Fig 3 variational double-bracket flow TLFIM L = 5.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from simple_exact_diagonalization_routines.local_matrix_class import *\n",
    "from scipy.linalg import expm\n",
    "import matplotlib.pyplot as plt\n",
    "import time\n",
    "\n",
    "\n",
    "# System size\n",
    "L = 5\n",
    "\n",
    "# Create objects of Pauli operators\n",
    "X = X_class(L)\n",
    "Y = Y_class(L)\n",
    "Z = Z_class(L)\n",
    "S_plus = S_plus_class(L)\n",
    "S_minus = S_minus_class(L)\n",
    "\n",
    "# Trivial initialization of the right size matrix\n",
    "hamiltonian_name = \"TLFIM_L_\" +str(L)\n",
    "H_TLFIM = 0*np.eye( 2**L ) \n",
    "\n",
    "for x in range(L-1):\n",
    "    H_TLFIM = H_TLFIM + 2*X.at(x+1).dot(X.at(x+2)) + Z.at(x+1)+ X.at(x+1)\n",
    "H_TLFIM = H_TLFIM + Z.at(L)    + X.at(L) \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Flow step  0\n",
      "    Found minimum norm =  25.162004614047625  for s =  0.09511718749999999\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZ  gave for s =  0.09511718749999999   minimal norm  25.162004614047625\n",
      "    Found minimum norm =  24.47003064806511  for s =  0.08144531250000002\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ1  gave for s =  0.08144531250000002   minimal norm  24.47003064806511\n",
      "    Found minimum norm =  24.086751971622455  for s =  0.0595703125\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1Z  gave for s =  0.0595703125   minimal norm  24.086751971622455\n",
      "    Found minimum norm =  24.675806736260835  for s =  0.0880859375\n",
      "Flow step output with generator type  single_commutator using string  ZZZ11  gave for s =  0.0880859375   minimal norm  24.675806736260835\n",
      "    Found minimum norm =  24.08675197162246  for s =  0.0595703125\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZ  gave for s =  0.0595703125   minimal norm  24.08675197162246\n",
      "    Found minimum norm =  23.371036802944545  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z1  gave for s =  0.0498046875   minimal norm  23.371036802944545\n",
      "    Found minimum norm =  23.80067215845854  for s =  0.0701171875\n",
      "Flow step output with generator type  single_commutator using string  ZZ11Z  gave for s =  0.0701171875   minimal norm  23.80067215845854\n",
      "    Found minimum norm =  24.855062846971677  for s =  0.09824218750000001\n",
      "Flow step output with generator type  single_commutator using string  ZZ111  gave for s =  0.09824218750000001   minimal norm  24.855062846971677\n",
      "    Found minimum norm =  24.08675197162246  for s =  0.0595703125\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZ  gave for s =  0.0595703125   minimal norm  24.08675197162246\n",
      "    Found minimum norm =  23.385936711463142  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ1  gave for s =  0.0498046875   minimal norm  23.385936711463142\n",
      "    Found minimum norm =  22.41313875028987  for s =  0.05136718750000001\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1Z  gave for s =  0.05136718750000001   minimal norm  22.41313875028987\n",
      "    Found minimum norm =  23.5451955012407  for s =  0.058007812500000006\n",
      "Flow step output with generator type  single_commutator using string  Z1Z11  gave for s =  0.058007812500000006   minimal norm  23.5451955012407\n",
      "    Found minimum norm =  23.80067215845854  for s =  0.0701171875\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZ  gave for s =  0.0701171875   minimal norm  23.80067215845854\n",
      "    Found minimum norm =  23.069353686966746  for s =  0.0626953125\n",
      "Flow step output with generator type  single_commutator using string  Z11Z1  gave for s =  0.0626953125   minimal norm  23.069353686966746\n",
      "    Found minimum norm =  24.027159318572984  for s =  0.07363281250000002\n",
      "Flow step output with generator type  single_commutator using string  Z111Z  gave for s =  0.07363281250000002   minimal norm  24.027159318572984\n",
      "    Found minimum norm =  23.679128187419888  for s =  0.0998046875\n",
      "Flow step output with generator type  single_commutator using string  Z1111  gave for s =  0.0998046875   minimal norm  23.679128187419888\n",
      "    Found minimum norm =  24.470030648065105  for s =  0.08144531250000002\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZ  gave for s =  0.08144531250000002   minimal norm  24.470030648065105\n",
      "    Found minimum norm =  23.80067215845854  for s =  0.0701171875\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ1  gave for s =  0.0701171875   minimal norm  23.80067215845854\n",
      "    Found minimum norm =  23.385936711463142  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1Z  gave for s =  0.0498046875   minimal norm  23.385936711463142\n",
      "    Found minimum norm =  24.027159318572984  for s =  0.07363281250000002\n",
      "Flow step output with generator type  single_commutator using string  1ZZ11  gave for s =  0.07363281250000002   minimal norm  24.027159318572984\n",
      "    Found minimum norm =  23.371036802944545  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZ  gave for s =  0.0498046875   minimal norm  23.371036802944545\n",
      "    Found minimum norm =  22.493752194945404  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z1  gave for s =  0.0498046875   minimal norm  22.493752194945404\n",
      "    Found minimum norm =  23.06935368696675  for s =  0.0626953125\n",
      "Flow step output with generator type  single_commutator using string  1Z11Z  gave for s =  0.0626953125   minimal norm  23.06935368696675\n",
      "    Found minimum norm =  22.41181472003877  for s =  0.07285156250000001\n",
      "Flow step output with generator type  single_commutator using string  1Z111  gave for s =  0.07285156250000001   minimal norm  22.41181472003877\n",
      "    Found minimum norm =  24.67580673626084  for s =  0.0880859375\n",
      "Flow step output with generator type  single_commutator using string  11ZZZ  gave for s =  0.0880859375   minimal norm  24.67580673626084\n",
      "    Found minimum norm =  24.027159318572988  for s =  0.07363281250000002\n",
      "Flow step output with generator type  single_commutator using string  11ZZ1  gave for s =  0.07363281250000002   minimal norm  24.027159318572988\n",
      "    Found minimum norm =  23.5451955012407  for s =  0.058007812500000006\n",
      "Flow step output with generator type  single_commutator using string  11Z1Z  gave for s =  0.058007812500000006   minimal norm  23.5451955012407\n",
      "    Found minimum norm =  22.411814720038766  for s =  0.07285156250000001\n",
      "Flow step output with generator type  single_commutator using string  11Z11  gave for s =  0.07285156250000001   minimal norm  22.411814720038766\n",
      "    Found minimum norm =  24.855062846971677  for s =  0.09824218750000001\n",
      "Flow step output with generator type  single_commutator using string  111ZZ  gave for s =  0.09824218750000001   minimal norm  24.855062846971677\n",
      "    Found minimum norm =  22.411814720038766  for s =  0.07285156250000001\n",
      "Flow step output with generator type  single_commutator using string  111Z1  gave for s =  0.07285156250000001   minimal norm  22.411814720038766\n",
      "    Found minimum norm =  23.67912818741989  for s =  0.0998046875\n",
      "Flow step output with generator type  single_commutator using string  1111Z  gave for s =  0.0998046875   minimal norm  23.67912818741989\n",
      "    Found minimum norm =  25.92296279363144  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  11111  gave for s =  0.0001953125   minimal norm  25.92296279363144\n",
      "    Found minimum norm =  19.615017200428703  for s =  0.040429687500000006\n",
      "Found that canonical is better because  19.615017200428703 22.411814720038766\n",
      "    Found minimum norm =  19.615017200428703  for s =  0.040429687500000006\n",
      "Flowing forwards with type  canonical\n",
      "[]\n",
      "Flow step  1\n",
      "    Found minimum norm =  18.776608593884706  for s =  0.0880859375\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZ  gave for s =  0.0880859375   minimal norm  18.776608593884706\n",
      "    Found minimum norm =  18.633779735547144  for s =  0.07207031250000001\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ1  gave for s =  0.07207031250000001   minimal norm  18.633779735547144\n",
      "    Found minimum norm =  18.655612792029885  for s =  0.0701171875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1Z  gave for s =  0.0701171875   minimal norm  18.655612792029885\n",
      "    Found minimum norm =  18.983882688746085  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ11  gave for s =  0.0498046875   minimal norm  18.983882688746085\n",
      "    Found minimum norm =  18.960659992228248  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZ  gave for s =  0.0498046875   minimal norm  18.960659992228248\n",
      "    Found minimum norm =  18.47429442647068  for s =  0.0705078125\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z1  gave for s =  0.0705078125   minimal norm  18.47429442647068\n",
      "    Found minimum norm =  19.106509603993988  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ11Z  gave for s =  0.0498046875   minimal norm  19.106509603993988\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    Found minimum norm =  18.975931535241333  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ111  gave for s =  0.0498046875   minimal norm  18.975931535241333\n",
      "    Found minimum norm =  18.655612792029885  for s =  0.0701171875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZ  gave for s =  0.0701171875   minimal norm  18.655612792029885\n",
      "    Found minimum norm =  18.480275641688635  for s =  0.0642578125\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ1  gave for s =  0.0642578125   minimal norm  18.480275641688635\n",
