/// <summary>
/// Method to perform row reduction on the given row
/// </summary>
/// <param name="row">Row being reduced</param>
/// <param name="factoringRow">helper row that is used to reduce the row</param>
/// <param name="factor">factor needed to reduce the row to upper triangular form</param>
private void RowReduce(int row, int factoringRow, BigFraction factor)
{
for (int column = 0; column < Size; column++)
{
upperMatrix[row, column] = upperMatrix[row, column].Subtract(factor.Multiply(upperMatrix[factoringRow, column]));
}
}
/// <summary>
/// Method to divide two BigFraction objects
/// </summary>
/// <param name="b">BigFraction object being divided from the current object</param>
/// <returns>result of division in its simplest form</returns>
public BigFraction Divide(BigFraction b)
{
/*When you divide a fraction by another fraction we multiply the dividend by the reciprocal of the divisor
* So, we will multiply the numerator of a with denominator of b and denominator of a with numerator of b
*/
BigInteger numeratorB = GetNumerator(b.ToString());
BigInteger denominatorB = GetDenominator(b.ToString());
//Negate the numerator and denominator if numerator is negative
if (numeratorB.Sign == -1)
{
numeratorB = -numeratorB;
denominatorB = -denominatorB;
}
BigInteger finalNumerator = BigInteger.One;
BigInteger finalDenominator = BigInteger.One;
if (numeratorB.IsZero)
{
finalNumerator = BigInteger.Zero;
finalDenominator = BigInteger.One;
}
else
{
finalNumerator = this.numerator * denominatorB;
finalDenominator = this.denominator * numeratorB;
}
BigFraction result = new BigFraction(finalNumerator.ToString() + "/" + finalDenominator.ToString());
return(GetSimplestForm(result));
}
/// <summary>
/// Method to multiply two BigFraction datatypes
/// </summary>
/// <param name="b">BigFraction being multiplied from current BigFraction</param>
/// <returns>result of multiplication in its simplest form</returns>
public BigFraction Multiply(BigFraction b)
{
BigInteger numeratorB = GetNumerator(b.ToString());
BigInteger denominatorB = GetDenominator(b.ToString());
BigInteger finalNumerator = this.numerator * numeratorB;
BigInteger finalDenominator = this.denominator * denominatorB;
BigFraction result = new BigFraction(finalNumerator.ToString() + "/" + finalDenominator.ToString());
return(GetSimplestForm(result));
}
/// <summary>
/// Method to subtract two BigFraction datatypes
/// </summary>
/// <param name="b">BigFraction being subtracted from current BigFraction</param>
/// <returns>result of subtraction in its simplest form</returns>
public BigFraction Subtract(BigFraction b)
{
BigInteger numeratorB = GetNumerator(b.ToString());
BigInteger denominatorB = GetDenominator(b.ToString());
BigInteger lcm = GetLCM(this.denominator, denominatorB);
BigInteger finalNumerator = this.numerator * (lcm / this.denominator) -
numeratorB * (lcm / denominatorB);
BigFraction result = new BigFraction(finalNumerator.ToString() + "/" + lcm.ToString());
return(GetSimplestForm(result));
}
/// <summary>
/// Method to solve the LY=B equation and store the value of Y
/// </summary>
private void SolveY()
{
for (int i = 0; i < Size; i++)
{
BigFraction tempSum = zero;
for (int j = 0; j < Size; j++)
{
tempSum = tempSum.Add(lowerMatrix[i, j].Multiply(yMatrix[j]));
//Console.WriteLine(tempSum);
}
yMatrix[i] = bMatrix[i].Subtract(tempSum);
}
}
/// <summary>
/// Method to get the fraction in its simplest form
/// </summary>
/// <param name="frac"></param>
/// <returns></returns>
private BigFraction GetSimplestForm(BigFraction frac)
{
BigInteger num = GetNumerator(frac.ToString());
BigInteger deno = GetDenominator(frac.ToString());
BigInteger gcf = GetGCF(num, deno);
while (!gcf.IsOne)
{
num = num / gcf;
deno = deno / gcf;
gcf = GetGCF(num, deno);
}
return(new BigFraction(num.ToString() + "/" + deno.ToString()));
}
/// <summary>
/// Method to solve the UX=Y and store the result in X
/// </summary>
private void SolveX()
{
for (int i = Size - 1; i >= 0; i--)
{
BigFraction tempSum = zero;
for (int j = Size - 1; j >= 0; j--)
{
if (i < j)
{
tempSum = tempSum.Add(upperMatrix[i, j].Multiply(xMatrix[j]));
}
}
xMatrix[i] = yMatrix[i].Subtract(tempSum).Divide(upperMatrix[i, i]);
}
}
static void Main(string[] args)
{
BigFraction temp = new BigFraction("2/4");
BigFraction[,] a = { { new BigFraction("1/1"), new BigFraction("2/1"), new BigFraction("2/1") },
{ new BigFraction("3/1"), new BigFraction("-2/1"), new BigFraction("1/1") },
{ new BigFraction("2/1"), new BigFraction("1/1"), new BigFraction("-1/1") } };
BigFraction[] b = { new BigFraction("5/1"), new BigFraction("-6/1"), new BigFraction("-1/1") };
LDUSolver solver = new LDUSolver(a, b, 3);
BigFraction[] answer = solver.GetResult();
for (int i = 0; i < 3; i++)
{
Console.WriteLine(answer[i]);
}
Console.ReadLine();
}
/// <summary>
/// Method to create final lower and upper matrix
/// </summary>
private void FactorizeLU()
{
//perform row-reduction on the matrix to get lowerMatrix
for (int i = 0; i < Size; i++)
{
for (int j = 0; j < Size; j++)
{
if (i > j)
{
BigFraction factor = upperMatrix[i, j].Divide(upperMatrix[j, j]);
//Perform row-reduction on the given row
RowReduce(i, j, factor);
//Populate the lower matrix with the factor
lowerMatrix[i, j] = factor;
}
}
}
}