From 90ae915b5a7961a36e6a33509b16229244c6615a Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Sun, 1 Jul 2018 00:52:31 -0400
Subject: fixed both the system for determining bond energy and how global
 state is tracked

---
 lib/cluster.c        |  91 --------------------------------
 lib/cluster_finite.c |  10 ++--
 lib/cluster_finite.h |   7 ++-
 lib/dihedral.c       |  23 ++++++--
 lib/dihedral.h       |   4 +-
 lib/initial_finite.c | 145 +++++++++++++++++++++++++++++++++++++++++++--------
 lib/symmetric.c      |  43 +++++++++++++++
 lib/symmetric.h      |   2 +
 src/wolff_finite.c   |  12 ++---
 9 files changed, 207 insertions(+), 130 deletions(-)

diff --git a/lib/cluster.c b/lib/cluster.c
index 7274eb9..96225a2 100644
--- a/lib/cluster.c
+++ b/lib/cluster.c
@@ -1,97 +1,6 @@
 
 #include "cluster.h"
 
-v_t flip_cluster(ising_state_t *s, v_t v0, q_t rot, gsl_rng *r) {
-  v_t nv = 0;
-
-  ll_t *stack = NULL;     // create a new stack
-  stack_push(&stack, v0); // push the initial vertex to the stack
-
-  bool *marks = (bool *)calloc(s->g->nv, sizeof(bool));
-
-  while (stack != NULL) {
-    v_t v = stack_pop(&stack);
-
-    if (!marks[v]) {
-      q_t s_old, s_new;
-      dihedral_t *R_new; 
-      bool external_flipped;
-
-      marks[v] = true;
-
-      if (v == s->g->nv - 1) {
-        R_new = dihedral_compose(s->q, rot, s->R);
-        external_flipped = true;
-      } else {
-        s_old = s->spins[v];
-        s_new = dihedral_act(s->q, rot, s_old);
-        external_flipped = false;
-      }
-
-      v_t nn = s->g->v_i[v + 1] - s->g->v_i[v];
-
-      for (v_t i = 0; i < nn; i++) {
-        q_t sn;
-        double prob;
-        bool external_neighbor = false;
-
-        v_t vn = s->g->v_adj[s->g->v_i[v] + i];
-
-        if (vn == s->g->nv - 1) {
-          external_neighbor = true;
-        } else {
-          sn = s->spins[vn];
-        }
-
-        if (external_flipped || external_neighbor) {
-          q_t rot_s_old, rot_s_new;
-
-          if (external_neighbor) {
-            rot_s_old = dihedral_inverse_act(s->q, s->R, s_old);
-            rot_s_new = dihedral_inverse_act(s->q, s->R, s_new);
-          } else {
-            rot_s_old = dihedral_inverse_act(s->q, s->R, sn);
-            rot_s_new = dihedral_inverse_act(s->q, R_new, sn);
-          }
-
-          prob = s->H_probs[rot_s_new * s->q + rot_s_old];
-
-          s->M[rot_s_old]--;
-          s->M[rot_s_new]++;
-
-          s->E += - s->H[rot_s_new] + s->H[rot_s_old];
-        } else {
-          q_t diff_old = (s_old + s->q - sn) % s->q;
-          q_t diff_new = (s_new + s->q - sn) % s->q;
-
-          prob = s->J_probs[diff_new * s->q + diff_old];
-
-          s->E += - s->J[diff_new] + s->J[diff_old];
-        }
-
-        if (gsl_rng_uniform(r) < prob) { // and with probability ps[e]...
-          stack_push(&stack, vn); // push the neighboring vertex to the stack
-        }
-      }
-
-      if (external_flipped) {
-        free(s->R);
-        s->R = R_new;
-      } else {
-        s->spins[v] = s_new;
-      }
-
-      if (v != s->g->nv - 1) { // count the number of non-external sites that flip
-        nv++;
-      }
-    }
-  }
-
-  free(marks);
-
-  return nv;
-}
-
 v_t flip_cluster_dgm(dgm_state_t *s, v_t v0, h_t rot, gsl_rng *r) {
   v_t nv = 0;
 
diff --git a/lib/cluster_finite.c b/lib/cluster_finite.c
index 71396e0..9392cf8 100644
--- a/lib/cluster_finite.c
+++ b/lib/cluster_finite.c
@@ -1,8 +1,8 @@
 
