static int Main(string[] args)
{
int N;
if (args.Length > 0)
{
N = int.Parse(args[0]);
}
else
{
N = 3;
}
int nm = N;
matrix A1 = randmatrix_sym(nm, nm);
matrix V = new matrix(nm, nm);
//vector e=jac_dia_red(A1,V,1);
jac_dia ja = new jac_dia(A1);
vector e = ja.e;
WriteLine($"{ja.n_rot}");
return(0);
}
static int Main()
{
int nm = 5;
matrix A1 = randmatrix_sym(nm, nm);
//matrix V= new matrix(nm,nm);
jac_dia jd = new jac_dia(A1);
vector ed = jd.e;
//matrix Ad=jd.A;
jac_clas jc = new jac_clas(A1);
vector ec = jc.e;
matrix Ac = jc.A;
WriteLine($"Part C:");
WriteLine("i) Test that calculated eigenvalues with classic Jacobi are the same as the ones calulated by the cyclic sweep for a given random matrix A:");
WriteLine($"Classic: cyclic:");
for (int n2 = 0; n2 < nm; n2++)
{
WriteLine($"{ec[n2]} {ed[n2]}");
}
WriteLine("That the clissic method diagonalize a given matrix A:");
for (int n1 = 0; n1 < nm; n1++)
{
for (int n2 = 0; n2 < nm; n2++)
{
Write($"{Ac[n1,n2]} ");
}
Write("\n");
}
WriteLine($"");
WriteLine($"ii) Does classic improve the number of rotation and the time?");
WriteLine($"In plot_rotations.svg and plot_time.svg is the number of rotations and the time used by the classic and the cyclic sweep methods compared.");
WriteLine($"The result indicate that classic Jacobi is slower then the cyclic sweep, but use fewer rotations.");
return(0);
}
static int Main(string[] args)
{
// input to vector...
var input = new System.IO.StreamReader("time_cyc.txt");
int input_lenght = 0;
while (input.ReadLine() != null)
{
input_lenght++;
}
input.Close();
input = new System.IO.StreamReader("time_cyc.txt");
vector N = new vector(input_lenght);
vector t = new vector(input_lenght);
string line;
for (int n = 0; n < input_lenght; n++)
{
line = input.ReadLine();
string[] words = line.Split(' ');
N[n] = double.Parse(words[0]);
t[n] = double.Parse(words[1]);
}
//end input to vector...
//using oslf to check O(n³)...
//function to fit:
var ft = new Func <double, double>[] { x => 1, x => x };
//error on time set to 1%:
vector dt = new vector(t.size);
vector lN = new vector(t.size);
vector lt = new vector(t.size);
for (int i = 0; i < t.size; i++)
{
lN[i] = Log(N[i]);
lt[i] = Log(t[i]);
dt[i] = lt[i] / 100;
} //end for
//using olsf:
olsf fit = new olsf(lN, lt, dt, ft);
WriteLine("Part B:");
WriteLine("");
WriteLine("i) Check that the time goes as O(n³).");
WriteLine($"By using my least square fit from Problem 3, i get that the time roughly depends of the matrix size N as t=N^(c), with c={fit.c[1]}.");
WriteLine("");
//check that eigenvalue by eigenvalue give same result as cyc
//new random matrix:
matrix A = randmatrix_sym(4, 4);
//using cyc:
jac_dia ja = new jac_dia(A);
int nr = 0; //number of rotation:
matrix V = new matrix(4, 4);
vector e1 = jac_dia_red(A, V, 4, ref nr);
WriteLine("ii) Implement the value-by-value method");
WriteLine("Check that the eigenvalues becomes the same as using cyclic sweeps.");
WriteLine("Random generated symmetic matrix A:");
for (int i = 0; i < A.size1; i++)
{
for (int k = 0; k < A.size1; k++)
{
Write($"{A[i,k]} ");
} //end for
Write("\n");
} //end for
Write("\n \n");
WriteLine("Calutaled eigenvalues:");
WriteLine("by cyclic: by value-by-value:");
for (int i = 0; i < ja.e.size; i++)
{
WriteLine($"{ja.e[i]} {e1[i]}");
} //end for
WriteLine("");
WriteLine("iii) and iv) Compare speed.");
WriteLine("In plot_time.svg the time used by the cyclic sweeps method to calculate alle the eigenvalues, is compared to the time used by the value-by-value method to calculate the first and all eigenvalue(s).");
WriteLine("It is faster to only calculate the first value by the value-by-value method then using cyclic sweeps. But cyclic sweeps is significant the calculated all eigenvalues by the value-by-value method.");
WriteLine("In plot_rotation.svg the number of rotationes is compared.");
WriteLine("");
//largest eigenvalue
matrix V2 = new matrix(4, 4);
int nr2 = 0;
vector eh = jac_dia_high_e(A, V2, 3, ref nr2);
WriteLine($"v) Largest eigenvalue.");
WriteLine($"By changing the theta angle from Atan2(2*Apq, Aq-Ap) to Atan2(-2*Apq, App-Aqq) the larges eigenvlaue can be calculated.");
WriteLine($"For vector A the value becomes: {eh[0]} the same as found by cyclic sweeps.");
return(0);
} // end Main
static int Main()
{
//testing the Jacobi dia..
