implemented the discrete gaussian model for roughening

11 files changed, 327 insertions, 48 deletions

diff --git a/CMakeLists.txt b/CMakeLists.txt
index 5269c48..84c8fb3 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -16,12 +16,15 @@ file(GLOB CPPSOURCES lib/*.cpp)
 
 add_executable(wolff_finite src/wolff_finite.c ${CSOURCES})
 add_executable(wolff_ising src/wolff_ising.cpp ${CPPSOURCES} ${CSOURCES})
+add_executable(wolff_dgm src/wolff_dgm.cpp ${CPPSOURCES} ${CSOURCES})
 add_executable(wolff_3potts src/wolff_potts.cpp ${CPPSOURCES} ${CSOURCES})
+add_executable(wolff_4potts src/wolff_potts.cpp ${CPPSOURCES} ${CSOURCES})
 add_executable(wolff_planar src/wolff_On.cpp ${CPPSOURCES} ${CSOURCES})
 add_executable(wolff_heisenberg src/wolff_On.cpp ${CPPSOURCES} ${CSOURCES})
 add_executable(analyze_correlations src/analyze_correlations.cpp ${CPPSOURCES} ${CSOURCES})
 
 SET_TARGET_PROPERTIES(wolff_3potts PROPERTIES COMPILE_FLAGS "-DPOTTSQ=3")
+SET_TARGET_PROPERTIES(wolff_4potts PROPERTIES COMPILE_FLAGS "-DPOTTSQ=4")
 SET_TARGET_PROPERTIES(wolff_planar PROPERTIES COMPILE_FLAGS "-DN_COMP=2")
 SET_TARGET_PROPERTIES(wolff_heisenberg PROPERTIES COMPILE_FLAGS "-DN_COMP=3")
 
@@ -37,19 +40,24 @@ target_link_libraries(wolff_finite cblas gsl m)
 target_link_libraries(analyze_correlations cblas gsl fftw3 m)
 if (${GLUT} MATCHES "GLUT-NOTFOUND")
   target_link_libraries(wolff_ising cblas gsl m)
+  target_link_libraries(wolff_dgm cblas gsl m)
   target_link_libraries(wolff_3potts cblas gsl m)
   target_link_libraries(wolff_heisenberg cblas gsl m)
   target_link_libraries(wolff_planar cblas gsl m)
 else()
   target_link_libraries(wolff_ising cblas gsl m glut GL GLU)
+  target_link_libraries(wolff_dgm cblas gsl m glut GL GLU)
   target_link_libraries(wolff_3potts cblas gsl m glut GL GLU)
+  target_link_libraries(wolff_4potts cblas gsl m glut GL GLU)
   target_link_libraries(wolff_heisenberg cblas gsl m glut GL GLU)
   target_link_libraries(wolff_planar cblas gsl m glut GL GLU)
   target_compile_definitions(wolff_ising PUBLIC HAVE_GLUT)
+  target_compile_definitions(wolff_dgm PUBLIC HAVE_GLUT)
   target_compile_definitions(wolff_3potts PUBLIC HAVE_GLUT)
+  target_compile_definitions(wolff_4potts PUBLIC HAVE_GLUT)
   target_compile_definitions(wolff_planar PUBLIC HAVE_GLUT)
   target_compile_definitions(wolff_heisenberg PUBLIC HAVE_GLUT)
 endif()
 
