private static Fraction Multiply(Fraction frac1, Fraction frac2)
{
int iNumerator=frac1.Numerator*frac2.Numerator;
int iDenominator=frac1.Denominator*frac2.Denominator;
return ( new Fraction(iNumerator, iDenominator) );
}
/// <summary>
/// internal function for negation
/// </summary>
private static Fraction Negate(Fraction frac1)
{
int iNumerator=-frac1.Numerator;
int iDenominator=frac1.Denominator;
return ( new Fraction(iNumerator, iDenominator) );
}
/// <summary>
/// The function reduces(simplifies) a Fraction object by dividing both its numerator
/// and denominator by their GCD
/// </summary>
public static void ReduceFraction(Fraction frac)
{
try
{
if (frac.Numerator==0)
{
frac.Denominator=1;
return;
}
int iGCD=GCD(frac.Numerator, frac.Denominator);
frac.Numerator/=iGCD;
frac.Denominator/=iGCD;
if ( frac.Denominator<0 ) // if -ve sign in denominator
{
//pass -ve sign to numerator
frac.Numerator*=-1;
frac.Denominator*=-1;
}
} // end try
catch(Exception exp)
{
throw new FractionException("Cannot reduce Fraction: " + exp.Message);
}
}
/// <summary>
/// The function replicates current Fraction object
/// </summary>
public Fraction Duplicate()
{
Fraction frac=new Fraction();
frac.Numerator=Numerator;
frac.Denominator=Denominator;
return frac;
}
/// <summary>
/// The function adds two rows for current matrix object
/// It performs the following calculation:
/// iTargetRow = iTargetRow + iMultiple*iSecondRow
/// </summary>
public void AddRow(int iTargetRow, int iSecondRow, Fraction iMultiple)
{
for (int j=0;j<this.Cols;j++)
this[iTargetRow,j]+=(this[iSecondRow,j]*iMultiple);
}
/// <summary>
/// The function returns the inverse of a Fraction object
/// </summary>
public static Fraction Inverse(Fraction frac1)
{
if (frac1.Numerator==0)
throw new FractionException("Operation not possible (Denominator cannot be assigned a ZERO Value)");
int iNumerator=frac1.Denominator;
int iDenominator=frac1.Numerator;
return ( new Fraction(iNumerator, iDenominator));
}
/// <summary>
/// The function takes a Fraction object and returns its value as double
/// </summary>
public static double ConvertToDouble(Fraction frac)
{
return ( (double)frac.Numerator/frac.Denominator );
}
/// <summary>
/// The function returns the determinent of a Matrix object as Fraction
/// </summary>
public static Fraction Determinent(Matrix matrix)
{
Fraction det=new Fraction(0);
if (matrix.Rows!=matrix.Cols)
throw new MatrixException("Determinent of a non-square matrix doesn't exist");
if (matrix.Rows==1)
return matrix[0,0];
for (int j=0;j<matrix.Cols;j++)
det+=(matrix[0,j]*Determinent(Matrix.Minor(matrix, 0,j))*(int)System.Math.Pow(-1,0+j));
return det;
}
public static void EquationSolver()
{
Console.Write("Enter no. of variables: ");
int iVarNo=Convert.ToInt32( Console.ReadLine() );
string str;
Matrix mat=new Matrix(iVarNo,iVarNo+1);
Console.Write("\nEnter value of coefficents and constants (can be an integer(e.g 3), a floating point no(e.g. 12.25), or a fraction(e.g. 15/19)");
int i,cnt;
for (i=0;i<iVarNo+1;i++)
{
cnt=1;
for (int k=0;k<i;k++)
{
Console.Write("\n"+"Equation "+(k+1)+": ");
for (int nn=0;nn<iVarNo+1;nn++)
{
if (nn>0 && nn<iVarNo)
Console.Write(" + ");
if (nn<iVarNo)
Console.Write("X"+(nn+1)+"*("+mat[k,nn].ConvertToString()+")");
else
Console.Write(" = "+mat[k,nn].ConvertToString() );
}
}
Console.Write("\n\n");
if (i==iVarNo) continue;
for(int j=0;j<iVarNo+1;j++,cnt++)
{
if (j>0 && j<iVarNo)
Console.Write("+");
if (j<iVarNo)
Console.Write("X"+cnt+"*");
else
Console.Write("=");
str=Console.ReadLine();
if ( str.Length==0 )
str="0";
mat[i,j]=new Fraction(str);
}
}
Console.WriteLine( "\naugmented matrix:\n"+ mat.ConvertToString() );
Matrix ech=mat.EchelonForm();
Console.WriteLine("\nechelon form:\n"+ech.ConvertToString());
ech=mat.ReducedEchelonForm();
for (i=0;i<iVarNo;i++)
if ( ech[i,i]==0 ) // if not unique solution
{
Console.WriteLine("The given system of Equation does not produce any unique solution");
return;
}
Console.Write("\nSolution for the given system:\n");
for (i=0;i<iVarNo;i++)
Console.Write("X"+(i+1)+"="+ech[i,iVarNo].ConvertToString()+"\t");
}
public static void MatrixDemo()
{
Console.WriteLine("Enter no. of Rows: ");
int iRows=Convert.ToInt32(Console.ReadLine());
