{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example of how to use Jupyter\n",
    "\n",
    "See also the web pages about:\n",
    "\n",
    "The notebook interface called Jupyter \n",
    "https://jupyter.readthedocs.io/en/latest/index.html\n",
    "\n",
    "The language used is Python (specifically python 2.7, but python 3 also works fine)  \n",
    "https://www.python.org/doc/\n",
    "\n",
    "The libraries providing the Maths and statistics functions: Scipy and Numpy  \n",
    "https://scipy.org/\n",
    "\n",
    "Finally the graphing engine matplotlib  \n",
    "http://matplotlib.org/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cell types\n",
    "Cell types can be either code (the default), results (generated by running code cells) or \"Markdown\" which is documentation for output, like this cell. You can set the cell type from the menu above.\n",
    "\n",
    "See http://jupyter-notebook.readthedocs.io/en/latest/examples/Notebook/Working%20With%20Markdown%20Cells.html for details of what you can do in a Markdown cell. Including headers, *highlighting*, \n",
    "    \n",
    "    print(\"and example code\")\n",
    "    \n",
    "Double click on this cell to see how it is formatted and note the \"Markdown\" cell type in the menu bar."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Python\n",
    "The language is very rich so this is not even a cursory introduction, but an example of some code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('one', 'two')\n"
     ]
    }
   ],
   "source": [
    "# Everything after a # is a comment for the reader only\n",
    "var=\"one\" # set a variable called var to the string \"one\"\n",
    "v2 = 'two' # set another variable, v2, to \"two\", variable must start with a letter but can contain numbers\n",
    "# note \"a\" and 'a' are both strings, the quotes just have to match\n",
    "print(var,v2) # note print automatically adds a space between elements if given a list and adds a new line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "i = 9 # integer\n",
    "j = 10. # float (as indicated by the decimal point)\n",
    "l = [11.1,12] # list of float, int\n",
    "m = (\"size\",\"fish\",7) # tuple of string, string, int (tuples can not be added to, lists can)\n",
    "n = [i,j,l,m] # list constructed from existing elements, including both other lists and tuples\n",
    "o = {'one':1,'two':2} # dictionary relating pairs of elements, first is the key, the second the value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('i', 9, <type 'int'>)\n",
      "('j', 10.0, <type 'float'>)\n",
      "('l', [11.1, 12], <type 'list'>)\n",
      "('m', ('size', 'fish', 7), <type 'tuple'>)\n",
      "('n', [9, 10.0, [11.1, 12], ('size', 'fish', 7)], <type 'list'>)\n",
      "('o', {'two': 2, 'one': 1}, <type 'dict'>)\n"
     ]
    }
   ],
   "source": [
    "print('i',i,type(i)) # type(x) gives the type of x, as a string if printed\n",
    "print('j',j,type(j))\n",
    "print('l',l,type(l))\n",
    "print('m',m,type(m))\n",
    "print('n',n,type(n))\n",
    "print('o',o,type(o))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('l[0] l[1]', 11.1, 12)\n",
      "('m[0] m[1] m[2]', 'size', 'fish', 7)\n",
      "('o[\"one\"] o[\"two\"]', 1, 2)\n"
     ]
    }
   ],
   "source": [
    "# access elements of lists or tuples\n",
    "print('l[0] l[1]',l[0],l[1])\n",
    "print('m[0] m[1] m[2]',m[0],m[1],m[2])\n",
    "print('o[\"one\"] o[\"two\"]',o[\"one\"],o[\"two\"]) # note if you start a string with ' you can use \" in it (and vice versa)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('1+2 =', 3)\n",