      "    Found minimum norm =  17.638973802481782  for s =  0.07792968750000001\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1Z  gave for s =  0.07792968750000001   minimal norm  17.638973802481782\n",
      "    Found minimum norm =  18.72197371592451  for s =  0.0724609375\n",
      "Flow step output with generator type  single_commutator using string  Z1Z11  gave for s =  0.0724609375   minimal norm  18.72197371592451\n",
      "    Found minimum norm =  19.106509603993988  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZ  gave for s =  0.0498046875   minimal norm  19.106509603993988\n",
      "    Found minimum norm =  18.88775984766721  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z11Z1  gave for s =  0.0498046875   minimal norm  18.88775984766721\n",
      "    Found minimum norm =  19.093732456689427  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z111Z  gave for s =  0.0498046875   minimal norm  19.093732456689427\n",
      "    Found minimum norm =  18.536129247120943  for s =  0.07480468750000001\n",
      "Flow step output with generator type  single_commutator using string  Z1111  gave for s =  0.07480468750000001   minimal norm  18.536129247120943\n",
      "    Found minimum norm =  18.63377973554714  for s =  0.07207031250000001\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZ  gave for s =  0.07207031250000001   minimal norm  18.63377973554714\n",
      "    Found minimum norm =  18.319257049988792  for s =  0.0634765625\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ1  gave for s =  0.0634765625   minimal norm  18.319257049988792\n",
      "    Found minimum norm =  18.480275641688632  for s =  0.0642578125\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1Z  gave for s =  0.0642578125   minimal norm  18.480275641688632\n",
      "    Found minimum norm =  18.70205297750022  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ11  gave for s =  0.0498046875   minimal norm  18.70205297750022\n",
      "    Found minimum norm =  18.47429442647068  for s =  0.0705078125\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZ  gave for s =  0.0705078125   minimal norm  18.47429442647068\n",
      "    Found minimum norm =  17.866876547237993  for s =  0.08066406250000002\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z1  gave for s =  0.08066406250000002   minimal norm  17.866876547237993\n",
      "    Found minimum norm =  18.887759847667205  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z11Z  gave for s =  0.0498046875   minimal norm  18.887759847667205\n",
      "    Found minimum norm =  17.917545245398465  for s =  0.07089843750000001\n",
      "Flow step output with generator type  single_commutator using string  1Z111  gave for s =  0.07089843750000001   minimal norm  17.917545245398465\n",
      "    Found minimum norm =  18.983882688746085  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11ZZZ  gave for s =  0.0498046875   minimal norm  18.983882688746085\n",
      "    Found minimum norm =  18.70205297750022  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11ZZ1  gave for s =  0.0498046875   minimal norm  18.70205297750022\n",
      "    Found minimum norm =  18.72197371592451  for s =  0.0724609375\n",
      "Flow step output with generator type  single_commutator using string  11Z1Z  gave for s =  0.0724609375   minimal norm  18.72197371592451\n",
      "    Found minimum norm =  17.735459221995928  for s =  0.0607421875\n",
      "Flow step output with generator type  single_commutator using string  11Z11  gave for s =  0.0607421875   minimal norm  17.735459221995928\n",
      "    Found minimum norm =  18.975931535241333  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  111ZZ  gave for s =  0.0498046875   minimal norm  18.975931535241333\n",
      "    Found minimum norm =  17.917545245398465  for s =  0.07089843750000001\n",
      "Flow step output with generator type  single_commutator using string  111Z1  gave for s =  0.07089843750000001   minimal norm  17.917545245398465\n",
      "    Found minimum norm =  18.536129247120943  for s =  0.07480468750000001\n",
      "Flow step output with generator type  single_commutator using string  1111Z  gave for s =  0.07480468750000001   minimal norm  18.536129247120943\n",
      "    Found minimum norm =  19.615017200428703  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  11111  gave for s =  0.0001953125   minimal norm  19.615017200428703\n",
      "    Found minimum norm =  16.24428203466039  for s =  0.0212890625\n",
      "Found that canonical is better because  16.24428203466039 17.638973802481782\n",
      "    Found minimum norm =  16.24428203466039  for s =  0.0212890625\n",
      "Flowing forwards with type  canonical\n",
      "[]\n",
      "Flow step  2\n",
      "    Found minimum norm =  15.808388569285984  for s =  0.04550781250000001\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZ  gave for s =  0.04550781250000001   minimal norm  15.808388569285984\n",
      "    Found minimum norm =  15.668611896683982  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ1  gave for s =  0.0498046875   minimal norm  15.668611896683982\n",
      "    Found minimum norm =  15.952192901206082  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1Z  gave for s =  0.0498046875   minimal norm  15.952192901206082\n",
      "    Found minimum norm =  15.66723844384269  for s =  0.04355468750000001\n",
      "Flow step output with generator type  single_commutator using string  ZZZ11  gave for s =  0.04355468750000001   minimal norm  15.66723844384269\n",
      "    Found minimum norm =  16.068402042601793  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZ  gave for s =  0.0498046875   minimal norm  16.068402042601793\n",
      "    Found minimum norm =  15.973109989113434  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z1  gave for s =  0.0498046875   minimal norm  15.973109989113434\n",
      "    Found minimum norm =  16.182056297843943  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZ11Z  gave for s =  0.024804687500000002   minimal norm  16.182056297843943\n",
      "    Found minimum norm =  15.828363935799054  for s =  0.0380859375\n",
      "Flow step output with generator type  single_commutator using string  ZZ111  gave for s =  0.0380859375   minimal norm  15.828363935799054\n",
      "    Found minimum norm =  15.952192901206082  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZ  gave for s =  0.0498046875   minimal norm  15.952192901206082\n",
      "    Found minimum norm =  15.569916520275795  for s =  0.0693359375\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ1  gave for s =  0.0693359375   minimal norm  15.569916520275795\n",
      "    Found minimum norm =  15.832626310862251  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1Z  gave for s =  0.0498046875   minimal norm  15.832626310862251\n",
      "    Found minimum norm =  15.995443916321083  for s =  0.03964843750000001\n",
      "Flow step output with generator type  single_commutator using string  Z1Z11  gave for s =  0.03964843750000001   minimal norm  15.995443916321083\n",
      "    Found minimum norm =  16.182056297843943  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZ  gave for s =  0.024804687500000002   minimal norm  16.182056297843943\n",
      "    Found minimum norm =  15.98445644181716  for s =  0.040429687500000006\n",
      "Flow step output with generator type  single_commutator using string  Z11Z1  gave for s =  0.040429687500000006   minimal norm  15.98445644181716\n",
      "    Found minimum norm =  16.169550217991357  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  Z111Z  gave for s =  0.0373046875   minimal norm  16.169550217991357\n",
      "    Found minimum norm =  15.466964563782714  for s =  0.06699218750000001\n",
      "Flow step output with generator type  single_commutator using string  Z1111  gave for s =  0.06699218750000001   minimal norm  15.466964563782714\n",
      "    Found minimum norm =  15.668611896683982  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZ  gave for s =  0.0498046875   minimal norm  15.668611896683982\n",
      "    Found minimum norm =  15.247956975449565  for s =  0.061914062500000006\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ1  gave for s =  0.061914062500000006   minimal norm  15.247956975449565\n",
      "    Found minimum norm =  15.569916520275793  for s =  0.0693359375\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1Z  gave for s =  0.0693359375   minimal norm  15.569916520275793\n",
      "    Found minimum norm =  15.665046024948117  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ11  gave for s =  0.0498046875   minimal norm  15.665046024948117\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    Found minimum norm =  15.973109989113436  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZ  gave for s =  0.0498046875   minimal norm  15.973109989113436\n",
      "    Found minimum norm =  15.785751217679387  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z1  gave for s =  0.0498046875   minimal norm  15.785751217679387\n",
      "    Found minimum norm =  15.984456441817166  for s =  0.040429687500000006\n",
      "Flow step output with generator type  single_commutator using string  1Z11Z  gave for s =  0.040429687500000006   minimal norm  15.984456441817166\n",
      "    Found minimum norm =  14.961324580172763  for s =  0.056054687500000006\n",
      "Flow step output with generator type  single_commutator using string  1Z111  gave for s =  0.056054687500000006   minimal norm  14.961324580172763\n",
      "    Found minimum norm =  15.667238443842688  for s =  0.04355468750000001\n",
      "Flow step output with generator type  single_commutator using string  11ZZZ  gave for s =  0.04355468750000001   minimal norm  15.667238443842688\n",
      "    Found minimum norm =  15.665046024948117  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11ZZ1  gave for s =  0.0498046875   minimal norm  15.665046024948117\n",
