/// <summary>
/// The function concatenates the two given matrices column-wise
/// it can be helpful in a equation solver class where the augmented MatrixClass is obtained by concatenation
/// </summary>
public static MatrixClass Concatenate(MatrixClass MatrixClass1, MatrixClass MatrixClass2)
{
if (MatrixClass1.Rows != MatrixClass2.Rows)
{
throw new MatrixClassException("Concatenation not possible");
}
MatrixClass MatrixClass = new MatrixClass(MatrixClass1.Rows, MatrixClass1.Cols + MatrixClass2.Cols);
for (int i = 0; i < MatrixClass.Rows; i++)
{
for (int j = 0; j < MatrixClass.Cols; j++)
{
if (j < MatrixClass1.Cols)
{
MatrixClass[i, j] = MatrixClass1[i, j];
}
else
{
MatrixClass[i, j] = MatrixClass2[i, j - MatrixClass1.Cols];
}
}
}
return(MatrixClass);
}
/// <summary>
/// The function return the Minor of element[Row,Col] of a MatrixClass object
/// </summary>
public static MatrixClass Minor(MatrixClass MatrixClass, int iRow, int iCol)
{
MatrixClass minor = new MatrixClass(MatrixClass.Rows - 1, MatrixClass.Cols - 1);
int m = 0, n = 0;
for (int i = 0; i < MatrixClass.Rows; i++)
{
if (i == iRow)
{
continue;
}
n = 0;
for (int j = 0; j < MatrixClass.Cols; j++)
{
if (j == iCol)
{
continue;
}
minor[m, n] = MatrixClass[i, j];
n++;
}
m++;
}
return(minor);
}
private static MatrixClass Multiply(MatrixClass MatrixClass, Fraction frac)
{
MatrixClass result = new MatrixClass(MatrixClass.Rows, MatrixClass.Cols);
for (int i = 0; i < MatrixClass.Rows; i++)
{
for (int j = 0; j < MatrixClass.Cols; j++)
{
result[i, j] = MatrixClass[i, j] * frac;
}
}
return(result);
}
/// <summary>
/// The function duplicates the current MatrixClass object
/// </summary>
public MatrixClass Duplicate()
{
MatrixClass MatrixClass = new MatrixClass(Rows, Cols);
for (int i = 0; i < Rows; i++)
{
for (int j = 0; j < Cols; j++)
{
MatrixClass[i, j] = this[i, j];
}
}
return(MatrixClass);
}
/// <summary>
/// The function returns the transpose of the current MatrixClass
/// </summary>
public MatrixClass Transpose()
{
MatrixClass TransposeMatrixClass = new MatrixClass(this.Cols, this.Rows);
for (int i = 0; i < TransposeMatrixClass.Rows; i++)
{
for (int j = 0; j < TransposeMatrixClass.Cols; j++)
{
TransposeMatrixClass[i, j] = this[j, i];
}
}
return(TransposeMatrixClass);
}
/// <summary>
/// The function returns a Null MatrixClass of dimension ( Row x Col )
/// </summary>
public static MatrixClass NullMatrixClass(int iRows, int iCols)
{
Fraction temp = new Fraction(0);
MatrixClass MatrixClass = new MatrixClass(iRows, iCols);
for (int i = 0; i < iRows; i++)
{
for (int j = 0; j < iCols; j++)
{
MatrixClass[i, j] = temp;
}
}
return(MatrixClass);
}
/// <summary>
/// The function returns the adjoint of the current MatrixClass
/// </summary>
public MatrixClass Adjoint(int b)
{
if (this.Rows != this.Cols)
{
throw new MatrixClassException("Adjoint of a non-square MatrixClass does not exists");
}
MatrixClass AdjointMatrixClass = new MatrixClass(this.Rows, this.Cols);
for (int i = 0; i < this.Rows; i++)
{
for (int j = 0; j < this.Cols; j++)
{
AdjointMatrixClass[i, j] = b * Math.Pow(-1, i + j) * (Minor(this, j, i).Determinent());
}
}
return(AdjointMatrixClass);
}
/// <summary>
/// The function returns the reduced echelon form of the current MatrixClass
/// </summary>
public MatrixClass ReducedEchelonForm()
{
try {
MatrixClass ReducedEchelonMatrixClass = this.Duplicate();
for (int i = 0; i < this.Rows; i++)
{
if (ReducedEchelonMatrixClass[i, i] == 0) // if diagonal entry is zero,
{
for (int j = i + 1; j < ReducedEchelonMatrixClass.Rows; j++)
{
if (ReducedEchelonMatrixClass[j, i] != 0) //check if some below entry is non-zero
{
ReducedEchelonMatrixClass.InterchangeRow(i, j); // then interchange the two rows
}
}
}
if (ReducedEchelonMatrixClass[i, i] == 0) // if not found any non-zero diagonal entry
{
continue; // increment i;
}
if (ReducedEchelonMatrixClass[i, i] != 1) // if diagonal entry is not 1 ,
