C++ Minimizer::improve_energy方法代码示例

double run_soft_sphere(double reduced_density, double temp) {
  Functional f = SoftFluid(sigma, 1, 0);
  const double mu = find_chemical_potential(OfEffectivePotential(f), temp, reduced_density*pow(2,-5.0/2.0));
  printf("mu is %g for reduced_density = %g at temperature %g\n", mu, reduced_density, temp);

  //printf("Filling fraction is %g with functional %s at temperature %g\n", reduced_density, teff);
  //fflush(stdout);
  temperature = temp;
  //if (kT == 0) kT = ;1

  Lattice lat(Cartesian(xmax,0,0), Cartesian(0,ymax,0), Cartesian(0,0,zmax));
  GridDescription gd(lat, dx);

  Grid softspherepotential(gd);
  softspherepotential.Set(soft_sphere_potential);

  f = SoftFluid(sigma, 1, mu); // compute approximate energy with chemical potential mu
  const double approx_energy = f(temperature, reduced_density*pow(2,-5.0/2.0))*xmax*ymax*zmax;
  const double precision = fabs(approx_energy*1e-9);

  f = OfEffectivePotential(SoftFluid(sigma, 1, mu) + ExternalPotential(softspherepotential));

  static Grid *potential = 0;
  potential = new Grid(gd);
  *potential = softspherepotential - temperature*log(reduced_density*pow(2,-5.0/2.0)/(1.0*radius*radius*radius))*VectorXd::Ones(gd.NxNyNz); // Bad starting guess
  printf("\tMinimizing to %g absolute precision from %g from %g...\n", precision, approx_energy, temperature);
  fflush(stdout);

  Minimizer min = Precision(precision,
                            PreconditionedConjugateGradient(f, gd, temperature,
                                potential,
                                QuadraticLineMinimizer));
  took("Setting up the variables");
  for (int i=0; min.improve_energy(true) && i<100; i++) {
  }

  took("Doing the minimization");
  min.print_info();

  Grid density(gd, EffectivePotentialToDensity()(temperature, gd, *potential));
  //printf("# per area is %g at filling fraction %g\n", density.sum()*gd.dvolume/dw/dw, reduced_density);

  char *plotname = (char *)malloc(1024);

  sprintf(plotname, "papers/fuzzy-fmt/figs/radial-wca-%06.4f-%04.2f.dat", temp, reduced_density);
  z_plot(plotname, Grid(gd, pow(2,5.0/2.0)*density));
  free(plotname);

  {
    //double peak = peak_memory()/1024.0/1024;
    //double current = current_memory()/1024.0/1024;
    //printf("Peak memory use is %g M (current is %g M)\n", peak, current);

  }

  took("Plotting stuff");
  printf("density %g gives ff %g for reduced_density = %g and T = %g\n", density(0,0,gd.Nz/2),
         density(0,0,gd.Nz/2)*4*M_PI/3, reduced_density, temp);
  return density(0, 0, gd.Nz/2)*4*M_PI/3; // return bulk filling fraction
}

int main(int, char **) {
  FILE *o = fopen("paper/figs/constrained-water.dat", "w");

  Functional f = OfEffectivePotential(SaftFluidSlow(water_prop.lengthscale,
                                                    water_prop.epsilonAB, water_prop.kappaAB,
                                                    water_prop.epsilon_dispersion,
                                                    water_prop.lambda_dispersion, water_prop.length_scaling, 0));
  double mu_satp = find_chemical_potential(f, water_prop.kT,
                                           water_prop.liquid_density);
  Lattice lat(Cartesian(width,0,0), Cartesian(0,width,0), Cartesian(0,0,zmax));
  GridDescription gd(lat, 0.1);

  Grid potential(gd);
  Grid constraint(gd);
  constraint.Set(notinwall);

  f = constrain(constraint,
                OfEffectivePotential(SaftFluidSlow(water_prop.lengthscale,
                                                   water_prop.epsilonAB, water_prop.kappaAB,
                                                   water_prop.epsilon_dispersion,
                                                   water_prop.lambda_dispersion, water_prop.length_scaling, mu_satp)));


  Minimizer min = Precision(0, PreconditionedConjugateGradient(f, gd, water_prop.kT, &potential,
                                                               QuadraticLineMinimizer));

  potential = water_prop.liquid_density*constraint
    + water_prop.vapor_density*VectorXd::Ones(gd.NxNyNz);
  //potential = water_prop.liquid_density*VectorXd::Ones(gd.NxNyNz);
  potential = -water_prop.kT*potential.cwise().log();

  const int numiters = 50;
  for (int i=0;i<numiters && min.improve_energy(true);i++) {
    fflush(stdout);
    Grid density(gd, EffectivePotentialToDensity()(water_prop.kT, gd, potential));
    density.epsNative1d("paper/figs/1d-constrained-plot.eps",
			Cartesian(0,0,0), Cartesian(0,0,zmax),
			water_prop.liquid_density, 1, "Y axis: , x axis: ");
  }
  min.print_info();

  double energy = min.energy()/width/width;
  printf("Energy is %.15g\n", energy);

  double N = 0;
  {
    Grid density(gd, EffectivePotentialToDensity()(water_prop.kT, gd, potential));
    for (int i=0;i<gd.NxNyNz;i++) N += density[i]*gd.dvolume;
  }
  N = N/width/width;
  printf("N is %.15g\n", N);

    Grid density(gd, EffectivePotentialToDensity()(water_prop.kT, gd, potential));
    density.epsNative1d("paper/figs/1d-constrained-plot.eps", Cartesian(0,0,0), Cartesian(0,0,zmax), water_prop.liquid_density, 1, "Y axis: , x axis: ");
    //potential.epsNative1d("hard-wall-potential.eps", Cartesian(0,0,0), Cartesian(0,0,zmax), 1, 1);

    fclose(o);
}

double run_walls(double reduced_density, const char *name, Functional fhs, double teff) {
  double kT = teff;
  if (kT == 0) kT = 1;

