rankine.ipynb

{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Header for necessary modules"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "\n",
      "from __future__ import division\n",
      "import numpy as np\n",
      "import matplotlib as mpl\n",
      "import matplotlib.pyplot as plt\n",
      "from scipy.spatial import Delaunay"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Load the temperature data from an online source."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Retrieve temperature data from online source.\n",
      "import requests, string\n",
      "# http://www.nws.noaa.gov/mdl/gfslamp/lavlamp.shtml\n",
      "# http://www.nws.noaa.gov/mdl/gfslamp/docs/stations_info.shtml (lat/lon)\n",
      "\n",
      "# Get latitude and longitude of stations.\n",
      "#   Load raw data as HTML string.\n",
      "r = requests.get('http://www.nws.noaa.gov/mdl/gfslamp/docs/stations_info.shtml')\n",
      "#   Find Illinois data segment (in a PRE tag).  We know (from examination) that inside of\n",
      "#   the PRE block containing ' IL ' (with whitespace and case matching) we can find the IL\n",
      "#   station data.  This solution isn't robust, but it's good enough for practical cases.\n",
      "il_start  = r.text.find(' IL ')\n",
      "tag_start = r.text.rfind('PRE', il_start-200, il_start) # The string.rfind() function looks backwards from an index.\n",
      "tag_end   = r.text.find('PRE', il_start)\n",
      "data = r.text[tag_start+4:tag_end-2]\n",
      "#print(data)\n",
      "\n",
      "#   Extract latitude and longitude of stations.  We know the columns are fixed (which is\n",
      "#   both inconvenient and convenient).  In this case, we will simply set the limits of\n",
      "#   the relevant columns by counting the number of columns over we need to go.\n",
      "r_stn  = (5, 9) #remember that the last index is an exclusive bound\n",
      "r_name = (10, 31)\n",
      "r_lat  = (36, 41) #we don't need the N/W designation; we know where we are\n",
      "r_lon  = (46, 51)\n",
      "locs = {}\n",
      "for line in data.split('\\n'):\n",
      "    stn  = line[r_stn[0]:r_stn[1]]\n",
      "    name = line[r_name[0]:r_name[1]]\n",
      "    try:\n",
      "        lat  =  float(line[r_lat[0]:r_lat[1]])\n",
      "        lon  = -float(line[r_lon[0]:r_lon[1]])\n",
      "    except ValueError:\n",
      "        # skip rows with invalid data\n",
      "        continue\n",
      "    locs[stn] = (lon, lat)\n",
      "\n",
      "sites = []\n",
      "for site in locs:\n",
      "    sites.append(locs[site])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Plot the temperature data thus loaded."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mpl.rcParams['figure.figsize']=[10,10]\n",
      "plt.plot(np.array(sites)[:,0],np.array(sites)[:,1],'go')\n",
      "for stn in list(locs.keys()):\n",
      "    tmp = locs[stn]\n",
      "    #plt.text(tmp[0]+0.04, tmp[1]+0.02, stn)\n",
      "\n",
      "#The borders of IL in lat/lon coordinates are located in this file and included for context.\n",
      "borders = np.load('borders_il.npy')\n",
      "plt.plot(borders[:,0], borders[:,1],'k-')\n",
      "#The borders of IL lie at:  Latitude 36\u00b058\u2032N to 42\u00b030\u2032N; Longitude 87\u00b030\u2032W to 91\u00b031\u2032W\n",
      "plt.axis('equal') #((-91.517, -87.5, 36.967, 42.5))\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Hz/4jWUtMTISNjQ26du0qOspzlbUNAH84UllYyIksC4+pIVnKzc3FunXrMGzY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\n/wekV1Tc1TNU9AAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x108525150>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Set up the interpolation."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Interpolate some points.  Plot a complete interpolation."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def dot(pt1, pt2):\n",
      "    \"\"\"Calculate dot product of two points from the origin.\"\"\"\n",
      "    return (pt1[0]*pt2[0] + pt1[1]*pt2[1])\n",
      "\n",
      "def calc_bary_coords(pt, pta, ptb, ptc):\n",
      "    \"\"\"Calculates the barycentric coordinates of the pair pt in the triangle of pairs pta, ptb, and ptc.\"\"\"\n",
      "    # Move the origin to pta.\n",
      "    vc = [None, None]\n",
