benkamphaus/binterp.ipynb

## binterp.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.special import jv\n",
    "from scipy.interpolate import interp1d\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n",
    "from random import random\n",
    "\n",
    "# normal generate an x stuff\n",
    "x = np.linspace(0, 6 * np.pi, num=13,  endpoint=True)\n",
    "\n",
    "# higher order functions and anonymous functions means we can gen y values\n",
    "# by mapping x to besselj function + random noise\n",
    "y = map(lambda z: jv(1, z) + random() * 0.01, x)\n",
    "\n",
    "# interp1d returns a _function_ that we can use to interpolate new x's to y's.\n",
    "besselj_interpolator = interp1d(x, y, kind='cubic')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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1oyniTi6kjCzsRt+/P2/c8k8aN2/MPke3qXc9vz6U9CWv2rTxQ+DCWGb5gw/8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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107446790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generate for the whole space with map\n",
    "new_x = np.linspace(0, 6 * np.pi, num=200, endpoint=True)\n",
    "new_y = map(besselj_interpolator, new_x)\n",
    "\n",
    "# scatter plot shows fit\n",
    "plt.scatter(x, y, color=\"red\")\n",
    "plt.plot(new_x, new_y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "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": 4,
	"metadata": {
	"collapsed": true
	},
	"outputs": [],
	"source": [
	"import numpy as np\n",
	"from scipy.special import jv\n",
	"from scipy.interpolate import interp1d\n",
	"from matplotlib import pyplot as plt\n",
	"%matplotlib inline\n",
	"from random import random\n",
	"\n",
	"# normal generate an x stuff\n",
	"x = np.linspace(0, 6 * np.pi, num=13, endpoint=True)\n",
	"\n",
	"# higher order functions and anonymous functions means we can gen y values\n",
	"# by mapping x to besselj function + random noise\n",
	"y = map(lambda z: jv(1, z) + random() * 0.01, x)\n",
	"\n",
	"# interp1d returns a _function_ that we can use to interpolate new x's to y's.\n",
	"besselj_interpolator = interp1d(x, y, kind='cubic')"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 5,
	"metadata": {
	"collapsed": false
	},
	"outputs": [
	{
	"data": {
	"image/png": 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1oyniTi6kjCzsRt+/P2/c8k8aN2/MPke3qXc9vz6U9CWv2rTxQ+DCWGb5gw/8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\nRK5CYII=\n",
	"text/plain": [
	"<matplotlib.figure.Figure at 0x107446790>"
	]
	},
	"metadata": {},
	"output_type": "display_data"
	}
	],
	"source": [
	"# generate for the whole space with map\n",
	"new_x = np.linspace(0, 6 * np.pi, num=200, endpoint=True)\n",
	"new_y = map(besselj_interpolator, new_x)\n",
	"\n",
	"# scatter plot shows fit\n",
	"plt.scatter(x, y, color=\"red\")\n",
	"plt.plot(new_x, new_y)\n",
	"plt.show()"
	]
	},
	{
	"cell_type": "code",
	"execution_count": null,
	"metadata": {
	"collapsed": true
	},
	"outputs": [],
	"source": []
	},
	{
	"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
	}