{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Micromagnetic standard problem 4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Author**: Marijan Beg, Marc-Antonio Bisotti\n",
    "\n",
    "**Date**: 18 Mar 2016\n",
    "\n",
    "This notebook can be downloaded from the github repository, found [here](https://github.com/computationalmodelling/fidimag/blob/master/doc/ipynb/standard_problem_4.ipynb)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem specification"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The simulated sample is a thin film cuboid with dimensions:\n",
    "- length $L = 500 \\,\\text{nm}$,\n",
    "- width $d = 125 \\,\\text{nm}$, and\n",
    "- thickness $t = 3 \\,\\text{nm}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from fidimag.common import CuboidMesh\n",
    "mesh = CuboidMesh(nx=160, ny=40, nz=1, dx=3.125, dy=3.125, dz=3, unit_length=1e-9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The material parameters (similar to permalloy) are:\n",
    "\n",
    "- exchange energy constant $A = 1.3 \\times 10^{-11} \\,\\text{J/m}$,\n",
    "- magnetisation saturation $M_\\text{s} = 8 \\times 10^{5} \\,\\text{A/m}$.\n",
    "\n",
    "Magnetisation dynamics is governed by the Landau-Lifshitz-Gilbert equation\n",
    "\n",
    "$$\\frac{d\\mathbf{m}}{dt} = -\\gamma_{0}(\\mathbf{m} \\times \\mathbf{H}_\\text{eff}) + \\alpha\\left(\\mathbf{m} \\times \\frac{d\\mathbf{m}}{dt}\\right)$$\n",
    "\n",
    "where $\\gamma_{0} = 2.211 \\times 10^{5} \\,\\text{m}\\,\\text{A}^{-1}\\,\\text{s}^{-1}$ is the gyromagnetic ratio and $\\alpha=0.02$ is the Gilbert damping."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "A = 13e-12\n",
    "Ms = 8.0e5\n",
    "alpha = 0.02\n",
    "gamma = 2.211e5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the standard problem 4, the system is firstly relaxed at zero external magnetic field and then, stating from the obtained equlibrium configuration, the magnetisation dynamics is simulated for each of two different external magnetic fields:\n",
    "\n",
    "1. $\\mathbf{H}_{1} = (-24.6, 4.3, 0.0) \\,\\text{mT}$\n",
    "2. $\\mathbf{H}_{2} = (-35.5, -6.3, 0.0) \\,\\text{mT}$\n",
    "\n",
    "The micromagnetic standard problem 4 specification can be also found in Ref. 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulation\n",
    "\n",
    "### Getting the Initial Magnetisation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The simulation object is created and parameters set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from fidimag.micro import Sim, UniformExchange, Demag, Zeeman, TimeZeeman\n",
    "\n",
    "sim = Sim(mesh)  # create simulation object\n",
    "\n",
    "sim.driver.set_tols(rtol=1e-10, atol=1e-10)\n",
    "sim.Ms = Ms\n",
    "sim.driver.alpha = 0.5  # large value since the magnetisation dynamics is not important in the relexation stage\n",
    "sim.driver.gamma = gamma\n",
    "sim.driver.do_precession = False  # speeds up the simulation\n",
    "\n",
    "\n",
    "# Starting magnetisation.\n",
    "sim.set_m((1, 0.25, 0.1))\n",
    "sim.add(UniformExchange(A=A))\n",
    "sim.add(Demag())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have ignored the decaying external field. Finally, the system can be relaxed and the obtained equilibrium configuration saved, so that it can be used as an initial state for simulating magnetisation dynamics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step=1, time=1e-13, max_dmdt=517 ode_step=0\n",
      "step=2, time=2e-13, max_dmdt=510 ode_step=1.8e-14\n",
      "step=3, time=3e-13, max_dmdt=502 ode_step=4.38e-14\n",
      "step=4, time=4e-13, max_dmdt=495 ode_step=4.38e-14\n",
      "step=5, time=5e-13, max_dmdt=489 ode_step=7.03e-14\n",
      "step=6, time=6e-13, max_dmdt=482 ode_step=7.03e-14\n",
      "step=7, time=7e-13, max_dmdt=476 ode_step=7.03e-14\n",
      "step=8, time=8e-13, max_dmdt=470 ode_step=7.03e-14\n",
      "step=9, time=9e-13, max_dmdt=464 ode_step=7.03e-14\n",
      "step=10, time=1e-12, max_dmdt=459 ode_step=7.03e-14\n",
      "step=11, time=1.14e-12, max_dmdt=453 ode_step=1.43e-13\n",
      "step=12, time=1.29e-12, max_dmdt=445 ode_step=1.43e-13\n",
      "step=13, time=1.43e-12, max_dmdt=439 ode_step=1.43e-13\n",
      "step=14, time=1.57e-12, max_dmdt=433 ode_step=1.43e-13\n",
      "step=15, time=1.72e-12, max_dmdt=428 ode_step=1.43e-13\n",
      "step=16, time=1.86e-12, max_dmdt=422 ode_step=1.43e-13\n",
      "step=17, time=2e-12, max_dmdt=417 ode_step=1.43e-13\n",
      "step=18, time=2.15e-12, max_dmdt=412 ode_step=1.43e-13\n",
      "step=19, time=2.29e-12, max_dmdt=407 ode_step=1.43e-13\n",
      "step=20, time=2.51e-12, max_dmdt=401 ode_step=2.15e-13\n",