-install(TARGETS wolff_finite wolff_ising wolff_3potts wolff_heisenberg wolff_planar analyze_correlations DESTINATION bin)
+install(TARGETS wolff_finite wolff_ising wolff_dgm wolff_3potts wolff_heisenberg wolff_planar analyze_correlations DESTINATION bin)
 
diff --git a/lib/dihedral_inf.h b/lib/dihedral_inf.h
new file mode 100644
index 0000000..f7c4297
--- /dev/null
+++ b/lib/dihedral_inf.h
@@ -0,0 +1,78 @@
+
+#include "types.h"
+#include <cmath>
+#include "height.h"
+
+template <class T>
+struct dihedral_inf_t { bool is_reflection; T x; };
+
+template <class T>
+void init(dihedral_inf_t<T> *ptr) {
+  ptr->is_reflection = false;
+  ptr->x = (T)0;
+}
+
+template <class T>
+dihedral_inf_t<T> copy(dihedral_inf_t<T> r) {
+  return r;
+}
+
+template <class T>
+void free_spin(dihedral_inf_t<T> r) {
+  // do nothing!
+}
+
+template <class T>
+height_t<T> act(dihedral_inf_t<T> r, height_t<T> h) {
+  height_t<T> h2;
+  if (r.is_reflection) {
+    h2.x = r.x - h.x;
+  } else {
+    h2.x = r.x + h.x;
+  }
+
+  return h2;
+}
+
+template <class T>
+dihedral_inf_t<T> act(dihedral_inf_t<T> r1, dihedral_inf_t<T> r2) {
+  dihedral_inf_t<T> r3;
+
+  if (r1.is_reflection) {
+    r3.is_reflection = !(r2.is_reflection);
+    r3.x = r1.x - r2.x;
+  } else {
+    r3.is_reflection = r2.is_reflection;
+    r3.x = r1.x + r2.x;
+  }
+
+  return r3;
+}
+
+template <class T>
+height_t<T> act_inverse(dihedral_inf_t<T> r, height_t<T> h) {
+  height_t<T> h2;
+  if (r.is_reflection) {
+    h2.x = r.x - h.x;
+  } else {
+    h2.x = h.x - r.x;
+  }
+
+  return h2;
+}
+
+template <class T>
+dihedral_inf_t<T> act_inverse(dihedral_inf_t<T> r1, dihedral_inf_t<T> r2) {
+  dihedral_inf_t<T> r3;
+
+  if (r1.is_reflection) {
+    r3.is_reflection = !(r2.is_reflection);
+    r3.x = r1.x - r2.x;
+  } else {
+    r3.is_reflection = r2.is_reflection;
+    r3.x = r2.x - r1.x;
+  }
+
+  return r3;
+}
+
diff --git a/lib/height.h b/lib/height.h
index 16c4dc5..81d3a2d 100644
--- a/lib/height.h
+++ b/lib/height.h
@@ -2,61 +2,88 @@
 #pragma once
 
 #include <cmath>
+#include <stdio.h>
 
 #include "types.h"
 
-// object definition
+/* The following is the minimum definition of a spin class.
+ *
+ * The class must contain an M_t and an F_t for holding the sum of an
+ * integer number of spins and a double-weighted number of spins,
+ * respectively.
+ *
+ * void init(X_t *p);
+ * void free_spin(X_t p);
+ * void free_spin(M_t p);
+ * void free_spin(F_t p);
+ * X_t copy(X_t x);
+ * void add(M_t *x1, int factor, X_t x2);
+ * void add(F_t *x1, double factor, X_t x2);
+ * M_t scalar_multiple(int factor, X_t x);
+ * F_t scalar_multiple(double factor, X_t x);
+ * double norm_squared(F_t x);
+ * void write_magnetization(M_t M, FILE *outfile);
+ *
+ */
+
 template <class T>
-struct height_t { T x; };
+struct height_t {
+  T x;
+
+  typedef T M_t;
+  typedef double F_t;
+};
 
-// init, copy, add, subtract, scalar_multiple, free_spin, and
-// write_magnetization are necessary for the operation of wolff.h
 template <class T>
-void init(height_t *ptr) {
+void init(height_t<T> *ptr) {
   ptr->x = (T)0;
 }
 
 template <class T>
-height_t <T> copy (height_t h) {
-  return h;
+void free_spin(height_t<T> h) {
+  // do nothing!
 }
 
 template <class T>
-void add (height_t <T> *h1, height_t <T> h2) {
-  h1->x += h2.x;
+void free_spin(T h) {
+  // do nothing!
 }
 
