exercises/ex01/ex01_tensors.ipynb

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   "source": [],
   "execution_count": 76,
   "outputs": []
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   "cell_type": "markdown",
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   "source": [
    "import torch\n",
    "print(torch.__version__)"
   ],
   "execution_count": 77,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.1.1\n"
     ]
    }
   ]
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   },
   "source": [],
   "execution_count": 77,
   "outputs": []
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "dHfhTFlgu1wl",
    "outputId": "3ae4031d-2b2b-4de5-b3ff-c09d2c10fa15",
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   },
   "source": [
    "# What does this torch.tensor() return?\n",
    "tensor = torch.tensor([1, 2, 3, 4, 5, 6])\n",
    "tensor\n",
    "\n",
    "# Constant 1-D Tensor populated with value list"
   ],
   "execution_count": 78,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor([1, 2, 3, 4, 5, 6])"
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
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   },
   "source": [
    "# What is the shape of the resulting tensor?\n",
    "tensor = torch.tensor([1, 2, 3, 4, 5, 6])\n",
    "tensor.shape\n",
    "\n",
    "# Size object"
   ],
   "execution_count": 79,
   "outputs": [
    {
     "data": {
      "text/plain": "torch.Size([6])"
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "ZTQDKKei0JNG",
    "outputId": "4df4ddb7-2471-4608-92df-5ef7404b5882",
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   },
   "source": [
    "# What is the content of the resulting Tensor?\n",
    "tensor = torch.tensor([1, 2, 3, 4, 5, 6])\n",
    "tensor = torch.reshape(tensor, (2, 3))\n",
    "tensor\n",
    "# A 2x3 matrix (two rows = the first dim, three\n",
    "# columns = the second dim)"
   ],
   "execution_count": 80,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor([[1, 2, 3],\n        [4, 5, 6]])"
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
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   "source": [
    "# What is the content of the resulting Tensor?\n",
    "tensor = torch.tensor([1, 2, 3, 4, 5, 6])\n",
    "tensor = torch.reshape(tensor, (3, 2))\n",
    "tensor\n",
    "# A 3x2 matrix (three rows = the first dim,\n",
    "# two columns = the second dim)"
   ],
   "execution_count": 81,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor([[1, 2],\n        [3, 4],\n        [5, 6]])"
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
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   "source": [
    "# What is the content of the resulting Tensor?\n",
    "tensor = torch.tensor([1, 2, 3, 4, 5, 6])\n",
    "tensor = torch.reshape(tensor, shape=(3, 2, 1))\n",
    "tensor\n",
    "# 3-D Tensor"
   ],
   "execution_count": 82,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor([[[1],\n         [2]],\n\n        [[3],\n         [4]],\n\n        [[5],\n         [6]]])"
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
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    "id": "-S6zogOBfbY5",
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     "height": 119
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     "start_time": "2023-11-23T09:26:22.270488Z"
    }
   },
   "source": [
    "# What is the content of the resulting Tensor?\n",
    "tensor = torch.tensor([1, 2, 3, 4, 5, 6])\n",
    "tensor = torch.reshape(tensor, shape=(3, 1, 2))\n",
    "tensor\n",
    "# 3-D Tensor with the second dimension kind of superfluous"
   ],
   "execution_count": 83,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor([[[1, 2]],\n\n        [[3, 4]],\n\n        [[5, 6]]])"
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
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    "id": "pTrvYqt11gmY",
    "outputId": "a5ed0c02-2956-40bd-e2ec-670a0b709c63",
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   "source": [],
   "execution_count": 83,
   "outputs": []
  },
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    "id": "j8kug86G1ypG",
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   },
   "source": [
    "# What is the output of torch.fill()?\n",
    "tensor = torch.full([2, 3], 9)\n",
    "tensor\n",
    "# A 2-rows 3-columns tensor populated with 9 as int"
   ],
   "execution_count": 84,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor([[9, 9, 9],\n        [9, 9, 9]])"
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
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   "execution_count": 84,
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     "height": 119
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   },
   "source": [],
   "execution_count": 84,
   "outputs": []
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "v7Z6VmbXf_6-",
    "outputId": "adf28c78-bead-4846-9ac7-8d1df95230ac",
    "colab": {
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     "height": 85
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     "end_time": "2023-11-23T09:26:24.291012Z",
     "start_time": "2023-11-23T09:26:22.299784Z"
    }
   },
   "source": [
    "# What is the output and shape of this code?\n",
    "x = torch.tensor([1, 4])\n",
    "y = torch.tensor([2, 5])\n",
    "z = torch.tensor([3, 6])\n",
    "torch.stack([x, y, z])\n",
    "# (3,2) tensor stacked along the first dimension"
   ],
