numpy_basics.ipynb

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   "source": [
    "import numpy, scipy, matplotlib.pyplot as plt, pandas, librosa"
   ]
  },
  {
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   "source": [
    "[&larr; Back to Index](index.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
    }
   },
   "source": [
    "# NumPy and SciPy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "The quartet of NumPy, SciPy, Matplotlib, and IPython is a popular combination in the Python world. We will use each of these libraries in this workshop."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "notes"
    }
   },
   "source": [
    "## Tutorial"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "[NumPy](http://www.numpy.org) is one of the most popular libraries for numerical computing in the world. It is used in several disciplines including image processing, finance, bioinformatics, and more.  This entire workshop is based upon NumPy and its derivatives.\n",
    "\n",
    "If you are new to NumPy, follow this [NumPy Tutorial](http://wiki.scipy.org/Tentative_NumPy_Tutorial).\n",
    "\n",
    "[SciPy](http://docs.scipy.org/doc/scipy/reference/) is a Python library for scientific computing which builds on top of NumPy. If NumPy is like the Matlab core, then SciPy is like the Matlab toolboxes. It includes support for linear algebra, sparse matrices, spatial data structions, statistics, and more.\n",
    "\n",
    "While there is a [SciPy Tutorial](http://docs.scipy.org/doc/scipy/reference/tutorial/index.html), it isn't critical that you follow it for this workshop."
   ]
  },
  {
   "cell_type": "markdown",
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    }
   },
   "source": [
    "## Special Arrays"
   ]
  },
  {
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   "execution_count": 28,
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4]\n"
     ]
    }
   ],
   "source": [
    "print(numpy.arange(5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
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     "slide_type": "subslide"
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.  0.5 1.  1.5 2.  2.5 3.  3.5 4.  4.5]\n"
     ]
    }
   ],
   "source": [
    "print(numpy.linspace(0, 5, 10, endpoint=False))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0. 0. 0. 0. 0.]\n"
     ]
    }
   ],
   "source": [
    "print(numpy.zeros(5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1. 1. 1. 1. 1.]\n"
     ]
    }
   ],
   "source": [
    "print(numpy.ones(5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
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     "slide_type": "subslide"
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 1.]\n",
      " [1. 1.]\n",
      " [1. 1.]\n",
      " [1. 1.]\n",
      " [1. 1.]]\n"
     ]
    }
   ],
   "source": [
    "print(numpy.ones((5,2)))"
   ]
  },
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   "cell_type": "code",
   "execution_count": 33,
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   "outputs": [
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     "name": "stdout",
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     "text": [
      "[ 0.01520245  0.31760492  0.48029266  0.52087331 -1.01995976]\n"
     ]
    }
   ],
   "source": [
    "print(numpy.random.randn(5)) # random Gaussian, zero-mean unit-variance"
   ]
  },
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   "execution_count": 34,
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     "text": [
      "[[-0.70059077  1.21971537]\n",
      " [-1.990304    0.11238149]\n",
      " [ 0.92774587  0.57935903]\n",
      " [ 0.18602804  1.14806358]\n",
      " [ 1.173989    0.23839278]]\n"
     ]
    }
   ],
   "source": [
    "print(numpy.random.randn(5,2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Slicing Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
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     "slide_type": "subslide"
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2 3]\n"
     ]
    }
   ],
   "source": [
    "x = numpy.arange(10)\n",
    "print(x[2:4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9\n"
     ]
    }
   ],
   "source": [
    "print(x[-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "The optional third parameter indicates the increment value:"
   ]
  },
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 2 4 6]\n"
     ]
    }
   ],
   "source": [
    "print(x[0:8:2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4 3]\n"
     ]
    }
   ],
   "source": [
    "print(x[4:2:-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "If you omit the start index, the slice implicitly starts from zero:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3]\n"
     ]
    }
   ],
   "source": [
    "print(x[:4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4 5 6 7 8 9]\n"
     ]
    }
   ],
   "source": [
    "print(x[:999])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[9 8 7 6 5 4 3 2 1 0]\n"
     ]
    }
   ],
   "source": [
    "print(x[::-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Array Arithmetic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
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     "slide_type": "subslide"
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2. 3. 4. 5. 6.]\n"
     ]
    }
   ],
   "source": [
    "x = numpy.arange(5)\n",
    "y = numpy.ones(5)\n",
    "print(x+2*y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "notes"
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   },
   "source": [
    "`dot` computes the dot product, or inner product, between arrays or matrices."
   ]
  },
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   "execution_count": 43,
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     "slide_type": "subslide"
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.7717245984355092\n"
     ]
    }
   ],
   "source": [
    "x = numpy.random.randn(5)\n",
    "y = numpy.ones(5)\n",
    "print(numpy.dot(x, y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
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     "slide_type": "subslide"
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   "outputs": [
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     "text": [
      "[[-1.38872379 -1.38872379]\n",
      " [-0.43601265 -0.43601265]\n",
      " [-2.43252325 -2.43252325]\n",
      " [-1.88940286 -1.88940286]\n",
      " [-2.11360515 -2.11360515]]\n"
     ]
    }
   ],
   "source": [
    "x = numpy.random.randn(5,3)\n",
    "y = numpy.ones((3,2))\n",
    "print(numpy.dot(x, y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Boolean Operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
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     "slide_type": "subslide"
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ True  True  True  True  True False False False False False]\n"
     ]
    }
   ],
   "source": [
    "x = numpy.arange(10)\n",
    "print(x < 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ True False False False False False False False False False]\n"
     ]
    }
   ],
   "source": [
    "y = numpy.ones(10)\n",
    "print(x < y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Distance Metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
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    "slideshow": {
     "slide_type": "subslide"
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.0\n",
      "25.0\n",
      "7\n",
      "4\n"
     ]
    }
   ],
   "source": [
    "from scipy.spatial import distance\n",
    "print(distance.euclidean([0, 0], [3, 4]))\n",
    "print(distance.sqeuclidean([0, 0], [3, 4]))\n",
    "print(distance.cityblock([0, 0], [3, 4]))\n",
    "print(distance.chebyshev([0, 0], [3, 4]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "The cosine distance measures the angle between two vectors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
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     "slide_type": "subslide"
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n",
      "1.0\n"
     ]
    }
   ],
   "source": [
    "print(distance.cosine([67, 0], [89, 0]))\n",
    "print(distance.cosine([67, 0], [0, 89]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Sorting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "NumPy arrays have a method, `sort`, which sorts the array *in-place*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
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     "slide_type": "subslide"
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.36507228  0.42198342 -0.29441486  0.12176386 -0.31285356]\n",
      "[-0.31285356 -0.29441486  0.12176386  0.36507228  0.42198342]\n"
     ]
    }
   ],
   "source": [
    "x = numpy.random.randn(5)\n",
    "print(x)\n",
    "x.sort()\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "`numpy.argsort` returns an array of indices, `ind`, such that `x[ind]` is a sorted version of `x`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
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     "text": [
      "[ 1.47703112  0.22232594 -0.99845825  1.24360623  0.9456978 ]\n",
      "[2 1 4 3 0]\n",
      "[-0.99845825  0.22232594  0.9456978   1.24360623  1.47703112]\n"
     ]
    }
   ],
   "source": [
    "x = numpy.random.randn(5)\n",
    "print(x)\n",
    "ind = numpy.argsort(x)\n",
    "print(ind)\n",
    "print(x[ind])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "[&larr; Back to Index](index.html)"
   ]
  }
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