  Functional f = OfEffectivePotential(fhs);

  const double zmax = width + 2*spacing;
  Lattice lat(Cartesian(dw,0,0), Cartesian(0,dw,0), Cartesian(0,0,zmax));
  GridDescription gd(lat, dx);

  Grid constraint(gd);
  constraint.Set(notinwall);
  f = constrain(constraint, f);

  Grid potential(gd);
  potential = pow(2,-5.0/2.0)*(reduced_density*constraint + 1e-4*reduced_density*VectorXd::Ones(gd.NxNyNz));
  potential = -kT*potential.cwise().log();

  const double approx_energy = fhs(kT, reduced_density*pow(2,-5.0/2.0))*dw*dw*width;
  const double precision = fabs(approx_energy*1e-11);
  printf("\tMinimizing to %g absolute precision from %g from %g...\n", precision, approx_energy, kT);
  fflush(stdout);

  Minimizer min = Precision(precision,
                            PreconditionedConjugateGradient(f, gd, kT,
                                                            &potential,
                                                            QuadraticLineMinimizer));
  took("Setting up the variables");
  if (strcmp(name, "hard") != 0 && false) {
    printf("For now, SoftFluid doesn't work properly, so we're skipping the\n");
    printf("minimization at temperature %g.\n", teff);
  } else {
    for (int i=0;min.improve_energy(false) && i<100;i++) {
    }
  }
  took("Doing the minimization");
  min.print_info();

  Grid density(gd, EffectivePotentialToDensity()(kT, gd, potential));
  //printf("# per area is %g at filling fraction %g\n", density.sum()*gd.dvolume/dw/dw, eta);

  char *plotname = (char *)malloc(1024);

  sprintf(plotname, "papers/fuzzy-fmt/figs/walls%s-%06.4f-%04.2f.dat", name, teff, reduced_density);
  z_plot(plotname, Grid(gd, density*pow(2,5.0/2.0)));
  free(plotname);

  took("Plotting stuff");
  printf("density %g gives ff %g for reduced density = %g and T = %g\n", density(0,0,gd.Nz/2),
         density(0,0,gd.Nz/2)*4*M_PI/3, reduced_density, teff);
  return density(0, 0, gd.Nz/2)*4*M_PI/3; // return bulk filling fraction
}

bool ConjugateGradientType::improve_energy(bool verbose) {
  iter++;
  //printf("I am running ConjugateGradient::improve_energy\n");
  const double E0 = energy();
  if (E0 != E0) {
    // There is no point continuing, since we're starting with a NaN!
    // So we may as well quit here.
    if (verbose) {
      printf("The initial energy is a NaN, so I'm quitting early from ConjugateGradientType::improve_energy.\n");
      f.print_summary("has nan:", E0);
      fflush(stdout);
    }
    return false;
  }
  double gdotd;
  {
    const VectorXd g = -grad();
    // Let's immediately free the cached gradient stored internally!
    invalidate_cache();

    // Note: my notation vaguely follows that of
    // [wikipedia](http://en.wikipedia.org/wiki/Nonlinear_conjugate_gradient_method).
    // I use the Polak-Ribiere method, with automatic direction reset.
    // Note that we could save some memory by using Fletcher-Reeves, and
    // it seems worth implementing that as an option for
    // memory-constrained problems (then we wouldn't need to store oldgrad).
    double beta = g.dot(g - oldgrad)/oldgradsqr;
    oldgrad = g;
    if (beta < 0 || beta != beta || oldgradsqr == 0) beta = 0;
    oldgradsqr = oldgrad.dot(oldgrad);
    direction = g + beta*direction;
    gdotd = oldgrad.dot(direction);
    if (gdotd < 0) {
      direction = oldgrad; // If our direction is uphill, reset to gradient.
      if (verbose) printf("reset to gradient...\n");
      gdotd = oldgrad.dot(direction);
    }
  }

  Minimizer lm = linmin(f, gd, kT, x, direction, -gdotd, &step);
  for (int i=0; i<100 && lm.improve_energy(verbose); i++) {
    if (verbose) lm.print_info("\t");
  }
  if (verbose) {
    //lm->print_info();
    print_info();
    printf("grad*dir/oldgrad*dir = %g\n", grad().dot(direction)/gdotd);
  }
  return (energy() < E0);
}

bool PreconditionedConjugateGradientType::improve_energy(bool verbose) {
  iter++;
  //printf("I am running ConjugateGradient::improve_energy\n");
  const double E0 = energy();
  if (isnan(E0)) {
    // There is no point continuing, since we're starting with a NaN!
    // So we may as well quit here.
    if (verbose) {
      printf("The initial energy is a NaN, so I'm quitting early.\n");
      fflush(stdout);
    }
    return false;
  }
  double beta;
  {
    // Note: my notation vaguely follows that of
    // [wikipedia](http://en.wikipedia.org/wiki/Nonlinear_conjugate_gradient_method).
    // I use the Polak-Ribiere method, with automatic direction reset.
    // Note that we could save some memory by using Fletcher-Reeves, and
    // it seems worth implementing that as an option for
    // memory-constrained problems (then we wouldn't need to store oldgrad).
    pgrad(); // compute pgrad first, since that computes both.
    beta = -pgrad().dot(-grad() - oldgrad)/oldgradsqr;
    oldgrad = -grad();
    if (beta < 0 || beta != beta || oldgradsqr == 0) beta = 0;
    if (verbose) printf("beta = %g\n", beta);
    oldgradsqr = -pgrad().dot(oldgrad);
    direction = -pgrad() + beta*direction;
    // Let's immediately free the cached gradient stored internally!
    invalidate_cache();
  } // free g and pg!

