Testing which way to calculate line intersections is the fastest

LFC_Development.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# LFC Development\n",
    "Develop calculation methods for the LFC and other problems that require the estimation of the intersection of two lines sampled at arbitrary spacing."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fake Data\n",
    "Make some fake data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x1 = np.linspace(5,30,17)\n",
    "y1 = 3*x1**2\n",
    "y2 = 100*x1 - 650"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x109cddf10>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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6SAVUJ1u4bILYhAnJ5OYm8vTTsGgRXHVVkCncrx80Uq+USJ0QrWDgQKaZHQSe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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1040ac8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x1,y1,'-o')\n",
    "plt.plot(x1,y2,'-o')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def _nearest_intersection_idx(x, a, b):\n",
    "    \"\"\"\n",
    "    Determines the index of the point just before two lines with\n",
    "    common x values.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    x : array-like\n",
    "        1-dimensional array of numeric x-values\n",
    "    a : array-like\n",
    "        1-dimensional array of y-values for line 1\n",
    "    b : array-like\n",
    "        1-dimensional array of y-values for line 2\n",
    "        \n",
    "    Returns\n",
    "    -------\n",
    "        An array of indexes representing the index of the values\n",
    "        just before the intersection(s) of the two lines. \n",
    "    \"\"\"\n",
    "    # Difference in the two y-value sets\n",
    "    difference = a-b\n",
    "    \n",
    "    # Determine the point just before the intersection of the lines\n",
    "    # Will return multiple points for multiple intersections\n",
    "    sign_change_idx = np.where(np.diff(np.sign(difference)))[0]\n",
    "    \n",
    "    return sign_change_idx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def find_intersections(x, a, b):\n",
    "    \n",
    "    \"\"\"\n",
    "    Calculates the best estimate of the intersection(s) of two y-value\n",
    "    data sets that share a common x-value set. Returns list of tuples\n",
    "    that are the intersections.\n",
    "    \"\"\"\n",
    "    \n",
    "    # Find the index of the points just before the intersection(s)\n",
    "    nearest_idx = _nearest_intersection_idx(x, a, b)\n",
    "    \n",
    "    # Build a list of dictionaries of intersections\n",
    "    intersections = []\n",
    "    for idx in nearest_idx:\n",
    "        intersection = {'x1': x[idx],\n",
    "                        'x2': x[idx + 1],\n",
    "                        'ya1': a[idx],\n",
    "                        'ya2': a[idx+1],\n",
    "                        'yb1': b[idx],\n",
    "                        'yb2': b[idx+1]}\n",
    "        \n",
    "        # Compute the slope of each line\n",
    "        intersection['m1'] = (intersection['ya2'] - intersection['ya1'])\\\n",
    "                             /(intersection['x2']-intersection['x1'])\n",
    "            \n",
    "        intersection['m2'] = (intersection['yb2'] - intersection['yb1'])\\\n",
    "                             /(intersection['x2']-intersection['x1'])\n",
    "        \n",
    "        # Compute the intercept of each line\n",
    "        intersection['b1'] = intersection['ya1'] -\\\n",
    "                             intersection['m1'] * intersection['x1']\n",
    "            \n",
    "        intersection['b2'] = intersection['yb1'] -\\\n",
    "                             intersection['m2'] * intersection['x1']\n",
    "        \n",
    "        # Compute the intersection\n",
    "        intersection['xi'] = (intersection['b2'] - intersection['b1'])\\\n",
    "                             / (intersection['m1'] - intersection['m2'])\n",
    "            \n",
    "        intersection['yi'] = intersection['m1'] * intersection['xi']\\\n",
    "                             + intersection['b1']\n",
    "        \n",
    "        # Add a tuple of the x and y values of the intersection to the list\n",
    "        # that will be returned\n",
    "        intersections.append((intersection['xi'], intersection['yi']))\n",
    "    \n",
    "    return intersections"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slowest run took 4.77 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