      "('119.9765/35478. =', 0.0033817154292801175)\n"
     ]
    }
   ],
   "source": [
    "# maths is supported (not supprisingly)\n",
    "print('1+2 =',1+2)\n",
    "print('119.9765/35478. =',119.9765/35478.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(9, 'is less than or equal to 10')\n",
      "Continuing false path\n",
      "do always (after conditional)\n"
     ]
    }
   ],
   "source": [
    "# conditional statements\n",
    "if(i>10):  # if thing in brackets is true do first part\n",
    "    print(i,'is bigger than 10') # python uses spaces at the start of the line to define blocks of code\n",
    "    print('Still on true path')\n",
    "else: # part to do if false\n",
    "    print(i,'is less than or equal to 10')\n",
    "    print('Continuing false path')\n",
    "# end a block by lining the first charater of the string up with the statement before the block\n",
    "print(\"do always (after conditional)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(9, <type 'int'>)\n",
      "(10.0, <type 'float'>)\n",
      "([11.1, 12], <type 'list'>)\n",
      "Content is\n",
      "(' + ', 11.1, <type 'float'>)\n",
      "(' + ', 12, <type 'int'>)\n",
      "(('size', 'fish', 7), <type 'tuple'>)\n",
      "Content is\n",
      "(' + ', 'size', <type 'str'>)\n",
      "(' + ', 'fish', <type 'str'>)\n",
      "(' + ', 7, <type 'int'>)\n"
     ]
    }
   ],
   "source": [
    "# loops\n",
    "for v in n: # all element of n are accessed as v in turn (n was defined above)\n",
    "    print(v,type(v)) # show v \n",
    "    # see if v can also be iterated over, \"is\" means compare (== means compare value), \"and\" and \"or\" allow complex queries\n",
    "    if(type(v) is tuple or type(v) is list): # if inside a loop \n",
    "        print(\"Content is\")\n",
    "        for w in v: # more indenting to make it clear this loop is inside the if statement\n",
    "            print(' + ',w,type(w)) # add a \" + \" to the output to get an indent there as well\n",
    "# note you do not have to provide an \"else\" if there is nothing to do for false"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0:  0**0=1  0**1=0  0**2=0  0**3=0  0**4=0 ()\n",
      "1:  1**0=1  1**1=1  1**2=1  1**3=1  1**4=1 ()\n",
      "2:  2**0=1  2**1=2  2**2=4  2**3=8  2**4=16 ()\n",
      "3:  3**0=1  3**1=3  3**2=9  3**3=27  3**4=81 ()\n",
      "4:  4**0=1  4**1=4  4**2=16  4**3=64  4**4=256 ()\n",
      "5:  5**0=1  5**1=5  5**2=25  5**3=125  5**4=625 ()\n",
      "6:  6**0=1  6**1=6  6**2=36  6**3=216  6**4=1296 ()\n",
      "7:  7**0=1  7**1=7  7**2=49  7**3=343  7**4=2401 ()\n",
      "8:  8**0=1  8**1=8  8**2=64  8**3=512  8**4=4096 ()\n",
      "9:  9**0=1  9**1=9  9**2=81  9**3=729  9**4=6561 ()\n",
      "10:  10**0=1  10**1=10  10**2=100  10**3=1000  10**4=10000 ()\n",
      "11:  11**0=1  11**1=11  11**2=121  11**3=1331  11**4=14641 ()\n",
      "12:  12**0=1  12**1=12  12**2=144  12**3=1728  12**4=20736 ()\n",
      "13:  13**0=1  13**1=13  13**2=169  13**3=2197  13**4=28561 ()\n",
      "14:  14**0=1  14**1=14  14**2=196  14**3=2744  14**4=38416 ()\n",
      "15:  15**0=1  15**1=15  15**2=225  15**3=3375  15**4=50625 ()\n",
      "16:  16**0=1  16**1=16  16**2=256  16**3=4096  16**4=65536 ()\n",
      "17:  17**0=1  17**1=17  17**2=289  17**3=4913  17**4=83521 ()\n",
      "18:  18**0=1  18**1=18  18**2=324  18**3=5832  18**4=104976 ()\n",
      "19:  19**0=1  19**1=19  19**2=361  19**3=6859  19**4=130321 ()\n"
     ]
    }
   ],
   "source": [
    "# loop over values\n",
