04_numpy.ipynb

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    "# Configuration for the slideshow, DO NOT RUN if you aren't presenting this\n",
    "from traitlets.config.manager import BaseJSONConfigManager\n",
    "path = \"/home/quickbeam/anaconda3/envs/cogsys-python-intro/etc/jupyter/nbconfig\"\n",
    "cm = BaseJSONConfigManager(config_dir=path)\n",
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   "source": [
    "# Numpy\n",
    "\n",
    "- Basis for most scientific computing libraries\n",
    "- Lots of linear algebra and random numbers\n",
    "- Sacrifices some of Python's flexibility for speed\n",
    "- Claim: C-like speed with Python-like simplicity"
   ]
  },
  {
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   "source": [
    "## Installation\n",
    "- Comes with scientific Python distributions such as Anaconda\n",
    "- Simple for Unix/Mac: `pip install numpy`\n",
    "- Can be troublesome for Windows: Download from http://www.lfd.uci.edu/%7Egohlke/pythonlibs/ instead"
   ]
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  {
   "cell_type": "markdown",
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   "source": [
    "## Arrays\n",
    "\n",
    "The basic \"unit\" in numpy are arrays (think tables). Arrays can be created from \"array-like\" Python objects such as lists or tuples:"
   ]
  },
  {
   "cell_type": "code",
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   "source": [
    "import numpy as np\n",
    "\n",
    "np.array([1,2,3,4,5,6])"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "Arrays can have more than one dimension:"
   ]
  },
  {
   "cell_type": "code",
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   "metadata": {},
   "outputs": [],
   "source": [
    "np.array([[1,2,3],[4,5,6]])"
   ]
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  {
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   "metadata": {
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   "outputs": [],
   "source": [
    "a = np.array([[(1,), [2]], [[3], [4]]])"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "Other than Python lists, you can't just put \"anything\" into arrays -- they have a *dtype*. A default is chosen depending on the elements:\n",
    "- any element is a float: dtype float64\n",
    "- all elements are integers: dtype int32\n",
    "- dtype can be specified when creating the array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.array([1,2.,3]).dtype"
   ]
  },
  {
   "cell_type": "code",
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   "metadata": {},
   "outputs": [],
   "source": [
    "np.array([1,2,3], dtype=\"float32\")"
   ]
  },
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   "outputs": [],
   "source": [
    "np.array([1.7, 2.3], dtype=\"int32\")"
   ]
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     "slide_type": "-"
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   "source": [
    "There is also an *object* dtype -- with it, we can create e.g. *arrays of arrays* which is very different from a 2D array!"
   ]
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  {
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   "outputs": [],
   "source": [
    "a = np.array([[1,2,3], [4,5]])\n",
    "print(a)\n",
    "print(a.dtype)"
   ]
  },
  {
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   "source": [
    "There are also numerous functions to create some \"default\" arrays (note the dtypes!!):"
   ]
  },
  {
   "cell_type": "code",
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   "metadata": {},
   "outputs": [],
   "source": [
    "np.zeros((2, 5))"
   ]
  },
  {
   "cell_type": "code",
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   "metadata": {},
   "outputs": [],
   "source": [
    "np.ones(7, dtype=\"int32\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "outputs": [],
   "source": [
    "np.arange(0, 18, step=0.5)"
   ]
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   "source": [
    "# this is preferred; with arange, stick to integer steps\n",
    "np.linspace(0, 18, num=21)"
   ]
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   "cell_type": "code",
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   "source": [
    "a = np.asarray([[1,2,3],[4,5,6]])  # does not copy data\n",
    "np.full_like(a, fill_value=12.4)"
   ]
  },
  {
   "cell_type": "code",
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   "source": [
    "np.full_like(a, fill_value=12.4, dtype=\"float32\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "Don't mix up *full* and *fill*:"
   ]
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  {
   "cell_type": "code",
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   "outputs": [],
   "source": [
    "a = np.full((3, 2), fill_value=5)\n",
    "print(a)\n",
    "a.fill(100)\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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   "outputs": [],
   "source": [
    "np.empty((11, 4))"
   ]
  },
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    }
   },
   "source": [
    "## Array Attributes\n",
    "\n",
    "We have already seen the `dtype` attribute. Here are some more important ones:"
   ]
  },
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   "outputs": [],
   "source": [
    "big_array = np.zeros((12, 9, 11, 24, 7))\n",
    "big_array.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "big_array.shape"
   ]
  },
  {
   "cell_type": "code",
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   "outputs": [],
   "source": [
    "big_array.size"
   ]
  },
  {
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   "source": [
    "big_array.itemsize"
   ]
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   "source": [
    "The shape of an array can be modified after creation:"
   ]
  },
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   "outputs": [],
   "source": [
    "a = np.array([[1,2,3],[4,5,6]])\n",
    "print(a.shape)\n",
    "a_r = a.reshape((6, 1))\n",