      "    Found minimum norm =  15.995443916321085  for s =  0.03964843750000001\n",
      "Flow step output with generator type  single_commutator using string  11Z1Z  gave for s =  0.03964843750000001   minimal norm  15.995443916321085\n",
      "    Found minimum norm =  14.90547779204353  for s =  0.052148437500000006\n",
      "Flow step output with generator type  single_commutator using string  11Z11  gave for s =  0.052148437500000006   minimal norm  14.90547779204353\n",
      "    Found minimum norm =  15.828363935799052  for s =  0.0380859375\n",
      "Flow step output with generator type  single_commutator using string  111ZZ  gave for s =  0.0380859375   minimal norm  15.828363935799052\n",
      "    Found minimum norm =  14.961324580172763  for s =  0.056054687500000006\n",
      "Flow step output with generator type  single_commutator using string  111Z1  gave for s =  0.056054687500000006   minimal norm  14.961324580172763\n",
      "    Found minimum norm =  15.466964563782712  for s =  0.06699218750000001\n",
      "Flow step output with generator type  single_commutator using string  1111Z  gave for s =  0.06699218750000001   minimal norm  15.466964563782712\n",
      "    Found minimum norm =  16.24428203466039  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  11111  gave for s =  0.0001953125   minimal norm  16.24428203466039\n",
      "    Found minimum norm =  14.07362400816175  for s =  0.011132812500000002\n",
      "Found that canonical is better because  14.07362400816175 14.90547779204353\n",
      "    Found minimum norm =  14.07362400816175  for s =  0.011132812500000002\n",
      "Flowing forwards with type  canonical\n",
      "[]\n",
      "Flow step  3\n",
      "    Found minimum norm =  13.688600393919083  for s =  0.0380859375\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZ  gave for s =  0.0380859375   minimal norm  13.688600393919083\n",
      "    Found minimum norm =  13.609755398803587  for s =  0.0439453125\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ1  gave for s =  0.0439453125   minimal norm  13.609755398803587\n",
      "    Found minimum norm =  13.89416235217237  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1Z  gave for s =  0.0498046875   minimal norm  13.89416235217237\n",
      "    Found minimum norm =  13.568206756801901  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ11  gave for s =  0.0498046875   minimal norm  13.568206756801901\n",
      "    Found minimum norm =  14.074011096907244  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZ  gave for s =  0.0001953125   minimal norm  14.074011096907244\n",
      "    Found minimum norm =  13.710604636249716  for s =  0.0716796875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z1  gave for s =  0.0716796875   minimal norm  13.710604636249716\n",
      "    Found minimum norm =  13.946736169636317  for s =  0.031835937499999994\n",
      "Flow step output with generator type  single_commutator using string  ZZ11Z  gave for s =  0.031835937499999994   minimal norm  13.946736169636317\n",
      "    Found minimum norm =  13.689224763558125  for s =  0.0419921875\n",
      "Flow step output with generator type  single_commutator using string  ZZ111  gave for s =  0.0419921875   minimal norm  13.689224763558125\n",
      "    Found minimum norm =  13.894162352172371  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZ  gave for s =  0.0498046875   minimal norm  13.894162352172371\n",
      "    Found minimum norm =  13.549455770195358  for s =  0.07480468750000001\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ1  gave for s =  0.07480468750000001   minimal norm  13.549455770195358\n",
      "    Found minimum norm =  13.652482425038578  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1Z  gave for s =  0.0498046875   minimal norm  13.652482425038578\n",
      "    Found minimum norm =  13.697407000201252  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z11  gave for s =  0.0498046875   minimal norm  13.697407000201252\n",
      "    Found minimum norm =  13.946736169636317  for s =  0.031835937499999994\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZ  gave for s =  0.031835937499999994   minimal norm  13.946736169636317\n",
      "    Found minimum norm =  13.600888956857696  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z11Z1  gave for s =  0.0498046875   minimal norm  13.600888956857696\n",
      "    Found minimum norm =  13.856054688682036  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z111Z  gave for s =  0.0498046875   minimal norm  13.856054688682036\n",
      "    Found minimum norm =  13.440420461570488  for s =  0.0693359375\n",
      "Flow step output with generator type  single_commutator using string  Z1111  gave for s =  0.0693359375   minimal norm  13.440420461570488\n",
      "    Found minimum norm =  13.60975539880359  for s =  0.0439453125\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZ  gave for s =  0.0439453125   minimal norm  13.60975539880359\n",
      "    Found minimum norm =  13.453610587600513  for s =  0.0568359375\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ1  gave for s =  0.0568359375   minimal norm  13.453610587600513\n",
      "    Found minimum norm =  13.549455770195356  for s =  0.07480468750000001\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1Z  gave for s =  0.07480468750000001   minimal norm  13.549455770195356\n",
      "    Found minimum norm =  13.606889256750224  for s =  0.0630859375\n",
      "Flow step output with generator type  single_commutator using string  1ZZ11  gave for s =  0.0630859375   minimal norm  13.606889256750224\n",
      "    Found minimum norm =  13.710604636249718  for s =  0.0716796875\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZ  gave for s =  0.0716796875   minimal norm  13.710604636249718\n",
      "    Found minimum norm =  13.34805005714477  for s =  0.07480468750000001\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z1  gave for s =  0.07480468750000001   minimal norm  13.34805005714477\n",
      "    Found minimum norm =  13.600888956857698  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z11Z  gave for s =  0.0498046875   minimal norm  13.600888956857698\n",
      "    Found minimum norm =  13.2068674902834  for s =  0.05722656250000001\n",
      "Flow step output with generator type  single_commutator using string  1Z111  gave for s =  0.05722656250000001   minimal norm  13.2068674902834\n",
      "    Found minimum norm =  13.568206756801903  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11ZZZ  gave for s =  0.0498046875   minimal norm  13.568206756801903\n",
      "    Found minimum norm =  13.606889256750224  for s =  0.0630859375\n",
      "Flow step output with generator type  single_commutator using string  11ZZ1  gave for s =  0.0630859375   minimal norm  13.606889256750224\n",
      "    Found minimum norm =  13.697407000201254  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11Z1Z  gave for s =  0.0498046875   minimal norm  13.697407000201254\n",
      "    Found minimum norm =  13.325958041352306  for s =  0.04941406250000001\n",
      "Flow step output with generator type  single_commutator using string  11Z11  gave for s =  0.04941406250000001   minimal norm  13.325958041352306\n",
      "    Found minimum norm =  13.689224763558126  for s =  0.0419921875\n",
      "Flow step output with generator type  single_commutator using string  111ZZ  gave for s =  0.0419921875   minimal norm  13.689224763558126\n",
      "    Found minimum norm =  13.206867490283402  for s =  0.05722656250000001\n",
      "Flow step output with generator type  single_commutator using string  111Z1  gave for s =  0.05722656250000001   minimal norm  13.206867490283402\n",
      "    Found minimum norm =  13.440420461570483  for s =  0.0693359375\n",
      "Flow step output with generator type  single_commutator using string  1111Z  gave for s =  0.0693359375   minimal norm  13.440420461570483\n",
      "    Found minimum norm =  14.07362400816175  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  11111  gave for s =  0.0001953125   minimal norm  14.07362400816175\n",
      "    Found minimum norm =  12.84118695628909  for s =  0.0087890625\n",
      "Found that canonical is better because  12.84118695628909 13.2068674902834\n",
      "    Found minimum norm =  12.84118695628909  for s =  0.0087890625\n",
      "Flowing forwards with type  canonical\n",
      "[]\n",
      "Flow step  4\n",
      "    Found minimum norm =  12.440648763038565  for s =  0.03769531250000001\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZ  gave for s =  0.03769531250000001   minimal norm  12.440648763038565\n",
      "    Found minimum norm =  12.459915611241202  for s =  0.03886718750000001\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ1  gave for s =  0.03886718750000001   minimal norm  12.459915611241202\n",
      "    Found minimum norm =  12.811684641634203  for s =  0.0412109375\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1Z  gave for s =  0.0412109375   minimal norm  12.811684641634203\n",
      "    Found minimum norm =  12.52666034190589  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ11  gave for s =  0.0498046875   minimal norm  12.52666034190589\n",
      "    Found minimum norm =  12.842289367667128  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZ  gave for s =  0.0001953125   minimal norm  12.842289367667128\n",
      "    Found minimum norm =  12.633943809410958  for s =  0.07285156250000001\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z1  gave for s =  0.07285156250000001   minimal norm  12.633943809410958\n",
      "    Found minimum norm =  12.66861476428402  for s =  0.0322265625\n",
      "Flow step output with generator type  single_commutator using string  ZZ11Z  gave for s =  0.0322265625   minimal norm  12.66861476428402\n",
      "    Found minimum norm =  12.517380620388634  for s =  0.036523437500000006\n",
