From 86643012e255f1aa2284efc816ed746f9b7ea11b Mon Sep 17 00:00:00 2001
From: Robert Altner <robert-altner@t-online.de>
Date: Thu, 24 Jan 2019 04:11:32 +0100
Subject: [PATCH] Function "Invert()" now inverts a matrix

---
 Matrix/Matrix.hpp | 71 ++++++++++++++++++++++++++++++++++++++++++++++-
 Matrix/main.cpp   | 33 ++++++++++++----------
 2 files changed, 88 insertions(+), 16 deletions(-)

diff --git a/Matrix/Matrix.hpp b/Matrix/Matrix.hpp
index 367e2c2..02fbd59 100644
--- a/Matrix/Matrix.hpp
+++ b/Matrix/Matrix.hpp
@@ -30,6 +30,8 @@ public:
 	// Constructional functions
 	friend void Zero(Matrix& mat);
 	friend void Identity(Matrix& mat);
+
+	friend Matrix Identity(uint dimension);
 	
 
 	// Setters / Getters
@@ -47,6 +49,7 @@ public:
 	// Transformation / arithmetic functions
 
 	void Transpose();
+	void Invert();
 	void MultiplyRow(uint row, double factor);
 	void SwapRows(uint left, uint right);
 	void AddMultiplesToRow(uint base, uint target, double factor);
@@ -54,6 +57,9 @@ public:
 	void TransformToEchelonForm();
 	void TransformToReducedEchelonForm();
 
+	void ConcatVertically(const Matrix& other);
+	void ConcatHorizontally(const Matrix& other);
+
 	friend double det(const Matrix& mat);
 	friend Matrix mul(const Matrix& left, const Matrix& right);
 	
@@ -139,6 +145,18 @@ inline void Identity(Matrix& mat)
 		mat.m_matrix[k][k] = 1;
 }
 
+////////////////////////////////////////////////////
+/// \brief Creates an identity matrix and returns it
+///
+////////////////////////////////////////////////////
+inline Matrix Identity(uint dimension)
+{
+	Matrix id(dimension, dimension);
+	Identity(id);
+
+	return id;
+}
+
 
 ////////////////////////////////////////////////////
 /// \brief Sets the number at a given position to a given value
@@ -251,6 +269,29 @@ inline void Matrix::Transpose()
 }
 
 
+////////////////////////////////////////////////////
+/// \brief Inverts the matrix
+///
+////////////////////////////////////////////////////
+inline void Matrix::Invert()
+{
+	if (!IsInvertable())
+		return;
+
+	Matrix holder = *this;
+	holder.ConcatVertically(Identity(m_rows));
+
+	holder.TransformToReducedEchelonForm();
+
+	Matrix inverse(m_rows, m_cols);
+	for (int row = 0; row < m_rows; row++)
+		for (int col = 0; col < m_cols; col++)
+			inverse.SetNumber(row, col, holder.GetNumber(row, col + m_cols));
+	*this = inverse;
+}
+
+
+
 ////////////////////////////////////////////////////
 /// \brief Multiplies each value of a given row by a given factor
 ///
@@ -338,7 +379,7 @@ inline Matrix mul(const Matrix& right, const Matrix& left)
 
 	for (uint row = 0; row < returnMatrix.m_rows; row++)
 		for (uint col = 0; col < returnMatrix.m_cols; col++)
-			for (uint k = 0; k < right.m_cols; k++)
+			for (uint k = 0; k < right.m_cols; k++) 
 				returnMatrix.m_matrix[row][col] += right.m_matrix[row][k] * left.m_matrix[k][col];
 
 	return returnMatrix;
@@ -491,6 +532,31 @@ inline void Matrix::TransformToReducedEchelonForm()
 			if (m_matrix[row][col] == -0) m_matrix[row][col] = 0;
 }
 
+inline void Matrix::ConcatVertically(const Matrix& other)
+{
+	if (m_rows != other.GetRows())
+		return;
+
+	Resize(m_rows, m_cols + other.GetColumns(), m_matrix);
+
+	for (int row = 0; row < m_rows; row++)
+		for (int col = other.GetColumns(); col < m_cols; col++)
+			m_matrix[row][col] = other.GetNumber(row, col - other.GetColumns());
+}
+
+
+inline void Matrix::ConcatHorizontally(const Matrix& other)
+{
+	if (m_cols != other.GetColumns())
+		return;
+
+	Resize(m_rows + other.GetRows(), m_cols, m_matrix);
+
+	for (int col = 0; col < m_cols; col++)
+		for (int row = other.GetRows(); row < m_rows; row++)
+			m_matrix[row][col] = other.GetNumber(row, col - other.GetColumns());
+}
+
 
 inline bool Matrix::InBounds(uint row, uint col) const
 {
@@ -510,6 +576,9 @@ inline void Matrix::Resize(uint rows, uint cols, doubleMatrix& matrix)
 	matrix.resize(rows);
 	for (int row = 0; row < rows; row++)
 		matrix[row].resize(cols);
+
+	m_rows = rows;
+	m_cols = cols;
 }
 
 
diff --git a/Matrix/main.cpp b/Matrix/main.cpp
index 57c3e99..02d3560 100644
--- a/Matrix/main.cpp
+++ b/Matrix/main.cpp
@@ -8,24 +8,27 @@ int main(int argc, char** argv)
 	std::default_random_engine engine(time(NULL));
 	std::uniform_int_distribution<int> range(0, 4);
 
-	Matrix myMatrix(4, 4);
-	for (int row = 0; row < 3; row++)
-		for (int col = 0; col < 4; col++)
-			myMatrix.SetNumber(row, col, range(engine));
+	// Hardcode a matrix
+	Matrix myMatrix(3, 3);
+	myMatrix.SetNumber(0, 0, 1);
+	myMatrix.SetNumber(0, 1, 1);
+	myMatrix.SetNumber(0, 2, 1);
+	myMatrix.SetNumber(1, 0, 0);
+	myMatrix.SetNumber(1, 1, 1);
+	myMatrix.SetNumber(1, 2, 1);
+	myMatrix.SetNumber(2, 0, 0);
+	myMatrix.SetNumber(2, 1, 0);
+	myMatrix.SetNumber(2, 2, 1);
 
-	Matrix otherMatrix(4, 4);
-	Identity(otherMatrix);
+	Matrix inverse = myMatrix;
+	inverse.Invert();
+	
 
-	Matrix addMatrix = myMatrix * otherMatrix;
+	std::cout << myMatrix << std::endl;
 
-	std::cout << myMatrix;
-	std::cout << std::endl << "-" << std::endl << std::endl;
-	std::cout << otherMatrix;
-	std::cout << std::endl << "=" << std::endl << std::endl;
-	std::cout << addMatrix << std::endl;
-	std::cout << det(addMatrix) << std::endl;
-	std::cout << addMatrix.IsInvertable() << std::endl;
-	std::cout << std::endl;
+	std::cout << inverse << std::endl;
+
+	std::cout << mul(myMatrix, inverse) << std::endl;
 
 	getchar();