{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Here I import the relevant function libraries\n",
    "#This can be done in many ways\n",
    "#To import an entire library (e.g. scipy) so that functions accessed by typing \"lib_name.func_name\"\n",
    "%matplotlib inline\n",
    "import matplotlib\n",
    "\n",
    "#To import a subsection of a library\n",
    "import scipy.optimize\n",
    "\n",
    "#To import the whole library under a different name, so you can type \"diff_name.func_name\"\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#To import just a particular function\n",
    "from time import time\n",
    "from math import sin\n",
    "#This may be confusing but I'm grabbing a function usually denoted with \"time.time\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#First of all we need to read the example data file into a list\n",
    "#I will create an empty list and append the data as I read the file\n",
    "#Note appending is a VERY inefficient opperation, however for less than a ~million repeats it's fine\n",
    "\n",
    "#Make an empty list:\n",
    "datalist = []\n",
    "\n",
    "#Open the file. Here the 'r' means 'read'\n",
    "f = open('ex_data.dat','r')\n",
    "\n",
    "#Now read all the lines of the file into a list called lines\n",
    "#For very large files this isn't always a good plan as you may not want to store the whole file in the memory, such files should be read line by line\n",
    "lines = f.readlines()\n",
    "\n",
    "#Now loop over ever line and record the value as a floating point number in datalist\n",
    "#Notice that python's loop functionality is very flexible\n",
    "for line in lines:\n",
    "    datalist.append(float(line))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb6c38209d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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       "xGCXJKkgBrskSQUx2CVJKojBLklSQQx2SZIK8v8BlmkknL1i79QAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb6c38209d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Now we want to we want to create a plot\n",
    "#Create a figure called 'fig' and a set of axes called 'ax'\n",
    "fig,ax = plt.subplots(figsize=(8,6))\n",
    "\n",
    "#Create a dummy list of numbers to plot along the x-axis\n",
    "#We will create a numpy array using the 'numpy.arange()' function\n",
    "#The syntax for this is (start_value,non_inclusive_end_value,step_size)\n",
    "#Here I also use the 'len()' function which returns the length of a list/array\n",
    "x_vals = np.arange(0,len(datalist),1)\n",
    "\n",
    "#Now plot the data on the axes\n",
    "#Here I choose to plot the data as blue dots\n",
    "ax.plot(x_vals,datalist,'b.')\n",
    "\n",
    "#Set the limits, and label the axes\n",
    "ax.set_xlim(0,100)\n",
    "ax.set_ylim(-5,50)\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('val')\n",
    "\n",
    "#Force the plot to be displayed\n",
    "plt.show()\n",
    "\n",
    "#Save the plot\n",
    "fig.savefig('ex_fig.jpg',dpi=300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Now make a function of a gaussian distribution\n",
    "def gaussian(x,mean,sigma,A):\n",
    "    \n",
    "    #Set the normalisation\n",
    "    norm = A/(sigma*np.sqrt(2.*np.pi))\n",
    "    \n",
    "    return norm*np.exp( -((x-mean)**2.) / (2.*sigma**2.) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A =  1010.0\n",
      "Mean =  56.0\n",
      "Sigma =  9.0\n",
      "A =  1010.0\n",
      "Mean =  56.0\n",
      "Sigma =  9.0\n"
     ]
    }
   ],
   "source": [
    "#First we will fit this the bad, slow way\n",
    "\n",
    "#Start with an impossibly large value of least_sq\n",
    "least_sq = 1000000000.\n",
    "\n",
    "#Loop over each parameter and over each value of x and calculate where least_sq is minimised\n",
    "#Make some value approximate guesses of where the min/max values of the parameters are\n",
    "for mean in np.arange(50.,60.,1.):\n",
    "    for sigma in np.arange(5.,15.,1.):\n",
    "        for A in np.arange(500.,1500.,10.):\n",
    "            least_sq_temp = 0.\n",
    "            for i in range(0,len(x_vals),1):\n",
    "                #Add the current deviations to the temp value of least_sq\n",
    "                least_sq_temp += (datalist[i] - gaussian(x_vals[i],mean,sigma,A))**2.\n",
    "            \n",
    "            #If least_sq_temp is a better fit than your current stored value then update the fit\n",
    "            if least_sq_temp < least_sq:\n",
    "                least_sq = least_sq_temp\n",
    "                A_fit = A\n",
    "                mean_fit = mean\n",
    "                sigma_fit = sigma\n",
    "\n",
    "print 'A = ',A_fit\n",
    "print 'Mean = ',mean_fit\n",
    "print 'Sigma = ',sigma_fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "Ik7sZmZmJeLEbmZmViL/HxrU9f1vViBFAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb6c0bb7b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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       "Ik7sZmZmJeLEbmZmViL/HxrU9f1vViBFAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb6c0bb7b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Reproduce the plot, but with the fit\n",
    "fig,ax = plt.subplots(figsize=(8,6))\n",
    "\n",
    "x_vals = np.arange(0,len(datalist),1)\n",
    "\n",
    "#Here I select the plot the fit as a green, dotted, 2pt line\n",
    "ax.plot(x_vals,gaussian(x_vals,mean_fit,sigma_fit,A_fit),lw=2,ls='dotted',color='green')\n",
    "ax.plot(x_vals,datalist,'b.')\n",
    "\n",
    "ax.set_xlim(0,100)\n",
    "ax.set_ylim(-5,50)\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('val')\n",
    "\n",
    "plt.show()\n",
    "\n",
    "#Save the plot\n",
