check_autocorrelationfunction.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "simulation.py:42: RuntimeWarning: divide by zero encountered in power\n",
      "  d2MSD=self.alpha*(self.alpha-1)*(self.t*self.dt)**(self.alpha-2.)*self.K_alpha\n"
     ]
    }
   ],
   "source": [
    "import main \n",
    "import matplotlib.pyplot as plt\n",
    "#%matplotlib inline\n",
    "import analyse_tool \n",
    "import numpy as np\n",
    "import matplotlib.cm as cm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# check influence of length change on konvergenz \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/mi/janekg89/miniconda2/lib/python2.7/site-packages/numpy/core/numeric.py:474: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return array(a, dtype, copy=False, order=order)\n"
     ]
    }
   ],
   "source": [
    "x=np.logspace(1,8,num=10,base=3)\n",
    "for i in x.astype(int):\n",
    "    c=analyse_tool.Analyse(D=2,particles=10,length=i,alpha=0.5,dt=0.5,x=1)\n",
    "    zt=np.fft.ifft(c.z())\n",
    "    plt.plot(zt)\n",
    "    #plt.plot(c.alpha*(c.alpha-1)*c.t**(c.alpha-2))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# check influence of alpha change on konvergenz \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/mi/janekg89/miniconda2/lib/python2.7/site-packages/ipykernel/__main__.py:6: RuntimeWarning: divide by zero encountered in power\n",
      "/home/mi/janekg89/miniconda2/lib/python2.7/site-packages/ipykernel/__main__.py:6: RuntimeWarning: invalid value encountered in multiply\n"
     ]
    }
   ],
   "source": [
    "x=np.logspace(0,1,num=5,base=2)-1\n",
    "for i in x:\n",
    "    c=analyse_tool.Analyse(D=2,particles=10,length=200,alpha=i,dt=0.5,x=1)\n",
    "    #zt=np.fft.ifft(c.z())\n",
    "    #plt.plot(zt)\n",
    "    plt.plot(c.alpha*(c.alpha-1)*c.t**(c.alpha-2))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  3.33333333e-05   1.38104521e-01   3.33366667e-01   6.09509042e-01\n",
      "   1.00003333e+00]\n"
     ]
    }
   ],
   "source": [
    "# check influence of detla t change on konvergenz\n",
    "print (np.logspace(0,1,num=5,base=4)-0.9999)/3.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x=(np.logspace(0,1,num=5,base=4)-0.5)/3.\n",
    "for i in x:\n",
    "    c=analyse_tool.Analyse(D=2,particles=10,length=200,alpha=0.5,dt=i,x=1)\n",
    "    zt=np.fft.ifft(c.z())\n",
    "    plt.plot(zt)\n",
    "    #plt.plot(c.alpha*(c.alpha-1)*c.t**(c.alpha-2))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "zww=c.alpha*(c.alpha-1)*c.K_alpha*np.fft.fft(c.t[1:]**(c.alpha-2))\n",
    "plt.plot((zww[:1000/2]-zww[0]))\n",
    "plt.plot(c.z()[:1000/2])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "c=analyse_tool.Analyse(D=2,particles=10,length=200,alpha=0.5,dt=i,x=1)\n",
    "zt=np.fft.ifft(c.z()+1)\n",
    "zt0=np.fft.ifft(c.z())\n",
    "plt.plot(zt)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<iterator object at 0x7faa0abcc690>\n",
      "0.1\n"
     ]
    }
   ],
   "source": [
    "colors = iter(cm.rainbow(np.linspace(0, 1, 10)))\n",
    "colors2 = iter(cm.rainbow(np.linspace(0, 1, 10)))\n",
    "\n",
    "print colors\n",
    "for i in np.linspace(0.1,1,1):\n",
    "    print i\n",
    "    c=analyse_tool.Analyse(D=2,particles=10,length=1000,alpha=0.5,dt=1, x=1)\n",
    "    msd=2*c.D*c.t**c.alpha\n",
    "    dmsd=np.diff(msd)\n",
    "    ddmsd=np.diff(dmsd)\n",
    "    #omega=np.linspace(0,1,1000)\n",
    "    z_omega=np.fft.fft(ddmsd/2)\n",
    "    frq=np.fft.fftfreq(c.n-2)*(np.pi*2./(c.dt))\n",
    "    plt.plot(frq,z_omega, color=next(colors))\n",
    "    ###########\n",
    "    #dd2msd=c.alpha*(c.alpha-1)*c.t**(c.alpha-2)\n",
    "    #z2_omega=np.fft.fft(dd2msd[1:])\n",
    "    #plt.plot( frq,z2_omega)\n",
    "    ####\n",
    "    plt.plot(c.frq,c.z(), color=next(colors),label=\"analytical from paper alpha= %f\" %i)\n",
    "    \n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "c=analyse_tool.Analyse(D=2,particles=10,length=500,alpha=0.4,dt=1, x=1)\n",
    "msd=2*c.D*c.t**c.alpha\n",
    "frq=np.fft.fftfreq(c.n)*(np.pi*2./(c.dt))\n",
    "z_omega=-((frq**2)/2.)*np.fft.fft(msd)\n",
    "plt.plot(frq,z_omega, color=next(colors))\n",
    "plt.plot(c.frq,c.z(), color=next(colors),label=\"analytical from paper\")\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "'''\n",
    "msd=2*c.t**c.alpha\n",
    "dmsd=np.diff(msd)\n",
    "ddmsd=np.diff(dmsd)\n",
    "\n",
    "\n",
    "#omega=np.linspace(0,1,1000)\n",
    "z_omega=np.fft.fft(ddmsd/2)\n",
    "frq=np.fft.fftfreq(c.n-2)*(np.pi*2./(c.dt))\n",
    "'''     \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'int' object has no attribute 'shape'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-26-4abdfd1c2353>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m: 'int' object has no attribute 'shape'"
     ]
