/// <summary>
/// AugmentedMatrixCheck Method returning an the solution state of the equation
/// </summary>
/// <returns></returns>
private SolutionState AugmentedMatrixCheck()
{
SolutionState state = SolutionState.Infinite;
Matrix <double> temp = AugmentedMatrix.Copy(AugmentedMatrix.RowCount, AugmentedMatrix.ColumnCount);
for (int i = 0; i < AugmentedMatrix.RowCount; i++)
{
for (int j = i + 1; j < AugmentedMatrix.RowCount; j++)
{
for (int k = i; k < AugmentedMatrix.ColumnCount; k++)
{
AugmentedMatrix[j][k] += ((-temp[j][i] / temp[i][i]) * temp[i][k]);
}
}
temp = AugmentedMatrix.Copy(temp.RowCount, temp.ColumnCount);
}
for (int i = 0; i < temp.ColumnCount; i++)
{
if (temp[temp.RowCount - 1][temp.ColumnCount - 1] != 0)
{
state = SolutionState.NoSolution;
}
}
return(state);
}
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);
}
public void AugmentedReducedRowEchelonFormTest()
{
var A = new Matrix(new double[, ] {
{ 1, 2, 3 }, { 0, 1, 4 }, { 5, 6, 0 }
});
var I = A.GetIdentity();
var aug = new AugmentedMatrix(new Matrix[] { A, I });
var augGE = aug.ReducedRowEchelonForm();
var identity = new Matrix(new double[, ] {
{ 1, 0, 0 }, { 0, 1, 0 }, { 0, 0, 1 }
});
var inverse = new Matrix(new double[, ] {
{ -24, 18, 5 }, { 20, -15, -4 }, { -5, 4, 1 }
});
Assert.That(augGE[0], Is.EqualTo(identity));
Assert.That(augGE[1], Is.EqualTo(inverse));
var B = new Matrix(new double[, ] {
{ 1, 2, 3, 6 }, { 0, 1, 4, 8 }, { 5, 6, 0, 9 }, { 9, 4, 7, 3 }
});
I = new Matrix(4, 4).GetIdentity();
var aug2 = new AugmentedMatrix(new Matrix[] { B, I });
var augRref2 = aug2.ReducedRowEchelonForm();
var identity2 = new Matrix(4, 4).GetIdentity();
var inverse2 =
new Matrix(
new double[, ]
{
{ -69.0 / 67.0, 36.0 / 67.0, 11.0 / 67.0, 9.0 / 67.0 },
{ 544.0 / 335.0, -69.0 / 67, -44.0 / 335.0, -36.0 / 335.0 },
{ 206.0 / 335.0, -18.0 / 67.0, -61.0 / 335.0, 11.0 / 335.0 },
{ -171.0 / 335.0, 26.0 / 67.0, 36.0 / 335.0, -1.0 / 335.0 }
});
Assert.That(augRref2[0], Is.EqualTo(identity2));
Assert.That(augRref2[1], Is.EqualTo(inverse2));
}
public void Gaussian()
{
for (int i = 0; i < M; i++)
{
// get the index of the leading variable
var j = 0;
var r = AugmentedMatrix.GetRow(i);
while (r[j].Equals(0))
{
j++;
}
var source = AugmentedMatrix[i, j];
// check if the leading var of the row is one
if (!source.Equals(1))
{
// if not, factor the row by itself with a factor of 1 / leading var
FactorRow(i, i, source);
}
// reassign source incase it changed, we should now have a leading factor of 1
source = AugmentedMatrix[i, j];
var clean = CleanColumn(AugmentedMatrix, i, j);
if (!clean)
{
for (int p = i + 1; p < M; p++)
{
if (!AugmentedMatrix[p, j].Equals(0))
{
var target = AugmentedMatrix[p, j];
var factor = source / target;
FactorRow(i, p, factor);
}
}
}
}
}
