int GetSiteNumber(Site t)
{
return t.t * Nxyz + t.z * Nxy + t.y * Nx + t.x;
}
public void Update(int x, int y, int z, int t, int dir, bool withOR)
{
Link A = GetSumOfStaples(x, y, z, t, dir);
//here A is the sum of staples!
//heatbath
//Link W = Mul(U[x, y, z, t, dir], A); double det;
//Link X = new Link(true);
////for heat-bath
//for (int i = 0; i < d; i++)
// for (int j = i + 1; j < d; j++)
// {
// Complex a = W.A[i, i];
// Complex B = W.A[i, j];
// Complex C = W.A[j, i];
// Complex D = W.A[j, j];
// // det = (W.A[i, i] * W.A[j, j] - W.A[i, j] * W.A[j, i]).x;
// double x0 = 1 / 2f * (a.x + D.x);
// double x1 = 1 / 2f * (B.y + C.y);
// double x2 = 1 / 2f * (B.x - C.x);
// double x3 = 1 / 2f * (a.y - D.y);
// // det = GetDet(A);
// det = x0 * x0 + x1 * x1 + x2 * x2 + x3 * x3;
// Link a_ = GetHeatBath(det, i, j);
// Link r = new Link(true);
// det = Math.Sqrt(det);
// x0 /= det;
// x1 /= det;
// x2 /= det;
// x3 /= det;
// r.A[i, i] = new Complex(x0, x3);
// r.A[i, j] = new Complex(x2, x1);
// r.A[j, i] = new Complex(-x2, x1);
// r.A[j, j] = new Complex(x0, -x3);
// r = Mul(a_, r.HermConj());
// W = Mul(r, W);
// X = Mul(r, X);
// }
//U[x, y, z, t, dir] = Mul(X, U[x, y, z, t, dir]);
//
//for overrelaxation
//if (GetRandom() < 0.1)
/* if (withOR)
{
//for (int or = 0; or < 0; or++)
//{
//calculating determinant of SU(2)
double det = Math.Pow(GetDet(A),1.0/3.0);
for (int i = 0; i < SU3.d; i++)
for (int j = 0; j < SU3.d; j++)
{
A.A[i, j].x /= det;
A.A[i, j].y /= det;
}
A = Mul(A.HermConj(), Mul(U[x, y, z, t, dir].HermConj(), A.HermConj()));
Orthogonalize(ref A);
U[x, y, z, t, dir]=A;
}
else
{*/
//for Metropolis
//for (int hit = 0; hit <= 10; hit++)
//{
// bool accepted = false; double dSG; Link X = new Link(true);
// while (!accepted)
// {
// X = GetRandomMetroLink();
// //-I
// for (int i = 0; i < d; i++) X.A[i, i].x--;
// dSG = -beta / SU3.d * ReTr(Mul(X, Mul(U[x, y, z, t, dir], A)));
// double r = GetRandom();
// if (r <= Math.Exp(-dSG)) accepted = true;
// }
// for (int i = 0; i < d; i++) X.A[i, i].x++;
// U[x, y, z, t, dir] = Mul(X, U[x, y, z, t, dir]);
//}
//for poor dynamical fermions
for (int hit = 0; hit <= 10; hit++)
{
bool accepted = false; double dSG; Link X = new Link(true);
while (!accepted)
{
X = GetRandomMetroLink();
Xsite = new Site(x, y, z, t); Xdir = dir;
Uprime = Mul(X, U[x, y, z, t, dir]);
Dirac D = new Dirac(this);
Vector chi = new Vector(Dirac.N);
chi.FillGaussRandom();
D.phi = D.MulD(chi);
double Fold = Dirac.V1hermV2(chi, chi).x;
D.Prepare();
D.IterPrime();
//here - D.x = D^-1*phi