      "step=21, time=2.72e-12, max_dmdt=394 ode_step=2.15e-13\n",
      "step=22, time=2.94e-12, max_dmdt=387 ode_step=2.15e-13\n",
      "step=23, time=3.15e-12, max_dmdt=381 ode_step=2.15e-13\n",
      "step=24, time=3.37e-12, max_dmdt=375 ode_step=2.15e-13\n",
      "step=25, time=3.58e-12, max_dmdt=369 ode_step=2.15e-13\n",
      "step=26, time=3.8e-12, max_dmdt=364 ode_step=2.15e-13\n",
      "step=27, time=4.01e-12, max_dmdt=358 ode_step=2.15e-13\n",
      "step=28, time=4.23e-12, max_dmdt=353 ode_step=2.15e-13\n",
      "step=29, time=4.44e-12, max_dmdt=348 ode_step=2.15e-13\n",
      "step=30, time=4.66e-12, max_dmdt=343 ode_step=2.15e-13\n",
      "step=31, time=4.87e-12, max_dmdt=338 ode_step=2.15e-13\n",
      "step=32, time=5.09e-12, max_dmdt=333 ode_step=2.15e-13\n",
      "step=33, time=5.3e-12, max_dmdt=328 ode_step=2.15e-13\n",
      "step=34, time=5.52e-12, max_dmdt=324 ode_step=2.15e-13\n",
      "step=35, time=5.73e-12, max_dmdt=320 ode_step=2.15e-13\n",
      "step=36, time=5.95e-12, max_dmdt=315 ode_step=2.15e-13\n",
      "step=37, time=6.16e-12, max_dmdt=311 ode_step=2.15e-13\n",
      "step=38, time=6.38e-12, max_dmdt=307 ode_step=2.15e-13\n",
      "step=39, time=6.59e-12, max_dmdt=303 ode_step=2.15e-13\n",
      "step=40, time=6.81e-12, max_dmdt=299 ode_step=2.15e-13\n",
      "step=41, time=7.02e-12, max_dmdt=295 ode_step=2.15e-13\n",
      "step=42, time=7.24e-12, max_dmdt=291 ode_step=2.15e-13\n",
      "step=43, time=7.45e-12, max_dmdt=288 ode_step=2.15e-13\n",
      "step=44, time=7.78e-12, max_dmdt=283 ode_step=3.29e-13\n",
      "step=45, time=8.11e-12, max_dmdt=278 ode_step=3.29e-13\n",
      "step=46, time=8.44e-12, max_dmdt=273 ode_step=3.29e-13\n",
      "step=47, time=8.77e-12, max_dmdt=268 ode_step=3.29e-13\n",
      "step=48, time=9.09e-12, max_dmdt=263 ode_step=3.29e-13\n",
      "step=49, time=9.42e-12, max_dmdt=258 ode_step=3.29e-13\n",
      "step=50, time=9.75e-12, max_dmdt=254 ode_step=3.29e-13\n",
      "step=51, time=1.01e-11, max_dmdt=249 ode_step=3.29e-13\n",
      "step=52, time=1.04e-11, max_dmdt=245 ode_step=3.29e-13\n",
      "step=53, time=1.07e-11, max_dmdt=240 ode_step=3.29e-13\n",
      "step=54, time=1.11e-11, max_dmdt=236 ode_step=3.29e-13\n",
      "step=55, time=1.14e-11, max_dmdt=232 ode_step=3.29e-13\n",
      "step=56, time=1.17e-11, max_dmdt=229 ode_step=3.29e-13\n",
      "step=57, time=1.21e-11, max_dmdt=225 ode_step=3.29e-13\n",
      "step=58, time=1.24e-11, max_dmdt=221 ode_step=3.29e-13\n",
      "step=59, time=1.27e-11, max_dmdt=218 ode_step=3.29e-13\n",
      "step=60, time=1.3e-11, max_dmdt=214 ode_step=3.29e-13\n",
      "step=61, time=1.34e-11, max_dmdt=211 ode_step=3.29e-13\n",
      "step=62, time=1.37e-11, max_dmdt=208 ode_step=3.29e-13\n",
      "step=63, time=1.4e-11, max_dmdt=204 ode_step=3.29e-13\n",
      "step=64, time=1.45e-11, max_dmdt=201 ode_step=4.94e-13\n",
      "step=65, time=1.5e-11, max_dmdt=196 ode_step=4.94e-13\n",
      "step=66, time=1.55e-11, max_dmdt=192 ode_step=4.94e-13\n",
      "step=67, time=1.6e-11, max_dmdt=188 ode_step=4.94e-13\n",
      "step=68, time=1.65e-11, max_dmdt=184 ode_step=4.94e-13\n",
      "step=69, time=1.7e-11, max_dmdt=180 ode_step=4.94e-13\n",
      "step=70, time=1.75e-11, max_dmdt=177 ode_step=4.94e-13\n",
      "step=71, time=1.8e-11, max_dmdt=173 ode_step=4.94e-13\n",
      "step=72, time=1.85e-11, max_dmdt=170 ode_step=4.94e-13\n",
      "step=73, time=1.9e-11, max_dmdt=167 ode_step=4.94e-13\n",
      "step=74, time=1.95e-11, max_dmdt=164 ode_step=4.94e-13\n",
      "step=75, time=2e-11, max_dmdt=161 ode_step=4.94e-13\n",
      "step=76, time=2.04e-11, max_dmdt=159 ode_step=4.94e-13\n",
      "step=77, time=2.09e-11, max_dmdt=156 ode_step=4.94e-13\n",
      "step=78, time=2.17e-11, max_dmdt=153 ode_step=7.48e-13\n",
      "step=79, time=2.24e-11, max_dmdt=150 ode_step=7.48e-13\n",
      "step=80, time=2.32e-11, max_dmdt=147 ode_step=7.48e-13\n",
      "step=81, time=2.39e-11, max_dmdt=144 ode_step=7.48e-13\n",
      "step=82, time=2.47e-11, max_dmdt=141 ode_step=7.48e-13\n",
      "step=83, time=2.54e-11, max_dmdt=138 ode_step=7.48e-13\n",
      "step=84, time=2.62e-11, max_dmdt=136 ode_step=7.48e-13\n",
      "step=85, time=2.69e-11, max_dmdt=134 ode_step=7.48e-13\n",
      "step=86, time=2.77e-11, max_dmdt=131 ode_step=7.48e-13\n",
      "step=87, time=2.84e-11, max_dmdt=129 ode_step=7.48e-13\n",
      "step=88, time=2.92e-11, max_dmdt=127 ode_step=7.48e-13\n",
      "step=89, time=2.99e-11, max_dmdt=125 ode_step=7.48e-13\n",
      "step=90, time=3.07e-11, max_dmdt=124 ode_step=7.48e-13\n",
      "step=91, time=3.14e-11, max_dmdt=122 ode_step=7.48e-13\n",
      "step=92, time=3.22e-11, max_dmdt=120 ode_step=7.48e-13\n",
      "step=93, time=3.29e-11, max_dmdt=119 ode_step=7.48e-13\n",
