public SquareMatrix Inverse()
{
var matrix = Augment(Identity(Size));
matrix.MakeRowEchelon();
var squareMatrix = new SquareMatrix(Size);
var squareMatrix2 = new SquareMatrix(Size);
for (var i = 0; i < Size; i++)
{
squareMatrix.SetColumn(i, matrix.GetColumn(i));
squareMatrix2.SetColumn(i, matrix.GetColumn(i + Size));
}
for (var j = 0; j < squareMatrix.Rows; j++)
{
if (squareMatrix.IsRowZero(j))
{
throw new MatrixException("Matrix is singular");
}
}
for (var k = Size - 1; k > 0; k--)
{
for (var l = k - 1; l >= 0; l--)
{
var scalar = -squareMatrix[l, k];
squareMatrix.AddRowTimesScalar(l, k, scalar);
squareMatrix2.AddRowTimesScalar(l, k, scalar);
}
}
return squareMatrix2;
}
public void LUDecomposition(out SquareMatrix l, out SquareMatrix u)
{
l = new SquareMatrix(Size);
u = new SquareMatrix(Size);
if (Math.Abs(base[0, 0] - 0.0) < 0.0001)
{
throw new MatrixException("Unable to decompose matrix");
}
l.SetColumn(0, GetColumn(0));
u.SetRow(0, GetRow(0));
u.MultiplyRow(0, 1.0/base[0, 0]);
for (var i = 1; i < Size; i++)
{
var array = new Vector[Size];
var array2 = new Vector[Size];
for (var j = 1; j < Size; j++)
{
array[j] = new Vector(i);
array2[j] = new Vector(i);
var row = l.GetRow(j);
var column = u.GetColumn(j);
for (var k = 0; k < i; k++)
{
array[j][k] = row[k];
array2[j][k] = column[k];
}
}
for (var m = i; m < Size; m++)
{
l[m, i] = base[m, i] - Vector.Dot(array[m], array2[i]);
if (m == i)
{
u[i, m] = 1.0;
}
else
{
if (Math.Abs(l[i, i] - 0.0) < 0.0001)
{
throw new MatrixException("Unable to decompose matrix");
}
u[i, m] = (base[i, m] - Vector.Dot(array[i], array2[m]))/l[i, i];
}
}
}
}