NumpyIntro5.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Good review of numpy https://www.youtube.com/watch?v=GB9ByFAIAH4 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numpy library - Remember to do      pip install numpy if running on your laptop\n",
    "### Numpy provides support for math and logical operations on arrays \n",
    "#### https://www.tutorialspoint.com/numpy/index.htm\n",
    "### It supports many more data types than python \n",
    "#### https://www.tutorialspoint.com/numpy/numpy_data_types.htm \n",
    "### Only a single data type is allowed in any particular array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 1.],\n",
       "       [1., 1.],\n",
       "       [1., 1.]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "a = np.array([1,2,3,4,5,6])\n",
    "b = a + 1\n",
    "c = np.reshape(a,(2,3))  # note the tuple\n",
    "d = np.transpose(c)\n",
    "d = np.ones((3,2))\n",
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "140478976930992\n",
      "b = 140478958887920\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([  0,   2,   4,   6,   8,  10,  12,  14,  16,  18,  20,  22,  24,\n",
       "        26,  28,  30,  32,  34,  36,  38,  40,  42,  44,  46,  48,  50,\n",
       "        52,  54,  56,  58,  60,  62,  64,  66,  68,  70,  72,  74,  76,\n",
       "        78,  80,  82,  84,  86,  88,  90,  92,  94,  96,  98, 100, 102,\n",
       "       104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128,\n",
       "       130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154,\n",
       "       156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 180,\n",
       "       182, 184, 186, 188, 190, 192, 194, 196, 198])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "a = np.array(np.arange(0,100))\n",
    "print(id(a))\n",
    "b = np.array(a)\n",
    "print(f'b = {id(b)}')\n",
    "a = a + b\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Remember slicing of an array \n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <img src='numpyArray.png' width ='400'>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.   2.5  5.   7.5 10. ]\n",
      "[0 5]\n"
     ]
    }
   ],
   "source": [
    "# arange vs linspace - both generate a numpy array of numbers\n",
    "import numpy as np\n",
    "a = np.linspace(0,10,5)   # specifies No. of values with 0 and 10 being first and last\n",
    "b = np.arange(0, 10, 5)   # specifies step size=5 starting at 0 up to but NOT including last\n",
    "print(a)\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.        ,  2.11111111,  3.22222222,  4.33333333,  5.44444444,\n",
       "        6.55555556,  7.66666667,  8.77777778,  9.88888889, 11.        ])"
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.linspace(0,10,10)  # generate 11 numbers \n",
    "x = x + 1                 # operates on all elements of the array\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'cost')"
      ]
     },
     "execution_count": 199,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generate points and use function to transform them\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x = np.arange(0,10,0.1)\n",
    "y = np.sin(x)\n",
    "plt.plot(x,y)\n",
    "plt.plot(x,-y)\n",
    "plt.plot(x, 2*y)\n",
    "plt.title('Sin Waves')\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('cost')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Subplots \n",
    "https://matplotlib.org/stable/gallery/subplots_axes_and_figures/subplots_demo.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f9f34ccaee0>]"
      ]
     },
     "execution_count": 200,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.array(np.arange(1,20,0.1))\n",
    "y = np.cos(x)\n",
    "fig, axs = plt.subplots(3)\n",
    "fig.suptitle('Vertically stacked subplots')\n",
    "axs[0].plot(x, y)\n",
    "axs[1].plot(x, -y)\n",
    "axs[2].plot(x, np.sin(2*x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src='figureax.png' width = '600'>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 8, 9, 5, 0, 0, 1, 7, 6, 9, 2, 4, 5, 2, 4, 2, 4, 7, 7, 9, 1, 7,\n",
