hila_healthcheck.cpp

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/**
 * @file hila_healthcheck.cpp
 * @author Kari Rummukainen
 * @brief HILA healthcheck application.
 * @details Performs a comprehensive health check on HILA libraries.
 */
#include "hila.h"
 
// unistd.h needed for isatty()
#include <unistd.h>
 
 
// report the result of the test -- TODO: nicer formatting?
bool report_pass(std::string message, double eps, double limit) {
 
    static int is_terminal = -1;
    static std::string ok_string, fail_string;
 
    if (is_terminal < 0) {
        is_terminal = isatty(fileno(stdout));
 
        if (is_terminal) {
            ok_string = "\x1B[32m --- \033[0m ";
            fail_string = "\x1B[31m *** \033[0m ";
        } else {
            ok_string = " ---  ";
            fail_string = " ***  ";
        }
    }
 
    if (eps < limit) {
        hila::out0 << ok_string << message << " passed" << std::endl;
        return true;
    } else {
        hila::out0 << fail_string << message << " FAILED: eps " << eps << " limit " << limit
                   << std::endl;
        return false;
    }
}
 
/////////////////////////////////////////////////////////////////////////////////////
 
void check_reductions() {
 
 
    // test reductions
 
    Field<Complex<double>> f;
    f[ALL] = expi(2 * M_PI * X.coordinate(e_x) / lattice.size(e_x));
 
    Complex<double> sum = 0;
    onsites(ALL) sum += f[X];
 
    sum /= lattice.volume();
    report_pass("Complex reduction value " + hila::prettyprint(sum), abs(sum), 1e-4);
 
    ReductionVector<Complex<double>> rv(lattice.size(e_x));
 
    onsites(ALL) {
        rv[X.coordinate(e_x)] += f[X];
    }
 
    sum = 0;
    for (int i = 0; i < lattice.size(e_x); i++) {
        sum +=
            expi(2 * M_PI * i / lattice.size(e_x)) - rv[i] / (lattice.volume() / lattice.size(e_x));
    }
    report_pass("Vector reduction, sum " + hila::prettyprint(sum), abs(sum), 1e-4);
}
 
 
// ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// write something to a location
 
void test_site_access() {
 
    Field<Complex<double>> f = 0;
    Complex<double> sum;
 
    CoordinateVector c;
    for (int i = 0; i < 3; i++) {
        foralldir(d) c[d] = hila::random() * lattice.size(d);
        hila::broadcast(c); // need to broadcast!
 
        f[c] = 4;   // write to location c
        sum = f[c]; // read back - does mpi comm
        report_pass("Setting and reading a value at " + hila::prettyprint(c.transpose()),
                    abs(sum - 4), 1e-10);
    }
}
 
 
// ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// test maxloc and minloc operation
 
void test_minmax() {
 
    CoordinateVector c, loc;
    Field<double> n;
    n[ALL] = hila::random();
    foralldir(d) c[d] = hila::random() * lattice.size(d);
    hila::broadcast(c);
    n[c] = 2;
 
    auto v = n.max(loc);
    report_pass("Maxloc is " + hila::prettyprint(loc.transpose()), (c - loc).norm(), 1e-8);
    report_pass("Max value " + hila::prettyprint(v), v - 2, 1e-9);
 
 
    foralldir(d) c[d] = hila::random() * lattice.size(d);
    hila::broadcast(c);
    n[c] = -1;
    v = n.min(loc);
    report_pass("Minloc is " + hila::prettyprint(loc.transpose()), (c - loc).norm(), 1e-8);
    report_pass("Min value " + hila::prettyprint(v), v + 1, 1e-9);
}
 
// ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// test random number properties
// rough test, testing spectrum of gaussians
 
void test_random() {
 
    constexpr int n_loops = 100;
 
    Field<double> f;
 
    double fsum = 0, fsqr = 0;
    for (int i=0; i<n_loops; i++) {
        f.gaussian_random();
        double s = 0, s2 = 0;
        onsites(ALL) {
            f[X] = hila::gaussrand();
            s += f[X];
            s2 += sqr(f[X]);
        }
        fsum += s/lattice.volume();
        fsqr += s2/lattice.volume();
    }
 
    fsum /= n_loops;
    fsqr /= n_loops;
 
    report_pass("Gaussian random average (6 sigma limit) " + hila::prettyprint(fsum), 
    abs(fsum), 6/sqrt(((double)n_loops)*lattice.volume()));
 
    report_pass("Gaussian random width^2 " + hila::prettyprint(fsqr),
    fsqr - 1, 6/sqrt(((double)n_loops)*lattice.volume()));
 