  const double gdotd = oldgrad.dot(direction);

  Minimizer lm = linmin(f, gd, kT, x, direction, -gdotd, &step);
  for (int i=0; i<100 && lm.improve_energy(verbose); i++) {
    if (verbose) lm.print_info("\t");
  }
  if (verbose) {
    //lm->print_info();
    print_info();
    printf("grad*oldgrad = %g\n", grad().dot(direction)/gdotd);
  }
  return (energy() < E0 || beta != 0);
}

void run_with_eta(double eta, const char *name, Functional fhs) {
  // Generates a data file for the pair distribution function, for filling fraction eta
  // and distance of first sphere from wall of z0. Data saved in a table such that the
  // columns are x values and rows are z1 values.
  printf("Now starting run_with_eta with eta = %g name = %s\n",
         eta, name);
  Functional f = OfEffectivePotential(fhs + IdealGas());
  double mu = find_chemical_potential(f, 1, eta/(4*M_PI/3));
  f = OfEffectivePotential(fhs + IdealGas()
                           + ChemicalPotential(mu));
  Lattice lat(Cartesian(width,0,0), Cartesian(0,width,0), Cartesian(0,0,width));
  GridDescription gd(lat, dx);
  Grid potential(gd);
  Grid constraint(gd);
  constraint.Set(notinsphere);
  f = constrain(constraint, f);
  potential = (eta*constraint + 1e-4*eta*VectorXd::Ones(gd.NxNyNz))/(4*M_PI/3);
  potential = -potential.cwise().log();

  const double approx_energy = (fhs + IdealGas() + ChemicalPotential(mu))(1, eta/(4*M_PI/3))*uipow(width,3);
  const double precision = fabs(approx_energy*1e-10);
  //printf("Minimizing to %g absolute precision...\n", precision);
  { // Put mimizer in block so as to free it when we finish minimizing to save memory.
    Minimizer min = Precision(precision,
                              PreconditionedConjugateGradient(f, gd, 1,
                                                              &potential,
                                                              QuadraticLineMinimizer));
    for (int i=0;min.improve_energy(true) && i<100;i++) {
      double peak = peak_memory()/1024.0/1024;
      double current = current_memory()/1024.0/1024;
      printf("Peak memory use is %g M (current is %g M)\n", peak, current);
      fflush(stdout);
    }
    took("Doing the minimization");
  }
  Grid density(gd, EffectivePotentialToDensity()(1, gd, potential));
  Grid gsigma(gd, gSigmaA(1.0)(1, gd, density));
  Grid nA(gd, ShellConvolve(2)(1, density)/(4*M_PI*4));
  Grid n3(gd, StepConvolve(1)(1, density));
  Grid nbar_sokolowski(gd, StepConvolve(1.6)(1, density));
  nbar_sokolowski /= (4.0/3.0*M_PI*ipow(1.6, 3));
  // Create the walls directory if it doesn't exist.
  if (mkdir("papers/pair-correlation/figs/walls", 0777) != 0 && errno != EEXIST) {
    // We failed to create the directory, and it doesn't exist.
    printf("Failed to create papers/pair-correlation/figs/walls: %s",
           strerror(errno));
    exit(1); // fail immediately with error code
  }

  // here you choose the values of z0 to use
  // dx is the resolution at which we compute the density.
  char *plotname = new char[4096];
  for (double z0 = 2.1; z0 < 4.5; z0 += 2.1) {
    // For each z0, we now pick one of our methods for computing the
    // pair distribution function:
    for (int version = 0; version < numplots; version++) {
      sprintf(plotname,
              "papers/pair-correlation/figs/triplet%s-%s-%04.2f-%1.2f.dat",
              name, fun[version], eta, z0);
      FILE *out = fopen(plotname,"w");
      FILE *xfile = fopen("papers/pair-correlation/figs/triplet-x.dat","w");
      FILE *zfile = fopen("papers/pair-correlation/figs/triplet-z.dat","w");
      // the +1 for z0 and z1 are to shift the plot over, so that a sphere touching the wall
      // is at z = 0, to match with the monte carlo data
      const Cartesian r0(0,0,z0);
      for (double x = 0; x < 4; x += dx) {
        for (double z1 = -4; z1 <= 9; z1 += dx) {
          const Cartesian r1(x,0,z1);
          double g2 = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
          double n_bulk = (3.0/4.0/M_PI)*eta;
          double g3 = g2*density(r0)*density(r1)/n_bulk/n_bulk;
          fprintf(out, "%g\t", g3);
          fprintf(xfile, "%g\t", x);
          fprintf(zfile, "%g\t", z1);
        }
        fprintf(out, "\n");
        fprintf(xfile, "\n");
        fprintf(zfile, "\n");
      }
      fclose(out);
      fclose(xfile);
      fclose(zfile);
    }
  }
  delete[] plotname;
  took("Dumping the triplet dist plots");
  const double ds = 0.01; // step size to use in path plots, FIXME increase for publication!
  const double delta = .1; //this is the value of radius of the
                           //particle as it moves around the contact
                           //sphere on its path
  char *plotname_path = new char[4096];
  for (int version = 0; version < numplots; version++) {
    sprintf(plotname_path,
            "papers/pair-correlation/figs/triplet%s-path-%s-%04.2f.dat",
            name, fun[version], eta);
    FILE *out_path = fopen(plotname_path, "w");
    if (!out_path) {
      fprintf(stderr, "Unable to create file %s!\n", plotname_path);
      return;
    }
//.........这里部分代码省略.........

double run_walls(double eta, const char *name, Functional fhs, double teff) {
  //printf("Filling fraction is %g with functional %s at temperature %g\n", eta, name, teff);
  //fflush(stdout);
  double kT = teff;
  if (kT == 0) kT = 1;

