/// <summary>
/// The function returns the reduced echelon form of a given matrix
/// </summary>
public static MATRIX ReducedEchelonForm(MATRIX matrix)
{
try
{
MATRIX ReducedEchelonMatrix = matrix.Duplicate();
for (int i = 0; i < matrix.Rows; i++)
{
if (ReducedEchelonMatrix[i, i] == 0) // if diagonal entry is zero,
{
for (int j = i + 1; j < ReducedEchelonMatrix.Rows; j++)
{
if (ReducedEchelonMatrix[j, i] != 0) //check if some below entry is non-zero
{
ReducedEchelonMatrix.InterchangeRow(i, j); // then interchange the two rows
}
}
}
if (ReducedEchelonMatrix[i, i] == 0) // if not found any non-zero diagonal entry
{
continue; // increment i;
}
if (ReducedEchelonMatrix[i, i] != 1) // if diagonal entry is not 1 ,
{
for (int j = i + 1; j < ReducedEchelonMatrix.Rows; j++)
{
if (ReducedEchelonMatrix[j, i] == 1) //check if some below entry is 1
{
ReducedEchelonMatrix.InterchangeRow(i, j); // then interchange the two rows
}
}
}
ReducedEchelonMatrix.MultiplyRow(i, Fraction.Inverse(ReducedEchelonMatrix[i, i]));
for (int j = i + 1; j < ReducedEchelonMatrix.Rows; j++)
{
ReducedEchelonMatrix.AddRow(j, i, -ReducedEchelonMatrix[j, i]);
}
for (int j = i - 1; j >= 0; j--)
{
ReducedEchelonMatrix.AddRow(j, i, -ReducedEchelonMatrix[j, i]);
}
}
return(ReducedEchelonMatrix);
}
catch (Exception)
{
throw new MatrixException("Matrix can not be reduced to Echelon form");
}
}
