From aa98e4dba7d771bd1e9519442f830542cff2860c Mon Sep 17 00:00:00 2001
From: Dennis Kobert <dennis@kobert.dev>
Date: Sun, 1 Dec 2019 01:58:10 +0100
Subject: Improve preformarce by calculating the hamilton once

---
 gnuplot/anim2d.plt    |  3 ++-
 gnuplot/anim3d.plt    |  4 +++-
 single_dequantify.py  |  4 ++--
 twoqbit_dequantify.py | 37 +++++++++++++++++++------------------
 4 files changed, 26 insertions(+), 22 deletions(-)

diff --git a/gnuplot/anim2d.plt b/gnuplot/anim2d.plt
index 38b8d5a..f131c1f 100644
--- a/gnuplot/anim2d.plt
+++ b/gnuplot/anim2d.plt
@@ -8,7 +8,8 @@ set yzeroaxis
 set object circle at 0,0 size 1
 
 do for [ii=start:end] {
-    plot 'data' every ::1::ii * states using 4:5:6 w points palette pointsize 2 pointtype 7
+    plot 'data' every ::ii::ii * states using 4:5:6 w points palette pointsize 2 pointtype 7, \
+         'data' every ::1::ii * states using 4:5:6 w l palette lw 3
     pause 0.1
 }
 
diff --git a/gnuplot/anim3d.plt b/gnuplot/anim3d.plt
index 99cfe10..05d9f51 100644
--- a/gnuplot/anim3d.plt
+++ b/gnuplot/anim3d.plt
@@ -2,9 +2,11 @@ set view equal xyz
 set parametric
 set isosamples 34,34
 
+ii = start
 do for [ii=start:end] {
     splot cos(u)*cos(v),cos(u)*sin(v),sin(u) w l lc rgb "#42a4f5", \
-        'data' every ::1::ii * states using 1:2:3:6 w points palette pointsize 2 pointtype 7#, \
+        'data' every ::ii - states::ii * states using 1:2:3:6 w points palette pointsize 1.2 pointtype 7, \
+        'data' every ::1::ii * states using 1:2:3:6 w l palette 
     pause 0.1
 }
 
diff --git a/single_dequantify.py b/single_dequantify.py
index 99ebdc4..e90142a 100644
--- a/single_dequantify.py
+++ b/single_dequantify.py
@@ -7,7 +7,7 @@ import scipy.linalg as sla
 
 dt = 0.08
 iterations = 100
-state_num = 3
+state_num = 5
 
 H = npy.array([[1,0],[0,2]])
 
@@ -59,5 +59,5 @@ for i in range(iterations):
         states[j] = time_evolution(states[j])
 f.close()
 
-plot.plot(1, iterations, state_num, "anim2d.plt")
+plot.plot(1, iterations, state_num, "anim3d.plt")
 
diff --git a/twoqbit_dequantify.py b/twoqbit_dequantify.py
index efc3304..af2e506 100644
--- a/twoqbit_dequantify.py
+++ b/twoqbit_dequantify.py
@@ -6,17 +6,10 @@ import cmath as cmt
 import numpy as npy
 import scipy.linalg as sla
 
-alpha = 2
-beta  = 0
-gamma = 1
-delta = 1+1j
 state_num = 1
-
-norm  = npy.linalg.norm([alpha, beta, gamma, delta])
-state = npy.array([alpha / norm, beta / norm, gamma / norm, delta / norm])
-
-dt = 0.05
-iterations = 200
+dt = 0.02
+accu = 100
+iterations = 5000
 
 
 M0 = [[1,0,0,0],[0,1,0,0],[0,0,-1,0],[0,0,0,-1]]
@@ -29,17 +22,24 @@ if len(sys.argv) == 3:
     beta = complex(sys.argv[2])
 
 def init_state(i):
-    alpha = 1
-    beta  = 1
+    alpha = 2
+    beta  = 0
+    gamma = 1
+    delta = 1+1j
     if state_num > 1:
         alpha = i / state_num
-        beta  = (state_num - i) / state_num
+        beta  = -(state_num - i) / state_num
+        gamma = alpha + beta
+        delta = delta * i
     H = npy.array([[1,0,0,1j],[0,2,0,0],[0,0,3,0],[-1j,0,0,4]])
-    return ([alpha, beta, gamma, delta], H)
+    H = sla.expm(-1j * (dt / accu) * H)
+    norm  = npy.linalg.norm([alpha, beta, gamma, delta])
+    state = npy.array([alpha / norm, beta / norm, gamma / norm, delta / norm])
+    return (state, H)
 
 
 def time_evolution(state, dt = dt):
-    return (npy.dot(state[0], sla.expm(-1j * dt * state[1])), state[1])
+    return (npy.dot(state[0], state[1]), state[1])
 
 def fibration(state):
     x0=npy.dot(npy.conj(state),npy.dot(M0,state))
@@ -67,9 +67,10 @@ for i in range(iterations):
         if state_num > 1:
             colour = j / state_num
         f.write(f"{hopf_state[0]}; {hopf_state[1]}; {hopf_state[2]}; {hopf_state[3]}; {hopf_state[4]}; {colour}\n")
-        states[j] = time_evolution(states[j])
+        for l in range(accu):
+            states[j] = time_evolution(states[j], dt / accu)
 f.close()
 
-#plot.plot(iterations, iterations, state_num, "anim3d.plt")
-plot.plot(iterations, iterations, state_num, "anim2d.plt")
+plot.plot(iterations, iterations, state_num, "anim3d.plt")
+#plot.plot(iterations, iterations, state_num, "anim2d.plt")
 
-- 
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