  Functional f = OfEffectivePotential(fhs);

  const double zmax = width + 2*spacing;
  Lattice lat(Cartesian(dw,0,0), Cartesian(0,dw,0), Cartesian(0,0,zmax));
  GridDescription gd(lat, dx);

  Grid constraint(gd);
  constraint.Set(notinwall);
  f = constrain(constraint, f);

  // We reuse the potential, which should give us a better starting
  // guess on each calculation.
  static Grid *potential = 0;
  if (strcmp(name, "hard") == 0) {
    // start over for each potential
    delete potential;
    potential = 0;
  }
  if (!potential) {
    potential = new Grid(gd);
    *potential = (eta*constraint + 1e-4*eta*VectorXd::Ones(gd.NxNyNz))/(4*M_PI/3);
    *potential = -kT*potential->cwise().log();
  }

  // FIXME below I use the HS energy because of issues with the actual
  // functional.
  const double approx_energy = fhs(kT, eta/(4*M_PI/3))*dw*dw*width;
  const double precision = fabs(approx_energy*1e-5);
  printf("\tMinimizing to %g absolute precision from %g from %g...\n", precision, approx_energy, kT);
  fflush(stdout);

  Minimizer min = Precision(precision,
                            PreconditionedConjugateGradient(f, gd, kT,
                                                            potential,
                                                            QuadraticLineMinimizer));
  took("Setting up the variables");
  for (int i=0;min.improve_energy(false) && i<100;i++) {
  }
  took("Doing the minimization");
  min.print_info();

  Grid density(gd, EffectivePotentialToDensity()(kT, gd, *potential));
  //printf("# per area is %g at filling fraction %g\n", density.sum()*gd.dvolume/dw/dw, eta);
  
  char *plotname = (char *)malloc(1024);

  sprintf(plotname, "papers/fuzzy-fmt/figs/walls%s-%06.4f-%04.2f.dat", name, teff, eta);
  z_plot(plotname, Grid(gd, 4*M_PI*density/3));
  free(plotname);

  {
    GridDescription gdj = density.description(); 
    double sep =  gdj.dz*gdj.Lat.a3().norm();
    int div = gdj.Nz;
    int mid = int (div/2.0);
    double Ntot_per_A = 0;
    double mydist = 0;
   
    for (int j=0; j<mid; j++){
      Ntot_per_A += density(0,0,j)*sep;
      mydist += sep;
    }
    
    double Extra_per_A = Ntot_per_A - eta/(4.0/3.0*M_PI)*width/2;
    
    FILE *fout = fopen("papers/fuzzy-fmt/figs/wallsfillingfracInfo.txt", "a");
    fprintf(fout, "walls%s-%04.2f.dat  -  If you want to match the bulk filling fraction of figs/walls%s-%04.2f.dat, than the number of extra spheres per area to add is %04.10f.  So you'll want to multiply %04.2f by your cavity volume and divide by (4/3)pi.  Then add %04.10f times the Area of your cavity to this number\n",
	    name, eta, name, eta, Extra_per_A, eta, Extra_per_A);
    
    int wallslen = 20;
    double Extra_spheres =  (eta*wallslen*wallslen*wallslen/(4*M_PI/3) + Extra_per_A*wallslen*wallslen);  
    fprintf (fout, "For filling fraction %04.02f and walls of length %d you'll want to use %.0f spheres.\n\n", eta, wallslen, Extra_spheres);
    
    fclose(fout); 
  }
  
  {
    //double peak = peak_memory()/1024.0/1024;
    //double current = current_memory()/1024.0/1024;
    //printf("Peak memory use is %g M (current is %g M)\n", peak, current);
  }
  
  took("Plotting stuff");
  printf("density %g gives ff %g for eta = %g and T = %g\n", density(0,0,gd.Nz/2),
         density(0,0,gd.Nz/2)*4*M_PI/3, eta, teff);
  return density(0, 0, gd.Nz/2)*4*M_PI/3; // return bulk filling fraction
}

int main(int argc, char *argv[]) {
  if (argc > 1) {
    if (sscanf(argv[1], "%lg", &diameter) != 1) {
      printf("Got bad argument: %s\n", argv[1]);
      return 1;
    }
    diameter *= nm;
    using_default_diameter = false;
    printf("Diameter is %g bohr\n", diameter);
  }
  
  const double ptransition  =(3.0*M_PI-4.0)*(diameter/2.0)/2.0;
  const double dmax = ptransition + 0.6*nm;
  double zmax = 2*diameter+dmax+2*nm;
  double ymax = 2*diameter+dmax+2*nm;

  char *datname = new char[1024];
  snprintf(datname, 1024, "papers/water-saft/figs/four-rods-in-water-%04.1fnm.dat", diameter/nm);
  
  FILE *o = fopen(datname, "w");
  delete[] datname;

  Functional f = OfEffectivePotential(WaterSaft(new_water_prop.lengthscale,
                                                new_water_prop.epsilonAB, new_water_prop.kappaAB,
                                                new_water_prop.epsilon_dispersion,
                                                new_water_prop.lambda_dispersion,
                                                new_water_prop.length_scaling, 0));
  double n_1atm = pressure_to_density(f, new_water_prop.kT, atmospheric_pressure,
                                      0.001, 0.01);

  double mu_satp = find_chemical_potential(f, new_water_prop.kT, n_1atm);

  f = OfEffectivePotential(WaterSaft(new_water_prop.lengthscale,
                                     new_water_prop.epsilonAB, new_water_prop.kappaAB,
                                     new_water_prop.epsilon_dispersion,
                                     new_water_prop.lambda_dispersion,
                                     new_water_prop.length_scaling, mu_satp));
  
  const double EperVolume = f(new_water_prop.kT, -new_water_prop.kT*log(n_1atm));
  const double EperCell = EperVolume*(zmax*ymax - 4*0.25*M_PI*diameter*diameter)*width;

