static void B2()
{
WriteLine("\n Problem B2\n");
int n = 8;
matrix A = rand_sym_mat(n);
matrix B = A.copy();
WriteLine("Random symmetric matrix A with size {0}", n);
WriteLine("Perform eigenvalue by eigenvalue calculation for first 4 values");
int evalnum = 4;
bool val_by_val = true;
jcbi_cycl test_vbv = new jcbi_cycl(B, val_by_val, evalnum);
Write("Found eigenvalues = ");
for (int i = 0; i < evalnum; i++)
{
Write(" {0:g3} ", test_vbv.Eigvals[i]);
}
Write("\n");
((test_vbv.V).T * A * test_vbv.V - test_vbv.D).print("V.T*A*V - D = ", "{0,10:f6}");
WriteLine("\n Total rotations used = {0}", test_vbv.Rotations);
B.print("\n Matrix copy used, after value by value operations = ", "{0,10:f6}");
matrix C = A.copy();
WriteLine("\nSimilar calculation with cyclic sweeps");
jcbi_cycl test_cycl = new jcbi_cycl(C);
test_cycl.Eigvals.print("Found eigenvalues = ");
(test_cycl.V.T * A * test_cycl.V - test_cycl.D).print("V.T*A*V - D = ", "{0,10:f6}");
WriteLine("\n Total rotations used = {0}", test_cycl.Rotations);
C.print("\n Matrix copy used, after cyclic sweeps = ", "{0,10:f6}");
}
static void B5()
{
WriteLine("\n Problem B5\n");
int n = 5;
matrix A = rand_sym_mat(n);
matrix B = A.copy();
matrix C = A.copy();
WriteLine($"Random symmetric matrix A with size {n}");
WriteLine("We find all eigenvalues with cyclic routine");
jcbi_cycl test_cycl = new jcbi_cycl(B);
test_cycl.Eigvals.print("Eigenvalues found by cyclic routine, low to high");
WriteLine("\nNow we use the value-by-value routine to calculate eigenvalues from last to first");
WriteLine("We do this by changing the calculation of " +
"rotation angle theta to 0.5*Atan2(-Apq, App-Aqq)\n");
bool invert = true;
int evalnum = n;
bool vbv = true;
jcbi_cycl test_vbv = new jcbi_cycl(C, vbv, evalnum, invert);
test_vbv.Eigvals.print("Eigenvalues value-by-value, in order of calculation");
}
static void B4()
{
WriteLine("\n Problem B4\n");
WriteLine("See PlotB4r.svg and PlotB4t.svg for results");
int l = 50; // max matrix size
int k = 5; // number of tries for each avg
Stopwatch sw = new Stopwatch();
var timewriter = new System.IO.StreamWriter("out.b4time.txt");
var rotwriter = new System.IO.StreamWriter("out.b4rot.txt");
vector tvbv = new vector(l);
vector tcyc = new vector(l);
vector rvbv = new vector(l);
vector rcyc = new vector(l);
for (int i = 0; i < l; i++)
{
tvbv[i] = 0;
tcyc[i] = 0;
rvbv[i] = 0;
rcyc[i] = 0;
for (int j = 0; j < k; j++)
{
matrix A = rand_sym_mat(i + 1);
sw.Reset();
matrix B = A.copy();
bool vbv = true;
int evalnum = l;
sw.Start();
jcbi_cycl test_vbv = new jcbi_cycl(B, vbv, evalnum);
sw.Stop();
tvbv[i] += sw.Elapsed.TotalMilliseconds;
rvbv[i] += test_vbv.Rotations;
matrix C = A.copy();
sw.Reset();
sw.Start();
jcbi_cycl test_cyc = new jcbi_cycl(C);
sw.Stop();
tcyc[i] += sw.Elapsed.TotalMilliseconds;
rcyc[i] += test_cyc.Rotations;
}
tvbv[i] = tvbv[i] / k;
tcyc[i] = tcyc[i] / k;
rvbv[i] = rvbv[i] / k;
rcyc[i] = rcyc[i] / k;
timewriter.WriteLine($"{i} {tvbv[i]} {tcyc[i]}");
rotwriter.WriteLine($"{i} {rvbv[i]} {rcyc[i]}");
}
timewriter.Close();
rotwriter.Close();
}
static int Main()
{
WriteLine("\n Problem A1: Test Jacobi functionality \n");
var rand = new System.Random();
int n = rand.Next(1, 15);
matrix A = rand_sym_mat(n);
WriteLine("Symmetric random test matrix A");
A.print("A = ");
matrix B = A.copy();
jcbi_cycl test = new jcbi_cycl(B);
