//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 RationalNumberRowVector ReplaceRow(int row, RationalNumberRowVector other)
{
//TODO: should they have to be the same size?
RationalNumberRowVector ret = new RationalNumberRowVector(GetRow(row).ToArray <RationalNumber>());
for (int i = 0; i < ColumnSize; i++)
{
Replace(row, i, other.Get(0, i));
}
return(ret);
}
public static void TestAlgebra()
{
RationalNumberMatrix rat1 = new RationalNumberMatrix(2, 2);
rat1.Replace(0, 0, new RationalNumber(3, 4));
rat1.Replace(0, 1, new RationalNumber(4, 3));
rat1.Replace(1, 0, new RationalNumber(2, 5));
rat1.Replace(1, 1, new RationalNumber(1, 7));
RationalNumberColumnVector col1 = new RationalNumberColumnVector(2);
col1.Replace(0, 0, new RationalNumber(1, 1));
col1.Replace(1, 0, new RationalNumber(1, 2));
Console.WriteLine(rat1.ToString());
AugmentedMatrix aug1 = new AugmentedMatrix(rat1, col1);
Console.WriteLine(aug1.ToString());
RationalNumber r1 = new RationalNumber(3, 4);
RationalNumber r2 = new RationalNumber(5, 6);
RationalNumber[] crosses = RationalNumber.CrossMultiply(r1, r2);
foreach (RationalNumber ra in crosses)
{
//Console.WriteLine(ra);
}
//RationalNumberRowVector toRow = aug1.SolveRow(0, 1, 1);
//Console.WriteLine(toRow);
//AugmentedMatrix aug2 = aug1.GaussMatrix();
//Console.WriteLine(aug2);
RationalNumber[] rary1 = { new RationalNumber(9), new RationalNumber(3), new RationalNumber(4) };
RationalNumber[] rary2 = { new RationalNumber(4), new RationalNumber(3), new RationalNumber(4) };
RationalNumber[] rary3 = { new RationalNumber(1), new RationalNumber(1), new RationalNumber(1) };
RationalNumber[] rcol1 = { new RationalNumber(7), new RationalNumber(8), new RationalNumber(3) };
RationalNumberRowVector rowv1 = new RationalNumberRowVector(rary1);
RationalNumberRowVector rowv2 = new RationalNumberRowVector(rary2);
RationalNumberRowVector rowv3 = new RationalNumberRowVector(rary3);
RationalNumberColumnVector colv1 = new RationalNumberColumnVector(rcol1);
RationalNumberMatrix asdf = new RationalNumberMatrix(new RationalNumberRowVector[] { rowv1, rowv2, rowv3 });
AugmentedMatrix aug3 = new AugmentedMatrix(asdf, colv1);
AugmentedMatrix aug3Gauss = aug3.GaussMatrix();
Console.WriteLine(aug3);
Console.WriteLine(aug3Gauss);
}
