Full solutions in C

hydrogen.h

@@ -34,6 +34,7 @@ double psi(double a, double *r, const int l) {
 double kinetic(double a, double *r, const int l) {
       double rnorm;
 
+      rnorm = 0.0;
       for (int i = 0; i < l; ++i) {
 	    rnorm += r[i]*r[i];
       }
@@ -50,6 +51,7 @@ double e_loc(double a, double *r, const int l) {
 void drift(double a, double *r, double *d, const int l) {
       double rnorm, fact;
 
+      rnorm = 0.0;
       for (int i = 0; i < l; ++i) {
 	    rnorm += r[i]*r[i];
       }

pdmc.c

@@ -0,0 +1,111 @@
+#include "hydrogen.h"
+#include "qmc_stats.h"
+
+void pdmc(double a, const int nmax, double dt,
+	  double *energy, double *accept, double tau, double e_ref) {
+      int n_accept;
+      double r_old[3], r_new[3], psi_old, psi_new;
+      double d_old[3], d_new[3], d2_old, d2_new;
+      double rnd[3], fact_a, fact_b, sq_dt, q, u;
+      double e, w, tau_current, norma;
+
+      sq_dt = sqrt(dt);
+
+      // Initial position
+      random_gauss(r_old, 3);
+
+      drift(a, r_old, d_old, 3);
+      d2_old = 0.0;
+      for (int j = 0; j < 3; ++j) {
+	    d2_old += d_old[j] * d_old[j];
+      }
+
+      psi_old = psi(a, r_old, 3);
+
+      *energy = 0.0;
+      *accept = 0.0;
+      n_accept = 0;
+      w = 1.0;
+      tau_current = 0.0;
+      norma = 0.0;
+      for (int i = 0; i < nmax; ++i) {
+	    // Compute local energy and weight
+	    e = e_loc(a, r_old, 3);
+	    w = w * exp(-dt * (e - e_ref));
+
+	    // Accumulate local energy and norm
+	    norma = norma + w; 
+	    *energy += w * e;
+
+	    // Increase time and reset if threshold reached
+	    tau_current += dt;
+	    if (tau_current > tau) {
+		  w = 1.0;
+		  tau_current = 0.0;
+	    }
+
+	    // Compute new position (correct variance of sampled Gaussian)
+	    random_gauss(rnd, 3);
+	    for (int j = 0; j < 3; ++j) {
+		  r_new[j] = r_old[j] + dt * d_old[j] + rnd[j] * sq_dt;
+	    }
+
+	    // New WF and acceptance probability
+            drift(a, r_new, d_new, 3);
+	    d2_new = 0.0;
+            for (int j = 0; j < 3; ++j) {
+		  d2_new += d_new[j] * d_new[j];
+            }
+
+	    psi_new = psi(a, r_new, 3);
+
+	    // Compute the ratio of probabilities q
+	    fact_b = 0.0;
+	    for (int j = 0; j < 3; ++j) {
+		  fact_b += (d_new[j] + d_old[j]) * (r_new[j] - r_old[j]);
+	    }
+	    fact_a = 0.5 * dt * (d2_new - d2_old) + fact_b;
+
+	    q = psi_new / psi_old;
+	    q = exp(-fact_a) * q * q;
+
+	    u = (double) rand() / RAND_MAX;
+
+	    if (u <= q) {
+		  n_accept += 1;
+		  for (int j = 0; j < 3; ++j) {
+			r_old[j] = r_new[j];
+			d_old[j] = d_new[j];
+		  }
+		  d2_old = d2_new;
+		  psi_old = psi_new;
+	    }
+      }
+      *energy /= norma;
+      *accept = (double) n_accept / nmax;
+}
+
+int main() {
+      const double a = 1.2;
+      const double dt = 0.05;
+      const double tau = 100.0;
+      const double e_ref = -0.5;
+      const long nmax = 1e5;
+      int nruns = 30;
+
+      srand(time(NULL));
+
+      double ene[nruns], acc[nruns], obs[2];
+
+      for (int i = 0; i < nruns; ++i) {
+	    pdmc(a, nmax, dt, &ene[i], &acc[i], tau, e_ref);
+      }
+
+      ave_error(ene, nruns, obs);
+      printf("E = %.5lf +/- %.5lf\n", obs[0], obs[1]);
+
+      ave_error(acc, nruns, obs);
+      printf("A = %.5lf +/- %.5lf\n", obs[0], obs[1]);
+      
+      return 0;
+}

qmc_gaussian.c

@@ -1,7 +1,44 @@
-#include <math.h>
-#include <stdio.h>
+#include "qmc_stats.h"
+#include "hydrogen.h"
 
 double gaussian(double *r) {
-      // Pending
+      const double norm_gauss = 1.0 / pow(2.0 * acos(-1.0), 1.5);
+      return norm_gauss * exp(-0.5 * (r[0]*r[0] + r[1]*r[1] + r[2]*r[2]));
+}
+
+double gaussian_montecarlo(double a, const int nmax) {
+      double r[3], energy, norm, w;
+
+      norm = 0.0;
+      energy = 0.0;
+      for (int i = 0; i < nmax; ++i) {
+	    random_gauss(r, 3);
+	    w = psi(a, r, 3) * psi(a, r, 3) / gaussian(r);
+	    norm += w;
+	    energy += w * e_loc(a, r, 3);
+      }
+
+      return energy / norm;
+
+}
+
+int main() {
+      const double a = 1.2;
+      const long nmax = 1e5;
+      int nruns = 30;
+
+      srand(time(NULL));
+
+      double x[nruns], obs[2];
+
+      for (int i = 0; i < nruns; ++i) {
+	    x[i] = gaussian_montecarlo(a, nmax);
+      }
+
+      ave_error(x, nruns, obs);
+
+      printf("E = %.5lf +/- %.5lf\n", obs[0], obs[1]);
+      
       return 0;
 }
+