      "step=94, time=3.37e-11, max_dmdt=118 ode_step=7.48e-13\n",
      "step=95, time=3.44e-11, max_dmdt=116 ode_step=7.48e-13\n",
      "step=96, time=3.52e-11, max_dmdt=115 ode_step=7.48e-13\n",
      "step=97, time=3.59e-11, max_dmdt=114 ode_step=7.48e-13\n",
      "step=98, time=3.67e-11, max_dmdt=113 ode_step=7.48e-13\n",
      "step=99, time=3.74e-11, max_dmdt=112 ode_step=7.48e-13\n",
      "step=100, time=3.82e-11, max_dmdt=111 ode_step=7.48e-13\n",
      "step=101, time=3.89e-11, max_dmdt=110 ode_step=7.48e-13\n",
      "step=102, time=3.97e-11, max_dmdt=109 ode_step=7.48e-13\n",
      "step=103, time=4.04e-11, max_dmdt=108 ode_step=7.48e-13\n",
      "step=104, time=4.12e-11, max_dmdt=107 ode_step=7.48e-13\n",
      "step=105, time=4.19e-11, max_dmdt=107 ode_step=7.48e-13\n",
      "step=106, time=4.26e-11, max_dmdt=106 ode_step=7.48e-13\n",
      "step=107, time=4.34e-11, max_dmdt=105 ode_step=7.48e-13\n",
      "step=108, time=4.41e-11, max_dmdt=104 ode_step=7.48e-13\n",
      "step=109, time=4.49e-11, max_dmdt=104 ode_step=7.48e-13\n",
      "step=110, time=4.56e-11, max_dmdt=103 ode_step=7.48e-13\n",
      "step=111, time=4.64e-11, max_dmdt=102 ode_step=7.48e-13\n",
      "step=112, time=4.71e-11, max_dmdt=102 ode_step=7.48e-13\n",
      "step=113, time=4.79e-11, max_dmdt=101 ode_step=7.48e-13\n",
      "step=114, time=4.86e-11, max_dmdt=101 ode_step=7.48e-13\n",
      "step=115, time=4.94e-11, max_dmdt=100 ode_step=7.48e-13\n",
      "step=116, time=5.01e-11, max_dmdt=99.6 ode_step=7.48e-13\n",
      "step=117, time=5.09e-11, max_dmdt=99.1 ode_step=7.48e-13\n",
      "step=118, time=5.16e-11, max_dmdt=98.6 ode_step=7.48e-13\n",
      "step=119, time=5.24e-11, max_dmdt=98.2 ode_step=7.48e-13\n",
      "step=120, time=5.31e-11, max_dmdt=97.7 ode_step=7.48e-13\n",
      "step=121, time=5.39e-11, max_dmdt=97.2 ode_step=7.48e-13\n",
      "step=122, time=5.46e-11, max_dmdt=96.8 ode_step=7.48e-13\n",
      "step=123, time=5.54e-11, max_dmdt=96.3 ode_step=7.48e-13\n",
      "step=124, time=5.61e-11, max_dmdt=95.9 ode_step=7.48e-13\n",
      "step=125, time=5.69e-11, max_dmdt=95.5 ode_step=7.48e-13\n",
      "step=126, time=5.8e-11, max_dmdt=95 ode_step=1.14e-12\n",
      "step=127, time=5.91e-11, max_dmdt=94.4 ode_step=1.14e-12\n",
      "step=128, time=6.03e-11, max_dmdt=93.8 ode_step=1.14e-12\n",
      "step=129, time=6.14e-11, max_dmdt=93.2 ode_step=1.14e-12\n",
      "step=130, time=6.26e-11, max_dmdt=92.7 ode_step=1.14e-12\n",
      "step=131, time=6.37e-11, max_dmdt=92.2 ode_step=1.14e-12\n",
      "step=132, time=6.48e-11, max_dmdt=91.6 ode_step=1.14e-12\n",
      "step=133, time=6.6e-11, max_dmdt=91.1 ode_step=1.14e-12\n",
      "step=134, time=6.71e-11, max_dmdt=90.6 ode_step=1.14e-12\n",
      "step=135, time=6.82e-11, max_dmdt=90.1 ode_step=1.14e-12\n",
      "step=136, time=6.94e-11, max_dmdt=89.6 ode_step=1.14e-12\n",
      "step=137, time=7.05e-11, max_dmdt=89.2 ode_step=1.14e-12\n",
      "step=138, time=7.17e-11, max_dmdt=88.7 ode_step=1.14e-12\n",
      "step=139, time=7.28e-11, max_dmdt=88.2 ode_step=1.14e-12\n",
      "step=140, time=7.39e-11, max_dmdt=87.8 ode_step=1.14e-12\n",
      "step=141, time=7.51e-11, max_dmdt=87.3 ode_step=1.14e-12\n",
      "step=142, time=7.62e-11, max_dmdt=86.9 ode_step=1.14e-12\n",
      "step=143, time=7.74e-11, max_dmdt=86.4 ode_step=1.14e-12\n",
      "step=144, time=7.85e-11, max_dmdt=86 ode_step=1.14e-12\n",
      "step=145, time=7.96e-11, max_dmdt=85.6 ode_step=1.14e-12\n",
      "step=146, time=8.08e-11, max_dmdt=85.2 ode_step=1.14e-12\n",
      "step=147, time=8.19e-11, max_dmdt=84.8 ode_step=1.14e-12\n",
      "step=148, time=8.3e-11, max_dmdt=84.4 ode_step=1.14e-12\n",
      "step=149, time=8.42e-11, max_dmdt=84 ode_step=1.14e-12\n",
      "step=150, time=8.53e-11, max_dmdt=83.5 ode_step=1.14e-12\n",
      "step=151, time=8.65e-11, max_dmdt=83.1 ode_step=1.14e-12\n",
      "step=152, time=8.76e-11, max_dmdt=82.7 ode_step=1.14e-12\n",
      "step=153, time=8.87e-11, max_dmdt=82.3 ode_step=1.14e-12\n",
      "step=154, time=8.99e-11, max_dmdt=82 ode_step=1.14e-12\n",
      "step=155, time=9.1e-11, max_dmdt=81.6 ode_step=1.14e-12\n",
      "step=156, time=9.21e-11, max_dmdt=81.2 ode_step=1.14e-12\n",
      "step=157, time=9.33e-11, max_dmdt=80.8 ode_step=1.14e-12\n",
      "step=158, time=9.44e-11, max_dmdt=80.4 ode_step=1.14e-12\n",
      "step=159, time=9.56e-11, max_dmdt=80 ode_step=1.14e-12\n",
      "step=160, time=9.67e-11, max_dmdt=79.6 ode_step=1.14e-12\n",
      "step=161, time=9.78e-11, max_dmdt=79.3 ode_step=1.14e-12\n",
      "step=162, time=9.9e-11, max_dmdt=78.9 ode_step=1.14e-12\n",
      "step=163, time=1.01e-10, max_dmdt=78.4 ode_step=1.75e-12\n",