      "Flow step output with generator type  single_commutator using string  ZZ111  gave for s =  0.036523437500000006   minimal norm  12.517380620388634\n",
      "    Found minimum norm =  12.811684641634203  for s =  0.0412109375\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZ  gave for s =  0.0412109375   minimal norm  12.811684641634203\n",
      "    Found minimum norm =  12.425741534283693  for s =  0.08105468750000001\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ1  gave for s =  0.08105468750000001   minimal norm  12.425741534283693\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    Found minimum norm =  12.453075301569358  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1Z  gave for s =  0.0498046875   minimal norm  12.453075301569358\n",
      "    Found minimum norm =  12.43680635250651  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z11  gave for s =  0.0498046875   minimal norm  12.43680635250651\n",
      "    Found minimum norm =  12.668614764284023  for s =  0.0322265625\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZ  gave for s =  0.0322265625   minimal norm  12.668614764284023\n",
      "    Found minimum norm =  12.2816813544535  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z11Z1  gave for s =  0.0498046875   minimal norm  12.2816813544535\n",
      "    Found minimum norm =  12.519294578396678  for s =  0.0630859375\n",
      "Flow step output with generator type  single_commutator using string  Z111Z  gave for s =  0.0630859375   minimal norm  12.519294578396678\n",
      "    Found minimum norm =  12.33156290694882  for s =  0.06503906250000001\n",
      "Flow step output with generator type  single_commutator using string  Z1111  gave for s =  0.06503906250000001   minimal norm  12.33156290694882\n",
      "    Found minimum norm =  12.459915611241202  for s =  0.03886718750000001\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZ  gave for s =  0.03886718750000001   minimal norm  12.459915611241202\n",
      "    Found minimum norm =  12.436301356722133  for s =  0.04941406250000001\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ1  gave for s =  0.04941406250000001   minimal norm  12.436301356722133\n",
      "    Found minimum norm =  12.425741534283693  for s =  0.08105468750000001\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1Z  gave for s =  0.08105468750000001   minimal norm  12.425741534283693\n",
      "    Found minimum norm =  12.477623440648793  for s =  0.07480468750000001\n",
      "Flow step output with generator type  single_commutator using string  1ZZ11  gave for s =  0.07480468750000001   minimal norm  12.477623440648793\n",
      "    Found minimum norm =  12.633943809410958  for s =  0.07285156250000001\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZ  gave for s =  0.07285156250000001   minimal norm  12.633943809410958\n",
      "    Found minimum norm =  12.187499202960716  for s =  0.07792968750000001\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z1  gave for s =  0.07792968750000001   minimal norm  12.187499202960716\n",
      "    Found minimum norm =  12.281681354453504  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z11Z  gave for s =  0.0498046875   minimal norm  12.281681354453504\n",
      "    Found minimum norm =  12.158924656723903  for s =  0.05253906250000001\n",
      "Flow step output with generator type  single_commutator using string  1Z111  gave for s =  0.05253906250000001   minimal norm  12.158924656723903\n",
      "    Found minimum norm =  12.526660341905892  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11ZZZ  gave for s =  0.0498046875   minimal norm  12.526660341905892\n",
      "    Found minimum norm =  12.477623440648793  for s =  0.07480468750000001\n",
      "Flow step output with generator type  single_commutator using string  11ZZ1  gave for s =  0.07480468750000001   minimal norm  12.477623440648793\n",
      "    Found minimum norm =  12.43680635250651  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11Z1Z  gave for s =  0.0498046875   minimal norm  12.43680635250651\n",
      "    Found minimum norm =  12.278343015128566  for s =  0.0431640625\n",
      "Flow step output with generator type  single_commutator using string  11Z11  gave for s =  0.0431640625   minimal norm  12.278343015128566\n",
      "    Found minimum norm =  12.517380620388638  for s =  0.036523437500000006\n",
      "Flow step output with generator type  single_commutator using string  111ZZ  gave for s =  0.036523437500000006   minimal norm  12.517380620388638\n",
      "    Found minimum norm =  12.158924656723904  for s =  0.05253906250000001\n",
      "Flow step output with generator type  single_commutator using string  111Z1  gave for s =  0.05253906250000001   minimal norm  12.158924656723904\n",
      "    Found minimum norm =  12.331562906948818  for s =  0.06503906250000001\n",
      "Flow step output with generator type  single_commutator using string  1111Z  gave for s =  0.06503906250000001   minimal norm  12.331562906948818\n",
      "    Found minimum norm =  12.84118695628909  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  11111  gave for s =  0.0001953125   minimal norm  12.84118695628909\n",
      "    Found minimum norm =  12.064910163425932  for s =  0.0064453125000000005\n",
      "Found that canonical is better because  12.064910163425932 12.158924656723903\n",
      "    Found minimum norm =  12.064910163425932  for s =  0.0064453125000000005\n",
      "Flowing forwards with type  canonical\n",
      "[]\n",
      "Flow step  5\n",
      "    Found minimum norm =  11.755673107445071  for s =  0.03964843750000001\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZ  gave for s =  0.03964843750000001   minimal norm  11.755673107445071\n",
      "    Found minimum norm =  11.775167942863801  for s =  0.0392578125\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ1  gave for s =  0.0392578125   minimal norm  11.775167942863801\n",
      "    Found minimum norm =  12.04922929960809  for s =  0.0427734375\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1Z  gave for s =  0.0427734375   minimal norm  12.04922929960809\n",
      "    Found minimum norm =  11.858828359813025  for s =  0.0537109375\n",
      "Flow step output with generator type  single_commutator using string  ZZZ11  gave for s =  0.0537109375   minimal norm  11.858828359813025\n",
      "    Found minimum norm =  12.066124246113436  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZ  gave for s =  0.0001953125   minimal norm  12.066124246113436\n",
      "    Found minimum norm =  11.890735927556388  for s =  0.08105468750000001\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z1  gave for s =  0.08105468750000001   minimal norm  11.890735927556388\n",
      "    Found minimum norm =  11.947664974384814  for s =  0.0322265625\n",
      "Flow step output with generator type  single_commutator using string  ZZ11Z  gave for s =  0.0322265625   minimal norm  11.947664974384814\n",
      "    Found minimum norm =  11.82890570404846  for s =  0.0353515625\n",
      "Flow step output with generator type  single_commutator using string  ZZ111  gave for s =  0.0353515625   minimal norm  11.82890570404846\n",
      "    Found minimum norm =  12.049229299608088  for s =  0.0427734375\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZ  gave for s =  0.0427734375   minimal norm  12.049229299608088\n",
      "    Found minimum norm =  11.754188722866582  for s =  0.07480468750000001\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ1  gave for s =  0.07480468750000001   minimal norm  11.754188722866582\n",
      "    Found minimum norm =  11.703658488182198  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1Z  gave for s =  0.0498046875   minimal norm  11.703658488182198\n",
      "    Found minimum norm =  11.642440688733588  for s =  0.06738281250000001\n",
      "Flow step output with generator type  single_commutator using string  Z1Z11  gave for s =  0.06738281250000001   minimal norm  11.642440688733588\n",
      "    Found minimum norm =  11.947664974384814  for s =  0.0322265625\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZ  gave for s =  0.0322265625   minimal norm  11.947664974384814\n",
      "    Found minimum norm =  11.477789449215726  for s =  0.06738281250000001\n",
      "Flow step output with generator type  single_commutator using string  Z11Z1  gave for s =  0.06738281250000001   minimal norm  11.477789449215726\n",
      "    Found minimum norm =  11.610247392636543  for s =  0.0853515625\n",
      "Flow step output with generator type  single_commutator using string  Z111Z  gave for s =  0.0853515625   minimal norm  11.610247392636543\n",
      "    Found minimum norm =  11.642706032719445  for s =  0.0615234375\n",
      "Flow step output with generator type  single_commutator using string  Z1111  gave for s =  0.0615234375   minimal norm  11.642706032719445\n",
      "    Found minimum norm =  11.775167942863803  for s =  0.0392578125\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZ  gave for s =  0.0392578125   minimal norm  11.775167942863803\n",
      "    Found minimum norm =  11.760563381256084  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ1  gave for s =  0.0498046875   minimal norm  11.760563381256084\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    Found minimum norm =  11.754188722866582  for s =  0.07480468750000001\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1Z  gave for s =  0.07480468750000001   minimal norm  11.754188722866582\n",
      "    Found minimum norm =  11.761813583223164  for s =  0.08222656250000002\n",
      "Flow step output with generator type  single_commutator using string  1ZZ11  gave for s =  0.08222656250000002   minimal norm  11.761813583223164\n",
      "    Found minimum norm =  11.890735927556388  for s =  0.08105468750000001\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZ  gave for s =  0.08105468750000001   minimal norm  11.890735927556388\n",
