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    "## Introduction to Scientific Computing\n",
    "### Lecture 05: Introduction to Data Visualization with Matplotlib\n",
    "#### J.R. Gladden, Spring 2018, Univ. of Mississippi"
   ]
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   "source": [
    "Matplotlib has become a robust and industry standard library for plotting in Python. Since we are working here in a Ipython notebook, we can use the %matplolib \"magic\" to display the graphical output on the browser page (inline), or popup in external windows using a variety of graphical backends (osx, gtk, qt, ...),"
   ]
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     "text": [
      "Warning: Cannot change to a different GUI toolkit: wx. Using qt4 instead.\n"
     ]
    }
   ],
   "source": [
    "%matplotlib wx"
   ]
  },
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "# Define a few functions to plot:\n",
    "\n",
    "def expdecay(x,lam=1.,A=1.):\n",
    "    return A*np.exp(-x*lam)\n",
    "\n",
    "def dampedsine(x,lam=1.,k=1.,A=1.):\n",
    "    apass=A\n",
    "    lampass=lam\n",
    "    return expdecay(x,lam=lampass,A=apass)*np.sin(k*x)\n",
    "\n",
    "def gauss(x,A=1.,sig=1.,x0=5.):\n",
    "    return A*np.exp(-(x-x0)**2/sig)\n",
    "\n",
    "#Lets close any open windows:\n",
    "plt.close('all')\n",
    "\n",
    "\n",
    "# Now create an array of x values\n",
    "\n",
    "x=np.arange(0,10,0.02)\n",
    "\n",
    "# Make the first plot using a green line \n",
    "plt.plot(x,dampedsine(x,lam=0.4,k=10),'g-')\n",
    "plt.title(\"A damped sine curve\")\n",
    "plt.xlabel(\"Time (s)\")\n",
    "plt.ylabel(\"Amplitude (m)\")\n",
    "#Won't pop up until you tell it to:\n",
    "plt.show()\n"
   ]
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   "source": [
    "We can add a second curve by simply adding another plot command. Note we adding 2 new curves here."
   ]
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       "[<matplotlib.lines.Line2D at 0x12540f750>]"
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   "source": [
    "plt.plot(x,expdecay(x,lam=0.4),'b--')\n",
    "plt.plot(x,-expdecay(x,lam=0.4),'b--')"
   ]
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   "cell_type": "code",
   "execution_count": 5,
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   "source": [
    "plt.figure(1)\n",
    "plt.plot(x,np.sin(10*x))\n",
    "\n",
    "plt.figure(2,figsize=(12,8)) #(size in inches wide,high)\n",
    "plt.plot(x,dampedsine(x,k=10)*gauss(x))\n",
    "\n",
    "#Make figure 1 active and save it to a file\n",
    "plt.figure(1)\n",
    "plt.savefig('test.png')\n",
    "\n",
    "plt.show()"
   ]
  },
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   "source": [
    "Plotting multiple data sets. We're also are adding a legend - note how we are dynamically updating the legend text based on the current parameters."
   ]
  },
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   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
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   "source": [
    "t=np.linspace(0,10,100)\n",
    "def V(t,RC):    \n",
    "   return 10*np.exp(-t/RC)\n",
    "RCvals=[0.1,1.0,2.0,4.0,10.0]\n",
    "markers=['o','s','^','+','D']\n",
    "for i in range(len(RCvals)):\n",
    "    marker=markers[i]    \n",
    "    RC=RCvals[i]    \n",
    "    plt.plot(t,V(t,RC),'b-'+marker, label='RC=%2.1f'%RC)\n",
    "plt.legend(loc=1)\n",
    "plt.xlabel('Time (s)', fontsize=16)\n",
    "plt.ylabel('Potential (V)',fontsize=16)\n",
    "plt.show()"
   ]
  },
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   "source": [
    "Best to use two different axes if your data sets have a large difference in scales."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
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   "source": [
    "plt.close('all')\n",
    "x=np.linspace(0,10,100)\n",
    "y1=np.sqrt(x)\n",
    "y2=x**3\n",
    "plt.plot(x,y1,'g-',lw=2,label='Sqrt(x)')\n",
    "plt.ylabel('Sqrt(x)')\n",
    "plt.legend(loc=2)\n",
    "ax2=plt.twinx()\n",
    "plt.plot(x,y2,'b--',lw=2,label='x^3')\n",
    "plt.ylabel('x^3')\n",
    "plt.xlabel('x')\n",
    "plt.legend(loc=4)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "This is how you do subplots. The subplot triple number (like 221) means a subplot 2x2 grid and the next plot command will go to the 1st plot in the grid."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
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   "source": [
    "x=np.linspace(-np.pi,np.pi,100)\n",
    "plt.subplot(221)\n",
    "plt.plot(x,np.sin(x))\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Sin(x)')\n",
    "plt.subplot(222)\n",
    "plt.plot(x,np.cos(x))\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Cos(x)')\n",
    "plt.subplot(223)\n",
    "plt.plot(x,np.tan(x))\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Tan(x)')\n",
    "plt.subplot(224)\n",
