double dSF()
{
Dirac D = new Dirac(this);
Vector chi = new Vector(Dirac.N, DateTime.Now.Millisecond);
D.phi = D.MulD(chi);
return 0;
}
public void Prepare()
{
x = phi;
ri = AXPY(Complex.MinOne, MulD(x0), phi);
rhat0 = ri;
alpha = wi = Complex.One;
roi = V1hermV2(rhat0, rhat0);
}
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]);
}
}
public Vector MulDold(Vector V)
{
Vector res = new Vector(N);
for (int i = 0; i < N; i++)
for (byte j = 0; j < 4; j++)
for (byte k = 0; k < 3; k++)
for (int i1 = 0; i1 < N; i1++)
for (byte j1 = 0; j1 < 4; j1++)
for (byte k1 = 0; k1 < 3; k1++)
res[i, j, k] += D(GetSite(i), GetSite(i1), j, j1, k, k1) * V[i1, j1, k1];
return res;
}
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 void Prepare()
//{
// rprev = AXPY(Complex.MinOne, MulD(x0), phi);
// rhat0 = rprev;
// alpha = wprev = Complex.One;
// roprev = V1hermV2(rhat0, rhat0);
//}
//public int Iter()
//{
// int Niter = 100;
// for (int i = 0; i < Niter; i++)
// {
// roi = V1hermV2(rhat0, rprev);
// if (roi.x == 0)
// return -i;
// beta = (roi / roprev) * (alpha / wprev);
// pi = AXPY(beta, AXPY(-wprev, vprev, pprev), rprev);
// vi = MulD(pi);
// alpha = roi / V1hermV2(rhat0, vi);//roprev
// s = AXPY(-alpha, vi, rprev);
// t = MulD(s);
// wi = V1hermV2(t, s) / V1hermV2(t, t);
// x = AXPY(alpha, pi, AXPY(wi, s, xprev));
// ri = AXPY(-wi, t, s);
// rprev = ri; pprev = pi; vprev = vi; xprev = x;
// roprev = roi; wprev = wi;
// if (Dirac.V1hermV2(ri, ri).Module() < 1E-5) return i;
// }
// return 100;
//}
public int IterPrime()
{
int Niter = 100; Complex roprev;
for (int i = 0; i < Niter; i++)
{
roprev = roi;
roi = V1hermV2(rhat0, ri);
if (roi.x == 0)
return -i;
beta = (roi / roprev) * (alpha / wi);
pi = AXPY(beta, AXPY(-wi, vi, pi), ri);
vi = MulDprime(pi);
alpha = roi / V1hermV2(rhat0, vi);//roprev
if (alpha.x==1 && alpha.y == 0) break;
s = AXPY(-alpha, vi, ri);
t = MulDprime(s);
wi = V1hermV2(t, s) / V1hermV2(t, t);
x = AXPY(alpha, pi, AXPY(wi, s, x));
ri = AXPY(-wi, t, s);
//rprev = ri; pprev = pi; vprev = vi; xprev = x;
//roprev = roi; wprev = wi;
if (Dirac.V1hermV2(ri, ri).Module() < 1E-1) return i;
}
return Niter;
}
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 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;
}
public Vector AXPY(Complex A, Vector X, Vector Y)
{
Vector res = new Vector(X.N);
for (int i = 0; i < X.N; i++)
for (byte j = 0; j < 4; j++)
for (byte k = 0; k < 3; k++)
res[i, j, k] = A * X[i, j, k] + Y[i, j, k];
return res;
}
public static Complex V1hermV2(Vector Vector1, Vector Vector2)
{
Complex res = Complex.Zero;
for (int i = 0; i < Vector1.N; i++)
for (byte j = 0; j<4;j++)
for (byte k = 0; k<3;k++)
res += (Vector1[i,j,k]).Conj() * Vector2[i,j,k];
return res;
}
public Dirac(SU3 GaugeField)
{
U = GaugeField;
OneMinusgamma = new Complex[4][,] { OneMinusGamma1, OneMinusGamma2, OneMinusGamma3, OneMinusGamma4 };
OnePlusgamma = new Complex[4][,] { OnePlusGamma1, OnePlusGamma2, OnePlusGamma3, OnePlusGamma4 };
Nx = U.Ns; Nxy = Nx * Nx; Nxyz = Nxy * Nx; N = Nxyz * U.Nt;
Ny = U.Ns; Nz = U.Ns; Nt = U.Nt;
phi = new Vector(N);
r0 = new Vector(N);
rhat0 = new Vector(N);
rprev = new Vector(N);
pi = new Vector(N);
vi = new Vector(N);
t = new Vector(N);
s = new Vector(N);
xprev = new Vector(N);
vprev = new Vector(N);
pprev = new Vector(N);
ri = new Vector(N);
x0 = new Vector(N);
x = new Vector(N);
}
private void button11_Click(object sender, EventArgs e)
{
////check Gaussness
//Vector v = new Vector(100);
//int N = 100; double a = 0, b = 10;
//int[] inters = new int[N];
//for (int i = 0; i < 10000; i++)
//{
// double r = v.GetGaussRandom()+5;
// if (r>a && r < b)
// inters[(int)(r * N/(b-a))]++;
//}
//for (int i = 0; i < N; i++)
// chart1.Series[0].Points.AddXY((double)i / (double)N, inters[i]);
////basic delta
//int K = 100, n = 3;
//Complex[][] chi = new Complex[K][];
//for (int i = 0; i < K; i++)
//{
// chi[i] = new Complex[n];
// for (int j = 0; j < n; j++)
// chi[i][j] = GetGaussRandom();
//}
//double[,] delta = new double[n, n];
//double res1 = 0, res2 = 0;
//for (int i = 0; i < n; i++)
// for (int j = 0; j < n; j++)
// {
// Complex t = new Complex();
// for (int k = 0; k < K; k++)
// t += (chi[k][i] * chi[k][j].Conj());
// delta[i, j] = 1 / (double)(2 * K) * t.x;// OneOverK;
// if (i == j) res1 += delta[i, j]; else res2 += delta[i, j];
// }
//Text = res1.ToString() + " " + (res2 / n).ToString();
//real delta
int K = 1, n = 10;
Vector[] chi = new Vector[K];
for (int i = 0; i < K; i++)
{
chi[i] = new Vector(n,rand.Next());
chi[i].FillGaussRandom();
}
double[, , , , ,] delta = new double[n, n, 4, 4, 3, 3];
double res1 = 0, res2 = 0;
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
for (byte alpha = 0; alpha < 4; alpha++)
for (byte beta = 0; beta < 4; beta++)
for (byte a = 0; a < 3; a++)
for (byte b = 0; b < 3; b++)
{
Complex OneOverK = new Complex(1 / (double)K, 0);
Complex t = new Complex();
for (int k = 0; k < K; k++)
t += (chi[k][i, alpha, a] * chi[k][j, beta, b].Conj());
delta[i, j, alpha, beta, a, b] = 1 / (double)(K) * t.x;// OneOverK;
if (i == j && alpha == beta && a == b) res1 += delta[i, j, alpha, beta, a, b]; else res2 += delta[i, j, alpha, beta, a, b];
}
Text = res1.ToString() + " " + (res2 / n / 12).ToString();
}