NumpyIntro.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "import numpy as np "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numpy library"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 9.,  8., 13.,  9., 12.,  5., 12., 11., 13., 15.]),\n",
       " array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 2,
     "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": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "a = np.random.choice(np.arange(0,100),1000)\n",
    "plt.hist(a,bins=np.arange(0,11,1))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0.08411215, 0.07476636, 0.12149533, 0.08411215, 0.11214953,\n",
       "        0.04672897, 0.11214953, 0.10280374, 0.12149533, 0.14018692]),\n",
       " array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 3,
     "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": [
    "plt.hist(a,bins=np.arange(0,11,1),density=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0.1682243 , 0.        , 0.14953271, 0.        , 0.24299065,\n",
       "        0.        , 0.1682243 , 0.        , 0.22429907, 0.        ,\n",
       "        0.09345794, 0.        , 0.22429907, 0.        , 0.20560748,\n",
       "        0.        , 0.24299065, 0.        , 0.11214953, 0.        ,\n",
       "        0.1682243 ]),\n",
       " array([ 0. ,  0.5,  1. ,  1.5,  2. ,  2.5,  3. ,  3.5,  4. ,  4.5,  5. ,\n",
       "         5.5,  6. ,  6.5,  7. ,  7.5,  8. ,  8.5,  9. ,  9.5, 10. , 10.5]),\n",
       " <BarContainer object of 21 artists>)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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VfQv4FPBzY55plP4jyQ8BdN+fGPM8zYS+z2UaLnjdpZ9vAx6uqj8Z9zyjUlXvrKq1VbWeuX+Xd1dVc48Aq+orwIkkL+9WXc3cp8hb8xjw6iTP736Gr6bBF50HDF4SZifwt2OcBVgmV69cque6TMOYxxqFK4G3AJ9P8lC37g+r6tD4RtIS/Rbwke4BynHg18Y8z9BV1X1JDgIPMPfOsQdZZpcIOFdJPgb8IrA6ySxwE3AzcHuSG4AvA78yvgnneAkESWpcK0/dSJKeg6GXpMYZeklqnKGXpMYZeklqnKGXpMYZeklq3P8BJKoQdY9mb8sAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#  Use Bins 1/2 wide - What does plot meean? \n",
    "plt.hist(a,bins=np.arange(0,11,0.5),density=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fa944459550>]"
      ]
     },
     "execution_count": 6,
     "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": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "a = np.arange(0,10,0.1)\n",
    "y = np.sin(a)\n",
    "plt.plot(a,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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",
    "a = np.random.choice(np.arange(0,10),100)\n",
    "a = np.random.random(100)*10.0\n",
    "a\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0. , 0. , 0.1, 0.2, 0.2, 0.3, 0.1, 0.1, 0. , 0. ]),\n",
       " array([ 5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 7,
     "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": [
    "# Normal Data \n",
    "\n",
    "a = np.random.normal(10,2,10)\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": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.hist(a,bins=np.arange(5,16,0.1), density=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.hist(a,bins=np.arange(5,16,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "a = np.random.normal(0,1,20)\n",
    "plt.hist(b, bins=np.arange(0,20,1), density = True)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise - Produce a 10x10 checkerboard of 1s and 0s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "from matplotlib.colors import ListedColormap as lc\n",
    "Z = np.zeros((8,8),dtype=int)\n",
    "Z[1::2,::2] = 1\n",
    "Z[::2,1::2] = 1\n",
    "print(Z)\n",
    "sns.heatmap(Z, annot=True,linewidths=5,cbar=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns\n",
    "sns.heatmap(Z, annot=True,linewidths=5,cbar=False)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as scipy\n",
    "from scipy.stats import norm\n",
    "\n",
    "plt.style.use('ggplot')\n",
    "fig, ax = plt.subplots()\n",
    "x= np.arange(34,40,0.01)\n",
    "y = np.random.normal(x)\n",
    "lines = ax.plot(x, norm.pdf(x,loc=37,scale=1))\n",
