Python Course Lecture 5 Matrices.ipynb

{
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   "metadata": {
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    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "from IPython.display import Image, HTML\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Introduction to Scientific Programming in Python\n",
    "\n",
    "## Python Course Lecture 5: Matrices and Image Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# A Matrix is a Multi-Dimensional Array.\n",
    "  - 1D Array: A **Row** of **Elements**\n",
    "  - 2D Array: A **Column** of **Rows** of **Elements**\n",
    "  - 3D Array: A **Sheet** of **Columns** of **Rows** of **Elements**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1, 2, 3], [4, 5, 6], [7, 8, 9]]"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]\n",
    "A\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## NumPy Arrays Understand Lists of Lists to be 2D!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6],\n",
       "       [7, 8, 9]])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "mat = np.array(A)\n",
    "mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 5, 10, 15],\n",
       "       [20, 25, 30],\n",
       "       [35, 40, 45]])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat * 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## New Array Properties: Shape, ndim"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**array.ndim**: The number of dimensions an array has."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat.ndim"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**array.shape**: The length in each dimension of the array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 3)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Transposing a Matrix\n",
    "Transposing a matrix means swapping the first and second axis, flipping it along its diagonal.  In NumPy, there is an equivalent **array.transpose()** method and an **array.T** property.  There's also the more general **array.swapaxes()** method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 4, 7],\n",
       "       [2, 5, 8],\n",
       "       [3, 6, 9]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat.transpose()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 4, 7],\n",
       "       [2, 5, 8],\n",
       "       [3, 6, 9]])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 4, 7],\n",
       "       [2, 5, 8],\n",
       "       [3, 6, 9]])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat.swapaxes(0, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Many Math Functions work on a default axis, which can be modified using the \"axis\" keyword argument."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.0"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(mat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4.,  5.,  6.])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(mat, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.,  5.,  8.])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(mat, axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## By default, NumPy will remove unnecessary dimensions.  To turn off this behavior, set  \"keepdims\" to True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.],\n",
       "       [ 5.],\n",
       "       [ 8.]])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(mat, axis=1, keepdims=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Indexing and Slicing Multidimensional Arrays: Rows, then Columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6],\n",
       "       [7, 8, 9]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# mat[0], mat[:,0], mat[0, :], mat[0, 0], mat[0][0], mat[:, [0]]\n",
    "mat[0][1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Array Broadcasting Applies across the Highest Dimension"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "mat[np.array([True, True, False])]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1,  40, 700],\n",
       "       [  2,  50, 800],\n",
       "       [  3,  60, 900]])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat.T * [1, 10, 100]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Reshaping arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_shape = (3, 4)\n",
    "B = np.arange(12).reshape((3, 4))\n",
    "B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.]])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros(new_shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## For Matrix (Dot) Multiplication, use numpy.dot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"https://www.mathsisfun.com/algebra/images/matrix-multiply-a.gif\" width=\"300\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(url=\"https://www.mathsisfun.com/algebra/images/matrix-multiply-a.gif\", width=300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (<ipython-input-65-6fd3df724377>, line 1)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;36m  File \u001b[1;32m\"<ipython-input-65-6fd3df724377>\"\u001b[1;36m, line \u001b[1;32m1\u001b[0m\n\u001b[1;33m    A_dot = A @ A.T\u001b[0m\n\u001b[1;37m              ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m invalid syntax\n"
     ]
    }
   ],
   "source": [
    "A_dot = A @ A.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Other Key Matrix Functions can be found in numpy.linalg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### numpy.linalg.norm: Length of a vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.4721359549995796"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm([2, 4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### numpy.linalg.inv: Inverse of the Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1. ,  1. ],\n",
       "       [ 1.5, -1. ]])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.inv([[2, 2], [3, 2]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Cross Product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-3,  6, -3])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.cross(mat[:, 0], mat[:, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Diagonal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 5, 9])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat.diagonal()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Alternative to np.array: np.matrix\n",
