suN_gauge_surface.cpp

#include "hila.h"
#include "gauge/staples.h"
#include "gauge/polyakov.h"
#include "gauge/stout_smear.h"
 
#include "gauge/sun_heatbath.h"
#include "gauge/sun_overrelax.h"
#include "checkpoint.h"
 
#include <fftw3.h>
 
#ifndef NCOLOR
#define NCOLOR 3
#endif
 
using mygroup = SU<NCOLOR, float>;
 
enum class poly_limit { OFF, RANGE, PARABOLIC };
 
// define a struct to hold the input parameters: this
// makes it simpler to pass the values around
struct parameters {
    double beta;
    double deltab;
    int n_overrelax;
    int n_update;
    int n_trajectories;
    int n_thermal;
    int n_save;
    int n_profile;
    std::string config_file;
    double time_offset;
    poly_limit polyakov_pot;
    double poly_min, poly_max, poly_m2;
    std::vector<int> n_smear;
    double smear_coeff;
    std::vector<int> z_smear;
    int n_surface;
    int n_dump_polyakov;
};
 
template <typename T>
void staplesum_db(const GaugeField<T> &U, Field<T> &staples, Direction d1, Parity par,
                  double deltab) {
 
    Field<T> lower;
 
    // zero staples just in case
    staples[par] = 0;
 
    foralldir(d2) if (d2 != d1) {
 
        // anticipate that these are needed
        // not really necessary, but may be faster
        U[d2].start_gather(d1, ALL);
        U[d1].start_gather(d2, par);
 
        // calculate first lower 'U' of the staple sum
        // do it on opp parity
        onsites(opp_parity(par)) {
            double m;
            if (2 * X.z() < lattice.size(e_z))
                m = 1.0 - deltab;
            else
                m = 1.0 + deltab;
 
            lower[X] = m * U[d2][X].dagger() * U[d1][X] * U[d2][X + d1];
        }
 
        // calculate then the upper 'n', and add the lower
        // lower could also be added on a separate loop
        onsites(par) {
            double m;
            if (2 * X.z() < lattice.size(e_z))
                m = 1.0 - deltab;
            else
                m = 1.0 + deltab;
 
            staples[X] += m * U[d2][X] * U[d1][X + d2] * U[d2][X + d1].dagger() + lower[X - d2];
        }
    }
}
 
template <typename group>
double measure_plaq_db(const GaugeField<group> &U, double db = 0.0) {
    Reduction<double> plaq;
    plaq.allreduce(false);
 
    foralldir(dir1) foralldir(dir2) if (dir1 < dir2) {
        if (db == 0.0) {
            onsites(ALL) {
                plaq += 1.0 - real(trace(U[dir1][X] * U[dir2][X + dir1] *
                                         U[dir1][X + dir2].dagger() * U[dir2][X].dagger())) /
                                  group::size();
            }
        } else {
            onsites(ALL) {
                double c;
                if (2 * X.z() < lattice.size(e_z))
                    c = 1 - db;
                else
                    c = 1 + db;
 
                plaq += c * (1.0 - real(trace(U[dir1][X] * U[dir2][X + dir1] *
                                              U[dir1][X + dir2].dagger() * U[dir2][X].dagger())) /
                                       group::size());
            }
        }
    }
    return plaq.value();
}
 
template <typename group>
double measure_action(const GaugeField<group> &U, const VectorField<Algebra<group>> &E,
                      const parameters &p) {
 
    auto plaq = measure_plaq_bp(U, p.deltab);
 
    return p.beta * plaq;
}
 
/////////////////////////////////////////////////////////////////////////////
/// Measure polyakov "field"
///
 
template <typename T>
void measure_polyakov_field(const Field<T> &Ut, Field<float> &pl) {
    Field<T> polyakov = Ut;
 
    // mult links so that polyakov[X.dir == 0] contains the polyakov loop
    for (int plane = lattice.size(e_t) - 2; plane >= 0; plane--) {
 
        // safe_access(polyakov) pragma allows the expression below, otherwise
        // hilapp would reject it because X and X+dir can refer to the same
        // site on different "iterations" of the loop.  However, here this
        // is restricted on single dir-plane so it works but we must tell it to hilapp.
 