       "       0, 6, 9, 9, 7, 6, 9, 1, 0, 1, 8, 8, 3, 9, 8, 7, 3, 6, 5, 1, 9, 3,\n",
       "       4, 8, 1, 4, 0, 3, 9, 2, 0, 4, 9, 2, 7, 7, 9, 8, 6, 9, 3, 7, 7, 4,\n",
       "       5, 9, 3, 6, 8, 0, 2, 7, 7, 9, 7, 3, 0, 8, 7, 7, 1, 1, 3, 0, 8, 6,\n",
       "       4, 5, 6, 2, 5, 7, 8, 4, 4, 7, 7, 4])"
      ]
     },
     "execution_count": 207,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "np.random.seed(1)\n",
    "a = np.random.choice([0,1,2,3,4,5,6,7,8,9],100)\n",
    "plt.hist(a,bins=10, density=True)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0.09, 0.08, 0.07, 0.08, 0.11, 0.07, 0.08, 0.18, 0.1 , 0.14]),\n",
       " array([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10.]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 208,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(a, bins = 10, range=(0,10) ,density=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0.18, 0.  , 0.16, 0.  , 0.14, 0.  , 0.16, 0.  , 0.22, 0.  , 0.14,\n",
       "        0.  , 0.16, 0.  , 0.36, 0.  , 0.2 , 0.  , 0.28]),\n",
       " array([0. , 0.5, 1. , 1.5, 2. , 2.5, 3. , 3.5, 4. , 4.5, 5. , 5.5, 6. ,\n",
       "        6.5, 7. , 7.5, 8. , 8.5, 9. , 9.5]),\n",
       " <BarContainer object of 19 artists>)"
      ]
     },
     "execution_count": 209,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#  Use Bins 1/2 wide - What does plot meean? \n",
    "plt.hist(a,bins=np.arange(0,10,0.5),density=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([8., 2., 4., 4., 5., 4., 4., 6., 7., 5., 7., 3., 7., 3., 5., 8., 7.,\n",
       "        4., 4., 3.]),\n",
       " array([0.19573401, 0.68179521, 1.16785641, 1.65391761, 2.1399788 ,\n",
       "        2.62604   , 3.1121012 , 3.5981624 , 4.0842236 , 4.57028479,\n",
       "        5.05634599, 5.54240719, 6.02846839, 6.51452959, 7.00059078,\n",
       "        7.48665198, 7.97271318, 8.45877438, 8.94483558, 9.43089677,\n",
       "        9.91695797]),\n",
       " <BarContainer object of 20 artists>)"
      ]
     },
     "execution_count": 216,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Data as sampling from an unseen population\n",
    "# Choose at random from 1 through 10 \n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "a = np.random.random(100)*10.0      # random.random produces numbers 0-1 \n",
    "plt.hist(a, bins=20)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.0\n"
     ]
    }
   ],
   "source": [
    "# what is the mean of the following \n",
    "a = np.array([9, 2, 9, 6, 4, 8, 7, 5, 3, 7])\n",
    "def mymean(ar):\n",
    "    n = len(ar)\n",
    "    total = 0\n",
    "    for x in ar:\n",
    "        total = total + x\n",
    "    return total/n\n",
    "print(mymean(a))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Normal Distribution \n",
    "\n",
    "$\n",
    "\\text{the normal distribution is given by} \\\\\n",
    "$\n",
    "$$\n",
    "f(x)=\\frac{1}{\\sqrt{2 \\pi}}e^{-x^2/2}  \n",
    "$$\n",
    "$\n",
    "\\text{This can be rewritten in term of the mean and variance} \\\\\n",
    "$\n",
    "$$\n",
    "f(x)=\\frac{1}{\\sigma \\sqrt{2 \\pi}}e^{-(x- \\mu)^2/2 \\sigma^2}\n",
    "$$\n",
    "The random variable $X$ described by the PDF is a normal variable that follows a normal distribution with mean $\\mu$ and variance $\\sigma^2$.\n",
    "\n",
    "$\n",
    "\\text{Normal distribution notation is} \\\\\n",
    "$\n",
    "$$\n",
    "X \\sim N(\\mu,\\sigma^2) \\\\\n",
    "$$\n",
    "\n",
    "The total area under the PDF curve equals 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mean and Variance\n",
    "\n",
    "$$\n",
    "\\mu = \\frac{\\sum(x)}{N}\n",
    "$$\n",
    "$$\n",
    "\\sigma^{2} =\\sum{\\frac{(x - \\mu)^{2}}{N} }\n",
    "$$\n",