-template <class T>
-void subtract (height_t <T> *h1, height_T <T> h2) {
-  h1->x -= h2.x;
+void free_spin(double h) {
+  // do nothing!
 }
 
 template <class T>
-height_t <T> scalar_multiple(v_t a, height_t <T> h) {
-  height_t <T> hm;
-  hm.x = a * h.x;
+height_t<T> copy(height_t<T> h) {
+  return h;
+}
 
-  return hm;
+template <class T>
+void add(T *h1, int a, height_t<T> h2) {
+  (*h1) += a * h2.x;
 }
 
 template <class T>
-void free_spin (height_t <T> h) {
+void add(double *h1, double a, height_t<T> h2) {
+  (*h1) += a * h2.x;
 }
 
 template <class T>
-void write_magnetization(height_t <T> M, FILE *outfile) {
-  fwrite(&(M.x), sizeof(T), 1, outfile);
+T scalar_multiple(int factor, height_t<T> h) {
+  return factor * h.x;
 }
 
 template <class T>
-double correlation_component(height_t <T> h) {
-  return (double)h.x;
+double scalar_multiple(double factor, height_t<T> h) {
+  return factor * h.x;
 }
 
-// below here are not necessary for operation
+double norm_squared(double h) {
+  return pow(h, 2);
+}
 
 template <class T>
-T dot(height_t <T> h1, height_t <T> h2) {
-  return (h1.x - h2.x) * (h1.x - h2.x);
+void write_magnetization(T M, FILE *outfile) {
+  fwrite(&M, sizeof(T), 1, outfile);
 }
 
diff --git a/lib/ising.h b/lib/ising.h
index b4856c3..d956d88 100644
--- a/lib/ising.h
+++ b/lib/ising.h
@@ -19,6 +19,7 @@
  * void add(M_t *x1, int factor, X_t x2);
  * void add(F_t *x1, double factor, X_t x2);
  * M_t scalar_multiple(int factor, X_t x);
+ * F_t scalar_multiple(double factor, X_t x);
  * double norm_squared(F_t x);
  * void write_magnetization(M_t M, FILE *outfile);
  *
diff --git a/lib/orthogonal.h b/lib/orthogonal.h
index 340ee2c..523fd54 100644
--- a/lib/orthogonal.h
+++ b/lib/orthogonal.h
@@ -144,7 +144,7 @@ orthogonal_t <q, T> act_inverse (orthogonal_t <q, T> m1, orthogonal_t <q, T> m2)
 }
 
 template <q_t q>
-orthogonal_t <q, double> generate_rotation_uniform (gsl_rng *r, const state_t <orthogonal_t <q, double>, vector_t <q, double>> *s) {
+orthogonal_t <q, double> generate_rotation_uniform (gsl_rng *r, vector_t <q, double> v) {
   orthogonal_t <q, double> ptr;
   ptr.is_reflection = true;
   ptr.x = (double *)calloc(q, sizeof(double));
@@ -166,7 +166,7 @@ orthogonal_t <q, double> generate_rotation_uniform (gsl_rng *r, const state_t <o
 }
 
 template <q_t q>
-orthogonal_t <q, double> generate_rotation_perturbation (gsl_rng *r, const state_t <orthogonal_t <q, double>, vector_t <q, double>> *s, double epsilon) {
+orthogonal_t <q, double> generate_rotation_perturbation (gsl_rng *r, vector_t <q, double> v, double epsilon) {
   orthogonal_t <q, double> m;
   vector_t <q, double> tmp_v;
   m.is_reflection = true;
@@ -179,15 +179,15 @@ orthogonal_t <q, double> generate_rotation_perturbation (gsl_rng *r, const state
 
   for (q_t i = 0; i < q; i++) {
     tmp_v.x[i] = gsl_ran_ugaussian(r);
-    M2 += pow(s->M.x[i], 2);
-    tmpM += tmp_v.x[i] * s->M.x[i];
+    M2 += pow(v.x[i], 2);
+    tmpM += tmp_v.x[i] * v.x[i];
   }
 
