01-tensor_tutorial.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "# What is PyTorch?\n",
    "\n",
    "It’s a Python based scientific computing package targeted at two sets of audiences:\n",
    "\n",
    "-  Tensorial library that uses the power of GPUs\n",
    "-  A deep learning research platform that provides maximum flexibility and speed\n",
    "\n",
    "## Import the library"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch  # <Ctrl> / <Shift> + <Return>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Getting help in Jupyter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function _VariableFunctionsClass.squeeze>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.squeeze # <Tab>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# What about all `*Tensor`s?\n",
    "# Press <esc> to get out of help\n",
    "torch.*Tensor?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Module()"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.nn.Module() # <Shift>+<Tab>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Annotate your functions / classes!\n",
    "torch.nn.Module?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "torch.nn.Module??"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dropping to Bash: magic!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total 1720\r\n",
      "-rw-r--r--   1 gianlucafugante  staff    29K 27 Ott 21:30 00-logic_neuron_programming.ipynb\r\n",
      "-rw-r--r--   1 gianlucafugante  staff    20K 28 Ott 20:06 01-tensor_tutorial.ipynb\r\n",
      "-rw-r--r--   1 gianlucafugante  staff   6,6K 27 Ott 20:38 02-space_stretching.ipynb\r\n",
      "-rw-r--r--   1 gianlucafugante  staff   6,7K 27 Ott 20:38 03-autograd_tutorial.ipynb\r\n",
      "-rw-r--r--   1 gianlucafugante  staff   7,3K 27 Ott 20:38 04-spiral_classification.ipynb\r\n",
      "-rw-r--r--   1 gianlucafugante  staff   9,3K 27 Ott 20:38 05-regression.ipynb\r\n",
      "-rw-r--r--   1 gianlucafugante  staff    14K 27 Ott 20:38 06-convnet.ipynb\r\n",
      "-rw-r--r--   1 gianlucafugante  staff   8,6K 27 Ott 20:38 07-listening_to_kernels.ipynb\r\n",
      "-rw-r--r--   1 gianlucafugante  staff    23K 27 Ott 20:38 08-seq_classification.ipynb\r\n",
      "-rw-r--r--   1 gianlucafugante  staff   7,2K 27 Ott 20:38 09-echo_data.ipynb\r\n",
      "-rw-r--r--   1 gianlucafugante  staff   7,3K 27 Ott 20:38 10-autoencoder.ipynb\r\n",
      "-rw-r--r--   1 gianlucafugante  staff    10K 27 Ott 20:38 11-VAE.ipynb\r\n",
      "-rw-r--r--   1 gianlucafugante  staff    19K 27 Ott 20:38 12-regularization.ipynb\r\n",
      "-rw-r--r--   1 gianlucafugante  staff   4,4K 27 Ott 20:38 13-bayesian_nn.ipynb\r\n",
      "-rw-r--r--   1 gianlucafugante  staff    13K 27 Ott 20:38 14-truck_backer-upper.ipynb\r\n",
      "-rw-r--r--   1 gianlucafugante  staff    25K 27 Ott 20:38 15-transformer.ipynb\r\n",
      "-rw-r--r--   1 gianlucafugante  staff   603K 27 Ott 20:38 16-gated_GCN.ipynb\r\n",
      "-rw-r--r--   1 gianlucafugante  staff   281B 27 Ott 20:38 LICENSE.md\r\n",
      "-rw-r--r--   1 gianlucafugante  staff   3,8K 27 Ott 20:38 README.md\r\n",
      "-rw-r--r--   1 gianlucafugante  staff    16B 27 Ott 20:38 apt.txt\r\n",
      "drwxr-xr-x  27 gianlucafugante  staff   864B 27 Ott 20:42 \u001b[34mdocs\u001b[m\u001b[m\r\n",
      "-rw-r--r--   1 gianlucafugante  staff   274B 27 Ott 20:38 environment.yml\r\n",
      "drwxr-xr-x   7 gianlucafugante  staff   224B 27 Ott 20:41 \u001b[34mextra\u001b[m\u001b[m\r\n",
      "drwxr-xr-x  12 gianlucafugante  staff   384B 28 Ott 20:00 \u001b[34mres\u001b[m\u001b[m\r\n",
      "drwxr-xr-x  18 gianlucafugante  staff   576B 28 Ott 19:52 \u001b[34mslides\u001b[m\u001b[m\r\n"
     ]
    }
   ],
   "source": [
    "# List all the files in the current directory\n",
    "!ls -lh"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "508 00-logic_neuron_programming.ipynb\n",
      "971 01-tensor_tutorial.ipynb\n",
      "273 02-space_stretching.ipynb\n",
      "331 03-autograd_tutorial.ipynb\n",
      "294 04-spiral_classification.ipynb\n",
      "362 05-regression.ipynb\n",
      "458 06-convnet.ipynb\n",
      "337 07-listening_to_kernels.ipynb\n",
      "660 08-seq_classification.ipynb\n",
      "255 09-echo_data.ipynb\n",
      "264 10-autoencoder.ipynb\n",
      "353 11-VAE.ipynb\n",
      "648 12-regularization.ipynb\n",
      "195 13-bayesian_nn.ipynb\n",
      "422 14-truck_backer-upper.ipynb\n",
      "772 15-transformer.ipynb\n",
      "1083 16-gated_GCN.ipynb\n",