{
for (int j = i + 1; j < ReducedEchelonMatrixClass.Rows; j++)
{
if (ReducedEchelonMatrixClass[j, i] == 1) //check if some below entry is 1
{
ReducedEchelonMatrixClass.InterchangeRow(i, j); // then interchange the two rows
}
}
}
ReducedEchelonMatrixClass.MultiplyRow(i, Fraction.Inverse(ReducedEchelonMatrixClass[i, i]));
for (int j = i + 1; j < ReducedEchelonMatrixClass.Rows; j++)
{
ReducedEchelonMatrixClass.AddRow(j, i, -ReducedEchelonMatrixClass[j, i]);
}
for (int j = i - 1; j >= 0; j--)
{
ReducedEchelonMatrixClass.AddRow(j, i, -ReducedEchelonMatrixClass[j, i]);
}
}
return(ReducedEchelonMatrixClass);
} catch (Exception) {
throw new MatrixClassException("MatrixClass can not be reduced to Echelon form");
}
}
private static MatrixClass Add(MatrixClass MatrixClass1, MatrixClass MatrixClass2)
{
if (MatrixClass1.Rows != MatrixClass2.Rows || MatrixClass1.Cols != MatrixClass2.Cols)
{
throw new MatrixClassException("Operation not possible");
}
MatrixClass result = new MatrixClass(MatrixClass1.Rows, MatrixClass1.Cols);
for (int i = 0; i < result.Rows; i++)
{
for (int j = 0; j < result.Cols; j++)
{
result[i, j] = MatrixClass1[i, j] + MatrixClass2[i, j];
}
}
return(result);
}
/// <summary>
/// The helper function for the above Determinent() method
/// it calls itself recursively and computes determinent using minors
/// </summary>
private Fraction Determinent(MatrixClass MatrixClass)
{
Fraction det = new Fraction(0);
if (MatrixClass.Rows != MatrixClass.Cols)
{
throw new MatrixClassException("Determinent of a non-square MatrixClass doesn't exist");
}
if (MatrixClass.Rows == 1)
{
return(MatrixClass[0, 0]);
}
for (int j = 0; j < MatrixClass.Cols; j++)
{
det += (MatrixClass[0, j] * Determinent(MatrixClass.Minor(MatrixClass, 0, j)) * (int)System.Math.Pow(-1, 0 + j));
}
return(det);
}
/// <summary>
/// The function returns the inverse of the current MatrixClass using Reduced Echelon Form method
/// The function is very fast and efficient but may raise overflow exceptions in some cases.
/// In such cases use the Inverse() method which computes inverse in the traditional way(using adjoint).
/// </summary>
public MatrixClass InverseFast()
{
if (this.DeterminentFast() == 0)
{
throw new MatrixClassException("Inverse of a singular MatrixClass is not possible");
}
try {
MatrixClass IdentityMatrixClass = MatrixClass.IdentityMatrixClass(this.Rows, this.Cols);
MatrixClass ReducedEchelonMatrixClass = this.Duplicate();
for (int i = 0; i < this.Rows; i++)
{
if (ReducedEchelonMatrixClass[i, i] == 0) // if diagonal entry is zero,
{
for (int j = i + 1; j < ReducedEchelonMatrixClass.Rows; j++)
{
if (ReducedEchelonMatrixClass[j, i] != 0) //check if some below entry is non-zero
{
ReducedEchelonMatrixClass.InterchangeRow(i, j); // then interchange the two rows
IdentityMatrixClass.InterchangeRow(i, j); // then interchange the two rows
}
}
}
IdentityMatrixClass.MultiplyRow(i, Fraction.Inverse(ReducedEchelonMatrixClass[i, i]));
ReducedEchelonMatrixClass.MultiplyRow(i, Fraction.Inverse(ReducedEchelonMatrixClass[i, i]));
for (int j = i + 1; j < ReducedEchelonMatrixClass.Rows; j++)
{
IdentityMatrixClass.AddRow(j, i, -ReducedEchelonMatrixClass[j, i]);
ReducedEchelonMatrixClass.AddRow(j, i, -ReducedEchelonMatrixClass[j, i]);
}
for (int j = i - 1; j >= 0; j--)
{
IdentityMatrixClass.AddRow(j, i, -ReducedEchelonMatrixClass[j, i]);
ReducedEchelonMatrixClass.AddRow(j, i, -ReducedEchelonMatrixClass[j, i]);
}
}
return(IdentityMatrixClass);
} catch (Exception) {
throw new MatrixClassException("Inverse of the given MatrixClass could not be calculated");
}
}
/// <summary>
/// The function returns the determinent of the current MatrixClass object as Fraction
/// It computes the determinent by reducing the MatrixClass to reduced echelon form using row operations
/// The function is very fast and efficient but may raise overflow exceptions in some cases.