    "<img src='normalDist.png' width = '400'>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'p' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                              Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-1-3d59fcc0fc5e>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      7\u001b[0m         \u001b[0mtotal\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      8\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mtotal\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mN\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 9\u001b[0;31m \u001b[0mpMean\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmyMean\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     10\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mf'mean= {pMean}'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     11\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'p' is not defined"
     ]
    }
   ],
   "source": [
    "# here calculate the mean and variance\n",
    "# then plot the theoretical curve by inputting the formula above\n",
    "def myMean(sample): \n",
    "    N = len(sample)                # calculate mean of data\n",
    "    total = 0\n",
    "    for x in sample:\n",
    "        total += x\n",
    "        return total/N\n",
    "pMean = myMean(p)\n",
    "print(f'mean= {pMean}')\n",
    "\n",
    "def myVar(sample,mean):            # calculate variance of data\n",
    "    N = len(sample)\n",
    "    tsample = sample - mean\n",
    "    var = np.sum(tsample * tsample)\n",
    "    return var/N\n",
    "\n",
    "pVar = myVar(p, pMean)\n",
    "print(f'variance= {pVar}')\n",
    "\n",
    "plt.hist(p, density=True)\n",
    "# Plot theoretical normal distribution \n",
    "x = np.linspace(-4,4,Npoints)\n",
    "y = np.exp(-(x*x)/(2*pVar))/(np.sqrt(2*np.pi*pVar))\n",
    "plt.plot(x,y)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean= 10.119616031068972\n",
      "variance= 4.063306476859725\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fa65b50bf10>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# EXERCISE  - use the above formula to plot the normal distribution over x = -4 to 4\n",
    "# take mean = 0, and sigma = 1\n",
    "# Compare data to the curve given by the formula\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "Npoints = 100\n",
    "np.random.seed(0)\n",
    "p = np.random.normal(10,2,Npoints)  # generate normal distribution with meaan of 0 and standard deviation of 1\n",
    "plt.hist(p, density=True)\n",
    "\n",
    "# here calculate the mean and variance\n",
    "# then plot the theoretical curve by inputting the formula above\n",
    "def myMean(sample):                # calculate mean of data\n",
    "    N = len(sample)\n",
    "    total = 0\n",
    "    for x in sample:\n",
    "        total = total + x\n",
    "    return total/N\n",
    "\n",
    "pMean = myMean(p)\n",
    "print(f'mean= {pMean}')\n",
    "\n",
    "def myVar(sample,mean):            # calculate variance of data\n",
    "    tsample = sample - mean\n",
    "    var = np.sum(tsample * tsample)\n",
    "    return var / len(sample)\n",
    "pVar = myVar(p, pMean)\n",
    "print(f'variance= {pVar}')\n",
    "\n",
    "# Plot theoretical normal distribution \n",
    "x = np.linspace(6,14,Npoints)\n",
    "tx = x - pMean\n",
    "y = np.exp(-(tx*tx)/(2*pVar))/(np.sqrt(2*np.pi*pVar))\n",
    "plt.plot(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 255,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean= 0.004019893634447017\n",
      "variance= 1.018938933760065\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f9f17471c70>]"
      ]
     },
     "execution_count": 255,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# here calculate the mean and variance\n",
    "# then plot the theoretical curve by inputting the formula above\n",
    "def myMean(sample):                # calculate mean of data\n",
    "    N = len(sample)\n",
    "    total = 0\n",
    "    for x in sample:\n",
    "        total = total + x\n",
    "    return x/N\n",
    "\n",
    "pMean = myMean(p)\n",
    "print(f'mean= {pMean}')\n",
    "\n",
    "def myVar(sample,mean):            # calculate variance of data\n",
    "    tsample = sample - mean\n",
    "    var = np.sum(tsample * tsample)\n",
    "    return var / len(sample)\n",
    "pVar = myVar(p, pMean)\n",
    "print(f'variance= {pVar}')\n",
    "\n",
    "\n",
    "\n",
    "# Plot theoretical normal distribution \n",
    "x = np.linspace(-4,4,Npoints)\n",
