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Julian Lenz
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@ -28,7 +28,7 @@ with this program; if not, write to the Free Software Foundation, Inc.,
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See the full license in the file "LICENSE" in the top level distribution
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directory
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*************************************************************************************/
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/* END LEGAL */
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/* END LEGAL */
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#ifndef QCD_UTIL_SUN_H
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#define QCD_UTIL_SUN_H
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@ -36,7 +36,7 @@ NAMESPACE_BEGIN(Grid);
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template <int ncolour>
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class SU {
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public:
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public:
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static const int Dimension = ncolour;
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static const int AdjointDimension = ncolour * ncolour - 1;
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static int su2subgroups(void) { return (ncolour * (ncolour - 1)) / 2; }
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@ -47,7 +47,7 @@ public:
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using iSU2Matrix = iScalar<iScalar<iMatrix<vtype, 2> > >;
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template <typename vtype>
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using iSUnAlgebraVector =
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iScalar<iScalar<iVector<vtype, AdjointDimension> > >;
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iScalar<iScalar<iVector<vtype, AdjointDimension> > >;
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//////////////////////////////////////////////////////////////////////////////////////////////////
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// Types can be accessed as SU<2>::Matrix , SU<2>::vSUnMatrix,
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@ -159,7 +159,7 @@ public:
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else
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generatorSigmaX(su2Index, ta);
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}
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template <class cplx>
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static void generatorSigmaY(int su2Index, iSUnMatrix<cplx> &ta) {
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ta = Zero();
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@ -169,7 +169,7 @@ public:
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ta()()(i2, i1) = 1.0;
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ta = ta * 0.5;
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}
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template <class cplx>
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static void generatorSigmaX(int su2Index, iSUnMatrix<cplx> &ta) {
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ta = Zero();
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@ -194,8 +194,6 @@ public:
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ta = ta * nrm;
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}
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////////////////////////////////////////////////////////////////////////
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// Map a su2 subgroup number to the pair of rows that are non zero
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////////////////////////////////////////////////////////////////////////
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@ -223,11 +221,10 @@ public:
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int i0, i1;
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su2SubGroupIndex(i0, i1, su2_index);
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autoView( subgroup_v , subgroup,AcceleratorWrite);
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autoView( source_v , source,AcceleratorRead);
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autoView( Determinant_v , Determinant,AcceleratorWrite);
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autoView(subgroup_v, subgroup, AcceleratorWrite);
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autoView(source_v, source, AcceleratorRead);
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autoView(Determinant_v, Determinant, AcceleratorWrite);
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accelerator_for(ss, grid->oSites(), 1, {
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subgroup_v[ss]()()(0, 0) = source_v[ss]()()(i0, i0);
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subgroup_v[ss]()()(0, 1) = source_v[ss]()()(i0, i1);
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subgroup_v[ss]()()(1, 0) = source_v[ss]()()(i1, i0);
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@ -241,7 +238,7 @@ public:
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// this should be purely real
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Determinant_v[ss] =
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Sigma()()(0, 0) * Sigma()()(1, 1) - Sigma()()(0, 1) * Sigma()()(1, 0);
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Sigma()()(0, 0) * Sigma()()(1, 1) - Sigma()()(0, 1) * Sigma()()(1, 0);
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});
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}
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@ -257,16 +254,14 @@ public:
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su2SubGroupIndex(i0, i1, su2_index);
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dest = 1.0; // start out with identity
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autoView( dest_v , dest, AcceleratorWrite);
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autoView( subgroup_v, subgroup, AcceleratorRead);
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accelerator_for(ss, grid->oSites(),1,
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{
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autoView(dest_v, dest, AcceleratorWrite);
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autoView(subgroup_v, subgroup, AcceleratorRead);
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accelerator_for(ss, grid->oSites(), 1, {
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dest_v[ss]()()(i0, i0) = subgroup_v[ss]()()(0, 0);
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dest_v[ss]()()(i0, i1) = subgroup_v[ss]()()(0, 1);
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dest_v[ss]()()(i1, i0) = subgroup_v[ss]()()(1, 0);
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dest_v[ss]()()(i1, i1) = subgroup_v[ss]()()(1, 1);
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});
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}
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///////////////////////////////////////////////
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@ -279,12 +274,12 @@ public:
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// in action.