WriteLine("\nJacobi diagonalisation A=V*D*V.T");
matrix V = test.V;
matrix D = test.D;
V.print("\nV = ");
D.print("\nD = ");
((V.T * A) * V - D).print("\n(V.T*A)*V - D =", "{0,10:f6}");
WriteLine("\n\n Problem A2: Quantum Particle in box \n");
n = 99;
double s = 1.0 / (n + 1);
matrix H = new matrix(n, n);
for (int i = 0; i < n - 1; i++)
{
H[i, i] = -2;
H[i, i + 1] = 1;
H[i + 1, i] = 1;
}
H[n - 1, n - 1] = -2;
H = H * (-1 / s / s);
matrix H1 = H.copy();
jcbi_cycl h_jac = new jcbi_cycl(H1);
matrix Vh = h_jac.V;
matrix Dh = h_jac.D;
vector eigvals = h_jac.Eigvals;
//H.print("\n H = ");
//WriteLine("\n Jacobi diagonalisation H=V*D*V.T");
//Vh.print("\n V = ");
//Dh.print("\n D = ");
WriteLine("\n");
// Calculate analytic energies and compare
WriteLine("Compare first {0} eigvals with analytic energies", n / 3);
for (int i = 0; i < n / 3; i++)
{
double exact = PI * PI * (i + 1) * (i + 1);
double calculated = eigvals[i];
WriteLine("{0} {1:f6} {2:f6}", i, calculated, exact);
}
var datw = new System.IO.StreamWriter("out.fun.txt");
// Write analytic function to file
//double a = 0.149;
//double a=0.141;
double a = Sqrt(2 * s);
int q = 1;
Func <double, double> psiev = (x) => a *Sin(q *x *PI);
Func <double, double> psiod = (x) => a *Sin(q *x *PI - PI);
for (int k = 0; k < 4; k++)
{
vector psinum = Vh.col_toVector(k);
Func <double, double> psi = pick_analytic_func(a, n, q, psinum);
datw.WriteLine($"{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($"{1} {0} \n\n");
}
datw.Close();
return(0);
}
static void B1()
{
WriteLine("\n Problem B1: Test Jacobi cycle time \n");
int n = 50;
WriteLine("Symmetric random test matrix A of size {0}", n);
Stopwatch sw = new Stopwatch();
double time_avg = 0;
int k = 15;
vector times = new vector(k);
for (int i = 0; i < k; i++)
{
sw.Reset();
matrix A = rand_sym_mat(n);
matrix B = A.copy();
sw.Start();
jcbi_cycl test = new jcbi_cycl(B);
sw.Stop();
times[i] = sw.Elapsed.TotalMilliseconds;
time_avg += times[i];
}
time_avg = time_avg / times.size;
WriteLine("Average Jacobi diagonalisation time");
WriteLine("time_avg = {0} ms\n", time_avg);
WriteLine("Perform calculation for different matrix sizes");
var timewriter = new System.IO.StreamWriter("out.time.txt");
k = 5; // number of tries for each avg
int l = 30; // upper range of matrix sizes;
vector tavgs = new vector(l - 5);
vector xs = new vector(l - 5);
vector terr = new vector(l - 5);
for (int i = 5; i < l; i++)
{
xs[i - 5] = i * 1.0;
tavgs[i - 5] = 0;
for (int j = 0; j < k; j++)
{
matrix A = rand_sym_mat(i);
sw.Reset();
matrix B = A.copy();
sw.Start();
jcbi_cycl test = new jcbi_cycl(B);
sw.Stop();
tavgs[i - 5] += sw.Elapsed.TotalMilliseconds;
}
tavgs[i - 5] = tavgs[i - 5] / k;
terr[i - 5] = tavgs[i - 5] * 0.025;
timewriter.WriteLine($"{i} {tavgs[i-5]}");
}
timewriter.Close();
Func <double, double>[] tfun = new Func <double, double> [2];
tfun[0] = (x) => 1; tfun[1] = (x) => x * x * x;
//tfun[0] = (x) => 1; tfun[1] = (x) => x; tfun[2] = (x) => x*x; tfun[3] = (x) => x*x*x;
lsfit tfit = new lsfit(xs, tavgs, terr, tfun);
WriteLine("exec time fit params {0} {1}", tfit.C[0], tfit.C[1]);
vector fiteval = tfit.evaluate(xs);
var tfunw = new System.IO.StreamWriter("out.tfun.txt");
for (int i = 0; i < xs.size; i++)
{
tfunw.WriteLine($"{xs[i]} {fiteval[i]}");
}
tfunw.Close();
WriteLine("See PlotB1.svg for execution time calculation and a+b*x^3 fit");
}
