{
 "metadata": {
  "name": "TideDataDemo"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#NumPy Demo\n",
      "\n",
      "We'll be using [this CSV file](https://raw.github.com/gist/4049563/385dd8c10e8e74eb05d8d83266a2acc8e2ccd7f7/BatteryParkTideData.csv) of tide level data for this demo. The data are from Battery Park, New York City on October 29-30, 2012, during Hurricane Sandy. The data in the CSV are a reformatted and cleaned version of [this data from NOAA](http://tidesandcurrents.noaa.gov/data_menu.shtml?plot_backup=1&bdate=20121029&edate=20121030&datum=6&unit=1&shift=d&stn=8518750+The+Battery%2C+NY&type=Tide+Data&format=View+Data)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Reading Data\n",
      "\n",
      "Basic read with [numpy.genfromtxt](http://docs.scipy.org/doc/numpy/reference/generated/numpy.genfromtxt.html#numpy.genfromtxt). Returns a 2d array of floats."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "!head -n 5 BatteryParkTideData.csv"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "TimeOffsetHours,Pred6,Backup,Acoustc\r\n",
        "0.0,1.5900000000000001,4.6799999999999997,4.6500000000000004\r\n",
        "0.10000000000000001,1.5,4.5499999999999998,4.54\r\n",
        "0.20000000000000001,1.3999999999999999,4.46,4.4400000000000004\r\n",
        "0.29999999999999999,1.3100000000000001,4.3600000000000003,4.3300000000000001\r\n"
       ]
      }
     ],
     "prompt_number": 82
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = np.genfromtxt('BatteryParkTideData.csv', delimiter=',', skip_header=1, missing='NA')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "array([[  0.  ,   1.59,   4.68,   4.65],\n",
        "       [  0.1 ,   1.5 ,   4.55,   4.54],\n",
        "       [  0.2 ,   1.4 ,   4.46,   4.44],\n",
        "       ..., \n",
        "       [ 47.7 ,   3.25,   4.32,   4.5 ],\n",
        "       [ 47.8 ,   3.14,   4.22,   4.39],\n",
        "       [ 47.9 ,   3.03,   4.12,   4.28]])"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Array Properties"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print 'Shape: ', data.shape\n",
      "print 'Size: ', data.size\n",
      "print 'Number of dimensions: ', data.ndim\n",
      "print 'Data type: ', data.dtype"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Shape:  (480, 4)\n",
        "Size:  1920\n",
        "Number of dimensions:  2\n",
        "Data type:  float64\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "array([ 0.  ,  1.59,  4.68,  4.65])"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data[0, 1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "1.5900000000000001"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data[:, 1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "array([ 1.59,  1.5 ,  1.4 ,  1.31,  1.22,  1.13,  1.04,  0.95,  0.87,\n",
        "        0.78,  0.7 ,  0.62,  0.55,  0.48,  0.41,  0.34,  0.28,  0.23,\n",
        "        0.18,  0.14,  0.1 ,  0.08,  0.06,  0.05,  0.05,  0.06,  0.08,\n",
        "        0.11,  0.14,  0.19,  0.25,  0.31,  0.39,  0.47,  0.56,  0.66,\n",
        "        0.76,  0.87,  0.98,  1.1 ,  1.22,  1.35,  1.48,  1.61,  1.74,\n",
        "        1.88,  2.01,  2.15,  2.28,  2.41,  2.55,  2.68,  2.81,  2.94,\n",
        "        3.06,  3.19,  3.31,  3.43,  3.55,  3.66,  3.78,  3.89,  3.99,\n",
        "        4.1 ,  4.2 ,  4.3 ,  4.39,  4.48,  4.57,  4.66,  4.73,  4.81,\n",
        "        4.89,  4.95,  5.02,  5.08,  5.13,  5.18,  5.23,  5.27,  5.3 ,\n",
        "        5.33,  5.35,  5.37,  5.38,  5.38,  5.38,  5.37,  5.36,  5.34,\n",
        "        5.31,  5.28,  5.24,  5.19,  5.13,  5.07,  5.  ,  4.93,  4.85,\n",
        "        4.76,  4.67,  4.57,  4.47,  4.37,  4.26,  4.15,  4.03,  3.92,\n",
        "        3.8 ,  3.68,  3.56,  3.44,  3.32,  3.21,  3.09,  2.97,  2.86,\n",
        "        2.74,  2.63,  2.52,  2.41,  2.3 ,  2.2 ,  2.09,  1.98,  1.88,\n",
        "        1.78,  1.68,  1.57,  1.47,  1.37,  1.27,  1.17,  1.08,  0.98,\n",
        "        0.89,  0.8 ,  0.71,  0.62,  0.54,  0.46,  0.39,  0.32,  0.26,\n",
        "        0.21,  0.16,  0.12,  0.09,  0.07,  0.06,  0.05,  0.06,  0.08,\n",
        "        0.1 ,  0.13,  0.18,  0.23,  0.29,  0.36,  0.44,  0.52,  0.61,\n",
        "        0.71,  0.81,  0.91,  1.02,  1.13,  1.25,  1.36,  1.49,  1.6 ,\n",
        "        1.73,  1.85,  1.97,  2.09,  2.21,  2.33,  2.45,  2.57,  2.68,\n",
        "        2.8 ,  2.91,  3.02,  3.13,  3.23,  3.33,  3.44,  3.53,  3.63,\n",
        "        3.72,  3.81,  3.9 ,  3.98,  4.06,  4.14,  4.21,  4.28,  4.34,\n",
        "        4.41,  4.46,  4.51,  4.56,  4.6 ,  4.64,  4.67,  4.69,  4.71,\n",
        "        4.73,  4.74,  4.74,  4.74,  4.72,  4.71,  4.69,  4.65,  4.62,\n",
        "        4.57,  4.52,  4.46,  4.4 ,  4.33,  4.25,  4.17,  4.08,  3.99,\n",
        "        3.89,  3.79,  3.68,  3.57,  3.46,  3.35,  3.23,  3.11,  3.  ,\n",
        "        2.88,  2.76,  2.65,  2.53,  2.42,  2.31,  2.2 ,  2.1 ,  1.99,\n",
        "        1.89,  1.79,  1.7 ,  1.6 ,  1.51,  1.42,  1.33,  1.25,  1.16,\n",
        "        1.08,  1.  ,  0.92,  0.85,  0.77,  0.7 ,  0.63,  0.56,  0.5 ,\n",
        "        0.44,  0.38,  0.33,  0.29,  0.24,  0.21,  0.18,  0.16,  0.15,\n",
        "        0.14,  0.14,  0.16,  0.18,  0.21,  0.25,  0.3 ,  0.36,  0.43,\n",
        "        0.5 ,  0.59,  0.68,  0.78,  0.89,  1.  ,  1.12,  1.24,  1.37,\n",
        "        1.5 ,  1.63,  1.77,  1.91,  2.05,  2.19,  2.32,  2.46,  2.6 ,\n",
        "        2.73,  2.87,  3.  ,  3.13,  3.25,  3.38,  3.5 ,  3.62,  3.73,\n",
        "        3.84,  3.95,  4.06,  4.16,  4.25,  4.35,  4.44,  4.52,  4.6 ,\n",
        "        4.68,  4.76,  4.83,  4.89,  4.95,  5.01,  5.07,  5.11,  5.16,\n",
        "        5.2 ,  5.23,  5.26,  5.29,  5.31,  5.32,  5.33,  5.33,  5.33,\n",
        "        5.32,  5.31,  5.29,  5.26,  5.23,  5.19,  5.14,  5.1 ,  5.04,\n",
        "        4.97,  4.9 ,  4.83,  4.75,  4.66,  4.57,  4.47,  4.37,  4.27,\n",
        "        4.16,  4.05,  3.93,  3.81,  3.69,  3.57,  3.45,  3.33,  3.21,\n",
        "        3.09,  2.97,  2.86,  2.74,  2.63,  2.51,  2.4 ,  2.29,  2.19,\n",
        "        2.08,  1.98,  1.88,  1.78,  1.68,  1.58,  1.49,  1.39,  1.3 ,\n",
        "        1.21,  1.12,  1.03,  0.94,  0.85,  0.77,  0.69,  0.6 ,  0.53,\n",
        "        0.46,  0.39,  0.33,  0.27,  0.22,  0.18,  0.14,  0.11,  0.09,\n",
        "        0.08,  0.08,  0.09,  0.1 ,  0.13,  0.16,  0.2 ,  0.26,  0.32,\n",
        "        0.39,  0.47,  0.55,  0.64,  0.74,  0.84,  0.95,  1.06,  1.17,\n",
        "        1.29,  1.41,  1.53,  1.66,  1.78,  1.9 ,  2.02,  2.15,  2.27,\n",
        "        2.39,  2.5 ,  2.62,  2.73,  2.84,  2.95,  3.05,  3.16,  3.26,\n",
        "        3.36,  3.45,  3.54,  3.63,  3.71,  3.8 ,  3.87,  3.95,  4.02,\n",
        "        4.09,  4.15,  4.22,  4.27,  4.32,  4.37,  4.42,  4.46,  4.49,\n",
