Einops.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from einops import rearrange,reduce,repeat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- https://einops.rocks/api/repeat/\n",
    "- https://zhuanlan.zhihu.com/p/342675997\n",
    "- https://mp.weixin.qq.com/s/9o5ZW-0-36MisCUwxZhs4Q\n",
    "\n",
    "as for depth-space conversion:\n",
    "- https://blog.csdn.net/qq_36556893/article/details/89471553\n",
    "- https://stackoverflow.com/questions/44264962/how-tf-space-to-depth-works-in-tensorflow?rq=1\n",
    "\n",
    "一个很棒的网站，展示了很多old方法用einops改写后的例子：\n",
    "- http://einops.rocks/pytorch-examples.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 定义"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([6, 3, 96, 96])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ndarray = np.load('./test_images.npy',allow_pickle=False)\n",
    "imgs = torch.from_numpy(ndarray).permute(0,3,1,2)\n",
    "imgs.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "size = int(math.sqrt(imgs.shape[0]))+1\n",
    "plt.figure()\n",
    "for i in range (imgs.shape[0]):\n",
    "    plt.subplot(size,size,i+1)\n",
    "    plt.imshow(ndarray[i])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 例子"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### rearrange"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([6, 96, 96, 3]), torch.Size([6, 96, 96, 3]))"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 转换维度，比如CHW -> HWC\n",
    "rearrange(imgs,'b c h w -> b h w c').shape,imgs.permute(0,2,3,1).shape\n",
    "                                    # numpy:transpose ~ torch:permute"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([6, 27648]), torch.Size([6, 27648]))"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# flatten\n",
    "rearrange(imgs,'b c h w ->b (c h w)').shape, imgs.reshape(imgs.shape[0],-1).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([3, 576, 96]) torch.Size([3, 96, 576])\n"
     ]
    }
   ],
   "source": [
    "# concat batches *along* different axis\n",
    "concat_height = rearrange(imgs,'b c h w -> c (b h) w')  # alone height-axis\n",
    "concat_width  = rearrange(imgs,'b c h w -> c h (b w)')  # along width-axis\n",
    "\n",
    "concats = [concat_height,concat_width]\n",
    "plt.figure()\n",
    "for i in range(2):\n",
    "    plt.subplot(1,2,i+1)\n",
    "    plt.imshow(concats[i].numpy().transpose(1,2,0))\n",
    "plt.show()\n",
    "    \n",
    "print(concat_height.shape,concat_width.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**在这里每一个字母就是batch中的一张图片!**<br>\n",
    "从矩阵坐标系易懂，height~axis0，即“沿着row方向”。所以**我上面的结果是正确的！**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我因为是基于torch tensor作为例子的，所以上面concat的例子中写为了'bchw'<br>\n",
    "而在官方例子(https://einops.rocks/api/rearrange/ )中，则是基于ndarray作为例子。所以是'bhwc'。<br>\n",
    "在这里，最终实现了和官方例子一样的效果(见：https://zhuanlan.zhihu.com/p/342675997 )！这说明我理解了concat的语法形式！<br>** nm为什么形式是这样，懂得这个形式代表concat即可！"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "注意，我一开始写作‘bcwh’，然后一切都旋转了，这说明w和h在einops中不只是”占位符“，而是和width和height一一对应的！ nm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([1, 6, 3, 96, 96]) torch.Size([1, 6, 3, 96, 96])\n",
      "torch.Size([6, 3, 96, 96]) torch.Size([6, 3, 96, 96])\n"
     ]
    }
   ],
   "source": [
    "# squeeze and unsqueeze\n",
    "print(rearrange(imgs,'b c h w -> 1 b c h w').shape, imgs.unsqueeze(0).shape)\n",
    "temp = imgs.unsqueeze(0)\n",
    "print(rearrange(temp,'1 b c h w -> b c h w').shape, imgs.squeeze(0).shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([6, 3, 2, 96, 48]) torch.Size([6, 3, 2, 96, 48])\n"
     ]
    }
   ],
   "source": [
    "# transpose + split\n",
    "num=2\n",
    "t1 = rearrange(imgs,'b c h (w w1) -> b c w1 h w',w1=num) # w*w1 ==> \"w*w1=96\"\n",
    "\n",
    "print(t1.shape,imgs.view(imgs.shape[0],imgs.shape[1],imgs.shape[2],imgs.shape[3]//num,num).permute(0,1,4,2,3).shape)\n",
    "# show = t1.numpy()[0,:,0,:,:].transpose(1,2,0)\n",
    "# plt.figure()\n",
    "# #plt.subplot(1,1,i+1)\n",
    "# plt.imshow(show.transpose(1,2,0))\n",
    "# plt.show()\n",
    "\n",
    "# 'b c h (w w1) -> b c w1 h w'  ==> 先view(reshape),再permute(transpose)\n",
    "# 看👆代码易懂。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### reduce"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([6, 3])\n",
      "torch.Size([6, 3, 1, 1])\n"
     ]
    }
   ],