}
 
 
 
// ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// test access to a list of sites
 
void test_set_elements_and_select() {
 
    Field<Complex<double>> f = 0;
    CoordinateVector c;
 
    std::vector<CoordinateVector> cvec;
    std::vector<Complex<double>> vals;
 
 
    if (hila::myrank() == 0) {
        int k = 1;
        for (int i = 0; i <= 50; i++) {
            foralldir(d) c[d] = hila::random() * lattice.size(d);
            bool found = false;
 
            // don't overwrite previous loc
            for (auto &r : cvec)
                if (r == c)
                    found = true;
            if (!found) {
                cvec.push_back(c);
                vals.push_back(Complex<double>(k, k));
                k++;
            }
        }
    }
 
    hila::broadcast(vals);
    hila::broadcast(cvec);
 
    f.set_elements(vals, cvec);
 
    vals = f.get_elements(cvec, true);
 
    Complex<double> sum = 0;
    for (int i = 0; i < vals.size(); i++) {
        sum += vals[i] - Complex<double>(i + 1, i + 1);
    }
 
    report_pass("Field set_elements and get_elements with " + hila::prettyprint(vals.size()) +
                    " coordinates",
                abs(sum), 1e-8);
 
    // use the same vector for siteselect
 
    SiteSelect s;
    SiteValueSelect<Complex<double>> sv;
 
    onsites(ALL) {
        if (squarenorm(f[X]) >= 1) {
            s.select(X);
            sv.select(X, f[X]);
        }
    }
 
    report_pass("SiteSelect size " + hila::prettyprint(s.size()), s.size() - cvec.size(), 1e-3);
    report_pass("SiteValueSelect size " + hila::prettyprint(sv.size()), sv.size() - cvec.size(),
                1e-3);
 
    int ok = 1;
 
    for (auto &c : cvec) {
        bool found = false;
        for (int i = 0; !found && i < s.size(); i++) {
            if (s.coordinates(i) == c)
                found = true;
        }
        if (!found)
            ok = 0;
    }
 
    report_pass("SiteSelect content", 1 - ok, 1e-6);
 
    ok = 1;
    for (int k = 0; k < cvec.size(); k++) {
 
        bool found = false;
        for (int i = 0; !found && i < sv.size(); i++) {
            if (sv.coordinates(i) == cvec[k] && sv.value(i) == vals[k])
                found = true;
        }
        if (!found)
            ok = 0;
    }
 
    report_pass("SiteValueSelect content", 1 - ok, 1e-6);
 
 
    onsites(ALL) {}
}
 
/////////////////////////////////////////////////////////////////////////////////////
 
void test_subvolumes() {
 
    bool ok = true;
    for (int i = 0; i < 20; i++) {
        CoordinateVector c;
        foralldir(d) c[d] = hila::random() * lattice.size(d);
        auto si = SiteIndex(c);
        if (si.coordinates() != c)
            ok = false;
    }
 
    report_pass("SiteIndex", ok == false, 1e-2);
 
 
    Field<SiteIndex> f;
    f[ALL] = SiteIndex(X.coordinates());
 
    CoordinateVector c;
    c.fill(-1);
    size_t vol = lattice.volume();
    foralldir(d) if (d < NDIM - 1) {
        c[d] = hila::random() * lattice.size(d);
        hila::broadcast(c);
 
        auto slice = f.get_slice(c);
 
        vol /= lattice.size(d);
        if (hila::myrank() == 0) {
 
            report_pass(hila::prettyprint(NDIM - (int)d - 1) + "-dimensional slice size " +
                            hila::prettyprint(vol),
                        slice.size() - vol, 1e-3);
 
 
            bool pass = true;
 
