{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Einops tutorial, part 1: basics\n",
    "\n",
    "<!-- <img src='http://arogozhnikov.github.io/images/einops/einops_logo_350x350.png' height=\"80\" /> -->\n",
    "\n",
    "## Welcome to einops-land!\n",
    "\n",
    "We don't write \n",
    "```python\n",
    "y = x.transpose(0, 2, 3, 1)\n",
    "```\n",
    "We write comprehensible code\n",
    "```python\n",
    "y = rearrange(x, 'b c h w -> b h w c')\n",
    "```\n",
    "\n",
    "\n",
    "`einops` supports widely used tensor packages (such as `numpy`, `pytorch`, `chainer`, `gluon`, `tensorflow`), and extends them.\n",
    "\n",
    "## What's in this tutorial?\n",
    "\n",
    "- fundamentals: reordering, composition and decomposition of axes\n",
    "- operations: `rearrange`, `reduce`, `repeat`\n",
    "- how much you can do with a single operation!\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Preparations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Examples are given for numpy. This code also setups ipython/jupyter\n",
    "# so that numpy arrays in the output are displayed as images\n",
    "import numpy\n",
    "from utils import display_np_arrays_as_images\n",
    "display_np_arrays_as_images()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load a batch of images to play with"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(6, 96, 96, 3) float64\n"
     ]
    }
   ],
   "source": [
    "ims = numpy.load('./resources/test_images.npy', allow_pickle=False)\n",
    "# There are 6 images of shape 96x96 with 3 color channels packed into tensor\n",
    "print(ims.shape, ims.dtype)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": []
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# display the first image (whole 4d tensor can't be rendered)\n",
    "ims[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGAAAABgCAIAAABt+uBvAAAEc0lEQVR4nO2cS0wTURSGZ/oAS2gxIkpLK6SgsqBGaEREMRobnxETBTS+mhh14U6BhRtNE1cmBo0rIxoTRDe6Qkk04gN5GIpYCEEBY6xOMdEiPoBWoeCCjUbpuaP3Ucn5tj1z5s+XO7czt70jD0wOSMj0aEQHiHV0Qs7a/7z/WvW1xw2PFb8SDoWTU5IdeY6N2zbu2LtDH6cXEmk6ZM6X2Pdv308ePVlzoWZiYuL3T9MWpJ29cnbl2pU8I0WHq6BwKFzmKmtvaY9So9Vqz1w6U+Yu45YqOlznoPKD5dHtSJIUiUQqD1V6m718IoHwG0E+r29z/mbC4qXLlta31TPNQwi/EVR7sZa82Of1dT/rZheGHH6Cmu83q6pvvNfIKIkq+AkKvAmoqldeK4ySqIKToNGR0bGxMVWHfBr6xCaLOjgJMiQYdDp1N6WmJBOjMKrgJEiWZbPVrOoQa7qVURhV8JuDVq1bpaq+yFXEKIkq+AnafXA3ebEjz7HEuYRdGHL4CXIWOIt3FpNU6nQ6T5VHlmXWkUjg+qhRdbkqb3le9BqNRnP6wumC1QV8IoFwFWRIMNx4cGPPoT0azZ/Pa7aar9+5vuvALp6posN7uWOKvp6+2ou1TfebAv5AKBRKTkl25Do2bNtQsq8kLj6Of54oiBH0H4FLrgAoCAAFAaAgABQEQO1nn3fKO6fNSavbFHWtdc4Cyj3VgiMIAAUBoCAAFASAggBQEAAKAkBBACgIAAUBUHvUMFvNhGtvH4Mfc1JyaJ2XNTiCAFAQAAoCQEEAKAgABQGgIAAUBICCAFAQAAoCQEEAKAgABQGgIAAUBICCAAQIipH/9xIiQJBWq+V/0r9GgCCdnnQhPDIeYZqEBAGC4mfFE1aODI8wTUKCmEss0ZhIUhl8H2QdBkTMt9jsObNJynq7exkHgREjaL5lPklZy8MW1klAxAgi3Czn8/pevnjJOkx0xAiyL7QTVnrKPUyTgIgRlO3IJqxsqG84fuQ4uCF4fHz80d1HlYcr3Vvd/5zuF8RsZlH8Sn5GPnl9RmaG+4i7aF2RxWYxJhnDofDXz18DbwPKa6Wnq6fjSYfP65u6JzCajL2faU7twnb7rMhc4X/lZ9G5Q+lITUul1U3Yw+r64vWMOvf19FHsJkxQ6f5SRp1niKCc3BxGG1P7n/dT7CZyPajCU8Gi7QwZQZIkFa4pLNlXQr3tzBEkSdKp86eysrPo9hwaHBr8MEirm2BBpiRTze0ai81Cty3FQSR+TTrdnn6r9RbFF1Ho4/QUF5LEC5IkKTUtta61rsJTYUgw/Esfi81y7MQxr9/r2uKilS229s0H3werz1XfvHpT1euqbBk21xbXpu2bCtcUTvdOh78mtgRNMTk52fW0q62prbO90//KP/B2YPjLcGg0JMtyoinRaDLOnTfXvsieuTgzKzsrNz+X+hT2M7EoKKaIiTkolkFBACgIAAUBoCAAFASAggBQEAAKAkBBACgIAAUBoCAAFASAggBQEAAKAkBBAD8ASE42MDbjHwUAAAAASUVORK5CYII=\n",
      "text/plain": []
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# second image in a batch\n",
    "ims[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# we'll use three operations\n",
    "from einops import rearrange, reduce, repeat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": []