      "    Found minimum norm =  11.379407269711702  for s =  0.0849609375\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z1  gave for s =  0.0849609375   minimal norm  11.379407269711702\n",
      "    Found minimum norm =  11.477789449215726  for s =  0.06738281250000001\n",
      "Flow step output with generator type  single_commutator using string  1Z11Z  gave for s =  0.06738281250000001   minimal norm  11.477789449215726\n",
      "    Found minimum norm =  11.49239616286847  for s =  0.0576171875\n",
      "Flow step output with generator type  single_commutator using string  1Z111  gave for s =  0.0576171875   minimal norm  11.49239616286847\n",
      "    Found minimum norm =  11.858828359813025  for s =  0.0537109375\n",
      "Flow step output with generator type  single_commutator using string  11ZZZ  gave for s =  0.0537109375   minimal norm  11.858828359813025\n",
      "    Found minimum norm =  11.761813583223162  for s =  0.08222656250000002\n",
      "Flow step output with generator type  single_commutator using string  11ZZ1  gave for s =  0.08222656250000002   minimal norm  11.761813583223162\n",
      "    Found minimum norm =  11.64244068873359  for s =  0.06738281250000001\n",
      "Flow step output with generator type  single_commutator using string  11Z1Z  gave for s =  0.06738281250000001   minimal norm  11.64244068873359\n",
      "    Found minimum norm =  11.62967491362948  for s =  0.044335937500000006\n",
      "Flow step output with generator type  single_commutator using string  11Z11  gave for s =  0.044335937500000006   minimal norm  11.62967491362948\n",
      "    Found minimum norm =  11.82890570404846  for s =  0.0353515625\n",
      "Flow step output with generator type  single_commutator using string  111ZZ  gave for s =  0.0353515625   minimal norm  11.82890570404846\n",
      "    Found minimum norm =  11.49239616286847  for s =  0.0576171875\n",
      "Flow step output with generator type  single_commutator using string  111Z1  gave for s =  0.0576171875   minimal norm  11.49239616286847\n",
      "    Found minimum norm =  11.642706032719445  for s =  0.0615234375\n",
      "Flow step output with generator type  single_commutator using string  1111Z  gave for s =  0.0615234375   minimal norm  11.642706032719445\n",
      "    Found minimum norm =  12.064910163425932  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  11111  gave for s =  0.0001953125   minimal norm  12.064910163425932\n",
      "    Found minimum norm =  11.524105597988001  for s =  0.005664062500000001\n",
      "Found that canonical is worse because  11.524105597988001 11.379407269711702\n",
      "    Found minimum norm =  11.379407269711702  for s =  0.0849609375\n",
      "Flowing forwards with type  single_commutator\n",
      "[]\n",
      "Flow step  6\n",
      "    Found minimum norm =  11.070993385887142  for s =  0.03574218750000001\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZ  gave for s =  0.03574218750000001   minimal norm  11.070993385887142\n",
      "    Found minimum norm =  10.873373522862996  for s =  0.0294921875\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ1  gave for s =  0.0294921875   minimal norm  10.873373522862996\n",
      "    Found minimum norm =  11.341649578035803  for s =  0.0134765625\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1Z  gave for s =  0.0134765625   minimal norm  11.341649578035803\n",
      "    Found minimum norm =  11.077656374329493  for s =  0.032617187500000006\n",
      "Flow step output with generator type  single_commutator using string  ZZZ11  gave for s =  0.032617187500000006   minimal norm  11.077656374329493\n",
      "    Found minimum norm =  11.283391767660044  for s =  0.015039062499999999\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZ  gave for s =  0.015039062499999999   minimal norm  11.283391767660044\n",
      "    Found minimum norm =  11.38022356118606  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z1  gave for s =  0.0001953125   minimal norm  11.38022356118606\n",
      "    Found minimum norm =  11.153721621489964  for s =  0.025585937500000003\n",
      "Flow step output with generator type  single_commutator using string  ZZ11Z  gave for s =  0.025585937500000003   minimal norm  11.153721621489964\n",
      "    Found minimum norm =  10.884773893579927  for s =  0.036523437500000006\n",
      "Flow step output with generator type  single_commutator using string  ZZ111  gave for s =  0.036523437500000006   minimal norm  10.884773893579927\n",
      "    Found minimum norm =  11.341649578035804  for s =  0.0134765625\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZ  gave for s =  0.0134765625   minimal norm  11.341649578035804\n",
      "    Found minimum norm =  11.205306996616484  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ1  gave for s =  0.024804687500000002   minimal norm  11.205306996616484\n",
      "    Found minimum norm =  11.162754108989256  for s =  0.019726562500000003\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1Z  gave for s =  0.019726562500000003   minimal norm  11.162754108989256\n",
      "    Found minimum norm =  11.060295348793023  for s =  0.044335937500000006\n",
      "Flow step output with generator type  single_commutator using string  Z1Z11  gave for s =  0.044335937500000006   minimal norm  11.060295348793023\n",
      "    Found minimum norm =  11.153721621489966  for s =  0.025585937500000003\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZ  gave for s =  0.025585937500000003   minimal norm  11.153721621489966\n",
      "    Found minimum norm =  11.256102037719048  for s =  0.020898437500000002\n",
      "Flow step output with generator type  single_commutator using string  Z11Z1  gave for s =  0.020898437500000002   minimal norm  11.256102037719048\n",
      "    Found minimum norm =  11.306978583287247  for s =  0.0244140625\n",
      "Flow step output with generator type  single_commutator using string  Z111Z  gave for s =  0.0244140625   minimal norm  11.306978583287247\n",
      "    Found minimum norm =  10.847372261280707  for s =  0.0314453125\n",
      "Flow step output with generator type  single_commutator using string  Z1111  gave for s =  0.0314453125   minimal norm  10.847372261280707\n",
      "    Found minimum norm =  10.873373522862996  for s =  0.0294921875\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZ  gave for s =  0.0294921875   minimal norm  10.873373522862996\n",
      "    Found minimum norm =  11.371584888235697  for s =  0.010351562500000001\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ1  gave for s =  0.010351562500000001   minimal norm  11.371584888235697\n",
      "    Found minimum norm =  11.20530699661648  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1Z  gave for s =  0.024804687500000002   minimal norm  11.20530699661648\n",
      "    Found minimum norm =  11.300103019467738  for s =  0.018554687500000003\n",
      "Flow step output with generator type  single_commutator using string  1ZZ11  gave for s =  0.018554687500000003   minimal norm  11.300103019467738\n",
      "    Found minimum norm =  11.380223561186062  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZ  gave for s =  0.0001953125   minimal norm  11.380223561186062\n",
      "    Found minimum norm =  10.932245589379274  for s =  0.0283203125\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z1  gave for s =  0.0283203125   minimal norm  10.932245589379274\n",
      "    Found minimum norm =  11.25610203771905  for s =  0.020898437500000002\n",
      "Flow step output with generator type  single_commutator using string  1Z11Z  gave for s =  0.020898437500000002   minimal norm  11.25610203771905\n",
      "    Found minimum norm =  10.860195399403448  for s =  0.03886718750000001\n",
      "Flow step output with generator type  single_commutator using string  1Z111  gave for s =  0.03886718750000001   minimal norm  10.860195399403448\n",
      "    Found minimum norm =  11.077656374329498  for s =  0.032617187500000006\n",
      "Flow step output with generator type  single_commutator using string  11ZZZ  gave for s =  0.032617187500000006   minimal norm  11.077656374329498\n",
      "    Found minimum norm =  11.30010301946774  for s =  0.018554687500000003\n",
      "Flow step output with generator type  single_commutator using string  11ZZ1  gave for s =  0.018554687500000003   minimal norm  11.30010301946774\n",
      "    Found minimum norm =  11.060295348793023  for s =  0.044335937500000006\n",
      "Flow step output with generator type  single_commutator using string  11Z1Z  gave for s =  0.044335937500000006   minimal norm  11.060295348793023\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    Found minimum norm =  10.63934107808478  for s =  0.032617187500000006\n",
      "Flow step output with generator type  single_commutator using string  11Z11  gave for s =  0.032617187500000006   minimal norm  10.63934107808478\n",
      "    Found minimum norm =  10.884773893579924  for s =  0.036523437500000006\n",
      "Flow step output with generator type  single_commutator using string  111ZZ  gave for s =  0.036523437500000006   minimal norm  10.884773893579924\n",
      "    Found minimum norm =  10.86019539940345  for s =  0.03886718750000001\n",
      "Flow step output with generator type  single_commutator using string  111Z1  gave for s =  0.03886718750000001   minimal norm  10.86019539940345\n",
      "    Found minimum norm =  10.847372261280706  for s =  0.0314453125\n",
      "Flow step output with generator type  single_commutator using string  1111Z  gave for s =  0.0314453125   minimal norm  10.847372261280706\n",
      "    Found minimum norm =  11.379407269711702  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  11111  gave for s =  0.0001953125   minimal norm  11.379407269711702\n",
      "    Found minimum norm =  10.660422073699154  for s =  0.0033203125000000003\n",
      "Found that canonical is worse because  10.660422073699154 10.63934107808478\n",
      "    Found minimum norm =  10.63934107808478  for s =  0.032617187500000006\n",