            CoordinateVector mycoord = 0;
            foralldir(d2) {
                if (c[d2] >= 0)
                    mycoord[d2] = c[d2];
            }
            foralldir(d2) {
                if (c[d2] < 0) {
                    mycoord[d2] = -1;
                    break;
                }
            }
 
            for (auto s : slice) {
 
                // get the coordinate which should be here
                bool add = true;
                foralldir(d2) {
                    if (add && c[d2] < 0) {
                        mycoord[d2]++;
                        if (mycoord[d2] < lattice.size(d2)) {
                            add = false;
                        } else {
                            mycoord[d2] = 0;
                        }
                    }
                }
 
                if (pass && mycoord != s.coordinates()) {
                    hila::out0 << "Slice coord error, should be "
                               << hila::prettyprint(mycoord.transpose()) << " is "
                               << hila::prettyprint(s.coordinates().transpose()) << " slice is "
                               << hila::prettyprint(c.transpose()) << '\n';
                    pass = false;
                    break;
                }
            }
 
            report_pass("slice content", pass == false, 1e-2);
        }
    }
}
 
/////////////////////////////////////////////////////////////////////////////////////
 
 
void fft_test() {
 
 
    using T = Complex<double>;
 
    Field<T> f, p, p2;
 
    // Start with unit field
    f = 1;
 
    // After one FFT the field is 0 except at coord 0
    p2 = 0;
 
    p2[{0, 0, 0}] = lattice.volume();
 
    FFT_field(f, p);
 
    double eps = squarenorm_relative(p, p2);
 
    report_pass("FFT constant field", eps, 1e-13 * sqrt(lattice.volume()));
 
    //-----------------------------------------------------------------
    // After two applications the field should be back to a constant * volume
 
    FFT_field(p, f, fft_direction::back);
 
    double sum = 0;
    double tnorm = 0;
    onsites(ALL) {
        sum += (f[X] - lattice.volume()).squarenorm();
        tnorm += f[X].squarenorm();
    }
 
    eps = fabs(sum / tnorm);
 
    report_pass("FFT inverse transform", eps, 1e-10);
 
    //-----------------------------------------------------------------
    for (int iter = 0; iter < 5; iter++) {
        Vector<NDIM, double> kv;
        CoordinateVector kx;
        foralldir(d) {
            kx[d] = hila::broadcast(hila::random()) * lattice.size(d);
        }
 
        kv = convert_to_k(kx);
 
        onsites(ALL) {
            double d = kv.dot(X.coordinates());
            f[X] = expi(d);
        }
 
        FFT_field(f, p);
 
        p2 = 0;
        p2[kx] = lattice.volume();
 
        eps = squarenorm_relative(p, p2);
 
        report_pass("FFT of wave vector " + hila::prettyprint(kx.transpose()), eps,
                    1e-13 * sqrt(lattice.volume()));
    }
 
    //-----------------------------------------------------------------
 
    {
        Field<double> r;
        onsites(ALL) r[X] = hila::gaussrand();
 
        f = r.FFT_real_to_complex();
        p = f.FFT(fft_direction::back) / lattice.volume();
        eps = squarenorm_relative(r, p);
 
        report_pass("FFT real to complex", eps, 1e-13 * sqrt(lattice.volume()));
 
        auto r2 = f.FFT_complex_to_real(fft_direction::back) / lattice.volume();
        eps = squarenorm_relative(r, r2);
 
        report_pass("FFT complex to real", eps, 1e-13 * sqrt(lattice.volume()));
    }
 
    //-----------------------------------------------------------------
    // Check fft norm
 
    onsites(ALL) {
        p[X] = hila::random() * exp(-convert_to_k(X.coordinates()).squarenorm());
    }
    f = p.FFT(fft_direction::back) / sqrt(lattice.volume());
 
    double nf = f.squarenorm();
    double np = p.squarenorm();
    report_pass("Norm of field = " + hila::prettyprint(nf) + " and FFT = " + hila::prettyprint(np),
                (nf - np) / nf, 1e-10);
 
    hila::k_binning b;
    b.k_max(M_PI * sqrt(3.0));
 
    auto bf = b.bin_k_field(p.conj() * p);
 
    double s = 0;
    for (auto b : bf) {
        s += abs(b);
    }
    hila::broadcast(s);
 
    report_pass("Norm of binned FFT = " + hila::prettyprint(s), (s - np) / np, 1e-10);
}
 
//---------------------------------------------------------------------------
 
void spectraldensity_test() {
 
 
    // test spectral density for single waves
 
    Field<Complex<double>> f, p;
 
    hila::k_binning b;
    b.k_max(M_PI * sqrt(3.0));
 
