Link GetRandomMetroLink()
{
double e = 0.1;
double x0m = 0, x1m = 0, x2m = 0, x3m = 0; Link X = new Link(true);
for (int i = 0; i < d; i++)
for (int j = i + 1; j < d; j++)
{
double r0 = GetRandom() - 0.5, r1 = GetRandom() - 0.5, r2 = GetRandom() - 0.5, r3 = GetRandom() - 0.5;
x0m = Math.Sqrt(1 - e * e);
// if (r0 < 0) x0m = -x0m;
double len = Math.Sqrt(r1 * r1 + r2 * r2 + r3 * r3);
x1m = e * r1 / len; x2m = e * r2 / len; x3m = e * r3 / len;
Complex A00 = new Complex(x0m, x3m);
Complex A01 = new Complex(x2m, x1m);
Complex A10 = new Complex(-x2m, x1m);
Complex A11 = new Complex(x0m, -x3m);
Link T = new Link(true);
T.A[i, i] = A00;
T.A[i, j] = A01;
T.A[j, i] = A10;
T.A[j, j] = A11;
X = Mul(T, X);
}
return X;
}
Link GetSumOfStaples(int x, int y, int z, int t, int dir)
{
Link A = new Link(false);
//calculating staples
for (int i = 1; i <= 4; i++)
{
if (i != dir)
{
//create staple
/* r+i----<----r+dir+i
* | |
* ^i \/ ^
* | |
r ->dir r+dir
*
*/
//up
Link A1 = new Link(false);
int x1 = x, y1 = y, z1 = z, t1 = t; int x2 = x, y2 = y, z2 = z, t2 = t;
GetNode(ref x1, ref y1, ref z1, ref t1, dir);
GetNode(ref x2, ref y2, ref z2, ref t2, i);
Link U1, U2, U3;
U1 = U[x1, y1, z1, t1, i];
U2 = U[x2, y2, z2, t2, dir];
U3 = U[x, y, z, t, i];
if (x1 == Ns) { if (i == 2) U1 = Mul(Temp, Mul(U[0, y1, z1, t1, i], Temp)); else U1 = U[0, y1, z1, t1, i]; }
if (x2 == Ns)
{
if (dir == 2) U2 = Mul(Temp, Mul(U[0, y2, z2, t2, dir], Temp)); else U2 = U[0, y2, z2, t2, dir];
}
//if (x == Ns) {
// if (i == 2) U3 = Mul(Temp, Mul(U[0, y, z, t, i], Temp)); else U3 = U[0, y, z, t, i]; }
A1 = Mul(U1, U2.HermConj());//CONJ!
A1 = Mul(A1, U3.HermConj());//CONJ!
/* r ->dir r+dir
* | |
* ^i ^ \/
* | |
* r-i----<----r+dir-i
*/
//down
Link A2 = new Link(false);
x1 = x; y1 = y; z1 = z; t1 = t;
GetNode(ref x1, ref y1, ref z1, ref t1, -i);
x2 = x1; y2 = y1; z2 = z1; t2 = t1;//2 - r-i
GetNode(ref x1, ref y1, ref z1, ref t1, dir);
U1 = U[x1, y1, z1, t1, i];
U2 = U[x2, y2, z2, t2, dir];
U3 = U[x2, y2, z2, t2, i];
if (x1 == Ns)
{
if (i == 2)
U1 = Mul(Temp, Mul(U[0, y1, z1, t1, i], Temp));
else U1 = U[0, y1, z1, t1, i];
}
//if (x2 == Ns) {
// if (dir == 2) U2 = Mul(Temp, Mul(U[0, y2, z2, t2, dir], Temp)); else U2 =U[0, y2, z2, t2, dir];}
//if (x2 == Ns)
//{ if (i == 2) U3 = Mul(Temp, Mul(U[0, y2, z2, t2, i], Temp)); else U3 = U[0, y2, z2, t2, i];}
A2 = Mul(U1.HermConj(), U2.HermConj());//CONJ!