    "for i in range(20): # the range(n) function creates all the integers from 0 -> n-1 inclusive\n",
    "    print(\"{}:\".format(i)), # \"string {}\".format(a) replaces the {} in the string with a text version of variable i\n",
    "    # comma at the end means no new line\n",
    "    for j in range(5): # loop inside a loop (must loop with different variables)\n",
    "        print(\" {}**{}={}\".format(i,j,i**j)), # print the first 5 powers of i (i**j means i to the power of j)\n",
    "    print() # print by itself just adds a new line\n",
    "    \n",
    "# for i in range(20) :\n",
    "#     print(\"{}: {}**{}={}\".format(i,i,j,i**j)) # this is a shorter version of the above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "?float\n",
      "On its own line gives a new window with the help text for the built in float function,\n",
      "you can do this for any variable or function\n"
     ]
    }
   ],
   "source": [
    "print(\"?float\")\n",
    "print(\"On its own line gives a new window with the help text for the built in float function,\\nyou can do this for any variable or function\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "?float"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n"
     ]
    }
   ],
   "source": [
    "# define a function\n",
    "def func(x,m,c):\n",
    "    \"\"\"Text in triple quotes is the help text for the function! This function just returns x*m + c\"\"\"\n",
    "    return x*m + c\n",
    "# call your new function\n",
    "print(func(1,2,3))\n",
    "?func"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numpy\n",
    "This adds better arrays to python for doing maths and brings in many maths functions (sqrt, sin, ... etc.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(<type 'numpy.ndarray'>, array([ 0.  ,  0.01,  0.02,  0.03,  0.04,  0.05,  0.06,  0.07,  0.08,\n",
      "        0.09,  0.1 ,  0.11,  0.12,  0.13,  0.14,  0.15,  0.16,  0.17,\n",
      "        0.18,  0.19,  0.2 ,  0.21,  0.22,  0.23,  0.24,  0.25,  0.26,\n",
      "        0.27,  0.28,  0.29,  0.3 ,  0.31,  0.32,  0.33,  0.34,  0.35,\n",
      "        0.36,  0.37,  0.38,  0.39,  0.4 ,  0.41,  0.42,  0.43,  0.44,\n",
      "        0.45,  0.46,  0.47,  0.48,  0.49,  0.5 ,  0.51,  0.52,  0.53,\n",
      "        0.54,  0.55,  0.56,  0.57,  0.58,  0.59,  0.6 ,  0.61,  0.62,\n",
      "        0.63,  0.64,  0.65,  0.66,  0.67,  0.68,  0.69,  0.7 ,  0.71,\n",
      "        0.72,  0.73,  0.74,  0.75,  0.76,  0.77,  0.78,  0.79,  0.8 ,\n",
      "        0.81,  0.82,  0.83,  0.84,  0.85,  0.86,  0.87,  0.88,  0.89,\n",
      "        0.9 ,  0.91,  0.92,  0.93,  0.94,  0.95,  0.96,  0.97,  0.98,\n",
      "        0.99,  1.  ]))\n"
     ]
    }
   ],
   "source": [
    "import numpy as np # import the package with a user chosen short name, that is used before all functions\n",
    "x = np.linspace(0,1,101) # make 101 equally spaced numbers from 0 to 100 inclusive\n",
    "print(type(x),x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 3.    3.02  3.04  3.06  3.08  3.1   3.12  3.14  3.16  3.18  3.2   3.22\n",
      "  3.24  3.26  3.28  3.3   3.32  3.34  3.36  3.38  3.4   3.42  3.44  3.46\n",
      "  3.48  3.5   3.52  3.54  3.56  3.58  3.6   3.62  3.64  3.66  3.68  3.7\n",
      "  3.72  3.74  3.76  3.78  3.8   3.82  3.84  3.86  3.88  3.9   3.92  3.94\n",
      "  3.96  3.98  4.    4.02  4.04  4.06  4.08  4.1   4.12  4.14  4.16  4.18\n",
      "  4.2   4.22  4.24  4.26  4.28  4.3   4.32  4.34  4.36  4.38  4.4   4.42\n",
      "  4.44  4.46  4.48  4.5   4.52  4.54  4.56  4.58  4.6   4.62  4.64  4.66\n",
