{
"cells": [
{
"cell_type": "markdown",
"source": [
"# Gross-Pitaevskii equation with external magnetic field"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"We solve the 2D Gross-Pitaevskii equation with a magnetic field.\n",
"This is similar to the\n",
"previous example (Gross-Pitaevskii equation in one dimension),\n",
"but with an extra term for the magnetic field.\n",
"We reproduce here the results of https://arxiv.org/pdf/1611.02045.pdf Fig. 10"
],
"metadata": {}
},
{
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Iter Function value Gradient norm \n",
" 0 3.064853e+01 8.031630e+00\n",
" * time: 0.0034520626068115234\n",
" 1 2.872422e+01 3.927619e+00\n",
" * time: 0.01581597328186035\n",
" 2 1.928271e+01 4.008898e+00\n",
" * time: 0.032022953033447266\n",
" 3 1.405867e+01 2.676105e+00\n",
" * time: 0.11735105514526367\n",
" 4 1.232810e+01 3.506580e+00\n",
" * time: 0.12948989868164062\n",
" 5 1.224701e+01 2.975797e+00\n",
" * time: 0.1411600112915039\n",
" 6 1.007523e+01 1.629148e+00\n",
" * time: 0.15286493301391602\n",
" 7 8.892682e+00 1.648603e+00\n",
" * time: 0.16461801528930664\n",
" 8 8.438044e+00 1.325825e+00\n",
" * time: 0.17624807357788086\n",
" 9 8.233540e+00 7.573126e-01\n",
" * time: 0.18779206275939941\n",
" 10 8.166378e+00 9.814119e-01\n",
" * time: 0.19676589965820312\n",
" 11 8.083050e+00 5.237860e-01\n",
" * time: 0.20556092262268066\n",
" 12 8.069300e+00 7.612078e-01\n",
" * time: 0.21447205543518066\n",
" 13 8.044603e+00 5.990265e-01\n",
" * time: 0.22327399253845215\n",
" 14 7.986142e+00 4.366388e-01\n",
" * time: 0.23208904266357422\n",
" 15 7.922525e+00 4.692781e-01\n",
" * time: 0.24103212356567383\n",
" 16 7.897134e+00 3.585648e-01\n",
" * time: 0.2503659725189209\n",
" 17 7.873650e+00 3.831230e-01\n",
" * time: 0.25938892364501953\n",
" 18 7.869721e+00 5.088469e-01\n",
" * time: 0.2683219909667969\n",
" 19 7.858000e+00 4.313498e-01\n",
" * time: 0.2777550220489502\n",
" 20 7.834704e+00 2.994196e-01\n",
" * time: 0.28693199157714844\n",
" 21 7.815244e+00 3.418351e-01\n",
" * time: 0.296065092086792\n",
" 22 7.801572e+00 2.418865e-01\n",
" * time: 0.30562710762023926\n",
" 23 7.789103e+00 3.094291e-01\n",
" * time: 0.3179469108581543\n",
" 24 7.776449e+00 1.570042e-01\n",
" * time: 0.33028697967529297\n",
" 25 7.763614e+00 1.599361e-01\n",
" * time: 0.33951401710510254\n",
" 26 7.756710e+00 2.514865e-01\n",
" * time: 0.3488318920135498\n",
" 27 7.756056e+00 2.415029e-01\n",
" * time: 0.3585491180419922\n",
" 28 7.749525e+00 3.524544e-01\n",
" * time: 0.3683810234069824\n",
" 29 7.740761e+00 1.920991e-01\n",
" * time: 0.38157010078430176\n",
" 30 7.733919e+00 2.491474e-01\n",
" * time: 0.3912670612335205\n",
" 31 7.722286e+00 1.710827e-01\n",
" * time: 0.40096092224121094\n",
" 32 7.718729e+00 2.739167e-01\n",
" * time: 0.4107019901275635\n",
" 33 7.715922e+00 2.116974e-01\n",
" * time: 0.4203629493713379\n",
" 34 7.708390e+00 1.547255e-01\n",
" * time: 0.4302220344543457\n",
" 35 7.707042e+00 3.066302e-01\n",
" * time: 0.44003796577453613\n",
" 36 7.701642e+00 2.172196e-01\n",
" * time: 0.45300793647766113\n",
" 37 7.696708e+00 2.410515e-01\n",
" * time: 0.4658939838409424\n",
" 38 7.691069e+00 1.642459e-01\n",
" * time: 0.4787099361419678\n",
" 39 7.687370e+00 1.320677e-01\n",
" * time: 0.48846912384033203\n",
" 40 7.684869e+00 1.052816e-01\n",
" * time: 0.4983189105987549\n",
" 41 7.684100e+00 1.585718e-01\n",
" * time: 0.5083110332489014\n",
" 42 7.682800e+00 1.423136e-01\n",
" * time: 0.5182199478149414\n",
" 43 7.679797e+00 1.042916e-01\n",
" * time: 0.5310111045837402\n",
" 44 7.677765e+00 1.356282e-01\n",
" * time: 0.5407040119171143\n",
" 45 7.673509e+00 1.401235e-01\n",
" * time: 0.6075088977813721\n",
" 46 7.670254e+00 8.285267e-02\n",
" * time: 0.6192500591278076\n",
" 47 7.666169e+00 1.283240e-01\n",
" * time: 0.6281208992004395\n",
" 48 7.665128e+00 1.666791e-01\n",
" * time: 0.6369531154632568\n",
" 49 7.662586e+00 1.195202e-01\n",
" * time: 0.645766019821167\n",
" 50 7.661456e+00 1.738547e-01\n",
" * time: 0.6545538902282715\n",
" 51 7.659635e+00 1.463413e-01\n",
" * time: 0.6636600494384766\n",
" 52 7.658185e+00 1.270792e-01\n",
" * time: 0.6725120544433594\n",
" 53 7.653346e+00 9.461236e-02\n",
" * time: 0.6812670230865479\n",
" 54 7.649535e+00 1.246124e-01\n",
" * time: 0.6900649070739746\n",
" 55 7.649355e+00 1.773132e-01\n",
" * time: 0.6987340450286865\n",
" 56 7.648321e+00 1.248029e-01\n",
" * time: 0.7076430320739746\n",
" 57 7.646454e+00 1.338393e-01\n",
" * time: 0.7164640426635742\n",
" 58 7.643501e+00 1.048567e-01\n",
" * time: 0.7253448963165283\n",
" 59 7.641085e+00 8.072875e-02\n",
" * time: 0.7370100021362305\n",
" 60 7.638532e+00 7.148484e-02\n",
" * time: 0.7457621097564697\n",
" 61 7.638208e+00 1.403919e-01\n",
" * time: 0.754709005355835\n",
" 62 7.637273e+00 1.084078e-01\n",
" * time: 0.7639811038970947\n",
" 63 7.637092e+00 1.406007e-01\n",
" * time: 0.7732589244842529\n",
" 64 7.635933e+00 1.082790e-01\n",
" * time: 0.782426118850708\n",
" 65 7.634022e+00 8.774640e-02\n",
" * time: 0.7916619777679443\n",
" 66 7.632019e+00 7.344738e-02\n",
" * time: 0.8038809299468994\n",
" 67 7.629759e+00 5.504603e-02\n",
" * time: 0.8161571025848389\n",
" 68 7.629059e+00 7.657035e-02\n",
" * time: 0.8254680633544922\n",
" 69 7.628610e+00 7.601238e-02\n",
" * time: 0.8349390029907227\n",
" 70 7.627950e+00 6.829508e-02\n",
" * time: 0.8445971012115479\n",
" 71 7.627402e+00 5.458241e-02\n",
" * time: 0.8544449806213379\n",
" 72 7.627078e+00 4.669210e-02\n",
" * time: 0.8642499446868896\n",
" 73 7.626630e+00 4.010358e-02\n",
" * time: 0.8773970603942871\n",
" 74 7.626158e+00 6.665720e-02\n",
" * time: 0.8873980045318604\n",
" 75 7.625656e+00 4.493045e-02\n",
" * time: 0.900360107421875\n",
" 76 7.625317e+00 4.144523e-02\n",
" * time: 0.9102649688720703\n",
" 77 7.624953e+00 3.902635e-02\n",
" * time: 0.9199678897857666\n",
" 78 7.624549e+00 2.875387e-02\n",
" * time: 0.929764986038208\n",
" 79 7.624247e+00 4.469483e-02\n",
" * time: 0.9394590854644775\n",
" 80 7.624067e+00 5.950494e-02\n",
" * time: 0.9490890502929688\n",
" 81 7.623787e+00 4.068272e-02\n",
" * time: 0.9619810581207275\n",
" 82 7.623463e+00 3.531159e-02\n",
" * time: 0.975074052810669\n",
" 83 7.623174e+00 6.333561e-02\n",
" * time: 0.984699010848999\n",
" 84 7.622899e+00 6.057601e-02\n",
" * time: 0.9943931102752686\n",
" 85 7.622876e+00 9.952892e-02\n",
" * time: 1.0040130615234375\n",
" 86 7.622760e+00 5.706444e-02\n",