#pragma hila safe_access(polyakov)
        onsites(ALL) {
            if (X.coordinate(e_t) == plane) {
                polyakov[X] = Ut[X] * polyakov[X + e_t];
            }
        }
    }
 
    onsites(ALL) if (X.coordinate(e_t) == 0) {
        pl[X] = real(trace(polyakov[X]));
    }
}
 
////////////////////////////////////////////////////////////////////
 
void smear_polyakov_field(Field<float> &pl, int nsmear, float smear_coeff) {
 
    if (nsmear > 0) {
        Field<float> pl2 = 0;
 
        for (int i = 0; i < nsmear; i++) {
            onsites(ALL) if (X.coordinate(e_t) == 0) {
                pl2[X] = pl[X] + smear_coeff * (pl[X + e_x] + pl[X - e_x] + pl[X + e_y] +
                                                pl[X - e_y] + pl[X + e_z] + pl[X - e_z]);
            }
 
            onsites(ALL) if (X.coordinate(e_t) == 0) {
                pl[X] = pl2[X] / (1 + 6 * smear_coeff);
            }
        }
    }
}
 
/////////////////////////////////////////////////////////////////////////////
 
std::vector<float> measure_polyakov_profile(Field<float> &pl, std::vector<float> &pro1) {
    ReductionVector<float> p(lattice.size(e_z)), p1(lattice.size(e_z));
    p.allreduce(false);
    p1.allreduce(false);
    onsites(ALL) if (X.coordinate(e_t) == 0) {
        p[X.z()] += pl[X];
        if (X.x() == 0 && X.y() == 0)
            p1[X.z()] += pl[X];
    }
    pro1 = p1.vector();
    return p.vector();
}
 
 
///////////////////////////////////////////////////////////////////////////////////
 
template <typename group>
void measure_plaq_profile(GaugeField<group> &U) {
    ReductionVector<float> p(lattice.size(e_z));
    p.allreduce(false);
    p.delayed(true);
    foralldir(dir1) foralldir(dir2) if (dir2 > dir1) {
        onsites(ALL) {
            p[X.z()] += 1.0 - real(trace(U[dir1][X] * U[dir2][X + dir1] *
                                         U[dir1][X + dir2].dagger() * U[dir2][X].dagger())) /
                                  group::size();
        }
    }
    p.reduce();
 
    for (int z = 0; z < lattice.size(e_z); z++) {
        hila::out0 << "PPLAQ " << z << ' '
                   << p[z] / (NDIM * (NDIM - 1) / 2 * lattice.volume() / lattice.size(e_z)) << '\n';
    }
}
 
 
///////////////////////////////////////////////////////////////////////////////////
 
template <typename group>
void measure_stuff(const GaugeField<group> &U, const parameters &p) {
 
    static bool first = true;
 
    if (first) {
        hila::out0 << "Legend:";
        if (p.polyakov_pot == poly_limit::PARABOLIC)
            hila::out0 << " -V(polyakov)";
        hila::out0 << " plaq  P.real  P.imag\n";
 
        first = false;
    }
 
    auto poly = measure_polyakov(U);
 
    auto plaq = measure_plaq_db(U) / (lattice.volume() * NDIM * (NDIM - 1) / 2);
 
    hila::out0 << "MEAS " << std::setprecision(14);
 
    // write the -(polyakov potential) first, this is used as a weight factor in aa
    if (p.polyakov_pot == poly_limit::PARABOLIC) {
        hila::out0 << -polyakov_potential(p, poly.real()) << ' ';
    }
 
    hila::out0 << plaq << ' ' << poly << '\n';
}
 
///////////////////////////////////////////////////////////////////////////////////
 
void spectraldensity_surface(std::vector<float> &surf, std::vector<double> &npow,
                             std::vector<int> &hits) {
 
    // do fft for the surface
    static bool first = true;
    static Complex<double> *buf;
    static fftw_plan fftwplan;
 
    int area = lattice.size(e_x) * lattice.size(e_y);
 
    if (first) {
        first = false;
 
        buf = (Complex<double> *)fftw_malloc(sizeof(Complex<double>) * area);
 