 #include "cluster_finite.h"
 
-v_t flip_cluster_finite(state_finite_t *s, v_t v0, q_t rot_ind, gsl_rng *r) {
-  q_t *rot = s->transformations + s->q * rot_ind;
+v_t flip_cluster_finite(state_finite_t *s, v_t v0, R_t rot_ind, gsl_rng *r) {
+  q_t *rot = s->transformations + s->q * s->involutions[rot_ind];
   q_t *R_inv = symmetric_invert(s->q, s->R);
   v_t nv = 0;
 
@@ -63,10 +63,10 @@ v_t flip_cluster_finite(state_finite_t *s, v_t v0, q_t rot_ind, gsl_rng *r) {
           s->M[rot_s_new]++;
 
         } else {
-          q_t diff_old = (s_old + s->q - sn) % s->q;
-          q_t diff_new = (s_new + s->q - sn) % s->q;
+          q_t diff_old = s->bond_with_zero_type[s->transformations[s->q * s->transform_site_to_zero[sn] + s_old]];
+          q_t diff_new = s->bond_with_zero_type[s->transformations[s->q * s->transform_site_to_zero[sn] + s_new]];
 
-          prob = s->J_probs[diff_new * s->q + diff_old];
+          prob = s->J_probs[diff_new * s->n_bond_types + diff_old];
 
           s->B[diff_old]--;
           s->B[diff_new]++;
diff --git a/lib/cluster_finite.h b/lib/cluster_finite.h
index 701c197..b2d764e 100644
--- a/lib/cluster_finite.h
+++ b/lib/cluster_finite.h
@@ -31,6 +31,11 @@ typedef struct {
   q_t q;
   R_t n_transformations;
   q_t *transformations;
+  R_t n_involutions;
+  R_t *involutions;
+  R_t *transform_site_to_zero;
+  q_t n_bond_types;
+  q_t *bond_with_zero_type;
   double T;
   double *J;
   double *H;
@@ -42,5 +47,5 @@ typedef struct {
   v_t *M;
 } state_finite_t;
 
-v_t flip_cluster_finite(state_finite_t *s, v_t v0, q_t rot, gsl_rng *r);
+v_t flip_cluster_finite(state_finite_t *s, v_t v0, R_t rot, gsl_rng *r);
 
diff --git a/lib/dihedral.c b/lib/dihedral.c
index ac74a23..8158b43 100644
--- a/lib/dihedral.c
+++ b/lib/dihedral.c
@@ -11,10 +11,14 @@ dihedral_t *dihedral_compose(q_t q, q_t g1i, const dihedral_t *g2) {
   return g3;
 }
 
-q_t dihedral_act(q_t q, q_t gi, q_t s) {
+q_t dihedral_act(q_t q, q_t gi, bool r, q_t s) {
   // we only need to consider the action of reflections
 
-  return (gi + q - s) % q;
+  if (r) {
+    return (gi + q - s) % q;
+  } else {
+    return (gi + s) % q;
+  }
 }
 
 q_t dihedral_inverse_act(q_t q, const dihedral_t *g, q_t s) {
@@ -26,15 +30,26 @@ q_t dihedral_inverse_act(q_t q, const dihedral_t *g, q_t s) {
 }
 
 q_t *dihedral_gen_transformations(q_t q) {
-  q_t *transformations = (q_t *)malloc(q * q * sizeof(q_t));
+  q_t *transformations = (q_t *)malloc(2 * q * q * sizeof(q_t));
 
   for (q_t i = 0; i < q; i++) {
     for (q_t j = 0; j < q; j++) {
-      transformations[q * i + j] = dihedral_act(q, i, j);
+      transformations[q * i + j] = dihedral_act(q, i, false, j);
+      transformations[q * q + q * i + j] = dihedral_act(q, i, true, j);
     }
   }
 