      "Flowing forwards with type  single_commutator\n",
      "[]\n",
      "Flow step  7\n",
      "    Found minimum norm =  10.37847604869571  for s =  0.05332031250000001\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZ  gave for s =  0.05332031250000001   minimal norm  10.37847604869571\n",
      "    Found minimum norm =  10.369486947371433  for s =  0.0439453125\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ1  gave for s =  0.0439453125   minimal norm  10.369486947371433\n",
      "    Found minimum norm =  10.639490896516643  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1Z  gave for s =  0.0001953125   minimal norm  10.639490896516643\n",
      "    Found minimum norm =  10.509804854525575  for s =  0.038476562500000006\n",
      "Flow step output with generator type  single_commutator using string  ZZZ11  gave for s =  0.038476562500000006   minimal norm  10.509804854525575\n",
      "    Found minimum norm =  10.64000603005213  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZ  gave for s =  0.0001953125   minimal norm  10.64000603005213\n",
      "    Found minimum norm =  10.640494359380412  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z1  gave for s =  0.0001953125   minimal norm  10.640494359380412\n",
      "    Found minimum norm =  10.623036042129485  for s =  0.0162109375\n",
      "Flow step output with generator type  single_commutator using string  ZZ11Z  gave for s =  0.0162109375   minimal norm  10.623036042129485\n",
      "    Found minimum norm =  10.17462827578284  for s =  0.0634765625\n",
      "Flow step output with generator type  single_commutator using string  ZZ111  gave for s =  0.0634765625   minimal norm  10.17462827578284\n",
      "    Found minimum norm =  10.639490896516643  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZ  gave for s =  0.0001953125   minimal norm  10.639490896516643\n",
      "    Found minimum norm =  10.571641113194808  for s =  0.03378906250000001\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ1  gave for s =  0.03378906250000001   minimal norm  10.571641113194808\n",
      "    Found minimum norm =  10.613065354019733  for s =  0.0134765625\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1Z  gave for s =  0.0134765625   minimal norm  10.613065354019733\n",
      "    Found minimum norm =  10.380555708744339  for s =  0.0716796875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z11  gave for s =  0.0716796875   minimal norm  10.380555708744339\n",
      "    Found minimum norm =  10.623036042129485  for s =  0.0162109375\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZ  gave for s =  0.0162109375   minimal norm  10.623036042129485\n",
      "    Found minimum norm =  10.639381127010614  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  Z11Z1  gave for s =  0.0001953125   minimal norm  10.639381127010614\n",
      "    Found minimum norm =  10.633329921333713  for s =  0.015039062499999999\n",
      "Flow step output with generator type  single_commutator using string  Z111Z  gave for s =  0.015039062499999999   minimal norm  10.633329921333713\n",
      "    Found minimum norm =  10.16821203646668  for s =  0.054101562500000006\n",
      "Flow step output with generator type  single_commutator using string  Z1111  gave for s =  0.054101562500000006   minimal norm  10.16821203646668\n",
      "    Found minimum norm =  10.369486947371433  for s =  0.0439453125\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZ  gave for s =  0.0439453125   minimal norm  10.369486947371433\n",
      "    Found minimum norm =  10.639620624600353  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ1  gave for s =  0.0001953125   minimal norm  10.639620624600353\n",
      "    Found minimum norm =  10.57164111319481  for s =  0.03378906250000001\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1Z  gave for s =  0.03378906250000001   minimal norm  10.57164111319481\n",
      "    Found minimum norm =  10.639837019629718  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1ZZ11  gave for s =  0.0001953125   minimal norm  10.639837019629718\n",
      "    Found minimum norm =  10.640494359380412  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZ  gave for s =  0.0001953125   minimal norm  10.640494359380412\n",
      "    Found minimum norm =  10.443397955989088  for s =  0.04160156250000001\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z1  gave for s =  0.04160156250000001   minimal norm  10.443397955989088\n",
      "    Found minimum norm =  10.639381127010614  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1Z11Z  gave for s =  0.0001953125   minimal norm  10.639381127010614\n",
      "    Found minimum norm =  10.252652674358984  for s =  0.0654296875\n",
      "Flow step output with generator type  single_commutator using string  1Z111  gave for s =  0.0654296875   minimal norm  10.252652674358984\n",
      "    Found minimum norm =  10.509804854525575  for s =  0.038476562500000006\n",
      "Flow step output with generator type  single_commutator using string  11ZZZ  gave for s =  0.038476562500000006   minimal norm  10.509804854525575\n",
      "    Found minimum norm =  10.639837019629718  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  11ZZ1  gave for s =  0.0001953125   minimal norm  10.639837019629718\n",
      "    Found minimum norm =  10.380555708744337  for s =  0.0716796875\n",
      "Flow step output with generator type  single_commutator using string  11Z1Z  gave for s =  0.0716796875   minimal norm  10.380555708744337\n",
      "    Found minimum norm =  10.322362069486708  for s =  0.04941406250000001\n",
      "Flow step output with generator type  single_commutator using string  11Z11  gave for s =  0.04941406250000001   minimal norm  10.322362069486708\n",
      "    Found minimum norm =  10.174628275782842  for s =  0.0634765625\n",
      "Flow step output with generator type  single_commutator using string  111ZZ  gave for s =  0.0634765625   minimal norm  10.174628275782842\n",
      "    Found minimum norm =  10.252652674358982  for s =  0.0654296875\n",
      "Flow step output with generator type  single_commutator using string  111Z1  gave for s =  0.0654296875   minimal norm  10.252652674358982\n",
      "    Found minimum norm =  10.16821203646668  for s =  0.054101562500000006\n",
      "Flow step output with generator type  single_commutator using string  1111Z  gave for s =  0.054101562500000006   minimal norm  10.16821203646668\n",
      "    Found minimum norm =  10.63934107808478  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  11111  gave for s =  0.0001953125   minimal norm  10.63934107808478\n",
      "    Found minimum norm =  10.17167723137851  for s =  0.005664062500000001\n",
      "Found that canonical is worse because  10.17167723137851 10.16821203646668\n",
      "    Found minimum norm =  10.16821203646668  for s =  0.054101562500000006\n",
      "Flowing forwards with type  single_commutator\n",
      "[]\n",
      "Flow step  8\n",
      "    Found minimum norm =  9.893999269636103  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZ  gave for s =  0.0498046875   minimal norm  9.893999269636103\n",
      "    Found minimum norm =  9.883260496190063  for s =  0.03574218750000001\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ1  gave for s =  0.03574218750000001   minimal norm  9.883260496190063\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    Found minimum norm =  10.158948446996686  for s =  0.0119140625\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1Z  gave for s =  0.0119140625   minimal norm  10.158948446996686\n",
      "    Found minimum norm =  10.113810659638782  for s =  0.019335937500000004\n",
      "Flow step output with generator type  single_commutator using string  ZZZ11  gave for s =  0.019335937500000004   minimal norm  10.113810659638782\n",
      "    Found minimum norm =  10.168276602066056  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZ  gave for s =  0.0001953125   minimal norm  10.168276602066056\n",
      "    Found minimum norm =  10.169205758883507  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z1  gave for s =  0.0001953125   minimal norm  10.169205758883507\n",
      "    Found minimum norm =  10.123878509352982  for s =  0.0181640625\n",
      "Flow step output with generator type  single_commutator using string  ZZ11Z  gave for s =  0.0181640625   minimal norm  10.123878509352982\n",
      "    Found minimum norm =  9.85915717148064  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ111  gave for s =  0.0498046875   minimal norm  9.85915717148064\n",
      "    Found minimum norm =  10.168119411008314  for s =  0.0009765625\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZ  gave for s =  0.0009765625   minimal norm  10.168119411008314\n",
      "    Found minimum norm =  10.145462438440784  for s =  0.014257812500000001\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ1  gave for s =  0.014257812500000001   minimal norm  10.145462438440784\n",
      "    Found minimum norm =  10.088213369267706  for s =  0.016992187500000002\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1Z  gave for s =  0.016992187500000002   minimal norm  10.088213369267706\n",
      "    Found minimum norm =  10.017137098708641  for s =  0.0693359375\n",
      "Flow step output with generator type  single_commutator using string  Z1Z11  gave for s =  0.0693359375   minimal norm  10.017137098708641\n",
      "    Found minimum norm =  10.112868858059285  for s =  0.020507812500000003\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZ  gave for s =  0.020507812500000003   minimal norm  10.112868858059285\n",
      "    Found minimum norm =  10.164795639594097  for s =  0.0076171875\n",
      "Flow step output with generator type  single_commutator using string  Z11Z1  gave for s =  0.0076171875   minimal norm  10.164795639594097\n",
      "    Found minimum norm =  10.168252671744478  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  Z111Z  gave for s =  0.0001953125   minimal norm  10.168252671744478\n",