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# rearrange, as its name suggests, rearranges elements\n",
    "# below we swapped height and width.\n",
    "# In other words, transposed first two axes (dimensions)\n",
    "rearrange(ims[0], 'h w c -> w h c')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Composition of axes\n",
    "transposition is very common and useful, but let's move to other capabilities provided by einops"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": []
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# einops allows seamlessly composing batch and height to a new height dimension\n",
    "# We just rendered all images by collapsing to 3d tensor!\n",
    "rearrange(ims, 'b h w c -> (b h) w c')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": []
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# or compose a new dimension of batch and width\n",
    "rearrange(ims, 'b h w c -> h (b w) c')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(96, 576, 3)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# resulting dimensions are computed very simply\n",
    "# length of newly composed axis is a product of components\n",
    "# [6, 96, 96, 3] -> [96, (6 * 96), 3]\n",
    "rearrange(ims, 'b h w c -> h (b w) c').shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(165888,)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# we can compose more than two axes. \n",
    "# let's flatten 4d array into 1d, resulting array has as many elements as the original\n",
    "rearrange(ims, 'b h w c -> (b h w c)').shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Decomposition of axis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 3, 96, 96, 3)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# decomposition is the inverse process - represent an axis as a combination of new axes\n",
    "# several decompositions possible, so b1=2 is to decompose 6 to b1=2 and b2=3\n",
    "rearrange(ims, '(b1 b2) h w c -> b1 b2 h w c ', b1=2).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": []
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# finally, combine composition and decomposition:\n",
    "rearrange(ims, '(b1 b2) h w c -> (b1 h) (b2 w) c ', b1=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMAAAAEgCAIAAABtjetmAAAdt0lEQVR4nO2dZ1hUV7eAD52BGbrSi1QloigQBbEriAoaQdSoQUyMsST6icYkKgYTNerntWE0GklUJBbUIIiKaIAoNkSK0i3A0JE2wAxt5v7weby5KLBn9j5nZsh6H5/8MGvWXjIvp+yqICovp4CeSTc2lnYJMo2itAsA5BsQCMACBAKwAIEALEAgAAsQCMACBAKwAIEALEAgAAsQCMACBAKwAIEALEAgAAsQCMACBAKwAIEALEAgAAsQCMACBAKwAIEALEAgAAsQCMACBAKwUJZi223t7Q/S01Pu38/KzS188aK8qqq5paWtvZ2lrq7BYhno6Q2ysLC2sHBzdvZwdbWxspJiqVKh7OXLx0lJOWlpJYWF3OfPeQ0NgpYWoVDI0tTU4HCMLCws7Ozshg1zGT/e3tlZUVE61wIF5hcWikSiG0lJkRcvxty40dzSgvgpu0GDAv38ggID7QYNorW8bjC/sLD81av406fjIyOLCwoQP6Ktrz81MNA3KGjoqFG01vYujAokFApPR0fvOnw4t7BQsgyKior+M2ZsXbfuAwcHsrX1BJMCvcjJObF9e8K5c8KuLskyOHt6fh4aOmrqVLKF9QJzAj1IT1/13XePs7LwU6moqIQsX741JERdTQ0/W+8wIxC/peVoaGjUgQMSq/NPxvv5bQwPNzQ3x0/VJ0wIJBQKdxw8+P3evV0kfjpvcR0+/HJEhBnNXzADAuWlp38dEFD28iXBnBocztaIiCkBAQRzvhfan7xa+XzfoKAtu3eTtYeiqLTMTDcfn/znz8mmZZjrUVHBY8aQtYeiqFYeb+PcuYc3bSKb9l3oFai+sXFKYGD8rVs05a+srp48d+7LkhKa8tPNnydObFm8uF0goCl/xI4du7/8kqbkb6BRIEFbm19Q0L3Hj+lrgqKossrKWcHBfNq+A/q4cfbsj8uWCYVCWls5Fx5+4Ouv6ctPo0CLv/zyzsOH9OV/S3Zu7trQUAYaIkhOWlrY0qUikYiBtk7t2RN36hRNyekS6PBvv0XHxdGU/F2ORUbeffSIseYwaW1u/jogoI3PZ6zF7cuXF+fn05GZFoHyioo2/PADHZl74ctNm5j5hcZn//r1FcXFTLbYLhCELV1Kx+2SFoHWbNnC/EPJk6dPryYmMtyoBOQ+fnzp2DHm281MTb1Kw42MfD9Q3M2bvkFB6PFaHI7/9OlTxo0b6eSkr6uro6XVyOPV1tU9zcuLv3Xr8rVrDU1NiKnGjR6dfOmSRFX3CPF+oJVTpz4QR3Q1FmvszJle8+ZZDR480NRURVW1pry8qrQ0JTY24dy5GnG+PhMrq0v5+SqqquJX3SPkBXKdNg2xu1lJSWnDihVfr1qlq63dU0x9Y+P2Awf2HTuGePktTE21JTrsSlagrHv3gj080OPdvb23RkQMMDF57//t6uw8FhYWsXMnev916IkTs5YuRS+gTwjfwm7fuYNoD4fNvnr69M7vvuvFHoqidLW1/xsaGn38OOKoxdk//0QJkxbnwsPRgxevXx9+/XpP9lAUpaSsvOKHH/bHxioqKSHmjD5yBL0AFAgLdCgiAiVMQUEhMjzce8IExLQf+fgc3rkTJfLytWuIOZmn8fXrW9HRiMGT/f3X7N6NEjnGx2fNrl2IaXPS0vKfPEEMRoGkQI1NTddu30aJXLZwoZ+Xl1jJl86f7zV+fJ9hGc+eNSI/MzFMUkxMR3s7SqSWnl7oiRMKCgqImReFhAweORIx+DbRx0SSAv15/Xobwg9ITVX1+5AQCfJvWLmyzxihUMhM76UEJCHfXj/dtInd6539XZYhd6WmxMaKlbl3SAqUkJyMEjZ98mRjQ0MJ8k9wd2dravYZRmTGCHGEQmHaX3+hRGqw2XNXrBA3/4RZs4wsLFAiCzIzG2prxc3fEyQFSk1LQwn7yMdHsvzKysojnZz6DMtBnsjHJC+ePWttbkaJHOfrq8ZiSdDEhFmzECNz0L4pFIgJVFVT86q0FCXSdfhwiVsxHDCgzxiJpzvSyjPkkZZJ/v6SNTF25kzESIICEZtUn1dUhBjpiPAsjENZZSWt+SWjBFlrR1dXyZqwd3ZGjCxF/rL6hNgVCPHywwB1DQ0dHR3SrqI7lWiDX2xtbWNLS8ma0Bs4UMfAAKkYcjOo+qFAIpGopq5O2lV0p4rLRQmztLfHacXc1hYlrBqtGBSICVTf2EgqFT4tra3SLqE7iE/QbB0dnFY0tbRQwvjIq6n6hJhArQzObukTgexNUBSgOc1GM6AnNDkcgsWgQEwgmZpUitKfyTCdaI9lkr3Ai/txxA5xFGBtPEOoqaujhGFOU0S8UWJq+k+ICaRBriZ8VIlOeSEC4neGaEBPtKCNA6rLoEAstN8wZlBVUZF2Cd1BHNviNTTgtIL4cXEH2nqBmEAGenqkUuGjqaEh7RK6Y2hmhhKG3t/4LiKRCHHmPMFVz8QEskT7ATGDHt7LMB0gjnQ21dXVVVVJ1gT3+XPE93PEYlAgNpRhhSx1ZWYmypBWP2PQkCGIkbnp6WMkGm9+hjyPxWrwYAnyvxdiVyD0/VbkdyUyDkNcXBAj/5Z0PV0i8nTHD9zcJGviXYgJpKejY29tjRJ5IymJVKNyhIW9PeKja0psrAQL3Fp5vLto03mVlJUdRowQN39PkOwH8kDz+ueTJ3l4L6vyiIKCwmi0fZ+qSkvR5y6+JWr/fsRNGpw9PVkI8/IQISmQL9oPqLq29ouNG+VlFSlBxvr6IkYeF3Ndb0Nt7an//hcxeBxyGSiQFGj65MkcNhslMury5c9CQmRw0gWtjPP1VUXrLct/8uTUnj2IaYVC4dYlSxC7EBUVFSdLOmHt/QkJ5lJXUwtEtjvi7Fk3H5+U+/dxWuzq6kpITg5asyZs716cPMygpas7de5cxOBD336L8kwjEon2rl175+pVxLTu06ZJPN/ovRAeCwv54gv0xSiZOTnj58wZO3v25WvXxBrMb2xqunj16pK1aw2HDfNesODUhQvp2dkS1cs081avRowUdnWt9fU9smVLV2dnTzFVXO7KqVPPHjqEXkAgwsoWsSC/tNn/s88uxceL+yl1NbVJnp4fOjs72ts72Nrq6+qyNTTYmpp8gaChqamhsfF1ff3TvLy0rKy0zMzcwsJuG+Y52Njk/f03uX/E/0F8bfxXM2bcFefnM8DExGvevHG+vkYWFgNMTDra26vLyl7m5iacO5cSGyvW7maOrq6nSW+CQ16glyUlH0yYwPDsDmVlZf6LF8rK5PdNJy5QfkbGIhcXujcmey/h16+7e3uTzUl+OscgC4tNa9YQT9s7nZ2dL+Skf9LB2XkezfsWvpcpAQHE7aFomg/0zerVkzw96cjcC3K0Xeuq7dvNbGyYbFFLT2+jOPs6oEOLQEpKSn/8/LOFqSkdyXsin9xSFbphaWruuXiRYG9e7ygqKe384w89iVYD952cjqQURQ00MLh94YKpkRFN+d9Fjq5AFEXZDx++7dQpZk5IWbN792gxt7JAh8Z/gI2V1V8XL5Ld7qkX5EsgiqImzZnDgEPLv/9+0bp19OWnt3q7QYMeXruGvg8QDnInEEVRPgsX/nT+PE33MkVFxa927fp861Y6kv9fK7RmpyhKV1v72pkzh3fs0EJbcSIx1bW16Lspyg6T/f1/S01FXBCIjpau7r4rV4Lo3GL8DUzcgxUUFFYuWZKTnLxs4UIVOmcry9Fz9D+xGzbsbGbmonXr0Heq651Jc+ZE5+R4zphBJFvvMH3gXDGXe/DEiciLF6vJbVEzQF9/lrd3wMyZkz09ifclMnxe2LGwsMQLFySequDs6bli2zbXiRPJFtYLUjixkKKozs7O63/9FZeYmJCcLNkERTVVVXdX14keHpM8Pd1dXJQI/e6+C/MnFpYWFV357bf4yEj0LRC0dHWnBgb6BQf38xML30tpeXnGs2eZz54VvHhRVllZVlFR39jIFwj4AoFIJNLU0HgzKMZhsy1MTQfb2r75M8zRkYHT5ihpCPSWV3l5j5OT89LTSwoLy1++bG5s5L89M5XNNrKwsLC3t3NyGjl+/OARI0jd/sRF+gLJOFIUSC6Apc0AFiAQgAUIBGABAgFYgEAAFiAQgAUIBGABAgFYgEAAFiAQgAUIBGABAgFYgEAAFiAQgAUIBGABAgFYgEAAFiAQgIVyBczY7JWR6dKuQLaBKxCABfkdmVAozC2M+jXq71t/c4u5Ar5Af4C+00inabOm+S/yV1GVuXNSgF5QKBcxuiqjva1963+2nv7l9Hu36DK1MN3/+/4xE8cwWVLvGKfDPb43GL2FCfiCgEkBJ4+c7GmDt7KSsvlT558/eZ7JqgAcGBUo5LOQtNQ+jrzv6urasGzDo7uE94IEaII5gTIeZVyOuowS2dHRsfU/9G5KApCCOYHOHD+DHpzxKOPpk6f0FQOQgjmB7t6+K1Z8SmIKTZUABGFOoLKSMrHiua+4NFUCEIQhgVpbWsU9WqWhvoGeWgCSMCQQS4Ml7tZPWtpaNBUDEIQhgRQUFIzNxOuRM7OUoVN8gZ5g7hnIc7J4e9ePnTKWpkoAgjAn0MeffYwe7DTSaZjLMPqKAUjBnEAuo1385vmhRCorK4ftC0M/dwyQIowOZeyL2Ddy1MjeYxQVFXf/snv0uNHMlARgwqhALA1W9F/RC5ct7Gl/f2Mz4z9u/DF/6XwmqwJwYHo6xxsKcgrOHD9z5/adsuIyPp+vP0DfaYST9yzvgMUBqmqqzNfTCzCdo3ekI5AcAQL1DkxpBbAAgQAsQCAACxAIwEI6qzKAd+G38QuKC4orirnVXG4Vt6ymjFvFramv4bfx+W38VkErX8Bv72xnqbE01DX0tPQsjS0tjS2dHZzdh7k72TopK0nnqyT2FlbBrXAxdyGS6i2x92JdRhPOKS70vYXxWnn3su49ePrgSd6TzILMVxWvJD5MXputPWvCrMCpgT4ePsycw/oWuAIxTQOvIfxc+NU7Vx89e9Ql7CKSs7G58VTcqVNxp2zNbdcvXr901lIVZYaW18EzENMUlRZtObLlfvZ9UvZ0S/7Fji9GfDwiJZ2hCcEgUD/k2fNnEz6fsOnwJonvieiAQP0TkUi0I2KH71pffhuf1oZAoP5M/N14v//40eoQCNTPSXyQuGjzIvryg0D9n0u3L/30+080JQeB/hVsPrz5Sf4TOjKDQP8KuoRdn//4OR0dByDQv4W0nLTI+EjiaYn1RBubGSOOitTV1g0dMJRUu/2YfSH77CzsDPUM9bT