        "        4.52,  4.55,  4.57,  4.58,  4.6 ,  4.6 ,  4.6 ,  4.59,  4.58,\n",
        "        4.56,  4.54,  4.51,  4.48,  4.43,  4.38,  4.33,  4.27,  4.2 ,\n",
        "        4.13,  4.05,  3.96,  3.87,  3.78,  3.68,  3.58,  3.47,  3.37,\n",
        "        3.25,  3.14,  3.03])"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### recarrays\n",
      "\n",
      "Have genfromtxt grab column names from the header and it returns a recarray. The recarray can be indexed numerically to get row data or with a column name to get a 1d array of data for that column."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = np.genfromtxt('BatteryParkTideData.csv', delimiter=',', names=True, missing='NA')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "array([(0.0, 1.59, 4.68, 4.65), (0.1, 1.5, 4.55, 4.54),\n",
        "       (0.2, 1.4, 4.46, 4.44), (0.3, 1.31, 4.36, 4.33),\n",
        "       (0.4, 1.22, 4.28, 4.26), (0.5, 1.13, 4.21, 4.18),\n",
        "       (0.6, 1.04, 4.15, 4.12), (0.7, 0.95, 4.08, 4.06),\n",
        "       (0.8, 0.87, 3.99, 3.97), (0.9, 0.78, 3.92, 3.89),\n",
        "       (1.0, 0.7, 3.87, 3.85), (1.1, 0.62, 3.86, 3.83),\n",
        "       (1.2, 0.55, 3.8, 3.78), (1.3, 0.48, 3.74, 3.73),\n",
        "       (1.4, 0.41, 3.68, 3.66), (1.5, 0.34, 3.63, 3.62),\n",
        "       (1.6, 0.28, 3.59, 3.58), (1.7, 0.23, 3.55, 3.53),\n",
        "       (1.8, 0.18, 3.5, 3.48), (1.9, 0.14, 3.45, 3.42),\n",
        "       (2.0, 0.1, 3.39, 3.35), (2.1, 0.08, 3.37, 3.34),\n",
        "       (2.2, 0.06, 3.33, 3.31), (2.3, 0.05, 3.31, 3.3),\n",
        "       (2.4, 0.05, 3.29, 3.26), (2.5, 0.06, 3.25, 3.22),\n",
        "       (2.6, 0.08, 3.21, 3.19), (2.7, 0.11, 3.19, 3.17),\n",
        "       (2.8, 0.14, 3.19, 3.17), (2.9, 0.19, 3.2, 3.18),\n",
        "       (3.0, 0.25, 3.23, 3.23), (3.1, 0.31, 3.29, 3.26),\n",
        "       (3.2, 0.39, 3.31, 3.29), (3.3, 0.47, 3.34, 3.32),\n",
        "       (3.4, 0.56, 3.39, 3.37), (3.5, 0.66, 3.44, 3.41),\n",
        "       (3.6, 0.76, 3.49, 3.46), (3.7, 0.87, 3.57, 3.54),\n",
        "       (3.8, 0.98, 3.67, 3.65), (3.9, 1.1, 3.78, 3.76),\n",
        "       (4.0, 1.22, 3.87, 3.85), (4.1, 1.35, 3.96, 3.95),\n",
        "       (4.2, 1.48, 4.09, 4.06), (4.3, 1.61, 4.19, 4.18),\n",
        "       (4.4, 1.74, 4.36, 4.33), (4.5, 1.88, 4.49, 4.46),\n",
        "       (4.6, 2.01, 4.59, 4.57), (4.7, 2.15, 4.68, 4.66),\n",
        "       (4.8, 2.28, 4.79, 4.77), (4.9, 2.41, 4.9, 4.88),\n",
        "       (5.0, 2.55, 5.01, 4.98), (5.1, 2.68, 5.12, 5.11),\n",
        "       (5.2, 2.81, 5.26, 5.24), (5.3, 2.94, 5.38, 5.35),\n",
        "       (5.4, 3.06, 5.52, 5.5), (5.5, 3.19, 5.69, 5.67),\n",
        "       (5.6, 3.31, 5.84, 5.83), (5.7, 3.43, 5.97, 5.96),\n",
        "       (5.8, 3.55, 6.13, 6.11), (5.9, 3.66, 6.26, 6.24),\n",
        "       (6.0, 3.78, 6.39, 6.38), (6.1, 3.89, 6.53, 6.51),\n",
        "       (6.2, 3.99, 6.68, 6.66), (6.3, 4.1, 6.84, 6.82),\n",
        "       (6.4, 4.2, 7.0, 6.98), (6.5, 4.3, 7.13, 7.1),\n",
        "       (6.6, 4.39, 7.25, 7.23), (6.7, 4.48, 7.36, 7.32),\n",
        "       (6.8, 4.57, 7.46, 7.43), (6.9, 4.66, 7.56, 7.53),\n",
        "       (7.0, 4.73, 7.65, 7.62), (7.1, 4.81, 7.71, 7.71),\n",
        "       (7.2, 4.89, 7.8, 7.78), (7.3, 4.95, 7.9, 7.88),\n",
        "       (7.4, 5.02, 8.02, 7.98), (7.5, 5.08, 8.07, 8.04),\n",
        "       (7.6, 5.13, 8.12, 8.1), (7.7, 5.18, 8.26, 8.23),\n",
        "       (7.8, 5.23, 8.36, 8.31), (7.9, 5.27, 8.47, 8.35),\n",
        "       (8.0, 5.3, 8.53, 8.35), (8.1, 5.33, 8.58, 8.35),\n",
        "       (8.2, 5.35, 8.58, 8.35), (8.3, 5.37, 8.6, 8.35),\n",
        "       (8.4, 5.38, 8.67, 8.36), (8.5, 5.38, 8.69, 8.35),\n",
        "       (8.6, 5.38, 8.67, 8.34), (8.7, 5.37, 8.71, 8.34),\n",
        "       (8.8, 5.36, 8.76, 8.34), (8.9, 5.34, 8.79, 8.35),\n",
        "       (9.0, 5.31, 8.8, 8.32), (9.1, 5.28, 8.85, 8.34),\n",
        "       (9.2, 5.24, 8.85, 8.34), (9.3, 5.19, 8.85, 8.29),\n",
        "       (9.4, 5.13, 8.85, 8.32), (9.5, 5.07, 8.81, 8.3),\n",
        "       (9.6, 5.0, 8.78, 8.33), (9.7, 4.93, 8.69, 8.34),\n",
        "       (9.8, 4.85, 8.6, 8.29), (9.9, 4.76, 8.58, 8.28),\n",
        "       (10.0, 4.67, 8.53, 8.25), (10.1, 4.57, 8.5, 8.26),\n",
        "       (10.2, 4.47, nan, nan), (10.3, 4.37, nan, nan),\n",
        "       (10.4, 4.26, nan, nan), (10.5, 4.15, nan, nan),\n",
        "       (10.6, 4.03, nan, nan), (10.7, 3.92, 8.1, 8.06),\n",
        "       (10.8, 3.8, 8.05, 7.99), (10.9, 3.68, 7.94, 7.88),\n",
        "       (11.0, 3.56, 7.83, 7.81), (11.1, 3.44, 7.77, 7.75),\n",
        "       (11.2, 3.32, 7.68, 7.64), (11.3, 3.21, 7.56, 7.53),\n",
        "       (11.4, 3.09, 7.45, 7.41), (11.5, 2.97, 7.33, 7.3),\n",
        "       (11.6, 2.86, 7.22, 7.18), (11.7, 2.74, 7.09, 7.06),\n",
        "       (11.8, 2.63, 6.96, 6.92), (11.9, 2.52, 6.84, 6.81),\n",
        "       (12.0, 2.41, 6.77, 6.73), (12.1, 2.3, 6.65, 6.63),\n",
        "       (12.2, 2.2, 6.58, 6.55), (12.3, 2.09, 6.5, 6.47),\n",
        "       (12.4, 1.98, 6.44, 6.41), (12.5, 1.88, 6.33, 6.3),\n",
        "       (12.6, 1.78, 6.24, 6.21), (12.7, 1.68, 6.16, 6.15),\n",
        "       (12.8, 1.57, 6.1, 6.09), (12.9, 1.47, 6.02, 6.0),\n",
        "       (13.0, 1.37, 5.91, 5.9), (13.1, 1.27, 5.87, 5.83),\n",
        "       (13.2, 1.17, 5.79, 5.76), (13.3, 1.08, 5.69, 5.67),\n",
        "       (13.4, 0.98, 5.61, 5.59), (13.5, 0.89, 5.55, 5.53),\n",
        "       (13.6, 0.8, 5.46, 5.44), (13.7, 0.71, 5.42, 5.39),\n",
        "       (13.8, 0.62, 5.37, 5.34), (13.9, 0.54, 5.33, 5.3),\n",
        "       (14.0, 0.46, 5.3, 5.26), (14.1, 0.39, 5.27, 5.24),\n",
        "       (14.2, 0.32, 5.26, 5.23), (14.3, 0.26, nan, 5.2),\n",
        "       (14.4, 0.21, 5.27, 5.24), (14.5, 0.16, 5.28, 5.25),\n",
        "       (14.6, 0.12, 5.29, 5.27), (14.7, 0.09, 5.38, 5.35),\n",
        "       (14.8, 0.07, 5.43, 5.4), (14.9, 0.06, 5.52, 5.5),\n",
        "       (15.0, 0.05, 5.6, 5.58), (15.1, 0.06, 5.69, 5.69),\n",
        "       (15.2, 0.08, 5.79, 5.77), (15.3, 0.1, 5.97, 5.97),\n",
        "       (15.4, 0.13, 6.11, 6.1), (15.5, 0.18, 6.24, 6.21),\n",
        "       (15.6, 0.23, 6.4, 6.36), (15.7, 0.29, 6.5, 6.46),\n",
        "       (15.8, 0.36, 6.61, 6.56), (15.9, 0.44, 6.7, 6.67),\n",
        "       (16.0, 0.52, 6.85, 6.82), (16.1, 0.61, 7.02, 6.97),\n",
        "       (16.2, 0.71, 7.15, 7.09), (16.3, 0.81, 7.28, 7.23),\n",
        "       (16.4, 0.91, 7.45, 7.4), (16.5, 1.02, 7.57, 7.51),\n",
        "       (16.6, 1.13, 7.75, 7.7), (16.7, 1.25, 7.91, 7.87),\n",
        "       (16.8, 1.36, 8.03, 8.0), (16.9, 1.49, 8.18, 8.14),\n",
        "       (17.0, 1.6, 8.27, 8.23), (17.1, 1.73, 8.38, 8.3),\n",
        "       (17.2, 1.85, 8.48, 8.33), (17.3, 1.97, 8.63, 8.32),\n",
