public static VEC LU_Solve(MAT A1, VEC b1)
{
MAT A = new MAT(A1);
VEC b = new VEC(b1);
int n = A.dim();
A = luFact(A);
MAT L = new MAT(n);
MAT U = new MAT(n);
for (int i = 1; i < n; i++)
{
for (int j = 0; j < i; j++)
{
L[i][j] = A[i][j];
}
}
for (int i = 0; i < n; i++)
{
L[i][i] = 1;
}
for (int i = 0; i < n; i++)
{
for (int j = i; j < n; j++)
{
U[i][j] = A[i][j];
}
}
VEC y = fwdSubs(L, b);
VEC x = bckSubs(U, y);
return(x);
}
public MAT(MAT m1)
{
n = m1.dim();
va = new VEC[n];
for (int i = 0; i < n; i++)
{
va[i] = new VEC(m1[i]);
}
}
public static MAT InverseM3(MAT A)
{
MAT I = unit(3);
int n = A.dim();
A = numericalFunctions.luFact(A);
MAT L = new MAT(n);
MAT U = new MAT(n);
for (int i = 1; i < n; i++)
{
for (int j = 0; j < i; j++)
{
L[i][j] = A[i][j];
}
}
for (int i = 0; i < n; i++)
{
L[i][i] = 1;
}
for (int i = 0; i < n; i++)
{
for (int j = i; j < n; j++)
{
U[i][j] = A[i][j];
}
}
MAT yT = new MAT(3);
for (int i = 0; i < 3; i++)
{
yT[i] = numericalFunctions.LU_Solve(L, I[i]);
}
MAT y = yT.tpose();
MAT xT = new MAT(3);
for (int i = 0; i < 3; i++)
{
xT[i] = numericalFunctions.LU_Solve(U, yT[i]);
}
return(xT.tpose());
}
public static MAT luFact(MAT m1)
{
int n = m1.dim();
for (int i = 0; i < n; i++)
{
for (int j = i + 1; j < n; j++)
{
m1[j][i] /= m1[i][i];
}
for (int j = i + 1; j < n; j++)
{
for (int k = i + 1; k < n; k++)
{
m1[j][k] -= m1[j][i] * m1[i][k];
}
}
}
return(m1);
}