" * time: 1.0138049125671387\n",
" 87 7.622095e+00 5.028931e-02\n",
" * time: 1.0235490798950195\n",
" 88 7.621818e+00 4.752382e-02\n",
" * time: 1.0822250843048096\n",
" 89 7.620863e+00 4.527760e-02\n",
" * time: 1.0912880897521973\n",
" 90 7.620535e+00 8.786624e-02\n",
" * time: 1.1001861095428467\n",
" 91 7.619746e+00 5.142631e-02\n",
" * time: 1.1117639541625977\n",
" 92 7.619159e+00 4.623085e-02\n",
" * time: 1.1204509735107422\n",
" 93 7.618688e+00 6.119446e-02\n",
" * time: 1.1291890144348145\n",
" 94 7.618070e+00 5.331830e-02\n",
" * time: 1.140815019607544\n",
" 95 7.617729e+00 6.318177e-02\n",
" * time: 1.1496551036834717\n",
" 96 7.617086e+00 7.101925e-02\n",
" * time: 1.1613030433654785\n",
" 97 7.616505e+00 5.422527e-02\n",
" * time: 1.1730530261993408\n",
" 98 7.616166e+00 6.203030e-02\n",
" * time: 1.1817739009857178\n",
" 99 7.615711e+00 4.276814e-02\n",
" * time: 1.1934270858764648\n",
" 100 7.615343e+00 5.922140e-02\n",
" * time: 1.202347993850708\n",
" 101 7.615040e+00 5.645076e-02\n",
" * time: 1.2110869884490967\n",
" 102 7.614801e+00 4.679424e-02\n",
" * time: 1.2198710441589355\n",
" 103 7.614424e+00 6.272480e-02\n",
" * time: 1.22900390625\n",
" 104 7.614331e+00 6.228596e-02\n",
" * time: 1.238158941268921\n",
" 105 7.614002e+00 4.768302e-02\n",
" * time: 1.2511720657348633\n",
" 106 7.613527e+00 4.600170e-02\n",
" * time: 1.2608489990234375\n",
" 107 7.613518e+00 6.340237e-02\n",
" * time: 1.2703170776367188\n",
" 108 7.613226e+00 4.098458e-02\n",
" * time: 1.280163049697876\n",
" 109 7.613144e+00 6.575054e-02\n",
" * time: 1.289659023284912\n",
" 110 7.613001e+00 7.402516e-02\n",
" * time: 1.298935890197754\n",
" 111 7.612605e+00 2.947488e-02\n",
" * time: 1.308255910873413\n",
" 112 7.612277e+00 4.520349e-02\n",
" * time: 1.3178589344024658\n",
" 113 7.612211e+00 5.992683e-02\n",
" * time: 1.3277499675750732\n",
" 114 7.611955e+00 3.864056e-02\n",
" * time: 1.3374249935150146\n",
" 115 7.611775e+00 4.342243e-02\n",
" * time: 1.3472249507904053\n",
" 116 7.611519e+00 3.591867e-02\n",
" * time: 1.3600969314575195\n",
" 117 7.611217e+00 3.598254e-02\n",
" * time: 1.369823932647705\n",
" 118 7.610815e+00 2.419189e-02\n",
" * time: 1.38264799118042\n",
" 119 7.610613e+00 2.835290e-02\n",
" * time: 1.3926301002502441\n",
" 120 7.610478e+00 3.254908e-02\n",
" * time: 1.4054429531097412\n",
" 121 7.610234e+00 1.491802e-02\n",
" * time: 1.4181859493255615\n",
" 122 7.610122e+00 1.770463e-02\n",
" * time: 1.430866003036499\n",
" 123 7.610034e+00 2.270566e-02\n",
" * time: 1.4404819011688232\n",
" 124 7.609917e+00 1.833947e-02\n",
" * time: 1.4535059928894043\n",
" 125 7.609865e+00 4.327749e-02\n",
" * time: 1.4633779525756836\n",
" 126 7.609669e+00 1.623283e-02\n",
" * time: 1.473134994506836\n",
" 127 7.609610e+00 4.239019e-02\n",
" * time: 1.482896089553833\n",
" 128 7.609396e+00 3.937529e-02\n",
" * time: 1.492691993713379\n",
" 129 7.609164e+00 3.238064e-02\n",
" * time: 1.5024070739746094\n",
" 130 7.608860e+00 2.409427e-02\n",
" * time: 1.546694040298462\n",
" 131 7.608820e+00 4.490076e-02\n",
" * time: 1.5554580688476562\n",
" 132 7.608593e+00 4.870038e-02\n",
" * time: 1.56427001953125\n",
" 133 7.608397e+00 3.562430e-02\n",
" * time: 1.5730130672454834\n",
" 134 7.608189e+00 3.055247e-02\n",
" * time: 1.5846021175384521\n",
" 135 7.608116e+00 5.698404e-02\n",
" * time: 1.5933520793914795\n",
" 136 7.608024e+00 4.765325e-02\n",
" * time: 1.6022100448608398\n",
" 137 7.607750e+00 4.310979e-02\n",
" * time: 1.6111729145050049\n",
" 138 7.607425e+00 2.691758e-02\n",
" * time: 1.6228001117706299\n",
" 139 7.607346e+00 4.195626e-02\n",
" * time: 1.631688117980957\n",
" 140 7.607143e+00 4.325139e-02\n",
" * time: 1.6405789852142334\n",
" 141 7.606939e+00 3.402186e-02\n",
" * time: 1.652216911315918\n",
" 142 7.606831e+00 3.892369e-02\n",
" * time: 1.6610889434814453\n",
" 143 7.606708e+00 3.816887e-02\n",
" * time: 1.669888973236084\n",
" 144 7.606674e+00 3.021847e-02\n",
" * time: 1.6787209510803223\n",
" 145 7.606553e+00 4.206216e-02\n",
" * time: 1.6875619888305664\n",
" 146 7.606274e+00 2.733714e-02\n",
" * time: 1.699700117111206\n",
" 147 7.606207e+00 4.129431e-02\n",
" * time: 1.7088780403137207\n",
" 148 7.606018e+00 2.502373e-02\n",
" * time: 1.7180750370025635\n",
" 149 7.605789e+00 3.076097e-02\n",
" * time: 1.7273080348968506\n",
" 150 7.605659e+00 3.417170e-02\n",
" * time: 1.7365849018096924\n",
" 151 7.605490e+00 1.980488e-02\n",
" * time: 1.748932123184204\n",
" 152 7.605372e+00 2.668823e-02\n",
" * time: 1.7612340450286865\n",
" 153 7.605312e+00 2.882685e-02\n",
" * time: 1.7704648971557617\n",
" 154 7.605305e+00 3.802600e-02\n",
" * time: 1.7801411151885986\n",
" 155 7.605230e+00 3.010860e-02\n",
" * time: 1.7899270057678223\n",
" 156 7.605127e+00 3.744252e-02\n",
" * time: 1.7996220588684082\n",
" 157 7.605029e+00 2.341336e-02\n",
" * time: 1.8124771118164062\n",
" 158 7.604905e+00 2.128131e-02\n",
" * time: 1.8253540992736816\n",
" 159 7.604818e+00 1.708001e-02\n",
" * time: 1.8380520343780518\n",
" 160 7.604804e+00 2.025791e-02\n",
" * time: 1.847733974456787\n",
" 161 7.604745e+00 1.430979e-02\n",
" * time: 1.8574531078338623\n",
" 162 7.604735e+00 1.822069e-02\n",
" * time: 1.8672130107879639\n",
" 163 7.604693e+00 1.270004e-02\n",
" * time: 1.8799901008605957\n",
" 164 7.604633e+00 1.523765e-02\n",
" * time: 1.8897581100463867\n",
" 165 7.604627e+00 1.676233e-02\n",
" * time: 1.8997249603271484\n",
" 166 7.604589e+00 1.532376e-02\n",
" * time: 1.909562110900879\n",
" 167 7.604579e+00 1.800365e-02\n",
" * time: 1.9193251132965088\n",
" 168 7.604554e+00 1.213322e-02\n",
" * time: 1.9291059970855713\n",
" 169 7.604523e+00 1.189675e-02\n",
" * time: 1.9389209747314453\n",
" 170 7.604501e+00 1.378389e-02\n",
" * time: 1.9489331245422363\n",
" 171 7.604466e+00 8.967032e-03\n",
" * time: 1.9618489742279053\n",
" 172 7.604447e+00 1.643008e-02\n",
" * time: 2.0028281211853027\n",
" 173 7.604417e+00 9.474755e-03\n",
" * time: 2.014698028564453\n",
" 174 7.604405e+00 1.378552e-02\n",
" * time: 2.0235280990600586\n",
" 175 7.604393e+00 1.322419e-02\n",
" * time: 2.032357931137085\n",
" 176 7.604384e+00 1.681210e-02\n",
" * time: 2.0411179065704346\n",
" 177 7.604361e+00 1.550413e-02\n",
" * time: 2.0499320030212402\n",
" 178 7.604349e+00 1.334120e-02\n",
" * time: 2.0586941242218018\n",
" 179 7.604330e+00 1.580802e-02\n",
" * time: 2.0675010681152344\n",
" 180 7.604291e+00 1.215444e-02\n",
" * time: 2.0762939453125\n",