   return transformations;
 }
 
+R_t *dihedral_gen_involutions(q_t q) {
+  R_t *transformations = (R_t *)malloc(q * sizeof(R_t));
+
+  for (q_t i = 0; i < q; i++) {
+    transformations[i] = q + i;
+  }
+
+  return transformations;
+}
+
 
diff --git a/lib/dihedral.h b/lib/dihedral.h
index e5e4cbd..c95b23a 100644
--- a/lib/dihedral.h
+++ b/lib/dihedral.h
@@ -11,9 +11,11 @@ typedef struct {
 
 dihedral_t *dihedral_compose(q_t q, q_t gti, const dihedral_t *g2);
 
-q_t dihedral_act(q_t q, q_t gi, q_t s);
+q_t dihedral_act(q_t q, q_t gi, bool r, q_t s);
 
 q_t dihedral_inverse_act(q_t q, const dihedral_t *g, q_t s);
 
 q_t *dihedral_gen_transformations(q_t q);
+R_t *dihedral_gen_involutions(q_t q);
 
+R_t factorial(q_t);
diff --git a/lib/initial_finite.c b/lib/initial_finite.c
index fb120f0..6ea76ef 100644
--- a/lib/initial_finite.c
+++ b/lib/initial_finite.c
@@ -23,6 +23,40 @@ q_t *initialize_R(q_t q) {
   return R;
 }
 
+R_t *transformation_bringing_to_zero(q_t q, R_t n_transformations, q_t *transformations) {
+  R_t *destination = (R_t *)malloc(q * sizeof(R_t));
+
+  for (q_t i = 0; i < q; i++) {
+    for (R_t j = 0; j < n_transformations; j++) {
+      if (transformations[q * j + i] == 0) {
+        destination[i] = j;
+      }
+    }
+  }
+
+  return destination;
+}
+
+R_t find_involutions(R_t *destination, q_t q, R_t n_transformations, q_t *transformations) {
+  R_t n_involutions = 0;
+
+  for (R_t i = 1; i < n_transformations; i++) {
+    bool is_involution = true;
+    for (q_t j = 0; j < q; j++) {
+      if (j != transformations[q * i + transformations[q * i + j]]) {
+        is_involution = false;
+        break;
+      }
+    }
+    if (is_involution) {
+      destination[n_involutions] = i;
+      n_involutions++;
+    }
+  }
+
+  return n_involutions;
+}
+
 state_finite_t *initial_finite_prepare_ising(D_t D, L_t L, double T, double *H) {
   state_finite_t *s = (state_finite_t *)calloc(1, sizeof(state_finite_t));
 
@@ -38,11 +72,26 @@ state_finite_t *initial_finite_prepare_ising(D_t D, L_t L, double T, double *H)
   }
 
   s->q = 2;
-  s->n_transformations = 1;
 
-  s->transformations = (q_t *)malloc(2 * sizeof(q_t));
-  s->transformations[0] = 1;
-  s->transformations[1] = 0;
+  s->n_transformations = 2;
+  s->transformations = (q_t *)malloc(2 * 2 * sizeof(q_t));
+  s->transformations[0] = 0;
+  s->transformations[1] = 1;
+  s->transformations[2] = 1;
+  s->transformations[3] = 0;
+
+  s->n_involutions = 1;
+  s->involutions = (R_t *)malloc(1 * sizeof(R_t));
+  s->involutions[0] = 1;
+
+  s->transform_site_to_zero = (R_t *)malloc(2 * sizeof(R_t));
+  s->transform_site_to_zero[0] = 0;
+  s->transform_site_to_zero[1] = 1;
+
+  s->n_bond_types = 2;
+  s->bond_with_zero_type = (q_t *)malloc(2 * sizeof(q_t));
+  s->bond_with_zero_type[0] = 0;
+  s->bond_with_zero_type[1] = 1;
 
