public void CalculatingLowerUpperMatrices()
{
MatrixMB mat = new MatrixMB(2, 2);
mat.Data[0][0] = 4;
mat.Data[0][1] = 7;
mat.Data[1][0] = 2;
mat.Data[1][1] = 6;
mat.MakeLU();
Assert.AreEqual(4, mat.Data[0][0]);
Assert.AreEqual(7, mat.Data[0][1]);
Assert.AreEqual(2, mat.Data[1][0]);
Assert.AreEqual(6, mat.Data[1][1]);
var L = mat.L;
Assert.AreEqual(1, L.Data[0][0]);
Assert.AreEqual(0, L.Data[0][1]);
Assert.AreEqual(0.5, L.Data[1][0]);
Assert.AreEqual(1, L.Data[1][1]);
var U = mat.U;
Assert.AreEqual(4, U.Data[0][0]);
Assert.AreEqual(7, U.Data[0][1]);
Assert.AreEqual(0, U.Data[1][0]);
Assert.AreEqual(2.5, U.Data[1][1]);
}
/// <summary>
/// Function solves Ax = b for A as an upper triangular matrix
/// </summary>
/// <param name="A">MatrixMB - upper triangular matrix</param>
/// <param name="b">MatrixMB</param>
/// <returns>MatrixMB</returns>
public static MatrixMB SubsBack(MatrixMB A, MatrixMB b)
{
if (A.L == null)
{
A.MakeLU();
}
int n = A.Rows;
MatrixMB x = new MatrixMB(n, 1);
for (int i = n - 1; i > -1; i--)
{
x[i, 0] = b[i, 0];
for (int j = n - 1; j > i; j--)
{
x[i, 0] -= A[i, j] * x[j, 0];
}
x[i, 0] = x[i, 0] / A[i, i];
}
return(x);
}
/// <summary>
/// Function solves Ax = b for A as a lower triangular matrix
/// </summary>
/// <param name="A">MatrixMB - lower triangular matrix</param>
/// <param name="b">MatrixMB</param>
/// <returns>MatrixMB</returns>
public static MatrixMB SubsForth(MatrixMB A, MatrixMB b)
{
if (A.L == null)
{
A.MakeLU();
}
int n = A.Rows;
MatrixMB x = new MatrixMB(n, 1);
for (int i = 0; i < n; i++)
{
x[i, 0] = b[i, 0];
for (int j = 0; j < i; j++)
{
x[i, 0] -= A[i, j] * x[j, 0];
}
x[i, 0] = x[i, 0] / A[i, i];
}
return(x);
}
/// <summary>
/// Function solves Ax = b for A as a lower triangular matrix
/// </summary>
/// <param name="A">MatrixMB - lower triangular matrix</param>
/// <param name="b">MatrixMB</param>
/// <returns>MatrixMB</returns>
public static MatrixMB SubsForth(MatrixMB A, MatrixMB b)
{
if (A.L == null) A.MakeLU();
int n = A.Rows;
MatrixMB x = new MatrixMB(n, 1);
for (int i = 0; i < n; i++)
{
x[i, 0] = b[i, 0];
for (int j = 0; j < i; j++) x[i, 0] -= A[i, j] * x[j, 0];
x[i, 0] = x[i, 0] / A[i, i];
}
return x;
}
/// <summary>
/// Function solves Ax = b for A as an upper triangular matrix
/// </summary>
/// <param name="A">MatrixMB - upper triangular matrix</param>
/// <param name="b">MatrixMB</param>
/// <returns>MatrixMB</returns>
public static MatrixMB SubsBack(MatrixMB A, MatrixMB b)
{
if (A.L == null) A.MakeLU();
int n = A.Rows;
MatrixMB x = new MatrixMB(n, 1);
for (int i = n - 1; i > -1; i--)
{
x[i, 0] = b[i, 0];
for (int j = n - 1; j > i; j--) x[i, 0] -= A[i, j] * x[j, 0];
x[i, 0] = x[i, 0] / A[i, i];
}
return x;
}