{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plotting Graphs with Matplotlib"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This work is licensed under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/)\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction: Matplotlib and Pyplot\n",
    "\n",
    "Numerical data is often presented with graphs, and the tools we use for this come from the module `matplotlib.pyplot` which is part of the Python *package* `matplotlib`. (A Python *package* is essentially a module that also contains other modules.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sources on Matplotlib\n",
    "\n",
    "Matplotlib is a huge collection of graphics tools, of which we see just a few here. For more information, the home site for Matplotlib is http://matplotlib.org\n",
    "and the section on pyplot is at http://matplotlib.org/1.3.1/api/pyplot_api.html\n",
    "\n",
    "However, another site that I find easier as an introduction is https://scipy-lectures.org/intro/matplotlib/\n",
    "\n",
    "In fact, that whole site https://scipy-lectures.org/ is quite useful a a reference on Python, Numpy, and so on."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note:** the descriptions here are for now about working in notebooks:\n",
    "see the note below on\n",
    "{ref}`differences when using Spyder and IPython<with-Spyder-IPython>`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Choosing where the graphs appear\n",
    "\n",
    "In a notebook, we can choose between having the figures produced by Matplotlib appear \"inline\" (that is, within the notebook window) or in separate windows.\n",
    "For now we will use the inline option, which is the default, but can also be specified explicitly with the command\n",
    "\n",
    "    %matplotlib inline\n",
    "\n",
    "To activate that, uncomment the line below;\n",
    "that is, remove the leading hash character \"#\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is an IPython *magic command*, indicated by starting with the percent character \"%\" — you can read more about them at\n",
    "https://ipython.org/ipython-doc/dev/interactive/magics.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively, one can have figures appear in separate windows, which might be useful when you want to save them to files, or zoom and pan around the image.\n",
    "That can be chosen with the magic command\n",
    "\n",
    "    %matplotlib tk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#%matplotlib tk"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As far as I know, this magic works for Windows and Linux as well as Mac OS; let me know if it does not!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need some Numpy stuff, for example to create arrays of numbers to plot.\n",
    "\n",
    "Note that this is Numpy only: Python lists and tuples do not work for this, and nor do the versions of functions like `sin` from module `math`!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import a few favorites, and let them be known by their first names:\n",
    "from numpy import linspace, sin, cos, pi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And for now, just the one main `matplotlib` graphics function, `plot`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib.pyplot import plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To access all of pyplot, add its common nickname `plt`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Producing arrays of \"x\" values with the numpy function  `linspace`\n",
    "\n",
    "To plot the graph of a function, we first need a collection of values for the abscissa (horizontal axis).\n",
    "The function <code>linspace</code> gives an array containing a specified number of equally spaced values over a specified interval, so that"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "tenvalues = linspace(1., 7., 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "gives ten equally spaced values ranging from 1 to 7:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Array 'tenvalues' is:\n",
      "[1.         1.66666667 2.33333333 3.         3.66666667 4.33333333\n",
      " 5.         5.66666667 6.33333333 7.        ]\n"
     ]
    }
   ],
   "source": [
    "print(f\"Array 'tenvalues' is:\\n{tenvalues}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not quite what you expected?  To get values with ten *intervals* in between them, you need 11 values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Array 'tenintervals' is: \n",
      " [1.  1.6 2.2 2.8 3.4 4.  4.6 5.2 5.8 6.4 7. ]\n"
     ]
    }
   ],
   "source": [
    "tenintervals = linspace(1., 7., 11)\n",
    "print(f\"Array 'tenintervals' is: \\n {tenintervals}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basic graphs with `plot`\n",
    "\n",
    "We could use these 11 values to graph a function, but the result is a bit rough, because the given points are joined with straight line segments:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fa69a063d30>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(tenintervals, sin(tenintervals))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we see the default behavior of joining the given points with straight lines."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Aside:* That text output above the graph is a message returned as the output value of function `plot`; that is what happens when you execute a function but do not \"use\" its return value by either saving its result into a variable or making it input to another function.\n",
    "\n",
    "You might want to suppress that, and that can be done by saving its `return` value into a variable (which you can then ignore)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotmessage = plot(tenintervals, sin(tenintervals))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(More on this output clean-up below.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For discrete data it might be better to mark each point, unconnected.\n",