      "  4.68  4.7   4.72  4.74  4.76  4.78  4.8   4.82  4.84  4.86  4.88  4.9\n",
      "  4.92  4.94  4.96  4.98  5.  ]\n"
     ]
    }
   ],
   "source": [
    "# the power comes as you can pass numpy arrays to many functions and get back an array with the results for\n",
    "# all of the inputs\n",
    "y = func(x,2.,3) # note func will work with any sane combination of types\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 3.    3.03  3.06  3.09  3.12  3.15  3.18  3.21  3.24  3.27  3.3   3.33\n",
      "  3.36  3.39  3.42  3.45  3.48  3.51  3.54  3.57  3.6   3.63  3.66  3.69\n",
      "  3.72  3.75  3.78  3.81  3.84  3.87  3.9   3.93  3.96  3.99  4.02  4.05\n",
      "  4.08  4.11  4.14  4.17  4.2   4.23  4.26  4.29  4.32  4.35  4.38  4.41\n",
      "  4.44  4.47  4.5   4.53  4.56  4.59  4.62  4.65  4.68  4.71  4.74  4.77\n",
      "  4.8   4.83  4.86  4.89  4.92  4.95  4.98  5.01  5.04  5.07  5.1   5.13\n",
      "  5.16  5.19  5.22  5.25  5.28  5.31  5.34  5.37  5.4   5.43  5.46  5.49\n",
      "  5.52  5.55  5.58  5.61  5.64  5.67  5.7   5.73  5.76  5.79  5.82  5.85\n",
      "  5.88  5.91  5.94  5.97  6.  ]\n"
     ]
    }
   ],
   "source": [
    "print(x+y) # if two arrays the same length we can add element by element"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.          0.00331126  0.00657895  0.00980392  0.01298701  0.01612903\n",
      "  0.01923077  0.02229299  0.02531646  0.02830189  0.03125     0.03416149\n",
      "  0.03703704  0.0398773   0.04268293  0.04545455  0.04819277  0.0508982\n",
      "  0.05357143  0.05621302  0.05882353  0.06140351  0.06395349  0.06647399\n",
      "  0.06896552  0.07142857  0.07386364  0.07627119  0.07865169  0.08100559\n",
      "  0.08333333  0.08563536  0.08791209  0.09016393  0.0923913   0.09459459\n",
      "  0.09677419  0.09893048  0.10106383  0.1031746   0.10526316  0.10732984\n",
      "  0.109375    0.11139896  0.11340206  0.11538462  0.11734694  0.11928934\n",
      "  0.12121212  0.12311558  0.125       0.12686567  0.12871287  0.13054187\n",
      "  0.13235294  0.13414634  0.13592233  0.13768116  0.13942308  0.14114833\n",
      "  0.14285714  0.14454976  0.14622642  0.14788732  0.14953271  0.15116279\n",
      "  0.15277778  0.15437788  0.1559633   0.15753425  0.15909091  0.16063348\n",
      "  0.16216216  0.16367713  0.16517857  0.16666667  0.16814159  0.16960352\n",
      "  0.17105263  0.17248908  0.17391304  0.17532468  0.17672414  0.17811159\n",
      "  0.17948718  0.18085106  0.18220339  0.1835443   0.18487395  0.18619247\n",
      "  0.1875      0.18879668  0.19008264  0.19135802  0.19262295  0.19387755\n",
      "  0.19512195  0.19635628  0.19758065  0.19879518  0.2       ]\n"
     ]
    }
   ],
   "source": [
    "print(x/y) # or divide "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 4.47712125  4.48000694  4.48287358  4.48572143  4.48855072  4.49136169\n",
      "  4.49415459  4.49692965  4.49968708  4.50242712  4.50514998  4.50785587\n",
      "  4.51054501  4.5132176   4.51587384  4.51851394  4.52113808  4.52374647\n",
      "  4.52633928  4.5289167   4.53147892  4.53402611  4.53655844  4.5390761\n",
      "  4.54157924  4.54406804  4.54654266  4.54900326  4.55145     4.55388303\n",
      "  4.5563025   4.55870857  4.56110138  4.56348109  4.56584782  4.56820172\n",
      "  4.57054294  4.5728716   4.57518784  4.5774918   4.5797836   4.58206336\n",
      "  4.58433122  4.5865873   4.58883173  4.59106461  4.59328607  4.59549622\n",
      "  4.59769519  4.59988307  4.60205999  4.60422605  4.60638137  4.60852603\n",
