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