      "step=164, time=1.02e-10, max_dmdt=77.8 ode_step=1.75e-12\n",
      "step=165, time=1.04e-10, max_dmdt=77.3 ode_step=1.75e-12\n",
      "step=166, time=1.06e-10, max_dmdt=76.7 ode_step=1.75e-12\n",
      "step=167, time=1.08e-10, max_dmdt=76.1 ode_step=1.75e-12\n",
      "step=168, time=1.09e-10, max_dmdt=75.6 ode_step=1.75e-12\n",
      "step=169, time=1.11e-10, max_dmdt=75 ode_step=1.75e-12\n",
      "step=170, time=1.13e-10, max_dmdt=74.5 ode_step=1.75e-12\n",
      "step=171, time=1.15e-10, max_dmdt=74 ode_step=1.75e-12\n",
      "step=172, time=1.16e-10, max_dmdt=73.4 ode_step=1.75e-12\n",
      "step=173, time=1.18e-10, max_dmdt=72.9 ode_step=1.75e-12\n",
      "step=174, time=1.2e-10, max_dmdt=72.4 ode_step=1.75e-12\n",
      "step=175, time=1.22e-10, max_dmdt=71.8 ode_step=1.75e-12\n",
      "step=176, time=1.23e-10, max_dmdt=71.3 ode_step=1.75e-12\n",
      "step=177, time=1.25e-10, max_dmdt=70.8 ode_step=1.75e-12\n",
      "step=178, time=1.27e-10, max_dmdt=70.3 ode_step=1.75e-12\n",
      "step=179, time=1.29e-10, max_dmdt=69.8 ode_step=1.75e-12\n",
      "step=180, time=1.3e-10, max_dmdt=69.3 ode_step=1.75e-12\n",
      "step=181, time=1.32e-10, max_dmdt=68.8 ode_step=1.75e-12\n",
      "step=182, time=1.34e-10, max_dmdt=68.3 ode_step=1.75e-12\n",
      "step=183, time=1.36e-10, max_dmdt=67.8 ode_step=1.75e-12\n",
      "step=184, time=1.37e-10, max_dmdt=67.3 ode_step=1.75e-12\n",
      "step=185, time=1.39e-10, max_dmdt=66.8 ode_step=1.75e-12\n",
      "step=186, time=1.41e-10, max_dmdt=66.3 ode_step=1.75e-12\n",
      "step=187, time=1.43e-10, max_dmdt=65.8 ode_step=1.75e-12\n",
      "step=188, time=1.44e-10, max_dmdt=65.3 ode_step=1.75e-12\n",
      "step=189, time=1.46e-10, max_dmdt=64.8 ode_step=1.75e-12\n",
      "step=190, time=1.48e-10, max_dmdt=64.4 ode_step=1.75e-12\n",
      "step=191, time=1.5e-10, max_dmdt=63.9 ode_step=1.75e-12\n",
      "step=192, time=1.52e-10, max_dmdt=63.3 ode_step=2.69e-12\n",
      "step=193, time=1.55e-10, max_dmdt=62.6 ode_step=2.69e-12\n",
      "step=194, time=1.58e-10, max_dmdt=61.9 ode_step=2.69e-12\n",
      "step=195, time=1.6e-10, max_dmdt=61.2 ode_step=2.69e-12\n",
      "step=196, time=1.63e-10, max_dmdt=60.5 ode_step=2.69e-12\n",
      "step=197, time=1.66e-10, max_dmdt=59.8 ode_step=2.69e-12\n",
      "step=198, time=1.69e-10, max_dmdt=59.1 ode_step=2.69e-12\n",
      "step=199, time=1.71e-10, max_dmdt=58.4 ode_step=2.69e-12\n",
      "step=200, time=1.74e-10, max_dmdt=57.8 ode_step=2.69e-12\n",
      "step=201, time=1.77e-10, max_dmdt=57.1 ode_step=2.69e-12\n",
      "step=202, time=1.79e-10, max_dmdt=56.5 ode_step=2.69e-12\n",
      "step=203, time=1.83e-10, max_dmdt=55.7 ode_step=4.09e-12\n",
      "step=204, time=1.87e-10, max_dmdt=54.7 ode_step=4.09e-12\n",
      "step=205, time=1.92e-10, max_dmdt=53.8 ode_step=4.09e-12\n",
      "step=206, time=1.96e-10, max_dmdt=52.8 ode_step=4.09e-12\n",
      "step=207, time=2e-10, max_dmdt=51.9 ode_step=4.09e-12\n",
      "step=208, time=2.04e-10, max_dmdt=51 ode_step=4.09e-12\n",
      "step=209, time=2.08e-10, max_dmdt=50.2 ode_step=4.09e-12\n",
      "step=210, time=2.12e-10, max_dmdt=49.3 ode_step=4.09e-12\n",
      "step=211, time=2.16e-10, max_dmdt=48.5 ode_step=4.09e-12\n",
      "step=212, time=2.2e-10, max_dmdt=47.6 ode_step=4.09e-12\n",
      "step=213, time=2.24e-10, max_dmdt=46.8 ode_step=4.09e-12\n",
      "step=214, time=2.28e-10, max_dmdt=46 ode_step=4.09e-12\n",
      "step=215, time=2.32e-10, max_dmdt=45.3 ode_step=4.09e-12\n",
      "step=216, time=2.37e-10, max_dmdt=44.5 ode_step=4.09e-12\n",
      "step=217, time=2.41e-10, max_dmdt=43.7 ode_step=4.09e-12\n",
      "step=218, time=2.45e-10, max_dmdt=43 ode_step=4.09e-12\n",
      "step=219, time=2.49e-10, max_dmdt=42.3 ode_step=4.09e-12\n",
      "step=220, time=2.53e-10, max_dmdt=41.6 ode_step=4.09e-12\n",
      "step=221, time=2.57e-10, max_dmdt=40.9 ode_step=4.09e-12\n",
      "step=222, time=2.61e-10, max_dmdt=40.2 ode_step=4.09e-12\n",
      "step=223, time=2.65e-10, max_dmdt=39.5 ode_step=4.09e-12\n",
      "step=224, time=2.69e-10, max_dmdt=38.9 ode_step=4.09e-12\n",
      "step=225, time=2.73e-10, max_dmdt=38.2 ode_step=4.09e-12\n",
      "step=226, time=2.77e-10, max_dmdt=37.6 ode_step=4.09e-12\n",
      "step=227, time=2.81e-10, max_dmdt=37 ode_step=4.09e-12\n",
      "step=228, time=2.86e-10, max_dmdt=36.4 ode_step=4.09e-12\n",
      "step=229, time=2.9e-10, max_dmdt=35.8 ode_step=4.09e-12\n",
      "step=230, time=2.94e-10, max_dmdt=35.2 ode_step=4.09e-12\n",
      "step=231, time=3e-10, max_dmdt=34.5 ode_step=6.13e-12\n",
      "step=232, time=3.06e-10, max_dmdt=33.6 ode_step=6.13e-12\n",
      "step=233, time=3.12e-10, max_dmdt=32.8 ode_step=6.13e-12\n",
      "step=234, time=3.18e-10, max_dmdt=32.1 ode_step=6.13e-12\n",