   double v2 = 0;
   double factor = gsl_ran_ugaussian(r);
 
   for (q_t i = 0; i < q; i++) {
-    tmp_v.x[i] = (tmp_v.x[i] - tmpM * s->M.x[i] / M2) + epsilon * factor * s->M.x[i] / sqrt(M2);
+    tmp_v.x[i] = (tmp_v.x[i] - tmpM * v.x[i] / M2) + epsilon * factor * v.x[i] / sqrt(M2);
     v2 += tmp_v.x[i] * tmp_v.x[i];
   }
 
@@ -197,9 +197,7 @@ orthogonal_t <q, double> generate_rotation_perturbation (gsl_rng *r, const state
     tmp_v.x[i] /= mag_v;
   }
 
-  vector_t <q, double> v = act_inverse(s->R, tmp_v);
-  free(tmp_v.x);
-  m.x = v.x;
+  m.x = tmp_v.x;
 
   v2 = 0;
 
diff --git a/lib/state.h b/lib/state.h
index 8630810..3c6cafa 100644
--- a/lib/state.h
+++ b/lib/state.h
@@ -5,7 +5,6 @@
 
 #include "types.h"
 #include "graph.h"
-#include "ising.h"
 
 template <class R_t, class X_t>
 class state_t {
diff --git a/lib/wolff.h b/lib/wolff.h
index 4e93d01..8286024 100644
--- a/lib/wolff.h
+++ b/lib/wolff.h
@@ -3,14 +3,14 @@
 #include "state.h"
 
 template <class R_t, class X_t>
-void wolff(count_t N, state_t <R_t, X_t> *s, std::function <R_t(gsl_rng *, const state_t <R_t, X_t> *)> gen_R, std::function <void(const state_t <R_t, X_t> *)> measurements, gsl_rng *r, bool silent) {
+void wolff(count_t N, state_t <R_t, X_t> *s, std::function <R_t(gsl_rng *, X_t s0)> gen_R, std::function <void(const state_t <R_t, X_t> *)> measurements, gsl_rng *r, bool silent) {
 
   if (!silent) printf("\n");
   for (count_t steps = 0; steps < N; steps++) {
     if (!silent) printf("\033[F\033[JWOLFF: step %" PRIu64 " / %" PRIu64 ": E = %.2f, S = %" PRIv "\n", steps, N, s->E, s->last_cluster_size);
 
     v_t v0 = gsl_rng_uniform_int(r, s->nv);
-    R_t step = gen_R(r, s);
+    R_t step = gen_R(r, s->spins[v0]);
     flip_cluster <R_t, X_t> (s, v0, step, r);
     free_spin(step);
 
diff --git a/src/wolff_On.cpp b/src/wolff_On.cpp
index a59876f..9f95f4a 100644
--- a/src/wolff_On.cpp
+++ b/src/wolff_On.cpp
@@ -125,7 +125,7 @@ int main(int argc, char *argv[]) {
 
   const char *pert_type;
 
-  std::function <orthogonal_R_t(gsl_rng *, const On_t *)> gen_R;
+  std::function <orthogonal_R_t(gsl_rng *, vector_R_t)> gen_R;
 
