lotka/q4

## q4
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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8evSmlML2wu2YlDDJtGOOjx+PXScN6F75y1+AH//Yngssd9XddwPvvw+cMHhI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\nY5ATEdkcg5yIyOb+Hyw5NJl0R46SAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5c84931b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "N = 1000\n",
    "x_axis = np.linspace(0,5,N)\n",
    "\n",
    "def getSigma(m):\n",
    "    return 0.04*m**2\n",
    "\n",
    "def garbageProbability(m):\n",
    "    return 0.12/float(m)\n",
    "\n",
    "def gauss(x,sigma,K,mean):\n",
    "    arg = (x-mean)/sigma\n",
    "    return np.exp(-(arg**2)) + K\n",
    "\n",
    "slice1_sigma = getSigma(1.0)\n",
    "slice2_sigma = getSigma(2.0)\n",
    "slice3_sigma = getSigma(3.0)\n",
    "\n",
    "slice_1_K = garbageProbability(1.0)\n",
    "slice_2_K = garbageProbability(2.0)\n",
    "slice_3_K = garbageProbability(3.0)\n",
    "\n",
    "slice1 = gauss(x_axis,slice1_sigma,slice_1_K,1.0)\n",
    "slice2 = gauss(x_axis,slice2_sigma,slice_2_K,2.0)\n",
    "slice3 = gauss(x_axis,slice3_sigma,slice_3_K,3.0)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(x_axis,slice1,label='slice 1')\n",
    "plt.plot(x_axis,slice2,label='slice 2')\n",
    "plt.plot(x_axis,slice3,label='slice 3')\n",
    "plt.legend()\n",
    "plt.ylim(0,2)\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": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
	{
	"cells": [
	{
	"cell_type": "code",
	"execution_count": 40,
	"metadata": {
	"collapsed": false
	},
	"outputs": [
	{
	"data": {
	"image/png": 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8evSmlML2wu2YlDDJtGOOjx+PXScN6F75y1+AH//Yngssd9XddwPvvw+cMHhI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\nY5ATEdkcg5yIyOb+Hyw5NJl0R46SAAAAAElFTkSuQmCC\n",
	"text/plain": [
	"<matplotlib.figure.Figure at 0x7f5c84931b50>"
	]
	},
	"metadata": {},
	"output_type": "display_data"
	}
	],
	"source": [
	"import numpy as np\n",
	"import matplotlib.pyplot as plt\n",
	"%matplotlib inline\n",
	"N = 1000\n",
	"x_axis = np.linspace(0,5,N)\n",
	"\n",
	"def getSigma(m):\n",
	" return 0.04m*2\n",
	"\n",
	"def garbageProbability(m):\n",
	" return 0.12/float(m)\n",
	"\n",
	"def gauss(x,sigma,K,mean):\n",
	" arg = (x-mean)/sigma\n",
	" return np.exp(-(arg**2)) + K\n",
	"\n",
	"slice1_sigma = getSigma(1.0)\n",
	"slice2_sigma = getSigma(2.0)\n",
	"slice3_sigma = getSigma(3.0)\n",
	"\n",
	"slice_1_K = garbageProbability(1.0)\n",
	"slice_2_K = garbageProbability(2.0)\n",
	"slice_3_K = garbageProbability(3.0)\n",
	"\n",
	"slice1 = gauss(x_axis,slice1_sigma,slice_1_K,1.0)\n",
	"slice2 = gauss(x_axis,slice2_sigma,slice_2_K,2.0)\n",
	"slice3 = gauss(x_axis,slice3_sigma,slice_3_K,3.0)\n",
	"\n",
	"plt.figure()\n",
	"plt.plot(x_axis,slice1,label='slice 1')\n",
	"plt.plot(x_axis,slice2,label='slice 2')\n",
	"plt.plot(x_axis,slice3,label='slice 3')\n",
	"plt.legend()\n",
	"plt.ylim(0,2)\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": "2.7.10"
	}
	},
	"nbformat": 4,
	"nbformat_minor": 0
	}