      "4 LICENSE.md\n",
      "71 README.md\n",
      "1 apt.txt\n",
      "20 environment.yml\n"
     ]
    }
   ],
   "source": [
    "%%bash\n",
    "# List all the files but with cleaner outputs for readability\n",
    "for f in $(ls *.*); do\n",
    "    echo $(wc -l $f)\n",
    "done"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Getting some general help\n",
    "%magic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Python native data types\n",
    "\n",
    "Python has many native datatypes. Here are the important ones:\n",
    "\n",
    " - **Booleans** are either `True` or `False`.\n",
    " - **Numbers** can be integers (1 and 2), floats (1.1 and 1.2), fractions (1/2 and 2/3), or even complex numbers.\n",
    " - **Strings** are sequences of Unicode characters, e.g. an html document.\n",
    " - **Lists** are ordered sequences of values.\n",
    " - **Tuples** are ordered, immutable sequences of values.\n",
    " - **Sets** are unordered bags of values.\n",
    " - **Dictionaries** are unordered bags of key-value pairs.\n",
    " \n",
    "See [here](http://www.diveintopython3.net/native-datatypes.html) for a complete overview.\n",
    "\n",
    "### More resources\n",
    "\n",
    " 1. Brief Python introduction [here](https://learnxinyminutes.com/docs/python3/).\n",
    " 2. Full Python tutorial [here](https://docs.python.org/3/tutorial/).\n",
    " 3. A Whirlwind Tour of Python [here](https://github.com/jakevdp/WhirlwindTourOfPython).\n",
    " 4. Python Data Science Handbook [here](https://github.com/jakevdp/PythonDataScienceHandbook)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Torch!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Tensor"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Generate a tensor of size 2x3x4\n",
    "t = torch.Tensor(2, 3, 4)\n",
    "type(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([2, 3, 4])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get the size of the tensor\n",
    "t.size()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t size: 2 × 3 × 4\n"
     ]
    }
   ],
   "source": [
    "# t.size() is a classic tuple =>\n",
    "print('t size:', ' \\u00D7 '.join(map(str, t.size())))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "point in a 24 dimensional space\n",
      "organised in 3 sub-dimensions\n"
     ]
    }
   ],
   "source": [
    "# prints dimensional space and sub-dimensions\n",
    "print(f'point in a {t.numel()} dimensional space')\n",
    "print(f'organised in {t.dim()} sub-dimensions')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[[ 0.0000e+00, -1.0842e-19,  0.0000e+00, -1.0842e-19],\n",
       "         [ 1.4013e-44,  0.0000e+00,  0.0000e+00,  0.0000e+00],\n",
       "         [ 0.0000e+00,  0.0000e+00,  7.0295e+28,  6.1949e-04]],\n",
       "\n",
       "        [[ 4.0995e+04,  1.8470e+25,  1.2709e+31,  1.9433e-19],\n",
       "         [ 7.0362e+22,  2.0022e-19,  2.9264e+29,  3.1999e+27],\n",
       "         [ 4.3055e+21,  4.7865e+22,  2.8826e+32,  1.8524e+28]]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[[2., 0., 5., 6.],\n",
       "         [0., 9., 8., 6.],\n",
       "         [9., 9., 4., 0.]],\n",
       "\n",
       "        [[7., 4., 0., 2.],\n",
       "         [4., 1., 4., 5.],\n",
       "         [3., 5., 6., 2.]]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Mind the underscore!\n",
    "# Any operation that mutates a tensor in-place is post-fixed with an _.\n",
    "# For example: x.copy_(y), x.t_(), x.random_(n) will change x.\n",
    "t.random_(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[[2., 0., 5., 6.],\n",
       "         [0., 9., 8., 6.],\n",
       "         [9., 9., 4., 0.]],\n",
       "\n",
       "        [[7., 4., 0., 2.],\n",
       "         [4., 1., 4., 5.],\n",
       "         [3., 5., 6., 2.]]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[2., 0., 5., 6., 0., 9., 8., 6.],\n",
       "        [9., 9., 4., 0., 7., 4., 0., 2.],\n",
       "        [4., 1., 4., 5., 3., 5., 6., 2.]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This resizes the tensor permanently \n",
    "r = torch.Tensor(t)\n",
    "r.resize_(3, 8)\n",
    "r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0., 0., 0., 0., 0., 0., 0., 0.],\n",
       "        [0., 0., 0., 0., 0., 0., 0., 0.],\n",
       "        [0., 0., 0., 0., 0., 0., 0., 0.]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# As you can see zero_ would replace r with 0's which was originally filled with integers\n",