      "  4.61066016  4.61278386  4.61489722  4.61700034  4.61909333  4.62117628\n",
      "  4.62324929  4.62531245  4.62736586  4.6294096   4.63144377  4.63346846\n",
      "  4.63548375  4.63748973  4.63948649  4.64147411  4.64345268  4.64542227\n",
      "  4.64738297  4.64933486  4.65127801  4.65321251  4.65513843  4.65705585\n",
      "  4.65896484  4.66086548  4.66275783  4.66464198  4.66651798  4.66838592\n",
      "  4.67024585  4.67209786  4.673942    4.67577834  4.67760695  4.6794279\n",
      "  4.68124124  4.68304704  4.68484536  4.68663627  4.68841982  4.69019608\n",
      "  4.6919651   4.69372695  4.69548168  4.69722934  4.69897   ]\n"
     ]
    }
   ],
   "source": [
    "print(np.log10(y)+4) # if the array is added to a single number then add to all elements"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scipy\n",
    "This adds a lot of high level routines, such as numerical integration, minimum finding and many other things\n",
    "See the documentation for everything it does"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.integrate import quad # import a single routine from a subpackage of scipy\n",
    "?quad # list all of the options for quad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "intergal of func(x,7,2) from x = 1 to 10 is 364.5 +- 4.04676292476e-12\n"
     ]
    }
   ],
   "source": [
    "# integrate func we defined above (func = m*x + c) from 1 to 10, with m=7 and c=2\n",
    "result, err = quad(func,a=1,b=10,args=(7,2)) # named arguments can be set by order or by name, here two values are returned\n",
    "print(\"intergal of func(x,7,2) from x = 1 to 10 is {} +- {}\".format(result,err))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which should be $\\int_1^{10} (7x + 2) dx = \\left[ \\frac{7}{2}x^2+2x \\right]_1^{10} = [700/2 + 20] - [7/2 + 2] = 370 - 5.5 = 364.5$  \n",
    "Double click on this cell to see how to add maths to the output, using the latex language"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## matplotlib\n",
    "Adds graphing to pyton, inside juptyer it can display the plots straigh into the output cells"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x45385c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# First \"magic\" command to juypter itself instead of python, %? for full list\n",
    "# This sets up jupyter to display plots from matplotlib\n",
    "# with an inline display in the cell, without make a new window.\n",
    "%matplotlib inline\n",
    "# then make the python functions to access matplotlib available\n",
    "import matplotlib.pyplot as plt\n",
    "# draw the arrays x and y defined above\n",
    "plt.plot(x,y) # plot is the most basic plotting routine, will do auto axies\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.show() # always put a plt.show() when you want the plot drawn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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IRfsXERUdRfc63RnSYgiz75ud6VHGjQQEBHjUEODKHqmHcckpegSilE3OxZxj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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x750fcf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# new plot for x verse np.log10(x)+4\n",
    "x = np.linspace(0.2,2,100) # note reusing x, so take care when running cells out of order\n",
    "y = np.log10(x)\n",
    "plt.plot(x,np.log10(x),label=\"log10(x)\") # new option to give a name to the curve\n",
    "plt.plot(x,np.log(x),label=\"log(x)\") # Another curve (automatically gets a new colour)\n",