        "       (17.4, 2.09, 8.77, 8.33), (17.5, 2.21, 8.9, 8.31),\n",
        "       (17.6, 2.33, 9.03, 8.32), (17.7, 2.45, 9.19, 8.29),\n",
        "       (17.8, 2.57, 9.33, 8.31), (17.9, 2.68, 9.48, 8.3),\n",
        "       (18.0, 2.8, 9.62, 7.85), (18.1, 2.91, 9.74, 7.83),\n",
        "       (18.2, 3.02, 9.95, 7.07), (18.3, 3.13, 10.1, 6.1),\n",
        "       (18.4, 3.23, 10.22, 6.09), (18.5, 3.33, 10.39, 6.11),\n",
        "       (18.6, 3.44, 10.55, 6.11), (18.7, 3.53, 10.69, 6.12),\n",
        "       (18.8, 3.63, 10.88, 6.6), (18.9, 3.72, 11.07, 6.91),\n",
        "       (19.0, 3.81, 11.25, 7.27), (19.1, 3.9, 11.41, 7.16),\n",
        "       (19.2, 3.98, 11.62, 7.07), (19.3, 4.06, 11.87, 7.31),\n",
        "       (19.4, 4.14, 12.09, 7.06), (19.5, 4.21, 12.33, 7.06),\n",
        "       (19.6, 4.28, 12.54, 7.24), (19.7, 4.34, 12.75, 7.13),\n",
        "       (19.8, 4.41, 12.93, 7.16), (19.9, 4.46, 13.04, 7.09),\n",
        "       (20.0, 4.51, 13.15, 7.16), (20.1, 4.56, 13.2, 7.16),\n",
        "       (20.2, 4.6, 13.26, 7.11), (20.3, 4.64, 13.34, 7.15),\n",
        "       (20.4, 4.67, 13.4, 7.26), (20.5, 4.69, 13.46, 7.13),\n",
        "       (20.6, 4.71, 13.54, 7.0), (20.7, 4.73, 13.65, 6.68),\n",
        "       (20.8, 4.74, 13.72, 6.85), (20.9, 4.74, 13.78, 7.12),\n",
        "       (21.0, 4.74, 13.81, 7.07), (21.1, 4.72, 13.85, 7.3),\n",
        "       (21.2, 4.71, 13.87, 7.3), (21.3, 4.69, 13.87, 7.32),\n",
        "       (21.4, 4.65, 13.88, 7.19), (21.5, 4.62, 13.79, 7.14),\n",
        "       (21.6, 4.57, 13.72, 7.18), (21.7, 4.52, 13.63, 7.03),\n",
        "       (21.8, 4.46, 13.54, 7.32), (21.9, 4.4, 13.41, 7.04),\n",
        "       (22.0, 4.33, 13.3, 7.23), (22.1, 4.25, 13.15, 6.88),\n",
        "       (22.2, 4.17, 12.99, 6.97), (22.3, 4.08, 12.86, 7.19),\n",
        "       (22.4, 3.99, 12.69, 7.1), (22.5, 3.89, 12.5, 7.18),\n",
        "       (22.6, 3.79, 12.27, 7.18), (22.7, 3.68, 12.07, 7.4),\n",
        "       (22.8, 3.57, 11.87, 7.09), (22.9, 3.46, 11.61, 7.03),\n",
        "       (23.0, 3.35, 11.32, 7.18), (23.1, 3.23, 11.04, 7.26),\n",
        "       (23.2, 3.11, 10.78, 7.24), (23.3, 3.0, 10.47, 6.43),\n",
        "       (23.4, 2.88, 10.15, 6.8), (23.5, 2.76, 9.81, 7.67),\n",
        "       (23.6, 2.65, 9.54, 8.14), (23.7, 2.53, 9.22, 8.31),\n",
        "       (23.8, 2.42, 8.92, 8.32), (23.9, 2.31, 8.62, 8.29),\n",
        "       (24.0, 2.2, 8.35, 8.17), (24.1, 2.1, 8.03, 7.94),\n",
        "       (24.2, 1.99, 7.77, 7.71), (24.3, 1.89, 7.58, 7.53),\n",
        "       (24.4, 1.79, 7.42, 7.36), (24.5, 1.7, 7.2, 7.19),\n",
        "       (24.6, 1.6, 7.06, 7.0), (24.7, 1.51, 6.87, 6.84),\n",
        "       (24.8, 1.42, 6.71, 6.68), (24.9, 1.33, 6.54, 6.51),\n",
        "       (25.0, 1.25, 6.4, 6.36), (25.1, 1.16, 6.26, 6.22),\n",
        "       (25.2, 1.08, 6.13, 6.09), (25.3, 1.0, 5.99, 5.96),\n",
        "       (25.4, 0.92, 5.85, 5.84), (25.5, 0.85, 5.77, 5.74),\n",
        "       (25.6, 0.77, 5.64, 5.62), (25.7, 0.7, 5.52, 5.51),\n",
        "       (25.8, 0.63, 5.36, 5.35), (25.9, 0.56, 5.21, 5.2),\n",
        "       (26.0, 0.5, 5.08, 5.08), (26.1, 0.44, 4.94, 4.94),\n",
        "       (26.2, 0.38, 4.8, 4.8), (26.3, 0.33, 4.7, 4.67),\n",
        "       (26.4, 0.29, 4.55, 4.53), (26.5, 0.24, 4.44, 4.41),\n",
        "       (26.6, 0.21, 4.32, 4.31), (26.7, 0.18, 4.21, 4.2),\n",
        "       (26.8, 0.16, 4.1, 4.08), (26.9, 0.15, 4.0, 3.96),\n",
        "       (27.0, 0.14, 3.91, 3.87), (27.1, 0.14, 3.81, 3.79),\n",
        "       (27.2, 0.16, 3.77, 3.75), (27.3, 0.18, 3.71, 3.68),\n",
        "       (27.4, 0.21, 3.67, 3.63), (27.5, 0.25, 3.64, 3.61),\n",
        "       (27.6, 0.3, 3.63, 3.61), (27.7, 0.36, 3.67, 3.64),\n",
        "       (27.8, 0.43, 3.69, 3.67), (27.9, 0.5, 3.72, 3.71),\n",
        "       (28.0, 0.59, 3.81, 3.79), (28.1, 0.68, 3.88, 3.87),\n",
        "       (28.2, 0.78, 4.0, 3.99), (28.3, 0.89, 4.07, 4.05),\n",
        "       (28.4, 1.0, 4.14, 4.14), (28.5, 1.12, 4.21, 4.2),\n",
        "       (28.6, 1.24, 4.3, 4.3), (28.7, 1.37, 4.41, 4.41),\n",
        "       (28.8, 1.5, 4.52, 4.53), (28.9, 1.63, 4.65, 4.66),\n",
        "       (29.0, 1.77, 4.79, 4.81), (29.1, 1.91, 4.95, 4.97),\n",
        "       (29.2, 2.05, 5.08, 5.13), (29.3, 2.19, 5.21, 5.28),\n",
        "       (29.4, 2.32, 5.36, 5.44), (29.5, 2.46, 5.5, 5.57),\n",
        "       (29.6, 2.6, 5.6, 5.71), (29.7, 2.73, 5.75, 5.87),\n",
        "       (29.8, 2.87, 5.89, 6.0), (29.9, 3.0, 5.99, 6.11),\n",
        "       (30.0, 3.13, 6.09, 6.21), (30.1, 3.25, 6.17, 6.27),\n",
        "       (30.2, 3.38, 6.27, 6.4), (30.3, 3.5, 6.37, 6.5),\n",
        "       (30.4, 3.62, 6.43, 6.54), (30.5, 3.73, 6.51, 6.62),\n",
        "       (30.6, 3.84, 6.56, 6.7), (30.7, 3.95, 6.61, 6.75),\n",
        "       (30.8, 4.06, 6.7, 6.8), (30.9, 4.16, 6.74, 6.86),\n",
        "       (31.0, 4.25, 6.81, 6.93), (31.1, 4.35, 6.84, 6.98),\n",
        "       (31.2, 4.44, 6.92, 7.04), (31.3, 4.52, 6.93, 7.07),\n",
        "       (31.4, 4.6, 6.93, 7.09), (31.5, 4.68, 6.96, 7.09),\n",
        "       (31.6, 4.76, 6.95, 7.1), (31.7, 4.83, 6.96, 7.12),\n",
        "       (31.8, 4.89, 6.97, 7.12), (31.9, 4.95, 7.01, 7.15),\n",
        "       (32.0, 5.01, 7.02, 7.15), (32.1, 5.07, 7.02, 7.15),\n",
        "       (32.2, 5.11, 7.03, 7.16), (32.3, 5.16, 7.02, 7.16),\n",
        "       (32.4, 5.2, 7.01, 7.15), (32.5, 5.23, 7.03, 7.17),\n",
        "       (32.6, 5.26, 7.05, 7.21), (32.7, 5.29, 7.13, 7.28),\n",
        "       (32.8, 5.31, 7.18, 7.32), (32.9, 5.32, 7.19, 7.34),\n",
        "       (33.0, 5.33, 7.17, 7.31), (33.1, 5.33, 7.13, 7.26),\n",
        "       (33.2, 5.33, 7.11, 7.24), (33.3, 5.32, 7.12, 7.26),\n",
        "       (33.4, 5.31, 7.12, 7.26), (33.5, 5.29, 7.11, 7.25),\n",
        "       (33.6, 5.26, 7.12, 7.25), (33.7, 5.23, 7.16, 7.3),\n",
        "       (33.8, 5.19, 7.2, 7.36), (33.9, 5.14, 7.24, 7.38),\n",
        "       (34.0, 5.1, 7.28, 7.41), (34.1, 5.04, 7.29, 7.44),\n",
        "       (34.2, 4.97, 7.33, 7.48), (34.3, 4.9, 7.31, 7.47),\n",
        "       (34.4, 4.83, 7.27, 7.42), (34.5, 4.75, 7.24, 7.4),\n",
        "       (34.6, 4.66, 7.19, 7.34), (34.7, 4.57, 7.11, 7.25),\n",
        "       (34.8, 4.47, 6.99, 7.14), (34.9, 4.37, 6.87, 7.01),\n",
        "       (35.0, 4.27, 6.72, 6.88), (35.1, 4.16, 6.64, 6.79),\n",
        "       (35.2, 4.05, 6.56, 6.69), (35.3, 3.93, 6.46, 6.61),\n",
        "       (35.4, 3.81, 6.37, 6.53), (35.5, 3.69, 6.25, 6.41),\n",
        "       (35.6, 3.57, 6.11, 6.28), (35.7, 3.45, 6.01, 6.18),\n",
        "       (35.8, 3.33, 5.91, 6.07), (35.9, 3.21, 5.78, 5.98),\n",
        "       (36.0, 3.09, 5.66, 5.83), (36.1, 2.97, 5.49, 5.64),\n",
        "       (36.2, 2.86, 5.31, 5.49), (36.3, 2.74, 5.15, 5.29),\n",
        "       (36.4, 2.63, 5.03, 5.16), (36.5, 2.51, 4.91, 5.02),\n",