   s->T = T;
   s->J = (double *)malloc(2 * sizeof(double)); 
@@ -81,19 +130,34 @@ state_finite_t *initial_finite_prepare_potts(D_t D, L_t L, q_t q, double T, doub
   }
 
   s->q = q;
-  s->n_transformations = q;
-  s->transformations = dihedral_gen_transformations(q);
+  s->n_transformations = factorial(q);
+  s->transformations = symmetric_gen_transformations(q);
+  s->involutions = (R_t *)malloc(s->n_transformations * sizeof(R_t));
+  s->n_involutions = find_involutions(s->involutions, q, s->n_transformations, s->transformations);
+
+  s->transform_site_to_zero = transformation_bringing_to_zero(q, s->n_transformations, s->transformations);
+
+  s->n_bond_types = 2;
+
+  s->bond_with_zero_type = (q_t *)malloc(q * sizeof(q_t));
+
+  s->bond_with_zero_type[0] = 0;
+
+  for (q_t i = 1; i < q; i++) {
+    s->bond_with_zero_type[i] = 1;
+  }
 
   s->T = T;
-  s->J = (double *)calloc(q, sizeof(double)); 
+  s->J = (double *)calloc(2, sizeof(double)); 
   s->J[0] = 1.0;
+  s->J[1] = 0.0;
 
   s->H = (double *)malloc(q * sizeof(double)); 
   for (q_t i = 0; i < q; i++) {
     s->H[i] = H[i];
   }
 
-  s->J_probs = Jprobs_from_J(q, T, s->J);
+  s->J_probs = Jprobs_from_J(s->n_bond_types, T, s->J);
   s->H_probs = Jprobs_from_J(q, T, s->H);
 
   s->spins = (q_t *)calloc(s->nv, sizeof(q_t));
@@ -101,7 +165,7 @@ state_finite_t *initial_finite_prepare_potts(D_t D, L_t L, q_t q, double T, doub
 
   s->M = (v_t *)calloc(q, sizeof(v_t));
   s->M[0] = s->nv; // everyone starts in state 0, remember?
-  s->B = (v_t *)calloc(q, sizeof(v_t));
+  s->B = (v_t *)calloc(s->n_bond_types, sizeof(v_t));
   s->B[0] = s->ne; // everyone starts in state 0, remember?
 
   return s;
@@ -122,13 +186,30 @@ state_finite_t *initial_finite_prepare_clock(D_t D, L_t L, q_t q, double T, doub
   }
 
   s->q = q;
-  s->n_transformations = q;
+
+  s->n_transformations = 2 * q;
   s->transformations = dihedral_gen_transformations(q);
+  s->n_involutions = q;
+  s->involutions = dihedral_gen_involutions(q);
+
+  s->transform_site_to_zero = transformation_bringing_to_zero(q, s->n_transformations, s->transformations);
+  s->bond_with_zero_type = malloc(q * sizeof(q_t));
+
+  s->n_bond_types = q / 2 + 1;
+
+  for (q_t i = 0; i < q / 2 + 1; i++) {
+    s->bond_with_zero_type[i] = i;
+  }
+
+  for (q_t i = 1; i < (q + 1) / 2; i++) { 
+    s->bond_with_zero_type[q - i] = i;
+  }
+
 
   s->T = T;
-  s->J = (double *)malloc(q * sizeof(double)); 
+  s->J = (double *)malloc(s->n_bond_types * sizeof(double)); 
 
-  for (q_t i = 0; i < q; i++) {
+  for (q_t i = 0; i < s->n_bond_types; i++) {
     s->J[i] = cos(2 * M_PI * i / ((double)q));
   }
 
@@ -138,7 +219,7 @@ state_finite_t *initial_finite_prepare_clock(D_t D, L_t L, q_t q, double T, doub
     s->H[i] = H[i];
   }
 