/// In such cases use the Determinent() function which computes determinent in the traditional
/// manner(by using minors)
/// </summary>
public Fraction DeterminentFast()
{
if (this.Rows != this.Cols)
{
throw new MatrixClassException("Determinent of a non-square MatrixClass doesn't exist");
}
Fraction det = new Fraction(1);
try {
MatrixClass ReducedEchelonMatrixClass = this.Duplicate();
for (int i = 0; i < this.Rows; i++)
{
if (ReducedEchelonMatrixClass[i, i] == 0) // if diagonal entry is zero,
{
for (int j = i + 1; j < ReducedEchelonMatrixClass.Rows; j++)
{
if (ReducedEchelonMatrixClass[j, i] != 0) //check if some below entry is non-zero
{
ReducedEchelonMatrixClass.InterchangeRow(i, j); // then interchange the two rows
det *= -1; //interchanging two rows negates the determinent
}
}
}
det *= ReducedEchelonMatrixClass[i, i];
ReducedEchelonMatrixClass.MultiplyRow(i, Fraction.Inverse(ReducedEchelonMatrixClass[i, i]));
for (int j = i + 1; j < ReducedEchelonMatrixClass.Rows; j++)
{
ReducedEchelonMatrixClass.AddRow(j, i, -ReducedEchelonMatrixClass[j, i]);
}
for (int j = i - 1; j >= 0; j--)
{
ReducedEchelonMatrixClass.AddRow(j, i, -ReducedEchelonMatrixClass[j, i]);
}
}
return(det);
} catch (Exception) {
throw new MatrixClassException("Determinent of the given MatrixClass could not be calculated");
}
}
private static MatrixClass Multiply(MatrixClass MatrixClass1, MatrixClass MatrixClass2)
{
if (MatrixClass1.Cols != MatrixClass2.Rows)
{
throw new MatrixClassException("Operation not possible");
}
MatrixClass result = MatrixClass.NullMatrixClass(MatrixClass1.Rows, MatrixClass2.Cols);
for (int i = 0; i < result.Rows; i++)
{
for (int j = 0; j < result.Cols; j++)
{
for (int k = 0; k < MatrixClass1.Cols; k++)
{
result[i, j] += MatrixClass1[i, k] * MatrixClass2[k, j];
}
}
}
return(result);
}
/// <summary>
/// The function returns a Scalar MatrixClass of dimension ( Row x Col ) and scalar K
/// </summary>
public static MatrixClass ScalarMatrixClass(int iRows, int iCols, int K)
{
Fraction zero = new Fraction(0);
Fraction scalar = new Fraction(K);
MatrixClass MatrixClass = new MatrixClass(iRows, iCols);
for (int i = 0; i < iRows; i++)
{
for (int j = 0; j < iCols; j++)
{
if (i == j)
{
MatrixClass[i, j] = scalar;
}
else
{
MatrixClass[i, j] = zero;
}
}
}
return(MatrixClass);
}
/// <summary>
/// Internal Fucntions for the above operators
/// </summary>
private static MatrixClass Negate(MatrixClass MatrixClass)
{
return(MatrixClass.Multiply(MatrixClass, -1));
}
public static MatrixClass operator /(MatrixClass MatrixClass1, Fraction frac)
{
return(MatrixClass.Multiply(MatrixClass1, Fraction.Inverse(frac)));
}
public static MatrixClass operator /(MatrixClass MatrixClass1, double dbl)
{
return(MatrixClass.Multiply(MatrixClass1, Fraction.Inverse(Fraction.ToFraction(dbl))));
}
public static MatrixClass operator /(MatrixClass MatrixClass1, int iNo)
{
return(MatrixClass.Multiply(MatrixClass1, Fraction.Inverse(new Fraction(iNo))));
}
public static MatrixClass operator *(Fraction frac, MatrixClass MatrixClass1)
{
return(MatrixClass.Multiply(MatrixClass1, frac));
}
public static MatrixClass operator *(double dbl, MatrixClass MatrixClass1)
{
return(MatrixClass.Multiply(MatrixClass1, Fraction.ToFraction(dbl)));
}
public static MatrixClass operator *(int iNo, MatrixClass MatrixClass1)
{
return(MatrixClass.Multiply(MatrixClass1, iNo));
}
/// <summary>
/// Operators for the MatrixClass object
/// includes -(unary), and binary opertors such as +,-,*,/
/// </summary>
public static MatrixClass operator -(MatrixClass MatrixClass)
{
return(MatrixClass.Negate(MatrixClass));
}
public static MatrixClass operator -(MatrixClass MatrixClass1, MatrixClass MatrixClass2)
{
return(MatrixClass.Add(MatrixClass1, -MatrixClass2));
}
public static MatrixClass operator *(MatrixClass MatrixClass1, MatrixClass MatrixClass2)
{
return(MatrixClass.Multiply(MatrixClass1, MatrixClass2));
}