        "       (36.6, 2.4, 4.78, 4.9), (36.7, 2.29, 4.64, 4.74),\n",
        "       (36.8, 2.19, 4.51, 4.59), (36.9, 2.08, 4.36, 4.44),\n",
        "       (37.0, 1.98, 4.21, 4.29), (37.1, 1.88, 4.05, 4.11),\n",
        "       (37.2, 1.78, 3.91, 3.96), (37.3, 1.68, 3.76, 3.81),\n",
        "       (37.4, 1.58, 3.63, 3.68), (37.5, 1.49, 3.51, 3.56),\n",
        "       (37.6, 1.39, 3.4, 3.43), (37.7, 1.3, 3.3, 3.34),\n",
        "       (37.8, 1.21, 3.21, 3.23), (37.9, 1.12, 3.08, 3.09),\n",
        "       (38.0, 1.03, 2.94, 2.96), (38.1, 0.94, 2.83, 2.83),\n",
        "       (38.2, 0.85, 2.73, 2.72), (38.3, 0.77, 2.62, 2.61),\n",
        "       (38.4, 0.69, 2.51, 2.49), (38.5, 0.6, 2.4, 2.39),\n",
        "       (38.6, 0.53, 2.34, 2.31), (38.7, 0.46, 2.23, 2.21),\n",
        "       (38.8, 0.39, 2.14, 2.11), (38.9, 0.33, 2.03, 2.0),\n",
        "       (39.0, 0.27, 1.92, 1.89), (39.1, 0.22, 1.84, 1.83),\n",
        "       (39.2, 0.18, 1.77, 1.77), (39.3, 0.14, 1.71, 1.69),\n",
        "       (39.4, 0.11, 1.67, 1.65), (39.5, 0.09, 1.64, 1.61),\n",
        "       (39.6, 0.08, 1.6, 1.58), (39.7, 0.08, 1.58, 1.56),\n",
        "       (39.8, 0.09, 1.58, 1.54), (39.9, 0.1, 1.56, 1.52),\n",
        "       (40.0, 0.13, 1.53, 1.51), (40.1, 0.16, 1.52, 1.51),\n",
        "       (40.2, 0.2, 1.53, 1.52), (40.3, 0.26, 1.55, 1.53),\n",
        "       (40.4, 0.32, 1.54, 1.53), (40.5, 0.39, 1.58, 1.57),\n",
        "       (40.6, 0.47, 1.64, 1.64), (40.7, 0.55, 1.7, 1.7),\n",
        "       (40.8, 0.64, 1.83, 1.8), (40.9, 0.74, 1.94, 1.93),\n",
        "       (41.0, 0.84, 2.03, 2.02), (41.1, 0.95, 2.14, 2.13),\n",
        "       (41.2, 1.06, 2.26, 2.26), (41.3, 1.17, 2.4, 2.41),\n",
        "       (41.4, 1.29, 2.57, 2.58), (41.5, 1.41, 2.73, 2.73),\n",
        "       (41.6, 1.53, 2.89, 2.89), (41.7, 1.66, 3.03, 3.04),\n",
        "       (41.8, 1.78, 3.17, 3.2), (41.9, 1.9, 3.33, 3.37),\n",
        "       (42.0, 2.02, 3.5, 3.54), (42.1, 2.15, 3.66, 3.71),\n",
        "       (42.2, 2.27, 3.83, 3.9), (42.3, 2.39, 4.01, 4.08),\n",
        "       (42.4, 2.5, 4.17, 4.25), (42.5, 2.62, 4.29, 4.4),\n",
        "       (42.6, 2.73, 4.44, 4.55), (42.7, 2.84, 4.6, 4.71),\n",
        "       (42.8, 2.95, 4.78, 4.88), (42.9, 3.05, 4.92, 5.03),\n",
        "       (43.0, 3.16, 4.99, 5.13), (43.1, 3.26, 5.1, 5.26),\n",
        "       (43.2, 3.36, 5.22, 5.38), (43.3, 3.45, 5.35, 5.5),\n",
        "       (43.4, 3.54, 5.41, 5.58), (43.5, 3.63, 5.5, 5.69),\n",
        "       (43.6, 3.71, 5.58, 5.76), (43.7, 3.8, 5.64, 5.83),\n",
        "       (43.8, 3.87, 5.68, 5.87), (43.9, 3.95, 5.73, 5.93),\n",
        "       (44.0, 4.02, 5.79, 5.98), (44.1, 4.09, 5.79, 6.0),\n",
        "       (44.2, 4.15, 5.81, 6.02), (44.3, 4.22, 5.83, 6.03),\n",
        "       (44.4, 4.27, 5.86, 6.06), (44.5, 4.32, 5.88, 6.08),\n",
        "       (44.6, 4.37, 5.89, 6.09), (44.7, 4.42, 5.88, 6.08),\n",
        "       (44.8, 4.46, 5.88, 6.07), (44.9, 4.49, 5.88, 6.07),\n",
        "       (45.0, 4.52, 5.88, 6.08), (45.1, 4.55, 5.91, 6.1),\n",
        "       (45.2, 4.57, 5.91, 6.1), (45.3, 4.58, 5.9, 6.1),\n",
        "       (45.4, 4.6, 5.9, 6.1), (45.5, 4.6, 5.87, 6.07),\n",
        "       (45.6, 4.6, 5.84, 6.05), (45.7, 4.59, 5.8, 6.01),\n",
        "       (45.8, 4.58, 5.79, 6.0), (45.9, 4.56, 5.77, 5.97),\n",
        "       (46.0, 4.54, 5.72, 5.93), (46.1, 4.51, 5.68, 5.89),\n",
        "       (46.2, 4.48, 5.64, 5.84), (46.3, 4.43, 5.58, 5.78),\n",
        "       (46.4, 4.38, 5.51, 5.71), (46.5, 4.33, 5.44, 5.63),\n",
        "       (46.6, 4.27, 5.38, 5.57), (46.7, 4.2, 5.32, 5.5),\n",
        "       (46.8, 4.13, 5.23, 5.41), (46.9, 4.05, 5.15, 5.32),\n",
        "       (47.0, 3.96, 5.07, 5.24), (47.1, 3.87, 4.96, 5.13),\n",
        "       (47.2, 3.78, 4.86, 5.03), (47.3, 3.68, 4.75, 4.92),\n",
        "       (47.4, 3.58, 4.63, 4.8), (47.5, 3.47, 4.52, 4.69),\n",
        "       (47.6, 3.37, 4.42, 4.6), (47.7, 3.25, 4.32, 4.5),\n",
        "       (47.8, 3.14, 4.22, 4.39), (47.9, 3.03, 4.12, 4.28)], \n",
        "      dtype=[('TimeOffsetHours', '<f8'), ('Pred6', '<f8'), ('Backup', '<f8'), ('Acoustc', '<f8')])"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "(0.0, 1.59, 4.68, 4.65)"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data['Pred6']"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "array([ 1.59,  1.5 ,  1.4 ,  1.31,  1.22,  1.13,  1.04,  0.95,  0.87,\n",
        "        0.78,  0.7 ,  0.62,  0.55,  0.48,  0.41,  0.34,  0.28,  0.23,\n",
        "        0.18,  0.14,  0.1 ,  0.08,  0.06,  0.05,  0.05,  0.06,  0.08,\n",
        "        0.11,  0.14,  0.19,  0.25,  0.31,  0.39,  0.47,  0.56,  0.66,\n",
        "        0.76,  0.87,  0.98,  1.1 ,  1.22,  1.35,  1.48,  1.61,  1.74,\n",
        "        1.88,  2.01,  2.15,  2.28,  2.41,  2.55,  2.68,  2.81,  2.94,\n",
        "        3.06,  3.19,  3.31,  3.43,  3.55,  3.66,  3.78,  3.89,  3.99,\n",
        "        4.1 ,  4.2 ,  4.3 ,  4.39,  4.48,  4.57,  4.66,  4.73,  4.81,\n",
        "        4.89,  4.95,  5.02,  5.08,  5.13,  5.18,  5.23,  5.27,  5.3 ,\n",
        "        5.33,  5.35,  5.37,  5.38,  5.38,  5.38,  5.37,  5.36,  5.34,\n",
        "        5.31,  5.28,  5.24,  5.19,  5.13,  5.07,  5.  ,  4.93,  4.85,\n",
        "        4.76,  4.67,  4.57,  4.47,  4.37,  4.26,  4.15,  4.03,  3.92,\n",
        "        3.8 ,  3.68,  3.56,  3.44,  3.32,  3.21,  3.09,  2.97,  2.86,\n",
        "        2.74,  2.63,  2.52,  2.41,  2.3 ,  2.2 ,  2.09,  1.98,  1.88,\n",
        "        1.78,  1.68,  1.57,  1.47,  1.37,  1.27,  1.17,  1.08,  0.98,\n",
        "        0.89,  0.8 ,  0.71,  0.62,  0.54,  0.46,  0.39,  0.32,  0.26,\n",
        "        0.21,  0.16,  0.12,  0.09,  0.07,  0.06,  0.05,  0.06,  0.08,\n",
        "        0.1 ,  0.13,  0.18,  0.23,  0.29,  0.36,  0.44,  0.52,  0.61,\n",
        "        0.71,  0.81,  0.91,  1.02,  1.13,  1.25,  1.36,  1.49,  1.6 ,\n",
        "        1.73,  1.85,  1.97,  2.09,  2.21,  2.33,  2.45,  2.57,  2.68,\n",
        "        2.8 ,  2.91,  3.02,  3.13,  3.23,  3.33,  3.44,  3.53,  3.63,\n",
        "        3.72,  3.81,  3.9 ,  3.98,  4.06,  4.14,  4.21,  4.28,  4.34,\n",
        "        4.41,  4.46,  4.51,  4.56,  4.6 ,  4.64,  4.67,  4.69,  4.71,\n",
        "        4.73,  4.74,  4.74,  4.74,  4.72,  4.71,  4.69,  4.65,  4.62,\n",
        "        4.57,  4.52,  4.46,  4.4 ,  4.33,  4.25,  4.17,  4.08,  3.99,\n",
        "        3.89,  3.79,  3.68,  3.57,  3.46,  3.35,  3.23,  3.11,  3.  ,\n",
        "        2.88,  2.76,  2.65,  2.53,  2.42,  2.31,  2.2 ,  2.1 ,  1.99,\n",
        "        1.89,  1.79,  1.7 ,  1.6 ,  1.51,  1.42,  1.33,  1.25,  1.16,\n",
        "        1.08,  1.  ,  0.92,  0.85,  0.77,  0.7 ,  0.63,  0.56,  0.5 ,\n",
        "        0.44,  0.38,  0.33,  0.29,  0.24,  0.21,  0.18,  0.16,  0.15,\n",