    "ax.set_ylim(0,0.45) # range\n",
    "\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": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.random.normal(10,1,20)\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculate the mean and subtract the mean from each data value\n",
    "$$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "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)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Numpy 2D Arrays\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Numpy 2_D Arrays\n",
    "a = [0,1,2]\n",
    "b = [3,4,5]\n",
    "c = [6,7,8]\n",
    "z = [a, \n",
    "     b, \n",
    "     c]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.arange(0,9)\n",
    "z = a.reshape(3,3)\n",
    "z\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "z[2,2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "z[0:3:2,0:3:2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Numpy Arrays "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Slices point back to the original array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "a = np.ones(10)\n",
    "a[:] = 2\n",
    "b = a[0:2]   # View of a NOT a copy\n",
    "b[:] = 3\n",
    "b = a.copy()\n",
    "b[:] = 6\n",
    "print(id(a), id(b))\n",
    "\n",
    "mybool = a < 3\n",
    "c = a[a < 3]     # Conditionals \n",
    "c\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### generate log normal dist and sample "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "mu, sigma = 3., 1. # mean and standard deviation\n",
    "s = np.random.lognormal(mu, sigma, 1000)\n",
    "plt.hist(s,bins=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "means = []\n",
    "N = 100\n",
    "a = [5,20,50]\n",
    "fig, axs = plt.subplots(3)\n",
    "fig.suptitle('Sampling of a Log-Normal Distribution')\n",
    "fig.tight_layout()\n",
    "for k,N in enumerate(a):\n",
    "    for i in np.arange(1000):\n",
    "        means.append(np.random.choice(s,N).sum()/N)\n",
    "    axs[k].hist(means,bins=20)\n",
    "   \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mu, sigma = 50., 1. # mean and standard deviation\n",
    "s = np.random.normal(mu, sigma, 1000)\n",
    "s = np.sort(s)\n",
    "means = []\n",
    "plt.plot(range(0,1000), (s - mu)/np.sqrt(sigma),'.')\n",
    "plt.title('Z-Score')\n",
    "N = 100\n",
    "a = [5,20,50]\n",
    "fig, axs = plt.subplots(3)\n",
    "fig.suptitle('Sampling of a Normal Distribution')\n",
    "fig.tight_layout()\n",
    "for k,N in enumerate(a):\n",
    "    for i in np.arange(1000):\n",
    "        means.append(np.random.choice(s,N).sum()/N)\n",
    "    axs[k].hist(var,bins=20)\n",
    "   \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\sigma_{mean}^{2} =  \\frac{\\sigma_{pop}^{2}} {N}$$\n",
    "where N is sample size\n",
    "$$\\sigma_{mean} =  \\frac{\\sigma_{pop}} {\\sqrt{N}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.stats as stats\n",
    "\n",
    "s = np.random.randint(1,1000,1000)\n",
    "\n",
    "sampArr = np.arange(2,3,1)\n",
    "skip = 2\n",
    "fig, axes = plt.subplots(nrows=np.int((1+len(sampArr))/skip), ncols=skip)\n",
    "fig.suptitle('Sampling Mean of a Uniform Distribution')\n",
    "fig.set_size_inches(10, 10)\n",
    "fig.tight_layout()\n",
    "Nloop = 1000\n",
    "\n",
    "for k,S in enumerate(sampArr):   # choose number S in a sample\n",
    "    means = []    # fill this with Nloop samples\n",
    "    for i in np.arange(Nloop):\n",
    "        mean = np.random.choice(s,S).mean()\n",
    "        means.append(mean)\n",
    "    df = pd.DataFrame(means)\n",
    "    right = k%skip\n",
    "    row = np.int(k/skip)\n",
    "    \n",
    "    df.plot(ax=axes[row,right], kind = \"kde\")\n",
    "    axes[row,right].set_title(f'sample= {S}')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "y = np.array([1,2,4,4,4,2,5,5,1])\n",
    "df = pd.DataFrame(y)\n",
    "df.plot()\n",
    "df.plot(kind = \"kde\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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