    "r.zero_()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[[0., 0., 0., 0.],\n",
       "         [0., 0., 0., 0.],\n",
       "         [0., 0., 0., 0.]],\n",
       "\n",
       "        [[0., 0., 0., 0.],\n",
       "         [0., 0., 0., 0.],\n",
       "         [0., 0., 0., 0.]]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# This *is* important, sigh...\n",
    "s = r.clone()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[1., 1., 1., 1., 1., 1., 1., 1.],\n",
       "        [1., 1., 1., 1., 1., 1., 1., 1.],\n",
       "        [1., 1., 1., 1., 1., 1., 1., 1.]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# In-place fill of 1's\n",
    "s.fill_(1)\n",
    "s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0., 0., 0., 0., 0., 0., 0., 0.],\n",
       "        [0., 0., 0., 0., 0., 0., 0., 0.],\n",
       "        [0., 0., 0., 0., 0., 0., 0., 0.]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Because we cloned r, even though we did an in-place operation, this doesn't affect r\n",
    "r"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vectors (1D Tensors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([1., 2., 3., 4.])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Creates a 1D tensor of integers 1 to 4\n",
    "v = torch.Tensor([1, 2, 3, 4])\n",
    "v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dim: 1, size: 4\n"
     ]
    }
   ],
   "source": [
    "# Print number of dimensions (1D) and size of tensor\n",
    "print(f'dim: {v.dim()}, size: {v.size()[0]}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([1., 0., 2., 0.])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w = torch.Tensor([1, 0, 2, 0])\n",
    "w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([1., 0., 6., 0.])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Element-wise multiplication\n",
    "v * w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(7.)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Scalar product: 1*1 + 2*0 + 3*2 + 4*0\n",
    "v @ w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([9., 0., 9., 9., 9.])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# In-place replacement of random number from 0 to 10\n",
    "x = torch.Tensor(5).random_(10)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "first: 9.0, last: 9.0\n"
     ]
    }
   ],
   "source": [
    "print(f'first: {x[0]}, last: {x[-1]}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0., 9.])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Extract sub-Tensor [from:to)\n",
    "x[1:2 + 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([1., 2., 3., 4.])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([1, 2, 3, 4])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a tensor with integers ranging from 1 to 5, excluding 5\n",
    "v = torch.arange(1, 4 + 1)\n",
    "v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 1,  4,  9, 16]) tensor([1, 2, 3, 4])\n"
     ]
    }
   ],
   "source": [
    "# Square all elements in the tensor\n",
    "print(v.pow(2), v)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matrices (2D Tensors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[2., 5., 3., 7.],\n",
       "        [4., 2., 1., 9.]])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a 2x4 tensor\n",
    "m = torch.Tensor([[2, 5, 3, 7],\n",
    "                  [4, 2, 1, 9]])\n",
    "m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m.dim()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2 -- 4 -- torch.Size([2, 4])\n"
     ]
    }
   ],
   "source": [
    "print(m.size(0), m.size(1), m.size(), sep=' -- ')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Returns the total number of elements, hence num-el (number of elements)\n",
    "m.numel()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(3.)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Indexing row 0, column 2 (0-indexed)\n",
    "m[0][2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(3.)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Indexing row 0, column 2 (0-indexed)\n",
    "m[0, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([5., 2.])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Indexing column 1, all rows (returns size 2)\n",
    "m[:, 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[5.],\n",
       "        [2.]])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Indexing column 1, all rows (returns size 2x2)\n",