        "        0.14,  0.14,  0.16,  0.18,  0.21,  0.25,  0.3 ,  0.36,  0.43,\n",
        "        0.5 ,  0.59,  0.68,  0.78,  0.89,  1.  ,  1.12,  1.24,  1.37,\n",
        "        1.5 ,  1.63,  1.77,  1.91,  2.05,  2.19,  2.32,  2.46,  2.6 ,\n",
        "        2.73,  2.87,  3.  ,  3.13,  3.25,  3.38,  3.5 ,  3.62,  3.73,\n",
        "        3.84,  3.95,  4.06,  4.16,  4.25,  4.35,  4.44,  4.52,  4.6 ,\n",
        "        4.68,  4.76,  4.83,  4.89,  4.95,  5.01,  5.07,  5.11,  5.16,\n",
        "        5.2 ,  5.23,  5.26,  5.29,  5.31,  5.32,  5.33,  5.33,  5.33,\n",
        "        5.32,  5.31,  5.29,  5.26,  5.23,  5.19,  5.14,  5.1 ,  5.04,\n",
        "        4.97,  4.9 ,  4.83,  4.75,  4.66,  4.57,  4.47,  4.37,  4.27,\n",
        "        4.16,  4.05,  3.93,  3.81,  3.69,  3.57,  3.45,  3.33,  3.21,\n",
        "        3.09,  2.97,  2.86,  2.74,  2.63,  2.51,  2.4 ,  2.29,  2.19,\n",
        "        2.08,  1.98,  1.88,  1.78,  1.68,  1.58,  1.49,  1.39,  1.3 ,\n",
        "        1.21,  1.12,  1.03,  0.94,  0.85,  0.77,  0.69,  0.6 ,  0.53,\n",
        "        0.46,  0.39,  0.33,  0.27,  0.22,  0.18,  0.14,  0.11,  0.09,\n",
        "        0.08,  0.08,  0.09,  0.1 ,  0.13,  0.16,  0.2 ,  0.26,  0.32,\n",
        "        0.39,  0.47,  0.55,  0.64,  0.74,  0.84,  0.95,  1.06,  1.17,\n",
        "        1.29,  1.41,  1.53,  1.66,  1.78,  1.9 ,  2.02,  2.15,  2.27,\n",
        "        2.39,  2.5 ,  2.62,  2.73,  2.84,  2.95,  3.05,  3.16,  3.26,\n",
        "        3.36,  3.45,  3.54,  3.63,  3.71,  3.8 ,  3.87,  3.95,  4.02,\n",
        "        4.09,  4.15,  4.22,  4.27,  4.32,  4.37,  4.42,  4.46,  4.49,\n",
        "        4.52,  4.55,  4.57,  4.58,  4.6 ,  4.6 ,  4.6 ,  4.59,  4.58,\n",
        "        4.56,  4.54,  4.51,  4.48,  4.43,  4.38,  4.33,  4.27,  4.2 ,\n",
        "        4.13,  4.05,  3.96,  3.87,  3.78,  3.68,  3.58,  3.47,  3.37,\n",
        "        3.25,  3.14,  3.03])"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Unpacking the Columns\n",
      "\n",
      "Can also have genfromtxt unpack the columns into separate arrays."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "time, pred, backup, accoustic = np.genfromtxt('BatteryParkTideData.csv', delimiter=',', skip_header=1, missing='NA', unpack=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pred"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "array([ 1.59,  1.5 ,  1.4 ,  1.31,  1.22,  1.13,  1.04,  0.95,  0.87,\n",
        "        0.78,  0.7 ,  0.62,  0.55,  0.48,  0.41,  0.34,  0.28,  0.23,\n",
        "        0.18,  0.14,  0.1 ,  0.08,  0.06,  0.05,  0.05,  0.06,  0.08,\n",
        "        0.11,  0.14,  0.19,  0.25,  0.31,  0.39,  0.47,  0.56,  0.66,\n",
        "        0.76,  0.87,  0.98,  1.1 ,  1.22,  1.35,  1.48,  1.61,  1.74,\n",
        "        1.88,  2.01,  2.15,  2.28,  2.41,  2.55,  2.68,  2.81,  2.94,\n",
        "        3.06,  3.19,  3.31,  3.43,  3.55,  3.66,  3.78,  3.89,  3.99,\n",
        "        4.1 ,  4.2 ,  4.3 ,  4.39,  4.48,  4.57,  4.66,  4.73,  4.81,\n",
        "        4.89,  4.95,  5.02,  5.08,  5.13,  5.18,  5.23,  5.27,  5.3 ,\n",
        "        5.33,  5.35,  5.37,  5.38,  5.38,  5.38,  5.37,  5.36,  5.34,\n",
        "        5.31,  5.28,  5.24,  5.19,  5.13,  5.07,  5.  ,  4.93,  4.85,\n",
        "        4.76,  4.67,  4.57,  4.47,  4.37,  4.26,  4.15,  4.03,  3.92,\n",
        "        3.8 ,  3.68,  3.56,  3.44,  3.32,  3.21,  3.09,  2.97,  2.86,\n",
        "        2.74,  2.63,  2.52,  2.41,  2.3 ,  2.2 ,  2.09,  1.98,  1.88,\n",
        "        1.78,  1.68,  1.57,  1.47,  1.37,  1.27,  1.17,  1.08,  0.98,\n",
        "        0.89,  0.8 ,  0.71,  0.62,  0.54,  0.46,  0.39,  0.32,  0.26,\n",
        "        0.21,  0.16,  0.12,  0.09,  0.07,  0.06,  0.05,  0.06,  0.08,\n",
        "        0.1 ,  0.13,  0.18,  0.23,  0.29,  0.36,  0.44,  0.52,  0.61,\n",
        "        0.71,  0.81,  0.91,  1.02,  1.13,  1.25,  1.36,  1.49,  1.6 ,\n",
        "        1.73,  1.85,  1.97,  2.09,  2.21,  2.33,  2.45,  2.57,  2.68,\n",
        "        2.8 ,  2.91,  3.02,  3.13,  3.23,  3.33,  3.44,  3.53,  3.63,\n",
        "        3.72,  3.81,  3.9 ,  3.98,  4.06,  4.14,  4.21,  4.28,  4.34,\n",
        "        4.41,  4.46,  4.51,  4.56,  4.6 ,  4.64,  4.67,  4.69,  4.71,\n",
        "        4.73,  4.74,  4.74,  4.74,  4.72,  4.71,  4.69,  4.65,  4.62,\n",
        "        4.57,  4.52,  4.46,  4.4 ,  4.33,  4.25,  4.17,  4.08,  3.99,\n",
        "        3.89,  3.79,  3.68,  3.57,  3.46,  3.35,  3.23,  3.11,  3.  ,\n",
        "        2.88,  2.76,  2.65,  2.53,  2.42,  2.31,  2.2 ,  2.1 ,  1.99,\n",
        "        1.89,  1.79,  1.7 ,  1.6 ,  1.51,  1.42,  1.33,  1.25,  1.16,\n",
        "        1.08,  1.  ,  0.92,  0.85,  0.77,  0.7 ,  0.63,  0.56,  0.5 ,\n",
        "        0.44,  0.38,  0.33,  0.29,  0.24,  0.21,  0.18,  0.16,  0.15,\n",
        "        0.14,  0.14,  0.16,  0.18,  0.21,  0.25,  0.3 ,  0.36,  0.43,\n",
        "        0.5 ,  0.59,  0.68,  0.78,  0.89,  1.  ,  1.12,  1.24,  1.37,\n",
        "        1.5 ,  1.63,  1.77,  1.91,  2.05,  2.19,  2.32,  2.46,  2.6 ,\n",
        "        2.73,  2.87,  3.  ,  3.13,  3.25,  3.38,  3.5 ,  3.62,  3.73,\n",
        "        3.84,  3.95,  4.06,  4.16,  4.25,  4.35,  4.44,  4.52,  4.6 ,\n",
        "        4.68,  4.76,  4.83,  4.89,  4.95,  5.01,  5.07,  5.11,  5.16,\n",
        "        5.2 ,  5.23,  5.26,  5.29,  5.31,  5.32,  5.33,  5.33,  5.33,\n",
        "        5.32,  5.31,  5.29,  5.26,  5.23,  5.19,  5.14,  5.1 ,  5.04,\n",
        "        4.97,  4.9 ,  4.83,  4.75,  4.66,  4.57,  4.47,  4.37,  4.27,\n",
        "        4.16,  4.05,  3.93,  3.81,  3.69,  3.57,  3.45,  3.33,  3.21,\n",
        "        3.09,  2.97,  2.86,  2.74,  2.63,  2.51,  2.4 ,  2.29,  2.19,\n",
        "        2.08,  1.98,  1.88,  1.78,  1.68,  1.58,  1.49,  1.39,  1.3 ,\n",
        "        1.21,  1.12,  1.03,  0.94,  0.85,  0.77,  0.69,  0.6 ,  0.53,\n",
        "        0.46,  0.39,  0.33,  0.27,  0.22,  0.18,  0.14,  0.11,  0.09,\n",
        "        0.08,  0.08,  0.09,  0.1 ,  0.13,  0.16,  0.2 ,  0.26,  0.32,\n",
        "        0.39,  0.47,  0.55,  0.64,  0.74,  0.84,  0.95,  1.06,  1.17,\n",
        "        1.29,  1.41,  1.53,  1.66,  1.78,  1.9 ,  2.02,  2.15,  2.27,\n",
        "        2.39,  2.5 ,  2.62,  2.73,  2.84,  2.95,  3.05,  3.16,  3.26,\n",
        "        3.36,  3.45,  3.54,  3.63,  3.71,  3.8 ,  3.87,  3.95,  4.02,\n",
        "        4.09,  4.15,  4.22,  4.27,  4.32,  4.37,  4.42,  4.46,  4.49,\n",
        "        4.52,  4.55,  4.57,  4.58,  4.6 ,  4.6 ,  4.6 ,  4.59,  4.58,\n",
        "        4.56,  4.54,  4.51,  4.48,  4.43,  4.38,  4.33,  4.27,  4.2 ,\n",
        "        4.13,  4.05,  3.96,  3.87,  3.78,  3.68,  3.58,  3.47,  3.37,\n",
        "        3.25,  3.14,  3.03])"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## (Aside: Manually Creating Arrays)\n",