double Fnew = Dirac.V1hermV2(D.x, D.x).x;
double dSF = Fnew - Fold;
//X-I
for (int i = 0; i < d; i++) X.A[i, i].x--;
dSG = -beta / SU3.d * ReTr(Mul(X, Mul(U[x, y, z, t, dir], A)));
double r = GetRandom();
if (r <= Math.Exp(-(dSG + dSF))) accepted = true;
}
for (int i = 0; i < d; i++) X.A[i, i].x++;
U[x, y, z, t, dir] = Mul(X, U[x, y, z, t, dir]);
}
}
Site GetSite(int n)
{
Site t = new Site(); int tempn;
t.t = n / Nxyz; tempn = n - t.t * Nxyz;
t.z = tempn / Nxy; tempn -= t.z * Nxy;
t.y = tempn / Nx;
t.x = tempn - t.y * Nx;
return t;
}
public Vector MulDprime(Vector V)
{
Vector res = new Vector(N);
Site[] AdjacentSites = new Site[9];
Link[] AdjacentLinks = new Link[9];
Complex g; double flipsign = 1.0; int mu = 0; Complex c;
for (int i = 0; i < N; i++)
{
AdjacentSites[0] = GetSite(i);
AdjacentLinks[0] = AdjacentSites[0] == U.Xsite ? U.Uprime : new Link(true);
for (int ai = 1; ai < 5; ai++)
{
mu = (ai - 1) % 4 + 1;
AdjacentSites[ai] = AdjacentSites[0];
U.GetNode(ref AdjacentSites[ai].x, ref AdjacentSites[ai].y, ref AdjacentSites[ai].z, ref AdjacentSites[ai].t, ai);
AdjacentLinks[ai] = AdjacentSites[ai] == U.Xsite ? U.Uprime : U.U[AdjacentSites[ai].x, AdjacentSites[ai].y, AdjacentSites[ai].z, AdjacentSites[ai].t, mu];
}
for (int ai = 5; ai < 9; ai++)
{
mu = (ai - 1) % 4 + 1;
AdjacentSites[ai] = AdjacentSites[0];
U.GetNode(ref AdjacentSites[ai].x, ref AdjacentSites[ai].y, ref AdjacentSites[ai].z, ref AdjacentSites[ai].t, -(ai - 4));
AdjacentLinks[ai] = AdjacentSites[ai] == U.Xsite ? U.Uprime : U.U[AdjacentSites[ai].x, AdjacentSites[ai].y, AdjacentSites[ai].z, AdjacentSites[ai].t, mu];
}
for (int ai = 0; ai < 9; ai++)
{
flipsign = ai < 5 ? 1.0 : -1.0;
mu = (ai - 1) % 4 + 1;
int i1 = GetSiteNumber(AdjacentSites[ai]);
for (byte j = 0; j < 4; j++)
for (byte j1 = 0; j1 < 4; j1++)
{
if (ai == 0) g = Complex.One;
else
g = (flipsign == 1.0) ? OneMinusgamma[mu - 1][j, j1] : OnePlusgamma[mu - 1][j, j1];
if (g.x != 0 || g.y != 0)
{
c = ai == 0 ? Complex.One : new Complex(-kappa, 0) * g;
for (byte k = 0; k < 3; k++)
for (byte k1 = 0; k1 < 3; k1++)
{
if (ai == 0 && j == j1 && k == k1) res[i, j, k] += Complex.One * V[i1, j1, k1];
else
{
if (ai != 0)
{
if (flipsign == 1.0)
res[i, j, k] += c * AdjacentLinks[ai].A[k, k1] * V[i1, j1, k1];
else
res[i, j, k] += c * AdjacentLinks[ai].A[k1, k].Conj() * V[i1, j1, k1];//u.HermConj().A[k, k1]
}
}
}
}
}
}
}
return res;
}
public Vector MulD(Vector V)
{
//Site s = new Site(1, 1, 1, 1);
//GetNode(s, 1);
//System.Windows.Forms.MessageBox.Show(s.x.ToString());
//Vector res = new Vector(N);