  //Functional X = Xassociation(new_water_prop.lengthscale, new_water_prop.epsilonAB, 
  //                            new_water_prop.kappaAB, new_water_prop.epsilon_dispersion,
  //                            new_water_prop.lambda_dispersion,
  //                            new_water_prop.length_scaling);
  
  Functional S = OfEffectivePotential(EntropySaftFluid2(new_water_prop.lengthscale, 
                                                        new_water_prop.epsilonAB,
                                                        new_water_prop.kappaAB,
                                                        new_water_prop.epsilon_dispersion,
                                                        new_water_prop.lambda_dispersion,
                                                        new_water_prop.length_scaling));
  //dmax, dstep already in bohrs (so it doesn't need to be converted from nm)
  double dstep = 0.25*nm;
  for (distance=0.0*nm; distance<=dmax; distance += dstep) {

    if ((distance >= ptransition - 0.5*nm) && (distance <= ptransition + 0.05*nm)) {
      if (distance >= ptransition - 0.25*nm) {
        dstep = 0.03*nm;
      } else {
        dstep = 0.08*nm;
      }
    } else {
      dstep = 0.25*nm;
    }

    Lattice lat(Cartesian(width,0,0), Cartesian(0,ymax,0), Cartesian(0,0,zmax));
    GridDescription gd(lat, 0.2);
    printf("Grid is %d x %d x %d\n", gd.Nx, gd.Ny, gd.Nz);
    Grid potential(gd);
    Grid constraint(gd);
    constraint.Set(notinwall);
    
    f = OfEffectivePotential(WaterSaft(new_water_prop.lengthscale,
                                       new_water_prop.epsilonAB, new_water_prop.kappaAB,
                                       new_water_prop.epsilon_dispersion,
                                       new_water_prop.lambda_dispersion,
                                       new_water_prop.length_scaling, mu_satp));
    f = constrain(constraint, f);
    
    printf("Diameter is %g bohr (%g nm)\n", diameter, diameter/nm);
    printf("Distance between rods = %g bohr (%g nm)\n", distance, distance/nm);


    potential = new_water_prop.liquid_density*constraint
      + 400*new_water_prop.vapor_density*VectorXd::Ones(gd.NxNyNz);
    //potential = new_water_prop.liquid_density*VectorXd::Ones(gd.NxNyNz);
    potential = -new_water_prop.kT*potential.cwise().log();

    const double surface_tension = 5e-5; // crude guess from memory...
    const double surfprecision = 1e-5*(4*M_PI*diameter)*width*surface_tension; // five digits accuracy
    const double bulkprecision = 1e-12*fabs(EperCell); // but there's a limit on our precision for small rods
    const double precision = bulkprecision + surfprecision;
    printf("Precision limit from surface tension is to %g based on %g and %g\n",
           precision, surfprecision, bulkprecision);
    Minimizer min = Precision(precision, PreconditionedConjugateGradient(f, gd, new_water_prop.kT,
                                                                     &potential,
                                                                     QuadraticLineMinimizer));
    const int numiters = 200;
    for (int i=0;i<numiters && min.improve_energy(false);i++) {
//.........这里部分代码省略.........

double surface_tension(Minimizer min, Functional f0, LiquidProperties prop,
                       bool verbose, const char *plotname) {
  int numptspersize = 100;
  int size = 64;
  const int gas_size = 10;
  Lattice lat(Cartesian(1,0,0), Cartesian(0,1,0), Cartesian(0,0,size*prop.lengthscale));
  GridDescription gd(lat, 1, 1, numptspersize*size);
  Grid potential(gd);

  // Set the density to range from vapor to liquid
  const double Veff_liquid = -prop.kT*log(prop.liquid_density);
  const double Veff_gas = -prop.kT*log(prop.vapor_density);
  for (int i=0; i<gd.NxNyNz*gas_size/size; i++) potential[i] = Veff_gas;
  for (int i=gd.NxNyNz*gas_size/size; i<gd.NxNyNz; i++) potential[i] = Veff_liquid;

  // Enable the following line for debugging...
  //f0.run_finite_difference_test("f0", prop.kT, potential);
  min.minimize(f0, gd, &potential);
  while (min.improve_energy(verbose))
    if (verbose) {
      printf("Working on liberated interface...\n");
      fflush(stdout);
    }
  const double Einterface = f0.integral(prop.kT, potential);
  double Ninterface = 0;
  Grid interface_density(gd, EffectivePotentialToDensity()(prop.kT, gd, potential));
  for (int i=0;i<gd.NxNyNz;i++) Ninterface += interface_density[i]*gd.dvolume;
  if (verbose) printf("Got interface energy of %g.\n", Einterface);
  
  for (int i=0; i<gd.NxNyNz; i++) potential[i] = Veff_gas;
  min.minimize(f0, gd, &potential);
  while (min.improve_energy(verbose))
    if (verbose) {
      printf("Working on gas...\n");
      fflush(stdout);
    }
  const double Egas = f0.integral(prop.kT, potential);
  double Ngas = 0;
  {
    Grid density(gd, EffectivePotentialToDensity()(prop.kT, gd, potential));
    for (int i=0;i<gd.NxNyNz;i++) Ngas += density[i]*gd.dvolume;
  }
  
  for (int i=0; i<gd.NxNyNz; i++) potential[i] = Veff_liquid;
  if (verbose) {
    printf("\n\n\nWorking on liquid...\n");
    fflush(stdout);
  }
  min.minimize(f0, gd, &potential);
  while (min.improve_energy(verbose))
    if (verbose) {
      printf("Working on liquid...\n");
      fflush(stdout);
    }
  const double Eliquid = f0.integral(prop.kT, potential);
  double Nliquid = 0;
  {
    Grid density(gd, EffectivePotentialToDensity()(prop.kT, gd, potential));
    for (int i=0;i<gd.NxNyNz;i++) Nliquid += density[i]*gd.dvolume;
  }
  