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//
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///////////////////////////////////////////////
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static void SubGroupHeatBath(GridSerialRNG &sRNG, GridParallelRNG &pRNG,
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RealD beta, // coeff multiplying staple in action (with no 1/Nc)
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LatticeMatrix &link,
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const LatticeMatrix &barestaple, // multiplied by action coeffs so th
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int su2_subgroup, int nheatbath, LatticeInteger &wheremask)
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{
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static void SubGroupHeatBath(
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GridSerialRNG &sRNG, GridParallelRNG &pRNG,
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RealD beta, // coeff multiplying staple in action (with no 1/Nc)
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LatticeMatrix &link,
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const LatticeMatrix &barestaple, // multiplied by action coeffs so th
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int su2_subgroup, int nheatbath, LatticeInteger &wheremask) {
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GridBase *grid = link.Grid();
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const RealD twopi = 2.0 * M_PI;
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@ -297,7 +292,8 @@ public:
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V = link * staple;
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// Subgroup manipulation in the lie algebra space
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LatticeSU2Matrix u(grid); // Kennedy pendleton "u" real projected normalised Sigma
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LatticeSU2Matrix u(
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grid); // Kennedy pendleton "u" real projected normalised Sigma
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LatticeSU2Matrix uinv(grid);
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LatticeSU2Matrix ua(grid); // a in pauli form
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LatticeSU2Matrix b(grid); // rotated matrix after hb
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@ -390,7 +386,7 @@ public:
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xi = 0.5 * sqrt(udet); // 4xi^2 = Det [ Sig - Sig^dag + 1 Tr Sigdag]
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u = 0.5 * u *
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pow(xi, -1.0); // u = 1/2xi [ Sig - Sig^dag + 1 Tr Sigdag]
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pow(xi, -1.0); // u = 1/2xi [ Sig - Sig^dag + 1 Tr Sigdag]
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// Debug test for sanity
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uinv = adj(u);
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@ -405,29 +401,24 @@ public:
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r) )
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= da0 r/2 sin theta dr dtheta dphi delta( (sqrt(1-a0^) - r) )
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Action factor Q(h) dh = e^-S[h] dh = e^{ xi Tr uh} dh // beta enters
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through xi
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= e^{2 xi (h.u)} dh
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= e^{2 xi h0u0}.e^{2 xi h1u1}.e^{2 xi
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h2u2}.e^{2 xi h3u3} dh
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Action factor Q(h) dh = e^-S[h] dh = e^{ xi Tr uh} dh // beta
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enters through xi = e^{2 xi (h.u)} dh = e^{2 xi h0u0}.e^{2 xi h1u1}.e^{2
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xi h2u2}.e^{2 xi h3u3} dh
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Therefore for each site, take xi for that site
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i) generate |a0|<1 with dist
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(1-a0^2)^0.5 e^{2 xi a0 } da0
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Take alpha = 2 xi = 2 xi [ recall 2 beta/Nc unmod staple norm]; hence 2.0/Nc
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factor in Chroma ]
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A. Generate two uniformly distributed pseudo-random numbers R and R', R'',
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R''' in the unit interval;
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B. Set X = -(ln R)/alpha, X' =-(ln R')/alpha;
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C. Set C = cos^2(2pi R"), with R" another uniform random number in [0,1] ;
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D. Set A = XC;
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E. Let d = X'+A;
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Take alpha = 2 xi = 2 xi [ recall 2 beta/Nc unmod staple norm];
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hence 2.0/Nc factor in Chroma ] A. Generate two uniformly distributed
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pseudo-random numbers R and R', R'', R''' in the unit interval; B. Set X =
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-(ln R)/alpha, X' =-(ln R')/alpha; C. Set C = cos^2(2pi R"), with R"
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another uniform random number in [0,1] ; D. Set A = XC; E. Let d = X'+A;
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F. If R'''^2 :> 1 - 0.5 d, go back to A;
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G. Set a0 = 1 - d;
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Note that in step D setting B ~ X - A and using B in place of A in step E will
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generate a second independent a 0 value.
