatrix, inverse) << std::endl;
 
+	std::cout << Transpose(myMatrix) << std::endl;
+	std::cout << Transpose(myMatrix) * myMatrix << std::endl;
+	std::cout << myMatrix.IsOrthogonal() << std::endl;
+
 	getchar();
 
 	return 0;