      "10000 loops, best of 3: 28.5 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "intersections =  find_intersections(x1,y1,y2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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ksXffVYKYSLqpAzmF6koH2PJNy5nw+gRWlKxgRJ8R3NzrZlodVrnaS8VoopId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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109dad910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "intersections =  find_intersections(x1,y1,y2)\n",
    "plt.plot(x1,y1,'-o')\n",
    "plt.plot(x1,y2,'-o')\n",
    "\n",
    "for intersection in intersections:\n",
    "    plt.axhline(y=intersection[1])\n",
    "    plt.axvline(x=intersection[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(8.8884228187919465, 238.84228187919462),\n",
       " (24.445364238410598, 1794.5364238410598)]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "intersections"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def find_intersections(x, a, b):\n",
    "    \n",
    "    \"\"\"\n",
    "    Calculates the best estimate of the intersection(s) of two y-value\n",
    "    data sets that share a common x-value set.\n",
    "    \"\"\"\n",
    "    \n",
    "    # Find the index of the points just before the intersection(s)\n",
    "    nearest_idx = _nearest_intersection_idx(x, a, b)\n",
    "    \n",
    "    # Make an empty array to hold what we'll need for calculating \n",
    "    # approximate intersections. Each row is an intersection\n",
    "    # x1, x2, ya1, ya2, yb1, yb2, m1, m2, b1, b2, xi, yi\n",
    "    intersections = np.zeros((np.size(nearest_idx), 12))\n",
    "    \n",
    "    # Place x values for each intersection\n",
    "    intersections[:,0] = x[nearest_idx]\n",
    "    intersections[:,1] = x[nearest_idx + 1]\n",
    "    \n",
    "    # Place y values for the first line\n",
    "    intersections[:,2] = a[nearest_idx]\n",
    "    intersections[:,3] = a[nearest_idx + 1]\n",
    "    \n",
    "    # Place y values for the second line\n",
    "    intersections[:,4] = b[nearest_idx]\n",
    "    intersections[:,5] = b[nearest_idx + 1]\n",
    "    \n",
    "    # Calculate the slope of each line (delta y / delta x)\n",
    "    intersections[:,6] = (intersections[:,3] - intersections[:,2])\\\n",
    "                        /(intersections[:,1] - intersections[:,0])\n",
    "        \n",
    "    intersections[:,7] = (intersections[:,5] - intersections[:,4])\\\n",
    "                        /(intersections[:,1] - intersections[:,0])\n",
    "    \n",
    "    # Calculate the intercept of each line\n",
    "    intersections[:,8] = intersections[:,2] - intersections[:,6] * intersections[:,0]\n",
    "    \n",
    "    intersections[:,9] = intersections[:,4] - intersections[:,7] * intersections[:,0]\n",
    "\n",
    "    # Calculate the x-intersection of the lines\n",
    "    # (b2-b1)/(m1-m2)\n",
    "    intersections[:,10] = (intersections[:,9] - intersections[:,8])\\\n",
    "                         /(intersections[:,6] - intersections[:,7])\n",
    "    \n",
    "    # Calculate the y-intersection of the lines\n",
    "    intersections[:,11] = intersections[:,6] * intersections[:,10] + intersections[:,8]\n",
    "    \n",
    "    return intersections [:,10:12]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slowest run took 5.55 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
      "10000 loops, best of 3: 63.1 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "intersections =  find_intersections(x1,y1,y2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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1hYaWppCGlorEzyzIJL7ituVsOXkCdFjBr/qO4OZeN9fpbOFkUJ5BhlMwEIlPeblzyCHG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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109dde190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "intersections =  find_intersections(x1,y1,y2)\n",
    "plt.plot(x1,y1,'-o')\n",
    "plt.plot(x1,y2,'-o')\n",
    "\n",
    "for intersection in intersections:\n",
    "    plt.axhline(y=intersection[1])\n",
    "    plt.axvline(x=intersection[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[    8.88842282,   238.84228188],\n",
       "       [   24.44536424,  1794.53642384]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "intersections"
   ]
  }
 ],
 "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
}