mirror of
https://github.com/paboyle/Grid.git
synced 2025-11-04 05:54:32 +00:00
Namespace
This commit is contained in:
paboyle
@@ -28,16 +28,15 @@ with this program; if not, write to the Free Software Foundation, Inc.,
|
||||
See the full license in the file "LICENSE" in the top level distribution
|
||||
directory
|
||||
*************************************************************************************/
|
||||
/* END LEGAL */
|
||||
/* END LEGAL */
|
||||
#ifndef QCD_UTIL_SUN_H
|
||||
#define QCD_UTIL_SUN_H
|
||||
|
||||
namespace Grid {
|
||||
namespace QCD {
|
||||
NAMESPACE_BEGIN(Grid);
|
||||
|
||||
template <int ncolour>
|
||||
class SU {
|
||||
public:
|
||||
public:
|
||||
static const int Dimension = ncolour;
|
||||
static const int AdjointDimension = ncolour * ncolour - 1;
|
||||
static int su2subgroups(void) { return (ncolour * (ncolour - 1)) / 2; }
|
||||
@@ -48,7 +47,7 @@ class SU {
|
||||
using iSU2Matrix = iScalar<iScalar<iMatrix<vtype, 2> > >;
|
||||
template <typename vtype>
|
||||
using iSUnAlgebraVector =
|
||||
iScalar<iScalar<iVector<vtype, AdjointDimension> > >;
|
||||
iScalar<iScalar<iVector<vtype, AdjointDimension> > >;
|
||||
|
||||
//////////////////////////////////////////////////////////////////////////////////////////////////
|
||||
// Types can be accessed as SU<2>::Matrix , SU<2>::vSUnMatrix,
|
||||
@@ -238,7 +237,7 @@ class SU {
|
||||
|
||||
// this should be purely real
|
||||
Determinant._odata[ss] =
|
||||
Sigma()()(0, 0) * Sigma()()(1, 1) - Sigma()()(0, 1) * Sigma()()(1, 0);
|
||||
Sigma()()(0, 0) * Sigma()()(1, 1) - Sigma()()(0, 1) * Sigma()()(1, 0);
|
||||
}
|
||||
}
|
||||
|
||||
@@ -273,11 +272,11 @@ class SU {
|
||||
//
|
||||
///////////////////////////////////////////////
|
||||
static void SubGroupHeatBath(
|
||||
GridSerialRNG &sRNG, GridParallelRNG &pRNG,
|
||||
RealD beta, // coeff multiplying staple in action (with no 1/Nc)
|
||||
LatticeMatrix &link,
|
||||
const LatticeMatrix &barestaple, // multiplied by action coeffs so th
|
||||
int su2_subgroup, int nheatbath, LatticeInteger &wheremask) {
|
||||
GridSerialRNG &sRNG, GridParallelRNG &pRNG,
|
||||
RealD beta, // coeff multiplying staple in action (with no 1/Nc)
|
||||
LatticeMatrix &link,
|
||||
const LatticeMatrix &barestaple, // multiplied by action coeffs so th
|
||||
int su2_subgroup, int nheatbath, LatticeInteger &wheremask) {
|
||||
GridBase *grid = link._grid;
|
||||
|
||||
int ntrials = 0;
|
||||
@@ -293,7 +292,7 @@ class SU {
|
||||
|
||||
// Subgroup manipulation in the lie algebra space
|
||||
LatticeSU2Matrix u(
|
||||
grid); // Kennedy pendleton "u" real projected normalised Sigma
|
||||
grid); // Kennedy pendleton "u" real projected normalised Sigma
|
||||
LatticeSU2Matrix uinv(grid);
|
||||
LatticeSU2Matrix ua(grid); // a in pauli form
|
||||
LatticeSU2Matrix b(grid); // rotated matrix after hb
|
||||
@@ -314,41 +313,41 @@ class SU {
|
||||
mask_false = 0;
|
||||
|
||||
/*
|
||||
PLB 156 P393 (1985) (Kennedy and Pendleton)
|
||||
PLB 156 P393 (1985) (Kennedy and Pendleton)
|
||||
|
||||
Note: absorb "beta" into the def of sigma compared to KP paper; staple
|
||||
passed to this routine has "beta" already multiplied in
|
||||
Note: absorb "beta" into the def of sigma compared to KP paper; staple
|
||||
passed to this routine has "beta" already multiplied in
|
||||
|
||||
Action linear in links h and of form:
|
||||
Action linear in links h and of form:
|
||||
|
||||
beta S = beta Sum_p (1 - 1/Nc Re Tr Plaq )
|
||||
|
||||
Writing Sigma = 1/Nc (beta Sigma') where sum over staples is "Sigma' "
|
||||
Writing Sigma = 1/Nc (beta Sigma') where sum over staples is "Sigma' "
|
||||
|
||||
beta S = const - beta/Nc Re Tr h Sigma'
|
||||
= const - Re Tr h Sigma
|
||||
beta S = const - beta/Nc Re Tr h Sigma'
|
||||
= const - Re Tr h Sigma
|
||||
|
||||
Decompose h and Sigma into (1, sigma_j) ; h_i real, h^2=1, Sigma_i complex
|
||||
arbitrary.