   "execution_count": 85,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor([[1, 4],\n        [2, 5],\n        [3, 6]])"
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
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    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 68
    },
    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.320808Z",
     "start_time": "2023-11-23T09:26:22.303207Z"
    }
   },
   "source": [
    "# What is the output and shape of this code?\n",
    "x = torch.tensor([1, 4])\n",
    "y = torch.tensor([2, 5])\n",
    "z = torch.tensor([3, 6])\n",
    "torch.stack([x, y, z], dim=1)\n",
    "# (2,3) tensor stacked along the second dimension"
   ],
   "execution_count": 86,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor([[1, 2, 3],\n        [4, 5, 6]])"
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "7t_E0gzG530U",
    "outputId": "27d485d7-1583-477b-a35f-652d648604a2",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.558141Z",
     "start_time": "2023-11-23T09:26:22.305100Z"
    }
   },
   "source": [
    "# What does this code produce and why?\n",
    "c = torch.tensor([[1.0, 2.0, 3.0],\n",
    "                 [4.0, 5.0, 6.0]])\n",
    "c.shape\n",
    "# A Size object with a list of Dimension objects\n",
    "# 2 and 3"
   ],
   "execution_count": 87,
   "outputs": [
    {
     "data": {
      "text/plain": "torch.Size([2, 3])"
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "sFJPGZax6NvG",
    "outputId": "47efafdd-9468-4edf-8ecd-051a0f0addae",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.558431Z",
     "start_time": "2023-11-23T09:26:22.306762Z"
    }
   },
   "source": [
    "# What does this code produce and why?\n",
    "tensor = torch.tensor([1, 2, 3, 4, 5, 6])\n",
    "tensor[2:-2]\n",
    "# Strip leading and trailing 2 elements"
   ],
   "execution_count": 88,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor([3, 4])"
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "1AR1-L3U97FS",
    "outputId": "7b4d2070-8700-432a-c22d-9dd48458ded8",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 68
    },
    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.560677Z",
     "start_time": "2023-11-23T09:26:22.308414Z"
    }
   },
   "source": [
    "# What does this code produce and why?\n",
    "tensor = torch.tensor([[1, 2, 3],\n",
    "                      [4, 5, 6],\n",
    "                      [7, 8, 9],\n",
    "                       [10, 11, 12]])\n",
    "tensor[::2,]\n",
    "# Skip every other row and reverse the order\n",
    "# of the columns"
   ],
   "execution_count": 89,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor([[1, 2, 3],\n        [7, 8, 9]])"
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "sXDmebI6km_Y",
    "outputId": "6877de56-4855-4bf1-afa4-f740d5f7b5a7",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.563041Z",
     "start_time": "2023-11-23T09:26:22.310075Z"
    }
   },
   "source": [
    "# What does this code produce and why?\n",
    "tensor = torch.tensor([[1, 2, 3],\n",
    "                      [4, 5, 6],\n",
    "                      [7, 8, 9]])\n",
    "tensor[torch.tensor(0), torch.tensor(2)]\n",
    "\n",
    "# The value at coordinates 0,2 as a scalar tensor"
   ],
   "execution_count": 90,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor(3)"
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "T78RfEwXhlHm",
    "outputId": "e356730b-1bde-4f1d-f493-0e1abee35480",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.563187Z",
     "start_time": "2023-11-23T09:26:22.311826Z"
    }
   },
   "source": [
    "# What does this code produce and why?\n",
    "tensor = torch.tensor([[1, 2, 3],\n",
    "                      [4, 5, 6],\n",
    "                      [7, 8, 9]])\n",
    "tensor[torch.tensor(0)]\n",
    "\n",
    "# A cut on position 0 in the first dimension;\n",
    "# the first row"
   ],
   "execution_count": 91,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor([1, 2, 3])"
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "GOmWYSpgh_2a",
    "outputId": "f7adbe58-4752-4465-f753-e17fe44d0d89",
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     "end_time": "2023-11-23T09:26:24.563617Z",
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    }
   },
   "source": [
    "# What does this code produce and why?\n",
    "tensor = torch.tensor([[1, 2, 3],\n",
    "                      [4, 5, 6],\n",
    "                      [7, 8, 9]])\n",
    "tensor[:, torch.tensor(0)]\n",
    "\n",
    "# A cut on position 0 in the second dimension;\n",
    "# the first column\n"
   ],
   "execution_count": 92,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor([1, 4, 7])"
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "EhdmUENjhTOg",
    "outputId": "258563d2-7128-4127-f97f-931a6f779541",
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     "base_uri": "https://localhost:8080/",
     "height": 34
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    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.563725Z",
     "start_time": "2023-11-23T09:26:22.317710Z"
    }
   },
   "source": [
    "# What are other two equivalent operations to selecting\n",
    "# the first row:\n",
    "tensor = torch.tensor([[1, 2, 3],\n",
    "                      [4, 5, 6],\n",
    "                      [7, 8, 9]])\n",
    "tensor[torch.tensor(0)]\n",
    "\n",
    "# With explicit ellipses for other dimensions\n",
    "tensor[torch.tensor(0), :]\n",
    "# With ellipsis\n",
    "tensor[torch.tensor(0), ...]"