      "    Found minimum norm =  9.958355499420906  for s =  0.0283203125\n",
      "Flow step output with generator type  single_commutator using string  Z1111  gave for s =  0.0283203125   minimal norm  9.958355499420906\n",
      "    Found minimum norm =  9.851712476405051  for s =  0.03574218750000001\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZ  gave for s =  0.03574218750000001   minimal norm  9.851712476405051\n",
      "    Found minimum norm =  10.136965697689877  for s =  0.0353515625\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ1  gave for s =  0.0353515625   minimal norm  10.136965697689877\n",
      "    Found minimum norm =  10.070070853986278  for s =  0.0283203125\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1Z  gave for s =  0.0283203125   minimal norm  10.070070853986278\n",
      "    Found minimum norm =  10.16812400051477  for s =  0.0009765625\n",
      "Flow step output with generator type  single_commutator using string  1ZZ11  gave for s =  0.0009765625   minimal norm  10.16812400051477\n",
      "    Found minimum norm =  10.169073531338457  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZ  gave for s =  0.0001953125   minimal norm  10.169073531338457\n",
      "    Found minimum norm =  9.98391392382726  for s =  0.029882812499999998\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z1  gave for s =  0.029882812499999998   minimal norm  9.98391392382726\n",
      "    Found minimum norm =  10.133726783525526  for s =  0.020507812500000003\n",
      "Flow step output with generator type  single_commutator using string  1Z11Z  gave for s =  0.020507812500000003   minimal norm  10.133726783525526\n",
      "    Found minimum norm =  9.856565511341287  for s =  0.046289062500000006\n",
      "Flow step output with generator type  single_commutator using string  1Z111  gave for s =  0.046289062500000006   minimal norm  9.856565511341287\n",
      "    Found minimum norm =  10.021935979123255  for s =  0.0314453125\n",
      "Flow step output with generator type  single_commutator using string  11ZZZ  gave for s =  0.0314453125   minimal norm  10.021935979123255\n",
      "    Found minimum norm =  10.168344474936607  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  11ZZ1  gave for s =  0.0001953125   minimal norm  10.168344474936607\n",
      "    Found minimum norm =  9.950452359018161  for s =  0.061914062500000006\n",
      "Flow step output with generator type  single_commutator using string  11Z1Z  gave for s =  0.061914062500000006   minimal norm  9.950452359018161\n",
      "    Found minimum norm =  9.772995971955018  for s =  0.038476562500000006\n",
      "Flow step output with generator type  single_commutator using string  11Z11  gave for s =  0.038476562500000006   minimal norm  9.772995971955018\n",
      "    Found minimum norm =  9.634347888778585  for s =  0.055273437499999994\n",
      "Flow step output with generator type  single_commutator using string  111ZZ  gave for s =  0.055273437499999994   minimal norm  9.634347888778585\n",
      "    Found minimum norm =  9.821614815362066  for s =  0.048242187500000006\n",
      "Flow step output with generator type  single_commutator using string  111Z1  gave for s =  0.048242187500000006   minimal norm  9.821614815362066\n",
      "    Found minimum norm =  9.678908587517157  for s =  0.0412109375\n",
      "Flow step output with generator type  single_commutator using string  1111Z  gave for s =  0.0412109375   minimal norm  9.678908587517157\n",
      "    Found minimum norm =  10.16821203646668  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  11111  gave for s =  0.0001953125   minimal norm  10.16821203646668\n",
      "    Found minimum norm =  9.78499328002133  for s =  0.0037109375\n",
      "Found that canonical is worse because  9.78499328002133 9.634347888778585\n",
      "    Found minimum norm =  9.634347888778585  for s =  0.055273437499999994\n",
      "Flowing forwards with type  single_commutator\n",
      "[]\n",
      "Flow step  9\n",
      "    Found minimum norm =  9.455893828486408  for s =  0.0466796875\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZ  gave for s =  0.0466796875   minimal norm  9.455893828486408\n",
      "    Found minimum norm =  9.341930421265221  for s =  0.0361328125\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ1  gave for s =  0.0361328125   minimal norm  9.341930421265221\n",
      "    Found minimum norm =  9.634458271592006  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1Z  gave for s =  0.0001953125   minimal norm  9.634458271592006\n",
      "    Found minimum norm =  9.565511699654722  for s =  0.017773437500000003\n",
      "Flow step output with generator type  single_commutator using string  ZZZ11  gave for s =  0.017773437500000003   minimal norm  9.565511699654722\n",
      "    Found minimum norm =  9.630521312727888  for s =  0.0044921875000000005\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZ  gave for s =  0.0044921875000000005   minimal norm  9.630521312727888\n",
      "    Found minimum norm =  9.634982231007688  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z1  gave for s =  0.0001953125   minimal norm  9.634982231007688\n",
      "    Found minimum norm =  9.505451753745476  for s =  0.0271484375\n",
      "Flow step output with generator type  single_commutator using string  ZZ11Z  gave for s =  0.0271484375   minimal norm  9.505451753745476\n",
      "    Found minimum norm =  9.414172207451157  for s =  0.0431640625\n",
      "Flow step output with generator type  single_commutator using string  ZZ111  gave for s =  0.0431640625   minimal norm  9.414172207451157\n",
      "    Found minimum norm =  9.577416099986536  for s =  0.019335937500000004\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZ  gave for s =  0.019335937500000004   minimal norm  9.577416099986536\n",
      "    Found minimum norm =  9.625681577386601  for s =  0.008398437500000001\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ1  gave for s =  0.008398437500000001   minimal norm  9.625681577386601\n",
      "    Found minimum norm =  9.50486534917288  for s =  0.022851562500000002\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1Z  gave for s =  0.022851562500000002   minimal norm  9.50486534917288\n",
      "    Found minimum norm =  9.56210102628467  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z11  gave for s =  0.0498046875   minimal norm  9.56210102628467\n",
      "    Found minimum norm =  9.610295855871131  for s =  0.015039062499999999\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZ  gave for s =  0.015039062499999999   minimal norm  9.610295855871131\n",
      "    Found minimum norm =  9.557111346433874  for s =  0.0236328125\n",
      "Flow step output with generator type  single_commutator using string  Z11Z1  gave for s =  0.0236328125   minimal norm  9.557111346433874\n",
      "    Found minimum norm =  9.633841134565591  for s =  0.0060546875\n",
      "Flow step output with generator type  single_commutator using string  Z111Z  gave for s =  0.0060546875   minimal norm  9.633841134565591\n",
      "    Found minimum norm =  9.324047633978031  for s =  0.034570312500000006\n",
      "Flow step output with generator type  single_commutator using string  Z1111  gave for s =  0.034570312500000006   minimal norm  9.324047633978031\n",
      "    Found minimum norm =  9.332179500025811  for s =  0.0349609375\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZ  gave for s =  0.0349609375   minimal norm  9.332179500025811\n",
      "    Found minimum norm =  9.614106575613887  for s =  0.022851562500000002\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ1  gave for s =  0.022851562500000002   minimal norm  9.614106575613887\n",
      "    Found minimum norm =  9.546749552543726  for s =  0.0240234375\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1Z  gave for s =  0.0240234375   minimal norm  9.546749552543726\n",
      "    Found minimum norm =  9.634995436878249  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1ZZ11  gave for s =  0.0001953125   minimal norm  9.634995436878249\n",
      "    Found minimum norm =  9.635390449097919  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZ  gave for s =  0.0001953125   minimal norm  9.635390449097919\n",
      "    Found minimum norm =  9.369521625580617  for s =  0.0341796875\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z1  gave for s =  0.0341796875   minimal norm  9.369521625580617\n",
      "    Found minimum norm =  9.634428654453407  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1Z11Z  gave for s =  0.0001953125   minimal norm  9.634428654453407\n",
      "    Found minimum norm =  9.300405869273215  for s =  0.04082031250000001\n",
      "Flow step output with generator type  single_commutator using string  1Z111  gave for s =  0.04082031250000001   minimal norm  9.300405869273215\n",
      "    Found minimum norm =  9.600461205193088  for s =  0.017773437500000003\n",
      "Flow step output with generator type  single_commutator using string  11ZZZ  gave for s =  0.017773437500000003   minimal norm  9.600461205193088\n",
      "    Found minimum norm =  9.626726432217437  for s =  0.0072265625\n",
      "Flow step output with generator type  single_commutator using string  11ZZ1  gave for s =  0.0072265625   minimal norm  9.626726432217437\n",
      "    Found minimum norm =  9.579893595170018  for s =  0.0353515625\n",
      "Flow step output with generator type  single_commutator using string  11Z1Z  gave for s =  0.0353515625   minimal norm  9.579893595170018\n",
      "    Found minimum norm =  9.10866746157777  for s =  0.0427734375\n",
      "Flow step output with generator type  single_commutator using string  11Z11  gave for s =  0.0427734375   minimal norm  9.10866746157777\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    Found minimum norm =  9.550195189008228  for s =  0.0212890625\n",