    "plt.plot(x,np.sqrt(x),label=\"sqrt(x)\",) # add a third curve, with an explicit colour and dash style\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "# can plot data with error bars too, look at the ?plt.errorbar for all of the options\n",
    "plt.errorbar(x=[0.5,1.0,1.5],y=[-0.5,-0.1,-0.01],yerr=[0.1,0.07,0.15],fmt=\"o\",label=\"random points\")\n",
    "plt.legend() # draw the labels to define the lines\n",
    "plt.show() # always put a plt.show() when you want the plot drawn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Many more things you can do, such as log axies, grid lines, several plots in the same output, set axies ranges etc. See documentaiton for details."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Subplots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZHQPMifaRWd6wk6YyJMAzz0Dz5nD66aEHRwmOiJT38suwxx6wxRZhlXMlOJIE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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1eb71978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# First \"magic\" command to juypter itself instead of python, %? for full list\n",
    "# This sets up jupyter to display plots from matplotlib\n",
    "# with an inline display in the cell, without make a new window.\n",
    "%matplotlib inline\n",
    "# then make the python functions to access matplotlib available\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "x = np.array([10,19,32])\n",
    "y = x**2 + 7\n",
    "fig = plt.figure(figsize=(8, 6)) # set the default figure size to 8,6 (slightly larger)\n",
    "# now make a 2x2 array of plots and plot into the top left one (i.e. subplot 1)\n",
    "p = plt.subplot(221)\n",
    "p.plot(x,y) # some data to plot as x,y\n",
    "p.set_title('Top Left')\n",
    "p.set_xlabel('x')\n",
    "p.set_ylabel('y')\n",
    "# plot into the top right (subplot 2)\n",
    "p = plt.subplot(222)\n",
    "p.plot(x,np.sqrt(y)) \n",
    "p.set_title('Top Right')\n",
    "p.set_xlabel('x')\n",
    "p.set_ylabel('$\\sqrt{y}$') # note use of maths in axis label using $ math $\n",
    "# plot into the bottom left (subplot 3)\n",
    "p = plt.subplot(223)\n",
    "p.plot(x,np.log(y)) \n",
    "p.set_title('Bottom Left')\n",
    "p.set_xlabel('x')\n",
    "p.set_ylabel('$\\ln{(y)}$')\n",
    "# plot into the bottom right (subplot 4)\n",
    "p = plt.subplot(224)\n",
    "p.plot(np.log10(x),np.log10(y)) \n",
    "p.set_title('Bottom Right')\n",
    "p.set_xlabel('$\\log{(x)}$')\n",
    "p.set_ylabel('$\\log{(y)}$')\n",
    "# now make space for the captions and axis labels\n",
    "plt.tight_layout()\n",
    "# always put a show command where a plot should be finished\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Welcome to Python 2.7!  This is the online help utility.\n",
      "\n",
      "If this is your first time using Python, you should definitely check out\n",
      "the tutorial on the Internet at http://docs.python.org/2.7/tutorial/.\n",
      "\n",
      "Enter the name of any module, keyword, or topic to get help on writing\n",
      "Python programs and using Python modules.  To quit this help utility and\n",
      "return to the interpreter, just type \"quit\".\n",
      "\n",
      "To get a list of available modules, keywords, or topics, type \"modules\",\n",
      "\"keywords\", or \"topics\".  Each module also comes with a one-line summary\n",
      "of what it does; to list the modules whose summaries contain a given word\n",
      "such as \"spam\", type \"modules spam\".\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [Root]",
   "language": "python",
   "name": "Python [Root]"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}