// Function solves Ax = b for A as a lower triangular matrix
public static Matrix4 SubsForth(Matrix4 A, Matrix4 b)
{
if (A.L == null) A.MakeLU();
int n = A.rows;
Matrix4 x = new Matrix4(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;
}
// Function solves Ax = b for A as an upper triangular matrix
public static Matrix4 SubsBack(Matrix4 A, Matrix4 b)
{
if (A.L == null) A.MakeLU();
int n = A.rows;
Matrix4 x = new Matrix4(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;
}