   if (use_pert) {
     gen_R = std::bind(generate_rotation_perturbation <N_COMP>, std::placeholders::_1, std::placeholders::_2, epsilon);
diff --git a/src/wolff_dgm.cpp b/src/wolff_dgm.cpp
new file mode 100644
index 0000000..6337a5e
--- /dev/null
+++ b/src/wolff_dgm.cpp
@@ -0,0 +1,168 @@
+
+#include <getopt.h>
+
+#ifdef HAVE_GLUT
+#include <GL/glut.h>
+#endif
+
+// include your group and spin space
+#include <dihedral_inf.h>
+#include <height.h>
+
+// include wolff.h
+#include <wolff.h>
+
+typedef state_t <dihedral_inf_t<int64_t>, height_t<int64_t>> sim_t;
+
+int main(int argc, char *argv[]) {
+
+  count_t N = (count_t)1e4;
+
+  D_t D = 2;
+  L_t L = 128;
+  double T = 2.26918531421;
+  double H = 0;
+
+  bool silent = false;
+  bool draw = false;
+  unsigned int window_size = 512;
+  uint64_t epsilon = 1;
+
+  int opt;
+
+  while ((opt = getopt(argc, argv, "N:D:L:T:H:sdw:e:")) != -1) {
+    switch (opt) {
+    case 'N': // number of steps
+      N = (count_t)atof(optarg);
+      break;
+    case 'D': // dimension
+      D = atoi(optarg);
+      break;
+    case 'L': // linear size
+      L = atoi(optarg);
+      break;
+    case 'T': // temperature 
+      T = atof(optarg);
+      break;
+    case 'H': // external field. nth call couples to state n
+      H = atof(optarg);
+      break;
+    case 'e': // external field. nth call couples to state n
+      epsilon = atof(optarg);
+      break;
+    case 's': // don't print anything during simulation. speeds up slightly
+      silent = true;
+      break;
+    case 'd':
+#ifdef HAVE_GLUT
+      draw = true;
+      break;
+#else
+      printf("You didn't compile this with the glut library installed!\n");
+      exit(EXIT_FAILURE);
+#endif
+    case 'w':
+      window_size = atoi(optarg);
+      break;
+    default:
+      exit(EXIT_FAILURE);
+    }
+  }
+
+  // initialize random number generator
+  gsl_rng *r = gsl_rng_alloc(gsl_rng_mt19937);
+  gsl_rng_set(r, rand_seed());
+
+  // define spin-spin coupling
+  std::function <double(height_t<int64_t>, height_t<int64_t>)> Z = [] (height_t<int64_t> h1, height_t<int64_t> h2) -> double {
+    return -pow(h1.x - h2.x, 2);
+  };
+
+  // define spin-field coupling
+  std::function <double(height_t<int64_t>)> B = [=] (height_t<int64_t> h) -> double {
+    return -H * pow(h.x, 2);;
+  };
+
+  // initialize state object
+  sim_t s(D, L, T, Z, B);
+
+  // define function that generates self-inverse rotations
+  std::function <dihedral_inf_t<int64_t>(gsl_rng *, height_t<int64_t>)> gen_R = [=] (gsl_rng *r, height_t<int64_t> h) -> dihedral_inf_t<int64_t> {
+    dihedral_inf_t<int64_t> rot;
+    rot.is_reflection = true;
+
+    int direction = gsl_rng_uniform_int(r, 2);
+    int64_t amount = gsl_rng_uniform_int(r, epsilon);
+
+    if (direction == 0) {
+      rot.x = 2 * h.x + (1 + amount);
+    } else {
+      rot.x = 2 * h.x - (1 + amount);
+    }
+
+    return rot;
+  };
+
+  // define function that updates any number of measurements
+  std::function <void(const sim_t *)> measurement;
+
+  double average_M = 0;
+  if (!draw) {
+    // a very simple example: measure the average magnetization
+    measurement = [&] (const sim_t *s) {
+      average_M += (double)s->M / (double)N / (double)s->nv;
+    };
+  } else {
+    // a more complex example: measure the average magnetization, and draw the spin configuration to the screen
+
+    // initialize glut
+    glutInit(&argc, argv);
+    glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
+    glutInitWindowSize(window_size, window_size);
+    glutCreateWindow("wolff");
+    glClearColor(0.0,0.0,0.0,0.0);
+    glMatrixMode(GL_PROJECTION);
+    glLoadIdentity();
+    gluOrtho2D(0.0, L, 0.0, L);
+
+    measurement = [&] (const sim_t *s) {
+      average_M += (double)s->M / (double)N / (double)s->nv;
+      glClear(GL_COLOR_BUFFER_BIT);
+      int64_t max_h = INT64_MIN;
+      int64_t min_h = INT64_MAX;
+      for (v_t i = 0; i < pow(L, 2); i++) {
+        int64_t cur_h = act_inverse(s->R, s->spins[i]).x;
+        if (cur_h < min_h) {
+          min_h = cur_h;
+        }
+        if (cur_h > max_h) {
+          max_h = cur_h;
+        }
+      }
+
+      for (v_t i = 0; i < pow(L, 2); i++) {
+        int64_t cur_h = act_inverse(s->R, s->spins[i]).x;
+        double mag = ((double)(cur_h - min_h)) / ((double)(max_h - min_h));
+        glColor3f(mag, mag, mag);
+        glRecti(i / L, i % L, (i / L) + 1, (i % L) + 1);
+      }
+      glFlush();
+    };
+  }
+
+  // run wolff for N cluster flips
+  wolff(N, &s, gen_R, measurement, r, silent);
+
+  // tell us what we found!
+  printf("%" PRIcount " DGM runs completed. D = %" PRID ", L = %" PRIL ", T = %g, H = %g, <M> = %g\n", N, D, L, T, H, average_M);
+
+  // free the random number generator
+  gsl_rng_free(r);
+
+  if (draw) {
+  }
+
+  return 0;
+
+}
+
diff --git a/src/wolff_ising.cpp b/src/wolff_ising.cpp
index 83b6448..e072d6a 100644
--- a/src/wolff_ising.cpp
+++ b/src/wolff_ising.cpp
@@ -88,7 +88,7 @@ int main(int argc, char *argv[]) {
   state_t <z2_t, ising_t> s(D, L, T, Z, B);
 
