From 8d96c4d30214a2c27561740b7b3f7e1e3b0bbfe4 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Mon, 23 Jul 2018 23:16:52 -0400
Subject: sped up orthogonal generation a bit

---
 lib/orthogonal.h | 51 ++++++++++++++++++++++++++++-----------------------
 1 file changed, 28 insertions(+), 23 deletions(-)

(limited to 'lib/orthogonal.h')

diff --git a/lib/orthogonal.h b/lib/orthogonal.h
index 523fd54..ce2d300 100644
--- a/lib/orthogonal.h
+++ b/lib/orthogonal.h
@@ -166,51 +166,56 @@ orthogonal_t <q, double> generate_rotation_uniform (gsl_rng *r, vector_t <q, dou
 }
 
 template <q_t q>
-orthogonal_t <q, double> generate_rotation_perturbation (gsl_rng *r, vector_t <q, double> v, double epsilon) {
+orthogonal_t <q, double> generate_rotation_perturbation (gsl_rng *r, vector_t <q, double> v0, double epsilon, unsigned int n) {
   orthogonal_t <q, double> m;
-  vector_t <q, double> tmp_v;
   m.is_reflection = true;
+  m.x = (double *)malloc(q * sizeof(double));
 
-  tmp_v.x = (double *)malloc(q * sizeof(double));
+  vector_t <q, double> v;
 
-  double tmp2 = 0;
-  double M2 = 0;
-  double tmpM = 0;
+  if (n > 1) {
+    unsigned int rotation = gsl_rng_uniform_int(r, n);
+    v.x = (double *)malloc(q * sizeof(double));
 
-  for (q_t i = 0; i < q; i++) {
-    tmp_v.x[i] = gsl_ran_ugaussian(r);
-    M2 += pow(v.x[i], 2);
-    tmpM += tmp_v.x[i] * v.x[i];
-  }
+    double cosr = cos(2 * M_PI * rotation / (double)n / 2.0);
+    double sinr = sin(2 * M_PI * rotation / (double)n / 2.0);
 
-  double v2 = 0;
-  double factor = gsl_ran_ugaussian(r);
+    v.x[0] = v0.x[0] * cosr - v0.x[1] * sinr;
+    v.x[1] = v0.x[1] * cosr + v0.x[0] * sinr;
 
-  for (q_t i = 0; i < q; i++) {
-    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];
+    for (q_t i = 2; i < q; i++) {
+      v.x[i] = v0.x[i];
+    }
+  } else {
+    v.x = v0.x;
   }
 
-  double mag_v = sqrt(v2);
+  double m2 = 0;
+  double m_dot_v = 0;
 
   for (q_t i = 0; i < q; i++) {
-    tmp_v.x[i] /= mag_v;
+    m.x[i] = gsl_ran_ugaussian(r);
+    m_dot_v += m.x[i] * v.x[i];
   }
 
-  m.x = tmp_v.x;
-
-  v2 = 0;
+  double v2 = 0;
+  double factor = epsilon * gsl_ran_ugaussian(r);
 
   for (q_t i = 0; i < q; i++) {
-    v2 += m.x[i] * m.x[i];
+    m.x[i] = m.x[i] - m_dot_v * v.x[i] + factor * v.x[i];
+    v2 += pow(m.x[i], 2);
   }
 
-  mag_v = sqrt(v2);
+  double mag_v = sqrt(v2);
 
   for (q_t i = 0; i < q; i++) {
     m.x[i] /= mag_v;
   }
 
+  if (n > 1) {
+    free(v.x);
+  }
+
   return m;
 }
 
-- 
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