      "Flow step output with generator type  single_commutator using string  111ZZ  gave for s =  0.0212890625   minimal norm  9.550195189008228\n",
      "    Found minimum norm =  9.50491378130754  for s =  0.0361328125\n",
      "Flow step output with generator type  single_commutator using string  111Z1  gave for s =  0.0361328125   minimal norm  9.50491378130754\n",
      "    Found minimum norm =  9.200525912242373  for s =  0.0419921875\n",
      "Flow step output with generator type  single_commutator using string  1111Z  gave for s =  0.0419921875   minimal norm  9.200525912242373\n",
      "    Found minimum norm =  9.634347888778585  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  11111  gave for s =  0.0001953125   minimal norm  9.634347888778585\n",
      "    Found minimum norm =  9.237297193907926  for s =  0.0037109375\n",
      "Found that canonical is worse because  9.237297193907926 9.10866746157777\n",
      "    Found minimum norm =  9.10866746157777  for s =  0.0427734375\n",
      "Flowing forwards with type  single_commutator\n",
      "[]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from class_double_bracket_flow import *\n",
    "\n",
    "\n",
    "flow = double_bracket_flow( H_TLFIM )\n",
    "\n",
    "flow.please_be_exhaustively_verbose = False\n",
    "flow.please_be_verbose = True\n",
    "\n",
    "flow.nmb_search_points_minimizing_s_search = 10\n",
    "flow.flow_step_max = 0.2\n",
    "flow.nmb_flow_steps = 10\n",
    "flow.please_use_binary_search =  True\n",
    "flow.please_compute_observables = False\n",
    "\n",
    "#flow.flow_forwards( )\n",
    "flow.flow_via_best_Z_search( please_also_check_canonical_bracket = True )\n",
    "\n",
    "flow.show_flow_forwards_results()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_90905/568403580.py:62: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
      "  axin1.set_xticklabels([1]+['']*(2**L-2)+[2**L])\n",
      "/tmp/ipykernel_90905/568403580.py:108: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
      "  axin2.set_xticklabels([1]+['']*(2**L-2)+[2**L])\n",
      "/tmp/ipykernel_90905/568403580.py:112: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
      "  axin3.set_xticklabels([1]+['']*(2**L-2)+[2**L])\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x504 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "\n",
    "def plot_iteration_results(  ):\n",
    "    flow.run_param_rc(fontsize=19)\n",
    "    flow_results = flow.flow_outputs\n",
    "\n",
    "    f=plt.figure(figsize = ( 8,7 ))\n",
    "    n=1\n",
    "    ax_a = f.add_subplot(1,n,1)\n",
    "    norms = flow_results['minimal_norm_sigma_H_s']\n",
    "    x_axis = [sum(flow_results['minimizing_flow_step'][:k])for k in range( 1, len(flow_results['minimizing_flow_step'])+1)]\n",
    "\n",
    "    plt.plot( x_axis, norms, '-o')   \n",
    "    N = 10\n",
    "    k=0\n",
    "    for xy in zip([x+.01 for x in x_axis[0:N]], \n",
    "                  [n - 0.03 for n in norms[0:N]]):  \n",
    "        if k == 0 or k == 9 or k == 8:\n",
    "            a=1\n",
    "        else:\n",
    "            plt.annotate('k = ' + str(k) + ': ' + flow_results['strs_of_minimizer_Z'][k-1], xy=xy, textcoords='data', fontsize=17)\n",
    "        k=k+1\n",
    "    \n",
    "    plt.annotate('k = ' + str(k) + ': ' + flow_results['strs_of_minimizer_Z'][k-1], \n",
    "                 xy=(x_axis[-1]-.11,norms[-1]-.7), textcoords='data', fontsize=17)\n",
    "\n",
    "    plt.annotate('k = ' + str(k-1) + ': ' + flow_results['strs_of_minimizer_Z'][k-2], \n",
    "                 xy=(x_axis[k-1]-.11,norms[k-1]-.5), textcoords='data', fontsize=17)\n",
    "    plt.annotate('k = ' + str(k-2) + ': ' + flow_results['strs_of_minimizer_Z'][k-3], \n",
    "                 xy=(x_axis[k-2]+.021,norms[k-2]-.13), textcoords='data', fontsize=17)\n",
    "    x_labels_rounded = [ round(x, 2 ) for x in x_axis ]\n",
    "    x_labels_rounded = [0] + x_labels_rounded[1:9]  + [max(x_labels_rounded)]\n",
    "    x_labels_rounded.pop(2)\n",
    "    x_labels_rounded.pop(2)\n",
    "    x_labels_rounded.pop(-2)\n",
    "    x_labels_rounded.pop(3)\n",
    "    \n",
    "    plt.xticks(x_labels_rounded)\n",
    "    y_labels_rounded = [ round(y, 1 ) for y in norms ]\n",
    "    y_labels_rounded = y_labels_rounded[0:5] + [min(y_labels_rounded)]\n",
    "    plt.yticks(y_labels_rounded)\n",
    "    plt.grid()\n",
    "    plt.xlabel(r'Total DBI duration $\\ell$')\n",
    "    plt.ylabel(r'$\\vert\\vert\\sigma(\\hat H_k)\\vert\\vert_{\\mathrm{HS}}$')\n",
    "    plt.title(r'Diagonalization DBI with $\\hat D_k = Z_{\\mu(k)}$ or $\\hat D_k =\\Delta(\\hat H_k)$')\n",
    "    a =-.1\n",
    "    b = 1.05\n",
    " \n",
    "    colorbar_max = max([np.max(H_TLFIM),np.max(flow_results['optimally_flowed_H'][-1]),\n",
    "                        np.max(flow_results['optimally_flowed_H'][2])])   \n",
    "    colorbar_min = min([np.min(H_TLFIM),np.min(flow_results['optimally_flowed_H'][-1]),\n",
    "                        np.min(flow_results['optimally_flowed_H'][2])])\n",
    "    axin1 = ax_a.inset_axes([0.2,.7, 0.31, 0.27])\n",
    "    inset1 = axin1.imshow( H_TLFIM, cmap='RdBu' )\n",
    "    divider1 = make_axes_locatable(axin1)\n",
    "    div_ax = divider1.append_axes(\"right\", size=\"10%\", pad=0.05)\n",
    "    cbar1 = plt.colorbar(inset1, cax = div_ax )\n",
    "    \n",
    "    range_plot = np.max( np.abs( H_TLFIM ) )\n",
    "#     cbar1.set_clim( -range_plot, range_plot )\n",
    "    axin1.set_yticks(range(2**L))  \n",
    "    axin1.set_xticklabels([1]+['']*(2**L-2)+[2**L])\n",
    "    axin1.set_yticklabels([1]+['']*(2**L-2)+[2**L])\n",
    "    axin1.set_xticks(range(2**L))\n",
    "    ax_a.annotate(' ',\n",
    "            xy=(x_axis[0]+.01, norms[0]),  # theta, radius\n",
    "            xytext=(0.24, 0.81),    # fraction, fraction\n",
    "            textcoords='figure fraction',\n",
    "            arrowprops=dict(facecolor='gray', shrink=0.01),\n",
    "            horizontalalignment='left',\n",
    "            verticalalignment='bottom')\n",
    "#     axin1.set_xlabel(r'$j$')\n",
    "#     axin1.set_title(r'$k$')\n",
    "#     axin1.grid()\n",
    "    axin2 = ax_a.inset_axes([0.62,.32, 0.31, 0.27])\n",
    "    inset2 = axin2.imshow(flow_results['optimally_flowed_H'][-1], cmap='RdBu')\n",
    "\n",
    "    divider2 = make_axes_locatable(axin2)\n",
    "    div_ax2 = divider2.append_axes(\"right\", size=\"10%\", pad=0.05)\n",
    "    ticks = [-colorbar_max,0,colorbar_max]\n",
    "    ticks = [ round(t,1) for t in ticks]\n",
    "    cbar2 = plt.colorbar(inset2, cax = div_ax2 )\n",
    "    inset2.set_clim(-colorbar_max,colorbar_max)\n",
    "  \n",
    "    ax_a.annotate(' ',\n",
    "        xy=(x_axis[-1], 11.4),  # theta, radius\n",
    "        xytext=(.95, .3),    # fraction, fraction\n",
    "        textcoords='axes fraction',\n",
    "        arrowprops=dict(facecolor='gray', shrink=0.05),\n",
    "        horizontalalignment='left',\n",
    "        verticalalignment='bottom')\n",
    "    \n",
    "    axin3 = ax_a.inset_axes([0.62,.7, 0.31, 0.27])\n",
    "    inset3 = axin3.imshow(flow_results['optimally_flowed_H'][2], cmap='RdBu')\n",
    "\n",
    "    divider3 = make_axes_locatable(axin3)\n",
    "    div_ax3 = divider3.append_axes(\"right\", size=\"10%\", pad=0.05)\n",
    "    cbar2 = plt.colorbar(inset3, cax = div_ax3 )\n",
    "    inset3.set_clim(-colorbar_max,colorbar_max)\n",
    "    ax_a.annotate(' ',\n",
    "        xy=(x_axis[2]+.01, norms[2]+.6),  # theta, radius\n",
    "        xytext=(0.65, 0.67),    # fraction, fraction\n",
    "        textcoords='axes fraction',\n",
    "        arrowprops=dict(facecolor='gray', shrink=0.05),\n",
    "        horizontalalignment='left',\n",
    "        verticalalignment='bottom')\n",
    "    axin2.set_yticks(range(2**L))  \n",
    "    axin2.set_xticklabels([1]+['']*(2**L-2)+[2**L])\n",
    "    axin2.set_yticklabels([1]+['']*(2**L-2)+[2**L])\n",
    "    axin2.set_xticks(range(2**L))    \n",
    "    axin3.set_yticks(range(2**L))  \n",
    "    axin3.set_xticklabels([1]+['']*(2**L-2)+[2**L])\n",
    "    axin3.set_yticklabels([1]+['']*(2**L-2)+[2**L])\n",
    "    axin3.set_xticks(range(2**L))\n",
    "    chosen_steps = [1,2]\n",
    "    plt.savefig( 'figs/mix_L_'+str(L)+'.pdf')\n",
    "    \n",
    "plot_iteration_results()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Some additional uses of the class"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The stored observables are these:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "flow.flow_outputs.keys()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(some of these are empty)\n",
    "The Hamiltonians are stored as optimally flowed in the sense that the flow step duration was optimized by a brute force grid search or local binary search.\n",
    "The first element is the initial Hamiltonin so "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "len(flow.flow_outputs['optimally_flowed_H'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we get 1 + nmb of steps"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Simple plot for debugging"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "H = flow.flow_outputs['final_flowed_H'][-1]\n",
    "\n",
    "plt.figure()\n",
    "plt.subplot(121)\n",
    "plt.imshow(abs(H_TLFIM), cmap='RdBu')\n",
    "plt.colorbar()\n",
    "plt.subplot(122)\n",
    "plt.imshow(abs(H), cmap='RdBu')\n",
    "plt.colorbar()\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This variable stores or strings that have been tested in each step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(flow.flow_outputs['all_Z_names'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and these are the strings that gave the optimal generator to decrease the norm of the off-diagonal restriction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "flow.flow_outputs['strs_of_minimizer_Z']"
   ]
  }
 ],
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