      "    vc[0] = ptc[0] - pta[0]; vc[1] = ptc[1] - pta[1] #vc is from pta to ptc\n",
      "    vb = [None, None]\n",
      "    vb[0] = ptb[0] - pta[0]; vb[1] = ptb[1] - pta[1] #vb is from pta to ptb\n",
      "    vp = [None, None]\n",
      "    vp[0] = pt[0] - pta[0];  vp[1] = pt[1] - pta[1]  #vt is from pta to pt\n",
      "    \n",
      "    # Compute the dot products.\n",
      "    dot_cc = dot(vc, vc)\n",
      "    dot_cb = dot(vc, vb)\n",
      "    dot_cp = dot(vc, vp)\n",
      "    dot_bb = dot(vb, vb)\n",
      "    dot_bp = dot(vb, vp)\n",
      "    \n",
      "    # Compute barycentric coordinates\n",
      "    invDenom = 1 / (dot_cc * dot_bb - dot_cb * dot_cb)\n",
      "    u = (dot_bb * dot_cp - dot_cb * dot_bp) * invDenom\n",
      "    v = (dot_cc * dot_bp - dot_cb * dot_cp) * invDenom\n",
      "    \n",
      "    # Check if point is in triangle.\n",
      "    in_tri = ((u >= 0) and (v >= 0) and (u + v < 1))\n",
      "    return ([u, v], in_tri)\n",
      " "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Make a list of all possible triangles of points (easy but not optimal as it repeats triangles).\n",
      "from itertools import permutations\n",
      "triangles = permutations(range(len(sites)), 3)\n",
      "\"\"\"\n",
      "# Interpolate to find the value at set points.\n",
      "pts = [[40.0,90.0]] # pts are the x-y coordinates of the desired site(s)\n",
      "pts_tri = []\n",
      "pts_bc  = []\n",
      "\n",
      "for pt in pts:\n",
      "    # For a given interpolant point, find the triangle in which it lies.\n",
      "    for triangle in triangles:\n",
      "        a = sites[triangle[0]]\n",
      "        b = sites[triangle[1]]\n",
      "        c = sites[triangle[2]]\n",
      "        \n",
      "        # Calculate the barycentric (weighted) coordinates of an interior point.\n",
      "        (pt_bc,in_tri) = calc_bary_coords(pt,a,b,c)\n",
      "        \n",
      "        if in_tri:\n",
      "            pts_tri.append(triangle)\n",
      "            pts_bc.append(pt_bc)\n",
      "            break\n",
      "\n",
      "mpl.rcParams['figure.figsize']=[10,10]\n",
      "for triangle in pts_tri:\n",
      "    data = []\n",
      "    for i in [0,1,2,0]:\n",
      "        data.append(sites[triangle[i]])\n",
      "    plt.plot(np.array(data).T[0], np.array(data).T[1], 'k-')\"\"\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "---"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Generate random data points.\n",
      "from random import random\n",
      "hi = 10\n",
      "sites = [] # sites are the x-y coordinates of the observed temperatures\n",
      "for i in range(0,hi):\n",
      "    site = [random()]\n",
      "    site.append(random())\n",
      "    sites.append(site)\n",
      "\n",
      "triangles = triangulate_points(sites)\n",
      "plot_triangulated_points(sites,triangles)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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9hw8fvmvdi3ufcq5kZ2fD3d0dlpaW2LVrl0yt0iUiqKqqyuQiRzZb5hsaGhqw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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10d143850>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def triangulate_points(points):\n",
      "    \"\"\"Triangulate a set of data.  Possible formats include 'list', 'pairs' and ''.\"\"\"\n",
      "    points = np.array(points)\n",
      "    triangles = Delaunay(points)\n",
      "    return triangles\n",
      "\n",
      "def plot_triangulated_points(points,triangles):\n",
      "    points = np.array(points)\n",
      "    plt.triplot(points[:,0], points[:,1], triangles.vertices.copy(), 'k-')\n",
      "    plt.plot(points[:,0], points[:,1], 'b.')\n",
      "    plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "\n",
      "\n",
      "for i, pt in enumerate(pts):\n",
      "    # For a given interpolant point, find the triangle in which it lies.\n",
      "    for j, triangle in enumerate(triangles.vertices):\n",
      "        a = points[triangle[0]]\n",
      "        b = points[triangle[1]]\n",
      "        c = points[triangle[2]]\n",
      "        \n",
      "        # Calculate the barycentric coordinates of an interior point.\n",
      "        (pt_bc,in_tri) = calc_bary_coords(pt,a,b,c)\n",
      "        \n",