12Cw2W4OtqqLa1NJUWFKYkp4SGR+ZVZglVsIdETsWTV+kpEjyhHkYypBd5nvPN9I36vaXelp6o4aOGjV01IZPNly8dXHlTyur66oRExYUF1xJvvLRxI8IFgm3MDnGf7J/WmSarbkt+kciYiLI1gACyTfmhuY3Dt/QZmsjxl+7e62mvoZgASCQ3GNtar1n7R7E4C5hV8L9BIKtg0D9gWC/YHtLe8RgEAjojrKS8qalmxCD72aIt1Vc74BA/YQ5k+aoq6qjRL4oe8Fr5ZFqFwTqJ7A12D5jfFAiRSLR0yJiG5iCQP2Hia4TESOLK4pJNQoC9R+c7JwQI8tqxNvwtBdAoP7DMDvULbkqaytJNQoC9R/0tPQQF2O08FtINQoC9Ss4GhyUMIKTXEGgfoU2B2lMo72jnVSLIFC/QiQSoYSpqhDbxQsE6lc0tzajhKmpqpFqEQTqVyA+HWuyNEm1KAWBYP9emuC18hCfjgfqDiTVqBQEUlIiOaUSeEv+q3zEyIF68iyQsgrqPNquTvKrCPoxBSUFiJGWxpakGpWCQGrqqE9wLc3E+rv+DaDvyOFg6UCqUencwtgcNkpkbXUt3cX0J+LvxKOEcTQ4pgNNSTUqnbcwHT0dlLD8p6g3dSA1M7W0qhQl0u0DN4LtSkcgQxNDlLDUpFS6K+k3bD+xHTHSY7gHwXalIxDiYXIZjzKK8oroLqYfkPggMf4u0v2LEmfaEArSEcjazhoxMiwkjNZK+gGvyl/N/xb1eBpttvbYESRP8pOOQIOdBiNG3oq/9e3Kb/s8sLezszM5IXnD5xuCfIOwq5MVvtr91dPnfcw9vXHvhvsS99eNrxFzzhw7k+z+m9I5bIVbzP3Q6kP0eCsbq6CVQWMnjzUxN+FocwR8Aa+RV1Zaxn3FzcnKSb+fnvEo4807P0eLk99I8tGb+Da/aTlpbovFeIx1tHac4Tlj5OCRTrZOhvqG2mztFn5LeU35o5xHkfGRtx7eQhxAfcOto7cmuU0Sv+oekdppPe427sUviM3M/Sfp3HQj0+5LyiVG6gIRxM7CLv9SPtmhJKkNpnr5edGUuSAHtUP238Y3S74hPhApNYHmfjKXpswg0HuxNbf9ZOYnxNNKTaChI4bSdDBqYW4hHWnlnfCN4XScpyHN+UDrw9bTkRauQO+yeMZib3dvOjJLUyCPCR4BiwOIpwWBuuFk63Tk2yM0JZfyjMQfD/1oO1iM/ZFQqH9d/7oGtV+k32NhZHFl3xWCUxC7IWWBtLS1Tl89bWJuQjYtXITeYGNmk3w82crEir4mpD8n2tLaMu5e3DAX1FWVfaKiqgITiSiK8h3nmxaZRqs9lCwIRFGUkalR7L3Y9WHrWRosnDwm5ibrQtc9Kn40ZcYUUrVJkamjpkr23mRsYHz6h9NX9l3R4eiQLqo7snVufG117a8Hfr0YebGsRIzV/+ZW5lNmTPGZ4+MxwYP4eX1S7ImuSKgQCoUnYk5EJ0Yj7ujraO24KnBV0Mwg+h56uiFbAr1BJBJlPc56eOdhZlpm8Yvi8tLy5qZmfitfQUGBrcXmaHEMBhpY21vbONjYDrYd8eEI4o9Q/0S6Ar3d5re0qvTm/ZvpeelZhVkllSUNvIbm1mZ1NXWOBsfM0GzIoCEuQ1ymeUwjOFcVEVkUSKaQEYFkFpl4BgLkFxAIwAIEArAAgQAsQCAACxAIwAIEArAAgQAsQCAACxAIwAIEArAAgQAsQCAACxAIwAIEArAAgQAsYEJZHxCfUNbPgCsQgIUyVQG/Yb0yMl3aFcg0cAUCsACBACxAIAALEAjAAgQCsACBACxAIAALEAjAAgQCsACBACxAIAALEAjAAgQCsACBACxAIAALEAjAAgQCsACBACxAIAALEAjAAgQCsACBACxAIAAL8odo9kJVVXlJyUsut7isrITLLeZyi1+/ruHzWwUC/pv/CgR8kUjEYmmoq7MMDAaamVlaWFg7O7u5uLhbWdkwWaosUFRUev9+dk7Oi7y8VxUVtVVVdQ0NPIGgra2tQ0VFWVNTXVOTpanJYrM1LC2NbWzM3vwZOtTW0FCPsSIVysvFOLZeLIRCYUFBTmbmo6ys9JyczNzc7KamBomz2doOnj17wYIFS42NzcjV2DfGxowuLBSJRMnJ6efOJcTF/c3lVkmWxMrKZNy4kd7e7j4+Hrq6WmQr7AZ5gZqaGk6ePJKamvT48b3mZh7Z5CoqqgsWLF2/PszAYCDZzD3BmEAdHZ0RETH79p3Jzy8mlVNVVWX69DFffBHg5TWa+InxbyAvUGZmmo8P0mk0EqOrq79jR/isWfNpbeUNzAiUmPhg9epdBNXpRkTE1uBgPzoyy+VDdH396xUrFuzevUXahRBAKBR+880hL69V9NlDUZSdnQVNmRl9iCbL/v0/dnV1ffvtDmkXIjmdnV2LFm0+dy6B7oaGDqXrFUQur0BvOXRo54ULp6RdheQsX76dAXvMzAx1dDg0JZdvgSiK2rz5y4oKrrSrkITjxy9HRMQw0BB9lx+qHwjE4zWFha2XdhViU11dFxLyP8y0BQL1QWzs+dxcpEONZYddu07yeK3MtDV0qC19yfuDQCKRKCIiXNpViEFbW/tvv11hrDm4AvVNTMxZPp+hX2h8bt9+VF/fxExbioqKjo7W9OWX5mv8tm37bWwcjIxM9PQGsFgsFktDKBTW1laXlr5KTIy7dCmqsrIMMVVzMy81NWny5Om0FkyKpKTH6MF6elrz53uPHTvCzs7CzMxQU1OdxVIXCoUCQTuP11JeXsPlVmdnF2Vk5KekpNfWNnT7uLW1KYulRrL6/480BfLzmzdwYPdz0U1NLUxNLUaPHrdmzeZNm1ZHR59GzJaUdENeBMrOLkKMDA72O3hwA5ut0e3vlZQUVVSUORwNE5MBrq6Os2dPoChKJBKlp+fFxCT9+WfS2yZovX9RstyRyOFo7d//e3V1ZUrKTZT47Gy52U61rKwaJczPb3xExFb0tAoKCi4uQ1xchmzbtuL5c25MTFJMTLKzs4OkZSIhuwJRFKWoqLhr11EPD1uRqO8Bu4KCHAZKIkJLCx8l7OOPp0nchI2N2bp1i9atWyRxBkRk/SHa0tJ6zJhJKJENDXW1tUi/2VJHTU0VJayoqJTuSvCRdYEoipoyZQZiZGFhLq2VkAJxYGHv3siXL1FfI6SFHAjk4uKOGFlc/JzWSkgxeLAVSlh9fZO7+5KEhPs0l4OFHAj0wQfDESN5PIY6VzAZNWooYmRVVZ2396rZs0MePHhKa0kSIwcCqauzdHX1USJbWprpLoYIfn7jFRXF+MnHxCSNHh3k6rro6NHo168b6StMAuRAIIqijIxMUcKIz6ClCSMj/XnzvMT91OPHuStW7DQ29vLx+fLYsUtVVXV01CYu8iGQnh7SFai1VT6uQBRF7dixSrI5Oh0dndevpy5fvt3U1NvLa+Xvv8c2NbUQLw8d+RBIVRWpM16OhsOsrExOngzDmeje1SW8efNBcPD3hoZTAgK+vnTpdltbO8EKEZEPgdTU1FHCUPobZQc/v/Ghocvw8wgE7Rcv3vL332BuPn3r1qMM39rkQyDEK5Dc8f33yw8d+lpJicy3UFNTv23bcUvLGatX72JutJ+ZZoCeWL16XlzcAWNjA1IJ29raDx8+7+Awh5kpRyCQ9Jk2zSM///K6dYtUVIgNTdbU1C9dGvbJJ6Ht7R2kcr4XEEgm4HA09u79T05O9KpVge9O3pCY06evenmtamigsXcDBJIhbG3Nw8M3lpbGHziwwcNjOJHFyMnJjxcs+I6+1wsQSObQ0eF89dX8u3cjSkvj9+9fP2YMrknXr6fu3n2SVHndAIFkF1PTgWvWLLhzJ4LLvRYevnHKlFESPyRt3vwz+jRIsQCB5AATkwGrVgXevPlzTc2tqKjtc+dOEXeac2dn17Ztx+moDQSSJ7S12QsWTDt/fldVVeLx41uGD7dH/2xMTBIdnUMgkFzC4Wh89tnsJ0+izpzZjjim1tHRScfUIhBIjlFQUPj442kpKb8i3tEyMwuI1wACSQGhUEgwm5OT7fLl/iiRL1+WE2z3DSCQFLh3L9vObvYPP/xaXFxBJCHi2p2mJvLTXUAgKZCdXVhUVBoaemTQIN+JEz8/ejQacwi9sLCEVG3iAgJJgbddMiKRKCnp8YoVO01MvMePX3bw4FkJlvJcu3Z3//4olEg6tpmS6YWF/ZWsrMJufyMUClNS0lNS0tes2WNpaTxmzHBnZwdHR2tzc0MTkwGamix1dVWhUNTR0dnSwm9o4FVWvi4ursjMLEhIuJ+RkY/YrrU1+R2SQSAp8PRpb8uPiosriosroqKuE2/Xzc2ReE64hTFNaWkVrcPjPaGqqjJ+vAvxtCAQ09A0JtUnvr7jtLXZxNOCQEyTnd39AYgZNm4MoiMtCMQ07z5BM0BwsJ+b2wd0ZAaBmIb5W5iTk+3BgxtoSg4CMUpHRyetRxq8i6OjdULCzwSnyXYDBGIUHq9VrDkYmMyePeHevd+NjJDW9UoGCMQoenpaDx+eun//ZHCwn6Ymi76GLCyMoqK2X768V0tLk75WKBBIKowaNTQiYmtFRcKvv24ZN24k2ZO8nJ0dfvllU2HhnwsWSL5DHjrQEy01OByNTz+d/emns0tKKi9cSIyLS7l7N7Ojo1OCVEpKis7ODjNmeH700US6d9XsBo1HXvYPmDzyksdrffIkLyOj4Nmz56WlVWVl1dXVda2tgra2jvb2DiUlRVVVFXV1VR0djoGBjqGh/qBBJra25k5Odm5ujrTeEHsBBOoDhs9MlTvgGQjAAgQCsACBACxAIAALEAjAAgQCsACBACxAIAALEAjAAgQCsACBACxAIAALEAjAAgQCsACBACxAIAALEAjAAgQCsPhfPLVVQZtx0KkAAAAASUVORK5CYII=\n",
      "text/plain": []
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# slightly different composition: b1 is merged with width, b2 with height\n",
    "# ... so letters are ordered by w then by h\n",
    "rearrange(ims, '(b1 b2) h w c -> (b2 h) (b1 w) c ', b1=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": []
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# move part of width dimension to height. \n",
    "# we should call this width-to-height as image width shrunk by 2 and height doubled. \n",
    "# but all pixels are the same!\n",
    "# Can you write reverse operation (height-to-width)?\n",
    "rearrange(ims, 'b h (w w2) c -> (h w2) (b w) c', w2=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Order of axes matters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": []
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compare with the next example\n",
    "rearrange(ims, 'b h w c -> h (b w) c')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": []
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# order of axes in composition is different\n",
    "# rule is just as for digits in the number: leftmost digit is the most significant, \n",
    "# while neighboring numbers differ in the rightmost axis.\n",
    "\n",
    "# you can also think of this as lexicographic sort\n",
    "rearrange(ims, 'b h w c -> h (w b) c')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": []
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# what if b1 and b2 are reordered before composing to width?\n",
    "rearrange(ims, '(b1 b2) h w c -> h (b1 b2 w) c ', b1=2) # produces 'einops'\n",
    "rearrange(ims, '(b1 b2) h w c -> h (b2 b1 w) c ', b1=2) # produces 'eoipns'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Meet einops.reduce\n",
    "\n",
    "In einops-land you don't need to guess what happened\n",
    "```python\n",
    "x.mean(-1)\n",
    "```\n",
    "Because you write what the operation does\n",
    "```python\n",
    "reduce(x, 'b h w c -> b h w', 'mean')\n",
    "```\n",
    "\n",
    "if axis is not present in the output — you guessed it — axis was reduced."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": []
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# average over batch\n",
    "reduce(ims, 'b h w c -> h w c', 'mean')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": []
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# the previous is identical to familiar:\n",
    "ims.mean(axis=0)\n",
    "# but is so much more readable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": []