" 181 7.604270e+00 1.886301e-02\n",
" * time: 2.084980010986328\n",
" 182 7.604248e+00 1.732085e-02\n",
" * time: 2.0937130451202393\n",
" 183 7.604194e+00 1.556568e-02\n",
" * time: 2.105380058288574\n",
" 184 7.604163e+00 1.463800e-02\n",
" * time: 2.114206075668335\n",
" 185 7.604133e+00 1.775350e-02\n",
" * time: 2.1258420944213867\n",
" 186 7.604099e+00 1.001496e-02\n",
" * time: 2.1375460624694824\n",
" 187 7.604066e+00 7.685736e-03\n",
" * time: 2.149385929107666\n",
" 188 7.604047e+00 8.924950e-03\n",
" * time: 2.158590078353882\n",
" 189 7.604029e+00 6.323236e-03\n",
" * time: 2.170898914337158\n",
" 190 7.604024e+00 9.338043e-03\n",
" * time: 2.1800179481506348\n",
" 191 7.604012e+00 1.136305e-02\n",
" * time: 2.189276933670044\n",
" 192 7.603992e+00 1.029057e-02\n",
" * time: 2.198496103286743\n",
" 193 7.603987e+00 1.091054e-02\n",
" * time: 2.207705020904541\n",
" 194 7.603969e+00 1.199465e-02\n",
" * time: 2.216926097869873\n",
" 195 7.603939e+00 1.348590e-02\n",
" * time: 2.2261669635772705\n",
" 196 7.603932e+00 8.823553e-03\n",
" * time: 2.2356419563293457\n",
" 197 7.603895e+00 8.155785e-03\n",
" * time: 2.2454020977020264\n",
" 198 7.603884e+00 2.372553e-02\n",
" * time: 2.255002021789551\n",
" 199 7.603838e+00 1.636150e-02\n",
" * time: 2.2647290229797363\n",
" 200 7.603828e+00 1.162792e-02\n",
" * time: 2.2744860649108887\n",
" 201 7.603823e+00 1.491861e-02\n",
" * time: 2.284147024154663\n",
" 202 7.603798e+00 1.282482e-02\n",
" * time: 2.2970879077911377\n",
" 203 7.603790e+00 1.670479e-02\n",
" * time: 2.3068559169769287\n",
" 204 7.603744e+00 1.519446e-02\n",
" * time: 2.319643020629883\n",
" 205 7.603740e+00 1.964022e-02\n",
" * time: 2.329369068145752\n",
" 206 7.603699e+00 2.262660e-02\n",
" * time: 2.339282989501953\n",
" 207 7.603640e+00 1.417637e-02\n",
" * time: 2.35246205329895\n",
" 208 7.603600e+00 1.605070e-02\n",
" * time: 2.362337112426758\n",
" 209 7.603551e+00 1.112042e-02\n",
" * time: 2.3751261234283447\n",
" 210 7.603540e+00 1.697648e-02\n",
" * time: 2.38496994972229\n",
" 211 7.603507e+00 1.247357e-02\n",
" * time: 2.3978030681610107\n",
" 212 7.603480e+00 1.139893e-02\n",
" * time: 2.410754919052124\n",
" 213 7.603454e+00 1.328567e-02\n",
" * time: 2.4205009937286377\n",
" 214 7.603410e+00 1.564419e-02\n",
" * time: 2.4644908905029297\n",
" 215 7.603395e+00 2.244253e-02\n",
" * time: 2.4734909534454346\n",
" 216 7.603358e+00 1.187735e-02\n",
" * time: 2.4852240085601807\n",
" 217 7.603338e+00 1.192945e-02\n",
" * time: 2.4940450191497803\n",
" 218 7.603304e+00 1.301269e-02\n",
" * time: 2.502798080444336\n",
" 219 7.603294e+00 1.648888e-02\n",
" * time: 2.5116209983825684\n",
" 220 7.603283e+00 1.490564e-02\n",
" * time: 2.520282030105591\n",
" 221 7.603255e+00 1.490893e-02\n",
" * time: 2.5318639278411865\n",
" 222 7.603232e+00 9.751160e-03\n",
" * time: 2.5433859825134277\n",
" 223 7.603219e+00 1.170834e-02\n",
" * time: 2.5521600246429443\n",
" 224 7.603192e+00 1.277754e-02\n",
" * time: 2.563755989074707\n",
" 225 7.603177e+00 1.174417e-02\n",
" * time: 2.5725018978118896\n",
" 226 7.603168e+00 1.407575e-02\n",
" * time: 2.5813310146331787\n",
" 227 7.603158e+00 9.410011e-03\n",
" * time: 2.5901060104370117\n",
" 228 7.603148e+00 1.438652e-02\n",
" * time: 2.5991721153259277\n",
" 229 7.603131e+00 1.209288e-02\n",
" * time: 2.611370086669922\n",
" 230 7.603114e+00 1.311686e-02\n",
" * time: 2.620457887649536\n",
" 231 7.603091e+00 1.074913e-02\n",
" * time: 2.632427930831909\n",
" 232 7.603069e+00 1.004680e-02\n",
" * time: 2.6415209770202637\n",
" 233 7.603053e+00 1.040856e-02\n",
" * time: 2.6506659984588623\n",
" 234 7.603049e+00 1.232012e-02\n",
" * time: 2.6598620414733887\n",
" 235 7.603034e+00 1.053043e-02\n",
" * time: 2.669128894805908\n",
" 236 7.603010e+00 1.345531e-02\n",
" * time: 2.6784260272979736\n",
" 237 7.602984e+00 1.216045e-02\n",
" * time: 2.6909399032592773\n",
" 238 7.602959e+00 8.631026e-03\n",
" * time: 2.7037899494171143\n",
" 239 7.602933e+00 6.136671e-03\n",
" * time: 2.7168209552764893\n",
" 240 7.602912e+00 7.608303e-03\n",
" * time: 2.7267799377441406\n",
" 241 7.602890e+00 7.085789e-03\n",
" * time: 2.7397210597991943\n",
" 242 7.602879e+00 7.595562e-03\n",
" * time: 2.7494099140167236\n",
" 243 7.602859e+00 1.211725e-02\n",
" * time: 2.7590830326080322\n",
" 244 7.602837e+00 6.497561e-03\n",
" * time: 2.7719619274139404\n",
" 245 7.602813e+00 6.722600e-03\n",
" * time: 2.784881114959717\n",
" 246 7.602800e+00 7.333481e-03\n",
" * time: 2.7948150634765625\n",
" 247 7.602782e+00 8.378259e-03\n",
" * time: 2.8044838905334473\n",
" 248 7.602766e+00 8.277066e-03\n",
" * time: 2.814276933670044\n",
" 249 7.602751e+00 5.842592e-03\n",
" * time: 2.8272531032562256\n",
" 250 7.602739e+00 6.189387e-03\n",
" * time: 2.8370730876922607\n",
" 251 7.602728e+00 4.304538e-03\n",
" * time: 2.850253105163574\n",
" 252 7.602718e+00 6.948819e-03\n",
" * time: 2.8601040840148926\n",
" 253 7.602711e+00 8.552319e-03\n",
" * time: 2.869892120361328\n",
" 254 7.602711e+00 1.326443e-02\n",
" * time: 2.8797109127044678\n",
" 255 7.602696e+00 4.785539e-03\n",
" * time: 2.9209139347076416\n",
" 256 7.602694e+00 1.154981e-02\n",
" * time: 2.9301071166992188\n",
" 257 7.602683e+00 1.096910e-02\n",
" * time: 2.9389500617980957\n",
" 258 7.602668e+00 9.013274e-03\n",
" * time: 2.9478859901428223\n",
" 259 7.602654e+00 7.238498e-03\n",
" * time: 2.959486961364746\n",
" 260 7.602641e+00 9.201631e-03\n",
" * time: 2.9682140350341797\n",
" 261 7.602640e+00 1.090358e-02\n",
" * time: 2.9770169258117676\n",
" 262 7.602631e+00 9.745874e-03\n",
" * time: 2.985766887664795\n",
" 263 7.602619e+00 1.247895e-02\n",
" * time: 2.9946420192718506\n",
" 264 7.602600e+00 1.043036e-02\n",
" * time: 3.0062880516052246\n",
" 265 7.602579e+00 1.235685e-02\n",
" * time: 3.01820707321167\n",
" 266 7.602570e+00 1.689629e-02\n",
" * time: 3.0269811153411865\n",
" 267 7.602517e+00 1.082138e-02\n",
" * time: 3.0386040210723877\n",
" 268 7.602483e+00 1.264261e-02\n",
" * time: 3.047513008117676\n",
" 269 7.602454e+00 1.130792e-02\n",
" * time: 3.060067892074585\n",
" 270 7.602417e+00 1.505659e-02\n",
" * time: 3.0692789554595947\n",
" 271 7.602382e+00 1.305829e-02\n",
" * time: 3.081265926361084\n",
" 272 7.602347e+00 1.936061e-02\n",
" * time: 3.093337059020996\n",
" 273 7.602323e+00 2.239616e-02\n",
" * time: 3.1026179790496826\n",
" 274 7.602253e+00 2.887275e-02\n",
" * time: 3.111785888671875\n",
" 275 7.602198e+00 2.636830e-02\n",