    "plt.plot(x,np.cosh(x))\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Cosh(x)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "** Fancy Stuff:** Adding arrows, add text annotations, even Latex equations!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
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   "source": [
    "plt.close('all')\n",
    "x=np.linspace(0,np.pi,100)\n",
    "plt.fill_between(x,np.tan(x),y2=0,lw=2,color='green')\n",
    "plt.annotate('A pole',xy=(np.pi/2.0,50), xytext=(0.25,10), \n",
    "             fontsize=16,arrowprops=dict(facecolor='blue',shrink=0.05))\n",
    "plt.text(2,40,'$\\int_0^\\pi \\mathrm{tan}(x) = 0$',fontsize=25)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "** Polar Plots: ** "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
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   "source": [
    "theta=np.arange(0,2*np.pi,np.pi/100)\n",
    "r1=3+np.sin(4*theta)\n",
    "r2=3+np.sin(6*theta)\n",
    "plt.polar(theta,r1)\n",
    "plt.polar(theta,r2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "** Quiver (Vector) Plots: ** These are 2D plots of a vector field.  So every point in the 2D space needs to have a vector (magnitude and direction) associated with it.  This requires generating a 'meshgrid' in the 2D space.  Also take care about the length of the vectors since they can vary wildly and obscure the story you are trying to tell."
   ]
  },
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   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
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    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x12adea490>"
      ]
     },
     "execution_count": 19,
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   ],
   "source": [
    "plt.close('all')\n",
    "gridvec=np.linspace(0,2*np.pi,50) \n",
    "x,y=np.meshgrid(gridvec,gridvec) # Make a uniform square mesh of 2D points.  Outputs 2 2D arrays.\n",
    "U=np.sin(y) # function for the 'x' component of the vector\n",
    "V=np.cos(x) # function for the 'y' component\n",
    "plt.quiver(x,y,U,V,np.sqrt(U**2+V**2)) # The last argument scales the color by the magnitude.\n",
    "plt.title('Vector (quiver) plot of V_x=sin(x), V_y=cos(y)', fontsize=20)\n",
    "plt.xlabel('x',fontsize=20)\n",
    "plt.ylabel('y',fontsize=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "plt.quiver?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
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   "source": [
    "** Interacting with plots: ** Matplotlib does provide tools for interacting with plots to make them more dynamic.  This requires capturing an 'event' (such as a click, button press, or mouse movment) and adjusting something on the plot when that event occurs.  This is rather basic \"event handling\" but sufficient for a lot of what we do as scientists.  This example plots a bunch of gaussians centered on where a user clicks in the plot area.  It also takes in some button clicks to clear of quit (and close the window).  ** NOTE: **  This **sometimes** works in the iPython notebook, but should work fine when run in Canopy or directly in the iPython command line."
   ]
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   "cell_type": "code",
   "execution_count": 28,
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   "source": [
    "plt.close('all')\n",
    "\n",
    "\n",
    "def click(event):\n",
    "    col=(np.random.rand(),np.random.rand(),np.random.rand())   #set a random RGB tuple for the current curve color\n",
    "    #OR could use: col=tuple(rand(3))\n",
    "    xClick,yClick= event.xdata, event.ydata  # grab the x,y coordinates of the click (floats)\n",
    "    plt.plot(x,gauss(x,A=yClick,x0=xClick),color=col)\n",
    "    plt.draw()\n",
    "\n",
    "def done(event1):\n",
    "    if event1.key == 'q': close('all')  \n",
    "    if event1.key == 'c': \n",
    "        plt.clf()\n",
    "        plt.plot([0],[0])        #clears existing graphs\n",
    "        plt.axis([0, 10, 0, 1])\n",
    "        plt.draw()\n",
    "# Define x values\n",
    "x=np.linspace(0,10,100)\n",
    "#now register the event to the above function\n",
    "cid = plt.connect('button_press_event',click)\n",
    "cid1= plt.connect('key_press_event',done)\n",
    "\n",
    "plt.title(\"Click anywhere in the graph to draw a new Gaussian.  \\n Type 'q' to quit\")\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Y\")\n",
    "plt.plot([0],[0])        #clears existing graphs\n",
    "plt.axis([min(x), max(x), 0, 1])\n",
    "plt.show()"
   ]
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   "execution_count": 26,
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    {
     "ename": "AttributeError",
     "evalue": "'module' object has no attribute 'random'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0mTraceback (most recent call last)",
      "\u001b[0;32m<ipython-input-26-2286aee8b50f>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrandom\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m: 'module' object has no attribute 'random'"
     ]
    }
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