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Example of reducing of several axes \n",
    "# besides mean, there are also min, max, sum, prod\n",
    "reduce(ims, 'b h w c -> h w', 'min')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": []
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# this is mean-pooling with 2x2 kernel\n",
    "# image is split into 2x2 patches, each patch is averaged\n",
    "reduce(ims, 'b (h h2) (w w2) c -> h (b w) c', 'mean', h2=2, w2=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": []
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# max-pooling is similar\n",
    "# result is not as smooth as for mean-pooling\n",
    "reduce(ims, 'b (h h2) (w w2) c -> h (b w) c', 'max', h2=2, w2=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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O4R6fPIa1vkcI0clp1rrjJeVV1VcbGm+5t2nbLrhD5+i4RI7YSIQQnRBwBLocUqqBQUA0DAKiYRAQDYOAaBgERMMgIBoGAdEwCIhGqyfwf7gwZiWQVGKaAAAAAElFTkSuQmCC\n",
      "text/plain": []
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# yet another example. Can you compute result shape?\n",
    "reduce(ims, '(b1 b2) h w c -> (b2 h) (b1 w)', 'mean', b1=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "source": [
    "## Stack and concatenate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'list'> with 6 tensors of shape (96, 96, 3)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(6, 96, 96, 3)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# rearrange can also take care of lists of arrays with the same shape\n",
    "x = list(ims)\n",
    "print(type(x), 'with', len(x), 'tensors of shape', x[0].shape)\n",
    "# that's how we can stack inputs\n",
    "# \"list axis\" becomes first (\"b\" in this case), and we left it there\n",
    "rearrange(x, 'b h w c -> b h w c').shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(96, 96, 3, 6)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# but new axis can appear in the other place:\n",
    "rearrange(x, 'b h w c -> h w c b').shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# that's equivalent to numpy stacking, but written more explicitly\n",
    "numpy.array_equal(rearrange(x, 'b h w c -> h w c b'), numpy.stack(x, axis=3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(96, 576, 3)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ... or we can concatenate along axes\n",
    "rearrange(x, 'b h w c -> h (b w) c').shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# which is equivalent to concatenation\n",
    "numpy.array_equal(rearrange(x, 'b h w c -> h (b w) c'), numpy.concatenate(x, axis=1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Addition or removal of axes\n",
    "\n",
    "You can write 1 to create a new axis of length 1. Similarly you can remove such axis.\n",
    "\n",
    "There is also a synonym `()` that you can use. That's a composition of zero axes and it also has a unit length."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(6, 1, 96, 96, 1, 3)\n",
      "(6, 96, 96, 3)\n"
     ]
    }
   ],
   "source": [
    "x = rearrange(ims, 'b h w c -> b 1 h w 1 c') # functionality of numpy.expand_dims\n",
    "print(x.shape)\n",
    "print(rearrange(x, 'b 1 h w 1 c -> b h w c').shape) # functionality of numpy.squeeze"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": []
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compute max in each image individually, then show a difference \n",
    "x = reduce(ims, 'b h w c -> b () () c', 'max') - ims\n",
    "rearrange(x, 'b h w c -> h (b w) c')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Repeating elements\n",
    "\n",
    "Third operation we introduce is `repeat`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(96, 5, 96, 3)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# repeat along a new axis. New axis can be placed anywhere\n",