    "This is done by adding a third argument, a text string specifying a marker, such as a star:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotmessage = plot(tenvalues, sin(tenvalues), '*')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or maybe both lines and markers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotmessage = plot(tenvalues, sin(tenvalues), '-*')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Smoother graphs\n",
    "\n",
    "It turns out that 50 points is often a good choice for a smooth-looking curve, so the function <code>linspace</code> has this as a *default input parameter*: you can omit that third input value, and get 50 points.\n",
    "\n",
    "Let's use this to plot some trig. functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = linspace(-pi, pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-3.14159265 -3.01336438 -2.88513611 -2.75690784 -2.62867957 -2.5004513\n",
      " -2.37222302 -2.24399475 -2.11576648 -1.98753821 -1.85930994 -1.73108167\n",
      " -1.60285339 -1.47462512 -1.34639685 -1.21816858 -1.08994031 -0.96171204\n",
      " -0.83348377 -0.70525549 -0.57702722 -0.44879895 -0.32057068 -0.19234241\n",
      " -0.06411414  0.06411414  0.19234241  0.32057068  0.44879895  0.57702722\n",
      "  0.70525549  0.83348377  0.96171204  1.08994031  1.21816858  1.34639685\n",
      "  1.47462512  1.60285339  1.73108167  1.85930994  1.98753821  2.11576648\n",
      "  2.24399475  2.37222302  2.5004513   2.62867957  2.75690784  2.88513611\n",
      "  3.01336438  3.14159265]\n"
     ]
    }
   ],
   "source": [
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# With a line through the points\n",
    "plotmessage = plot(x, sin(x), '-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multiple curves on a single figure\n",
    "As we have seen when using `plot` to produce inline figures in a Jupyter notebook, `plot` commands in different cells produce separate figures.\n",
    "\n",
    "To combine curves on a single graph, one way is to use successive `plot` commands within the same cell:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(x, cos(x), '*')\n",
    "plotmessage = plot(x, sin(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On the other hand, when plotting externally, or from a Python script file or the IPython command line, successive `plot` commands keep adding to the same figure until you explicitly specify otherwise, with the function `figure` introduced below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Aside on message clean up: a Juypter cell only displays the output of the last function invoked in the cell (along with anything explicitly output with a `print` function), so I only needed to intercept the message from the last `plot` command.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Two curves with a single `plot` command\n",
    "\n",
    "Several curves can be specified in a single `plot` command (which also works with external figure windows of course.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EVrsYWCAic4EXgR7qhNw21piMv1lZgyisGOfmIG5/Z8KTANj/KCo1GsEpf4VvB7lqsCkkLiOLA6d7RhZZ1j/o+svAy+Fua9KblTWI0IH9MPo+OLQRtLouKbu0/1GU2t8Bc96HcQ9Azw+9jiZsVmvIeMLmz43At+9B/mJXYrps+aTt1v5HUah8GJx2GywbBauneR1N2KzEhDF+tncnvNgcahwFV49yNfGNv+3dCS+1hGpHwrVjffU/szLUxqSi6f1hxyY3aMlHXyimBNmVoOM9sG4mLB7hdTRhsURgjF/t2gpfPQ/HdIb6bbyOxkSieU/IOR7GPZgScxZYIjDGr756AXZvd4XlTGopk+WO4rZ8B7Pe8TqaUlkiMMaPfvkBvukPJ14CtZp6HY2JxjGdoMFpMOlJ35eesERgjB9NegoK9kHHu72OxERLxPX0+jUfpoXsPe8blghMQlmtmihsWQmzB0LLv7jeQj5k/9cw1W0JTbrC16/Arz95HU2xLBGYhLJaNVGY8BiUKecGJ/mU/V8j0OEe2LsDpr3gdSTFsnEEJiGsVk2UfpgP/U+H0/4GZ9/vdTQHsf9rlD65HhYNh1vnQJVanoVh4whMUlmtmiiNf9hNPdnuFq8jCcn+r1HqcBcc2AtTnvM6kpAsEZiEsFo1UVj9NSwf7Y4GKh7qdTQh2f81SjWOgpP/7MqIb1tb+vpJZonAJIzVqomAKox/CA6pBa2u9zqaEtn/NUpn3On+Tn7K2zhCsDYCY/zguy/hve5w3jNJqzBqPDDqLpjxBvSdCYcdnfTdWxuBMX6l6noKVa0LLa70OhqTSKf9HbKy3SAzH7FEYIzXVox3Bcra357UMtPGA1WOgNa9Yd4QN/WoT8QlEYhIZxFZKiIrRKRfiPt7ici8wGWaiDQLum+ViMwXkTkiYud7TGZRhQmPQrX60LyX19GYZGh3G2Qf4o4CfSLmRCAiWcArQBegCXC5iDQpstr3wBmqehLwMDCgyP0dVbV5qHNXxqS1ZaNhw2w44w4om+11NCYZKtWAtje5EtUb5ngdDRCfI4JWwApVXamqe4EPga7BK6jqNFXdGrj5DVA3Dvs1JrWpwsTH4NCG0Oxyr6MxydT2RqhQ3R0N+kA8EsGRQHDH2HWBZcW5FhgVdFuBMSIyS0R6F7eRiPQWkTwRycvPz48pYBN/VnsmCktHwsa5bkL6rHJeRxM39l4IQ4Vq0O5WWD4G1s3yOpq4JIJQ0yaF7JMqIh1xieCuoMXtVLUF7tTSTSLSPtS2qjpAVXNVNTcnJyfWmE2cWe2ZCBUUwITH3UCjky7zOpq4svdCmFpdBxVrwKQnvI6EsnF4jHVAvaDbdYENRVcSkZOA/wBdVPW3MnyquiHwd7OIDMOdapoch7hMEhStPTNo+hoGTV9jtWdKs+R/sGk+dB8AWfH4GHrP3gsRKl8FTr0Zxj/ojgrqtvQslHgcEcwEGotIIxHJBnoAv5uoU0TqA58AV6jqsqDllUWkSuF14FxgQRxiMklitWeiUFAAE5+AwxrDiRd7HU3c2HshCq2uc+VEPD4qiDkRqOp+oC8wGlgMDFHVhSLSR0T6BFb7F3AY8GqRbqJHAFNFZC4wA/hcVb+INSaTPFZ7JgqLPoXNi6BDPzelYZqw90IUCo8Klo+B9d61FcTlmFRVRwIjiyzrH3T9r8BfQ2y3EmhWdLlJLYW1Z3q2qs/gGWvIt0bC4hUccEcDOcfBCd29jibu7L0QhVa9YdpLMPFJ6DXEkxCs1pAxyTT/Yxh6LVz8NjT9o9fRGL+Y8qwrOnjdl3Bk4toKrNaQMV4rKIDJT7ujgSbdvI7G+Emr3q6tYKI3NYgsERiTLIuHQ/4SNwVlGfvomSC/tRWM9qStwN6NxiRDQQFMegpqHpOWbQMmDjw8KrBEYEwyLPnM9RRqf0da9RQycVS+CrTt68lRgSUCYxKt8GigxtFwgjUQmxJ4dFRgicCYRFs2yo0ibn9H2owiNglSoWrQUcHspO3WEoGJiBUUi5CqGzdwaCM48RKvo/GUvXfC1Kq3K0o3+Zmk7dISgYmIFRSL0LLR8MM8N/tYhh8N2HsnTBWqQpubYOnnsHFeUnZpA8pMWIoWFCtkBcVKoApvdISdW+DmWWlVajoS9t6Jwq5t8PyJcFQHuOy9uD2sDSgzMbGCYlFYMQ42fAun/yNjkwDYeycqFatD6+vdLGabFiV8d5YITFisoFiECtsGqtXP+NnH7L0TpTY3urmNpyS+rcASgQlbYUGxYTe2o1frBuTv2ON1SP713ZewPg9O/5vNRYy9d6JSqYYrU73gE8hfVvr6MbA2AmPiTRXe6gw/r4NbZkPZ8l5HZFLVrz+6toLjL4Q/Doj54ayNwJhkWTUF1n4Dp91mScDEpnJNyL0G5n8EP32XsN1YIjAm3iY9BYfUgpOv8DoSkw5OvQWysmHKcwnbRVwSgYh0FpGlIrJCRPqFuF9E5MXA/fNEpEW42xqTUlZPc0cE7W6FctYYauKgyhHQ8mqY+wFsXZWQXcScCEQkC3gF6AI0AS4XkSZFVusCNA5cegOvRbCtMalj0lNQOQda/sXrSEw6aXcrlCmbsKOCeBwRtAJWqOpKVd0LfAh0LbJOV+Bddb4BqotI7TC3jZ9Z78DQg2bMNCY+1s6ElRNcXfnsSl5HY9JJ1drQ4gqYMxi2rY37w8cjERwJBEe2LrAsnHXC2RYAEektInkikpefnx9dpHt+cY0ua6ZHt30GsbowUZj8FFSsAbnXeh1JSrH3Wpja3QbV68G21XF/6HgkAgmxrGif1OLWCWdbt1B1gKrmqmpuTk5OhCEG5F4DlQ5zH1hTIqsLE6H1s2H5GGh7E5Q/xOtoUoq918JUvR70nQUNT4v7Q8ejCtY6oF7Q7brAhjDXyQ5j2/jJruxKvI5/0E38kMBJolNV0bowg6avYdD0NVYXpjSTn3EVI1v19jqSlGHvtSgkaIrTeDzqTKCxiDQSkWygBzCiyDojgCsDvYfaAD+r6sYwt42vVte5iR8mPZ3Q3aQqqwsThR/mu0qRbW50lSNNWOy95h8xJwJV3Q/0BUYDi4EhqrpQRPqISJ/AaiOBlcAK4A3gxpK2jTWmEpWv4kq8LhsFG+cmdFepyOrCRGHy01C+qisSZsJm7zX/iEuBdFUdifuyD17WP+i6AjeFu