A2 = Mul(A2, U3);
for (int m = 0; m < SU3.d; m++)
for (int n = 0; n < SU3.d; n++)
A.A[m, n] += A1.A[m, n] + A2.A[m, n];
}
}
return A;
}
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]);
}
}
double GetDet(Link W)
{
return (W.A[0, 0] * W.A[1, 1] * W.A[2, 2] + W.A[0, 1] * W.A[1, 2] * W.A[2, 0] + W.A[0, 2] * W.A[1, 0] * W.A[2, 1] - W.A[0, 2] * W.A[1, 1] * W.A[2, 0] - W.A[0, 1] * W.A[1, 0] * W.A[2, 2] - W.A[1, 2] * W.A[2, 1] * W.A[0, 0]).Module();
// return (W.A[0,0]*W.A[1,1]-W.A[0,1]*W.A[1,0]).x;
}
public void Orthogonalize(ref Link U)
{
// double x0 = U.a0, x1 = U.a1, x2 = U.a2, x3 = U.a3;
//double len = Math.Sqrt(x1 * x1 + x2 * x2 + x3 * x3);
//x1 /= len; x2 /= len; x3 /= len;
// x0 = Math.Sqrt(1 - x1 * x1 - x2 * x2 - x3 * x3);
// if (x0<=1) U.a0 = x0;
double module = Math.Sqrt(U.A[0, 0].Module() * U.A[0, 0].Module() +
U.A[0, 1].Module() * U.A[0, 1].Module() +
U.A[0, 2].Module() * U.A[0, 2].Module());
//U'=U/|U|
U.A[0,0].x /= module; U.A[0,0].y /= module;
U.A[0,1].x /= module; U.A[0,1].y /= module;
U.A[0,2].x /= module; U.A[0,2].y /= module;
//V'=V-(V U'*)U'
Complex VU = U.A[1,0] * U.A[0,0].Conj() + U.A[1,1] * U.A[0,1].Conj() +U.A[1,2] * U.A[0,2].Conj();
U.A[1,0]=U.A[1,0]-VU*U.A[0,0];
U.A[1,1]=U.A[1,1]-VU*U.A[0,1];
U.A[1,2]=U.A[1,2]-VU*U.A[0,2];
//V'=V/|V|
module = Math.Sqrt(U.A[1, 0].Module() * U.A[1, 0].Module() +
U.A[1, 1].Module() * U.A[1, 1].Module() +
U.A[1, 2].Module()*U.A[1, 2].Module());
U.A[1,0].x /= module; U.A[1,0].y /= module;
U.A[1,1].x /= module; U.A[1,1].y /= module;
U.A[1,2].x /= module; U.A[1,2].y /= module;
U.A[2,0]=(U.A[0,1] * U.A[1,2] - U.A[0,2] * U.A[1,1]).Conj();
U.A[2,1]=(U.A[0,2] * U.A[1,0] - U.A[0,0] * U.A[1,2]).Conj();
U.A[2,2]=(U.A[0,0] * U.A[1,1] - U.A[0,1] * U.A[1,0]).Conj();
}
public double ReTr(Link L)
{
Complex C= new Complex();
for (int i = 0; i < SU3.d; i++)
C += L.A[i, i];
return C.x;
}
public double MeasureS()
{
int n = 0; double S = 0;
for (int Mu = 1; Mu <= 3; Mu++)
{
for (int Nu = Mu + 1; Nu <= 4; Nu++)
{
for (int i = 0; i < Ns; i++)
for (int j = 0; j < Ns; j++)
for (int k = 0; k < Ns; k++)
for (int t = 0; t < Nt; t++)
{
Link A1 = new Link(false);
int i1 = i, j1 = j, k1 = k, t1 = t; int i2 = i, j2 = j, k2 = k, t2 = t;
GetNode(ref i1, ref j1, ref k1, ref t1, Mu);
GetNode(ref i2, ref j2, ref k2, ref t2, Nu);
if (i == Ns) i = 0; if (i1 == Ns) i1 = 0; if (i2 == Ns) i2 = 0;
A1 = Mul(U[i, j, k, t, Mu], U[i1, j1, k1, t1, Nu]);//U_mu(x)*U_nu(x+mu)