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "x and y must have same first dimension",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-16-f8ff28d6b94f>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfrq\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mz\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfrq\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mz_omega\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m2.22\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32m/home/mi/janekg89/miniconda2/lib/python2.7/site-packages/matplotlib/pyplot.pyc\u001b[0m in \u001b[0;36mplot\u001b[1;34m(*args, **kwargs)\u001b[0m\n\u001b[0;32m   3152\u001b[0m         \u001b[0max\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mhold\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mhold\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   3153\u001b[0m     \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 3154\u001b[1;33m         \u001b[0mret\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0max\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   3155\u001b[0m     \u001b[1;32mfinally\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   3156\u001b[0m         \u001b[0max\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mhold\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mwashold\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m/home/mi/janekg89/miniconda2/lib/python2.7/site-packages/matplotlib/__init__.pyc\u001b[0m in \u001b[0;36minner\u001b[1;34m(ax, *args, **kwargs)\u001b[0m\n\u001b[0;32m   1810\u001b[0m                     warnings.warn(msg % (label_namer, func.__name__),\n\u001b[0;32m   1811\u001b[0m                                   RuntimeWarning, stacklevel=2)\n\u001b[1;32m-> 1812\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0max\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1813\u001b[0m         \u001b[0mpre_doc\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0minner\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__doc__\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1814\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mpre_doc\u001b[0m \u001b[1;32mis\u001b[0m \u001b[0mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m/home/mi/janekg89/miniconda2/lib/python2.7/site-packages/matplotlib/axes/_axes.pyc\u001b[0m in \u001b[0;36mplot\u001b[1;34m(self, *args, **kwargs)\u001b[0m\n\u001b[0;32m   1422\u001b[0m             \u001b[0mkwargs\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'color'\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mc\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1423\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1424\u001b[1;33m         \u001b[1;32mfor\u001b[0m \u001b[0mline\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_get_lines\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1425\u001b[0m             \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0madd_line\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mline\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1426\u001b[0m             \u001b[0mlines\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mline\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m/home/mi/janekg89/miniconda2/lib/python2.7/site-packages/matplotlib/axes/_base.pyc\u001b[0m in \u001b[0;36m_grab_next_args\u001b[1;34m(self, *args, **kwargs)\u001b[0m\n\u001b[0;32m    384\u001b[0m                 \u001b[1;32mreturn\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    385\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mremaining\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m<=\u001b[0m \u001b[1;36m3\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 386\u001b[1;33m                 \u001b[1;32mfor\u001b[0m \u001b[0mseg\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_plot_args\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mremaining\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    387\u001b[0m                     \u001b[1;32myield\u001b[0m \u001b[0mseg\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    388\u001b[0m                 \u001b[1;32mreturn\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m/home/mi/janekg89/miniconda2/lib/python2.7/site-packages/matplotlib/axes/_base.pyc\u001b[0m in \u001b[0;36m_plot_args\u001b[1;34m(self, tup, kwargs)\u001b[0m\n\u001b[0;32m    362\u001b[0m             \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mindex_of\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtup\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    363\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 364\u001b[1;33m         \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_xy_from_xy\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    365\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    366\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcommand\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;34m'plot'\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m/home/mi/janekg89/miniconda2/lib/python2.7/site-packages/matplotlib/axes/_base.pyc\u001b[0m in \u001b[0;36m_xy_from_xy\u001b[1;34m(self, x, y)\u001b[0m\n\u001b[0;32m    221\u001b[0m         \u001b[0my\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_check_1d\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0my\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    222\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m!