23Cte4N015yXf16vJ/UXaeCwrowPVvVZ/CMNeRbI17xNi+GRcPh9NvdkaaJiL3X/CFzaw1NeAwmPQk3TIMjTohPYCbzfHwNLP0CbpsPlQ/zOhpjSmS1hopq3Qeyq7jDemOikb/MVYZsdZ0lAZPSMjcRVKrhThEt/BQ2L/E6GpOKJj8N5Sq6AWTGpLDMTQTgGo3LVUrKxA8mzfy4AhZ8DKdc6ypEGpPCMjsRVD7MfZAXDHUfbGPCNeUZyCrvKkMak+IyOxGAO6zPKg9TnvU6EpMqfvoO5g1xI9UPOdzraIyJmSWCQw53H+h5/4UtK72OxqSCKc+5yejb3ep1JMbEhSUCgHa3uA/25Mw6KrBiX1HYusrVhW95tasTbxLG3p/JY4kAoEqt/5/4IYOOCqzYVxSmPOvqwtvRQMLZ+zN5MndAWVG//AAvNIOmF0O3V+L72D5TtNhXISv2VYpta+DFk92pxPNs/Emi2PszcWxAWWky6KjAin1FacpzIGVcXXiTMPb+TD5LBMFOuy0j2gqs2FcUfl4H3w5yE9JXCzl3kokTe38mnyWCYBl0VFBY7GvYje3o1boB+Tv2eB2Sv039t/t72t+8jSND2PszuayNoKjCtoITL4au6d1WYMK0bS281AKa94QLX/A6GmOiZm0E4So8KpjzAWz53utojB9MeRZUXalpY9KQJYJQ2t3qughaDSKzdTV8+x60vMrNGWtMGoopEYhIDREZKyLLA38PmplDROqJyAQRWSwiC0Xk1qD7HhCR9SIyJ3A5L5Z44qZqbci1owKD+zEgWXDa372OxJiEifWIoB8wXlUbA+MDt4vaD/xDVY8H2gA3iUiToPv/rarNA5fkzlRWkna32VFBptuyEr593/0osJ5CJo3Fmgi6AgMD1wcC3YquoKobVXV24PovuLmJ/f+p+t1RQXr3IDLFmPyM605sPYVMmos1ERyhqhvBfeEDJZZiFJGGwMnA9KDFfUVknoi8FerUUtC2vUUkT0Ty8vPzYww7TO1uc18Ek1J7FKnVbInCT9+5bsS517oOBMY37P0cf6UmAhEZJyILQly6RrIjETkEGArcpqrbA4tfA44GmgMbgWJHcqnqAFXNVdXcnJycSHYdvaq14ZS/wrwP3bSEKcpqtkRh0lOuPPlpt3kdiSnC3s/xF9M4AhFZCnRQ1Y0iUhuYqKrHhlivHPAZMFpVnyvmsRoCn6lq09L2m9BxBEX9+iM8fxIc0wkueTs5+4wTq9kSpfxl8GpraNsXzn3Y62hMgL2fY5eocQQjgKsC168ChofYsQBvAouLJoFA8ijUHVgQYzzxV7kmtLkBFn4CP8z3OpqIWM2WKE16EspWtAqjPmPv58SJNRE8AZwjIsuBcwK3EZE6IlLYA6gdcAVwZohuok+JyHwRmQd0BPzZKndqXyhfDSY85nUkEbGaLVHYvNhNXdq6t81F7DP2fk6csrFsrKo/AWeFWL4BOC9wfSogxWx/RSz7T5qKh0K7m+HLR2DdLKjb0uuIwlZYs6Vnq/oMnrGGfGtgK9mkJyG7ss1F7FP2fk4MqzUUrj2/uBpEtZvBFcOSu2+THBvnwuvtof0dcOZ9XkdjTNxZraFYla/i+pN/9yWs+srraEwijH/YHf2derPXkRiTVJYIInHKX+GQWu4UUQoeSZkSrPoKVox1yb5CNa+jMSapLBFEolxFaH87rJnmjgxMelCF8Q9CldrQqrfX0RiTdJYIItXiKqhW344K0smyL2DtdDjjLpfsjckwlggiVTYbOtwFG2bDUv/UyDNRKjgA4x+CGkfByX/2OhpjPGGJIBon9YDD/uC+QA7s9zqa31gNlijM/xg2L3K9hLLKeR2NiZF9BqJjiSAaWWXhrPshfwnMHex1NL+xGiwR2r8XJjwKtU6EJt29jsbEgX0GomPjCKKlCm+eCz+vhZtnQ3Ylz0KxGixRmvEGjLwdeg2Fxmd7HY2JgX0GwmPjCOJNBM55CH7ZCN+86mkoVoMlCnt/dRVGG7SDPxw0ON6kGPsMxMYSQSwatIVjz4epz7sqpR6xGixRmN4fft3sTvFJyAooJoXYZyA2lghidfb9sO9XmOzt5DWFNViG3diOXq0bkL9jj6fx+NrOLTD1BTimC9Rv7XU0Jk7sMxA9ayOIhxG3wJzB0Hcm1GjkdTSmNKP6wYzXoc9UOOIEr6MxJmmsjSCROtztJrr/0iYx8b0fV8DMN6DFlZYEjAmwRBAPVWtD25tcHfv1s7yOxpRk7L+gbAXoeK/XkRjjGzElAhGpISJjRWR54G/IyedFZFVgApo5IpIX6fYpod2tUOkwGHu/lZ7wq+8nw9LP4fS/wyGHex2NMb4R6xFBP2C8qjYGxgduF6ejqjYvcn4qku39rUJVV6tm1RRYMc7raExRBQdg9D1QrR60udHraIzxlVgTQVdgYOD6QKBbkrf3l5ZXw6GNYMx9CS09YcPoozD3Azfn9NkPWGG5DGSfmZLFmgiOUNWNAIG/xR1vKzBGRGaJSHCd33C3R0R6i0ieiOTl5+fHGHaClM2Gcx9xpSfy3kzYbmwYfYT27HCTzhyZC03/5HU0xgP2mSlZqd1HRWQcUCvEXfcCA1W1etC6W1X1oPP8IlJHVTeIyOHAWOBmVZ0sItvC2b4o33UfDaYK73WDDd+60hNxnADdhtFHacJjbi7ia8bYuIEMY5+Z34u6+6iqnq2qTUNchgObRKR2YAe1gc3FPMaGwN/NwDCgVeCusLZPKSLQ+Un3KzTO3UltGH0Ufl4PX70IJ3S3JJCB7DMTnlhPDY0ArgpcvwoYXnQFEaksIlUKrwPnAgvC3T4lHX4ctL4eZg2EDXPi97A2jD5yXz4MWgBnP+h1JMYD9pkJT6yJ4AngHBFZDpwTuI2I1BGRwllbjgCmishcYAbwuap+UdL2aeGMu1x30lF3xbU7qQ2jj8D62a6RuM0NcGgDr6MxHrHPTOmsxEQizX4XRtwMf/wPnHSJ19FkloID8J+z3Kmhm/NsQnpjsBIT3mj+Z6jdHMb+07UZmOSZ9bZrsO/0mCUBY0phiSCRypSBLk+5OQumPud1NJljx2YY9xA0ag8nXux1NMb4niWCRKvf2s1xPO0l2LLS62gyw5h/wr6dcN6zNteAMWGwRJAMZz8AWdnwxT1eR5L+vp8C8z50tZ9yjvE6GmNSgiWCZKhaG864E5aNgkUjwt7MhsVHaP9e+PwfUL0+nP4Pr6MxKcA+Y44lgmRpcyPUOtFNlr5rW1ib2LD4CH39Mvy4FM57BrIreR2NSQH2GXOs+2gybZgDb5wJJ/eCi14qdjUbFh+FravhldZuIvoe73sdjfG5TP2MWfdRP6jTHE7t68YXfD+52NVsWHwUvugXKO+RPmMSTeLYZ+z3LBEkW4e7ocZRbp7jvTtDrmLD4iO0ZCQsHQkd+kH1el5HY1KAfcZ+zxJBspWrCBe+CFu/h4mPF7uaDYsP084t8NltcPgJNuGMiYh9xv6ftRF4ZcQt8O17cN2XUOdkr6NJXR9fA4uGw3UToPZJXkdjjK9ZG4HfnPMQVD4cht8MB/Z5HU1qWvAJLBgKZ/SzJGBMDCwReKVidTj/Wdg0H6a96HU0qeeXTfD53+HIlnDa37yOxpiUZonAS8dfwO7GF7J3/OP8tGqu19GkDlX43y2wbxd06w9ZZb2OyKSZTBtoZonAY/8udx3btSL7PrzafbGZ0n07CJZ9AWfdb2UkTEJk2kAzayz2SPCAljPKzGVg9pO8u/8cHuXatB7QErOtq+G1dm5MxpUjXIVXY+Ik3QeaJaSxWERqiMhYEVke+Btq4vpjRWRO0GW7iNwWuO8BEVkfdN95scSTSoIHtEwqaMZbBedzZdmxTP+jHRUUq6AAht8EKHR9xZKAibtMHWgW6yepHzBeVRsD4wO3f0dVl6pqc1VtDrQEduImsC/078L7VXVk0e3TVdEBLU/su4x1FY+j+pi/wc/rvA7Pn2YMgFVT3GQzNvWkSYBMHWgWayLoCgwMXB8IdCtl/bOA71R1dYz7TQvBA1oubX00/XPugYL9MPQ6OLDf6/D8ZV2em+ntmM7Q4kqvozFpLBMHmsXURiAi21S1etDtrap60OmhoPvfAmar6suB2w8AfwG2A3nAP1R1azHb9gZ6A9SvX7/l6tVpmkvm/heG9XZ94zve7XU0/rAjH15vD1nloPdEqFTD64iMSUlRtxGIyDgRWRDi0jXCALKBi4CPgha/BhwNNAc2As8Wt72qDlDVXFXNzcnJiWTXqaXZZdDscpj8FKya6nU03juwHz6+GnZtgcvesyRgTAKUmghU9WxVbRriMhzYJCK1AQJ/N5fwUF1wRwObgh57k6oeUNUC4A2gVWxPx78i6pd83tNwaEN3imjnloTH5mvjH3DtAhe+ALWbeR2NyXDpOr4g1jaCEcBVgetXAcNLWPdy4IPgBYVJJKA7sCDGeHwron7J5avAxW/Bzh9hyJVu5q1MtOATN9fzKddBsx5eR2NM2o4viLWN4DBgCFAfWANcoqpbRKQO8B9VPS+wXiVgLXCUqv4ctP17uNNCCqwCrlfVjaXtN5XGEcTUL7mwvaBZT+j2amZNxL55MbxxFtRqCld9BmWzvY7IZLB0GV9QXBuBDShLsM3bd/PIyMWMWfgDu/cVUKFcGTqdUIt7zz8+vC5pEx6HSU/AmfdB+zsSH7Af7P4ZBnSEPb/A9ZPdnM/GeCjmz7FPFJcIrEhLgsXcL7lDPzd3wZePuAltmv4psQF7reAADOsD21bDVf+zJGB8Id3HF1giSILCfsk9W9Vn8Iw15EfS0CTi5jfethaG3QBV60L91okL1ksFBa6Y3NKR0OVpaHCq1xEZ85uYPsc+Z6eGUsXOLfCfs2H3NvjrOHd0kE5U4Yu7YfprcMZd0PEeryMyJu3YxDRJkrDuZZVqQK+PQAvg/UthV8hxd6lr4uMuCbS50c3rbEyKSeWupZYI4iyh3csOOxp6DHbnzwf9KX3GGHz1Ikx6Ek6+wtURyqTeUSZtpHLXUjs1FCdJ7V62ZCR8dBUc1hiuGAZVjojv4ydT3ttu8vkTusOf3oQyWV5HZExEUqlrqZ0aSrCklq897jzoOcT1Jnq7M2xbE/99JMO8IfDZ36BxJ+g+wJKASUnpULraEkGcJL172dEd4crhsPMneKsL/LgiMftJlLy3XDfRhqfBpQNtwJhJWenQtdQSQRwlvXxtvVZu1O3+3e7I4If5id1fPBzYB5/f7o4Eju4Il38A5Sp6HZUxMUn10tXWRhClzdt30/eDb3m558neZ/4fl8O7XWHvDuj5kX/HGezc4to2vp8MbfvCOQ/Z6SCT9vz0XWFtBHHmqx4CNRvDNV9ApcPgnfPhqxfcCF0/yV8Kb5wJa76Bbq9Bp0ctCZiM4KvvimLYEUGEfN1DYOcWNzJ38f+g4enuC7d6PW9jAlg2BoZeC2UrwGWD/HvEYkwc+fG7wo4I4sTXPQQq1YBL33MTu2/4Fl5rB/M/9i6e3T/D6Hth8KVufoXeEywJmIzh6++KIiwRlKLoaEHf9xAQgZP/DH2mQM6x7pf40Otg17bkxVBwAGYNhBdbwNevuDmGr/kCqtVNXgzGeKy07wo/jUS2RFCKUOf3UqKHQI2j4OpR0OEeWDAUXm0D0152pZ0TafXX8EZHd4rqsD+4OYYvehGyKyd2v8b4UEnfFX5qO7A2AkK36vvx/F7U1uXB2Pth9VQoXw1y/wKt+0DVOvHbx4/LYeITsOBjqHqk6xHU9E9WLsKYIkr7bklkL6OEtBGIyCUislBECkTkoAcPWq+ziCwVkRUi0i9oeQ0RGSsiywN/D40lntIUdygWKjOn0vm9UtXNhas/h+u+hD+c5aZ/fP5EN6Br4zxX+TNSqrBpkZs459W28HIuLPnMVQ7tOxNOvNiSgDEhlPbdUtKRQqJOJ8U6H8EC4I/A68WtICJZwCvAOcA6YKaIjFDVRUA/YLyqPhFIEP2Au2KMqVjBL/Aj3U88KDMPmr6GQdPX/JaZfd0WEI0jW8Ilb8PW++Gb12D2uzD3A6hYw00MX6e5+1u7GRzayH2RFxxwjb67t7l2hl1bYfVXsGg4/LQCEKjfFjo/AU262UQyxpSiuLaD05+cUOL3ERz8HRYvcTk1JCITgdtV9aDzNSLSFnhAVTsFbt8NoKqPi8hSoIOqbgxMZD9RVY8tbX+Rnhoq7lAsO0vofGLtYqefu/69PHKqVPjdRBSvX1HsgU/q2bkFFg5zPYw2znXzBBfsc/dlV3GJYM/2g7eTLGh0Ohx/ERx3QWoXvTPGA6G+Wx7u2rTY6TCLJolCkZ6q9nKqyiNxE9cXWgcU9iE8onCy+kAyOLy4BxGR3kBvgPr160cUwJQ7Oxb7Ar8wbnmxv/qDv/Qf6dY0on2mhEo14JRr///2/j0uGWycC5sWuC/8CtWgYnWoUD3wtxrkHOe2NcZEpbjvluLOQpT0HRYPpSYCERkH1Apx172qOjyMfYQ6URzxYYiqDgAGgDsiiGTbkrpxpfP0cxErW96dHqrT3OtIjMlIxX0fJbrbeqmJQFXPjnEf64Dg4a11gQ2B65tEpHbQqaHNMe6rWMW9wGn/q98YkzJK+j5K5I/WZLQRlAWWAWcB64GZQE9VXSgiTwM/BTUW11DVO0vbnx+KzhljTKpJVPfR7iKyDmgLfC4iowPL64jISABV3Q/0BUYDi4Ehqrow8BBPAOeIyHJcr6InYonHGGNM5GxAmTHGZAgrOmeMMSYkSwTGGJPhLBEYY0yGs0RgjDEZLiUbi0UkH1idgIeuCfyYgMdNllSPH1L/OaR6/JD6zyHV44fEPYcGqppTdGFKJoJEEZG8UC3qqSLV44fUfw6pHj+k/nNI9fgh+c/BTg0ZY0yGs0RgjDEZzhLB7w3wOoAYpXr8kPrPIdXjh9R/DqkePyT5OVgbgTHGZDg7IjDGmAxnicAYYzKcJYIiRORhEZknInNEZIyI1PE6pkiIyNMisiTwHIaJSHWvY4qUiFwiIgtFpEBEUqYboIh0FpGlIrIiUFY9pYjIWyKyWUQWeB1LNESknohMEJHFgffPrV7HFAkRqSAiM0RkbiD+B5O2b2sj+D0Rqaqq2wPXbwGaqGofj8MKm4icC3ypqvtF5EkAVb3L47AiIiLHAwXA6xQzz4XfiEgWbt6Nc3CTMc0ELlfVRZ4GFgERaQ/sAN5V1ZSbpSkwuVVtVZ0tIlWAWUC3VPkfiIgAlVV1h4iUA6YCt6rqN4netx0RFFGYBAIqE8W0ml5S1TGBOSAAvsHNCJdSVHWxqi71Oo4ItQJWqOpKVd0LfAh09TimiKjqZGCL13FES1U3qurswPVfcPOfHOltVOFTZ0fgZrnAJSnfP5YIQhCRR0VkLdAL+JfX8cTgGmCU10FkiCOBtUG315FCX0LpRkQaAicD0z0OJSIikiUic3DT9o5V1aTEn5GJQETGiciCEJeuAKp6r6rWA97Hza7mK6XFH1jnXmA/7jn4TjjPIcVIiGUpdTSZLkTkEGAocFuRI3zfU9UDqtocdyTfSkSScoqu1Mnr05Gqnh3mqoOBz4H7ExhOxEqLX0SuAi4AzlKfNgJF8D9IFeuAekG36wIbPIolYwXOrQ8F3lfVT7yOJ1qqui0wF3xnIOGN9xl5RFASEWkcdPMiYIlXsURDRDoDdwEXqepOr+PJIDOBxiLSSESygR7ACI9jyiiBxtY3gcWq+pzX8URKRHIKe/mJSEXgbJL0/WO9hooQkaHAsbheK6uBPqq63tuowiciK4DywE+BRd+kUq8nABHpDrwE5ADbgDmq2snToMIgIucBzwNZwFuq+qi3EUVGRD4AOuBKIG8C7lfVNz0NKgIichowBZiP+/wC3KOqI72LKnwichIwEPf+KQMMUdWHkrJvSwTGGJPZ7NSQMcZkOEsExhiT4SwRGGNMhrNEYIwxGc4SgTHGZDhLBMYYk+EsERhjTIb7P+KkrPFAuElXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotmessage = plot(x, cos(x), '*', x, sin(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that even with multiple curves in a single plot command, markers can be specified on some, none or all: Matplotlib uses the difference between an array and a text string to recognize which arguments specify markers instead of data.\n",
    "\n",
    "Here are some other marker options — particularly useful if you need to print in back-and-white."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotmessage = plot(x, cos(x), '.', x, sin(x), ':')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multiple curves in one figure\n",
    "\n",
    "There can be any number of curves in a single `plot` command:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = linspace(-1,1)\n",
    "plotmessage = plot(x, x, x, x**2, x, x**3, x, x**4, x, x**5, x, x**6, x, x**7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note the color sequence."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With enough curves (more than ten? It depends on the version of matplotlib in use) the color sequence eventually repeats – but you probably don't want that many curves on one graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = linspace(-1,1)\n",
    "plotmessage = plot(x, x, x, x**2, x, x**3, x, x**4, x, x**5,\n",
    "                x, x**6, x, x**7, x, x**8, x, x**9, x, x**10,\n",
    "                x, -x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Aside on long lines of code:** *The above illustrates a little Python coding hack: one way to have a long command continue over several lines is simply to have parentheses wrapped around the part that spans multiple lines—when a line ends with an opening parenthesis not yet matched, Python knowns that something is still to come.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(with-Spyder-IPython)=\n",
    "### Aside: using IPython magic commands in Spyder and with the IPython command line\n",
    "\n",
    "If using Spyder and the IPython command line, there is a similar choice of where graphs appear, but with a few differences to note:\n",
    "- With the \"inline\" option (which is again the default) figures then appear in a pane within the Spyder window.\n",
    "- The \"tk\" option works exactly as with notebooks, with each figure appearing in its own window.\n",
    "- **Note:** Any such IPython magic commands must be entered at the IPython interactive command line, not in a Python code file."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting sequences\n",
    "\n",
    "A curve can also be specified by a single array of numbers: these are taken as the values of a sequence, indexed Pythonically from zero, and plotted as the ordinates (vertical values):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotmessage = plot(tenvalues**2, '.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting curves in separate figures (from a single cell)\n",
    "\n",
    "From within a single Jupyter cell, or when working with Python files or in the IPython command window (as used within Spyder), successive `plot` commands keep adding to the previous figure.\n",
    "To instead start the next `plot` in a separate figure, first create a new \"empty\" figure, with the function `matplotlib.pyplot.figure`.\n",
    "\n",
    "With a full name as long as that, it is worth importing so that it can be used on a first name basis:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib.pyplot import figure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = linspace(0, 2*pi)\n",
    "plot(x, sin(x))\n",
    "figure()\n",
    "plotmessage = plot(x, cos(x), 'o')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `figure` command can also do other things, like attach a name or number to a figure when it is displayed externally, and change from the default size.\n",
    "\n",