" * time: 3.124008893966675\n",
" 276 7.602138e+00 2.180380e-02\n",
" * time: 3.1361849308013916\n",
" 277 7.602106e+00 2.194599e-02\n",
" * time: 3.148715019226074\n",
" 278 7.602035e+00 1.661420e-02\n",
" * time: 3.1615869998931885\n",
" 279 7.601967e+00 1.608810e-02\n",
" * time: 3.174489974975586\n",
" 280 7.601881e+00 2.140315e-02\n",
" * time: 3.18416690826416\n",
" 281 7.601760e+00 1.985140e-02\n",
" * time: 3.1939890384674072\n",
" 282 7.601689e+00 1.404572e-02\n",
" * time: 3.206860065460205\n",
" 283 7.601671e+00 1.870529e-02\n",
" * time: 3.216625928878784\n",
" 284 7.601617e+00 2.400773e-02\n",
" * time: 3.2262449264526367\n",
" 285 7.601552e+00 2.905163e-02\n",
" * time: 3.2359659671783447\n",
" 286 7.601460e+00 2.165801e-02\n",
" * time: 3.2457149028778076\n",
" 287 7.601313e+00 2.497425e-02\n",
" * time: 3.2554380893707275\n",
" 288 7.601191e+00 2.063394e-02\n",
" * time: 3.2681379318237305\n",
" 289 7.601165e+00 2.598575e-02\n",
" * time: 3.277941942214966\n",
" 290 7.601154e+00 3.374985e-02\n",
" * time: 3.287677049636841\n",
" 291 7.601002e+00 2.817131e-02\n",
" * time: 3.2974979877471924\n",
" 292 7.600984e+00 3.100217e-02\n",
" * time: 3.3072750568389893\n",
" 293 7.600907e+00 2.860326e-02\n",
" * time: 3.317244052886963\n",
" 294 7.600753e+00 3.375668e-02\n",
" * time: 3.3302600383758545\n",
" 295 7.600544e+00 2.310708e-02\n",
" * time: 3.3400111198425293\n",
" 296 7.600486e+00 2.956915e-02\n",
" * time: 3.3811779022216797\n",
" 297 7.600389e+00 2.824945e-02\n",
" * time: 3.390315055847168\n",
" 298 7.600348e+00 3.479060e-02\n",
" * time: 3.3991169929504395\n",
" 299 7.600244e+00 3.881410e-02\n",
" * time: 3.4079160690307617\n",
" 300 7.600093e+00 3.185301e-02\n",
" * time: 3.4194979667663574\n",
" 301 7.599864e+00 1.748742e-02\n",
" * time: 3.4311180114746094\n",
" 302 7.599742e+00 2.494470e-02\n",
" * time: 3.4399020671844482\n",
" 303 7.599567e+00 2.253750e-02\n",
" * time: 3.4515140056610107\n",
" 304 7.599456e+00 1.256655e-02\n",
" * time: 3.463089942932129\n",
" 305 7.599411e+00 1.690332e-02\n",
" * time: 3.471951961517334\n",
" 306 7.599296e+00 1.538068e-02\n",
" * time: 3.480778932571411\n",
" 307 7.599236e+00 2.368510e-02\n",
" * time: 3.4894580841064453\n",
" 308 7.599171e+00 2.580510e-02\n",
" * time: 3.4982380867004395\n",
" 309 7.599129e+00 4.112526e-02\n",
" * time: 3.5070300102233887\n",
" 310 7.599047e+00 3.146344e-02\n",
" * time: 3.516123056411743\n",
" 311 7.598871e+00 3.227715e-02\n",
" * time: 3.5253989696502686\n",
" 312 7.598575e+00 2.473981e-02\n",
" * time: 3.534795045852661\n",
" 313 7.598324e+00 3.578868e-02\n",
" * time: 3.5438849925994873\n",
" 314 7.598310e+00 4.566215e-02\n",
" * time: 3.553041934967041\n",
" 315 7.598122e+00 2.637006e-02\n",
" * time: 3.5621559619903564\n",
" 316 7.597854e+00 2.853247e-02\n",
" * time: 3.5742440223693848\n",
" 317 7.597697e+00 4.394871e-02\n",
" * time: 3.583591938018799\n",
" 318 7.597520e+00 3.042377e-02\n",
" * time: 3.5928120613098145\n",
" 319 7.597241e+00 3.237831e-02\n",
" * time: 3.6021010875701904\n",
" 320 7.597036e+00 2.380645e-02\n",
" * time: 3.6146790981292725\n",
" 321 7.597016e+00 4.428527e-02\n",
" * time: 3.6244630813598633\n",
" 322 7.596927e+00 3.083468e-02\n",
" * time: 3.634300947189331\n",
" 323 7.596714e+00 2.563071e-02\n",
" * time: 3.643911123275757\n",
" 324 7.596545e+00 3.428291e-02\n",
" * time: 3.6536829471588135\n",
" 325 7.596362e+00 2.300933e-02\n",
" * time: 3.6665689945220947\n",
" 326 7.596343e+00 3.005302e-02\n",
" * time: 3.676269054412842\n",
" 327 7.596242e+00 2.576625e-02\n",
" * time: 3.6859920024871826\n",
" 328 7.596239e+00 3.101523e-02\n",
" * time: 3.6957459449768066\n",
" 329 7.596223e+00 2.297109e-02\n",
" * time: 3.705441951751709\n",
" 330 7.596144e+00 1.704902e-02\n",
" * time: 3.715204954147339\n",
" 331 7.596081e+00 1.674268e-02\n",
" * time: 3.724848985671997\n",
" 332 7.596045e+00 2.777442e-02\n",
" * time: 3.734637975692749\n",
" 333 7.596020e+00 2.342090e-02\n",
" * time: 3.7443389892578125\n",
" 334 7.595976e+00 1.803131e-02\n",
" * time: 3.7540690898895264\n",
" 335 7.595912e+00 1.501865e-02\n",
" * time: 3.7637929916381836\n",
" 336 7.595853e+00 2.393060e-02\n",
" * time: 3.77354097366333\n",
" 337 7.595774e+00 1.136574e-02\n",
" * time: 3.7863049507141113\n",
" 338 7.595748e+00 2.100673e-02\n",
" * time: 3.7961580753326416\n",
" 339 7.595701e+00 1.318760e-02\n",
" * time: 3.840725898742676\n",
" 340 7.595662e+00 1.052936e-02\n",
" * time: 3.8525500297546387\n",
" 341 7.595627e+00 9.041211e-03\n",
" * time: 3.8643710613250732\n",
" 342 7.595613e+00 1.596107e-02\n",
" * time: 3.8732869625091553\n",
" 343 7.595579e+00 1.223803e-02\n",
" * time: 3.884953022003174\n",
" 344 7.595537e+00 1.520004e-02\n",
" * time: 3.8940200805664062\n",
" 345 7.595516e+00 1.443503e-02\n",
" * time: 3.9027581214904785\n",
" 346 7.595483e+00 1.373488e-02\n",
" * time: 3.9115331172943115\n",
" 347 7.595434e+00 1.270183e-02\n",
" * time: 3.9201269149780273\n",
" 348 7.595386e+00 1.783785e-02\n",
" * time: 3.9289989471435547\n",
" 349 7.595370e+00 3.146141e-02\n",
" * time: 3.937875986099243\n",
" 350 7.595295e+00 1.780111e-02\n",
" * time: 3.9466400146484375\n",
" 351 7.595231e+00 2.092296e-02\n",
" * time: 3.9554619789123535\n",
" 352 7.595208e+00 2.660733e-02\n",
" * time: 3.9642679691314697\n",
" 353 7.595133e+00 2.109035e-02\n",
" * time: 3.975861072540283\n",
" 354 7.595091e+00 1.893761e-02\n",
" * time: 3.984808921813965\n",
" 355 7.595017e+00 1.604037e-02\n",
" * time: 3.9970180988311768\n",
" 356 7.594956e+00 1.293477e-02\n",
" * time: 4.009113073348999\n",
" 357 7.594904e+00 1.808969e-02\n",
" * time: 4.018378973007202\n",
" 358 7.594853e+00 1.858039e-02\n",
" * time: 4.027673959732056\n",
" 359 7.594818e+00 2.294824e-02\n",
" * time: 4.037117004394531\n",
" 360 7.594734e+00 1.462532e-02\n",
" * time: 4.049299955368042\n",
" 361 7.594682e+00 1.934193e-02\n",
" * time: 4.058629989624023\n",
" 362 7.594653e+00 2.501321e-02\n",
" * time: 4.067961931228638\n",
" 363 7.594597e+00 1.736596e-02\n",
" * time: 4.080883026123047\n",
" 364 7.594534e+00 1.308780e-02\n",
" * time: 4.090611934661865\n",
" 365 7.594487e+00 1.377003e-02\n",
" * time: 4.100481986999512\n",
" 366 7.594442e+00 1.765504e-02\n",
" * time: 4.110431909561157\n",
" 367 7.594421e+00 2.097161e-02\n",
" * time: 4.120074987411499\n",
" 368 7.594354e+00 2.166976e-02\n",
" * time: 4.130012035369873\n",
" 369 7.594320e+00 2.021827e-02\n",