=\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 223\u001b[1;33m             \u001b[1;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"x and y must have same first dimension\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    224\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[1;33m>\u001b[0m \u001b[1;36m2\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[1;33m>\u001b[0m \u001b[1;36m2\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    225\u001b[0m             \u001b[1;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"x and y can be no greater than 2-D\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mValueError\u001b[0m: x and y must have same first dimension"
     ]
    }
   ],
   "source": [
    "plt.plot(c.frq,c.z())\n",
    "plt.plot(frq,(z_omega+1)*2*2.22)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "dd2msd=c.alpha*(c.alpha-1)*c.t**(c.alpha-2)\n",
    "z2_omega=np.fft.fft(dd2msd[1:])\n",
    "#plt.plot(z2_omega)\n",
    "#plt.show()\n",
    "#print frq.shape , c.frq.shape\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#plt.plot(c.frq,c.z())\n",
    "plt.plot(c.frq[:-1],z2_omega)\n",
    "plt.plot(frq,(z_omega))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "z_t=np.fft.ifft(c.z())\n",
    "plt.plot(z_t)\n",
    "plt.plot(dd2msd)\n",
    "plt.plot(ddmsd)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "x and y must have same first dimension",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-14-932e1179485d>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      9\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     10\u001b[0m \u001b[0mz2_omega\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfft\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mhfft\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdd2msd\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 11\u001b[1;33m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m \u001b[0mfrq\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mz2_omega\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     12\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m \u001b[0mfrq111\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mz2_omega111\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     13\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m/home/mi/janekg89/miniconda2/lib/python2.7/site-packages/matplotlib/pyplot.pyc\u001b[0m in \u001b[0;36mplot\u001b[1;34m(*args, **kwargs)\u001b[0m\n\u001b[0;32m   3152\u001b[0m         \u001b[0max\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mhold\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mhold\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   3153\u001b[0m     \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 3154\u001b[1;33m         \u001b[0mret\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0max\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   3155\u001b[0m     \u001b[1;32mfinally\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   3156\u001b[0m         \u001b[0max\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mhold\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mwashold\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m/home/mi/janekg89/miniconda2/lib/python2.7/site-packages/matplotlib/__init__.pyc\u001b[0m in \u001b[0;36minner\u001b[1;34m(ax, *args, **kwargs)\u001b[0m\n\u001b[0;32m   1810\u001b[0m                     warnings.warn(msg % (label_namer, func.__name__),\n\u001b[0;32m   1811\u001b[0m                                   RuntimeWarning, stacklevel=2)\n\u001b[1;32m-> 1812\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0max\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1813\u001b[0m         \u001b[0mpre_doc\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0minner\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__doc__\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1814\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mpre_doc\u001b[0m \u001b[1;32mis\u001b[0m \u001b[0mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m/home/mi/janekg89/miniconda2/lib/python2.7/site-packages/matplotlib/axes/_axes.pyc\u001b[0m in \u001b[0;36mplot\u001b[1;34m(self, *args, **kwargs)\u001b[0m\n\u001b[0;32m   1422\u001b[0m             \u001b[0mkwargs\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'color'\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mc\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1423\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1424\u001b[1;33m         \u001b[1;32mfor\u001b[0m \u001b[0mline\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_get_lines\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1425\u001b[0m             \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0madd_line\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mline\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1426\u001b[0m             \u001b[0mlines\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mline\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m/home/mi/janekg89/miniconda2/lib/python2.7/site-packages/matplotlib/axes/_base.pyc\u001b[0m in \u001b[0;36m_grab_next_args\u001b[1;34m(self, *args, **kwargs)\u001b[0m\n\u001b[0;32m    384\u001b[0m                 \u001b[1;32mreturn\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    385\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mremaining\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m<=\u001b[0m \u001b[1;36m3\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 386\u001b[1;33m                 \u001b[1;32mfor\u001b[0m \u001b[0mseg\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_plot_args\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mremaining\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    387\u001b[0m                     \u001b[1;32myield\u001b[0m \u001b[0mseg\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    388\u001b[0m                 \u001b[1;32mreturn\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m/home/mi/janekg89/miniconda2/lib/python2.7/site-packages/matplotlib/axes/_base.pyc\u001b[0m in \u001b[0;36m_plot_args\u001b[1;34m(self, tup, kwargs)\u001b[0m\n\u001b[0;32m    362\u001b[0m             \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mindex_of\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtup\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    363\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 364\u001b[1;33m         \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_xy_from_xy\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    365\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    366\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcommand\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;34m'plot'\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m/home/mi/janekg89/miniconda2/lib/python2.7/site-packages/matplotlib/axes/_base.pyc\u001b[0m in \u001b[0;36m_xy_from_xy\u001b[1;34m(self, x, y)\u001b[0m\n\u001b[0;32m    221\u001b[0m         \u001b[0my\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_check_1d\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0my\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    222\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m!=\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 223\u001b[1;33m             \u001b[1;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"x and y must have same first dimension\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    224\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[1;33m>\u001b[0m \u001b[1;36m2\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[1;33m>\u001b[0m \u001b[1;36m2\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    225\u001b[0m             \u001b[1;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"x and y can be no greater than 2-D\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mValueError\u001b[0m: x and y must have same first dimension"
     ]
    }
   ],
   "source": [
    "c=analyse_tool.Analyse(D=2,particles=10,length=1000,alpha=0.3,dt=1, x=1)\n",
    "d=analyse_tool.Analyse(D=2,particles=10,length=2000,alpha=0.3,dt=1, x=1)\n",
    "dd2msd=c.alpha*(c.alpha-1)*c.t[1:]**(c.alpha-2)\n",
    "dd2msd111=c.alpha*(c.alpha-1)*d.t[1:]**(c.alpha-2)\n",
    "frq111=np.fft.fftfreq(d.n-1)*(np.pi*2./(c.dt))\n",
    "frq=np.fft.fftfreq(c.n-1)*(np.pi*2./(c.dt))\n",
    "#print dd2msd\n",
    "z2_omega111=np.fft.hfft(dd2msd111)\n",
    "\n",
    "z2_omega=np.fft.hfft(dd2msd)\n",
    "plt.plot( frq[:],z2_omega)\n",
    "plt.plot( frq111[:],z2_omega111)\n",
    "\n",
    "plt.show()\n",
    "print c.n\n",
    "#print z2_omega[0]\n",
    "#print z2_omega.shape\n",
    "#print frq.shape\n",
    "#print c.frq.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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VK1OcxqWUCmHx8VJXq1kzeOWVNJu1aCEbso8ener7g09o0k/H2fhEivRozg2Z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\n722iSC7fAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f14dbe007d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "z2_omega=np.fft.fft(dd2msd)\n",
    "z3_omega=np.fft.rfft(dd2msd)\n",
    "\n",
    "plt.plot((z2_omega-z2_omega[0])/(z2_omega.max()-z2_omega.min()))\n",
    "plt.plot((z3_omega-z3_omega[0])/(z3_omega.max()-z3_omega.min()))\n",
    "plt.plot(c.z())\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}