  const double X = Ninterface/Nliquid; // Fraction of volume effectively filled with liquid.
  const double surface_tension = (Einterface - Eliquid*X - Egas*(1-X))/2;
  if (verbose) {
    printf("\n\n");
    printf("interface energy is %.15g\n", Einterface);
    printf("gas energy is %.15g\n", Egas);
    printf("liquid energy is %.15g\n", Eliquid);
    printf("Ninterface/liquid/gas = %g/%g/%g\n", Ninterface, Nliquid, Ngas);
    printf("X is %g\n", X);
    printf("surface tension is %.10g\n", surface_tension);
  }
  if (plotname)
    interface_density.Dump1D(plotname, Cartesian(0,0,0),
                             Cartesian(0,0,size*prop.lengthscale));
  return surface_tension;
}

int main(int argc, char *argv[]) {
  clock_t start_time = clock();
  if (argc > 1) {
    if (sscanf(argv[1], "%lg", &diameter) != 1) {
      printf("Got bad argument: %s\n", argv[1]);
      return 1;
    }
    diameter *= nm;
    using_default_diameter = false;
  }
  printf("Diameter is %g bohr = %g nm\n", diameter, diameter/nm);
  const double padding = 1*nm;
  xmax = ymax = zmax = diameter + 2*padding;

  char *datname = (char *)malloc(1024);
  sprintf(datname, "papers/hughes-saft/figs/sphere-%04.2fnm-energy.dat", diameter/nm);
  
  Functional f = OfEffectivePotential(SaftFluid2(hughes_water_prop.lengthscale,
						hughes_water_prop.epsilonAB, hughes_water_prop.kappaAB,
						hughes_water_prop.epsilon_dispersion,
						hughes_water_prop.lambda_dispersion,
						hughes_water_prop.length_scaling, 0));
  double n_1atm = pressure_to_density(f, hughes_water_prop.kT, atmospheric_pressure,
				      0.001, 0.01);

  double mu_satp = find_chemical_potential(f, hughes_water_prop.kT, n_1atm);

  f = OfEffectivePotential(SaftFluid2(hughes_water_prop.lengthscale,
				     hughes_water_prop.epsilonAB, hughes_water_prop.kappaAB,
				     hughes_water_prop.epsilon_dispersion,
				     hughes_water_prop.lambda_dispersion,
				     hughes_water_prop.length_scaling, mu_satp));
  Functional S = OfEffectivePotential(EntropySaftFluid2(new_water_prop.lengthscale,
                                                        new_water_prop.epsilonAB,
                                                        new_water_prop.kappaAB,
                                                        new_water_prop.epsilon_dispersion,
                                                        new_water_prop.lambda_dispersion,
                                                        new_water_prop.length_scaling));
  
  const double EperVolume = f(hughes_water_prop.kT, -hughes_water_prop.kT*log(n_1atm));
  const double EperNumber = EperVolume/n_1atm;
  const double SperNumber = S(hughes_water_prop.kT, -hughes_water_prop.kT*log(n_1atm))/n_1atm;
  const double EperCell = EperVolume*(zmax*ymax*xmax - (M_PI/6)*diameter*diameter*diameter);

  //for (diameter=0*nm; diameter<3.0*nm; diameter+= .1*nm) {
    Lattice lat(Cartesian(xmax,0,0), Cartesian(0,ymax,0), Cartesian(0,0,zmax));
    GridDescription gd(lat, 0.2);
    
    Grid potential(gd);
    Grid constraint(gd);
    constraint.Set(notinwall);
    
    f = OfEffectivePotential(SaftFluid2(hughes_water_prop.lengthscale,
				       hughes_water_prop.epsilonAB, hughes_water_prop.kappaAB,
				       hughes_water_prop.epsilon_dispersion,
				       hughes_water_prop.lambda_dispersion,
				       hughes_water_prop.length_scaling, mu_satp));
    f = constrain(constraint, f);
    //constraint.epsNativeSlice("papers/hughes-saft/figs/sphere-constraint.eps",
    // 			      Cartesian(0,ymax,0), Cartesian(0,0,zmax), 
    // 			      Cartesian(0,ymax/2,zmax/2));
    //printf("Constraint has become a graph!\n");
   
    potential = hughes_water_prop.liquid_density*constraint
      + 100*hughes_water_prop.vapor_density*VectorXd::Ones(gd.NxNyNz);
    //potential = hughes_water_prop.liquid_density*VectorXd::Ones(gd.NxNyNz);
    potential = -hughes_water_prop.kT*potential.cwise().log();
    
    double energy;
    {
      const double surface_tension = 5e-5; // crude guess from memory...
      const double surfprecision = 1e-4*M_PI*diameter*diameter*surface_tension; // four digits precision
      const double bulkprecision = 1e-12*fabs(EperCell); // but there's a limit on our precision for small spheres
      const double precision = bulkprecision + surfprecision;
      Minimizer min = Precision(precision,
                                PreconditionedConjugateGradient(f, gd, hughes_water_prop.kT, 
                                                                &potential,
                                                                QuadraticLineMinimizer));
      
      printf("\nDiameter of sphere = %g bohr (%g nm)\n", diameter, diameter/nm);
      
      const int numiters = 200;
      for (int i=0;i<numiters && min.improve_energy(true);i++) {
        //fflush(stdout);
        //Grid density(gd, EffectivePotentialToDensity()(hughes_water_prop.kT, gd, potential));
        
        //density.epsNativeSlice("papers/hughes-saft/figs/sphere.eps", 
        //			     Cartesian(0,ymax,0), Cartesian(0,0,zmax), 
        //			     Cartesian(0,ymax/2,zmax/2));
        