      "step=235, time=3.24e-10, max_dmdt=31.3 ode_step=6.13e-12\n",
      "step=236, time=3.31e-10, max_dmdt=30.6 ode_step=6.13e-12\n",
      "step=237, time=3.37e-10, max_dmdt=29.9 ode_step=6.13e-12\n",
      "step=238, time=3.43e-10, max_dmdt=29.3 ode_step=6.13e-12\n",
      "step=239, time=3.49e-10, max_dmdt=28.6 ode_step=6.13e-12\n",
      "step=240, time=3.55e-10, max_dmdt=28 ode_step=6.13e-12\n",
      "step=241, time=3.61e-10, max_dmdt=27.4 ode_step=6.13e-12\n",
      "step=242, time=3.67e-10, max_dmdt=27 ode_step=6.13e-12\n",
      "step=243, time=3.73e-10, max_dmdt=26.6 ode_step=6.13e-12\n",
      "step=244, time=3.8e-10, max_dmdt=26.2 ode_step=6.13e-12\n",
      "step=245, time=3.86e-10, max_dmdt=25.8 ode_step=6.13e-12\n",
      "step=246, time=3.92e-10, max_dmdt=25.4 ode_step=6.13e-12\n",
      "step=247, time=3.98e-10, max_dmdt=25.1 ode_step=6.13e-12\n",
      "step=248, time=4.04e-10, max_dmdt=24.7 ode_step=6.13e-12\n",
      "step=249, time=4.1e-10, max_dmdt=24.3 ode_step=6.13e-12\n",
      "step=250, time=4.16e-10, max_dmdt=24 ode_step=6.13e-12\n",
      "step=251, time=4.22e-10, max_dmdt=23.6 ode_step=6.13e-12\n",
      "step=252, time=4.29e-10, max_dmdt=23.3 ode_step=6.13e-12\n",
      "step=253, time=4.35e-10, max_dmdt=22.9 ode_step=6.13e-12\n",
      "step=254, time=4.41e-10, max_dmdt=22.6 ode_step=6.13e-12\n",
      "step=255, time=4.51e-10, max_dmdt=22.2 ode_step=9.71e-12\n",
      "step=256, time=4.6e-10, max_dmdt=21.7 ode_step=9.71e-12\n",
      "step=257, time=4.7e-10, max_dmdt=21.2 ode_step=9.71e-12\n",
      "step=258, time=4.8e-10, max_dmdt=20.7 ode_step=9.71e-12\n",
      "step=259, time=4.89e-10, max_dmdt=20.2 ode_step=9.71e-12\n",
      "step=260, time=4.99e-10, max_dmdt=19.7 ode_step=9.71e-12\n",
      "step=261, time=5.09e-10, max_dmdt=19.4 ode_step=9.71e-12\n",
      "step=262, time=5.19e-10, max_dmdt=19.2 ode_step=9.71e-12\n",
      "step=263, time=5.28e-10, max_dmdt=19 ode_step=9.71e-12\n",
      "step=264, time=5.38e-10, max_dmdt=18.8 ode_step=9.71e-12\n",
      "step=265, time=5.48e-10, max_dmdt=18.7 ode_step=9.71e-12\n",
      "step=266, time=5.57e-10, max_dmdt=18.5 ode_step=9.71e-12\n",
      "step=267, time=5.67e-10, max_dmdt=18.3 ode_step=9.71e-12\n",
      "step=268, time=5.77e-10, max_dmdt=18.1 ode_step=9.71e-12\n",
      "step=269, time=5.87e-10, max_dmdt=18 ode_step=9.71e-12\n",
      "step=270, time=5.96e-10, max_dmdt=17.8 ode_step=9.71e-12\n",
      "step=271, time=6.06e-10, max_dmdt=17.6 ode_step=9.71e-12\n",
      "step=272, time=6.16e-10, max_dmdt=17.4 ode_step=9.71e-12\n",
      "step=273, time=6.25e-10, max_dmdt=17.2 ode_step=9.71e-12\n",
      "step=274, time=6.35e-10, max_dmdt=17.1 ode_step=9.71e-12\n",
      "step=275, time=6.45e-10, max_dmdt=16.9 ode_step=9.71e-12\n",
      "step=276, time=6.54e-10, max_dmdt=16.7 ode_step=9.71e-12\n",
      "step=277, time=6.64e-10, max_dmdt=16.5 ode_step=9.71e-12\n",
      "step=278, time=6.74e-10, max_dmdt=16.3 ode_step=9.71e-12\n",
      "step=279, time=6.84e-10, max_dmdt=16.1 ode_step=9.71e-12\n",
      "step=280, time=6.93e-10, max_dmdt=15.9 ode_step=9.71e-12\n",
      "step=281, time=7.03e-10, max_dmdt=15.7 ode_step=9.71e-12\n",
      "step=282, time=7.13e-10, max_dmdt=15.5 ode_step=9.71e-12\n",
      "step=283, time=7.22e-10, max_dmdt=15.3 ode_step=9.71e-12\n",
      "step=284, time=7.32e-10, max_dmdt=15.1 ode_step=9.71e-12\n",
      "step=285, time=7.42e-10, max_dmdt=14.9 ode_step=9.71e-12\n",
      "step=286, time=7.52e-10, max_dmdt=14.7 ode_step=9.71e-12\n",
      "step=287, time=7.61e-10, max_dmdt=14.5 ode_step=9.71e-12\n",
      "step=288, time=7.71e-10, max_dmdt=14.3 ode_step=9.71e-12\n",
      "step=289, time=7.81e-10, max_dmdt=14.2 ode_step=9.71e-12\n",
      "step=290, time=7.9e-10, max_dmdt=14 ode_step=9.71e-12\n",
      "step=291, time=8.06e-10, max_dmdt=13.7 ode_step=1.53e-11\n",
      "step=292, time=8.21e-10, max_dmdt=13.4 ode_step=1.53e-11\n",
      "step=293, time=8.36e-10, max_dmdt=13.1 ode_step=1.53e-11\n",
      "step=294, time=8.52e-10, max_dmdt=12.8 ode_step=1.53e-11\n",
      "step=295, time=8.67e-10, max_dmdt=12.5 ode_step=1.53e-11\n",
      "step=296, time=8.82e-10, max_dmdt=12.2 ode_step=1.53e-11\n",
      "step=297, time=8.97e-10, max_dmdt=11.9 ode_step=1.53e-11\n",
      "step=298, time=9.13e-10, max_dmdt=11.6 ode_step=1.53e-11\n",
      "step=299, time=9.28e-10, max_dmdt=11.3 ode_step=1.53e-11\n",
      "step=300, time=9.43e-10, max_dmdt=11.1 ode_step=1.53e-11\n",
      "step=301, time=9.59e-10, max_dmdt=10.8 ode_step=1.53e-11\n",
      "step=302, time=9.74e-10, max_dmdt=10.5 ode_step=1.53e-11\n",
      "step=303, time=9.89e-10, max_dmdt=10.2 ode_step=1.53e-11\n",
      "step=304, time=1e-09, max_dmdt=9.99 ode_step=1.53e-11\n",