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  {
   "cell_type": "markdown",
   "source": [
    "## Broadcasting"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "S-1rd5yiKQc_"
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  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "qFSMWx-CM9Ba",
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     "start_time": "2023-11-23T09:26:22.382359Z"
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   "source": [
    "# Broadcasting in torch: what is the output?\n",
    "a = torch.tensor(3)\n",
    "b = torch.tensor(4)\n",
    "a + b\n",
    "\n",
    "# Simple scalar: 7"
   ],
   "execution_count": 94,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor(7)"
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "8LPxB23ZNKAL",
    "outputId": "40097450-e96d-40a6-9935-a68eba875f5c",
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     "height": 34
    },
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     "end_time": "2023-11-23T09:26:24.579412Z",
     "start_time": "2023-11-23T09:26:22.384867Z"
    }
   },
   "source": [
    "# Broadcasting in torch: what is the output and why?\n",
    "a = torch.tensor([1, 2])\n",
    "b = torch.tensor(4)\n",
    "a + b\n",
    "\n",
    "# b is broadcast to all items in a"
   ],
   "execution_count": 95,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor([5, 6])"
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "PJnGgO0BNZ9N",
    "outputId": "12cbe92a-9f71-40b2-8e33-614aeefeecdc",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.579518Z",
     "start_time": "2023-11-23T09:26:22.387845Z"
    }
   },
   "source": [
    "# Broadcasting in torch: what is the output and why?\n",
    "a = torch.tensor([1, 2, 3])\n",
    "b = torch.tensor([4, 5, 6])\n",
    "a + b\n",
    "\n",
    "# Element-wise operation"
   ],
   "execution_count": 96,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor([5, 7, 9])"
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "8dQy_74oN06b",
    "outputId": "832bf392-98b6-47b5-c3b5-627c5d2142dd",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 68
    },
    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.579627Z",
     "start_time": "2023-11-23T09:26:22.391383Z"
    }
   },
   "source": [
    "# Broadcasting in torch: what is the output and why?\n",
    "a = torch.tensor([[1, 2, 3], [4, 5, 6]])\n",
    "b = torch.tensor([[1, 2, 3], [4, 5, 6]])\n",
    "a + b\n",
    "\n",
    "# Elementwise addition"
   ],
   "execution_count": 97,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor([[ 2,  4,  6],\n        [ 8, 10, 12]])"
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "hcwgWRjeN-cc",
    "outputId": "204aab6d-af20-4fc6-8a0a-7dd3e316840b",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 68
    },
    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.579719Z",
     "start_time": "2023-11-23T09:26:22.394032Z"
    }
   },
   "source": [
    "# Broadcasting in torch: what is the output and why?\n",
    "a = torch.tensor([[1, 2, 3], [4, 5, 6]])\n",
    "b = torch.tensor([10, 20, 30])\n",
    "a + b\n",
    "\n",
    "# b is broadcast along each row in a"
   ],
   "execution_count": 98,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor([[11, 22, 33],\n        [14, 25, 36]])"
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "1ivO38B9OLsw",
    "outputId": "54c12792-4ea8-4109-cdbd-6b62a3bde2b1",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 68
    },
    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.579808Z",
     "start_time": "2023-11-23T09:26:22.397285Z"
    }
   },
   "source": [
    "# Broadcasting in torch: what is the output and why?\n",
    "a = torch.tensor([[1, 2, 3], [4, 5, 6]])\n",
    "b = torch.tensor([[1], [2]])\n",
    "a + b\n",
    "\n",