//Site mainsite, adjacentsite; Complex g;
//for (int i = 0; i < N; i++)
//{
// mainsite = GetSite(i);
// for (int ai = 1; ai < 5; ai++)
// {
// adjacentsite = mainsite;
// U.GetNode(ref adjacentsite.x, ref adjacentsite.y, ref adjacentsite.z, ref adjacentsite.t, ai);
// int i1 = GetSiteNumber(adjacentsite);
// for (byte j = 0; j < 4; j++)
// for (byte j1 = 0; j1 < 4; j1++)
// {
// //g = OneMinusgamma[ai - 1][j, j1];
// //if (g.x != 0 || g.y != 0)
// //{
// for (byte k = 0; k < 3; k++)
// for (byte k1 = 0; k1 < 3; k1++)
// {
// res[i, j, k] += D(mainsite, adjacentsite, j, j1, k, k1) * V[i1, j1, k1];
// }
// // }
// }
// }
// for (int ai = 1; ai < 5; ai++)
// {
// adjacentsite = mainsite;
// U.GetNode(ref adjacentsite.x, ref adjacentsite.y, ref adjacentsite.z, ref adjacentsite.t, -ai);
// int i1 = GetSiteNumber(adjacentsite);
// for (byte j = 0; j < 4; j++)
// for (byte j1 = 0; j1 < 4; j1++)
// {
// //g = OneMinusgamma[ai - 1][j, j1];
// //if (g.x != 0 || g.y != 0)
// //{
// for (byte k = 0; k < 3; k++)
// for (byte k1 = 0; k1 < 3; k1++)
// res[i, j, k] += D(mainsite, adjacentsite, j, j1, k, k1) * V[i1, j1, k1];
// // }
// }
// }
//}
//Site[] AdjacentSites = new Site[9]; Complex g; int mu = 0;
//for (int i = 0; i < N; i++)
//{
// AdjacentSites[0] = GetSite(i);
// for (int ai = 1; ai < 5; ai++)
// {
// AdjacentSites[ai] = AdjacentSites[0];
// U.GetNode(ref AdjacentSites[ai].x, ref AdjacentSites[ai].y, ref AdjacentSites[ai].z, ref AdjacentSites[ai].t, ai);
// }
// for (int ai = 5; ai < 9; ai++)
// {
// AdjacentSites[ai] = AdjacentSites[0];
// U.GetNode(ref AdjacentSites[ai].x, ref AdjacentSites[ai].y, ref AdjacentSites[ai].z, ref AdjacentSites[ai].t, -(ai - 4));
// }
// for (int ai = 0; ai < 9; ai++)
// {
// mu = (ai - 1) % 4;
// int i1 = GetSiteNumber(AdjacentSites[ai]);
// for (byte j = 0; j < 4; j++)
// for (byte j1 = 0; j1 < 4; j1++)
// {
// if (ai == 0) g = Complex.One;
// else
// g = OneMinusgamma[mu][j, j1];
// if (g.x != 0 || g.y != 0)
// for (byte k = 0; k < 3; k++)
// for (byte k1 = 0; k1 < 3; k1++)
// {
// res[i, j, k] += D(AdjacentSites[0], AdjacentSites[ai], j, j1, k, k1) * V[i1, j1, k1];
// }
// }
// }
//}
//return res;
Vector res = new Vector(N);
Site[] AdjacentSites = new Site[9];
Link[] AdjacentLinks = new Link[9];
Complex g; double flipsign = 1.0; int mu = 0; Complex c;
for (int i = 0; i < N; i++)
{
AdjacentSites[0] = GetSite(i);
AdjacentLinks[0] = new Link(true);
for (int ai = 1; ai < 5; ai++)
{
mu = (ai - 1) % 4 + 1;
AdjacentSites[ai] = AdjacentSites[0];