      "step=305, time=1.02e-09, max_dmdt=9.73 ode_step=1.53e-11\n",
      "step=306, time=1.04e-09, max_dmdt=9.48 ode_step=1.53e-11\n",
      "step=307, time=1.05e-09, max_dmdt=9.24 ode_step=1.53e-11\n",
      "step=308, time=1.07e-09, max_dmdt=9 ode_step=1.53e-11\n",
      "step=309, time=1.08e-09, max_dmdt=8.76 ode_step=1.53e-11\n",
      "step=310, time=1.1e-09, max_dmdt=8.54 ode_step=1.53e-11\n",
      "step=311, time=1.11e-09, max_dmdt=8.32 ode_step=1.53e-11\n",
      "step=312, time=1.13e-09, max_dmdt=8.1 ode_step=1.53e-11\n",
      "step=313, time=1.14e-09, max_dmdt=7.89 ode_step=1.53e-11\n",
      "step=314, time=1.16e-09, max_dmdt=7.68 ode_step=1.53e-11\n",
      "step=315, time=1.17e-09, max_dmdt=7.48 ode_step=1.53e-11\n",
      "step=316, time=1.19e-09, max_dmdt=7.28 ode_step=1.53e-11\n",
      "step=317, time=1.2e-09, max_dmdt=7.09 ode_step=1.53e-11\n",
      "step=318, time=1.22e-09, max_dmdt=6.91 ode_step=1.53e-11\n",
      "step=319, time=1.23e-09, max_dmdt=6.72 ode_step=1.53e-11\n",
      "step=320, time=1.25e-09, max_dmdt=6.54 ode_step=1.53e-11\n",
      "step=321, time=1.26e-09, max_dmdt=6.37 ode_step=1.53e-11\n",
      "step=322, time=1.28e-09, max_dmdt=6.2 ode_step=1.53e-11\n",
      "step=323, time=1.3e-09, max_dmdt=6.04 ode_step=1.53e-11\n",
      "step=324, time=1.31e-09, max_dmdt=5.88 ode_step=1.53e-11\n",
      "step=325, time=1.33e-09, max_dmdt=5.72 ode_step=1.53e-11\n",
      "step=326, time=1.34e-09, max_dmdt=5.57 ode_step=1.53e-11\n",
      "step=327, time=1.36e-09, max_dmdt=5.42 ode_step=1.53e-11\n",
      "step=328, time=1.37e-09, max_dmdt=5.28 ode_step=1.53e-11\n",
      "step=329, time=1.39e-09, max_dmdt=5.14 ode_step=1.53e-11\n",
      "step=330, time=1.4e-09, max_dmdt=5 ode_step=1.53e-11\n",
      "step=331, time=1.43e-09, max_dmdt=4.84 ode_step=2.31e-11\n",
      "step=332, time=1.45e-09, max_dmdt=4.64 ode_step=2.31e-11\n",
      "step=333, time=1.47e-09, max_dmdt=4.46 ode_step=2.31e-11\n",
      "step=334, time=1.49e-09, max_dmdt=4.28 ode_step=2.31e-11\n",
      "step=335, time=1.52e-09, max_dmdt=4.11 ode_step=2.31e-11\n",
      "step=336, time=1.54e-09, max_dmdt=3.95 ode_step=2.31e-11\n",
      "step=337, time=1.56e-09, max_dmdt=3.79 ode_step=2.31e-11\n",
      "step=338, time=1.59e-09, max_dmdt=3.65 ode_step=2.31e-11\n",
      "step=339, time=1.61e-09, max_dmdt=3.5 ode_step=2.31e-11\n",
      "step=340, time=1.63e-09, max_dmdt=3.37 ode_step=2.31e-11\n",
      "step=341, time=1.66e-09, max_dmdt=3.24 ode_step=2.31e-11\n",
      "step=342, time=1.68e-09, max_dmdt=3.11 ode_step=2.31e-11\n",
      "step=343, time=1.7e-09, max_dmdt=2.99 ode_step=2.31e-11\n",
      "step=344, time=1.73e-09, max_dmdt=2.87 ode_step=2.31e-11\n",
      "step=345, time=1.75e-09, max_dmdt=2.76 ode_step=2.31e-11\n",
      "step=346, time=1.77e-09, max_dmdt=2.66 ode_step=2.31e-11\n",
      "step=347, time=1.8e-09, max_dmdt=2.55 ode_step=2.31e-11\n",
      "step=348, time=1.82e-09, max_dmdt=2.46 ode_step=2.31e-11\n",
      "step=349, time=1.84e-09, max_dmdt=2.36 ode_step=2.31e-11\n",
      "step=350, time=1.86e-09, max_dmdt=2.27 ode_step=2.31e-11\n",
      "step=351, time=1.89e-09, max_dmdt=2.19 ode_step=2.31e-11\n",
      "step=352, time=1.91e-09, max_dmdt=2.1 ode_step=2.31e-11\n",
      "step=353, time=1.93e-09, max_dmdt=2.02 ode_step=2.31e-11\n",
      "step=354, time=1.96e-09, max_dmdt=1.95 ode_step=2.31e-11\n",
      "step=355, time=1.98e-09, max_dmdt=1.87 ode_step=2.31e-11\n",
      "step=356, time=2e-09, max_dmdt=1.8 ode_step=2.31e-11\n",
      "step=357, time=2.03e-09, max_dmdt=1.74 ode_step=2.31e-11\n",
      "step=358, time=2.05e-09, max_dmdt=1.67 ode_step=2.31e-11\n",
      "step=359, time=2.07e-09, max_dmdt=1.61 ode_step=2.31e-11\n",
      "step=360, time=2.1e-09, max_dmdt=1.55 ode_step=2.31e-11\n",
      "step=361, time=2.12e-09, max_dmdt=1.49 ode_step=2.31e-11\n",
      "step=362, time=2.14e-09, max_dmdt=1.44 ode_step=2.31e-11\n",
      "step=363, time=2.16e-09, max_dmdt=1.38 ode_step=2.31e-11\n",
      "step=364, time=2.19e-09, max_dmdt=1.33 ode_step=2.31e-11\n",
      "step=365, time=2.21e-09, max_dmdt=1.28 ode_step=2.31e-11\n",
      "step=366, time=2.23e-09, max_dmdt=1.23 ode_step=2.31e-11\n",
      "step=367, time=2.26e-09, max_dmdt=1.19 ode_step=2.31e-11\n",
      "step=368, time=2.28e-09, max_dmdt=1.15 ode_step=2.31e-11\n",
      "step=369, time=2.3e-09, max_dmdt=1.1 ode_step=2.31e-11\n",
      "step=370, time=2.33e-09, max_dmdt=1.06 ode_step=2.31e-11\n",
      "step=371, time=2.35e-09, max_dmdt=1.02 ode_step=2.31e-11\n",
      "step=372, time=2.37e-09, max_dmdt=0.988 ode_step=2.31e-11\n",
      "step=373, time=2.4e-09, max_dmdt=0.952 ode_step=2.31e-11\n",
      "step=374, time=2.43e-09, max_dmdt=0.909 ode_step=3.51e-11\n",
      "step=375, time=2.47e-09, max_dmdt=0.859 ode_step=3.51e-11\n",