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Note that in step D setting B ~ X - A and using B in place of A in step E
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will generate a second independent a 0 value.
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*/
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/////////////////////////////////////////////////////////
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@ -449,7 +440,7 @@ public:
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LatticeReal alpha(grid);
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// std::cout<<GridLogMessage<<"xi "<<xi <<std::endl;
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xi = 2.0 *xi;
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xi = 2.0 * xi;
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alpha = toReal(xi);
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do {
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@ -522,7 +513,7 @@ public:
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a[2] = a123mag * sin_theta * sin(phi);
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a[3] = a123mag * cos_theta;
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ua = toComplex(a[0]) * ident + toComplex(a[1]) * pauli1 +
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ua = toComplex(a[0]) * ident + toComplex(a[1]) * pauli1 +
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toComplex(a[2]) * pauli2 + toComplex(a[3]) * pauli3;
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b = 1.0;
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@ -568,8 +559,6 @@ public:
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}
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}
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static void testGenerators(void) {
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Matrix ta;
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Matrix tb;
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@ -610,8 +599,8 @@ public:
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// reunitarise??
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template <typename LatticeMatrixType>
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static void LieRandomize(GridParallelRNG &pRNG, LatticeMatrixType &out, double scale = 1.0)
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{
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static void LieRandomize(GridParallelRNG &pRNG, LatticeMatrixType &out,
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double scale = 1.0) {
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GridBase *grid = out.Grid();
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typedef typename LatticeMatrixType::vector_type vector_type;
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@ -620,7 +609,8 @@ public:
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typedef iSinglet<vector_type> vTComplexType;
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typedef Lattice<vTComplexType> LatticeComplexType;
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typedef typename GridTypeMapper<typename LatticeMatrixType::vector_object>::scalar_object MatrixType;
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typedef typename GridTypeMapper<
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typename LatticeMatrixType::vector_object>::scalar_object MatrixType;
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LatticeComplexType ca(grid);
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LatticeMatrixType lie(grid);
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@ -642,7 +632,6 @@ public:
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la = ci * ca * ta;
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lie = lie + la; // e^{i la ta}
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}
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taExp(lie, out);
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}
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@ -681,57 +670,61 @@ public:
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out += la;
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}
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}
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/*
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* Fundamental rep gauge xform
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*/
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template<typename Fundamental,typename GaugeMat>
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static void GaugeTransformFundamental( Fundamental &ferm, GaugeMat &g){
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/*
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* Fundamental rep gauge xform
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*/
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template <typename Fundamental, typename GaugeMat>
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static void GaugeTransformFundamental(Fundamental &ferm, GaugeMat &g) {
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GridBase *grid = ferm._grid;
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conformable(grid,g._grid);
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ferm = g*ferm;
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conformable(grid, g._grid);
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ferm = g * ferm;
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}
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/*
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* Adjoint rep gauge xform
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*/
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/*
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* Adjoint rep gauge xform
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*/
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template<typename GaugeField,typename GaugeMat>
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static void GaugeTransform( GaugeField &Umu, GaugeMat &g){
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template <typename GaugeField, typename GaugeMat>
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static void GaugeTransform(GaugeField &Umu, GaugeMat &g) {
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GridBase *grid = Umu.Grid();
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conformable(grid,g.Grid());
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conformable(grid, g.Grid());
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GaugeMat U(grid);