U.GetNode(ref AdjacentSites[ai].x, ref AdjacentSites[ai].y, ref AdjacentSites[ai].z, ref AdjacentSites[ai].t, ai);
AdjacentLinks[ai] = U.U[AdjacentSites[ai].x, AdjacentSites[ai].y, AdjacentSites[ai].z, AdjacentSites[ai].t, mu];
}
for (int ai = 5; ai < 9; ai++)
{
mu = (ai - 1) % 4 + 1;
AdjacentSites[ai] = AdjacentSites[0];
U.GetNode(ref AdjacentSites[ai].x, ref AdjacentSites[ai].y, ref AdjacentSites[ai].z, ref AdjacentSites[ai].t, -(ai - 4));
AdjacentLinks[ai] = U.U[AdjacentSites[ai].x, AdjacentSites[ai].y, AdjacentSites[ai].z, AdjacentSites[ai].t, mu];
}
for (int ai = 0; ai < 9; ai++)
{
flipsign = ai < 5 ? 1.0 : -1.0;
mu = (ai - 1) % 4 + 1;
int i1 = GetSiteNumber(AdjacentSites[ai]);
for (byte j = 0; j < 4; j++)
for (byte j1 = 0; j1 < 4; j1++)
{
if (ai == 0) g = Complex.One;
else
g = (flipsign == 1.0) ? OneMinusgamma[mu - 1][j, j1] : OnePlusgamma[mu - 1][j, j1];
if (g.x != 0 || g.y != 0)
{
c = ai == 0 ? Complex.One : new Complex(-kappa, 0) * g;
for (byte k = 0; k < 3; k++)
for (byte k1 = 0; k1 < 3; k1++)
{
if (ai == 0 && j == j1 && k == k1) res[i, j, k] += Complex.One * V[i1, j1, k1];
else
{
if (ai != 0)
{
if (flipsign == 1.0)
res[i, j, k] += c * AdjacentLinks[ai].A[k, k1] * V[i1, j1, k1];
else
res[i, j, k] += c * AdjacentLinks[ai].A[k1, k].Conj() * V[i1, j1, k1];//u.HermConj().A[k, k1]
}
}
}
}
}
}
}
return res;
}
public void GetNode(Site s, int dir)
{
if (dir == 1) s.x++; if (dir == -1) s.x--;
if (dir == 2) s.y++; if (dir == -2) s.y--;
if (dir == 3) s.z++; if (dir == -3) s.z--;
if (dir == 4) s.t++; if (dir == -4) s.t--;
if (s.x == -1) s.x = Nx - 1; if (s.x == Nx) s.x = 0;//comment if (x == Ns) x = 0; to use flux!!!
if (s.y == -1) s.y = Ny - 1; if (s.y == Ny) s.y = 0;
if (s.z == -1) s.z = Nz - 1; if (s.z == Nz) s.z = 0;
if (s.t == -1) s.t = Nt - 1; if (s.t == Nt) s.t = 0;
}
public Complex D(Site n, Site m, byte alpha, byte beta, byte a, byte b)
{
Complex r = new Complex(); int c = 0;
if (n == m && alpha == beta && a == b) { r += Complex.One; c++; }
Site t;
for (int i = 1; i <= 4; i++)
{
t = n;
U.GetNode(ref t.x, ref t.y, ref t.z, ref t.t, i);
if (t == m) { r += new Complex(-kappa, 0) * OneMinusgamma[i - 1][alpha, beta] * U.U[n.x, n.y, n.z, n.t, i].A[a, b];
c++;
// if (c > 1)
// System.Windows.Forms.MessageBox.Show("WTF?");
}
}
for (int i = 1; i <= 4; i++)
{
t = n;
U.GetNode(ref t.x, ref t.y, ref t.z, ref t.t, -i);
if (t == m)
{
r += new Complex(-kappa, 0) * OnePlusgamma[i - 1][alpha, beta] * U.U[t.x, t.y, t.z, t.t, i].A[b, a].Conj();//.HermConj().A[a, b]; - much more efficient!
c++; // if (c > 1)
// System.Windows.Forms.MessageBox.Show("WTF?");
}
}
return r;
}