    "repeat(ims[0], 'h w c -> h new_axis w c', new_axis=5).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(96, 5, 96, 3)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# shortcut\n",
    "repeat(ims[0], 'h w c -> h 5 w c').shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": []
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# repeat along w (existing axis)\n",
    "repeat(ims[0], 'h w c -> h (repeat w) c', repeat=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": []
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# repeat along two existing axes\n",
    "repeat(ims[0], 'h w c -> (2 h) (2 w) c')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": []
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# order of axes matters as usual - you can repeat each element (pixel) 3 times \n",
    "# by changing order in parenthesis\n",
    "repeat(ims[0], 'h w c -> h (w repeat) c', repeat=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: `repeat` operation covers functionality identical to `numpy.repeat`, `numpy.tile` and actually more than that."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Reduce ⇆ repeat\n",
    "\n",
    "reduce and repeat are like opposite of each other: first one reduces amount of elements, second one increases.\n",
    "\n",
    "In the following example each image is repeated first, then we reduce over new axis to get back original tensor. Notice that operation patterns are \"reverse\" of each other"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "repeated = repeat(ims, 'b h w c -> b h new_axis w c', new_axis=2)\n",
    "reduced = reduce(repeated, 'b h new_axis w c -> b h w c', 'min')\n",
    "assert numpy.array_equal(ims, reduced)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fancy examples in random order\n",
    "\n",
    "(a.k.a. mad designer gallery)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": []
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# interweaving pixels of different pictures\n",
    "# all letters are observable\n",
    "rearrange(ims, '(b1 b2) h w c -> (h b1) (w b2) c ', b1=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": []
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# interweaving along vertical for couples of images\n",
    "rearrange(ims, '(b1 b2) h w c -> (h b1) (b2 w) c', b1=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": []
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# interweaving lines for couples of images\n",
    "# exercise: achieve the same result without einops in your favourite framework\n",
    "reduce(ims, '(b1 b2) h w c -> h (b2 w) c', 'max', b1=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": []
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# color can be also composed into dimension\n",
    "# ... while image is downsampled\n",
    "reduce(ims, 'b (h 2) (w 2) c -> (c h) (b w)', 'mean')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": []
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# disproportionate resize\n",
    "reduce(ims, 'b (h 4) (w 3) c -> (h) (b w)', 'mean')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": []
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# spilt each image in two halves, compute mean of the two\n",
    "reduce(ims, 'b (h1 h2) w c -> h2 (b w)', 'mean', h1=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": []
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# split in small patches and transpose each patch\n",
    "rearrange(ims, 'b (h1 h2) (w1 w2) c -> (h1 w2) (b w1 h2) c', h2=8, w2=8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": []
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# stop me someone!\n",