        //sleep(3);

        double peak = peak_memory()/1024.0/1024;
        double current = current_memory()/1024.0/1024;
        printf("Peak memory use is %g M (current is %g M)\n", peak, current);
      }
      
      double peak = peak_memory()/1024.0/1024;
      double current = current_memory()/1024.0/1024;
      printf("Peak memory use is %g M (current is %g M)\n", peak, current);
//.........这里部分代码省略.........

int main(int, char **) {
    for (double eta = 0.3; eta < 0.35; eta += 0.1) {
        // Generates a data file for the pair distribution function, for filling fraction eta
        // and distance of first sphere from wall of z0. Data saved in a table such that the
        // columns are x values and rows are z1 values.
        printf("Now starting sphere_with_wall with eta = %g\n",eta);
        Lattice lat(Cartesian(width,0,0), Cartesian(0,width,0), Cartesian(0,0,width+2*spacing));
        GridDescription gd(lat, dx); //the resolution here dramatically affects our memory use

        Functional f = OfEffectivePotential(WB + IdealGas());
        double mu = find_chemical_potential(f, 1, eta/(4*M_PI/3));
        f = OfEffectivePotential(WB + IdealGas()
                                 + ChemicalPotential(mu));

        Grid potential(gd);
        Grid constraint(gd);

        constraint.Set(*notinwall_or_sphere);
        constraint.epsNativeSlice("myconstraint.eps",
                                  Cartesian(0, 0, 2*(width+2*spacing)),
                                  Cartesian(2*width, 0, 0),
                                  Cartesian(0, 0, 0));

        f = constrain(constraint, f);

        potential = (eta*constraint + 1e-4*eta*VectorXd::Ones(gd.NxNyNz))/(4*M_PI/3);
        potential = -potential.cwise().log();

        const double approx_energy = (WB + IdealGas() + ChemicalPotential(mu))(1, eta/(4*M_PI/3))*dw*dw*width;
        const double precision = fabs(approx_energy*1e-4);
        //printf("Minimizing to %g absolute precision...\n", precision);
        Minimizer min = Precision(precision,
                                  PreconditionedConjugateGradient(f, gd, 1,
                                          &potential,
                                          QuadraticLineMinimizer));
        {
            double peak = peak_memory()/1024.0/1024;
            double current = current_memory()/1024.0/1024;
            printf("Peak memory use is %g M (current is %g M)\n", peak, current);
            fflush(stdout);
        }

        for (int i=0; min.improve_energy(true) && i<100; i++) {
            double peak = peak_memory()/1024.0/1024;
            double current = current_memory()/1024.0/1024;
            printf("Peak memory use is %g M (current is %g M)\n", peak, current);
            fflush(stdout);
        }
        Grid density(gd, EffectivePotentialToDensity()(1, gd, potential));

        char *plotname = new char[1024];
        sprintf(plotname, "papers/pair-correlation/figs/walls/wallsWB-sphere-dft-%04.2f.dat", eta);
        pair_plot(plotname, density);
        delete[] plotname;

        char *plotname_path = new char[1024];
        sprintf(plotname_path, "papers/pair-correlation/figs/walls/wallsWB-sphere-dft-path-%04.2f.dat", eta);
        path_plot(plotname_path, density, constraint);
        delete[] plotname_path;
        fflush(stdout);
        {
            double peak = peak_memory()/1024.0/1024;
            double current = current_memory()/1024.0/1024;
            printf("Peak memory use is %g M (current is %g M)\n", peak, current);
            fflush(stdout);
        }
        fflush(stdout);
    }
    fflush(stdout);
    // Just create this file so make knows we have run.
    if (!fopen("papers/pair-correlation/figs/walls_sphere.dat", "w")) {
        printf("Error creating walls.dat!\n");
        return 1;
    }
    fflush(stdout);
    return 1;
}

//.........这里部分代码省略.........

  Functional X = WaterX(hughes_water_prop.lengthscale,
                        hughes_water_prop.epsilonAB, hughes_water_prop.kappaAB,
                        hughes_water_prop.epsilon_dispersion,
                        hughes_water_prop.lambda_dispersion,
                        hughes_water_prop.length_scaling, mu);
  
  Functional HB = HughesHB(hughes_water_prop.lengthscale,
                           hughes_water_prop.epsilonAB, hughes_water_prop.kappaAB,
                           hughes_water_prop.epsilon_dispersion,
                           hughes_water_prop.lambda_dispersion,
                           hughes_water_prop.length_scaling, mu);

  externalpotential.epsNativeSlice("papers/water-saft/figs/hughes-lj-potential.eps",
                                   Cartesian(0,ymax,0), Cartesian(0,0,zmax), 
                                   Cartesian(0,ymax/2,zmax/2));
  printf("Done outputting hughes-lj-potential.eps\n");

  potential = 0*externalpotential - temperature*log(n_1atm)*VectorXd::Ones(gd.NxNyNz); // ???
    
  double energy;
  {
    const double surface_tension = 5e-5; // crude guess from memory...
    const double surfprecision = 1e-4*M_PI*sigma*sigma*surface_tension; // four digits precision
    const double bulkprecision = 1e-12*fabs(EperCell); // but there's a limit on our precision
    const double precision = (bulkprecision + surfprecision)*1e-6;
    Minimizer min = Precision(precision,
                              PreconditionedConjugateGradient(f, gd, temperature, 
                                                              &potential,
                                                              QuadraticLineMinimizer));
      
      
    const int numiters = 200;
    for (int i=0;i<numiters && min.improve_energy(true);i++) {
      double peak = peak_memory()/1024.0/1024;
      double current = current_memory()/1024.0/1024;
      printf("Peak memory use is %g M (current is %g M)\n", peak, current);
      fflush(stdout);
      {
        char* name = new char[1000];
        sprintf(name, "papers/water-saft/figs/hughes-lj-%s-%gK-density-%d.eps", argv[1], temperature/kB, i);
        Grid density(gd, EffectivePotentialToDensity()(temperature, gd, potential));
        density.epsNativeSlice(name,
                               Cartesian(0,ymax,0), Cartesian(0,0,zmax), 
                               Cartesian(0,ymax/2,zmax/2));
      }
      Grid gradient(gd, potential);
      gradient *= 0;
      f.integralgrad(temperature, potential, &gradient); 
      char* gradname = new char[1000];
      sprintf(gradname, "papers/water-saft/figs/hughes-lj-%s-%gK-gradient-%d.eps", argv[1], temperature/kB, i);
      gradient.epsNativeSlice(gradname,
                              Cartesian(0,ymax,0), Cartesian(0,0,zmax), 
                              Cartesian(0,ymax/2,zmax/2));