      "        if in_tri:\n",
      "            pts_tri[i] = j\n",
      "            break\n",
      "\n",
      "#for i in range(0,len(pts)):\n",
      "#    print(pts[i], pts_tri[i], triangles.vertices[i],points[triangles.vertices[pts_tri[i]][0]],points[triangles.vertices[pts_tri[i]][1]],points[triangles.vertices[pts_tri[i]][2]])\n",
      "\n",
      "sites = np.array(sites)\n",
      "pts = np.array(pts)\n",
      "plt.triplot(sites[:,0], sites[:,1], triangles.vertices.copy(), 'k-')\n",
      "plt.plot(sites[:,0], sites[:,1], 'b.')\n",
      "plt.plot(pts[:,0], pts[:,1], 'g.')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "AttributeError",
       "evalue": "'itertools.permutations' object has no attribute 'vertices'",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
        "\u001b[0;32m<ipython-input-13-e02eef0fce90>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpt\u001b[0m \u001b[0;32min\u001b[0m \u001b[0menumerate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpts\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0;31m# For a given interpolant point, find the triangle in which it lies.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m     \u001b[0;32mfor\u001b[0m \u001b[0mj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtriangle\u001b[0m \u001b[0;32min\u001b[0m \u001b[0menumerate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtriangles\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvertices\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      7\u001b[0m         \u001b[0ma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpoints\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mtriangle\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      8\u001b[0m         \u001b[0mb\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpoints\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mtriangle\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;31mAttributeError\u001b[0m: 'itertools.permutations' object has no attribute 'vertices'"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(triangles.vertices)\n",
      "print(sites)\n",
      "\n",
      "for i in range(0,len(pts)):\n",
      "    print(pts[i], pts_tri[i], triangles.vertices[pts_tri[i]], sites[triangles.vertices[pts_tri[i]][0]], sites[triangles.vertices[pts_tri[i]][1]], sites[triangles.vertices[pts_tri[i]][2]])\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "AttributeError",
       "evalue": "'itertools.permutations' object has no attribute 'vertices'",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
        "\u001b[0;32m<ipython-input-14-d53b563aafd1>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtriangles\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvertices\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msites\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpts\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpts\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpts_tri\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtriangles\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvertices\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mpts_tri\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msites\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mtriangles\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvertices\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mpts_tri\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msites\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mtriangles\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvertices\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mpts_tri\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msites\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mtriangles\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvertices\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mpts_tri\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;31mAttributeError\u001b[0m: 'itertools.permutations' object has no attribute 'vertices'"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Interpolate the proper value from the triangle vertices.\n",
      "#scipy.interpolate.griddata is an alternative way to do this"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 171
    }
   ],
   "metadata": {}
  }
 ]
}