A1 = Mul(A1, U[i2, j2, k2, t2, Mu].HermConj());//*U_mu+(x+Nu)
A1 = Mul(A1, U[i, j, k, t, Nu].HermConj());//*U_nu+(x)
//here A1 is U_mu_nu
n++;
// S += A1.a0; //1/2 Re(Tr(U_mu_nu)
S += ReTr(A1)/3;
}
}
}
// S = /*beta / 3 **/ (1 - S/(3*n));//S=beta/3*Sum(x,Sum(mu<nu,{Re(Tr(1-U_mu_nu))}))
return Math.Abs(1 - S /(n));
}
public Link Mul(Link U, Link V)
{
Link R = new Link(false);
for (int i = 0; i < SU3.d; i++)
for (int j = 0; j < SU3.d; j++)
for (int k = 0; k < SU3.d; k++)
R.A[i, j] += U.A[i, k] * V.A[k, j];
/* R.a0 = U.a0 * V.a0 - U.a1 * V.a1 - U.a2 * V.a2 - U.a3 * V.a3;
R.a1 = U.a0 * V.a1 + U.a1 * V.a0 - U.a2 * V.a3 + U.a3 * V.a2;
R.a2 = U.a0 * V.a2 + U.a2 * V.a0 - U.a3 * V.a1 + U.a1 * V.a3;
R.a3 = U.a0 * V.a3 + U.a3 * V.a0 - U.a1 * V.a2 + U.a2 * V.a1;
*/
/*
//multiplying the matrices
U.U1 = Link1.U1 * Link2.U1 + Link1.U2 * Link2.V1 + Link1.U3 * Link2.W1();
U.U2 = Link1.U1 * Link2.U2 + Link1.U2 * Link2.V2 + Link1.U3 * Link2.W2();
U.U3 = Link1.U1 * Link2.U3 + Link1.U3 * Link2.V1 + Link1.U3 * Link2.W3();
U.V1 = Link1.V1 * Link2.U1 + Link1.V2 * Link2.V1 + Link1.V3 * Link2.W1();
U.V2 = Link1.V1 * Link2.U2 + Link1.V2 * Link2.V2 + Link1.V3 * Link2.W2();
U.V3 = Link1.V1 * Link2.U3 + Link1.V3 * Link2.V1 + Link1.V3 * Link2.W3();
*/
return R;
}
//return 2x2 SU(2) matrix by given determinant of staples near link.
public Link GetHeatBath(double det, int I, int J)
{
Complex[,] SU2 = new Complex[2, 2];
//calculating elements of SU(2) matrix according to distribution dP~exp(-S(u))du
double a = Math.Sqrt(Math.Abs(det));
double x0=0, x1=0, x2=0, x3=0;
/*
//dP(x0)~exp(beta*a*x0) dx0
//make t from [exp(-b*a),1]
double pow = Math.Exp(-beta*a);
bool accepted = false;
while (!accepted)
{
double t = GetRandom() * (pow-1/pow)+1/pow;
x0 = 1 / (beta * a) * Math.Log(t);
//and accept it with probability Math.Sqrt(1-x0^2)
t = GetRandom();
if (t * t < 1 - x0 * x0) accepted = true;
}
*/
bool accepted = false;
double r1 = 0; double r2 = 0; double r3 = 0; double r = 0; double lambda2 = 0;
while (!accepted)
{
r1=GetRandom();r2=GetRandom();r3=GetRandom();
r=GetRandom();
lambda2 = -d / (4 * a * beta) * (Math.Log(r1) + Math.Pow(Math.Cos((2 * Math.PI * r2)), 2) * Math.Log(r3));
//and accept it with probability Math.Sqrt(1-lambda2)
if (r * r < 1 - lambda2) accepted = true;
}
x0 = 1 - 2 * lambda2;
//x1,x2,x3 with probability dOmega = d(cos(teta))d(fi), but on practice, may be (!check it!!!)