      "\n",
      "As an aside, you can manually create arrays too. A common situation is to want to create an array from a list or other sequence. Easy:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.array([2.3, 42, 5.6])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "array([  2.3,  42. ,   5.6])"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "NumPy also has routines for creating arrays of ones and zeros:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.ones(10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "array([ 1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.])"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.zeros((2, 2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "array([[ 0.,  0.],\n",
        "       [ 0.,  0.]])"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "And for creating arrays over ranges, either using a step size or a set number of points:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.arange(10, 20, 1.6)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "array([ 10. ,  11.6,  13.2,  14.8,  16.4,  18. ,  19.6])"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.linspace(10, 20, 16)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "array([ 10.        ,  10.66666667,  11.33333333,  12.        ,\n",
        "        12.66666667,  13.33333333,  14.        ,  14.66666667,\n",
        "        15.33333333,  16.        ,  16.66666667,  17.33333333,\n",
        "        18.        ,  18.66666667,  19.33333333,  20.        ])"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "And for getting random numbers:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.random.random((2, 2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "array([[ 0.76633572,  0.81414299],\n",
        "       [ 0.81736843,  0.27763528]])"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.random.standard_normal((2, 2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "array([[-1.34426401, -0.8267184 ],\n",
        "       [-0.61234629, -0.9110464 ]])"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Array Stats\n",
      "\n",
      "Back to the task at hand! We have these `time`, `pred`, `backup`, and `accoustic` arrays. What can we learn about them? There are a number of stats methods:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print pred.min()\n",
      "print pred.max()\n",
      "print pred.mean()\n",
      "print pred.std()\n",
      "print np.median(pred)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.05\n",
        "5.38\n",
        "2.65491666667\n",
        "1.75053229801\n",
        "2.74\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# peak-to-peak\n",
      "print pred.ptp()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "5.33\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "backup.max()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "nan"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The `backup` array contains `nan` values in places where data was missing. `nan` combined with anything else gives `nan` so all of our stats methods return `nan`. To get our data without `nan` we'll need to do some fancy indexing."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Indexing\n",
      "\n",
      "One of the powerful features of NumPy arrays is the many ways they can be indexed. You can, for example, use a list or array of integers to grab specific elements from an array. The list can contain indices in any order and can even contain repeated indices:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pred[[100, 5, 1, 5, 100]]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 24,
       "text": [
        "array([ 4.67,  1.13,  1.5 ,  1.13,  4.67])"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "(Note: The array used to index must have the same number of dimensions as the array being indexed.)\n",
      "\n",
      "It's also possible to index arrays using boolean expressions, similar to an `if` statement:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pred[pred > 5]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "array([ 5.02,  5.08,  5.13,  5.18,  5.23,  5.27,  5.3 ,  5.33,  5.35,\n",
        "        5.37,  5.38,  5.38,  5.38,  5.37,  5.36,  5.34,  5.31,  5.28,\n",
        "        5.24,  5.19,  5.13,  5.07,  5.01,  5.07,  5.11,  5.16,  5.2 ,\n",
        "        5.23,  5.26,  5.29,  5.31,  5.32,  5.33,  5.33,  5.33,  5.32,\n",
        "        5.31,  5.29,  5.26,  5.23,  5.19,  5.14,  5.1 ,  5.04])"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pred[(pred > 5) | (pred < 0.5)]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "array([ 0.48,  0.41,  0.34,  0.28,  0.23,  0.18,  0.14,  0.1 ,  0.08,\n",
        "        0.06,  0.05,  0.05,  0.06,  0.08,  0.11,  0.14,  0.19,  0.25,\n",
        "        0.31,  0.39,  0.47,  5.02,  5.08,  5.13,  5.18,  5.23,  5.27,\n",
        "        5.3 ,  5.33,  5.35,  5.37,  5.38,  5.38,  5.38,  5.37,  5.36,\n",
        "        5.34,  5.31,  5.28,  5.24,  5.19,  5.13,  5.07,  0.46,  0.39,\n",
        "        0.32,  0.26,  0.21,  0.16,  0.12,  0.09,  0.07,  0.06,  0.05,\n",
        "        0.06,  0.08,  0.1 ,  0.13,  0.18,  0.23,  0.29,  0.36,  0.44,\n",
        "        0.44,  0.38,  0.33,  0.29,  0.24,  0.21,  0.18,  0.16,  0.15,\n",
        "        0.14,  0.14,  0.16,  0.18,  0.21,  0.25,  0.3 ,  0.36,  0.43,\n",
        "        5.01,  5.07,  5.11,  5.16,  5.2 ,  5.23,  5.26,  5.29,  5.31,\n",
        "        5.32,  5.33,  5.33,  5.33,  5.32,  5.31,  5.29,  5.26,  5.23,\n",
        "        5.19,  5.14,  5.1 ,  5.04,  0.46,  0.39,  0.33,  0.27,  0.22,\n",
        "        0.18,  0.14,  0.11,  0.09,  0.08,  0.08,  0.09,  0.1 ,  0.13,\n",
        "        0.16,  0.2 ,  0.26,  0.32,  0.39,  0.47])"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "How exactly does this work? The truthy expressions with arrays produce another array: an array of boolean values with the same shape as the original array with `True` where the expression is true, and `False` elsewhere. Let's see how that looks on a small array:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.arange(10) > 5"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 27,
       "text": [
        "array([False, False, False, False, False, False,  True,  True,  True,  True], dtype=bool)"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "These boolean arrays can be saved in their own variables, combined logically with other boolean arrays, and used to index any array with the same shape.\n",
      "\n",