" * time: 4.139777898788452\n",
" 370 7.594279e+00 2.468631e-02\n",
" * time: 4.149518013000488\n",
" 371 7.594229e+00 2.278888e-02\n",
" * time: 4.159159898757935\n",
" 372 7.594161e+00 1.889996e-02\n",
" * time: 4.168898105621338\n",
" 373 7.594112e+00 1.641527e-02\n",
" * time: 4.178692102432251\n",
" 374 7.594112e+00 3.159993e-02\n",
" * time: 4.188417911529541\n",
" 375 7.594049e+00 2.178060e-02\n",
" * time: 4.201427936553955\n",
" 376 7.594011e+00 1.614525e-02\n",
" * time: 4.21114706993103\n",
" 377 7.593947e+00 2.104274e-02\n",
" * time: 4.223963022232056\n",
" 378 7.593907e+00 8.980192e-03\n",
" * time: 4.2369160652160645\n",
" 379 7.593880e+00 1.103577e-02\n",
" * time: 4.24665904045105\n",
" 380 7.593875e+00 1.887837e-02\n",
" * time: 4.256398916244507\n",
" 381 7.593837e+00 1.247712e-02\n",
" * time: 4.300352096557617\n",
" 382 7.593825e+00 1.481823e-02\n",
" * time: 4.309344053268433\n",
" 383 7.593791e+00 1.824779e-02\n",
" * time: 4.318031072616577\n",
" 384 7.593755e+00 1.692344e-02\n",
" * time: 4.32689905166626\n",
" 385 7.593750e+00 2.276148e-02\n",
" * time: 4.335663080215454\n",
" 386 7.593729e+00 2.229608e-02\n",
" * time: 4.344280958175659\n",
" 387 7.593704e+00 1.563635e-02\n",
" * time: 4.353125095367432\n",
" 388 7.593634e+00 1.273050e-02\n",
" * time: 4.361804008483887\n",
" 389 7.593569e+00 1.392164e-02\n",
" * time: 4.370595932006836\n",
" 390 7.593522e+00 1.723043e-02\n",
" * time: 4.379470109939575\n",
" 391 7.593480e+00 9.321325e-03\n",
" * time: 4.391181945800781\n",
" 392 7.593461e+00 1.640120e-02\n",
" * time: 4.399971008300781\n",
" 393 7.593432e+00 1.498716e-02\n",
" * time: 4.411499977111816\n",
" 394 7.593408e+00 1.111439e-02\n",
" * time: 4.42038893699646\n",
" 395 7.593391e+00 1.604840e-02\n",
" * time: 4.429321050643921\n",
" 396 7.593340e+00 1.960804e-02\n",
" * time: 4.441320896148682\n",
" 397 7.593312e+00 2.574316e-02\n",
" * time: 4.450484037399292\n",
" 398 7.593264e+00 2.260387e-02\n",
" * time: 4.459635019302368\n",
" 399 7.593202e+00 2.354532e-02\n",
" * time: 4.468825101852417\n",
" 400 7.593143e+00 2.133190e-02\n",
" * time: 4.478231906890869\n",
" 401 7.593103e+00 2.793262e-02\n",
" * time: 4.4876549243927\n",
" 402 7.593060e+00 2.172745e-02\n",
" * time: 4.4999449253082275\n",
" 403 7.592983e+00 1.564724e-02\n",
" * time: 4.5121378898620605\n",
" 404 7.592928e+00 1.609697e-02\n",
" * time: 4.521260976791382\n",
" 405 7.592921e+00 2.030494e-02\n",
" * time: 4.530972003936768\n",
" 406 7.592892e+00 1.560455e-02\n",
" * time: 4.540647983551025\n",
" 407 7.592853e+00 1.396382e-02\n",
" * time: 4.553520917892456\n",
" 408 7.592813e+00 1.281235e-02\n",
" * time: 4.5663440227508545\n",
" 409 7.592765e+00 1.037150e-02\n",
" * time: 4.57918906211853\n",
" 410 7.592763e+00 2.205158e-02\n",
" * time: 4.588956117630005\n",
" 411 7.592734e+00 1.866307e-02\n",
" * time: 4.59868597984314\n",
" 412 7.592729e+00 2.521551e-02\n",
" * time: 4.6085569858551025\n",
" 413 7.592700e+00 1.498748e-02\n",
" * time: 4.621575117111206\n",
" 414 7.592690e+00 1.520258e-02\n",
" * time: 4.631542921066284\n",
" 415 7.592654e+00 1.341266e-02\n",
" * time: 4.6413350105285645\n",
" 416 7.592645e+00 2.092474e-02\n",
" * time: 4.650995969772339\n",
" 417 7.592618e+00 1.547482e-02\n",
" * time: 4.660833120346069\n",
" 418 7.592614e+00 2.109676e-02\n",
" * time: 4.670553922653198\n",
" 419 7.592591e+00 1.351353e-02\n",
" * time: 4.683409929275513\n",
" 420 7.592566e+00 1.249484e-02\n",
" * time: 4.693144083023071\n",
" 421 7.592540e+00 1.018641e-02\n",
" * time: 4.706105947494507\n",
" 422 7.592532e+00 1.223752e-02\n",
" * time: 4.715807914733887\n",
" 423 7.592517e+00 8.304211e-03\n",
" * time: 4.759813070297241\n",
" 424 7.592505e+00 9.079048e-03\n",
" * time: 4.768728971481323\n",
" 425 7.592491e+00 8.283963e-03\n",
" * time: 4.780416965484619\n",
" 426 7.592484e+00 8.080636e-03\n",
" * time: 4.789212942123413\n",
" 427 7.592480e+00 8.947962e-03\n",
" * time: 4.7980101108551025\n",
" 428 7.592466e+00 9.663725e-03\n",
" * time: 4.806731939315796\n",
" 429 7.592448e+00 7.194001e-03\n",
" * time: 4.818300008773804\n",
" 430 7.592444e+00 8.302991e-03\n",
" * time: 4.827141046524048\n",
" 431 7.592427e+00 1.020154e-02\n",
" * time: 4.835989952087402\n",
" 432 7.592426e+00 8.747969e-03\n",
" * time: 4.844785928726196\n",
" 433 7.592412e+00 7.330739e-03\n",
" * time: 4.856379985809326\n",
" 434 7.592410e+00 1.135692e-02\n",
" * time: 4.865123987197876\n",
" 435 7.592403e+00 9.236657e-03\n",
" * time: 4.873826026916504\n",
" 436 7.592393e+00 7.070824e-03\n",
" * time: 4.882528066635132\n",
" 437 7.592385e+00 5.401047e-03\n",
" * time: 4.894408941268921\n",
" 438 7.592378e+00 3.773982e-03\n",
" * time: 4.906470060348511\n",
" 439 7.592371e+00 4.913462e-03\n",
" * time: 4.915544033050537\n",
" 440 7.592371e+00 7.493474e-03\n",
" * time: 4.924777030944824\n",
" 441 7.592369e+00 6.332865e-03\n",
" * time: 4.934017896652222\n",
" 442 7.592366e+00 6.061542e-03\n",
" * time: 4.943247079849243\n",
" 443 7.592361e+00 2.920183e-03\n",
" * time: 4.955476999282837\n",
" 444 7.592358e+00 5.896661e-03\n",
" * time: 4.964792966842651\n",
" 445 7.592355e+00 4.274751e-03\n",
" * time: 4.976959943771362\n",
" 446 7.592352e+00 3.006875e-03\n",
" * time: 4.989557981491089\n",
" 447 7.592350e+00 3.741405e-03\n",
" * time: 4.999213933944702\n",
" 448 7.592348e+00 2.869180e-03\n",
" * time: 5.009023904800415\n",
" 449 7.592346e+00 2.457786e-03\n",
" * time: 5.018950939178467\n",
" 450 7.592345e+00 3.616645e-03\n",
" * time: 5.028742074966431\n",
" 451 7.592344e+00 2.485592e-03\n",
" * time: 5.0415990352630615\n",
" 452 7.592343e+00 3.123882e-03\n",
" * time: 5.0511860847473145\n",
" 453 7.592341e+00 2.364690e-03\n",
" * time: 5.060987949371338\n",
" 454 7.592340e+00 2.255514e-03\n",
" * time: 5.074065923690796\n",
" 455 7.592339e+00 1.727282e-03\n",
" * time: 5.087038993835449\n",
" 456 7.592338e+00 2.048835e-03\n",
" * time: 5.096975088119507\n",
" 457 7.592338e+00 2.170625e-03\n",
" * time: 5.106727123260498\n",
" 458 7.592337e+00 1.730047e-03\n",
" * time: 5.119596004486084\n",
" 459 7.592337e+00 1.962076e-03\n",
" * time: 5.129317998886108\n",
" 460 7.592336e+00 1.627901e-03\n",
" * time: 5.139055967330933\n",
" 461 7.592336e+00 2.095592e-03\n",
" * time: 5.149046897888184\n",
" 462 7.592335e+00 1.819989e-03\n",
" * time: 5.158703088760376\n",
" 463 7.592335e+00 2.041779e-03\n",
" * time: 5.168447971343994\n",
" 464 7.592335e+00 1.559972e-03\n",
" * time: 5.209891080856323\n",