        // note: we had x as the "fast" dimension, but fftw wants the 2nd dim to be
        // the "fast" one. thus, first y, then x.
        fftwplan = fftw_plan_dft_2d(lattice.size(e_y), lattice.size(e_x), (fftw_complex *)buf,
                                    (fftw_complex *)buf, FFTW_FORWARD, FFTW_ESTIMATE);
    }
 
    for (int i = 0; i < area; i++) {
        buf[i] = surf[i];
    }
 
    fftw_execute(fftwplan);
 
    int pow_size = npow.size();
 
    for (int i = 0; i < area; i++) {
        int x = i % lattice.size(e_x);
        int y = i / lattice.size(e_x);
        x = (x <= lattice.size(e_x) / 2) ? x : (lattice.size(e_x) - x);
        y = (y <= lattice.size(e_y) / 2) ? y : (lattice.size(e_y) - y);
 
        int k = x * x + y * y;
        if (k < pow_size) {
            npow[k] += buf[i].squarenorm() / (area * area);
            hits[k]++;
        }
    }
}
 
///////////////////////////////////////////////////////////////////////////////////
// helper function to get valid z-coordinate index
 
int z_ind(int z) {
    return (z + lattice.size(e_z)) % lattice.size(e_z);
}
 
///////////////////////////////////////////////////////////////////////////////////
 
template <typename group>
void measure_polyakov_surface(GaugeField<group> &U, const parameters &p, int traj) {
 
    Field<float> pl;
 
 
    if (0) {
        // this section does local sums of poly lines
        Field<group> staples, Ut;
 
        Ut = U[e_t];
 
        for (int s = 0; s < 20; s++) {
            staplesum(U, staples, e_t);
            U[e_t][ALL] = (U[e_t][X] + 0.5 * staples[X]) / (1 + 6 * 0.5);
        }
 
        measure_polyakov_field(U[e_t], pl);
 
        U[e_t] = Ut;
 
    } else {
        // here standard non-link integrated field
        measure_polyakov_field(U[e_t], pl);
    }
 
    hila::out0 << std::setprecision(7);
 
    std::vector<float> profile, prof1;
 
    int prev_smear = 0;
    for (int sl = 0; sl < p.n_smear.size(); sl++) {
 
        int smear = p.n_smear.at(sl);
        smear_polyakov_field(pl, smear - prev_smear, p.smear_coeff);
        prev_smear = smear;
 
        Field<float> plz = pl;
        if (p.z_smear.at(sl) > 0) {
            Field<float> pl2;
            for (int j = 0; j < p.z_smear.at(sl); j++) {
                onsites(ALL) if (X.coordinate(e_t) == 0) {
                    pl2[X] = plz[X] + p.smear_coeff * (plz[X + e_z] + plz[X - e_z]);
                }
                onsites(ALL) if (X.coordinate(e_t) == 0) {
                    plz[X] = pl2[X] / (1 + 2 * p.smear_coeff);
                }
            }
        }
 
        profile = measure_polyakov_profile(plz, prof1);
 
        double m = 1.0 / (lattice.size(e_x) * lattice.size(e_y));
        for (int i = 0; i < profile.size(); i++) {
            profile[i] *= m;
            hila::out0 << "PRO" << sl << ' ' << i << ' ' << profile[i] << ' ' << prof1[i] << '\n';
        }
 
        float min = 1e8, max = 0;
        int minloc, maxloc;
        for (int i = 0; i < profile.size(); i++) {
            if (min > profile[i]) {
                min = profile[i];
                minloc = i;
            }
            if (max < profile[i]) {
                max = profile[i];
                maxloc = i;
            }
        }
 
        // find the surface between minloc and maxloc
        float surface_level = max * 0.5; // assume min is really 0
        int area = lattice.size(e_x) * lattice.size(e_y);
 
        hila::out0 << "Surface_level" << sl << ' ' << surface_level << '\n';
 
        int startloc, startloc2;
        if (maxloc > minloc)
            startloc = (maxloc + minloc) / 2;
        else
            startloc = ((maxloc + minloc + lattice.size(e_z)) / 2) % lattice.size(e_z);
 