|
||||
Decompose h and Sigma into (1, sigma_j) ; h_i real, h^2=1, Sigma_i complex
|
||||
arbitrary.
|
||||
|
||||
Tr h Sigma = h_i Sigma_j Tr (sigma_i sigma_j) = h_i Sigma_j 2 delta_ij
|
||||
Re Tr h Sigma = 2 h_j Re Sigma_j
|
||||
Re Tr h Sigma = 2 h_j Re Sigma_j
|
||||
|
||||
Normalised re Sigma_j = xi u_j
|
||||
Normalised re Sigma_j = xi u_j
|
||||
|
||||
With u_j a unit vector and U can be in SU(2);
|
||||
With u_j a unit vector and U can be in SU(2);
|
||||
|
||||
Re Tr h Sigma = 2 h_j Re Sigma_j = 2 xi (h.u)
|
||||
Re Tr h Sigma = 2 h_j Re Sigma_j = 2 xi (h.u)
|
||||
|
||||
4xi^2 = Det [ Sig - Sig^dag + 1 Tr Sigdag]
|
||||
u = 1/2xi [ Sig - Sig^dag + 1 Tr Sigdag]
|
||||
4xi^2 = Det [ Sig - Sig^dag + 1 Tr Sigdag]
|
||||
u = 1/2xi [ Sig - Sig^dag + 1 Tr Sigdag]
|
||||
|
||||
xi = sqrt(Det)/2;
|
||||
xi = sqrt(Det)/2;
|
||||
|
||||
Write a= u h in SU(2); a has pauli decomp a_j;
|
||||
Write a= u h in SU(2); a has pauli decomp a_j;
|
||||
|
||||
Note: Product b' xi is unvariant because scaling Sigma leaves
|
||||
normalised vector "u" fixed; Can rescale Sigma so b' = 1.
|
||||
Note: Product b' xi is unvariant because scaling Sigma leaves
|
||||
normalised vector "u" fixed; Can rescale Sigma so b' = 1.
|
||||
*/
|
||||
|
||||
////////////////////////////////////////////////////////
|
||||
@@ -386,7 +385,7 @@ class SU {
|
||||
|
||||
xi = 0.5 * sqrt(udet); // 4xi^2 = Det [ Sig - Sig^dag + 1 Tr Sigdag]
|
||||
u = 0.5 * u *
|
||||
pow(xi, -1.0); // u = 1/2xi [ Sig - Sig^dag + 1 Tr Sigdag]
|
||||
pow(xi, -1.0); // u = 1/2xi [ Sig - Sig^dag + 1 Tr Sigdag]
|
||||
|
||||
// Debug test for sanity
|
||||
uinv = adj(u);
|
||||
@@ -394,36 +393,36 @@ class SU {
|
||||
assert(norm2(b) < 1.0e-4);
|
||||
|
||||
/*
|
||||
Measure: Haar measure dh has d^4a delta(1-|a^2|)
|
||||
In polars:
|
||||
da = da0 r^2 sin theta dr dtheta dphi delta( 1 - r^2 -a0^2)
|
||||
= da0 r^2 sin theta dr dtheta dphi delta( (sqrt(1-a0^) - r)(sqrt(1-a0^) +
|
||||
r) )
|
||||
= da0 r/2 sin theta dr dtheta dphi delta( (sqrt(1-a0^) - r) )
|
||||
Measure: Haar measure dh has d^4a delta(1-|a^2|)
|
||||
In polars:
|
||||
da = da0 r^2 sin theta dr dtheta dphi delta( 1 - r^2 -a0^2)
|
||||
= da0 r^2 sin theta dr dtheta dphi delta( (sqrt(1-a0^) - r)(sqrt(1-a0^) +
|
||||
r) )
|
||||
= da0 r/2 sin theta dr dtheta dphi delta( (sqrt(1-a0^) - r) )
|
||||
|
||||
Action factor Q(h) dh = e^-S[h] dh = e^{ xi Tr uh} dh // beta enters
|
||||
through xi
|
||||
= e^{2 xi (h.u)} dh
|
||||
= e^{2 xi h0u0}.e^{2 xi h1u1}.e^{2 xi
|
||||
h2u2}.e^{2 xi h3u3} dh
|
||||
Action factor Q(h) dh = e^-S[h] dh = e^{ xi Tr uh} dh // beta enters
|
||||
through xi
|
||||
= e^{2 xi (h.u)} dh
|
||||
= e^{2 xi h0u0}.e^{2 xi h1u1}.e^{2 xi
|
||||
h2u2}.e^{2 xi h3u3} dh
|
||||
|
||||
Therefore for each site, take xi for that site
|
||||
i) generate |a0|<1 with dist
|
||||
(1-a0^2)^0.5 e^{2 xi a0 } da0
|
||||
Therefore for each site, take xi for that site
|
||||
i) generate |a0|<1 with dist
|
||||
(1-a0^2)^0.5 e^{2 xi a0 } da0
|
||||
|
||||