    "print(a_r.shape)\n",
    "print(a.shape)"
   ]
  },
  {
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   "outputs": [],
   "source": [
    "a.resize((3, 2))\n",
    "print(a.shape)\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   },
   "outputs": [],
   "source": [
    "print(a.ravel())\n",
    "print(a.ravel(order=\"F\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a.reshape((100,3))"
   ]
  },
  {
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   "metadata": {
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   "outputs": [],
   "source": [
    "a.reshape((-1, 3, 2, 1, 1, 1, 2, 1))"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "## Combining arrays\n",
    "\n",
    "The following operations require copying the array data every time they are called which can lead to massive run time increases. Try to use them only with list comprehensions, or *preallocate* an array with the correct shape and then fill it instead."
   ]
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   "outputs": [],
   "source": [
    "a = np.array([[1,2,3],[4,5,6]])\n",
    "b = np.array([[7,8,9]])\n",
    "np.concatenate((a,b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.concatenate((a,b), axis=1)"
   ]
  },
  {
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   "metadata": {
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   "outputs": [],
   "source": [
    "c = np.array([[7,8,9], [10,11,12]])\n",
    "np.stack(a,c)"
   ]
  },
  {
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   "outputs": [],
   "source": [
    "np.stack((a,c), axis=0)"
   ]
  },
  {
   "cell_type": "code",
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    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.stack((a,c), axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.stack((a,c), axis=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Don't use: `vstack, hstack, dstack`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.append(a, [7,8,9])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.append(a, [[7,8,9]], axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.append(a, [[7],[8]], axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## More **FUN** Array Operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.tile(a, reps=[2,4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.repeat(np.arange(5), 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.repeat(a, 2, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.flip(a, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
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   },
   "outputs": [],
   "source": [
    "np.roll(a, shift=2, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "why = np.arange(20)[:, None, None, None, None].repeat(2, axis=3)\n",
    "why.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "why.squeeze().shape"
   ]
  },
  {
   "cell_type": "markdown",
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     "slide_type": "slide"
    }
   },
   "source": [
    "## Indexing\n",
    "\n",
    "Indexing works a lot like Python lists, but is somewhat more complex."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a1 = np.arange(20)\n",
    "a2 = a1.reshape((4, 5))\n",
    "a1 = a1[::-1]\n",
    "print(a1)\n",
    "print(a2)"
   ]
  },
  {
   "cell_type": "code",
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   "metadata": {
    "collapsed": true,
    "slideshow": {
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   "outputs": [],
   "source": [
    "a1[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a2[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a2[1,3]"
   ]
  },
  {
   "cell_type": "code",
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   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
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   },
   "outputs": [],
   "source": [
    "a2[:, 1:4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "a2[..., 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a1[0:1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "*Slicing* arrays as above returns *views* of the array, meaning that **no data is copied**!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "orig = np.array([[1,2,3],[4,5,6]])\n",
    "a_slice = orig[:, 1]\n",
    "print(a_slice)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a_slice[0] = 10999\n",
    "print(a_slice)\n",
    "print(orig)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Advanced Indexing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Index arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "inds = [3, 3, 2, 4, 1]\n",
    "a1[inds]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a2[[0, 3, 1, 1]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "a2[[0, 3, 1, 1], [2, 3, 1, 2]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a2[[0, 3, 1, 1], 0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note the difference!!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "print(\"Basic:\")\n",
    "print(a2[0, 1])\n",
    "print(\"Advanced:\")\n",
    "print(a2[[0, 1]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Be *very* careful with tuples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a2[(0, 1)]  # basic indexing!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Super-advanced:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a2[[[0, 0,], [3, 3]], [[0, 4], [0, 4]]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Boolean Indices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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    "collapsed": true
   },
   "outputs": [],
   "source": [
    "bools = a1 > 10\n",
    "bools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a1[bools]"
   ]
  },
  {
   "cell_type": "code",
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   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "bools2 = a2 % 2 == 0\n",