   // define function that generates self-inverse rotations
-  std::function <z2_t(gsl_rng *, const state_t <z2_t, ising_t> *)> gen_R = [] (gsl_rng *, const state_t <z2_t, ising_t> *) -> z2_t {
+  std::function <z2_t(gsl_rng *, ising_t)> gen_R = [] (gsl_rng *, ising_t s) -> z2_t {
     z2_t rot;
     rot.x = true;
     return rot;
diff --git a/src/wolff_potts.cpp b/src/wolff_potts.cpp
index 3b55472..74e0ea9 100644
--- a/src/wolff_potts.cpp
+++ b/src/wolff_potts.cpp
@@ -90,21 +90,21 @@ int main(int argc, char *argv[]) {
   state_t <symmetric_t<POTTSQ>, potts_t<POTTSQ>> s(D, L, T, Z, B);
 
   // define function that generates self-inverse rotations
-  std::function <symmetric_t<POTTSQ>(gsl_rng *, const sim_t *)> gen_R = [] (gsl_rng *r, const sim_t *s) -> symmetric_t<POTTSQ> {
+  std::function <symmetric_t<POTTSQ>(gsl_rng *, potts_t<POTTSQ>)> gen_R = [] (gsl_rng *r, potts_t<POTTSQ> v) -> symmetric_t<POTTSQ> {
     symmetric_t<POTTSQ> rot;
     init(&rot);
 
-    for (int i = POTTSQ - 1; i >= 0; i--) {
-      if (rot.perm[i] == i) {
-        q_t j = gsl_rng_uniform_int(r, i + 1);
-        if (rot.perm[j] == j) {
-          q_t tmp = rot.perm[i];
-          rot.perm[i] = rot.perm[j];
-          rot.perm[j] = tmp;
-        }
-      }
+    q_t j = gsl_rng_uniform_int(r, POTTSQ - 1);
+    q_t swap_v;
+    if (j < v.x) {
+      swap_v = j;
+    } else {
+      swap_v = j + 1;
     }
 
+    rot.perm[v.x] = swap_v;
+    rot.perm[swap_v] = v.x;
+
     return rot;
   };