      "To get the indices where a condition is true use the [numpy.where](http://docs.scipy.org/doc/numpy/reference/generated/numpy.where.html) function:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.where(np.arange(10) > 5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "(array([6, 7, 8, 9]),)"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "How does this help with the `nan` issue? Much like Python's standard library has a [math.isnan](http://docs.python.org/2/library/math.html#math.isnan) function that works on floats, there is a [numpy.isnan](http://docs.scipy.org/doc/numpy/reference/generated/numpy.isnan.html) function that works on arrays. (In fact, NumPy has array equivalents to most of the functions in the `math` module.) Here's a small example of `np.isnan`:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = np.array([1, 2, np.nan, 4, 5, np.nan])\n",
      "np.isnan(a)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "array([False, False,  True, False, False,  True], dtype=bool)"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "`np.isnan` returns an array of booleans just like the logical expressions up above, so that looks promising! Let's try it:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a[np.isnan(a)]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 30,
       "text": [
        "array([ nan,  nan])"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Of course, that grabbed the `nan` values because `np.isnan` gives `True` where `a` has `nan` values. One thing to do perform a logical flip on the boolean array using the `~` operator:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a[~np.isnan(a)]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 31,
       "text": [
        "array([ 1.,  2.,  4.,  5.])"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Or we could see what other kinds of [logical functions](http://docs.scipy.org/doc/numpy/reference/routines.logic.html) there are in NumPy. One is [numpy.isfinite](http://docs.scipy.org/doc/numpy/reference/generated/numpy.isfinite.html#numpy.isfinite):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a[np.isfinite(a)]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 32,
       "text": [
        "array([ 1.,  2.,  4.,  5.])"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can use these functions, along with the [any](http://docs.scipy.org/doc/numpy/reference/generated/numpy.any.html#numpy.any) or [all](http://docs.scipy.org/doc/numpy/reference/generated/numpy.all.html#numpy.all) fuctions/methods on arrays, to test for the presence of missing data:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# are there any nan values?\n",
      "print 'time:', np.isnan(time).any()\n",
      "print 'backup:', np.isnan(backup).any()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "time: False\n",
        "backup: True\n"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# are all of the values finite?\n",
      "print 'pred:', np.isfinite(pred).all()\n",
      "print 'accoustic:', np.isfinite(accoustic).all()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "pred: True\n",
        "accoustic: False\n"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Both `backup` and `accoustic` have missing data. (These are the two columns of actual instrument measurements so it shouldn't be too shocking to see missing data.) We can use logical comparisons with arrays to make a boolean array of where `backup` and `accoustic` are both good:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "not_nan = np.isfinite(backup) & np.isfinite(accoustic)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 35
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "And then use this to make new copies of `time`, `pred`, `backup`, and `accoustic` without the rows where `backup` and `accoustic` are missing data:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "time = time[not_nan]\n",
      "pred = pred[not_nan]\n",
      "backup = backup[not_nan]\n",
      "accoustic = accoustic[not_nan]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 36
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "How many rows did we lose?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "not_nan.size - time.size"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 37,
       "text": [
        "6"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Not too bad. Now we can get down to business!"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Data Analysis (and Plots)\n",
      "\n",
      "So what are we actually looking at here?\n",
      "\n",
      "* `time`: time in hours since the first measurement in the file\n",
      "* `pred`: predicted water level\n",
      "* `accoustic`: a measured water level\n",
      "* `backup`: another measured water level\n",
      "\n",
      "All water levels are in feet above [Mean Lower Low Water](http://tidesandcurrents.noaa.gov/mllw.html). Let's take a quick look:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print time[:5]\n",
      "print pred[:5]\n",
      "print accoustic[:5]\n",
      "print backup[:5]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0.   0.1  0.2  0.3  0.4]\n",
        "[ 1.59  1.5   1.4   1.31  1.22]\n",
        "[ 4.65  4.54  4.44  4.33  4.26]\n",
        "[ 4.68  4.55  4.46  4.36  4.28]\n"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Honestly, looking at a ton of numbers is a great way to get a feal for things. We could compare maxima:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "backup.max() - pred.max()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 39,
       "text": [
        "8.5"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "But are those at the same time? We can use the [argmax method](http://docs.scipy.org/doc/numpy/reference/generated/numpy.argmax.html) to get the index of the maxima of one and use that index in the other for a more apples-to-apples comparison:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "m = backup.argmax()\n",
      "print m\n",
      "backup[m] - pred[m]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "208\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 40,
       "text": [
        "9.2300000000000004"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So at least according to the `backup` measurements the MLLW was 9 feet higher than predicted at one point during Hurricane Sandy!\n",
      "\n",
      "But that's just one data point. To really see trends you want a plot. We'll start by turning on the IPython Notebook's inline plotting mode so that plots show up right here in our notebook:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n",
        "For more information, type 'help(pylab)'.\n"
       ]
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Then conigure plots to display as SVG (default is PNG):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%config InlineBackend.figure_format = 'svg'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 42
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Then we'll import [matplotlib](http://matplotlib.org):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pyplot as plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 43