    "y = np.exp(-(x*x)/(2*pVar))/(np.sqrt(2*np.pi*pVar))\n",
    "plt.plot(x,y)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Something to think about - What is the area under the curve between say -4 to 4\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0.04166667, 0.08333333, 0.10416667, 0.13541667, 0.20833333,\n",
       "        0.1875    , 0.15625   , 0.07291667, 0.        , 0.01041667]),\n",
       " array([ 5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Normal Data \n",
    "\n",
    "a = np.random.normal(10,2,100)\n",
    "plt.hist(a,bins=np.arange(5,16,1),density=True)\n",
    "#plt.scatter(np.arange(0,10),a)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0.02083333, 0.0625    , 0.04166667, 0.125     , 0.08333333,\n",
       "        0.125     , 0.14583333, 0.125     , 0.1875    , 0.22916667,\n",
       "        0.16666667, 0.20833333, 0.14583333, 0.16666667, 0.08333333,\n",
       "        0.0625    , 0.        , 0.        , 0.        , 0.02083333,\n",
       "        0.        ]),\n",
       " array([ 5. ,  5.5,  6. ,  6.5,  7. ,  7.5,  8. ,  8.5,  9. ,  9.5, 10. ,\n",
       "        10.5, 11. , 11.5, 12. , 12.5, 13. , 13.5, 14. , 14.5, 15. , 15.5]),\n",
       " <BarContainer object of 21 artists>)"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(a,bins=np.arange(5,16,0.5), density=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 4.,  8., 10., 13., 20., 18., 15.,  7.,  0.,  1.]),\n",
       " array([ 5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(a,bins=np.arange(5,16,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0.0625836 , 0.0730142 , 0.0834448 , 0.21904261, 0.13559781,\n",
       "        0.19818141, 0.14602841, 0.0834448 , 0.0312918 , 0.0104306 ]),\n",
       " array([-4.46785731, -3.50913974, -2.55042217, -1.59170461, -0.63298704,\n",
       "         0.32573053,  1.28444809,  2.24316566,  3.20188323,  4.1606008 ,\n",
       "         5.11931836]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "a = np.random.normal(0,2,100)  # normal takes mean and SD as args\n",
    "plt.hist(a, density = True)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mean and Variance\n",
    "\n",
    "$$\n",
    "\\mu = \\frac{\\sum(x)}{N}\n",
    "$$\n",
    "$$\n",
    "\\sigma^{2} =\\sum{\\frac{(x - \\mu)^{2}}{N} }\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "COMPLETE THIS\n",
      "mean= None\n",
      "Variance = False\n"
     ]
    }
   ],
   "source": [
    "# IN CLASS - Generate a Population and calculate its mean and variance\n",
    "import matplotlib.pyplot as plt\n",
    "Npoints = 10\n",
    "p = np.random.normal(0,10,Npoints)\n",
    "\n",
    "def myMean(sample):\n",
    "    print('COMPLETE THIS')\n",
    "pmean = myMean(p)\n",
    "print(f'mean= {pmean}')\n",
    "\n",
    "def myVar(sample,mean):\n",
    "    print('COMPLETE THIS')\n",
    "    \n",
    "print(f'Variance = {False}')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Problem of Variance in Sample vs Population\n",
    "\n",
    "population = np.array([5, 4, 4, 9, 9, 8, 2, 0, 3, 6])\n",
    "sample = np.array([5, 4, 4, 8, 6])\n",
    "\n",
    "def variance(sample, mean, bias):\n",
    "    N = len(sample)\n",
    "    s2 = 0\n",
    "    for i in range(0,N):\n",
    "        x = sample[i]-mean\n",
    "        s2 = s2 + (x * x) \n",
    "    var = s2/(N - bias)\n",
    "    return var\n",
    "\n",
    "N = 10\n",
    "\n",
    "var_pop = []\n",
    "var_sample = []\n",
    "\n",
    "for mean in range(0,N):   # shift the mean from 0 to N\n",
    "    var_pop.append( variance(population, mean, 0))\n",
    "\n",
    "for mean in range(0,N):   # shift the mean from 0 to N\n",
    "    var_sample.append( variance(sample, mean, 1))\n",
    "# Plotting\n",
    "plt.scatter(range(N),var_pop,color='b', label='Population')\n",
    "\n",
    "plt.scatter(range(N),var_sample,color='r', label='Sample')\n",
    "plt.ylim([0, 50])\n",
    "plt.ylabel('Variance')\n",
    "plt.xlabel('Mean')\n",