double len = Math.Sqrt(1 - x0 * x0);
accepted = false;
double templen=1;
while (!accepted)
{
x1 = GetRandom() * 2 - 1; x2 = GetRandom() * 2 - 1; x3 = GetRandom() * 2 - 1;
templen = x1 * x1 + x2 * x2 + x3 * x3;
if (templen < 1) accepted = true;
}
//normalizing to length len
templen = Math.Sqrt(templen);
x1 *= len/templen; x2 *= len/templen; x3 *= len/templen;
Link Res = new Link(true);
// Res.a0 = x0; Res.a1 = x1; Res.a2= x2; Res.a3 = x3;
Res.A[I, I] = new Complex(x0, x3);
Res.A[I, J] = new Complex(x2, x1);
Res.A[J, I] = new Complex(-x2, x1);
Res.A[J, J] = new Complex(x0, -x3);
return Res;
}
public SU3(int Nspace, int Ntemp, double b, double flux, bool ColdStart)
{
Ns = Nspace; Nt = Ntemp; beta = b;
U = new Link[Ns+1, Ns, Ns, Nt, 5];//x1,x2,x3,x4 (x0 omitted)
InitializeRandom(DateTime.Now.Millisecond);
if (ColdStart)
{
for (int d = 1; d <= 4; d++)
for (int i = 0; i < Ns; i++)
for (int j = 0; j < Ns; j++)
for (int k = 0; k < Ns; k++)
for (int t = 0; t < Nt; t++)
{
/* U[i, j, k, t, d].a0 = 1;
U[i, j, k, t, d].a1 = 0;
U[i, j, k, t, d].a2 = 0;
U[i, j, k, t, d].a3 = 0;
*/
U[i, j, k, t, d] = new Link(true);
}
}
else
{
for (int d = 1; d <= 4; d++)
for (int i = 0; i < Ns; i++)
for (int j = 0; j < Ns; j++)
for (int k = 0; k < Ns; k++)
for (int t = 0; t < Nt; t++)
{
//for SU(2)
double x0 = GetRandom() * 2 - 1;
double x1 = GetRandom() - 0.5, x2 = GetRandom() - 0.5, x3 = GetRandom() - 0.5;
double tlen = Math.Sqrt(x1 * x1 + x2 * x2 + x3 * x3);
double len = Math.Sqrt(1-x0 * x0);
x1 *= len/tlen; x2 *= len/tlen; x3 *= len/tlen;
/* U[i, j, k, t, d].a0 = x0;
U[i, j, k, t, d].a1 = x1;
U[i, j, k, t, d].a2 = x2;
U[i, j, k, t, d].a3 = x3;
*/
//Orthogonalize2(ref U[i, j, k, t, d]);
// double det = GetDet(U[i, j, k, t, d].GetMatrix());
}
}
//exppos2xi = new Complex(Math.Cos(flux), Math.Sin(flux));
expposxi = new Complex(Math.Cos(flux/2), Math.Sin(flux/2));
//expneg2xi = new Complex(Math.Cos(flux), -Math.Sin(flux));
expnegxi = new Complex(Math.Cos(flux / 2),- Math.Sin(flux / 2));
Temp.A[0, 0] = expposxi;
Temp.A[1, 1] = expnegxi;
}
public Link HermConj()
{
Link L = new Link(false);
for (int i = 0; i < SU3.d; i++)
for (int j = 0; j < SU3.d; j++)
L.A[i, j] = A[j, i].Conj();
return L;
}
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;
}