Take alpha = 2 xi = 2 xi [ recall 2 beta/Nc unmod staple norm]; hence 2.0/Nc
|
||||
factor in Chroma ]
|
||||
A. Generate two uniformly distributed pseudo-random numbers R and R', R'',
|
||||
R''' in the unit interval;
|
||||
B. Set X = -(ln R)/alpha, X' =-(ln R')/alpha;
|
||||
C. Set C = cos^2(2pi R"), with R" another uniform random number in [0,1] ;
|
||||
D. Set A = XC;
|
||||
E. Let d = X'+A;
|
||||
F. If R'''^2 :> 1 - 0.5 d, go back to A;
|
||||
G. Set a0 = 1 - d;
|
||||
Take alpha = 2 xi = 2 xi [ recall 2 beta/Nc unmod staple norm]; hence 2.0/Nc
|
||||
factor in Chroma ]
|
||||
A. Generate two uniformly distributed pseudo-random numbers R and R', R'',
|
||||
R''' in the unit interval;
|
||||
B. Set X = -(ln R)/alpha, X' =-(ln R')/alpha;
|
||||
C. Set C = cos^2(2pi R"), with R" another uniform random number in [0,1] ;
|
||||
D. Set A = XC;
|
||||
E. Let d = X'+A;
|
||||
F. If R'''^2 :> 1 - 0.5 d, go back to A;
|
||||
G. Set a0 = 1 - d;
|
||||
|
||||
Note that in step D setting B ~ X - A and using B in place of A in step E will
|
||||
generate a second independent a 0 value.
|
||||
Note that in step D setting B ~ X - A and using B in place of A in step E will
|
||||
generate a second independent a 0 value.
|
||||
*/
|
||||
|
||||
/////////////////////////////////////////////////////////
|
||||
@@ -518,7 +517,7 @@ class SU {
|
||||
a[3] = a123mag * cos_theta;
|
||||
|
||||
ua = toComplex(a[0]) * ident + toComplex(a[1]) * pauli1 +
|
||||
toComplex(a[2]) * pauli2 + toComplex(a[3]) * pauli3;
|
||||
toComplex(a[2]) * pauli2 + toComplex(a[3]) * pauli3;
|
||||
|
||||
b = 1.0;
|
||||
b = where(wheremask, uinv * ua, b);
|
||||
@@ -616,7 +615,7 @@ class SU {
|
||||
|
||||
typedef Lattice<vTComplexType> LatticeComplexType;
|
||||
typedef typename GridTypeMapper<
|
||||
typename LatticeMatrixType::vector_object>::scalar_object MatrixType;
|
||||
typename LatticeMatrixType::vector_object>::scalar_object MatrixType;
|
||||
|
||||
LatticeComplexType ca(grid);
|
||||
LatticeMatrixType lie(grid);
|
||||
@@ -675,11 +674,11 @@ class SU {
|
||||
out += la;
|
||||
}
|
||||
}
|
||||
/*
|
||||
add GaugeTrans
|
||||
*/
|
||||
/*
|
||||
add GaugeTrans
|
||||
*/
|
||||
|
||||
template<typename GaugeField,typename GaugeMat>
|
||||
template<typename GaugeField,typename GaugeMat>
|
||||
static void GaugeTransform( GaugeField &Umu, GaugeMat &g){
|
||||
GridBase *grid = Umu._grid;
|
||||
conformable(grid,g._grid);
|
||||
@@ -694,7 +693,7 @@ template<typename GaugeField,typename GaugeMat>
|
||||
}
|
||||
}
|
||||
template<typename GaugeMat>
|
||||
static void GaugeTransform( std::vector<GaugeMat> &U, GaugeMat &g){
|
||||
static void GaugeTransform( std::vector<GaugeMat> &U, GaugeMat &g){
|
||||
GridBase *grid = g._grid;
|
||||
GaugeMat ag(grid); ag = adj(g);
|
||||
for(int mu=0;mu<Nd;mu++){
|
||||
@@ -793,6 +792,5 @@ typedef SU<5> SU5;
|
||||
|
||||
typedef SU<Nc> FundamentalMatrices;
|
||||
|
||||
}
|
||||
}
|
||||
NAMESPACE_END(Grid);
|
||||
#endif
|
||||
|
||||
Reference in New Issue
Block a user