-  s->J_probs = Jprobs_from_J(q, T, s->J);
+  s->J_probs = Jprobs_from_J(s->n_bond_types, T, s->J);
   s->H_probs = Jprobs_from_J(q, T, s->H);
 
   s->spins = (q_t *)calloc(s->nv, sizeof(q_t));
@@ -146,7 +227,7 @@ state_finite_t *initial_finite_prepare_clock(D_t D, L_t L, q_t q, double T, doub
 
   s->M = (v_t *)calloc(q, sizeof(v_t));
   s->M[0] = s->nv; // everyone starts in state 0, remember?
-  s->B = (v_t *)calloc(q, sizeof(v_t));
+  s->B = (v_t *)calloc(s->n_bond_types, sizeof(v_t));
   s->B[0] = s->ne; // everyone starts in state 0, remember?
 
   return s;
@@ -168,17 +249,30 @@ state_finite_t *initial_finite_prepare_dgm(D_t D, L_t L, q_t q, double T, double
   }
 
   s->q = q;
-  s->n_transformations = q;
+
+  s->n_transformations = 2 * q;
   s->transformations = dihedral_gen_transformations(q);
+  s->n_involutions = q;
+  s->involutions = dihedral_gen_involutions(q);
 
-  s->T = T;
-  s->J = (double *)malloc(q * sizeof(double)); 
+  s->transform_site_to_zero = transformation_bringing_to_zero(q, s->n_transformations, s->transformations);
+  s->bond_with_zero_type = malloc(q * sizeof(q_t));
+
+  s->n_bond_types = q / 2 + 1;
 
   for (q_t i = 0; i < q / 2 + 1; i++) {
-    s->J[i] = -pow(i, 2);
+    s->bond_with_zero_type[i] = i;
   }
-  for (q_t i = 1; i < (q + 1) / 2; i++) {
-    s->J[q - i] = -pow(i, 2);
+
+  for (q_t i = 1; i < (q + 1) / 2; i++) { 
+    s->bond_with_zero_type[(int)q - (int)i] = i;
+  }
+
+  s->T = T;
+  s->J = (double *)malloc(s->n_bond_types * sizeof(double)); 
+
+  for (q_t i = 0; i < s->n_bond_types; i++) {
+    s->J[i] = -pow(i, 2);
   }
 
   s->H = (double *)malloc(q * sizeof(double)); 
@@ -186,7 +280,7 @@ state_finite_t *initial_finite_prepare_dgm(D_t D, L_t L, q_t q, double T, double
     s->H[i] = H[i];
   }
 
-  s->J_probs = Jprobs_from_J(q, T, s->J);
+  s->J_probs = Jprobs_from_J(s->n_bond_types, T, s->J);
   s->H_probs = Jprobs_from_J(q, T, s->H);
 
   s->spins = (q_t *)calloc(s->nv, sizeof(q_t));
@@ -194,6 +288,8 @@ state_finite_t *initial_finite_prepare_dgm(D_t D, L_t L, q_t q, double T, double
 
   s->M = (v_t *)calloc(q, sizeof(v_t));
   s->M[0] = s->nv; // everyone starts in state 0, remember?
+  s->B = (v_t *)calloc(s->n_bond_types, sizeof(v_t));
+  s->B[0] = s->nv; // everyone starts in state 0, remember?
 
   return s;
 }
@@ -201,8 +297,10 @@ state_finite_t *initial_finite_prepare_dgm(D_t D, L_t L, q_t q, double T, double
 double state_finite_energy(state_finite_t *s) {
   double E = 0;
 
-  for (q_t i = 0; i < s->q; i++) {
+  for (q_t i = 0; i < s->n_bond_types; i++) {
     E += s->J[i] * s->B[i];
+  }
+  for (q_t i = 0; i < s->q; i++) {
     E += s->H[i] * s->M[i];
   }
 
@@ -220,6 +318,9 @@ void state_finite_free(state_finite_t *s) {
   free(s->M);
   free(s->B);
   free(s->transformations);
+  free(s->involutions);
+  free(s->transform_site_to_zero);
+  free(s->bond_with_zero_type);
   free(s);
 }
 
diff --git a/lib/symmetric.c b/lib/symmetric.c
index 729b38c..4487538 100644
--- a/lib/symmetric.c
+++ b/lib/symmetric.c
@@ -25,3 +25,46 @@ q_t *symmetric_invert(q_t q, const q_t *g) {
   return g_inv;
 }
 