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GaugeMat ag(grid); ag = adj(g);
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GaugeMat ag(grid);
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ag = adj(g);
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for(int mu=0;mu<Nd;mu++){
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U= PeekIndex<LorentzIndex>(Umu,mu);
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U = g*U*Cshift(ag, mu, 1);
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PokeIndex<LorentzIndex>(Umu,U,mu);
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for (int mu = 0; mu < Nd; mu++) {
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U = PeekIndex<LorentzIndex>(Umu, mu);
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U = g * U * Cshift(ag, mu, 1);
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PokeIndex<LorentzIndex>(Umu, U, mu);
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}
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}
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template<typename GaugeMat>
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static void GaugeTransform( std::vector<GaugeMat> &U, GaugeMat &g){
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template <typename GaugeMat>
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static void GaugeTransform(std::vector<GaugeMat> &U, GaugeMat &g) {
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GridBase *grid = g.Grid();
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GaugeMat ag(grid); ag = adj(g);
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for(int mu=0;mu<Nd;mu++){
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U[mu] = g*U[mu]*Cshift(ag, mu, 1);
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GaugeMat ag(grid);
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ag = adj(g);
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for (int mu = 0; mu < Nd; mu++) {
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U[mu] = g * U[mu] * Cshift(ag, mu, 1);
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}
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}
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template<typename GaugeField,typename GaugeMat>
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static void RandomGaugeTransform(GridParallelRNG &pRNG, GaugeField &Umu, GaugeMat &g){
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LieRandomize(pRNG,g,1.0);
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GaugeTransform(Umu,g);
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template <typename GaugeField, typename GaugeMat>
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static void RandomGaugeTransform(GridParallelRNG &pRNG, GaugeField &Umu,
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GaugeMat &g) {
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LieRandomize(pRNG, g, 1.0);
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GaugeTransform(Umu, g);
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}
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// Projects the algebra components a lattice matrix (of dimension ncol*ncol -1 )
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// inverse operation: FundamentalLieAlgebraMatrix
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static void projectOnAlgebra(LatticeAlgebraVector &h_out, const LatticeMatrix &in, Real scale = 1.0) {
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// Projects the algebra components a lattice matrix (of dimension ncol*ncol -1
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// ) inverse operation: FundamentalLieAlgebraMatrix
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static void projectOnAlgebra(LatticeAlgebraVector &h_out,
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const LatticeMatrix &in, Real scale = 1.0) {
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conformable(h_out, in);
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h_out = Zero();
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Matrix Ta;
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for (int a = 0; a < AdjointDimension; a++) {
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generator(a, Ta);
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pokeColour(h_out, - 2.0 * (trace(timesI(Ta) * in)) * scale, a);
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pokeColour(h_out, -2.0 * (trace(timesI(Ta) * in)) * scale, a);
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}
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}
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@ -747,37 +740,37 @@ public:
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PokeIndex<LorentzIndex>(out, Umu, mu);
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}
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}
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template<typename GaugeField>
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static void TepidConfiguration(GridParallelRNG &pRNG,GaugeField &out){
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template <typename GaugeField>
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static void TepidConfiguration(GridParallelRNG &pRNG, GaugeField &out) {
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typedef typename GaugeField::vector_type vector_type;
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typedef iSUnMatrix<vector_type> vMatrixType;
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typedef Lattice<vMatrixType> LatticeMatrixType;
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LatticeMatrixType Umu(out.Grid());
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for(int mu=0;mu<Nd;mu++){
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LieRandomize(pRNG,Umu,0.01);
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PokeIndex<LorentzIndex>(out,Umu,mu);
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for (int mu = 0; mu < Nd; mu++) {
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LieRandomize(pRNG, Umu, 0.01);
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PokeIndex<LorentzIndex>(out, Umu, mu);
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}
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}
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template<typename GaugeField>
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static void ColdConfiguration(GaugeField &out){
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template <typename GaugeField>