    "So even though this is not always needed in a notebook, from now on each new figure will get an explicit `figure` command. Revisiting the last example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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P+PeXmRSUlHGf/bB4vb7xEVwzII4Xl+9k79Eip+MY4xWsELhpX14xL63YxdX940iJbe10HFMLvx6XjABPLLabzIwBKwRue9x1x+rdY7s7nMTUVkx4C356QSIfrM1h6wG7ycwYKwRu2HKggPfWZPPTCxLt5jEfM/WSrrQMCeIfC7c6HcUYx1khcMOj87fQqlkQtw23m8d8TZuwEH5xSRcWbTpI+u5jTscxxlFWCOrpqx2H+WJrLtNGdiMi1OYa8EU3D+tMu5Yh/H3BFnzx6jljPMUKQT2oKo/O30JcRAtuHJrodBxTT2HNgpg2ohsrs46ybPthp+MY4xgrBPWwYONB1mfnc9foJJoH21ASvmzykATi27Tgbwu2UFlpvQLjn6wQ1FFFpfL4oq10iQrj6gE+PVCqoWroiRmju5ORU8D8jANOxzHGEVYI6ujj9fvYdvA4M0Z3t5nHmoirBsTRPboljy3cagPSGb9kv2R1UF5RyT8Xb6dHh1Zc1ifG6TjGQwIDhF+NTSbr8AneTc92Oo4xjc4KQR28vyaHnYdPcM/YZBtYrokZkxLNgIQInlyynZKyCqfjGNOorBDU0snyCp5csp1+8eGM7tne6TjGw0SEey/twf78Ev7z9W6n4xjTqKwQ1NLbq/eSk1fMPWOTcU2tYJqYoV3bclFSO577cgdFpeVOxzGm0VghqIXi0gqe+iyTwYmRXJTUzuk4pgHdNbo7R06U8qr1CowfsUJQC6+t3E1u4UnuGdvdegNN3KBObbikexTPf7mD4yetV2D8g0cKgYiME5GtIpIpIvfVsP4nIrLe9fhKRPpVW7dLRDaIyDoR8Z7ZZlyOnyzn2S93cFFSO4Z0aet0HNMIZozpzrGiMl75apfTUYxpFG4XAhEJBJ4BxgMpwGQRSTlts53AJaraF/gjMPO09SNUtX9NM+c47aXlOzl6opR7xiY7HcU0kv4dIxjVoz0zl2ZRYFNaGj/giR7BYCBTVbNUtRR4C5hYfQNV/UpVTw3xuBKI98B+G1x+cRkzl2Uxumc0/TtGOB3HNKIZY7qTX1zGyyt2OR3FmAbniUIQB+yt9j7btexMfgbMr/ZegYUiki4iU87USESmiEiaiKTl5ua6Fbi2Zi/fSWFJOTPGJDXK/oz36B0XzpiUaF5YlkV+sfUKTNPmiUJQ09nTGkfvEpERVBWC31RbPExVB1J1aOl2Ebm4praqOlNVU1U1NSoqyt3M55RfXMbsFTu5tFc0vWLDG3x/xvvcNTqJwpJyXly+0+koxjQoTxSCbKBjtffxwL7TNxKRvsAsYKKqHjm1XFX3uZ4PAR9QdajJcad6A9NHWW/AX/WKDWd87w68tHwneUWlTscxpsF4ohCsBpJEpLOIhADXAXOrbyAiCcD7wA2quq3a8jARaXXqNTAWyPBAJrdYb8Ccctfo7hwvLWfWMusVmKbL7UKgquXANGABsBl4R1U3ishUEZnq2uwPQFvg36ddJhoNLBeRb4FVwCeq+qm7mdxlvQFzSnKHVkzoE8NLK6quHjOmKQryxIeo6jxg3mnLnqv2+lbg1hraZQH9Tl/uJOsNmNPdNSqJeRv2M3NpFveN7+F0HGM8zu4sPs1LK6w3YL4rKboVV/SN5dWvd1mvwDRJVgiqyS8u48Xl1hsw3zd9VDeKyyqYtSzL6SjGeJwVgmqsN2DOpFv7qsmIXvlql11BZJocKwQu1hsw53LHyCROlFbYfQWmybFC4GK9AXMuVVcQdeDlFbvIL7K7jU3TYYUA6w2Y2rtjZBKFJ8uZvcJ6BabpsEIAvLxil/UGTK30jGnNpb2imb1ip41MapoMvy8EhSVV9w2MSbHegKmdO0ZWjUFkI5OapsLvC8GrX+8mv7iM6SOtN2Bqp3dcOKN7RvPi8p0UWq/ANAF+XQhOnCxn1rIsRiRH0SfeegOm9u4clUR+cZnNbWyaBL8uBK+t3M2xojLusHMDpo76xIczskd7XliWZXMbG5/nt4WguLSCF5ZlcVFSOwYmtHE6jvFB00clkVdUxn+sV2B8nN8WgjdW7eHw8VK7UsjUW/+OEVzSPYoXlmVRVGq9AuO7/LIQlJRV8NyXOxjapS3nJUY6Hcf4sOmjkjh6opTXV+5xOoox9eaXheDt1XvJLTxpvQHjtkGd2jCsW1ueX5pFSVmF03GMqRe/KwQny6t6A+cltuH8LtYbMO6bPjKJw8dP8uYq6xUY3+SRQiAi40Rkq4hkish9NawXEfmXa/16ERlY27ae9m56NvvzS5g+KgkRaejdGT8wpEtbBneO5Lkvd1ivwPgktwuBiAQCzwDjgRRgsoiknLbZeCDJ9ZgCPFuHth5TWl7Jvz/fwYCECC7s1q6hdmP80J2jkjhYcJI56dlORzGmzjzRIxgMZKpqlqqWAm8BE0/bZiLwqlZZCUSISEwt23rMB2uzyckrZvpI6w0Yz7qga1sGJkTw3Bc7KC2vdDqOaYKOnSjl+lnfkJGT7/HP9kQhiAP2Vnuf7VpWm21q0xYAEZkiImkikpabm1uvoLmFJ0nt1IbhyVH1am/MmYgI00clkZNXzPtrrFdgPO/F5TtZnnmYkCDPn9r1xCfW9Ke11nKb2rStWqg6U1VTVTU1Kqp+P+TTRibx9i+GWm/ANIhLukfRNz6cZ77IpKzCegXGc/KLynj5q11M6NOB7tGtPP75nigE2UDHau/jgX213KY2bT0qMMCKgGkYIsIdI5PYe7SYj9Y16H/Gxs+89NVOjp8sZ9qIhrnk3ROFYDWQJCKdRSQEuA6Ye9o2c4EbXVcPnQ/kq+r+WrY1xmeM7tmenjGteebzTCoqa+zcGlMnBSVlzF5eNVR+SmzrBtmH24VAVcuBacACYDPwjqpuFJGpIjLVtdk8IAvIBF4AbjtbW3czGeMUEWH6yG7sPHyCj9dbr8C479WvdlFQUt6gQ+UHeeJDVHUeVT/21Zc9V+21ArfXtq0xvuzSXh3oHt2Spz7L5Iq+sQTY4UhTT8dPljNr+U5G9mjfoEPl+92dxcY0tIAAYdrIJDIPHWdexn6n4xgf9trK3eQVlXHHyG4Nuh8rBMY0gMv6xNA1KoynlmRSaecKTD0UlZbzwtKqofIHNPBQ+VYIjGkAgQFVVxBtPVjIwk0HnI5jfNAb3+zhyIlS7myEwTGtEBjTQK7oF0uXdmE8ab0CU0clZRU8vzSLC7q2JbURhsq3QmBMAwkMEG4f0Y3N+wtYvPmg03GMD3lr1Z5GHSrfCoExDWhi/1g6tQ3lySXbqbp4zpizqxoqP4vBiZGc36Vto+zTCoExDSgoMIDbR3Rj474Clmw+5HQc4wPeScvmQEFJo06cZYXAmAZ29YA4Oka24F+fWa/AnN3J8gqe/TyTgQkRDOvWOL0BsEJgTIMLDgzg9uHdWJ+dzxdb6zdyrvEPc9Ky2Zdfwowx3Rt1cEwrBMY0gmsGxhMX0cLOFZgzOllewb8/z2RQpzaNPnGWFQJjGkFIUAC3jejKur15LN1+2Ok4xgud6g3c6cA0ulYIjGkkPxwUT2x4c55cvM16BeY7TvUGBiZEcFFS40+ja4XAmEbSLCiQXw7vypo9eazIPOJ0HONF3k2v6g3cNbpxzw2cYoXAmEY06byOxIQ35wnrFRiX0vJKnvnMud4AWCEwplE1CwrkthHdSN99zM4VGADmpO91tDcAVgiMaXSTUquuIHpikfUK/J039AbAzUIgIpEiskhEtruevzdWqoh0FJHPRWSziGwUkTurrXtIRHJEZJ3rMcGdPMb4gmZBgUwb2Y11e/PsvgI/d6o3cKeDvQFwv0dwH7BEVZOAJa73pysH7lHVnsD5wO0iklJt/ROq2t/1sJnKjF/44aB4Oka2sHMFfqy0vJJ/f76DAQkRXOxgbwDcLwQTgVdcr18Brjp9A1Xdr6prXK8LqZqbOM7N/Rrj04IDA7hjRBLrs/NtDCI/9W56Njl5xY6eGzjF3UIQrar7oeoHH2h/to1FJBEYAHxTbfE0EVkvIrNrOrRUre0UEUkTkbTcXOtOG9939cA4OrUN5XE7V+B3SsoqeOqz7V7RG4BaFAIRWSwiGTU8JtZlRyLSEngPuEtVC1yLnwW6Av2B/cBjZ2qvqjNVNVVVU6Oiouqya2O8UnBgANNHJrFpfwELNtp8Bf7krVV72J9fwq/GJjveG4BaFAJVHa2qvWt4fAQcFJEYANdzjX1cEQmmqgi8rqrvV/vsg6paoaqVwAvAYE98KWN8xcT+sXRuF8Y/F2+zWcz8RFFpOU9/voPzu0RyQdfGG2H0bNw9NDQXuMn1+ibgo9M3kKpy9yKwWVUfP21dTLW3VwMZbuYxxqcEBQZw56gkthwo5NONNrexP3j1690cPn7Sa3oD4H4heBQYIyLbgTGu94hIrIicugJoGHADMLKGy0T/JiIbRGQ9MAKY4WYeY3zOFf1i6RoVxhOLtlFhvYImrbCkjOe+3MHw5KhGmYu4toLcaayqR4BRNSzfB0xwvV4O1Fj2VPUGd/ZvTFMQGCDcObo7099cyycb9nNlv1inI5kGMnv5LvKKyrhnTLLTUb7D7iw2xgtc3ieG5OhW/HPRNsorKp2OYxpAXlEps5ZlMa5XB/rEhzsd5zusEBjjBQIChHvGdifr8AneTc92Oo5pAM8vzeJ4aTkzxnR3Osr3WCEwxkuMSYlmQEIE/1y8nZKyCqfjGA/KLTzJyyt2cWW/WJI7tHI6zvdYITDGS4gI917agwMFJfzn691OxzEe9O8vMimtqOSu0d7XGwArBMZ4laFd23Jx9yie+SKTgpIyp+MYD9iXV8zrK/fww4HxdG4X5nScGlkhMMbL3HtpMnlFZcxamuV0FOMBT3+eiaLcMaqb01HOyAqBMV6md1w4l/WNYdbyneQWnnQ6jnHDjtzjvL16L5MHJxDfJtTpOGdkhcAYL3TPmO6cLK/kmc8znY5i3PD3T7fSPCiA6aOSnI5yVlYIjPFCXaJacu2geN74Zg97jxY5HcfUQ/ruY3y68QBTLu5Ku5bNnI5zVlYIjPFSd45OAoF/Lt7udBRTR6rKo/M3065lM269qLPTcc7JCoExXiomvAU3De3EB2uz2Xaw0Ok4pg4Wbz7E6l3HmDEmibBmbo3k0yisEBjjxW4b3o2wkCD+vmCr01FMLZVXVPLo/M10iQrjR6kdnY5TK1YIjPFibcJC+MUlXVi06SDfZB1xOo6phTnp2ezIPcG9l/YgKNA3fmJ9I6UxfuzWi7oQG96cP32y2Sav8XJFpeU8sWgbgzq14dJe0U7HqTUrBMZ4uebBgdw7rgcbcvL5cF2O03HMWby4bCeHCk9y//geXjPpTG24VQhEJFJEFonIdtdzjZPPi8gu1wQ060Qkra7tjfF3V/aLpV98OH/7dCvFpTYgnTc6cvwkzy/NYmxKtFdNOlMb7vYI7gOWqGoSsMT1/kxGqGp/VU2tZ3tj/FZAgPC7y1M4UFDCC8ts6Alv9NRnmRSXVXDvuB5OR6kzdwvBROAV1+tXgKsaub0xfuO8xEgm9OnAs1/s4GBBidNxTDU7co/z+je7mZTakW7tWzodp87cLQTRqrofwPXc/gzbKbBQRNJFZEo92htjgN+M60FFpfLYQruc1Jv88eNNNA8K5G4vnHSmNs5ZCERksYhk1PCYWIf9DFPVgcB44HYRubiuQUVkioikiUhabm5uXZsb0yR0ahvGT4clMic9m4378p2OY4DPthzki6253Dk6iahW3j2UxJmcsxCo6mhV7V3D4yPgoIjEALieD53hM/a5ng8BHwCDXatq1d7VdqaqpqpqalRUVF2+ozFNyu0juhHRIpg/f7IZVbuc1Eknyyt4+L+b6BoVxo1DE52OU2/uHhqaC9zken0T8NHpG4hImIi0OvUaGAtk1La9Mea7wlsEM2NMd77acYQlm8/4t5NpBLOX72LXkSIevKIXIUG+ezW+u8kfBcaIyHZgjOs9IhIrIvNc20QDy0XkW2AV8Imqfnq29saYs5s8OIGuUWE8Mm8zpeWVTsfxSwcLSnj6s+2M7hnNxd19+yiFW6MhqeoRYFQNy/cBE1yvs4B+dWlvjDm74MAAfnd5Cje/tJpZy7O4bbj3zn7VVP11/hbKKpTfX97T6Shu892+jDF+bkRyey7tFc2/lmy3OQsaWfruo7y/NoefX9yZTm29cx7iurBCYIwPe/CKXgSI8H//3eR0FL9RWak8NHcTHVo3bzI9MSsExviw2IgW3DkqicWbD7Jo00Gn4/iFOel72ZCTz/0TevjEXAO1YYXAGB93y4WdSY5uxUNzN1JUWu50nCYtv7iMv326ldRObbiyX6zTcTzGCoExPi44MIA/Xd2bnLxinvrMJrtvSI/O38KxolIeurKXT40uei5WCIxpAs5LjOSHg+J5YWkW221aywaxMusIb67aw60XdaF3XLjTcTzKCoExTcT946uOWf/uwwy749jDSsoquO+99SREhjJjtG+OJ3Q2VgiMaSLatmzGb8b14JudR/lgrU1g40lPLtnOriNF/OWaPrQICXQ6jsdZITCmCbnuvI707xjBnz/ZTF5RqdNxmoSMnHxmLs1iUmo8w7q1czpOg7BCYEwTEhAg/Pnq3uQVl/HQ3I1Ox/F55RWV3Pf+etqEhvDAhBSn4zQYKwTGNDG9YsOZNqIbH67bx/wN+52O49NmLd9JRk4BD0/sRXhosNNxGowVAmOaoGkju9EnLpwHPswgt/Ck03F80s7DJ3hi0TbGpkQzvncHp+M0KCsExjRBwYEBPD6pH8dPlvPABxvsKqI6UlXuf389IUEB/PGq3k3qnoGaWCEwpolKim7Fr8cms3DTQd5fY1cR1cUbq/awMusov53Qk+jWzZ2O0+CsEBjThN1yYWcGJ0by0NyN7MsrdjqOT9h+sJA/fryJi5Lacd15HZ2O0yisEBjThAUGCP+4th8Vqtz77no7RHQOJWUVTHtjLWEhQTw2qV+TPyR0iluFQEQiRWSRiGx3PbepYZtkEVlX7VEgIne51j0kIjnV1k1wJ48x5vsS2obywGU9WZ55mNdW7nY6jlf70yeb2HqwkMcm9aN9q6Z/SOgUd3sE9wFLVDUJWOJ6/x2qulVV+6tqf2AQUETVBPanPHFqvarOO729McZ9Px6cwCXdo3hk3hZ2Hj7hdByv9GnGAV5buYefX9SZ4cntnY7TqNwtBBOBV1yvXwGuOsf2o4Adqmp/lhjTiESEv/6gLyFBAdz2+hqKSyucjuRVcvKK+c176+kTF86vL+3hdJxG524hiFbV/QCu53OV0euAN09bNk1E1ovI7JoOLZ0iIlNEJE1E0nJzc91LbYwf6hDenCev68+WAwV2SWk15RWV3PXWWsorKnlq8gBCgvzv1Ok5v7GILBaRjBoeE+uyIxEJAa4E5lRb/CzQFegP7AceO1N7VZ2pqqmqmhoVFVWXXRtjXIYnt2fG6O68vzaH/9j5AgD+9Vkmq3cd409X9yaxne/PP1wf55xnTVVHn2mdiBwUkRhV3S8iMcChs3zUeGCNqv5vPr3qr0XkBeDj2sU2xtTXtBHdWJ+dx8P/3URKTGtSEyOdjuSYlVlHePqz7VwzII6rB8Q7Hccx7vaB5gI3uV7fBHx0lm0nc9phIVfxOOVqIMPNPMaYcwgIEB6b1J/4Ni247fU1HCoscTqSI/YeLWLaG2tIiAzl4at6Ox3HUe4WgkeBMSKyHRjjeo+IxIrI/64AEpFQ1/r3T2v/NxHZICLrgRHADDfzGGNqIbxFMM/dMIjCknKmvb6WsopKpyM1qvziMm55eTWl5ZXMuimVlk1kEvr6El88YZSamqppaWlOxzDG5839dh/T31zLzcMSefCKXk7HaRRlFZXc/NJqVmYd4dVbBnNBE51joCYikq6qqacv9+8yaIyfu7JfLOv25DF7xU76xoc3+ePkqsrvP8xgeeZh/vbDvn5VBM7G/66TMsZ8x/0TenB+l0jufXc9n2852/Uevu/5pVm8tXovt4/oyqRU/xhHqDasEBjj54IDA5h5YyrJHVox9bV0vt5xxOlIDWL+hv08On8Ll/eN4Z4xyU7H8SpWCIwxtG4ezKu3DCEhMpRbX1nNur15TkfyqHV787jr7XUMTIjgH9f2IyDAPwaTqy0rBMYYACLDQnjt1iG0bdmMm2avYsuBAqcjeURGTj63vLya9q2b8cKNqTQPDnQ6ktexQmCM+Z/o1s15/dYhNA8O4PpZq3x+gLq0XUeZ/MJKWgQH8uotVUXOfJ8VAmPMd3SMDOX1W4dQqcr1s74hx0cntFm2PZcbXlxFu5bNeGfqUDr76fARtWGFwBjzPd3at+LVWwZTUFLGdTO/JvNQodOR6uTTjAP87OU0OrUN5Z1fDCUuooXTkbyaFQJjTI16x4Xzn58Nobi0kquf+cpnLi39YG02t7+xhpTY1rw9ZShRrexw0LlYITDGnFH/jhHMnTaMhLah3PLKamYu3eHVw1f/Z+VuZrz9LUM6R/LarUMIDw12OpJPsEJgjDmr2IgWzJk6lAm9Y3hk3hZ+NWc9J8u9a2KbwpIyfjXnW37/YQaje7Zn9k/P8/vxg+rC/kkZY84pNCSIp388gO5LWvHE4m3sPHyc524Y5BXz+qbtOsqMd9aRc6yY6SO7cceoJIID7W/curB/WsaYWhER7hydxLM/Gcjm/YVc+dQK5m/Y79ihorKKSh5buJVJz38NwJypQ7l7bLIVgXqwHoExpk7G94khoW0o97zzLb98fQ1Du7TlwStT6NGhdaNl2Hn4BHe9vY5v9+bxw0HxPHhFCq2a2/mA+rJhqI0x9VJeUcmbq/fy2MKtFBSX8ZMhnbh7THfahIU02D4PFpTw0opdvPLVLkKCAvjLNX2Y0Cfm3A0NcOZhqK0QGGPckldUyhOLtvHaN3to2SyIu8d059rUeEJDPHfAYeuBQl5YlsVH63KoqFTG94nh95el0CHc+XMUvqRBCoGIXAs8BPQEBqtqjb/OIjIOeBIIBGap6qmZzCKBt4FEYBcwSVWPnWu/VgiM8T5bDxTy8McbWZF5hObBAYxIbs+43h0Y2aN9vQ7bqCpf7TjCzKVZfLktlxbBgfzovI7cMqwzCW1DG+AbNH0NVQh6ApXA88CvaioEIhIIbKNqqspsYDUwWVU3icjfgKOq+qiI3Ae0UdXfnGu/VgiM8U6qyjc7jzJvw34+zTjAocKThAQGcFFSO8b17kDPmNa0bh5MeItgWjUP+t8ooJWVyu6jRWzIyWdjTj4Z+/LJyCkgv7iMdi2b8dMLOnH9+Z2ICG24w07+oEFmKFPVza4PP9tmg4FMVc1ybfsWMBHY5Hoe7truFeAL4JyFwBjjnUSE87u05fwubXnoil6s3XuMeRsO8GnGAZacdmeyCLRsFkR4i2Dyiso4frIcgJDAAJI7tGJCnw6kdorksr4xNmJoA2uMq4bigL3V3mcDQ1yvo1V1P4Cq7heR9mf6EBGZAkwBSEhIaKCoxhhPCQgQBnWKZFCnSH53WU827itgX14xBSXl5BeXkV9cRoHruWWzIPrEhdMrrjVJ7VsREmSXgDamcxYCEVkMdKhh1QOq+lEt9lFTd6HOx6NUdSYwE6oODdW1vTHGOSJC77hweseFOx3F1OCchUBVR7u5j2yg+uSg8cA+1+uDIhLj6g3EAL4xqpUxxjQhjdH/Wg0kiUhnEQkBrgPmutbNBW5yvb4JqE0PwxhjjAe5VQhE5GoRyQaGAp+IyALX8lgRmQegquXANGABsBl4R1U3uj7iUWCMiGyn6qqiR93JY4wxpu7shjJjjPETZ7p81E7NG2OMn7NCYIwxfs4KgTHG+DkrBMYY4+d88mSxiOQCu+vZvB1w2INxnODr38HyO8/Xv4Ov5wdnvkMnVY06faFPFgJ3iEhaTWfNfYmvfwfL7zxf/w6+nh+86zvYoSFjjPFzVgiMMcbP+WMhmOl0AA/w9e9g+Z3n69/B1/ODF30HvztHYIwx5rv8sUdgjDGmGisExhjj5/yqEIjIOBHZKiKZrjmSfYqIzBaRQyKS4XSW+hCRjiLyuYhsFpGNInKn05nqQkSai8gqEfnWlf//nM5UHyISKCJrReRjp7PUh4jsEpENIrJORHxu9EkRiRCRd0Vki+v/haGOZ/KXcwQiEghso2q462yq5kmYrKqbHA1WByJyMXAceFVVezudp65ckw/FqOoaEWkFpANX+cq/A6manDtMVY+LSDCwHLhTVVc6HK1ORORuIBVoraqXO52nrkRkF5Cqqj55Q5mIvAIsU9VZrjlaQlU1z8lM/tQjGAxkqmqWqpYCbwETHc5UJ6q6FDjqdI76UtX9qrrG9bqQqvkp4pxNVXta5bjrbbDr4VN/SYlIPHAZMMvpLP5IRFoDFwMvAqhqqdNFAPyrEMQBe6u9z8aHfoSaGhFJBAYA3zgcpU5ch1XWUTWt6iJV9an8wD+Be4FKh3O4Q4GFIpIuIlOcDlNHXYBc4CXX4blZIhLmdCh/KgRSwzKf+muuqRCRlsB7wF2qWuB0nrpQ1QpV7U/V3NuDRcRnDtGJyOXAIVVNdzqLm4ap6kBgPHC765CprwgCBgLPquoA4ATg+PlKfyoE2UDHau/jgX0OZfFbrmPr7wGvq+r7TuepL1d3/gtgnLNJ6mQYcKXrGPtbwEgRec3ZSHWnqvtcz4eAD6g67OsrsoHsaj3Jd6kqDI7yp0KwGkgSkc6uEzTXAXMdzuRXXCdbXwQ2q+rjTuepKxGJEpEI1+sWwGhgi6Oh6kBV71fVeFVNpOq//89U9XqHY9WJiIS5LjTAdUhlLOAzV9Gp6gFgr4gkuxaNAhy/WCLI6QCNRVXLRWQasAAIBGar6kaHY9WJiLwJDAfaiUg28KCqvuhsqjoZBtwAbHAdZwf4rarOcy5SncQAr7iuQAsA3lFVn7wE04dFAx9U/U1BEPCGqn7qbKQ6uwN43fUHaRZws8N5/OfyUWOMMTXzp0NDxhhjamCFwBhj/JwVAmOM8XNWCIwxxs9ZITDGGD9nhcAYY/ycFQJjjPFz/w9WJi4Pj0Q8HAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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mMEL0M0kerKrXV9Urkrw9ydM7d6iq+5NcTPJDrbXf2tH+yqr65u3HSb4/ybOHUBMAANw1Bx7O0Vr7elW9K8lKkpkk72+tfaqqfnSy/b1J/kaSb03yv1ZVknx9MsvxtUk+NGm7J8nPt9Z+6aA1AQDA3XTgJe6GYIk7AACOwt1c4g4AAKaKEA0AAJ2EaAAA6CREAwBAJyEaAAA6CdEAANBJiAYAgE5CNAAAdBKiAQCgkxANAACd7hm6ADgNLl3ZyPLKeja3xjk7P5elxYWcf/jc0GUBHGuunZxkQjQc0KUrG7lwcS3ja9eTJBtb41y4uJYkOgOAPbh2ctIZzgEHtLyy/lInsG187XqWV9YHqgjg+HPt5KQTouGANrfGXe0AuHZy8gnRcEBn5+e62gFw7eTkE6LhgJYWFzI3O3NT29zsTJYWFwaqCOD4c+3kpDOxEA5oewKMGeYA++fayUlXrbWha+g2Go3a6urq0GUAAHDKVdXl1tpod7vhHAAA0EmIBgCATkI0AAB0EqIBAKCTEA0AAJ2EaAAA6CREAwBAJyEaAAA6CdEAANBJiAYAgE5CNAAAdBKiAQCgkxANAACdhGgAAOgkRAMAQCchGgAAOgnRAADQ6Z6hC4BpdOnKRpZX1rO5Nc7Z+bksLS7k/MPnhi4L4EBc25gmQjQcsUtXNnLh4lrG164nSTa2xrlwcS1JdDbAieXaxrQxnAOO2PLK+kudzLbxtetZXlkfqCKAg3NtY9oI0XDENrfGXe0AJ4FrG9NGiIYjdnZ+rqsd4CRwbWPaCNFwxJYWFzI3O3NT29zsTJYWFwaqCODgXNuYNocSoqvqrVW1XlXPVdWTt9heVfX3J9s/WVXfsd9j4bQ5//C5vPvxh3Jufi6V5Nz8XN79+EMm3gAnmmsb06Zaawf7AVUzSX4rySNJriZ5Jsk7Wmuf3rHPo0n+apJHk7w5yf/UWnvzfo69ldFo1FZXVw9UNwAAvJyqutxaG+1uP4xPot+U5LnW2udba19L8sEkj+3a57EkP9tu+PUk81V17z6PBQCAY+UwQvS5JF/c8fzqpG0/++znWAAAOFYOI0TXLdp2jxHZa5/9HHvjB1Q9UVWrVbX64osvdpYIAACH5zBC9NUkr9vx/L4km/vcZz/HJklaa0+11kattdGZM2cOXDQAANypwwjRzyR5sKpeX1WvSPL2JE/v2ufpJD88WaXjO5P8Xmvt+X0eCwAAx8o9B/0BrbWvV9W7kqwkmUny/tbap6rqRyfb35vkI7mxMsdzSf4wyY/c7tiD1gQAAHfTgZe4G4Il7gAAOAp3c4k7AACYKkI0AAB0EqIBAKCTEA0AAJ2EaAAA6CREAwBAJyEaAAA6CdEAANBJiAYAgE5CNAAAdBKiAQCg0z1DFwDsz6UrG1leWc/m1jhn5+eytLiQ8w+fG7os4BRz3YG9CdFwAly6spELF9cyvnY9SbKxNc6Fi2tJokMD7grXHbg9wzngBFheWX+pI9s2vnY9yyvrA1UEnHauO3B7QjScAJtb4652gINy3YHbE6LhBDg7P9fVDnBQrjtwe0I0nABLiwuZm525qW1udiZLiwsDVQScdq47cHsmFsIJsD2Jxyx54Ki47sDtVWtt6Bq6jUajtrq6OnQZAACcclV1ubU22t1uOAcAAHQSogEAoJMQDQAAnYRoAADoJEQDAEAnIRoAADoJ0QAA0EmIBgCATkI0AAB0EqIBAKCTEA0AAJ2EaAAA6CREAwBAJyEaAAA6CdEAANBJiAYAgE5CNAAAdLpn6AKAu+PSlY0sr6xnc2ucs/NzWVpcyPmHzw1dFjAQ1wQ4XEI0nEKXrmzkwsW1jK9dT5JsbI1z4eJakug0YQq5JsDhM5wDTqHllfWXOstt42vXs7yyPlBFwJBcE+DwCdFwCm1ujbvagdPNNQEO34FCdFW9qqo+WlWfm3z/llvs87qq+mdV9Zmq+lRV/diObT9ZVRtV9YnJ16MHqQe44ez8XFc7cLq5JsDhO+gn0U8m+Vhr7cEkH5s83+3rSf5aa+3fTfKdSf5KVb1hx/a/21p74+TrIwesB0iytLiQudmZm9rmZmeytLgwUEXAkFwT4PAddGLhY0m+a/L4A0n+eZL/ducOrbXnkzw/efz7VfWZJOeSfPqArw3sYXuikJn4QOKaAHdDtdbu/OCqrdba/I7nX2mtfcOQjh3bH0jy8STf3lr7alX9ZJL/IslXk6zmxifWX3m51x2NRm11dfWO6wYAgP2oqsuttdHu9pcdzlFVv1JVz97i67HOAv5kkl9M8uOtta9Omn86yZ9J8sbc+LT6b9/m+CeqarWqVl988cWelwYAgEP1ssM5Wmvft9e2qvpSVd3bWnu+qu5N8sIe+83mRoD+udbaxR0/+0s79vkHSf7xbep4KslTyY1Pol+ubgAAuFsOOrHw6STvnDx+Z5IP796hqirJzyT5TGvt7+zadu+Opz+Y5NkD1gMAAHfdQUP0e5I8UlWfS/LI5Hmq6mxVba+08ZYkP5Tke26xlN3fqqq1qvpkku9O8hMHrAcAAO66A63O0Vr7cpLvvUX7ZpJHJ49/LUntcfwPHeT1AQBgCO5YCAAAnYRoAADoJEQDAEAnIRoAADoJ0QAA0EmIBgCATkI0AAB0EqIBAKCTEA0AAJ2EaAAA6CREAwBAp3uGLgA4Pi5d2cjyyno2t8Y5Oz+XpcWFnH/43NBlAbfg7xWGJUQDSW50yBcurmV87XqSZGNrnAsX15JExwzHjL9XGJ7hHECSZHll/aUOedv42vUsr6wPVBGwF3+vMDwhGkiSbG6Nu9qB4fh7heEJ0UCS5Oz8XFc7MBx/rzA8IRpIkiwtLmRuduamtrnZmSwtLgxUEbAXf68wPBMLgSR/PBnJbH84/vy9wvCqtTZ0Dd1Go1FbXV0dugwAAE65qrrcWhvtbjecAwAAOgnRAADQSYgGAIBOQjQAAHQSogEAoJMQDQAAnYRoAADoJEQDAEAnIRoAADoJ0QAA0EmIBgCATkI0AAB0EqIBAKCTEA0AAJ2EaAAA6HTP0AUAJ9elKxtZXlnP5tY4Z+fnsrS4kPMPnxu6LDhx/C3BySNEA3fk0pWNXLi4lvG160mSja1xLlxcSxKdP3TwtwQnk+EcwB1ZXll/qdPfNr52Pcsr6wNVBCeTvyU4mYRo4I5sbo272oFb87cEJ5MQDdyRs/NzXe3ArflbgpNJiAbuyNLiQuZmZ25qm5udydLiwkAVwcnkbwlOJhMLgTuyPeHJigJwMP6W4GSq1tqdH1z1qiT/Z5IHknwhyX/aWvvKLfb7QpLfT3I9yddba6Oe43cbjUZtdXX1jusGAID9qKrL29l1p4MO53gyycdaaw8m+djk+V6+u7X2xl1F9BwPAADHwkFD9GNJPjB5/IEk54/4eAAAOHIHDdGvba09nyST76/ZY7+W5Jer6nJVPXEHxwMAwLHxshMLq+pXknzbLTb99Y7XeUtrbbOqXpPko1X12dbaxzuOzyR8P5Ek999/f8+hAABwqF42RLfWvm+vbVX1paq6t7X2fFXdm+SFPX7G5uT7C1X1oSRvSvLxJPs6fnLsU0meSm5MLHy5ugEA4G456HCOp5O8c/L4nUk+vHuHqnplVX3z9uMk35/k2f0eDwAAx81BQ/R7kjxSVZ9L8sjkearqbFV9ZLLPa5P8WlX9ZpJ/neSftNZ+6XbHAwDAcXagm6201r6c5Htv0b6Z5NHJ488n+XM9xwMAwHHmtt8AANBJiAYAgE5CNAAAdBKiAQCgkxANAACdhGgAAOh0oCXuAHpdurKR5ZX1bG6Nc3Z+LkuLCzn/8Lmhy4JD5X0Op58QDRyZS1c2cuHiWsbXridJNrbGuXBxLUkEDE4N73OYDoZzAEdmeWX9pWCxbXztepZX1geqCA6f9zlMByEaODKbW+OudjiJvM9hOgjRwJE5Oz/X1Q4nkfc5TAchGjgyS4sLmZudualtbnYmS4sLA1UEh8/7HKaDiYXAkdmeVGXVAk4z73OYDtVaG7qGbqPRqK2urg5dBgAAp1xVXW6tjXa3G84BAACdhGgAAOgkRAMAQCchGgAAOgnRAADQSYgGAIBOQjQAAHQSogEAoJMQDQAAnYRoAADoJEQDAEAnIRoAADrdM3QBALdz6cpGllfWs7k1ztn5uSwtLuT8w+eGLosp4j0I3IoQDRxbl65s5MLFtYyvXU+SbGyNc+HiWpIIMRwJ70FgL4ZzAMfW8sr6S+Fl2/ja9SyvrA9UEdPGexDYixANHFubW+Oudjhs3oPAXoRo4Ng6Oz/X1Q6HzXsQ2IsQDRxbS4sLmZudualtbnYmS4sLA1XEtPEeBPZiYiFwbG1P3LIyAkPxHgT2Uq21oWvoNhqN2urq6tBlAABwylXV5dbaaHe74RwAANBJiAYAgE5CNAAAdBKiAQCgkxANAACdhGgAAOh0oBBdVa+qqo9W1ecm37/lFvssVNUndnx9tap+fLLtJ6tqY8e2Rw9SDwAAHIWDfhL9ZJKPtdYeTPKxyfObtNbWW2tvbK29Mcm/n+QPk3xoxy5/d3t7a+0jB6wHAADuuoOG6MeSfGDy+ANJzr/M/t+b5P9prf32AV8XAAAGc9Dbfr+2tfZ8krTWnq+q17zM/m9P8gu72t5VVT+cZDXJX2utfeWANQFT7NKVDbdo5ra8R4DD8LKfRFfVr1TVs7f4eqznharqFUl+IMn/taP5p5P8mSRvTPJ8kr99m+OfqKrVqlp98cUXe14amBKXrmzkwsW1bGyN05JsbI1z4eJaLl3ZGLo0jgnvEeCwvGyIbq19X2vt22/x9eEkX6qqe5Nk8v2F2/yotyX5jdbal3b87C+11q631v4oyT9I8qbb1PFUa23UWhudOXNmv78fMEWWV9Yzvnb9prbxtetZXlkfqCKOG+8R4LAcdEz000neOXn8ziQfvs2+78iuoRzbAXziB5M8e8B6gCm2uTXuamf6eI8Ah+WgIfo9SR6pqs8leWTyPFV1tqpeWmmjqr5psv3iruP/VlWtVdUnk3x3kp84YD3AFDs7P9fVzvTxHgEOy4FCdGvty621722tPTj5/ruT9s3W2qM79vvD1tq3ttZ+b9fxP9Rae6i19mdbaz+wPUkR4E4sLS5kbnbmpra52ZksLS4MVBHHjfcIcFgOujoHwLGxvcKClRfYi/cIcFiqtTZ0Dd1Go1FbXV0dugwAAE65qrrcWhvtbj/omGgAAJg6QjQAAHQSogEAoJMQDQAAnYRoAADoJEQDAEAnIRoAADq52Qow9S5d2XDzjRPM+QOGIEQDU+3SlY1cuLiW8bXrSZKNrXEuXFxLEkHsBHD+gKEYzgFMteWV9ZcC2LbxtetZXlkfqCJ6OH/AUIRoYKptbo272jlenD9gKEI0MNXOzs91tXO8OH/AUIRoYKotLS5kbnbmpra52ZksLS4MVBE9nD9gKCYWAlNte/KZ1R1OJucPGEq11oauodtoNGqrq6tDlwEAwClXVZdba6Pd7YZzAABAJyEaAAA6CdEAANBJiAYAgE5CNAAAdLLEHUCnS1c2LKl2l/i3BU4KIRqgw6UrG7lwcS3ja9eTJBtb41y4uJYkwt4B+bcFThLDOQA6LK+svxTyto2vXc/yyvpAFZ0e/m2Bk0SIBuiwuTXuamf//NsCJ4kQDdDh7PxcVzv7598WOEmEaIAOS4sLmZudualtbnYmS4sLA1V0evi3BU4SEwsBOmxPcLOCxOHzbwucJNVaG7qGbqPRqK2urg5dBgAAp1xVXW6tjXa3G84BAACdDOcAOALTehORaf29gdNPiAa4y6b1JiLT+nsD08FwDoC7bFpvIjKtvzcwHYRogLtsWm8iMq2/NzAdhGiAu2xabyIyrb83MB2EaIC7bFpvIjKtvzcwHUwsBLjLpvUmItP6ewPTwc1WAI6h47g03HGsCeBu2+tmKz6JBjhmjuPScMexJoAhGRMNcMwcx6XhjmNNAEM6UIiuqr9cVZ+qqj+qqm/4mHvHfm+tqvWqeq6qntzR/qqq+mhVfW7y/VsOUg/AaXCnS8NdurKRt7znV/P6J/9J3vKeX82lKxuHtr/l6gBudtBPop9N8niSj++1Q1XNJPmpJG9L8oYk76iqN0w2P5nkY621B5N8bPIcYKrdydJw28MtNrbGafnj4RZ7BePe/S1XB3CzA4Xo1tpnWmsv9//y3pTkudba51trX0vywSSPTbY9luQDk8cfSHL+IPUAnAZ3sjRc73CL3v0tVwdws6OYWHguyRd3PL+a5M2Tx69trT2fJK2156vqNXv9kKp6IskTSXL//fffpVIBhncnS8P1DrfobbdcHcDNXjZEV9WvJPm2W2z66621D+/jNeoWbd3r6rXWnkryVHJjibve4wFOkvMPn+sKqGfn57JxiwB8u2EYPfvfSU0Ap9nLDudorX1fa+3bb/G1nwCd3Pjk+XU7nt+XZHPy+EtVdW+STL6/0FM8ADf0DrcwPAPgYI5iibtnkjxYVa+vqlckeXuSpyfbnk7yzsnjdybZbzAHYIfzD5/Lux9/KOfm51JJzs3P5d2PP7TnJ8e9+wNwswPdsbCqfjDJ/5zkTJKtJJ9orS1W1dkk72utPTrZ79Ekfy/JTJL3t9b+x0n7tyb5h0nuT/L/JvnLrbXffbnXdcdCAACOwl53LHTbbwAA2MNeIdodCwEAoJMQDQAAnYRoAADoJEQDAEAnIRoAADoJ0QAA0EmIBgCATkI0AAB0EqIBAKCTEA0AAJ2EaAAA6CREAwBAJyEaAAA6CdEAANCpWmtD19Ctql5M8tsDvPSrk/zOAK/LH3MOhuccDM85GJ5zMDznYHjTcg7+dGvtzO7GExmih1JVq6210dB1TDPnYHjOwfCcg+E5B8NzDoY37efAcA4AAOgkRAMAQCchus9TQxeAc3AMOAfDcw6G5xwMzzkY3lSfA2OiAQCgk0+iAQCgkxC9T1X11qpar6rnqurJoeuZNlX1/qp6oaqeHbqWaVVVr6uqf1ZVn6mqT1XVjw1d07Spqn+rqv51Vf3m5Bz890PXNI2qaqaqrlTVPx66lmlUVV+oqrWq+kRVrQ5dzzSqqvmq+kdV9dlJn/Dnh65pCIZz7ENVzST5rSSPJLma5Jkk72itfXrQwqZIVf2FJH+Q5Gdba98+dD3TqKruTXJva+03quqbk1xOct7fwdGpqkryytbaH1TVbJJfS/JjrbVfH7i0qVJV/3WSUZI/1Vr7i0PXM22q6gtJRq21aVif+Fiqqg8k+RettfdV1SuSfFNrbWvgso6cT6L3501Jnmutfb619rUkH0zy2MA1TZXW2seT/O7QdUyz1trzrbXfmDz+/SSfSXJu2KqmS7vhDyZPZydfPgk5QlV1X5L/OMn7hq4FhlBVfyrJX0jyM0nSWvvaNAboRIjer3NJvrjj+dUID0yxqnogycNJ/u+BS5k6k6EEn0jyQpKPttacg6P195L8N0n+aOA6pllL8stVdbmqnhi6mCn07yR5Mcn/NhnW9L6qeuXQRQ1BiN6fukWbT3+YSlX1J5P8YpIfb619deh6pk1r7Xpr7Y1J7kvypqoyvOmIVNVfTPJCa+3y0LVMube01r4jyduS/JXJcD+Ozj1JviPJT7fWHk7yb5JM5VwxIXp/riZ53Y7n9yXZHKgWGMxkHO4vJvm51trFoeuZZpP/ffrPk7x12EqmyluS/MBkTO4Hk3xPVf0fw5Y0fVprm5PvLyT5UG4MueToXE1ydcf/BftHuRGqp44QvT/PJHmwql4/GUD/9iRPD1wTHKnJpLafSfKZ1trfGbqeaVRVZ6pqfvJ4Lsn3JfnsoEVNkdbahdbafa21B3KjH/jV1tp/PnBZU6WqXjmZ2JzJEILvT2LVpiPUWvv/knyxqhYmTd+bZConmN8zdAEnQWvt61X1riQrSWaSvL+19qmBy5oqVfULSb4ryaur6mqSv9la+5lhq5o6b0nyQ0nWJmNyk+S/a619ZLiSps69ST4wWTHoTyT5h601y6wxTV6b5EM3/ps+9yT5+dbaLw1b0lT6q0l+bvLB4ueT/MjA9QzCEncAANDJcA4AAOgkRAMAQCchGgAAOgnRAADQSYgGAIBOQjQAAHQSogEAoJMQDQAAnf5/16oQfHlihb0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = linspace(0, 2*pi)\n",