Console.WriteLine("Enter no. of Cols: ");
int iCols=Convert.ToInt32(Console.ReadLine());
Matrix m1=new Matrix(iRows,iCols);
Matrix m2=new Matrix(iRows,iCols);
System.Random rnd=new System.Random();
for ( int i=0;i<iRows;i++)
{
for ( int j=0;j<iCols;j++)
{
m1[i,j]=new Fraction( Convert.ToString( (rnd.Next()%10)-5 ) );
// m1[i,j]=new Fraction(Console.ReadLine());
m2[i,j]=new Fraction( Convert.ToString( (rnd.Next()%5.5)-2 ) );
}
}
Console.WriteLine("\n\nLet the two matrices be:");
Console.WriteLine( "\nm1\n"+ m1.ConvertToString() );
Console.WriteLine( "\nm2\n"+ m2.ConvertToString() );
Console.ReadLine();
Console.WriteLine("\nm1+m2=\n"+ (m1+m2).ConvertToString());
Console.WriteLine("\nm1*m2=\n");
Console.WriteLine( (m1*m2).ConvertToString());
Console.ReadLine();
Console.WriteLine( "\nEchelon Form for m1:\n"+ m1.EchelonForm().ConvertToString() );
Console.WriteLine( "\nReduced Echelon Form for m1:\n"+ m1.ReducedEchelonForm().ConvertToString() );
Console.ReadLine();
Console.WriteLine("\nDeterminent of m1="+ m1.Determinent().ConvertToString());
Console.WriteLine("\nTranspose m1:\n"+ m1.Transpose().ConvertToString());
Console.WriteLine("\nInverse of m1:\n "+ m1.Inverse().ConvertToString() );
}
private void SetElement(int iRow, int iCol, Fraction value)
{
if ( iRow<0 || iRow>Rows-1 || iCol<0 || iCol>Cols-1 )
throw new MatrixException("Invalid index specified");
m_iElement[iRow,iCol]=value.Duplicate();
}
private static Matrix Multiply(Matrix matrix, Fraction frac)
{
Matrix result=new Matrix(matrix.Rows,matrix.Cols);
for (int i=0;i<matrix.Rows;i++)
for (int j=0;j<matrix.Cols;j++)
result[i,j]=matrix[i,j]*frac;
return result;
}
/// <summary>
/// The function multiplies the given row of the current matrix object by a Fraction
/// </summary>
public void MultiplyRow(int iRow, Fraction frac)
{
for (int j=0;j<this.Cols;j++)
{
this[iRow,j]*=frac;
Fraction.ReduceFraction(this[iRow,j]);
}
}
/// <summary>
/// Constructors
/// </summary>
public Matrix(Fraction[,] elements)
{
m_iElement=elements;
m_iRows=elements.GetLength(0);
m_iCols=elements.GetLength(1);
}
/// <summary>
/// The function takes a floating point number as an argument
/// and returns its corresponding reduced fraction
/// </summary>
public static Fraction ConvertToFraction(double dValue)
{
try
{
Fraction frac;
if (dValue>2147483647 && dValue<1.0/2147483647)
throw new FractionException("Conversion not possible");
if (dValue%1==0) // if whole number
{
frac=new Fraction( (int) dValue );
}
else
{
double dTemp=dValue;
int iMultiple=1;
string strTemp=dValue.ToString();
int i=0;
while ( strTemp[i]!='.' )
i++;
int iDigitsAfterDecimal=strTemp.Length-i-1;
while ( dTemp*10<2147483647 && iMultiple*10<2147483647 && iDigitsAfterDecimal>0 )
{
dTemp*=10;
iMultiple*=10;
iDigitsAfterDecimal--;
}
frac=new Fraction( (int)Math.Round(dTemp) , iMultiple );
}
return frac;
}
catch(Exception)
{
throw new FractionException("Conversion not possible");
}
}
public Matrix(int[,] elements)
{
m_iRows=elements.GetLength(0);
m_iCols=elements.GetLength(1);;
m_iElement=new Fraction[m_iRows,m_iCols];
for(int i=0;i<elements.GetLength(0);i++)
{
for(int j=0;j<elements.GetLength(1);j++)
{
this[i,j]=new Fraction( elements[i,j] );
}
}
}
/// <summary>
/// The function takes a Fraction object and returns it as a string
/// </summary>
public static string ConvertToString(Fraction frac1)
{
string str;
if ( frac1.Denominator==1 )
str=frac1.Numerator.ToString();
else
str=frac1.Numerator + "/" + frac1.Denominator;
return str;
}
/// <summary>
/// The function returns a Null Matrix of dimension ( Row x Col )
/// </summary>
public static Matrix NullMatrix(int iRows, int iCols)
{
Fraction temp=new Fraction(0);
Matrix matrix=new Matrix(iRows,iCols);
for (int i=0;i<iRows;i++)
for (int j=0;j<iCols;j++)
matrix[i,j]=temp;
return matrix;
}
/// <summary>
/// The function returns a Scalar Matrix of dimension ( Row x Col ) and scalar K
/// </summary>
public static Matrix ScalarMatrix(int iRows, int iCols, int K)
{
Fraction zero=new Fraction(0);
Fraction scalar=new Fraction(K);
Matrix matrix=new Matrix(iRows,iCols);
for (int i=0;i<iRows;i++)
for (int j=0;j<iCols;j++)
{
if (i==j)
matrix[i,j]=scalar;
else
matrix[i,j]=zero;
}
return matrix;
}