    "rearrange(ims, 'b (h1 h2 h3) (w1 w2 w3) c -> (h1 w2 h3) (b w1 h2 w3) c', h2=2, w2=2, w3=2, h3=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": []
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rearrange(ims, '(b1 b2) (h1 h2) (w1 w2) c -> (h1 b1 h2) (w1 b2 w2) c', h1=3, w1=3, b2=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": []
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# patterns can be arbitrarily complicated\n",
    "reduce(ims, '(b1 b2) (h1 h2 h3) (w1 w2 w3) c -> (h1 w1 h3) (b1 w2 h2 w3 b2) c', 'mean', \n",
    "       h2=2, w1=2, w3=2, h3=2, b2=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": []
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# subtract background in each image individually and normalize\n",
    "# pay attention to () - this is composition of 0 axis, a dummy axis with 1 element.\n",
    "im2 = reduce(ims, 'b h w c -> b () () c', 'max') - ims\n",
    "im2 /= reduce(im2, 'b h w c -> b () () c', 'max')\n",
    "rearrange(im2, 'b h w c -> h (b w) c')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": []
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# pixelate: first downscale by averaging, then upscale back using the same pattern\n",
    "averaged = reduce(ims, 'b (h h2) (w w2) c -> b h w c', 'mean', h2=6, w2=8)\n",
    "repeat(averaged, 'b h w c -> (h h2) (b w w2) c', h2=6, w2=8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": []
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rearrange(ims, 'b h w c -> w (b h) c')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": []
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's bring color dimension as part of horizontal axis\n",
    "# at the same time horizontal axis is downsampled by 2x\n",
    "reduce(ims, 'b (h h2) (w w2) c -> (h w2) (b w c)', 'mean', h2=3, w2=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ok, numpy is fun, but how do I use einops with some other framework?\n",
    "\n",
    "If that's what you've done with `ims` being numpy array:\n",
    "```python\n",
    "rearrange(ims, 'b h w c -> w (b h) c')\n",
    "```\n",
    "That's how you adapt the code for other frameworks:\n",
    "\n",
    "```python\n",
    "# pytorch:\n",
    "rearrange(ims, 'b h w c -> w (b h) c')\n",
    "# tensorflow:\n",
    "rearrange(ims, 'b h w c -> w (b h) c')\n",
    "# chainer:\n",
    "rearrange(ims, 'b h w c -> w (b h) c')\n",
    "# gluon:\n",
    "rearrange(ims, 'b h w c -> w (b h) c')\n",
    "# cupy:\n",
    "rearrange(ims, 'b h w c -> w (b h) c')\n",
    "# jax:\n",
    "rearrange(ims, 'b h w c -> w (b h) c')\n",
    "\n",
    "...well, you got the idea.\n",
    "```\n",
    "\n",
    "Einops allows backpropagation as if all operations were native to framework.\n",
    "Operations do not change when moving to another framework - einops notation is universal"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "# Summary\n",
    "\n",
    "- `rearrange` doesn't change number of elements and covers different numpy functions (like `transpose`, `reshape`, `stack`, `concatenate`,  `squeeze` and `expand_dims`)\n",
    "- `reduce` combines same reordering syntax with reductions (`mean`, `min`, `max`, `sum`, `prod`, and any others)\n",
    "- `repeat` additionally covers repeating and tiling\n",
    "- composition and decomposition of axes are a corner stone, they can and should be used together\n",
    "\n",
    "\n",
    "\n",
    "- [Second part of tutorial](https://github.com/arogozhnikov/einops/tree/master/docs) shows how einops works with other frameworks\n",
    "- [Third part of tutorial](https://arogozhnikov.github.io/einops/pytorch-examples.html) shows how to improve your DL code with einops"
   ]
  }
 ],
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