public qr_decomp_GS(matrix A)
{
int n = A.size1;
int m = A.size2;
q = A.copy();
r = new matrix(m, m);
vector qi = new vector(n);
vector qj = new vector(n);
for (int i = 0; i < m; i++)
{
qi = q.col_toVector(i);
r[i, i] = Sqrt(qi.dot(qi));
for (int k = 0; k < n; k++)
{
q[k, i] = q[k, i] / r[i, i];
}
for (int j = i + 1; j < m; j++)
{
qi = q.col_toVector(i);
qj = q.col_toVector(j);
r[i, j] = qi.dot(qj);
for (int k = 0; k < n; k++)
{
q[k, j] = q[k, j] - q[k, i] * r[i, j];
}
}
}
}
public matrix inverse()
{
matrix I = new matrix(q.size2, q.size2);
I.set_identity();
matrix B = new matrix(q.size1, q.size2);
for (int i = 0; i < q.size2; i++)
{
vector ei = I.col_toVector(i);
vector x = solve(ei);
for (int j = 0; j < B.size1; j++)
{
B[j, i] = x[j];
}
}
return(B);
}
static int Main()
{
WriteLine("\n Problem A1: Test Jacobi functionality \n");
var rand = new System.Random();
int n = rand.Next(1, 15);
matrix A = rand_sym_mat(n);
WriteLine("Symmetric random test matrix A");
A.print("A = ");
matrix B = A.copy();
jcbi_cycl test = new jcbi_cycl(B);
WriteLine("\nJacobi diagonalisation A=V*D*V.T");
matrix V = test.V;
matrix D = test.D;
V.print("\nV = ");
D.print("\nD = ");
((V.T * A) * V - D).print("\n(V.T*A)*V - D =", "{0,10:f6}");
WriteLine("\n\n Problem A2: Quantum Particle in box \n");
n = 99;
double s = 1.0 / (n + 1);
matrix H = new matrix(n, n);
for (int i = 0; i < n - 1; i++)
{
H[i, i] = -2;
H[i, i + 1] = 1;
H[i + 1, i] = 1;
}
H[n - 1, n - 1] = -2;
H = H * (-1 / s / s);
matrix H1 = H.copy();
jcbi_cycl h_jac = new jcbi_cycl(H1);
matrix Vh = h_jac.V;
matrix Dh = h_jac.D;
vector eigvals = h_jac.Eigvals;
//H.print("\n H = ");
//WriteLine("\n Jacobi diagonalisation H=V*D*V.T");
//Vh.print("\n V = ");
//Dh.print("\n D = ");
WriteLine("\n");
// Calculate analytic energies and compare
WriteLine("Compare first {0} eigvals with analytic energies", n / 3);
for (int i = 0; i < n / 3; i++)
{
double exact = PI * PI * (i + 1) * (i + 1);
double calculated = eigvals[i];
WriteLine("{0} {1:f6} {2:f6}", i, calculated, exact);
}
var datw = new System.IO.StreamWriter("out.fun.txt");
// Write analytic function to file
//double a = 0.149;
//double a=0.141;
double a = Sqrt(2 * s);
int q = 1;
Func <double, double> psiev = (x) => a *Sin(q *x *PI);
Func <double, double> psiod = (x) => a *Sin(q *x *PI - PI);
for (int k = 0; k < 4; k++)
{
vector psinum = Vh.col_toVector(k);
Func <double, double> psi = pick_analytic_func(a, n, q, psinum);
datw.WriteLine($"{0} {0}");
for (double x = 0.005; x < 1; x += 0.005)
{
datw.WriteLine($"{x} {psi(x)/a}");
/* if (k % 2 == 0)
* {
* datw.WriteLine($"{x} {psi(x)}");
* }
* else
* {
* datw.WriteLine($"{x} {psiod(x)}");
* }
*/ }
datw.WriteLine($"{1} {0}\n\n");
q++;
}
// Write function plot data to file
for (int k = 0; k < 4; k++)
{
datw.WriteLine($"{0} {0}");
for (int i = 0; i < n; i++)
{
datw.WriteLine($"{(i+1.0)/(n+1)} {Vh[i, k]/a}");
}
datw.WriteLine($"{1} {0} \n\n");
}
datw.Close();
return(0);
}