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static void ColdConfiguration(GaugeField &out) {
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typedef typename GaugeField::vector_type vector_type;
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typedef iSUnMatrix<vector_type> vMatrixType;
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typedef Lattice<vMatrixType> LatticeMatrixType;
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LatticeMatrixType Umu(out.Grid());
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Umu=1.0;
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for(int mu=0;mu<Nd;mu++){
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PokeIndex<LorentzIndex>(out,Umu,mu);
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Umu = 1.0;
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for (int mu = 0; mu < Nd; mu++) {
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PokeIndex<LorentzIndex>(out, Umu, mu);
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}
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}
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template<typename GaugeField>
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static void ColdConfiguration(GridParallelRNG &pRNG,GaugeField &out){
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template <typename GaugeField>
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static void ColdConfiguration(GridParallelRNG &pRNG, GaugeField &out) {
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ColdConfiguration(out);
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}
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template<typename LatticeMatrixType>
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static void taProj( const LatticeMatrixType &in, LatticeMatrixType &out){
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template <typename LatticeMatrixType>
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static void taProj(const LatticeMatrixType &in, LatticeMatrixType &out) {
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out = Ta(in);
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}
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template <typename LatticeMatrixType>
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@ -799,85 +792,88 @@ public:
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}
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};
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template<int N>
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LatticeComplexD Determinant(const Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu)
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{
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GridBase *grid=Umu.Grid();
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template <int N>
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LatticeComplexD Determinant(
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const Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
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GridBase *grid = Umu.Grid();
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auto lvol = grid->lSites();
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LatticeComplexD ret(grid);
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autoView(Umu_v,Umu,CpuRead);
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autoView(ret_v,ret,CpuWrite);
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thread_for(site,lvol,{
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Eigen::MatrixXcd EigenU = Eigen::MatrixXcd::Zero(N,N);
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autoView(Umu_v, Umu, CpuRead);
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autoView(ret_v, ret, CpuWrite);
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thread_for(site, lvol, {
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Eigen::MatrixXcd EigenU = Eigen::MatrixXcd::Zero(N, N);
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Coordinate lcoor;
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grid->LocalIndexToLocalCoor(site, lcoor);
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iScalar<iScalar<iMatrix<ComplexD, N> > > Us;
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peekLocalSite(Us, Umu_v, lcoor);
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for(int i=0;i<N;i++){
|
||||
for(int j=0;j<N;j++){
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EigenU(i,j) = Us()()(i,j);
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}}
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||||
for (int i = 0; i < N; i++) {
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||||
for (int j = 0; j < N; j++) {
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EigenU(i, j) = Us()()(i, j);
|
||||
}
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||||
}
|
||||
ComplexD det = EigenU.determinant();
|
||||
pokeLocalSite(det,ret_v,lcoor);
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pokeLocalSite(det, ret_v, lcoor);
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});
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return ret;
|
||||
}
|
||||
template<int N>
|
||||
static void ProjectSUn(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu)
|
||||
{
|
||||
Umu = ProjectOnGroup(Umu);
|
||||
template <int N>
|
||||
static void ProjectSUn(
|
||||
Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
|
||||
Umu = ProjectOnGroup(Umu);
|
||||
auto det = Determinant(Umu);
|
||||
|
||||
det = conjugate(det);
|
||||
|
||||
for(int i=0;i<N;i++){
|
||||
auto element = PeekIndex<ColourIndex>(Umu,N-1,i);
|
||||
for (int i = 0; i < N; i++) {
|
||||
auto element = PeekIndex<ColourIndex>(Umu, N - 1, i);
|
||||
element = element * det;
|
||||
PokeIndex<ColourIndex>(Umu,element,Nc-1,i);
|
||||
PokeIndex<ColourIndex>(Umu, element, Nc - 1, i);
|
||||
}
|
||||
}
|
||||
template<int N>
|
||||
static void ProjectSUn(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >,Nd> > &U)
|
||||
{
|
||||
GridBase *grid=U.Grid();
|
||||
template <int N>
|
||||
static void ProjectSUn(
|
||||
Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U) {
|
||||
GridBase *grid = U.Grid();
|
||||
// Reunitarise
|
||||
for(int mu=0;mu<Nd;mu++){
|
||||
auto Umu = PeekIndex<LorentzIndex>(U,mu);
|
||||
Umu = ProjectOnGroup(Umu);
|
||||
for (int mu = 0; mu < Nd; mu++) {
|
||||
auto Umu = PeekIndex<LorentzIndex>(U, mu);
|
||||
Umu = ProjectOnGroup(Umu);
|
||||
ProjectSUn(Umu);
|
||||
PokeIndex<LorentzIndex>(U,Umu,mu);
|
||||
PokeIndex<LorentzIndex>(U, Umu, mu);
|
||||
}
|
||||
}
|
||||
// Explicit specialisation for SU(3).