+void swap(q_t *q1, q_t *q2) {
+  q_t temp = *q1;
+  *q1 = *q2;
+  *q2 = temp;
+}
+
+R_t factorial(q_t q) {
+  if (q == 0) {
+    return 1;
+  } else {
+    return q * factorial(q - 1);
+  }
+}
+
+void permute(q_t *a, q_t l, q_t r, R_t pos, q_t *transformations) {
+  if (l == r - 1) {
+    for (q_t i = 0; i < r; i++) {
+      transformations[r * pos + i] = a[i];
+    }
+  } else {
+    for (q_t i = l; i < r; i++) {
+      swap((a+l), (a+i));
+      permute(a, l+1, r, pos + (i - l) * factorial(r - l - 1), transformations);
+      swap((a+l), (a+i));
+    }
+  }
+}
+
+q_t *symmetric_gen_transformations(q_t q) {
+  q_t *transformations = (q_t *)malloc(q * factorial(q) * sizeof(q_t));
+  q_t *tmp = (q_t *)malloc(q * sizeof(q_t));
+
+  for (q_t i = 0; i < q; i++) {
+    tmp[i] = i;
+  }
+
+  permute(tmp, 0, q, 0, transformations);
+
+  free(tmp);
+
+  return transformations;
+}
+
diff --git a/lib/symmetric.h b/lib/symmetric.h
index 6e00f52..c71521d 100644
--- a/lib/symmetric.h
+++ b/lib/symmetric.h
@@ -11,3 +11,5 @@ q_t symmetric_act(const q_t *g, q_t s);
 
 q_t *symmetric_invert(q_t q, const q_t *g);
 
+q_t *symmetric_gen_transformations(q_t q);
+
diff --git a/src/wolff_finite.c b/src/wolff_finite.c
index e41c326..4bf96b9 100644
--- a/src/wolff_finite.c
+++ b/src/wolff_finite.c
@@ -96,7 +96,7 @@ int main(int argc, char *argv[]) {
   char *filename_S = (char *)malloc(256 * sizeof(char));
 
   sprintf(filename_M, "wolff_%s_%" PRIq "_%" PRID "_%" PRIL "_%.8f", finite_model_t_strings[model], q, D, L, T);
-  for (q_t i = 0; i < q; i++) {
+  for (q_t i = 0; i < s->q; i++) {
     sprintf(filename_M + strlen(filename_M), "_%.8f", s->H[i]);
   }
 
@@ -126,8 +126,8 @@ int main(int argc, char *argv[]) {
      
     bool changed = false;
     while (!changed) {
-      step = gsl_rng_uniform_int(r, s->n_transformations);
-      if (symmetric_act(s->transformations + q * step, s->spins[v0]) != s->spins[v0]) {
+      step = gsl_rng_uniform_int(r, s->n_involutions);
+      if (symmetric_act(s->transformations + s->q * s->involutions[step], s->spins[v0]) != s->spins[v0]) {
         changed = true;
       }
     }
@@ -138,9 +138,9 @@ int main(int argc, char *argv[]) {
     // as a fast time many machines will actually have it be 64 bits. we cast
     // it down here to halve space.
 
-    for (q_t i = 0; i < q - 1; i++) {
-      fwrite(&(s->M[i]), sizeof(uint32_t), 1, outfile_M); // if we know the occupation of the first q - 1 states, we know the occupation of the last
-      fwrite(&(s->B[i]), sizeof(uint32_t), 1, outfile_B); // if we know the occupation of the first q - 1 states, we know the occupation of the last
+    for (q_t i = 0; i < s->q - 1; i++) { // if we know the occupation of the first q - 1 states, we know the occupation of the last
+      fwrite(&(s->M[i]), sizeof(uint32_t), 1, outfile_M); 
+      fwrite(&(s->B[i]), sizeof(uint32_t), 1, outfile_B);
     }
 
     fwrite(&cluster_size, sizeof(uint32_t), 1, outfile_S);
-- 
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