    // test std binning first
 
    for (int iter = 0; iter < 3; iter++) {
        Vector<NDIM, double> kv;
        CoordinateVector kx;
        foralldir(d) {
            kx[d] = hila::broadcast(hila::random()) * lattice.size(d);
        }
        kv = convert_to_k(kx);
        auto absk = kv.norm();
 
        // test first std. binning (normally )
        f = 0;
        f[kx] = 1;
 
        auto fb = b.bin_k_field(f);
 
        double sum = 0;
        for (int i = 0; i < b.bins(); i++) {
            if (b.bin_min(i) <= absk && b.bin_max(i) > absk) {
                // should be one hit here
                sum += squarenorm(fb[i] - 1);
            } else {
                sum += squarenorm(fb[i]);
            }
        }
 
        report_pass("Binning test at vector " + hila::prettyprint(kx.transpose()), sum, 1e-10);
 
        // then test the spectral density extraction
        // set single wave
        onsites(ALL) {
            double d = kv.dot(X.coordinates());
            f[X] = expi(d);
        }
 
        auto fsd = b.spectraldensity(f);
 
        sum = 0;
        for (int i = 0; i < b.bins(); i++) {
            if (b.bin_min(i) <= absk && b.bin_max(i) > absk) {
                // should be one hit here
                sum += fabs(fsd[i] / pow(lattice.volume(), 2) - 1);
            } else {
                sum += fabs(fsd[i]);
            }
        }
 
        report_pass("Spectral density test with above vector ", sum, 1e-10);
    }
}
 
//--------------------------------------------------------------------------------
 
void test_field_slices() {
 
    Field<SiteIndex> s;
    onsites(ALL) {
        s[X] = SiteIndex(X.coordinates());
    }
}
 
 
//--------------------------------------------------------------------------------
 
void test_matrix_algebra() {
 
    using myMatrix = SquareMatrix<4, Complex<double>>;
 
    Field<myMatrix> M;
    Field<double> delta;
 
    M.gaussian_random(2.0);
 
    // eigenvalue test - show that  M = U D U^*, where D is diagonal eigenvalue matrix and U matrix
    // of eigenvectors
 
    onsites(ALL) {
        auto H = M[X] * M[X].dagger(); // make hermitean
 
        auto r = H.eigen_hermitean();
        delta[X] = (H - r.eigenvectors * r.eigenvalues * r.eigenvectors.dagger()).norm();
    }
 
    auto max_delta = delta.max();
 
    report_pass("Eigenvalue analysis with " + hila::prettyprint(myMatrix::rows()) + "x" +
                    hila::prettyprint(myMatrix::columns()) + " Hermitean matrix",
                max_delta, 1e-10);
 
    // Singular value test - non-pivoted
 
    onsites(ALL) {
        auto r = M[X].svd();
        delta[X] = (M[X] - r.U * r.singularvalues * r.V.dagger()).norm();
    }
 
    max_delta = delta.max();
 
    report_pass("SVD with " + hila::prettyprint(myMatrix::rows()) + "x" +
                    hila::prettyprint(myMatrix::columns()) + " Complex matrix",
                max_delta, 1e-10);
 
    // pivoted singular values
 
    M.gaussian_random();
 
    onsites(ALL) {
        auto r = M[X].svd_pivot(hila::sort::ascending);
        delta[X] = (M[X] - r.U * r.singularvalues * r.V.dagger()).norm();
    }
 
    max_delta = delta.max();
 
    report_pass("Fully pivoted SVD with " + hila::prettyprint(myMatrix::rows()) + "x" +
                    hila::prettyprint(myMatrix::columns()) + " Complex matrix",
                max_delta, 1e-10);
 
 
}
 
 
//////////////////////////////////////////////////////////////////////////////////////////
 
int main(int argc, char **argv) {
 
    hila::initialize(argc, argv);
 
    hila::input par("parameters");
 
    CoordinateVector lsize = par.get("lattice size"); // reads NDIM numbers
    long seed = par.get("random seed");
 
    par.close();
 
    // setting up the lattice is convenient to do after reading
    // the parameters
    lattice.setup(lsize);
 
    // We need random number here
    hila::seed_random(seed);
 
 
    ///////////////////////////////////////////////////////////////
    // start tests
 
    check_reductions();
 
    test_site_access();
 
    test_minmax();
 
    test_random();
 
    test_set_elements_and_select();
 
    test_subvolumes();
 
    fft_test();
 
    spectraldensity_test();
 
    test_matrix_algebra();
 
    hila::finishrun();
}