        // starting positio for the other surface
        startloc2 = z_ind(startloc + lattice.size(e_z) / 2);
 
        std::vector<float> surf1, surf2;
        if (hila::myrank() == 0) {
            surf1.resize(area);
            surf2.resize(area);
        }
 
        hila::out0 << std::setprecision(6);
 
        std::vector<float> poly;
        std::vector<float> line(lattice.size(e_z));
 
        // get full xyz-volume t=0 slice to main node
        // poly = plz.get_slice({-1, -1, -1, 0});
 
        for (int y = 0; y < lattice.size(e_y); y++) {
            // get now full xz-plane polyakov line to main node
            // reduces MPI calls compared with doing line-by-line
            poly = plz.get_slice({-1, y, -1, 0});
            if (hila::myrank() == 0) {
                for (int x = 0; x < lattice.size(e_x); x++) {
                    // line = plz.get_slice({x, y, -1, 0});
 
                    // copy ploop data to line - x runs fastest
                    for (int z = 0; z < lattice.size(e_z); z++) {
                        line[z] = poly[x + lattice.size(e_x) * (z)];
                    }
 
                    // if (hila::myrank() == 0) {
                    // start search of the surface from the center between min and max
                    int z = startloc;
 
                    while (line[z_ind(z)] > surface_level && startloc - z < lattice.size(e_z) * 0.4)
                        z--;
 
                    while (line[z_ind(z + 1)] <= surface_level &&
                           z - startloc < lattice.size(e_z) * 0.4)
                        z++;
 
 
                    // do linear interpolation
                    // surf[x + y * lattice.size(e_x)] = z;
                    surf1[x + y * lattice.size(e_x)] =
                        z +
                        (surface_level - line[z_ind(z)]) / (line[z_ind(z + 1)] - line[z_ind(z)]);
 
                    if (p.n_surface > 0 && (traj + 1) % p.n_surface == 0) {
                        hila::out0 << "SURF" << sl << ' ' << x << ' ' << y << ' '
                                   << surf1[x + y * lattice.size(e_x)] << '\n';
                    }
 
                    // and locate the other surface - start from Lz/2 offset
 
                    z = startloc2;
 
                    while (line[z_ind(z)] <= surface_level &&
                           startloc2 - z < lattice.size(e_z) * 0.4)
                        z--;
 
                    while (line[z_ind(z + 1)] > surface_level &&
                           z - startloc2 < lattice.size(e_z) * 0.4)
                        z++;
 
                    // do linear interpolation
                    // surf[x + y * lattice.size(e_x)] = z;
                    surf2[x + y * lattice.size(e_x)] =
                        z +
                        (surface_level - line[z_ind(z)]) / (line[z_ind(z + 1)] - line[z_ind(z)]);
                }
            }
        }
 
        if (hila::myrank() == 0) {
            constexpr int pow_size = 200;
            std::vector<double> npow(pow_size);
            std::vector<int> hits(pow_size);
 
            spectraldensity_surface(surf1, npow, hits);
            spectraldensity_surface(surf2, npow, hits);
 
            for (int i = 0; i < pow_size; i++) {
                if (hits[i] > 0)
                    hila::out0 << "POW" << sl << ' ' << i << ' ' << npow[i] / hits[i] << ' '
                               << hits[i] << '\n';
            }
        }
    }
}
 
 
////////////////////////////////////////////////////////////////
 
template <typename group>
void update(GaugeField<group> &U, const parameters &p, bool relax) {
 
    for (const auto &dp : hila::shuffle_directions_and_parities()) {
 
        update_parity_dir(U, p, dp.parity, dp.direction, relax);
    }
}
 
////////////////////////////////////////////////////////////////
 
template <typename group>
void update_parity_dir(GaugeField<group> &U, const parameters &p, Parity par, Direction d,
                       bool relax) {
 
    static hila::timer hb_timer("Heatbath");
    static hila::timer or_timer("Overrelax");
    static hila::timer staples_timer("Staplesum");
 
    Field<group> staples;
 
    staples_timer.start();
    if (p.deltab != 0)
        staplesum_db(U, staples, d, par, p.deltab);
    else
        staplesum(U, staples, d, par);
    staples_timer.stop();
 
    if (relax) {
 
        or_timer.start();
        onsites(par) {
#ifdef SUN_OVERRELAX_dFJ
            suN_overrelax_dFJ(U[d][X], staples[X], p.beta);
#else
            suN_overrelax(U[d][X], staples[X]);
#endif
        }
        or_timer.stop();
 