|
||||
// Explicit specialisation for SU(3).
|
||||
static void
|
||||
ProjectSU3 (Lattice<iScalar<iScalar<iMatrix<vComplexD, 3> > > > &Umu)
|
||||
{
|
||||
GridBase *grid=Umu.Grid();
|
||||
const int x=0;
|
||||
const int y=1;
|
||||
const int z=2;
|
||||
static void ProjectSU3(
|
||||
Lattice<iScalar<iScalar<iMatrix<vComplexD, 3> > > > &Umu) {
|
||||
GridBase *grid = Umu.Grid();
|
||||
const int x = 0;
|
||||
const int y = 1;
|
||||
const int z = 2;
|
||||
// Reunitarise
|
||||
Umu = ProjectOnGroup(Umu);
|
||||
autoView(Umu_v,Umu,CpuWrite);
|
||||
thread_for(ss,grid->oSites(),{
|
||||
auto cm = Umu_v[ss];
|
||||
cm()()(2,x) = adj(cm()()(0,y)*cm()()(1,z)-cm()()(0,z)*cm()()(1,y)); //x= yz-zy
|
||||
cm()()(2,y) = adj(cm()()(0,z)*cm()()(1,x)-cm()()(0,x)*cm()()(1,z)); //y= zx-xz
|
||||
cm()()(2,z) = adj(cm()()(0,x)*cm()()(1,y)-cm()()(0,y)*cm()()(1,x)); //z= xy-yx
|
||||
Umu_v[ss]=cm;
|
||||
autoView(Umu_v, Umu, CpuWrite);
|
||||
thread_for(ss, grid->oSites(), {
|
||||
auto cm = Umu_v[ss];
|
||||
cm()()(2, x) = adj(cm()()(0, y) * cm()()(1, z) -
|
||||
cm()()(0, z) * cm()()(1, y)); // x= yz-zy
|
||||
cm()()(2, y) = adj(cm()()(0, z) * cm()()(1, x) -
|
||||
cm()()(0, x) * cm()()(1, z)); // y= zx-xz
|
||||
cm()()(2, z) = adj(cm()()(0, x) * cm()()(1, y) -
|
||||
cm()()(0, y) * cm()()(1, x)); // z= xy-yx
|
||||
Umu_v[ss] = cm;
|
||||
});
|
||||
}
|
||||
static void ProjectSU3(Lattice<iVector<iScalar<iMatrix<vComplexD, 3> >,Nd> > &U)
|
||||
{
|
||||
GridBase *grid=U.Grid();
|
||||
static void ProjectSU3(
|
||||
Lattice<iVector<iScalar<iMatrix<vComplexD, 3> >, Nd> > &U) {
|
||||
GridBase *grid = U.Grid();
|
||||
// Reunitarise
|
||||
for(int mu=0;mu<Nd;mu++){
|
||||
auto Umu = PeekIndex<LorentzIndex>(U,mu);
|
||||
Umu = ProjectOnGroup(Umu);
|
||||
for (int mu = 0; mu < Nd; mu++) {
|
||||
auto Umu = PeekIndex<LorentzIndex>(U, mu);
|
||||
Umu = ProjectOnGroup(Umu);
|
||||
ProjectSU3(Umu);
|
||||
PokeIndex<LorentzIndex>(U,Umu,mu);
|
||||
PokeIndex<LorentzIndex>(U, Umu, mu);
|
||||
}
|
||||
}
|
||||
|
||||
@ -886,7 +882,6 @@ typedef SU<3> SU3;
|
||||
typedef SU<4> SU4;
|
||||
typedef SU<5> SU5;
|
||||
|
||||
|
||||
typedef SU<Nc> FundamentalMatrices;
|
||||
|
||||
NAMESPACE_END(Grid);
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user