    "fig.savefig('ex_fit1_fig.jpg',dpi=300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean =  56.0803931592\n",
      "Sigma =  8.9931758567\n",
      "A =  1008.72516827\n",
      "Mean =  56.0803931592\n",
      "Sigma =  8.9931758567\n",
      "A =  1008.72516827\n"
     ]
    }
   ],
   "source": [
    "#Now do the fit the smart way, by using a built in curve fitting function\n",
    "#The function returns the fit parameters and the covariances\n",
    "#The syntax is (function_to_fit, x_values, data_values, p0 = list_of_initial_guesses)\n",
    "fit,cov = scipy.optimize.curve_fit(gaussian, x_vals, datalist, p0 = [55.,10.,800.])\n",
    "\n",
    "print 'Mean = ',fit[0]\n",
    "print 'Sigma = ',fit[1]\n",
    "print 'A = ',fit[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb6c0e43dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb6c0e43dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Reproduce the plot, but with the new fit\n",
    "fig,ax = plt.subplots(figsize=(8,6))\n",
    "\n",
    "x_vals = np.arange(0,len(datalist),1)\n",
    "\n",
    "ax.plot(x_vals,gaussian(x_vals,fit[0],fit[1],fit[2]),lw=2,ls='dashed',color='red')\n",
    "ax.plot(x_vals,datalist,'b.')\n",
    "\n",
    "ax.set_xlim(0,100)\n",
    "ax.set_ylim(-5,50)\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('val')\n",
    "\n",
    "plt.show()\n",
    "\n",
    "#Save the plot\n",
    "fig.savefig('ex_fit2_fig.jpg',dpi=300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#This is the end of the example, but below are some useful things to note"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loop time:  0.311264038086 sec\n",
      "Array arithmetic time:  0.0395338535309 sec\n",
      "Loop time:  0.311264038086 sec\n",
      "Array arithmetic time:  0.0395338535309 sec\n"
     ]
    }
   ],
   "source": [
    "#Array Arithmetic\n",
    "\n",
    "#When dealing with large lists (the norm in astronomy) array arithmetic is nearly always namy times faster\n",
    "#You should write as much of your code using numpy arrays as you possibly can\n",
    "#The only real drawback of arrays is that you cannot append values to them, they have fixed length\n",
    "\n",
    "#Here I will take the sine of a million element array using a loop and using array arithmetic \n",
    "#Look at the difference in duration\n",
    "\n",
    "#Generate an array of 10 million numbers between 0 and pi\n",
    "val_arr = np.random.uniform(0.,np.pi,1E6)\n",
    "\n",
    "\n",
    "#Recast these arrays as lists\n",
    "val_list = list(val_arr)\n",
    "\n",
    "start_time = time()\n",
    "#Note I've used the shorthand version of range here (the default start is 0 and default step is 1)\n",
    "for i in range(1000000):\n",
    "    #This will overwrite the current value with it's sine\n",
    "    val_list[i] = sin(val_list[i])\n",
    "print \"Loop time: \",(time()-start_time),\"sec\"\n",
    "\n",
    "start_time = time()\n",
    "val_arr = np.sin(val_arr)\n",
    "print \"Array arithmetic time: \",(time()-start_time),\"sec\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "1.5\n"
     ]
    }
   ],
   "source": [
    "#Integer Arithmetic\n",
    "\n",
    "#If you're not used to coding, I've got some bad news for you, computer are pretty dumb\n",
    "#Python will identify what a number you give is by how you write it\n",
    "#If the number doesn't have a decimal point it will assume it's an integer\n",
    "\n",
    "print 3/2\n",
    "\n",
    "print 3./2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2, 3, 4, 5] [1, 2, 3, 4, 5]\n",
      "[1, 2, 4, 5] [1, 2, 4, 5]\n"
     ]
    }
   ],
   "source": [
    "#Pass by Reference vs Pass by Value\n",
    "\n",
    "#In most cases python defaults to passing by reference\n",
    "#This means that when you say 'a = b' you are essentially telling the computer that they are the same thing\n",
    "#Whatever you do to b is also done to a\n",
    "\n",
    "a = [1,2,3,4,5]\n",
    "b = a\n",
    "\n",
    "print a,b\n",
    "\n",
    "#Delete the value 3 from the list a\n",
    "a.remove(3)\n",
    "\n",
    "print a,b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2, 4, 5] [1, 2, 3, 4, 5]\n",
      "[1, 2, 4, 5] [1, 2, 3, 4, 5]\n"
     ]
    }
   ],
   "source": [
    "#To overcome this you have to trick the computer into duplicating the list\n",
    "\n",
    "a = [1,2,3,4,5]\n",
    "#This will copy the array from 'start_point:end_point', the default is the start/end of the list\n",
    "b = a[:]\n",
    "\n",
    "a.remove(3)\n",
    "\n",
    "print a,b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5, 4, 3, 2, 1]\n",
      "[1, 3, 5]\n",
      "[5, 4, 3, 2, 1]\n",
      "[1, 3, 5]\n"
     ]
    }
   ],
   "source": [
    "#There some other tricks you can play with this\n",
    "\n",
    "a = [1,2,3,4,5]\n",
    "\n",
    "#To return the list in reverse\n",
    "#This is saying go through the whole list, but stepping one place backwards each time\n",
    "print a[::-1]\n",
    "\n",
    "#To return every other value\n",
    "print a[::2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2, 3, 4, 5]\n",
      "[1, 2, 3, 4, 5]\n"
     ]
    }
   ],
   "source": [
    "#Another python is to use sets\n",
    "#If you want to remove duplicates from a list you don't have to do a complicated algorithm\n",
    "\n",
    "a = [1,1,2,3,3,3,3,4,5,5,5]\n",
    "\n",
    "#To remove duplicates you can define the list as a set\n",
    "#Sets are mathematical objects that cannot have duplicates\n",
    "#Then you can redefine as a list\n",
    "#Doing this all at once\n",
    "\n",
    "print list(set(a))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  }
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