    "Arrays can do everything, but numpy also has a matrix type for doing matrix math specifically.  This can be formed using **np.matrix**, **np.mat**, or **np.asmatrix**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[2, 3],\n",
       "        [2, 2]])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M = np.matrix([[2, 3], [2, 2]])\n",
    "M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[10, 12],\n",
       "        [ 8, 10]])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Matrix objects do matrix multiplication by default\n",
    "M * M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[-1. ,  1.5],\n",
       "        [ 1. , -1. ]])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Matrix inversion is also easier!\n",
    "M.I"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 3],\n",
       "       [2, 2]])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Convert back to array:\n",
    "np.array(M)\n",
    "M.getA()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Visualizing Matrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.3359663807,  0.0022161774,  1.2006316976],\n",
       "       [-0.3578795743,  0.4400112299,  0.5494289088],\n",
       "       [ 1.0960110649,  0.5616341139,  0.6446998002],\n",
       "       [ 0.3500686213,  0.8417919824,  0.7610858836],\n",
       "       [ 1.2896489464,  0.6961206804,  0.3441509424]])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.linspace(0, 4 * np.pi, 50)\n",
    "signal = np.array([np.sin(x), np.sin(x), np.cos(x)]).T\n",
    "noise = np.random.randn(*signal.shape) * .4\n",
    "data = signal + noise\n",
    "data[:5, :]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## numpy.set_printoptions(suppress=True, precision=2)\n",
    "Makes the numbers print differently, without changing their actual values.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.34,  0.  ,  1.2 ],\n",
       "       [-0.36,  0.44,  0.55],\n",
       "       [ 1.1 ,  0.56,  0.64],\n",
       "       [ 0.35,  0.84,  0.76],\n",
       "       [ 1.29,  0.7 ,  0.34]])"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.set_printoptions(suppress=True, precision=2)\n",
    "data[:5, :]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## plt.imshow() displays matrix values using color values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7f835c45a610>"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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/min2mqcItHGeJ90y88467x8D3ps+309y2XBLuPMUgQ1jbUA+3HmKgC9POLnpwp2ETiy6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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f835c5c1a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(data[:12, :], interpolation='nearest')\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Color-value mappings are represented by a \"colormap\"\n",
    "There are lots of pre-made colormaps out there, each serving different purposes!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"http://www.astrouw.edu.pl/~jskowron/python/cmap_all.png\" width=\"600\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(url=\"http://www.astrouw.edu.pl/~jskowron/python/cmap_all.png\", width=600)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Quick Discussion: Colormaps Can Be Misleading when Used Inappropriately"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7f835c05fb50>"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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XAv+c9Mj6gDvM7D5JjwN3SboC2EnlyixmtlXSXcBWYBq4yoOdcy4ETQ9pnXMu\nr7pSl1bShyQ9LenHyXA4CJJuSSqeP1m1LtgEa0nLJT0g6SlJWyR9NgdtHpD0SJLE/pSkL4be5qQN\nPZJ+KGl9TtrrPxaoxcw6ulAJsj+hMuG5ANgEvK3T7ajTtnOAM4Anq9bdAPxx8vjzwPXJ49OAJ6gM\n81clf5M63N5lwBnJ42EqldjfFnKbk3YsSv7dC2wE1uagzb8P/D2wPvTPRdKOZ6nMq1evC7rNnVi6\n0cM7C9huZjvNbBq4k0oSc9eZ2UPAK7NWZ06wbhcz22Nmm5LH48A2YHnIbQYws4PJwwEqX4CvEHCb\nJS0HLgL+rmp1sO1NtOXHAnnXjYA3OzF5F2EnJi+xHCRYS1pFpXe6kcCTwpPh4RPAHmCDmW0l7DZ/\nCfgjXpvOFnJ7wX8sUJPfLaV5wV3lkTQM3A18zirpQ/OcFD6/rJKxukbSKHCvpHXMeyL7/JD068Be\nM9uUtLOeINpbpQM/FsifbvTwdgMrqp4vT9aFaq+kpQBJgvVLyfrdwElV23Xl75DURyXY3W5m9ySr\ng27zYWY2BnwTeDfhtnktcLGkZ4H/C3xA0u3AnkDbC4CZvZj8+2Xg61SGqKGe447pRsB7DDhF0kpJ\n/cBlwPoutKMe8dpfNq0HLk8efwK4p2r9ZZL6Ja0GTgEe7VQjq3wF2GpmX65aF2ybJR1/+OqgpIXA\n+VQmzINss5lda2YrzOxkKp/VB8zs48A3QmwvVH4skPT6SX4scAGwhUDPcUd140oJ8CEqVxS3A1d3\n+8pNVbu+BrwATALPAZ8EjgXuT9p7H3BM1fbXULmitQ24oAvtXUvltrObqASNHybn9riA2/zOpJ1P\nAJuB/5asD7bNVe34VY5epQ22vcDqqs/ElsP/j4Xc5k4tnnjsnItGVxKPnXOuGzzgOeei4QHPORcN\nD3jOuWh4wHPORcMDnnMuGh7wnHPR8IDnnIvG/wcDGbdTne5IJAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f835c6c4e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sines = np.repeat(np.matrix(np.sin(np.linspace(0, 5 * np.pi, 500))), 500, axis=0)\n",
    "plt.imshow(sines, cmap='magma')\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Tip: Use 'viridis', 'magma',  instead of the default 'jet' colormap. \n",
    "\n",
    "For More Info on perception and colormaps: \n",
    "  - https://bids.github.io/colormap/\n",
    "  - https://jakevdp.github.io/blog/2014/10/16/how-bad-is-your-colormap/\n",
    "  - http://web.stanford.edu/~mwaskom/software/seaborn/tutorial/color_palettes.html\n",
    "  - http://matplotlib.org/users/colormaps.html\n",
    "  - http://www.husl-colors.org/  \n",
    "  \n",
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Correlation Matrices!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.  ,  0.73,  0.07],\n",
       "       [ 0.73,  1.  ,  0.09],\n",
       "       [ 0.07,  0.09,  1.  ]])"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_corr = np.corrcoef(data, rowvar=False)\n",
    "data_corr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7f835be44f50>"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f835bf4c150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(data_corr, interpolation='nearest', cmap='gray')\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Discussion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}