1 files changed, 206 insertions, 0 deletions
diff --git a/lib/wolff_models/orthogonal.hpp b/lib/wolff_models/orthogonal.hpp
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+++ b/lib/wolff_models/orthogonal.hpp
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+
+#ifndef WOLFF_MODELS_ORTHOGONAL_H
+#define WOLFF_MODELS_ORTHOGONAL_H
+
+#include <random>
+#include <cmath>
+
+#include <wolff.hpp>
+#include "vector.hpp"
+
+namespace wolff {
+
+  template <unsigned q, class T>
+  class orthogonal_t : public std::array<std::array<T, q>, q> {
+    public :
+    bool is_reflection;
+
+    orthogonal_t() : is_reflection(false) {
+      for (unsigned i = 0; i < q; i++) {
+        (*this)[i].fill(0);
+        (*this)[i][i] = (T)1;
+      }
+    }
+
+    vector_t<q, T> act(const vector_t <q, T>& v) const {
+      vector_t <q, T> v_rot;
+      v_rot.fill(0);
+
+      if (is_reflection) {
+        double prod = 0;
+        for (unsigned i = 0; i < q; i++) {
+          prod += v[i] * (*this)[0][i];
+        }
+        for (unsigned i = 0; i < q; i++) {
+          v_rot[i] = v[i] - 2 * prod * (*this)[0][i];
+        }
+      } else {
+        for (unsigned i = 0; i < q; i++) {
+          for (unsigned j = 0; j < q; j++) {
+            v_rot[i] += (*this)[i][j] * v[j];
+          }
+        }
+      }
+
+      return v_rot;
+    }
+
+    orthogonal_t<q, T> act(const orthogonal_t <q, T>& m) const {
+      orthogonal_t <q, T> m_rot;
+
+      m_rot.is_reflection = false;
+
+      if (is_reflection) {
+        for (unsigned i = 0; i < q; i++) {
+          double akOki = 0;
+
+          for (unsigned k = 0; k < q; k++) {
+            akOki += (*this)[0][k] * m[k][i];
+          }
+
+          for (unsigned j = 0; j < q; j++) {
+            m_rot[j][i] = m[j][i] - 2 * akOki * (*this)[0][j];
+          }
+        }
+      } else {
+        for (unsigned i = 0; i < q; i++) {
+          m_rot[i].fill(0);
+          for (unsigned j = 0; j < q; j++) {
+            for (unsigned k = 0; k < q; k++) {
+              m_rot[i][j] += (*this)[i][j] * m[j][k];
+            }
+          }
+        }
+      }
+
+      return m_rot;
+    }
+
+    vector_t <q, T> act_inverse(const vector_t <q, T>& v) const {
+      if (is_reflection) {
+        return this->act(v); // reflections are their own inverse
+      } else {
+        vector_t <q, T> v_rot;
+        v_rot.fill(0);
+
+        for (unsigned i = 0; i < q; i++) {
+          for (unsigned j = 0; j < q; j++) {
+            v_rot[i] += (*this)[j][i] * v[j];
+          }
+        }
+
+        return v_rot;
+      }
+    }
+
+    vector_t <q, T> act_inverse(const orthogonal_t <q, T>& m) const {
+      if (is_reflection) {
+        return this->act(m); // reflections are their own inverse
+      } else {
+        orthogonal_t <q, T> m_rot;
+        m_rot.is_reflection = false;
+
+        for (unsigned i = 0; i < q; i++) {
+          m_rot[i].fill(0);
+          for (unsigned j = 0; j < q; j++) {
+            for (unsigned k = 0; k < q; k++) {
+              m_rot[i][j] += (*this)[j][i] * m[j][k];
+            }
+          }
+        }
+
+        return m_rot;
+      }
+    }
+
+  };
+
+  template <unsigned q, class G_t>
+  orthogonal_t <q, double> generate_rotation_uniform (std::mt19937& r, const system<orthogonal_t<q, double>, vector_t<q, double>, G_t>&, const typename G_t::vertex&) {
+    std::normal_distribution<double> dist(0.0,1.0);
+    orthogonal_t <q, double> ptr;
+    ptr.is_reflection = true;
+
+    double v2 = 0;
+
+    for (unsigned i = 0; i < q; i++) {
+      ptr[0][i] = dist(r);
+      v2 += ptr[0][i] * ptr[0][i];
+    }
+
+    double mag_v = sqrt(v2);
+
+    for (unsigned i = 0; i < q; i++) {
+      ptr[0][i] /= mag_v;
+    }
+
+    return ptr;
+  }
+
+  template <unsigned q, class G_t>
+  orthogonal_t <q, double> generate_rotation_perturbation (std::mt19937& r, const system<orthogonal_t<q, double>, vector_t<q, double>, G_t>& S, const typename G_t::vertex& v0, double epsilon, unsigned int n) {
+    std::normal_distribution<double> dist(0.0,1.0);
+    orthogonal_t <q, double> m;
+    m.is_reflection = true;
+
+    vector_t <q, double> v;
+
+    if (n > 1) {
+      std::uniform_int_distribution<unsigned int> udist(0, n);
+      unsigned int rotation = udist(r);
+
+      double cosr = cos(2 * M_PI * rotation / (double)n / 2.0);
+      double sinr = sin(2 * M_PI * rotation / (double)n / 2.0);
+
+      v[0] = S.s[v0.ind][0] * cosr - S.s[v0.ind][1] * sinr;
+      v[1] = S.s[v0.ind][1] * cosr + S.s[v0.ind][0] * sinr;
+
+      for (unsigned i = 2; i < q; i++) {
+        v[i] = S.s[v0.ind][i];
+      }
+    } else {
+      v = S.s[v0.ind];
+    }
+
+    double m_dot_v = 0;
+
+    for (unsigned i = 0; i < q; i++) {
+      m[0][i] = dist(r); // create a random vector
+      m_dot_v += m[0][i] * v[i];
+    }
+
+    double v2 = 0;
+
+    for (unsigned i = 0; i < q; i++) {
+      m[0][i] = m[0][i] - m_dot_v * v[i]; // find the component orthogonal to v
+      v2 += pow(m[0][i], 2);
+    }
+
+    double mag_v = sqrt(v2);
+
+    for (unsigned i = 0; i < q; i++) {
+      m[0][i] /= mag_v; // normalize
+    }
+
+    v2 = 0;
+
+    double factor = epsilon * dist(r);
+
+    for (unsigned i = 0; i < q; i++) {
+      m[0][i] += factor * v[i]; // perturb orthogonal vector in original direction
+      v2 += pow(m[0][i], 2);
+    }
+
+    mag_v = sqrt(v2);
+
+    for (unsigned i = 0; i < q; i++) {
+      m[0][i] /= mag_v; // normalize
+    }
+
+    return m;
+  }
+
+}
+
+#endif
+