      Grid density(gd, EffectivePotentialToDensity()(temperature, gd, potential));
      char *plotname = (char *)malloc(1024);
      sprintf(plotname, "papers/water-saft/figs/hughes-lj-%s-%gK-%d.dat", argv[1], temperature/kB, i);
      plot_grids_y_direction(plotname, density, gradient);

      // Grid gradient(gd, potential);
      // gradient *= 0;
      // f.integralgrad(temperature, potential, &gradient);
      // sprintf(name, "papers/water-saft/figs/lj-%s-%d-gradient-big.eps", argv[1], i);
      // gradient.epsNativeSlice("papers/water-saft/figs/lj-gradient-big.eps",
      //                         Cartesian(0,ymax,0), Cartesian(0,0,zmax), 

int main(int, char **) {
  FILE *o = fopen("papers/hughes-saft/figs/single-rod-in-water-low-res.dat", "w");

  Functional f = OfEffectivePotential(SaftFluid2(hughes_water_prop.lengthscale,
						hughes_water_prop.epsilonAB, hughes_water_prop.kappaAB,
						hughes_water_prop.epsilon_dispersion,
						hughes_water_prop.lambda_dispersion,
						hughes_water_prop.length_scaling, 0));
  double n_1atm = pressure_to_density(f, hughes_water_prop.kT, atmospheric_pressure,
					      0.001, 0.01);

  double mu_satp = find_chemical_potential(f, hughes_water_prop.kT, n_1atm);

  f = OfEffectivePotential(SaftFluid2(hughes_water_prop.lengthscale,
				     hughes_water_prop.epsilonAB, hughes_water_prop.kappaAB,
				     hughes_water_prop.epsilon_dispersion,
				     hughes_water_prop.lambda_dispersion,
				     hughes_water_prop.length_scaling, mu_satp));
  
  const double EperVolume = f(hughes_water_prop.kT, -hughes_water_prop.kT*log(n_1atm));

  for (cavitysize=1.0*nm; cavitysize<=1.1*nm; cavitysize += 0.5*nm) {
    Lattice lat(Cartesian(width,0,0), Cartesian(0,ymax,0), Cartesian(0,0,zmax));
    GridDescription gd(lat, 0.5);
    
    Grid potential(gd);
    Grid constraint(gd);
    constraint.Set(notinwall);
    
    f = OfEffectivePotential(SaftFluid2(hughes_water_prop.lengthscale,
				       hughes_water_prop.epsilonAB, hughes_water_prop.kappaAB,
				       hughes_water_prop.epsilon_dispersion,
				       hughes_water_prop.lambda_dispersion,
				       hughes_water_prop.length_scaling, mu_satp));
    f = constrain(constraint, f);
    // constraint.epsNativeSlice("papers/hughes-saft/figs/single-rod-in-water-constraint.eps",
    // 			      Cartesian(0,ymax,0), Cartesian(0,0,zmax), 
    // 			      Cartesian(0,ymax/2,zmax/2));
    //printf("Constraint has become a graph!\n");
   
    potential = hughes_water_prop.liquid_density*constraint
      + 1000*hughes_water_prop.vapor_density*VectorXd::Ones(gd.NxNyNz);
    //potential = hughes_water_prop.liquid_density*VectorXd::Ones(gd.NxNyNz);
    potential = -hughes_water_prop.kT*potential.cwise().log();
    
    Minimizer min = Precision(1e-11, PreconditionedConjugateGradient(f, gd, hughes_water_prop.kT,
                                                                     &potential,
                                                                     QuadraticLineMinimizer));
    
    //printf("\nDiameter of rod = %g bohr (%g nm)\n", cavitysize, cavitysize/nm);
    
    const int numiters = 50;
    for (int i=0;i<numiters && min.improve_energy(false);i++) {
      fflush(stdout);
      //Grid density(gd, EffectivePotentialToDensity()(hughes_water_prop.kT, gd, potential));
     
      //density.epsNativeSlice("papers/hughes-saft/figs/single-rod-in-water.eps", 
      //			     Cartesian(0,ymax,0), Cartesian(0,0,zmax), 
      //			     Cartesian(0,ymax/2,zmax/2));
      
      // sleep(3);
    }

    const double EperCell = EperVolume*(zmax*ymax - 0.25*M_PI*cavitysize*cavitysize)*width;
    //printf("The bulk energy per cell should be %g\n", EperCell);
    double energy = (min.energy() - EperCell)/width;
    //printf("Energy is %.15g\n", energy);

    fprintf(o, "%g\t%.15g\n", cavitysize/nm, energy);

    char *plotname = (char *)malloc(1024);
    sprintf(plotname, "papers/hughes-saft/figs/single-rod-res0.5-slice-%04.1f.dat", cavitysize/nm);
    Grid density(gd, EffectivePotentialToDensity()(hughes_water_prop.kT, gd, potential));
    plot_grids_y_direction(plotname, density);
    free(plotname);

  }
  fclose(o);
}