      "step=376, time=2.5e-09, max_dmdt=0.812 ode_step=3.51e-11\n",
      "step=377, time=2.54e-09, max_dmdt=0.768 ode_step=3.51e-11\n",
      "step=378, time=2.57e-09, max_dmdt=0.727 ode_step=3.51e-11\n",
      "step=379, time=2.61e-09, max_dmdt=0.688 ode_step=3.51e-11\n",
      "step=380, time=2.64e-09, max_dmdt=0.651 ode_step=3.51e-11\n",
      "step=381, time=2.68e-09, max_dmdt=0.616 ode_step=3.51e-11\n",
      "step=382, time=2.71e-09, max_dmdt=0.583 ode_step=3.51e-11\n",
      "step=383, time=2.75e-09, max_dmdt=0.552 ode_step=3.51e-11\n",
      "step=384, time=2.78e-09, max_dmdt=0.522 ode_step=3.51e-11\n",
      "step=385, time=2.82e-09, max_dmdt=0.494 ode_step=3.51e-11\n",
      "step=386, time=2.85e-09, max_dmdt=0.468 ode_step=3.51e-11\n",
      "step=387, time=2.89e-09, max_dmdt=0.443 ode_step=3.51e-11\n",
      "step=388, time=2.92e-09, max_dmdt=0.42 ode_step=3.51e-11\n",
      "step=389, time=2.96e-09, max_dmdt=0.397 ode_step=3.51e-11\n",
      "step=390, time=2.99e-09, max_dmdt=0.376 ode_step=3.51e-11\n",
      "step=391, time=3.03e-09, max_dmdt=0.357 ode_step=3.51e-11\n",
      "step=392, time=3.06e-09, max_dmdt=0.338 ode_step=3.51e-11\n",
      "step=393, time=3.1e-09, max_dmdt=0.32 ode_step=3.51e-11\n",
      "step=394, time=3.13e-09, max_dmdt=0.303 ode_step=3.51e-11\n",
      "step=395, time=3.17e-09, max_dmdt=0.287 ode_step=3.51e-11\n",
      "step=396, time=3.2e-09, max_dmdt=0.272 ode_step=3.51e-11\n",
      "step=397, time=3.24e-09, max_dmdt=0.258 ode_step=3.51e-11\n",
      "step=398, time=3.27e-09, max_dmdt=0.245 ode_step=3.51e-11\n",
      "step=399, time=3.31e-09, max_dmdt=0.232 ode_step=3.51e-11\n",
      "step=400, time=3.34e-09, max_dmdt=0.22 ode_step=3.51e-11\n",
      "step=401, time=3.38e-09, max_dmdt=0.208 ode_step=3.51e-11\n",
      "step=402, time=3.42e-09, max_dmdt=0.197 ode_step=3.51e-11\n",
      "step=403, time=3.45e-09, max_dmdt=0.187 ode_step=3.51e-11\n",
      "step=404, time=3.49e-09, max_dmdt=0.177 ode_step=3.51e-11\n",
      "step=405, time=3.52e-09, max_dmdt=0.168 ode_step=3.51e-11\n",
      "step=406, time=3.56e-09, max_dmdt=0.159 ode_step=3.51e-11\n",
      "step=407, time=3.59e-09, max_dmdt=0.151 ode_step=3.51e-11\n",
      "step=408, time=3.63e-09, max_dmdt=0.143 ode_step=3.51e-11\n",
      "step=409, time=3.66e-09, max_dmdt=0.136 ode_step=3.51e-11\n",
      "step=410, time=3.7e-09, max_dmdt=0.129 ode_step=3.51e-11\n",
      "step=411, time=3.76e-09, max_dmdt=0.12 ode_step=5.91e-11\n",
      "step=412, time=3.81e-09, max_dmdt=0.11 ode_step=5.91e-11\n",
      "step=413, time=3.87e-09, max_dmdt=0.101 ode_step=5.91e-11\n",
      "step=414, time=3.93e-09, max_dmdt=0.092 ode_step=5.91e-11\n",
      "step=415, time=3.99e-09, max_dmdt=0.0841 ode_step=5.91e-11\n",
      "step=416, time=4.05e-09, max_dmdt=0.077 ode_step=5.91e-11\n",
      "step=417, time=4.11e-09, max_dmdt=0.0705 ode_step=5.91e-11\n",
      "step=418, time=4.17e-09, max_dmdt=0.0645 ode_step=5.91e-11\n",
      "step=419, time=4.23e-09, max_dmdt=0.059 ode_step=5.91e-11\n",
      "step=420, time=4.29e-09, max_dmdt=0.054 ode_step=5.91e-11\n",
      "step=421, time=4.35e-09, max_dmdt=0.0494 ode_step=5.91e-11\n",
      "step=422, time=4.41e-09, max_dmdt=0.0453 ode_step=5.91e-11\n",
      "step=423, time=4.47e-09, max_dmdt=0.0414 ode_step=5.91e-11\n",
      "step=424, time=4.52e-09, max_dmdt=0.0379 ode_step=5.91e-11\n",
      "step=425, time=4.58e-09, max_dmdt=0.0347 ode_step=5.91e-11\n",
      "step=426, time=4.64e-09, max_dmdt=0.0318 ode_step=5.91e-11\n",
      "step=427, time=4.7e-09, max_dmdt=0.0291 ode_step=5.91e-11\n",
      "step=428, time=4.76e-09, max_dmdt=0.0267 ode_step=5.91e-11\n",
      "step=429, time=4.82e-09, max_dmdt=0.0244 ode_step=5.91e-11\n",
      "step=430, time=4.88e-09, max_dmdt=0.0224 ode_step=5.91e-11\n",
      "step=431, time=4.94e-09, max_dmdt=0.0205 ode_step=5.91e-11\n",
      "step=432, time=5e-09, max_dmdt=0.0187 ode_step=5.91e-11\n",
      "step=433, time=5.09e-09, max_dmdt=0.0168 ode_step=8.9e-11\n",
      "step=434, time=5.18e-09, max_dmdt=0.0147 ode_step=8.9e-11\n",
      "step=435, time=5.26e-09, max_dmdt=0.0129 ode_step=8.9e-11\n",
      "step=436, time=5.35e-09, max_dmdt=0.0113 ode_step=8.9e-11\n",
      "step=437, time=5.44e-09, max_dmdt=0.0099 ode_step=8.9e-11\n"
     ]
    }
   ],
   "source": [
    "# PYTEST_VALIDATE_IGNORE_OUTPUT\n",
    "sim.driver.relax(dt=1e-13, stopping_dmdt=0.01, max_steps=5000, save_m_steps=None, save_vtk_steps=None);\n",