    "print(bools2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a2[bools2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a2[np.array([True, True, False])]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Using index arrays or boolean indices *copies* the data!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "orig = np.array([[1,2,3],[4,5,6]])\n",
    "a_slice = orig[[0, 1], [1, 1]]\n",
    "print(a_slice)"
   ]
  },
  {
   "cell_type": "code",
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   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "a_slice[0] = 10999\n",
    "print(a_slice)\n",
    "print(orig)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "However, we can still use index/boolean arrays for modifying arrays:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "orig[[0, 1], [1, 1]] = 2000\n",
    "print(orig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "orig[:, 1] = [500, -31]\n",
    "print(orig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "orig[orig > 5] = 0\n",
    "print(orig) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Array Math and Broadcasting\n",
    "\n",
    "Most operations involving arrays are *element-wise*. This includes multiplication!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = np.array([[1,2,3],[4,5,6]])\n",
    "b = np.array([[6,5,4],[3,2,1]])\n",
    "a + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a * b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "What happens in these cases?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a * 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a + 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Turns out arrays are automatically *broadcast* to compatible dimensions, if possible. Let's we what we can do with this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a + np.array([1, 2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a + np.array([1,2,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a + np.array([[1], [2]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "a = np.arange(1,6)\n",
    "# all these result in the same:\n",
    "b = a[:, None]\n",
    "b = a[:, np.newaxis]\n",
    "b = a.reshape(a.shape + (1,))\n",
    "print(a)\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "a*b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a*b.reshape((1, 5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Common Array Operations\n",
    "\n",
    "Many common mathematical functions are implemented already (again, generally applied element-wise)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = np.array([[1,2,3],[4,5,6]])\n",
    "b = np.array([[6,5,4],[3,2,1]])\n",
    "np.exp(a)  # or sin, cos, ..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Matrix multiplication requires us to call a function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.dot(a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "b.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.dot(a, b.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "inner_prod = np.dot([1,2,3], [4,5,6])\n",
    "print(inner_prod)\n",
    "print(type(inner_prod))\n",
    "print(inner_prod.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "There are many summary operations for arrays:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a.max(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a.max(axis=1, keepdims=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Many functions can be called as array methods or as \"regular\" functions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "print(np.max(a))\n",
    "print(np.reshape(a, (1, 6)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Other important functions: min(), mean(), sum(), argmax()..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Logic\n",
    "\n",
    "We've seen that comparison operators such as > work fine element-wise. What about boolean logic?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = np.array([True, True, False])\n",
    "b = np.array([False, True, True])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "a and b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Turns out Python tries to convert the arrays to scalar truth values, but it's unclear how this should be done."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "np.logical_and(a, b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Comparing arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.array([1,2,3])\n",
    "b = np.array([1,2,3])\n",
    "a == b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.all(a == b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "a = np.array([0.3, 0.3], dtype=\"float64\")\n",
    "b = np.array([0.1, 0.1], dtype=\"float64\")\n",
    "b = 3*b\n",
    "np.all(a == b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(a)\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Never use \"true\" equality for floating point numbers!! This applies to all programming in all languages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.allclose(a, b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Random numbers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.standard_normal((5, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.uniform(-2, 3, (2, 4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "np.random.seed(5)\n",
    "np.random.uniform(-2, 3, (2,4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# quick access to uniform [0, 1)\n",
    "np.random.random((3,))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.rand(3,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "np.random.randint(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.randint(-2, 3, (3, 5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "a = np.arange(20)\n",
    "np.random.choice(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.choice(20, size=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.choice(a, size=10, replace=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.choice([0, 100], size=20, replace=True, p=[0.9, 0.1])"
   ]
  }
 ],
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