{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tutorial Pytorch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "source: https://github.com/jhui/jhui.github.io/blob/master/_posts/2018-02-09-PyTorch-Basic-operations.markdown"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[2.5226e-18, 2.5930e-09, 1.0186e-11],\n",
      "        [3.0883e-09, 2.6707e-06, 4.0744e-11]])\n"
     ]
    }
   ],
   "source": [
    "x = torch.Tensor(2, 3)    # Create an un-initialized Tensor of size 2x3\n",
    "print(x)                  # Print out the Tensor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Tensor"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.is_tensor(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sample programs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[0.3785, 0.9980, 0.9008],\n",
      "        [0.4766, 0.1663, 0.8045]])\n"
     ]
    }
   ],
   "source": [
    "# Initialize\n",
    "\n",
    "x = torch.Tensor(2, 3)  # An un-initialized Tensor object. x holds garbage data.\n",
    "y = torch.rand(2, 3)    # Initialize with random values\n",
    "\n",
    "# Operations\n",
    "\n",
    "z1 = x + y\n",
    "z2 = torch.add(x, y)             # Same as above\n",
    "\n",
    "print(z2)                        # [torch.FloatTensor of size 2x3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Operations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### in place"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0.3785, 0.9980, 0.9008],\n",
       "        [0.4766, 0.1663, 0.8045]])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.add_(y)        # Same as x = x + y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[1., 2., 3.],\n",
       "        [4., 5., 6.]])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = torch.Tensor([[1,2,3],[4,5,6]])\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[1., 1., 1.],\n",
       "        [1., 1., 1.]])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = torch.ones(2,3)\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[2., 3., 4.],\n",
       "        [5., 6., 7.]])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r1 = torch.add(x, y)\n",
    "r1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[2., 3., 4.],\n",
       "        [5., 6., 7.]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x+y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### indexing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([2., 5.])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[:, 1]                          # Can use numpy type indexing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0., 2., 3.],\n",
       "        [0., 5., 6.]])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[:, 0] = 0                      # For assignment\n",
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### conversion between NumPy ndarray and Tensor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([1, 2, 3])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Conversion\n",
    "a = np.array([1, 2, 3])\n",
    "v = torch.from_numpy(a)         # Convert a numpy array to a Tensor\n",
    "v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = v.numpy()                   # Tensor to numpy\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "b[1] = -1                       # Numpy and Tensor share the same memory\n",
    "assert(a[1] == b[1])            # Change Numpy will also change the Tensor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1, -1,  3])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([ 1, -1,  3])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1, -1,  3])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tensor meta-data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([2, 3])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = torch.Tensor(2,3)\n",
    "x.size()                        # torch.Size([2, 3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([2, 3])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.numel(x)                  # 6: number of elements in x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reshape tensor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[-0.1663,  0.0727,  1.3484],\n",
       "        [-0.8737, -0.2693, -0.5124]])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = torch.randn(2, 3)            # Size 2x3\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([-0.1663,  0.0727,  1.3484, -0.8737, -0.2693, -0.5124])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = x.view(6)                    # Resize x to size 6\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[-0.1663,  0.0727],\n",
       "        [ 1.3484, -0.8737],\n",
       "        [-0.2693, -0.5124]])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z = x.view(-1, 2)                # Size 3x2\n",
    "z"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create a Tensor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Creating and initializing a Tensor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "v = torch.Tensor(2, 3)          # An un-initialized torch.FloatTensor of size 2x3\n",
    "v = torch.Tensor([[1,2],[4,5]]) # A Tensor initialized with a specific array\n",
    "v = torch.LongTensor([1,2,3])   # A Tensor of type Long\n",
    "v = torch.FloatTensor([1,2,3])   # A Tensor of type Float"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([1., 2., 3.])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create a random Tensor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<torch._C.Generator at 0x7f1ae00bdc30>"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.manual_seed(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "v = torch.randperm(4)           # Size 4. Random permutation of integers from 0 to 3\n",
    "v = torch.rand(2, 3)            # Initialize with random number (uniform distribution)\n",
    "v = torch.randn(2, 3)           # With normal distribution (SD=1, mean=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[-0.6617, -0.0426, -1.3328],\n",
       "        [ 0.5161,  0.7455, -0.0751]])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tensor type"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[-0.6919, -0.4043,  0.2222],\n",
       "        [ 0.5773, -1.7637,  0.2264],\n",
       "        [-0.2355,  0.3019, -0.2770],\n",
       "        [ 0.4771, -0.1103,  0.2913],\n",
       "        [ 0.5848,  0.2149, -0.4090]])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = torch.randn(5, 3)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[ 0,  0,  0],\n",
