//row operations: multiply a row by a constant, add a multiple of a row to another, swap rows
public AugmentedMatrix GaussMatrix()
{
if (RowSize == 1 && ColumnSize == 2)
{
return(this.GenerateClone()); //already solved
}
//break down into solving two rows
AugmentedMatrix copy = this.GenerateClone();
for (int k = 0; k < RowSize; k++)
{
for (int i = k + 1; i < RowSize; i++)
{
RationalNumber[] orig = GetRow(i).ToArray <RationalNumber>();
for (int j = 0; j < ColumnSize - 1; j++)
{
RationalNumberRowVector vec = SetToZero(i, k, j);
copy.ReplaceRow(k, vec);
}
}
}
for (int k = RowSize - 1; k >= 0; k--)
{
for (int i = k - 1; i >= 0; i--)
{
RationalNumber[] orig = GetRow(i).ToArray <RationalNumber>();
for (int j = ColumnSize - 2; j >= k; j--)
{
RationalNumberRowVector vec = SetToZero(k, i, j);
copy.ReplaceRow(k, vec);
}
}
}
return(copy);
}
public AugmentedMatrix SwapRows(int row1, int row2)
{
AugmentedMatrix ret = GenerateClone();
RationalNumber[] ary1 = GetRow(row1).ToArray <RationalNumber>();
RationalNumber[] ary2 = GetRow(row2).ToArray <RationalNumber>();
for (int i = 0; i < ary1.Length; i++)
{
ret.Replace(row1, i, ary2[i]);
ret.Replace(row2, i, ary1[i]);
}
return(ret);
}