    } else {
 
        hb_timer.start();
        onsites(par) {
            suN_heatbath(U[d][X], staples[X], p.beta);
        }
        hb_timer.stop();
    }
}
 
 
////////////////////////////////////////////////////////////////
 
template <typename group>
void do_trajectory(GaugeField<group> &U, const parameters &p) {
 
    for (int n = 0; n < p.n_update; n++) {
        for (int i = 0; i < p.n_overrelax; i++) {
            update(U, p, true);
        }
        update(U, p, false);
    }
    U.reunitarize_gauge();
}
 
////////////////////////////////////////////////////////////////
 
double polyakov_potential(const parameters &p, const double poly) {
 
    return p.poly_m2 * (sqr(poly - p.poly_min));
}
 
 
////////////////////////////////////////////////////////////////
 
bool accept_polyakov(const parameters &p, const double p_old, const double p_new) {
 
    if (p.polyakov_pot == poly_limit::PARABOLIC) {
        double dpot = polyakov_potential(p, p_new) - polyakov_potential(p, p_old);
 
        bool accept = hila::broadcast(hila::random() < exp(-dpot));
 
        return accept;
    } else {
        if (p_new >= p.poly_min && p_new <= p.poly_max)
            return true;
        if (p_new > p.poly_max && p_new < p_old)
            return true;
        if (p_new < p.poly_min && p_new > p_old)
            return true;
        return false;
    }
}
 
////////////////////////////////////////////////////////////////
 
template <typename group>
double update_once_with_range(GaugeField<group> &U, const parameters &p, double &poly, bool relax) {
 
    Field<group> Ut_old;
 
    Ut_old = U[e_t];
 
    // spatial links always updated, t-links are conditional
    // acc/rej separately for parities
 
    foralldir(d) if (d < e_t) {
        for (Parity par : {EVEN, ODD})
            update_parity_dir(U, p, par, d, relax);
    }
 
    // t-links
    double acc = 0;
    for (Parity par : {EVEN, ODD}) {
        update_parity_dir(U, p, par, e_t, relax);
 
        double p_now = measure_polyakov(U).real();
 
        bool acc_update = accept_polyakov(p, poly, p_now);
 
        if (acc_update) {
            poly = p_now;
            acc += 0.5;
        } else {
            U[e_t][par] = Ut_old[X]; // restore rejected
        }
    }
    return acc;
}
 
////////////////////////////////////////////////////////////////
 
template <typename group>
double trajectory_with_range(GaugeField<group> &U, const parameters &p, double &poly) {
 
    double acc_or = 0;
    double acc_hb = 0;
 
    double p_now = measure_polyakov(U).real();
 
    for (int n = 0; n < p.n_update; n++) {
        for (int i = 0; i < p.n_overrelax; i++) {
 
            // OR updates
            acc_or += update_once_with_range(U, p, p_now, true);
        }
 
        // and then HBs
 
        acc_hb += update_once_with_range(U, p, p_now, false);
 
        U.reunitarize_gauge();
    }
    return (acc_or + acc_hb) / (p.n_update * (p.n_overrelax + 1));
}
 
/////////////////////////////////////////////////////////////////
 
 
int main(int argc, char **argv) {
 
    // hila::initialize should be called as early as possible
    hila::initialize(argc, argv);
 
    // hila provides an input class hila::input, which is
    // a convenient way to read in parameters from input files.
    // parameters are presented as key - value pairs, as an example
    //  " lattice size  64, 64, 64, 64"
    // is read below.
    //
    // Values are broadcast to all MPI nodes.
    //
    // .get() -method can read many different input types,
    // see file "input.h" for documentation
 
    parameters p;
 
    hila::out0 << "SU(" << mygroup::size() << ") heat bath + overrelax update\n";
 
    hila::input par("parameters");
 
    CoordinateVector lsize;
    lsize = par.get("lattice size"); // reads NDIM numbers
 
    p.beta = par.get("beta");
    // deltab sets system to different beta on different sides, by beta*(1 +- deltab)
    // use for initial config generation only
    p.deltab = par.get("delta beta fraction");
    // trajectory length in steps
    p.n_overrelax = par.get("overrelax steps");
    p.n_update = par.get("updates in trajectory");
    p.n_trajectories = par.get("trajectories");
    p.n_thermal = par.get("thermalization");
 