       "        [ 0, -1,  0],\n",
       "        [ 0,  0,  0],\n",
       "        [ 0,  0,  0],\n",
       "        [ 0,  0,  0]])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.type(torch.LongTensor)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Identity matrices, Fill Tensor with 0, 1 or values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([3., 3., 3.])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eye = torch.eye(3)              # Create an identity 3x3 tensor\n",
    "\n",
    "v = torch.ones(10)              # A tensor of size 10 containing all ones\n",
    "v = torch.ones(2, 1, 2, 1)      # Size 2x1x2x1\n",
    "v = torch.ones_like(eye)        # A tensor with same shape as eye. Fill it with 1.\n",
    "\n",
    "v = torch.zeros(10)             # A tensor of size 10 containing all zeros\n",
    "\n",
    "# 1  1  1\n",
    "# 2  2  2\n",
    "# 3  3  3\n",
    "v = torch.ones(3, 3)\n",
    "v[1].fill_(2)\n",
    "v[2].fill_(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[1., 1., 1.],\n",
       "        [1., 1., 1.],\n",
       "        [1., 1., 1.]])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = torch.ones(3, 3)\n",
    "v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([2., 2., 2.])"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v[1].fill_(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[1., 1., 1.],\n",
       "        [2., 2., 2.],\n",
       "        [1., 1., 1.]])"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Initialize Tensor with a range of value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "v = torch.arange(5)             # similar to range(5) but creating a Tensor\n",
    "v = torch.arange(0, 5, step=1)  # Size 5. Similar to range(0, 5, 1)\n",
    "\n",
    "# 0 1 2\n",
    "# 3 4 5\n",
    "# 6 7 8\n",
    "v = torch.arange(9)\n",
    "v = v.view(3, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0, 1, 2],\n",
       "        [3, 4, 5],\n",
       "        [6, 7, 8]])"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Initialize a linear or log scale Tensor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "v = torch.linspace(1, 10, steps=10) # Create a Tensor with 10 linear points for (1, 10) inclusively\n",
    "v = torch.logspace(start=-10, end=10, steps=5) # Size 5: 1.0e-10 1.0e-05 1.0e+00, 1.0e+05, 1.0e+10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([1.0000e-10, 1.0000e-05, 1.0000e+00, 1.0000e+05, 1.0000e+10])"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Indexing, Slicing, Joining, Mutating Ops"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0, 1, 2],\n",
       "        [3, 4, 5],\n",
       "        [6, 7, 8]])"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 0 1 2\n",
    "# 3 4 5\n",
    "# 6 7 8\n",
    "x = torch.arange(9)\n",
    "x = x.view(3, 3)\n",
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Concatenate, Stack"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0, 1, 2],\n",
       "        [3, 4, 5],\n",
       "        [6, 7, 8],\n",
       "        [0, 1, 2],\n",
       "        [3, 4, 5],\n",
       "        [6, 7, 8],\n",
       "        [0, 1, 2],\n",
       "        [3, 4, 5],\n",
       "        [6, 7, 8]])"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Concatenation\n",
    "r = torch.cat((x, x, x), 0)          # Concatenate in the 0 dimension\n",
    "r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([[0, 1, 2, 0, 1, 2, 0, 1, 2],\n",
       "         [3, 4, 5, 3, 4, 5, 3, 4, 5],\n",
       "         [6, 7, 8, 6, 7, 8, 6, 7, 8]]),\n",
       " torch.Size([3, 9]))"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Concatenation\n",
    "r = torch.cat((x, x, x), 1)          # Concatenate in the 1 dimension\n",
    "r, r.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([[1.0000e-10, 1.0000e-05, 1.0000e+00, 1.0000e+05, 1.0000e+10],\n",
       "         [1.0000e-10, 1.0000e-05, 1.0000e+00, 1.0000e+05, 1.0000e+10]]),\n",
       " torch.Size([2, 5]))"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Stack\n",
    "r = torch.stack((v, v))\n",
    "r, r.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Squeeze and unsqueeze"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "``unsqueeze()`` \"adds\" superficial 1 dimension to tensor (at specified dimension), while ``squeeze()`` removes all superficial 1 dimensions from tensor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([2, 2])"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = torch.ones(2,1,2,1) # Size 2x1x2x1\n",
    "r = torch.squeeze(t)     # Size 2x2\n",
    "r.size()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([2, 2, 1])"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r = torch.squeeze(t, 1)  # Squeeze dimension 1: Size 2x2x1\n",
    "r.size()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[1.],\n",
       "        [2.],\n",
       "        [3.]])"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Un-squeeze a dimension\n",
    "x = torch.Tensor([1, 2, 3])\n",
    "r = torch.unsqueeze(x, 0)       # Size: 1x3\n",
    "r = torch.unsqueeze(x, 1)       # Size: 3x1\n",
    "r"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reduction operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "v = torch.arange(9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([ 0,  1,  3,  6, 10, 15, 21, 28, 36])"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Accumulate sum\n",
    "#  0   1   2\n",
    "#  3   5   7\n",
    "#  9  12  15\n",
    "r = torch.cumsum(v, dim=0)\n",
    "r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([[0., 1., 2.],\n",
       "         [3., 4., 5.],\n",
       "         [6., 7., 8.]]),\n",
       " tensor([1., 4., 7.]))"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Mean\n",
    "# 1 4 7\n",
    "w = v.type(torch.FloatTensor)\n",
    "w = w.view(3,3)\n",
    "r = torch.mean(w, 1)         # Size 3: Mean in dim 1\n",
    "w,r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([ 3, 12, 21])"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Sum\n",
    "# 3 12 21\n",
    "w = v.view(3,3)\n",
    "r = torch.sum(w, 1)          # Sum over dim 1\n",
    "r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "36"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 36\n",
    "r = torch.sum(w)\n",
    "r.item()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# END"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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