Matrix used in linear algebra
/*
Copyright (c) 2010 <a href="http://www.gutgames.com">James Craig</a>
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#region Usings
using System;
using System.Text;
using System.Xml.Serialization;
#endregion
namespace Utilities.Math
{
/// <summary>
/// Matrix used in linear algebra
/// </summary>
[Serializable()]
public class Matrix
{
#region Constructor
/// <summary>
/// Constructor
/// </summary>
/// <param name="Width">Width of the matrix</param>
/// <param name="Height">Height of the matrix</param>
public Matrix(int Width,int Height)
{
_Width = Width;
_Height = Height;
_Values = new double[Width, Height];
}
#endregion
#region Public Properties
/// <summary>
/// Width of the matrix
/// </summary>
[XmlElement]
public int Width
{
get { return _Width; }
set { _Width = value; _Values = new double[Width, Height]; }
}
/// <summary>
/// Height of the matrix
/// </summary>
[XmlElement]
public int Height
{
get { return _Height; }
set { _Height = value; _Values = new double[Width, Height]; }
}
/// <summary>
/// Sets the values of the matrix
/// </summary>
/// <param name="X">X position</param>
/// <param name="Y">Y position</param>
/// <returns>the value at a point in the matrix</returns>
public double this[int X, int Y]
{
get
{
if (X < _Width && X >= 0 && Y < _Height && Y >= 0)
{
return _Values[X, Y];
}
throw new Exception("Index out of bounds");
}
set
{
if (X < _Width && X >= 0 && Y < _Height && Y >= 0)
{
_Values[X, Y] = value;
return;
}
throw new Exception("Index out of bounds");
}
}
/// <summary>
/// Values for the matrix
/// </summary>
[XmlElement]
public double[,] Values
{
get { return _Values; }
set { _Values = value; }
}
#endregion
#region Private Variables
private int _Width = 1;
private int _Height = 1;
private double[,] _Values = null;
#endregion
#region Operators
public static bool operator ==(Matrix M1, Matrix M2)
{
if (M1.Width != M2.Width || M1.Height != M2.Height)
return false;
for (int x = 0; x <= M1.Width; ++x)
{
for (int y = 0; y <= M1.Height; ++y)
{
if (M1[x, y] != M2[x, y])
return false;
}
}
return true;
}
public static bool operator !=(Matrix M1, Matrix M2)
{
return !(M1 == M2);
}
public static Matrix operator +(Matrix M1, Matrix M2)
{
if (M1.Width != M2.Width || M1.Height != M2.Height)
throw new ArgumentException("Both matrices must be the same dimensions.");
Matrix TempMatrix = new Matrix(M1.Width, M1.Height);
for (int x = 0; x < M1.Width; ++x)
{
for (int y = 0; y < M1.Height; ++y)
{
TempMatrix[x, y] = M1[x, y] + M2[x, y];
}
}
return TempMatrix;
}
public static Matrix operator -(Matrix M1, Matrix M2)
{
if (M1.Width != M2.Width || M1.Height != M2.Height)
throw new ArgumentException("Both matrices must be the same dimensions.");
Matrix TempMatrix = new Matrix(M1.Width, M1.Height);
for (int x = 0; x < M1.Width; ++x)
{
for (int y = 0; y < M1.Height; ++y)
{
TempMatrix[x, y] = M1[x, y] - M2[x, y];
}
}
return TempMatrix;
}
public static Matrix operator -(Matrix M1)
{
Matrix TempMatrix = new Matrix(M1.Width, M1.Height);
for (int x = 0; x < M1.Width; ++x)
{
for (int y = 0; y < M1.Height; ++y)
{
TempMatrix[x, y] = -M1[x, y];
}
}
return TempMatrix;
}
public static Matrix operator *(Matrix M1, Matrix M2)
{
if (M1.Width != M2.Width || M1.Height != M2.Height)
throw new ArgumentException("Dimensions for the matrices are incorrect.");
Matrix TempMatrix = new Matrix(M2.Width, M1.Height);
for (int x = 0; x < M2.Width; ++x)
{
for (int y = 0; y < M1.Height; ++y)
{
TempMatrix[x,y]=0.0;
for (int i = 0; i < M1.Width; ++i)
{
for (int j = 0; j < M2.Height; ++j)
{
TempMatrix[x, y] += (M1[i, y] * M2[x, j]);
}
}
}
}
return TempMatrix;
}
public static Matrix operator *(Matrix M1,double D)
{
Matrix TempMatrix = new Matrix(M1.Width, M1.Height);
for (int x = 0; x < M1.Width; ++x)
{
for (int y = 0; y < M1.Height; ++y)
{
TempMatrix[x, y] = M1[x, y] * D;
}
}
return TempMatrix;
}
public static Matrix operator *(double D, Matrix M1)
{
Matrix TempMatrix = new Matrix(M1.Width, M1.Height);
for (int x = 0; x < M1.Width; ++x)
{
for (int y = 0; y < M1.Height; ++y)
{
TempMatrix[x, y] = M1[x, y] * D;
}
}
return TempMatrix;
}
public static Matrix operator /(Matrix M1, double D)
{
return M1 * (1 / D);
}
public static Matrix operator /(double D, Matrix M1)
{
return M1 * (1 / D);
}
#endregion
#region Public Overridden Functions
public override bool Equals(object obj)
{
if (obj is Matrix)
{
return this == (Matrix)obj;
}
return false;
}
public override int GetHashCode()
{
double Hash=0;
for (int x = 0; x < Width; ++x)
{
for (int y = 0; y < Height; ++y)
{
Hash += this[x, y];
}
}
return (int)Hash;
}
public override string ToString()
{
StringBuilder Builder = new StringBuilder();
string Seperator = "";
Builder.Append("{" + System.Environment.NewLine);
for (int x = 0; x < Width; ++x)
{
Builder.Append("{");
for (int y = 0; y < Height; ++y)
{
Builder.Append(Seperator + this[x, y]);
Seperator = ",";
}
Builder.Append("}" + System.Environment.NewLine);
Seperator = "";
}
Builder.Append("}");
return Builder.ToString();
}
#endregion
#region Public Functions
/// <summary>
/// Transposes the matrix
/// </summary>
/// <returns>Returns a new transposed matrix</returns>
public Matrix Transpose()
{
Matrix TempValues = new Matrix(Height, Width);
for (int x = 0; x < Width; ++x)
{
for (int y = 0; y < Height; ++y)
{
TempValues[y, x] = _Values[x, y];
}
}
return TempValues;
}
/// <summary>
/// Gets the determinant of a square matrix
/// </summary>
/// <returns>The determinant of a square matrix</returns>
public double Determinant()
{
if (Width != Height)
throw new Exception("The determinant can not be calculated for a non square matrix");
if (Width == 2)
{
return (this[0, 0] * this[1, 1]) - (this[0, 1] * this[1, 0]);
}
double Answer = 0.0;
for (int x = 0; x < Width; ++x)
{
Matrix TempMatrix = new Matrix(Width - 1, Height - 1);
int WidthCounter = 0;
for (int y = 0; y < Width; ++y)
{
if (y != x)
{
for (int z = 1; z < Height; ++z)
{
TempMatrix[WidthCounter, z - 1] = this[y, z];
}
++WidthCounter;
}
}
if (x % 2 == 0)
{
Answer += TempMatrix.Determinant();
}
else
{
Answer -= TempMatrix.Determinant();
}
}
return Answer;
}
#endregion
}
}
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