    // random seed = 0 -> get seed from time
    uint64_t seed = par.get("random seed");
    // save config and checkpoint
    p.n_save = par.get("traj/saved");
    // measure surface properties and print "profile"
    p.config_file = par.get("config name");
 
    // if polyakov range is off, do nothing with
    int p_item = par.get_item("polyakov potential", {"off", "min", "range"});
    if (p_item == 0) {
        p.polyakov_pot = poly_limit::OFF;
    } else if (p_item == 1) {
        p.polyakov_pot = poly_limit::PARABOLIC;
        p.poly_min = par.get();
        p.poly_m2 = par.get("mass2");
    } else {
        p.polyakov_pot = poly_limit::RANGE;
        Vector<2, double> r;
        r = par.get();
        p.poly_min = r[0];
        p.poly_max = r[1];
    }
 
    if (par.get_item("updates/profile meas", {"off", "%i"}) == 1) {
        p.n_profile = par.get();
    } else {
        p.n_profile = 0;
    }
 
    if (p.n_profile) {
        p.n_smear = par.get("smearing steps");
        p.smear_coeff = par.get("smear coefficient");
        p.z_smear = par.get("z smearing steps");
        p.n_surface = par.get("traj/surface");
        p.n_dump_polyakov = par.get("traj/polyakov dump");
 
        if (p.n_smear.size() != p.z_smear.size()) {
            hila::out0 << "Error in input file: number of values in 'smearing steps' != 'z "
                          "smearing steps'\n";
            hila::terminate(0);
        }
 
    } else {
        p.n_dump_polyakov = 0;
    }
 
    par.close(); // file is closed also when par goes out of scope
 
    // setting up the lattice is convenient to do after reading
    // the parameter
    lattice.setup(lsize);
 
    // Alloc gauge field
    GaugeField<mygroup> U;
 
    U = 1;
 
    // use negative trajectory for thermal
    int start_traj = -p.n_thermal;
 
    hila::timer update_timer("Updates");
    hila::timer measure_timer("Measurements");
 
    restore_checkpoint(U, p.config_file, p.n_trajectories, start_traj);
 
    // We need random number here
    if (!hila::is_rng_seeded())
        hila::seed_random(seed);
 
    double p_now = measure_polyakov(U).real();
 
    for (int trajectory = start_traj; trajectory < p.n_trajectories; trajectory++) {
 
        double ttime = hila::gettime();
 
        update_timer.start();
 
        double acc = 0;
        if (p.polyakov_pot != poly_limit::OFF) {
            acc += trajectory_with_range(U, p, p_now);
        } else {
            do_trajectory(U, p);
        }
 
        // put sync here in order to get approx gpu timing
        hila::synchronize_threads();
        update_timer.stop();
 
        // trajectory is negative during thermalization
        if (trajectory >= 0) {
            measure_timer.start();
 
            hila::out0 << "Measure_start " << trajectory << '\n';
 
            measure_stuff(U, p);
 
            if (p.n_profile && (trajectory + 1) % p.n_profile == 0) {
                measure_polyakov_surface(U, p, trajectory);
                measure_plaq_profile(U);
            }
 
            if (p.n_dump_polyakov && (trajectory + 1) % p.n_dump_polyakov == 0) {
                Field<float> pl;
                std::ofstream poly;
                if (hila::myrank() == 0) {
                    poly.open("polyakov", std::ios::out | std::ios::app);
                }
                measure_polyakov_field(U[e_t], pl);
                pl.write_slice(poly, {-1, -1, -1, 0});
            }
 
            if (p.polyakov_pot != poly_limit::OFF) {
                hila::out0 << "ACCP " << acc << '\n';
            }
 
            hila::out0 << "Measure_end " << trajectory << std::endl;
 
            measure_timer.stop();
        }
 
        if (p.n_save > 0 && (trajectory + 1) % p.n_save == 0) {
            checkpoint(U, p.config_file, p.n_trajectories, trajectory);
        }
    }
 
    hila::finishrun();
}