" 465 7.592334e+00 1.502821e-03\n",
" * time: 5.219028949737549\n",
" 466 7.592334e+00 1.437800e-03\n",
" * time: 5.227859973907471\n",
" 467 7.592333e+00 1.949373e-03\n",
" * time: 5.236726999282837\n",
" 468 7.592333e+00 1.196632e-03\n",
" * time: 5.2483789920806885\n",
" 469 7.592332e+00 1.454682e-03\n",
" * time: 5.257167100906372\n",
" 470 7.592332e+00 9.125931e-04\n",
" * time: 5.268656969070435\n",
" 471 7.592331e+00 7.501192e-04\n",
" * time: 5.280106067657471\n",
" 472 7.592331e+00 1.159463e-03\n",
" * time: 5.288991928100586\n",
" 473 7.592331e+00 1.243092e-03\n",
" * time: 5.297919034957886\n",
" 474 7.592331e+00 9.554176e-04\n",
" * time: 5.309523105621338\n",
" 475 7.592331e+00 1.225489e-03\n",
" * time: 5.318265914916992\n",
" 476 7.592331e+00 1.054291e-03\n",
" * time: 5.327164888381958\n",
" 477 7.592330e+00 1.504981e-03\n",
" * time: 5.3359150886535645\n",
" 478 7.592330e+00 1.009481e-03\n",
" * time: 5.344696998596191\n",
" 479 7.592330e+00 1.180422e-03\n",
" * time: 5.353562116622925\n",
" 480 7.592330e+00 1.143505e-03\n",
" * time: 5.3628270626068115\n",
" 481 7.592329e+00 1.396141e-03\n",
" * time: 5.372052907943726\n",
" 482 7.592329e+00 1.337683e-03\n",
" * time: 5.381311893463135\n",
" 483 7.592329e+00 8.382808e-04\n",
" * time: 5.393502950668335\n",
" 484 7.592329e+00 6.514706e-04\n",
" * time: 5.405740976333618\n",
" 485 7.592328e+00 9.864539e-04\n",
" * time: 5.41497802734375\n",
" 486 7.592328e+00 4.808101e-04\n",
" * time: 5.427232980728149\n",
" 487 7.592328e+00 9.591372e-04\n",
" * time: 5.436336040496826\n",
" 488 7.592328e+00 9.781714e-04\n",
" * time: 5.445810079574585\n",
" 489 7.592328e+00 1.251503e-03\n",
" * time: 5.45555305480957\n",
" 490 7.592328e+00 7.679474e-04\n",
" * time: 5.465156078338623\n",
" 491 7.592328e+00 8.659455e-04\n",
" * time: 5.474786996841431\n",
" 492 7.592328e+00 9.779491e-04\n",
" * time: 5.484482049942017\n",
" 493 7.592328e+00 7.170241e-04\n",
" * time: 5.494213104248047\n",
" 494 7.592328e+00 5.367899e-04\n",
" * time: 5.50383996963501\n",
" 495 7.592328e+00 9.546729e-04\n",
" * time: 5.513556003570557\n",
" 496 7.592327e+00 6.522341e-04\n",
" * time: 5.523233890533447\n",
" 497 7.592327e+00 1.082971e-03\n",
" * time: 5.533021926879883\n",
" 498 7.592327e+00 8.094269e-04\n",
" * time: 5.5459229946136475\n",
" 499 7.592327e+00 1.185019e-03\n",
" * time: 5.55560302734375\n",
" 500 7.592327e+00 7.501806e-04\n",
" * time: 5.568403005599976\n",
" 501 7.592327e+00 6.529665e-04\n",
" * time: 5.581425905227661\n",
" 502 7.592327e+00 5.961661e-04\n",
" * time: 5.59437108039856\n",
" 503 7.592327e+00 9.801370e-04\n",
" * time: 5.604233026504517\n",
" 504 7.592327e+00 5.670885e-04\n",
" * time: 5.617047071456909\n",
" 505 7.592327e+00 7.441720e-04\n",
" * time: 5.626878976821899\n",
" 506 7.592327e+00 4.550668e-04\n",
" * time: 5.671191930770874\n",
" 507 7.592327e+00 7.059030e-04\n",
" * time: 5.680143117904663\n",
" 508 7.592327e+00 4.104881e-04\n",
" * time: 5.689081907272339\n",
" 509 7.592327e+00 6.392020e-04\n",
" * time: 5.698200941085815\n",
" 510 7.592327e+00 9.700262e-04\n",
" * time: 5.707016944885254\n",
" 511 7.592326e+00 7.792334e-04\n",
" * time: 5.715724945068359\n",
" 512 7.592326e+00 1.119517e-03\n",
" * time: 5.724883079528809\n",
" 513 7.592326e+00 1.258885e-03\n",
" * time: 5.733505964279175\n",
" 514 7.592326e+00 5.519868e-04\n",
" * time: 5.744997978210449\n",
" 515 7.592326e+00 7.762452e-04\n",
" * time: 5.753850936889648\n",
" 516 7.592326e+00 4.938860e-04\n",
" * time: 5.762639999389648\n",
" 517 7.592326e+00 6.062477e-04\n",
" * time: 5.771485090255737\n",
" 518 7.592326e+00 7.284044e-04\n",
" * time: 5.78027606010437\n",
" 519 7.592326e+00 5.350015e-04\n",
" * time: 5.791903018951416\n",
" 520 7.592326e+00 9.267055e-04\n",
" * time: 5.800689935684204\n",
" 521 7.592326e+00 5.344616e-04\n",
" * time: 5.812412977218628\n",
" 522 7.592326e+00 8.578093e-04\n",
" * time: 5.8214709758758545\n",
" 523 7.592326e+00 1.357936e-03\n",
" * time: 5.8306920528411865\n",
" 524 7.592325e+00 8.061516e-04\n",
" * time: 5.842741012573242\n",
" 525 7.592325e+00 9.712815e-04\n",
" * time: 5.8518640995025635\n",
" 526 7.592325e+00 8.248700e-04\n",
" * time: 5.861193895339966\n",
" 527 7.592325e+00 6.508819e-04\n",
" * time: 5.870413064956665\n",
" 528 7.592325e+00 1.316635e-03\n",
" * time: 5.879657030105591\n",
" 529 7.592325e+00 1.121573e-03\n",
" * time: 5.8889360427856445\n",
" 530 7.592325e+00 7.700161e-04\n",
" * time: 5.901305913925171\n",
" 531 7.592325e+00 1.036684e-03\n",
" * time: 5.914150953292847\n",
" 532 7.592325e+00 9.291447e-04\n",
" * time: 5.9237449169158936\n",
" 533 7.592325e+00 1.177647e-03\n",
" * time: 5.933551073074341\n",
" 534 7.592324e+00 9.559855e-04\n",
" * time: 5.946425914764404\n",
" 535 7.592324e+00 1.232605e-03\n",
" * time: 5.9563539028167725\n",
" 536 7.592324e+00 7.672271e-04\n",
" * time: 5.969274997711182\n",
" 537 7.592324e+00 5.012191e-04\n",
" * time: 5.982131004333496\n",
" 538 7.592324e+00 6.505304e-04\n",
" * time: 5.991950988769531\n",
" 539 7.592324e+00 3.390358e-04\n",
" * time: 6.005017995834351\n",
" 540 7.592324e+00 2.552939e-04\n",
" * time: 6.01774001121521\n",
" 541 7.592324e+00 3.761909e-04\n",
" * time: 6.027425050735474\n",
" 542 7.592324e+00 5.943432e-04\n",
" * time: 6.037230968475342\n",
" 543 7.592324e+00 8.264915e-04\n",
" * time: 6.046969890594482\n",
" 544 7.592323e+00 1.001665e-03\n",
" * time: 6.0566489696502686\n",
" 545 7.592323e+00 1.114243e-03\n",
" * time: 6.06644606590271\n",
" 546 7.592323e+00 1.049214e-03\n",
" * time: 6.076236009597778\n",
" 547 7.592323e+00 1.063977e-03\n",
" * time: 6.085987091064453\n",
" 548 7.592323e+00 1.537692e-03\n",
" * time: 6.127165079116821\n",
" 549 7.592323e+00 1.234097e-03\n",
" * time: 6.136106014251709\n",
" 550 7.592322e+00 1.225870e-03\n",
" * time: 6.144830942153931\n",
" 551 7.592322e+00 1.164343e-03\n",
" * time: 6.15359902381897\n",
" 552 7.592322e+00 1.227824e-03\n",
" * time: 6.162276983261108\n",
" 553 7.592322e+00 9.446011e-04\n",
" * time: 6.17098593711853\n",
" 554 7.592322e+00 1.124422e-03\n",
" * time: 6.179795026779175\n",
" 555 7.592321e+00 8.848509e-04\n",
" * time: 6.191364049911499\n",
" 556 7.592321e+00 1.325449e-03\n",
" * time: 6.200123071670532\n",
" 557 7.592321e+00 7.469741e-04\n",
" * time: 6.2116169929504395\n",
" 558 7.592321e+00 1.149620e-03\n",
" * time: 6.220439910888672\n",
" 559 7.592320e+00 7.171785e-04\n",
" * time: 6.232008934020996\n",