    "np.save(\"m0.npy\", sim.spin)  # save equilibrium configuration"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We not plot the magnetisation configuration,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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aB+yq0+MU1tSMprQ01c0pvPXWD/nss0NoNJJLS51Ce7t9wK5+PU5hdXUWJSWp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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc3e0ada050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  9.66821767e-01   1.25543432e-01   3.11232500e-18]\n"
     ]
    }
   ],
   "source": [
    "# PYTEST_VALIDATE_IGNORE_OUTPUT\n",
    "m = sim.spin\n",
    "m.shape = (-1,3)\n",
    "mx = m[:,0]\n",
    "my = m[:,1]\n",
    "mx.shape = (40, 160)\n",
    "my.shape = (40, 160)\n",
    "fig = plt.figure(figsize=(15,5))\n",
    "plt.axes().set_aspect('equal')\n",
    "plt.quiver(mx[1::4,1::4], my[::4,::4], my[::4,::4], pivot='mid', alpha=0.9, scale=45, cmap=plt.get_cmap('jet'), edgecolors='None' )\n",
    "plt.xlim([-0.5,39.5])\n",
    "plt.xticks([])\n",
    "plt.yticks([])\n",
    "plt.show()\n",
    "print(np.average(m[:,:], axis=0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the obtained relaxed magnetisation, the magnetisation evolution can be simulated for the two different external magnetic fields using the following function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def field_simulation(H, name):\n",
    "    print(name)\n",
    "    sim = Sim(mesh, name)\n",
    "    sim.driver.alpha = alpha\n",
    "    sim.driver.gamma = gamma\n",
    "    sim.Ms = Ms\n",
    "    sim.add(UniformExchange(A=A))\n",
    "    sim.add(Demag())\n",
    "    sim.add(Zeeman(H))\n",
    "    sim.set_m(np.load('m0.npy'))  # load the equilibrium magnetisation from the previous step\n",
    "    \n",
    "    timesteps = np.linspace(0, 0.2e-9, 21)\n",
    "    for i, t in enumerate(timesteps):\n",
    "        sim.driver.run_until(t)\n",
    "        if i % 10 == 0:\n",
    "            print(\"\\tsimulated {} s\".format(t))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the created field_simulation function, we obtain the average magnetisation components time evolutions. Note that we only run the simulation for a short time, a full version of this standard problem 4 can be found in folder examples/micromagnetic/std4."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "field_1\n",
      "\tsimulated 0.0 s\n",
      "\tsimulated 1e-10 s\n",
      "\tsimulated 2e-10 s\n"
     ]
    }
   ],
   "source": [
    "# PYTEST_VALIDATE_IGNORE_OUTPUT\n",
    "mu0 = 4 * np.pi * 1e-7  # magnetic constant (H/m)\n",
    "mT = 1e-3 / mu0  # millitesla\n",
    "\n",
    "field_simulation([-24.6 * mT,  4.3 * mT, 0], \"field_1\")\n",
    "#field_simulation([-35.5 * mT, -6.3 * mT, 0], \"field_2\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We could have saved the magnetisation dynamics in python objects on the fly. Instead, we chose to make use of fidimag's automatic saving capabilities and will now read our simulation results back in. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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QR46EZs1g+nR1pkrca9sWxo936w/s2+d1NXJId93lWgi+/97rSiQKBLTOgDGm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\nL70ErVp5XVH8UzeBiIhElZYtYc4c6N/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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc3e148f110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# PYTEST_VALIDATE_IGNORE_OUTPUT\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "from fidimag.common.fileio import DataReader\n",
    "\n",
    "def do_plot(data_name):\n",
    "    dynamics = DataReader(data_name)\n",
    "    # we could load the data with np.loadtxt, but using the DataReader gives \n",
    "    # us the possibility to use the column headers to access our data\n",
    "    fig = plt.figure(figsize=(8, 6))\n",
    "    axes = fig.add_subplot(111)\n",
    "    axes.plot(dynamics[\"time\"] * 1e9, dynamics[\"m_x\"], \"b-\", label=\"m_x\")\n",
    "    axes.plot(dynamics[\"time\"] * 1e9, dynamics[\"m_y\"], \"r--\", label=\"m_y\")\n",
    "    axes.plot(dynamics[\"time\"] * 1e9, dynamics[\"m_z\"], \"g--\", label=\"m_z\")\n",
    "    axes.set_xlabel(\"time (ns)\")                                             \n",
    "    axes.set_xlim((0, 0.25))\n",
    "    axes.set_ylabel(\"unit magnetisation (1)\")                                \n",
    "    axes.set_ylim((-1.05, 1))                                                \n",
    "    axes.legend()\n",
    "    plt.show()\n",
    "    \n",
    "do_plot('field_1.txt')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### References"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[1] muMAG Micromagnetics Website. URL: http://www.ctcms.nist.gov/~rdm/mumag.org.html (Date of access: 26/02/2016)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  },
  "widgets": {
   "state": {},
   "version": "1.1.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}