    "plt.legend(loc='upper right')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# How would you check that your functions are working ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Use this plotting to draw a normal distribution\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x= np.arange(34,40,0.01)\n",
    "y = np.random.normal(x)\n",
    "\n",
    "# Plot it\n",
    "plt.style.use('ggplot')\n",
    "fig, ax = plt.subplots()\n",
    "lines = ax.plot(x, norm.pdf(x,loc=37,scale=1))\n",
    "ax.set_ylim(0,0.45) # range\n",
    "ax.set_xlabel('x',fontsize=20) # set x label\n",
    "ax.set_ylabel('pdf(x)',fontsize=20,rotation=90) # set y label\n",
    "ax.xaxis.set_label_coords(0.55, -0.05) # x label coordinate\n",
    "ax.yaxis.set_label_coords(-0.1, 0.5) # y label coordinate\n",
    "px=np.arange(36,37,0.1)\n",
    "plt.fill_between(px,norm.pdf(px,loc=37,scale=1),color='r',alpha=0.5)\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Numpy 2D Arrays\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Multi-Dimensional Arrays\n",
    "<img src='multiArray.png' width = 500>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2],\n",
       "       [3, 4, 5]])"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "a = np.arange(0,9)\n",
    "z = a.reshape(3,3)\n",
    "y = z[0:2,0:2]\n",
    "q = z[0:2][0:2]   # This is legal but DO NOT USE IT  - can you tell me why\n",
    "q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create Numpy 2_D Arrays - Remember [1,2,3] is different to np.array([1,2,3])\n",
    "a = np.array([0,1,2])\n",
    "b = np.array([3,4,5])\n",
    "c = np.array([6,7,8])\n",
    "z = np.array([a, \n",
    "     b, \n",
    "     c])\n",
    "type(z)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2],\n",
       "       [3, 4, 5],\n",
       "       [6, 7, 8]])"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(0,9)\n",
    "z = a.reshape(3,3)\n",
    "z\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z[2,2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 2],\n",
       "       [6, 8]])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z[0:3:2,0:3:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Exercise - Produce a 8x8 checkerboard of 1s and 0s\n",
    "### Code it so you could also produce a 20x20 checkerboard later\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1, 1, 1], [2, 2, 2], [3, 3, 3]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import seaborn as sns\n",
    "from matplotlib.colors import ListedColormap as lc\n",
    "Z = [[1,1,1],[2,2,2],[3,3,3]]\n",
    "print(Z)\n",
    "sns.heatmap(Z, annot=True,linewidths=5,cbar=False)\n",
    "import seaborn as sns\n",
    "sns.heatmap(Z, annot=True,linewidths=5,cbar=False)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Your solution should look like this\n",
    "<img src='checker8.png' width ='400'>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Fancy Plotting\n",
    "from matplotlib import collections as matcoll\n",
    "Npoints = 20\n",
    "x = np.arange(0,Npoints)\n",
    "y = np.random.normal(loc=10, scale=2, size=Npoints )\n",
    "lines = []\n",
    "for i in range(Npoints):\n",
    "    pair=[(x[i],0), (x[i], y[i])]\n",
    "    lines.append(pair)\n",
    "linecoll = matcoll.LineCollection(lines)\n",
    "fig, ax = plt.subplots()\n",
    "ax.add_collection(linecoll)\n",
    "\n",
    "plt.scatter(x,y, marker='o', color='blue')\n",
    "plt.xticks(x)\n",
    "plt.ylim(0,40)\n",
    "plt.show()\n",
    "ylim=(0,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# More Fancy plotting using other libraries\n",
    "\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111,projection='3d')\n",
    "for c, z in zip(['r', 'g', 'b', 'y'], [30, 20, 10, 0]):\n",
    "    xs = np.arange(20)\n",
    "    ys = np.random.rand(20)\n",
    "\n",
    "    # You can provide either a single color or an array. To demonstrate this,\n",
    "    # the first bar of each set will be colored cyan.\n",
    "    cs = [c] * len(xs)\n",
    "    cs[0] = 'c'\n",
    "    ax.bar(xs, ys, zs=z, zdir='y', color=cs, alpha=0.8)\n",
    "\n",
    "ax.set_xlabel('X')\n",
    "ax.set_ylabel('Y')\n",
    "ax.set_zlabel('Z')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}