   "source": [
    "# mean/max\n",
    "# -------------------------\n",
    "# global average pooling\n",
    "print(reduce(imgs,'b c h w -> b c','mean').shape)\n",
    "# global max pooling\n",
    "print(reduce(imgs,'b c h w -> b c () ()','max').shape)\n",
    "# 加()后，起到占位符的作用，会存在1的dim。\n",
    "# 为什么要占位，见👇紧接着的两个cell易懂。\n",
    "# -------------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([1, 3, 1, 1]), torch.Size([3]))"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Subtracting mean over batch for each channel\n",
    "temp1 = reduce(imgs,'b c h w -> () c () ()','mean')\n",
    "temp2 = reduce(imgs,'b c h w -> c','mean')\n",
    "temp1.shape,temp2.shape\n",
    "# 同理自己可以写出subtract mean for each hw plane"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([5, 3, 32, 32])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(x - temp1).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "ename": "RuntimeError",
     "evalue": "The size of tensor a (32) must match the size of tensor b (3) at non-singleton dimension 3",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mRuntimeError\u001b[0m                              Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-56-877989a9e6dd>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mtemp2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mRuntimeError\u001b[0m: The size of tensor a (32) must match the size of tensor b (3) at non-singleton dimension 3"
     ]
    }
   ],
   "source": [
    "(x-temp2).shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "由此可知，如果不加占位符，那么得到结果就会是一个低维向量，<br>\n",
    "在一些情况下会出现维度对不齐的情况，比如上面的temp2。**所以()是必须的**。<br>\n",
    "** 也可以用 1 代替 ()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### repeat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "image = np.random.randn(30, 40)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(30, 40, 3)"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 比如灰度图转三通道图\n",
    "repeat(image, 'h w -> h w c', c=3).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60, 40)"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# repeat 2x along height/width, e.g. height\n",
    "repeat(image,'h w -> (repeat h) w',repeat=2).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(30, 80)"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# repeat 2x along height/width, e.g. width\n",
    "repeat(image,'h w -> h (repeat w)',repeat=2).shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PyTorch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### torch & einops"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "见：https://mp.weixin.qq.com/s/9o5ZW-0-36MisCUwxZhs4Q 易懂，主要思路是把einops作为torch的layer！"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### torch.einsum <br>\n",
    "- https://pytorch.org/docs/stable/generated/torch.einsum.html?highlight=einsum\n",
    "- **最好是看对应的OneNote笔记！**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[-0.0584, -2.0269,  0.9480],\n",
       "        [-2.5766, -1.5123, -1.5205],\n",
       "        [ 0.1925,  0.5576, -2.1396]])"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "src = torch.randn(3,3)\n",
    "src"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(-3.7103)"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# trace\n",
    "torch.einsum('ii', src)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([-0.0584, -1.5123, -2.1396])"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# diagonal\n",
    "torch.einsum('ii->i', src)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([ 1.4697, -1.7374,  1.2483]),\n",
       " '\\n',\n",
       " tensor([-1.6772,  0.0747, -1.6694]))"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = torch.randn(3)\n",
    "y = torch.randn(3)\n",
    "x,'\\n',y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[-2.4650,  0.1099, -2.4536],\n",
       "        [ 2.9139, -0.1299,  2.9004],\n",
       "        [-2.0936,  0.0933, -2.0839]])"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# outer product\n",
    "torch.einsum('i,j->ij', x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(-4.6787)"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# inner product\n",
    "torch.einsum('i,i->',x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(-4.6787)"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(x*y).sum()"
   ]
  }
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