" 560 7.592320e+00 1.308065e-03\n",
" * time: 6.240684986114502\n",
" 561 7.592320e+00 9.923394e-04\n",
" * time: 6.252180099487305\n",
" 562 7.592320e+00 9.186575e-04\n",
" * time: 6.263736009597778\n",
" 563 7.592320e+00 1.272761e-03\n",
" * time: 6.272619962692261\n",
" 564 7.592320e+00 7.612571e-04\n",
" * time: 6.28172492980957\n",
" 565 7.592319e+00 7.237127e-04\n",
" * time: 6.290860891342163\n",
" 566 7.592319e+00 1.262472e-03\n",
" * time: 6.300031900405884\n",
" 567 7.592319e+00 1.064429e-03\n",
" * time: 6.309211015701294\n",
" 568 7.592319e+00 1.191268e-03\n",
" * time: 6.318428039550781\n",
" 569 7.592319e+00 1.149823e-03\n",
" * time: 6.327678918838501\n",
" 570 7.592319e+00 1.088151e-03\n",
" * time: 6.336900949478149\n",
" 571 7.592319e+00 6.737654e-04\n",
" * time: 6.349281072616577\n",
" 572 7.592318e+00 9.255690e-04\n",
" * time: 6.358701944351196\n",
" 573 7.592318e+00 7.262259e-04\n",
" * time: 6.368396997451782\n",
" 574 7.592318e+00 4.846294e-04\n",
" * time: 6.381277084350586\n",
" 575 7.592318e+00 1.159499e-03\n",
" * time: 6.390894889831543\n",
" 576 7.592318e+00 7.718043e-04\n",
" * time: 6.400695085525513\n",
" 577 7.592318e+00 1.871600e-03\n",
" * time: 6.410484075546265\n",
" 578 7.592318e+00 1.894727e-03\n",
" * time: 6.420233964920044\n",
" 579 7.592317e+00 1.687998e-03\n",
" * time: 6.4331440925598145\n",
" 580 7.592316e+00 8.586119e-04\n",
" * time: 6.445894956588745\n",
" 581 7.592316e+00 1.063838e-03\n",
" * time: 6.455600023269653\n",
" 582 7.592316e+00 1.508208e-03\n",
" * time: 6.465229034423828\n",
" 583 7.592315e+00 1.093277e-03\n",
" * time: 6.4750049114227295\n",
" 584 7.592315e+00 1.520590e-03\n",
" * time: 6.48478889465332\n",
" 585 7.592315e+00 1.609745e-03\n",
" * time: 6.494534969329834\n",
" 586 7.592314e+00 1.291360e-03\n",
" * time: 6.5073840618133545\n",
" 587 7.592314e+00 1.893526e-03\n",
" * time: 6.517067909240723\n",
" 588 7.592314e+00 1.319726e-03\n",
" * time: 6.530025005340576\n",
" 589 7.592313e+00 8.270000e-04\n",
" * time: 6.542897939682007\n",
" 590 7.592313e+00 1.337971e-03\n",
" * time: 6.584053993225098\n",
" 591 7.592313e+00 7.843867e-04\n",
" * time: 6.59597110748291\n",
" 592 7.592312e+00 1.004725e-03\n",
" * time: 6.605078935623169\n",
" 593 7.592312e+00 1.461998e-03\n",
" * time: 6.614120006561279\n",
" 594 7.592312e+00 2.404159e-03\n",
" * time: 6.6228179931640625\n",
" 595 7.592312e+00 2.179463e-03\n",
" * time: 6.6314849853515625\n",
" 596 7.592311e+00 1.328550e-03\n",
" * time: 6.643203973770142\n",
" 597 7.592311e+00 1.153270e-03\n",
" * time: 6.651928901672363\n",
" 598 7.592310e+00 1.448547e-03\n",
" * time: 6.660712003707886\n",
" 599 7.592310e+00 1.027454e-03\n",
" * time: 6.672194957733154\n",
" 600 7.592310e+00 1.456277e-03\n",
" * time: 6.681010961532593\n",
" 601 7.592310e+00 1.243354e-03\n",
" * time: 6.6897759437561035\n",
" 602 7.592310e+00 1.122124e-03\n",
" * time: 6.698492050170898\n",
" 603 7.592310e+00 1.022768e-03\n",
" * time: 6.707295894622803\n",
" 604 7.592309e+00 1.538068e-03\n",
" * time: 6.716093063354492\n",
" 605 7.592309e+00 1.610365e-03\n",
" * time: 6.724905014038086\n",
" 606 7.592309e+00 1.344360e-03\n",
" * time: 6.733966112136841\n",
" 607 7.592309e+00 9.973585e-04\n",
" * time: 6.74330997467041\n",
" 608 7.592309e+00 7.219773e-04\n",
" * time: 6.752471923828125\n",
" 609 7.592309e+00 1.052421e-03\n",
" * time: 6.761723041534424\n",
" 610 7.592309e+00 7.093293e-04\n",
" * time: 6.770914077758789\n",
" 611 7.592308e+00 8.741400e-04\n",
" * time: 6.783221960067749\n",
" 612 7.592308e+00 4.678143e-04\n",
" * time: 6.795396089553833\n",
" 613 7.592308e+00 5.332545e-04\n",
" * time: 6.807571887969971\n",
" 614 7.592308e+00 5.131612e-04\n",
" * time: 6.817116975784302\n",
" 615 7.592308e+00 8.223674e-04\n",
" * time: 6.826802015304565\n",
" 616 7.592308e+00 7.470239e-04\n",
" * time: 6.8397040367126465\n",
" 617 7.592308e+00 5.170166e-04\n",
" * time: 6.852629899978638\n",
" 618 7.592308e+00 6.266819e-04\n",
" * time: 6.862382888793945\n",
" 619 7.592308e+00 6.010936e-04\n",
" * time: 6.872162103652954\n",
" 620 7.592308e+00 5.094341e-04\n",
" * time: 6.882075071334839\n",
" 621 7.592308e+00 5.158477e-04\n",
" * time: 6.892052888870239\n",
" 622 7.592308e+00 5.330892e-04\n",
" * time: 6.901587009429932\n",
" 623 7.592308e+00 6.805574e-04\n",
" * time: 6.911298990249634\n",
" 624 7.592308e+00 7.116852e-04\n",
" * time: 6.921005010604858\n",
" 625 7.592308e+00 5.896968e-04\n",
" * time: 6.933785915374756\n",
" 626 7.592307e+00 2.527110e-04\n",
" * time: 6.94661808013916\n",
" 627 7.592307e+00 4.579147e-04\n",
" * time: 6.956408977508545\n",
" 628 7.592307e+00 5.030096e-04\n",
" * time: 6.966232061386108\n",
" 629 7.592307e+00 5.975834e-04\n",
" * time: 6.975974082946777\n",
" 630 7.592307e+00 8.096380e-04\n",
" * time: 6.985892057418823\n",
" 631 7.592307e+00 9.882606e-04\n",
" * time: 6.995687007904053\n",
" 632 7.592307e+00 5.392521e-04\n",
" * time: 7.039995908737183\n",
" 633 7.592307e+00 8.195765e-04\n",
" * time: 7.049139022827148\n",
" 634 7.592307e+00 1.191321e-03\n",
" * time: 7.057804107666016\n",
" 635 7.592307e+00 6.560508e-04\n",
" * time: 7.069370985031128\n",
" 636 7.592306e+00 8.355319e-04\n",
" * time: 7.0781331062316895\n",
" 637 7.592306e+00 1.058108e-03\n",
" * time: 7.086961984634399\n",
" 638 7.592306e+00 5.076497e-04\n",
" * time: 7.095710039138794\n",
" 639 7.592306e+00 8.435335e-04\n",
" * time: 7.104475975036621\n",
" 640 7.592306e+00 1.051932e-03\n",
" * time: 7.113246917724609\n",
" 641 7.592306e+00 6.611367e-04\n",
" * time: 7.12487006187439\n",
" 642 7.592306e+00 9.691595e-04\n",
" * time: 7.13359808921814\n",
" 643 7.592306e+00 7.725163e-04\n",
" * time: 7.142280101776123\n",
" 644 7.592306e+00 1.342541e-03\n",
" * time: 7.15104603767395\n",
" 645 7.592305e+00 7.297925e-04\n",
" * time: 7.162626028060913\n",
" 646 7.592305e+00 7.026027e-04\n",
" * time: 7.174267053604126\n",
" 647 7.592305e+00 8.022325e-04\n",
" * time: 7.183095932006836\n",
" 648 7.592305e+00 5.439403e-04\n",
" * time: 7.195167064666748\n",
" 649 7.592305e+00 8.556021e-04\n",
" * time: 7.204315900802612\n",
" 650 7.592305e+00 7.473927e-04\n",
" * time: 7.216418027877808\n",
" 651 7.592305e+00 4.080620e-04\n",
" * time: 7.228554010391235\n",
" 652 7.592304e+00 8.911549e-04\n",
" * time: 7.237834930419922\n",
" 653 7.592304e+00 7.910937e-04\n",
" * time: 7.2503039836883545\n",
" 654 7.592304e+00 9.272278e-04\n",
" * time: 7.259514093399048\n",