    "m[:, [1]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[2., 5., 3., 7.]])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Indexes row 0, all columns (returns 1x4)\n",
    "m[[0], :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([2., 5., 3., 7.])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Indexes row 0, all columns (returns size 4)\n",
    "m[0, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([1., 2., 3., 4.])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create tensor of numbers from 1 to 5 (excluding 5)\n",
    "v = torch.arange(1., 4 + 1)\n",
    "v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[2., 5., 3., 7.],\n",
       "        [4., 2., 1., 9.]])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([49., 47.])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Scalar product\n",
    "m @ v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([49.])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculated by 1*2 + 2*5 + 3*3 + 4*7\n",
    "m[[0], :] @ v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([47.])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculated by \n",
    "m[[1], :] @ v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[2.0879, 5.8372, 3.0257, 7.0192],\n",
       "        [4.1963, 2.5956, 1.9690, 9.3813]])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Add a random tensor of size 2x4 to m\n",
    "m + torch.rand(2, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[1.6088, 4.1871, 2.0786, 6.8190],\n",
       "        [3.5546, 1.2946, 0.1235, 8.7189]])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Subtract a random tensor of size 2x4 to m\n",
    "m - torch.rand(2, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0.7807, 0.7004, 1.6707, 4.7318],\n",
       "        [2.6537, 1.6940, 0.2418, 0.8716]])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Multiply a random tensor of size 2x4 to m\n",
    "m * torch.rand(2, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[30.8899, 56.7995,  3.2979, 76.0491],\n",
       "        [ 6.1137, 37.5251,  1.3603, 11.1492]])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Divide m by a random tensor of size 2x4\n",
    "m / torch.rand(2, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([2, 4])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m.size()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[2., 4.],\n",
       "        [5., 2.],\n",
       "        [3., 1.],\n",
       "        [7., 9.]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Transpose tensor m, which is essentially 2x4 to 4x2\n",
    "m.t()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[2., 4.],\n",
       "        [5., 2.],\n",
       "        [3., 1.],\n",
       "        [7., 9.]])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Same as\n",
    "m.transpose(0, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constructors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([3., 4., 5., 6., 7., 8.])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create tensor from 3 to 8, with each having a space of 1\n",
    "torch.arange(3., 8 + 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([ 5.7000,  2.7000, -0.3000])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create tensor from 5.7 to -2.1 with each having a space of -3\n",
    "torch.arange(5.7, -2.1, -3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[3.0000, 3.2632, 3.5263, 3.7895, 4.0526, 4.3158, 4.5789, 4.8421, 5.1053,\n",
       "         5.3684, 5.6316, 5.8947, 6.1579, 6.4211, 6.6842, 6.9474, 7.2105, 7.4737,\n",
       "         7.7368, 8.0000]])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# returns a 1D tensor of steps equally spaced points between start=3, end=8 and steps=20\n",
    "torch.linspace(3, 8, 20).view(1, -1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0., 0., 0., 0., 0.],\n",
       "        [0., 0., 0., 0., 0.],\n",
       "        [0., 0., 0., 0., 0.]])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a tensor filled with 0's\n",
    "torch.zeros(3, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[[1., 1., 1., 1., 1.],\n",
       "         [1., 1., 1., 1., 1.]],\n",
       "\n",
       "        [[1., 1., 1., 1., 1.],\n",
       "         [1., 1., 1., 1., 1.]],\n",
       "\n",
       "        [[1., 1., 1., 1., 1.],\n",
       "         [1., 1., 1., 1., 1.]]])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a tensor filled with 1's\n",