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "And make a basic plot of our data, using `time` along the x-axis and plotting the predicted and measured levels as three separate lines:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = plt.subplots()\n",
      "ax.plot(time, pred)\n",
      "ax.plot(time, accoustic)\n",
      "ax.plot(time, backup)\n",
      "ax.set_ylabel('Feet above MLLW')\n",
      "ax.set_xlabel('Hours Since First Measurement')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 44,
       "text": [
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       ]
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      "And to keep the lines straight we can throw in a legend:"
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      "fig, ax = plt.subplots()\n",
      "ax.plot(time, pred, label='Predicted')\n",
      "ax.plot(time, accoustic, label='Accoustic')\n",
      "ax.plot(time, backup, label='Backup')\n",
      "ax.set_ylabel('Feet above MLLW')\n",
      "ax.set_xlabel('Hours Since First Measurement')\n",
      "ax.legend(loc='upper right')"
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     "language": "python",
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      "Great! We can see that maybe something got a bit weird with the `accoustic` measurements and maybe we should trust the `backup` measurements more. Now maybe we'd like to quantify and plot the difference between the measured and predicted tide levels. Piece of cake:"
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      "ax.plot(time, pred, label='Predicted')\n",
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      "Wait a minute, what did we just do there? We just used a minus sign to do an element-wise subtraction of two arrays! Pretty handy. Let's look at array arithmetic for a bit."
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     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Array Math\n",
      "\n",
      "Arrays can be used in arithmetic expressions using the same binary operators we use for numbers: `+`, `-`, `*`, `/`, `**`, etc. These expressions return new arrays in which the mathematical operation has been applied elementwise. It's easiest to see this when combining an array and a scalar:"
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     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = np.arange(5, dtype=np.float) # float to avoid integer surprises\n",
      "print a"
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     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0.  1.  2.  3.  4.]\n"
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     "cell_type": "code",
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       "output_type": "pyout",
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        "array([ 5.,  6.,  7.,  8.,  9.])"
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        "array([  0.,   5.,  10.,  15.,  20.])"
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      "To get this same effect with lists you'd need to use a list or comprehension. With arrays it's as simple as `a + 5`. When combining arrays and scalars the same operation is applied to every element of the array. When combining two arrays it's slightly different:"
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     "cell_type": "code",
     "collapsed": false,
     "input": [
      "b = np.arange(10, 20, 2, dtype=np.float)\n",
      "print b"
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     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 10.  12.  14.  16.  18.]\n"
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     "cell_type": "code",
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      "b - a"
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     "language": "python",
     "metadata": {},
     "outputs": [
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       "output_type": "pyout",
       "prompt_number": 65,
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        "array([ 10.,  11.,  12.,  13.,  14.])"
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      "a / b"
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     "outputs": [
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       "output_type": "pyout",
       "prompt_number": 66,
       "text": [
        "array([ 0.        ,  0.08333333,  0.14285714,  0.1875    ,  0.22222222])"
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     "prompt_number": 66
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      "In these cases the first element of `a` operates with the first element of `b`, and so on. So long as the two arrays are the same size and shape you will see this behavior. Arrays with different shapes can sometimes be combined with binary operators via an implicit resizing/reshaping called [broadcasting](http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html), but that's a topic for another day."
     ]
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    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## More Data Analysis\n",
      "\n",
      "There might be more we could do with this data. When was the peak water height?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "time[backup.argmax()]"
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     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 81,
       "text": [
        "21.399999999999999"
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      }
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     "prompt_number": 81
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     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "These are hours past midnight on Oct 29, so the peak water height was sometime around 9:24 PM on Oct. 29. The biggest difference between the predicted and observed tide heights were around the same time:"
     ]
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     "cell_type": "code",
     "collapsed": false,
     "input": [
      "time[obs_minus_pred.argmax()]"
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     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 79,
       "text": [
        "21.399999999999999"
       ]
      }
     ],
     "prompt_number": 79
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    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Which is one reason NYC had such bad flooding."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Learn More\n",
      "\n",
      "These are just some ways of working with data in NumPy arrays. Learn more by diving into the documentation at http://docs.scipy.org/doc/."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
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