WriteLine("Part A:");
WriteLine("i) Test of Jacobi diagonalization with cyclic sweeps:");
WriteLine("In the file test.txt the implementation is tested for a random sysmetic matrix.");
var test = new System.IO.StreamWriter("test.txt");
int nm = 4; //matrix size
matrix A1 = randmatrix_sym(nm, nm); //random matrix
jac_dia ja = new jac_dia(A1); //diagonalization
matrix A = ja.A;
matrix D = new matrix(A.size1, A.size2);
vector e = ja.e;
for (int n = 0; n < A.size1; n++)
{
D[n, n] = e[n];
}
matrix V = ja.V;
matrix vdvt = V * D * V.T;
matrix vtav = V.T * A1 * V;
test.WriteLine("Test ofJacobi diagonalization with cyclic sweeps.");
test.WriteLine($"");
test.WriteLine("Random symmetric matrix A:");
for (int n1 = 0; n1 < A.size1; n1++)
{
for (int n2 = 0; n2 < A.size1; n2++)
{
test.Write($"{A1[n1,n2]} ");
}
test.Write("\n \n");
}
test.WriteLine("Reduced matrix A:");
for (int n1 = 0; n1 < A.size1; n1++)
{
for (int n2 = 0; n2 < A.size1; n2++)
{
test.Write($"{A[n1,n2]} ");
}
test.Write("\n \n");
}
test.WriteLine("the Diagonal matrix with the corresponding eigenvaluesmatrix D:");
for (int n1 = 0; n1 < A.size1; n1++)
{
for (int n2 = 0; n2 < A.size1; n2++)
{
test.Write($"{D[n1,n2]} ");
}
test.Write("\n \n");
}
test.WriteLine("The orthogonal matrix of eigenvectorsmatrix V:");
for (int n1 = 0; n1 < A.size1; n1++)
{
for (int n2 = 0; n2 < A.size1; n2++)
{
test.Write($"{V[n1,n2]} ");
}
test.Write("\n \n");
}
test.WriteLine("Test VDVT=A... VDVT is given as:");
for (int n1 = 0; n1 < A.size1; n1++)
{
for (int n2 = 0; n2 < A.size1; n2++)
{
test.Write($"{vdvt[n1,n2]} ");
}
test.Write("\n \n");
}
test.WriteLine("Test VTAV=D... VTAV is given as:");
for (int n1 = 0; n1 < A.size1; n1++)
{
for (int n2 = 0; n2 < A.size1; n2++)
{
test.Write($"{vtav[n1,n2]} ");
}
test.Write("\n");
}
test.Close();
//particle in box:
//build H
int nh = 50;
double s = 1.0 / (nh + 1);
matrix H = new matrix(nh, nh);
for (int i = 0; i < nh - 1; i++)
{
matrix.set(H, i, i, -2);
matrix.set(H, i, i + 1, 1);
matrix.set(H, i + 1, i, 1);
} //end for
matrix.set(H, nh - 1, nh - 1, -2);
matrix.scale(H, -1 / s / s);
//diagonalize H
jac_dia jah = new jac_dia(H);
//matrix H_dia=jah.A;
vector eh = jah.e;
matrix Vh = jah.V;
WriteLine("ii) Particle in a box.");
WriteLine("The following is a comparison between the first 5 the caculated and exact energies:");
WriteLine("Number: Calculated: Exact:");
//check energies
for (int n1 = 0; n1 < 5; n1++)
{
double exact = Pow(PI * (n1 + 1), 2);
WriteLine($"{n1} {eh[n1]} {exact}");
} //end for
WriteLine("");
WriteLine("In plotA.svg the 5 lowest eigenfunctions are plotted. The result have same form as the analytic result.");
var data = new System.IO.StreamWriter("data.txt");
for (int k = 0; k < (5 + 1); k++)
{
data.Write($"{0} ");
} //end for
data.Write("\n");
for (int j = 0; j < nh; j++)
{
data.Write($"{(j+1.0)/(nh+1)} ");
for (int k = 0; k < 5; k++)
{
data.Write($"{matrix.get(Vh,j,k)} ");
} //end for
data.Write("\n");
} // end for
data.Write($"{1} ");
for (int k = 0; k < (5); k++)
{
data.Write($"{0} ");
} //end for
data.Close();
return(0);
}