    "figure(99)\n",
    "# What does 99 do?\n",
    "# See with external \"tk\" display of figures,\n",
    "# as with `%matplotlib tk`\n",
    "plot(x, sin(x))\n",
    "figure(figsize=(12,8))\n",
    "plotmessage = plot(x, cos(x), 'o')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Decorating the Curves\n",
    "\n",
    "Curves can be decorated in different ways.  We have already seen some options, and there are many more.\n",
    "One can specify the color, line styles like dashed or dash-dot instead of solid, many different markers, and to have both markers and lines.\n",
    "As seen above, this can be controlled by an optional text string argument after the arrays of data for a curve:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure()\n",
    "plot(x, sin(x), '*-')\n",
    "plotmessage = plot(x, cos(x), 'r--')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These three-part curve specifications can be combined:\n",
    "in the following, `plot` knows that there are two curves each specified by three arguments, not three curves each specified by just an \"x-y\" pair:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure()\n",
    "plotmessage = plot(x, sin(x), 'g-.', x, cos(x), 'm+-.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name=Exercise-A></a>\n",
    "### Exercise A: Explore ways to refine your figures\n",
    "\n",
    "There are many commands for refining the appearance of a figure after its initial creation with `plot`.\n",
    "Experiment yourself with the commands `title`, `xlabel`, `ylabel`, `grid`, and `legend`.\n",
    "\n",
    "Using the functions mentioned above, produce a refined version of the above sine and cosine graph, with:\n",
    "\n",
    "- a *title* at the top\n",
    "- *labels* on both axes\n",
    "- a *legend* identifying each curve\n",
    "- a *grid* or \"graph paper\" background, to make it easier to judge details like where a function has zeros."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name=Exercise-B></a>\n",
    "### Exercise B: Saving externally displayed figures to files\n",
    "\n",
    "Then work out how to save this figure to a file (probably in format PNG), and turn that in, along with the file used to create it.\n",
    "\n",
    "This ismost readily done with externally displayed figures; that is, with `%matplotlib tk`.\n",
    "Making that change to `tk` in a notebook requires then restarting the kernel for it to take effect; use the menu *Kernel* above and select \"Restart Kernel and Run All Cells ...*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For your own edification, explore other features of externally displayed figures, like zooming and panning: this cannot be done with inline figures."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Getting help from the documentation\n",
    "\n",
    "For some of these, you will probably need to read up. For simple things, there is a function `help`, which is best used in the IPython interactive input window (within Spyder for example), but I will illustrate it here.\n",
    "\n",
    "The entry for `plot` is unusually long! It provides details about all the options mentioned above, like marker styles.\n",
    "So this might be a good time to learn how to clear the output in a cell, to unclutter the view: either use the above menu \"Edit* or open the menu with Control-click or right-click on the code cell; then use \"Clear Outputs\" to remove the output of just the current cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "help(plot)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The jargon used in `help` can be confusing at first; fortunately there are other online sources that are more readable and better illustrated, like http://scipy-lectures.github.io/intro/matplotlib/matplotlib.html mentioned above.\n",
    "\n",
    "However, that does not cover everything; the official pyplot documentation at http://matplotlib.org/1.3.1/api/pyplot_api.html is more complete: explore its search feature."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## P. S. A shortcut revealed: the IPython \"magic\" command pylab\n",
    "\n",
    "So far I have encourage you to use explicit, specific import commands, because this is good practice when developing larger programs.\n",
    "However, for quick interactive work in the IPython command window and Jupyter notebooks, there is a sometimes useful shortcut: the IPython \"magic\" command\n",
    "\n",
    "    %pylab\n",
    "adds everything from Numpy and the main parts of Matplotlib, including all the items imported above. (This creates the so-called **pylab** environment: that name combines \"Python\" with \"Matlab\", as its goal is to produce an environment very similar to Matlab.)\n",
    "\n",
    "Note that such \"magic\" commands are part of the IPython interactive interface, not Python language commands, so they must be used either in a IPython notebook or in the IPython command window (within Spyder), not in a Python \".py\" file."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, there is a way to access magics in python scripts; the above can be achieved in such a file with:\n",
    "\n",
    "    get_ipython().run_line_magic('pylab', '')\n",
    "and the magic\n",
    "\n",
    "    %matplotlib inline\n",
    "is achieved with\n",
    "\n",
    "    get_ipython().run_line_magic('matplotlib', 'inline')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
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