public static void Main(string[] args)
{
int n = 5; //size of real symmetric matrix
matrix A = new matrix(n, n);
var rnd = new Random(1);
for (int i = 0; i < n; i++) /* Construction of a random vector */
{
for (int j = 0; j < n; j++)
{
A[i, j] = (rnd.NextDouble() * 10);
A[j, i] = A[i, j]; /* We make sure that the matrix is symmetric */
}
}
A.print("Random symmetric matrix, A:");
matrix V = new matrix(n, n);
vector e = new vector(n);
matrix B = A.copy(); /* We make a copy of A */
int sweeps = jacobi.cyclic(A, e, V); /* We use the jacobi matlib for the implementation of the cyclic sweeps: public static int cyclic(matrix A, vector e, matrix V=null){...} */
WriteLine($"\nNumber of sweeps: {sweeps}");
matrix D = (V.T * B * V);
// D.print("\nEigenvalue-decomposition, V^T*A*V (should be diagonal):");
D.printfloat("\nEigenvalue-decomposition, V^T*A*V (should be diagonal):"); /* using my print2 to get 0's instead of values with e.g. "e-16"*/
e.print("\nEigenvalues:\n");
}
static void Main()
{
int n = 5; //size of real symmetric matrix
matrix A = new matrix(n, n);
var rnd = new Random(1);
for (int i = 0; i < n; i++) /* Construction of a random vector */
{
for (int j = 0; j < n; j++)
{
A[i, j] = (rnd.NextDouble() * 10);
A[j, i] = A[i, j]; /* We make sure that the matrix is symmetric */
}
}
A.printfloat("Random symmetric matrix, A:");
matrix V = new matrix(n, n);
matrix V2 = new matrix(n, n);
vector e = new vector(n);
vector e2 = new vector(n);
// matrix B=A.copy();
matrix B2 = A.copy();
int rotations = jacobi.classic2(A, e, V); /* We use the jacobi matlib for the implementation of the cyclic sweeps: public static int cyclic(matrix A, vector e, matrix V=null){...} */
WriteLine($"\nNumber of rotations: {rotations}");
// matrix D=(V.T*B*V);
// D.printfloat("\nClassic: Eigenvalue-decomposition, V^T*A*V (should be diagonal):");
int sweeps = jacobi.cyclic(B2, e2, V2);
WriteLine($"Number of sweeps: {sweeps}");
// matrix D2=(V2.T*B*V2);
// D2.printfloat("\nCyclic: Eigenvalue-decomposition, V^T*A*V (should be diagonal):");
// var rnd = new Random(1);
// int n = 4;
// matrix v_c = new matrix(n,n);
// matrix v_classic = new matrix(n,n);
// vector e_classic = new vector(n);
// var A_c = new matrix(n,n);
// for(int i=0;i<n;i++){
// for(int j=i;j<n;j++){
// A_c[i,j]=2*(rnd.NextDouble()-0.5);
// A_c[j,i]=A_c[i,j];
// }
// }
// matrix B=A_c.copy();
// var A_classic = A_c.copy();
// int rotations = classic(A_classic,e_classic,v_classic);
// A_classic.printfloat("A classic transformed");
// // e_classic.print("Eigenvalues calculated with classic:");
// // v_classic.print("Eigenvectors calculated with classic:");
// var VTAV=v_classic.T*B*v_classic;
// VTAV.printfloat("V^T*A*V:");
}
static public int classic(matrix B, vector e, matrix V = null)
{
/* Jacobi diagonalization. Upper triangle of A is destroyed.
* e and V accumulate eigenvalues and eigenvectors */
matrix A = B.copy();
bool changed; int rotations = 0, n = A.size1;
for (int i = 0; i < n; i++)
{
e[i] = A[i, i];
}
for (int i = 0; i < n; i++)
{
V[i, i] = 1.0; for (int j = i + 1; j < n; j++)
{
V[i, j] = 0; V[j, i] = 0;
}
}
do
{
rotations++; changed = false;
WriteLine($"{A[0,0]} {A[0,1]} {A[0,2]} {A[0,3]} {A[0,4]}");
for (int p = 0; p < n - 1; p++)
{
WriteLine($"p: {p}");
int q = p + 1;
double max = Abs(A[p, q]);
for (int j = p + 2; j < n; j++)
{
WriteLine($"A0: {A[0,0]} {A[0,1]} {A[0,2]} {A[0,3]} {A[0,4]}");
if (max <= Abs(A[p, j]))
{
max = Abs(A[p, j]);
q = j;
// WriteLine($"max:({p},{q}), A[p,q]: {A[p,q]} A[1,4]: {A[1,4]}");
}
}
// WriteLine($"q: {q}");
double app = e[p];
double aqq = e[q];
double apq = A[p, q];
double phi = 0.5 * Atan2(2 * apq, aqq - app);
double c = Cos(phi), s = Sin(phi);
double app1 = c * c * app - 2 * s * c * apq + s * s * aqq;
double aqq1 = s * s * app + 2 * s * c * apq + c * c * aqq;
if (app1 != app || aqq1 != aqq)
{
changed = true;
e[p] = app1;
e[q] = aqq1;
A[p, q] = 0.0;
for (int i = 0; i < p; i++)
{
double aip = A[i, p];
double aiq = A[i, q];
A[i, p] = c * aip - s * aiq;
A[i, q] = c * aiq + s * aip;
}
for (int i = p + 1; i < q; i++)
{
double api = A[p, i];
double aiq = A[i, q];
A[p, i] = c * api - s * aiq;
A[i, q] = c * aiq + s * api;
}
for (int i = q + 1; i < n; i++)
{
double api = A[p, i];
double aqi = A[q, i];
A[p, i] = c * api - s * aqi;
A[q, i] = c * aqi + s * api;
}
if (V != null)
{
for (int i = 0; i < n; i++)
{
double vip = V[i, p];
double viq = V[i, q];
V[i, p] = c * vip - s * viq;
V[i, q] = c * viq + s * vip;
}
}
}
A.printfloat("After rotation:");
}
}while(changed);
return(rotations);
}
