dft_tools/test/triqs/gfs/test_fourier_matsubara.ipynb

{
 "metadata": {
  "name": "fourier_real_time"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pytriqs.archive import HDFArchive\n",
      "from pytriqs.gf.local import GfReFreq, GfReTime\n",
      "from pytriqs.plot.mpl_interface import oplot\n",
      "\n",
      "# Opens the file G.h5, in read mode\n",
      "R = HDFArchive('../../../../build/test/triqs/gf/fourier_real_time.h5', 'r')\n",
      "Gw1 = R['Gw1']\n",
      "Gt1 = R['Gt1']\n",
      "Gw1b = R['Gw1b']\n",
      "Gt1b = R['Gt1b']\n",
      "Gt2 = R['Gt2']\n",
      "Gw2 = R['Gw2']\n",
      "Gw2b = R['Gw2b']\n",
      "Gt3 = R['Gt3']\n",
      "Gw3 = R['Gw3']"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a0=0.632456\n",
      "def lorentz(x,a=a0):\n",
      "    return 2.0*a / (x*x + a*a)\n",
      "def lorentz_inv(x,a=a0):\n",
      "    return exp(-a*abs(x))\n",
      "oplot(Gw1,'o',lorentz,'-')\n",
      "show()\n",
      "#verification that TF(TF^{-1})=Id\n",
      "oplot(Gw1b,'-o')\n",
      "show()\n",
      "oplot(Gt1,'-o',lorentz_inv,'-',x_window=(-100,100))\n",
      "show()\n",
      "#verification that TF(lorentz)=lorentz_inv\n",
      "oplot(Gt1b,'o')\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAuIAAAHuCAYAAADayWnZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ns2fPnouO27t3L+Hh4fbXrVu3
      },
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAvAAAAHuCAYAAAD5kjgMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nPf7441qzZk2F/WbNmqVDhw7p
      },
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAuUAAAHiCAYAAABP17LbAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nnBBxrcXFxQoEAiosLJTX61VB
      },
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAvMAAAHiCAYAAABlZ0N0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nL7+s8PBwZWRkaP78+Vq7dq3a
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a0=7.03184\n",
      "def expo(x,a=a0):\n",
      "    if(x>0):return -0.5*1j*exp(-a*x)\n",
      "    else:return 0.5*1j*exp(a*x)\n",
      "def expo_inv(x,a=a0):\n",
      "    return 0.5/(x+a*1j)+0.5/(x-a*1j)\n",
      "\n",
      "oplot(Gt2,'o',expo,'-')\n",
      "show()\n",
      "oplot(Gw2,'o',expo_inv,'-',x_window=(-50,50))\n",
      "show()\n",
      "oplot(Gw2b,'o',x_window=(-50,50))\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
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      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAuoAAAH1CAYAAACgD9t1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nyMjIMD766CNXnrvuusv4yU9+
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "oplot(Gt3,'o')\n",
      "show()\n",
      "oplot(Gw3,'o',x_window=(-15,15))\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAukAAAHiCAYAAABV61JVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nWVmJe++9F//5z38ivrdr1y4c
      },
      {
       "output_type": "display_data",
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      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}