    "torch.ones(3, 2, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[1., 0., 0.],\n",
       "        [0., 1., 0.],\n",
       "        [0., 0., 1.]])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a tensor with the diagonal filled with 1\n",
    "torch.eye(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set default plots\n",
    "from res.plot_lib import set_default\n",
    "from matplotlib import pyplot as plt\n",
    "set_default()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Numpy bridge!\n",
    "plt.hist(torch.randn(1000).numpy(), 100);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(torch.randn(10**6).numpy(), 100);  # how much does this chart weight?\n",
    "# use rasterized=True for SVG/EPS/PDF!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(torch.rand(10**6).numpy(), 100);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Casting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Helper to get what kind of tensor types\n",
    "torch.*Tensor?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[2., 5., 3., 7.],\n",
       "        [4., 2., 1., 9.]])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[2., 5., 3., 7.],\n",
       "        [4., 2., 1., 9.]], dtype=torch.float64)"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This is basically a 64 bit float tensor\n",
    "m_double = m.double()\n",
    "m_double"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[2, 5, 3, 7],\n",
       "        [4, 2, 1, 9]], dtype=torch.uint8)"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This creates a tensor of type int8\n",
    "m_byte = m.byte()\n",
    "m_byte"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[2., 5., 3., 7.],\n",
       "        [4., 2., 1., 9.]])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Move your tensor to GPU device 0 if there is one (first GPU in the system)\n",
    "device = torch.device(\"cuda:0\" if torch.cuda.is_available() else \"cpu\")\n",
    "m.to(device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2., 5., 3., 7.],\n",
       "       [4., 2., 1., 9.]], dtype=float32)"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Converts tensor to numpy array\n",
    "m_np = m.numpy()\n",
    "m_np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.,  5.,  3.,  7.],\n",
       "       [ 4.,  2.,  1.,  9.]], dtype=float32)"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# In-place fill of column 0 and row 0 with value -1\n",
    "m_np[0, 0] = -1\n",
    "m_np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[-1.,  5.,  3.,  7.],\n",
       "        [ 4.,  2.,  1.,  9.]])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4] tensor([0, 1, 2, 3, 4])\n"
     ]
    }
   ],
   "source": [
    "# Create a tensor of integers ranging from 0 to 4\n",
    "import numpy as np\n",
    "n_np = np.arange(5)\n",
    "n = torch.from_numpy(n_np)\n",
    "print(n_np, n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 2, 4, 6, 8])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# In-place multiplication of all elements by 2 for tensor n\n",
    "# Because n is essentiall n_np, not a clone, this affects n_np\n",
    "n.mul_(2)\n",
    "n_np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## More fun"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([1, 4]) tensor([[5., 6., 7., 8.]])\n"
     ]
    }
   ],
   "source": [
    "# Creates two tensor of size 1x4\n",
    "a = torch.Tensor([[1, 2, 3, 4]])\n",
    "b = torch.Tensor([[5, 6, 7, 8]])\n",
    "print(a.size(), b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[1., 2., 3., 4.],\n",
       "        [5., 6., 7., 8.]])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Concatenate on axis 0, so you get 2x4\n",
    "torch.cat((a, b), 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[1., 2., 3., 4., 5., 6., 7., 8.]])"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Concatenate on axis 1, so you get 1x8\n",
    "torch.cat((a, b), 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Much more\n",
    "\n",
    "There's definitely much more, but this was the basics about `Tensor`s fun.\n",
    "\n",
    "*Torch* full API should be read at least once.\n",
    "Hence, go [here](https://pytorch.org/docs/stable/index.html).\n",
    "You'll find 100+ `Tensor` operations, including transposing, indexing, slicing, mathematical operations, linear algebra, random numbers, etc are described."
   ]
  }
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