" 655 7.592304e+00 8.384160e-04\n",
" * time: 7.268996000289917\n",
" 656 7.592304e+00 7.563084e-04\n",
" * time: 7.278757095336914\n",
" 657 7.592304e+00 5.946355e-04\n",
" * time: 7.288717031478882\n",
" 658 7.592304e+00 1.277367e-03\n",
" * time: 7.298348903656006\n",
" 659 7.592304e+00 1.267159e-03\n",
" * time: 7.308145046234131\n",
" 660 7.592304e+00 6.772797e-04\n",
" * time: 7.317905902862549\n",
" 661 7.592304e+00 6.378612e-04\n",
" * time: 7.327642917633057\n",
" 662 7.592304e+00 8.405640e-04\n",
" * time: 7.337323904037476\n",
" 663 7.592304e+00 8.467834e-04\n",
" * time: 7.346930027008057\n",
" 664 7.592303e+00 7.962879e-04\n",
" * time: 7.356574058532715\n",
" 665 7.592303e+00 6.169636e-04\n",
" * time: 7.36939001083374\n",
" 666 7.592303e+00 6.641147e-04\n",
" * time: 7.382055997848511\n",
" 667 7.592303e+00 9.316604e-04\n",
" * time: 7.391762018203735\n",
" 668 7.592303e+00 5.678135e-04\n",
" * time: 7.401498079299927\n",
" 669 7.592303e+00 5.417629e-04\n",
" * time: 7.414341926574707\n",
" 670 7.592303e+00 4.270726e-04\n",
" * time: 7.427259922027588\n",
" 671 7.592303e+00 5.092397e-04\n",
" * time: 7.437057971954346\n",
" 672 7.592303e+00 7.663222e-04\n",
" * time: 7.446779012680054\n",
" 673 7.592303e+00 5.964642e-04\n",
" * time: 7.459805011749268\n",
" 674 7.592303e+00 7.692522e-04\n",
" * time: 7.500978946685791\n",
" 675 7.592302e+00 4.707212e-04\n",
" * time: 7.509960889816284\n",
" 676 7.592302e+00 6.465102e-04\n",
" * time: 7.518795013427734\n",
" 677 7.592302e+00 5.926652e-04\n",
" * time: 7.5275719165802\n",
" 678 7.592302e+00 6.074850e-04\n",
" * time: 7.539161920547485\n",
" 679 7.592302e+00 5.583509e-04\n",
" * time: 7.5478880405426025\n",
" 680 7.592302e+00 4.857214e-04\n",
" * time: 7.556641101837158\n",
" 681 7.592302e+00 5.894926e-04\n",
" * time: 7.565669059753418\n",
" 682 7.592302e+00 7.734037e-04\n",
" * time: 7.577194929122925\n",
" 683 7.592302e+00 4.763698e-04\n",
" * time: 7.588795900344849\n",
" 684 7.592302e+00 5.450799e-04\n",
" * time: 7.597620964050293\n",
" 685 7.592302e+00 2.434395e-04\n",
" * time: 7.609303951263428\n",
" 686 7.592302e+00 5.470845e-04\n",
" * time: 7.618089914321899\n",
" 687 7.592302e+00 4.397230e-04\n",
" * time: 7.626935005187988\n",
" 688 7.592302e+00 4.250486e-04\n",
" * time: 7.6357200145721436\n",
" 689 7.592302e+00 3.265013e-04\n",
" * time: 7.644603967666626\n",
" 690 7.592302e+00 5.590110e-04\n",
" * time: 7.653826951980591\n",
" 691 7.592302e+00 3.999739e-04\n",
" * time: 7.6630730628967285\n",
" 692 7.592302e+00 2.930297e-04\n",
" * time: 7.672240972518921\n",
" 693 7.592302e+00 2.657512e-04\n",
" * time: 7.681602954864502\n",
" 694 7.592302e+00 2.763599e-04\n",
" * time: 7.690948963165283\n",
" 695 7.592302e+00 2.240598e-04\n",
" * time: 7.703001022338867\n",
" 696 7.592302e+00 2.366300e-04\n",
" * time: 7.712255001068115\n",
" 697 7.592302e+00 2.532983e-04\n",
" * time: 7.724397897720337\n",
" 698 7.592302e+00 1.912812e-04\n",
" * time: 7.737028121948242\n",
" 699 7.592302e+00 1.619428e-04\n",
" * time: 7.749849081039429\n",
" 700 7.592302e+00 2.504797e-04\n",
" * time: 7.75954008102417\n",
" 701 7.592302e+00 1.751467e-04\n",
" * time: 7.772309064865112\n",
" 702 7.592302e+00 2.961705e-04\n",
" * time: 7.781970024108887\n",
" 703 7.592302e+00 4.512521e-04\n",
" * time: 7.791887044906616\n",
" 704 7.592302e+00 2.398919e-04\n",
" * time: 7.801624059677124\n",
" 705 7.592301e+00 2.425935e-04\n",
" * time: 7.811363935470581\n",
" 706 7.592301e+00 2.401652e-04\n",
" * time: 7.821069955825806\n",
" 707 7.592301e+00 3.969697e-04\n",
" * time: 7.830740928649902\n",
" 708 7.592301e+00 2.756439e-04\n",
" * time: 7.843619108200073\n",
" 709 7.592301e+00 5.245574e-04\n",
" * time: 7.853432893753052\n",
" 710 7.592301e+00 4.864512e-04\n",
" * time: 7.8631041049957275\n",
" 711 7.592301e+00 3.222718e-04\n",
" * time: 7.875938892364502\n",
" 712 7.592301e+00 3.256756e-04\n",
" * time: 7.885921955108643\n",
" 713 7.592301e+00 2.875080e-04\n",
" * time: 7.898927927017212\n",
" 714 7.592301e+00 5.403833e-04\n",
" * time: 7.908740997314453\n",
" 715 7.592301e+00 2.765364e-04\n",
" * time: 7.922034978866577\n",
" 716 7.592301e+00 3.841330e-04\n",
" * time: 7.962731122970581\n",
" 717 7.592301e+00 3.422202e-04\n",
" * time: 7.971642017364502\n",
" 718 7.592301e+00 4.010781e-04\n",
" * time: 7.9805519580841064\n",
" 719 7.592301e+00 3.411993e-04\n",
" * time: 7.989356994628906\n",
" 720 7.592301e+00 6.415255e-04\n",
" * time: 7.998102903366089\n",
" 721 7.592301e+00 3.351041e-04\n",
" * time: 8.009592056274414\n",
" 722 7.592301e+00 3.147649e-04\n",
" * time: 8.018649101257324\n",
" 723 7.592301e+00 5.587827e-04\n",
" * time: 8.027425050735474\n",
" 724 7.592301e+00 3.309039e-04\n",
" * time: 8.036287069320679\n",
" 725 7.592301e+00 2.095549e-04\n",
" * time: 8.047943115234375\n",
" 726 7.592301e+00 3.098101e-04\n",
" * time: 8.056720972061157\n"
]
},
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=1}",
"image/png": "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",
"text/html": [
"\n",
"\n"
],
"image/svg+xml": [
"\n",
"\n"
]
},
"metadata": {},
"execution_count": 1
}
],
"cell_type": "code",
"source": [
"using DFTK\n",
"using StaticArrays\n",
"using Plots\n",
"\n",
"# Unit cell. Having one of the lattice vectors as zero means a 2D system\n",
"a = 15\n",
"lattice = a .* [[1 0 0.]; [0 1 0]; [0 0 0]];\n",
"\n",
"# Confining scalar potential, and magnetic vector potential\n",
"pot(x, y, z) = ((x - a/2)^2 + (y - a/2)^2)/2\n",
"ω = .6\n",
"Apot(x, y, z) = ω * @SVector [y - a/2, -(x - a/2), 0]\n",
"Apot(X) = Apot(X...);\n",
"\n",
"\n",
"# Parameters\n",
"Ecut = 20 # Increase this for production\n",
"η = 500\n",
"C = η/2\n",
"α = 2\n",
"n_electrons = 1; # Increase this for fun\n",
"\n",
"# Collect all the terms, build and run the model\n",
"terms = [Kinetic(),\n",
" ExternalFromReal(X -> pot(X...)),\n",
" LocalNonlinearity(ρ -> C * ρ^α),\n",
" Magnetic(Apot),\n",
"]\n",
"model = Model(lattice; n_electrons, terms, spin_polarization=:spinless) # spinless electrons\n",
"basis = PlaneWaveBasis(model; Ecut, kgrid=(1, 1, 1))\n",
"scfres = direct_minimization(basis, tol=1e-5) # Reduce tol for production\n",
"heatmap(scfres.ρ[:, :, 1, 1], c=:blues)"
],
"metadata": {},
"execution_count": 1
}
],
"nbformat_minor": 3,
"metadata": {
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.9.0"
},
"kernelspec": {
"name": "julia-1.9",
"display_name": "Julia 1.9.0",
"language": "julia"
}
},
"nbformat": 4
}