    "# b is broadcast along each column in a"
   ],
   "execution_count": 99,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor([[2, 3, 4],\n        [6, 7, 8]])"
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "p7NEm-jTOu_C",
    "outputId": "083c294e-9a82-4c5f-f4cc-3fbca818d312",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 153
    },
    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.579898Z",
     "start_time": "2023-11-23T09:26:22.400825Z"
    }
   },
   "source": [
    "# Broadcasting in torch: what is the output and why?\n",
    "a = torch.tensor([\n",
    "    [\n",
    "        [1, 2, 3],\n",
    "        [4, 5, 6],\n",
    "        [7, 8, 9]\n",
    "    ], [\n",
    "        [11, 12, 13],\n",
    "        [14, 15, 16],\n",
    "        [17, 18, 19]\n",
    "    ]])\n",
    "b = torch.tensor([10, 20, 30])\n",
    "a + b\n",
    "\n",
    "# b is broadcast along the inner-most dimension in a"
   ],
   "execution_count": 100,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor([[[11, 22, 33],\n         [14, 25, 36],\n         [17, 28, 39]],\n\n        [[21, 32, 43],\n         [24, 35, 46],\n         [27, 38, 49]]])"
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "Eja7wC47Pe8x",
    "outputId": "7cb19713-91d3-4b35-ba07-73ebdba6c606",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 153
    },
    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.579982Z",
     "start_time": "2023-11-23T09:26:22.404500Z"
    }
   },
   "source": [
    "# Broadcasting in torch: what is the output and why?\n",
    "a = torch.tensor([\n",
    "    [\n",
    "        [1, 2, 3],\n",
    "        [4, 5, 6],\n",
    "        [7, 8, 9]\n",
    "    ], [\n",
    "        [11, 12, 13],\n",
    "        [14, 15, 16],\n",
    "        [17, 18, 19]\n",
    "    ]])\n",
    "b = torch.tensor([[10], [20], [30]])\n",
    "a + b\n",
    "\n",
    "# b is broadcast along the second dimension in a"
   ],
   "execution_count": 101,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor([[[11, 12, 13],\n         [24, 25, 26],\n         [37, 38, 39]],\n\n        [[21, 22, 23],\n         [34, 35, 36],\n         [47, 48, 49]]])"
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "g_3yHVvEP0LN",
    "outputId": "3887cc15-2e38-4f57-a47a-63e4b60067d4",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 153
    },
    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.580072Z",
     "start_time": "2023-11-23T09:26:22.407591Z"
    }
   },
   "source": [
    "# Broadcasting in torch: what is the output and why?\n",
    "a = torch.tensor([\n",
    "    [\n",
    "        [1, 2, 3],\n",
    "        [4, 5, 6],\n",
    "        [7, 8, 9]\n",
    "    ], [\n",
    "        [11, 12, 13],\n",
    "        [14, 15, 16],\n",
    "        [17, 18, 19]\n",
    "    ]])\n",
    "b = torch.tensor([[[10]], [[20]]])\n",
    "a + b\n",
    "\n",
    "# b is broadcast along the first dimension in a"
   ],
   "execution_count": 102,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor([[[11, 12, 13],\n         [14, 15, 16],\n         [17, 18, 19]],\n\n        [[31, 32, 33],\n         [34, 35, 36],\n         [37, 38, 39]]])"
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "MNkprrEGQOBf",
    "outputId": "6e716dbf-fe26-453f-db26-030db52dd9d9",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 153
    },
    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.580158Z",
     "start_time": "2023-11-23T09:26:22.411045Z"
    }
   },
   "source": [
    "# Broadcasting in torch: what is the output and why?\n",
    "a = torch.tensor([\n",
    "    [\n",
    "        [1, 2, 3],\n",
    "        [4, 5, 6],\n",
    "        [7, 8, 9]\n",
    "    ], [\n",
    "        [11, 12, 13],\n",
    "        [14, 15, 16],\n",
    "        [17, 18, 19]\n",
    "    ]])\n",
    "b = torch.tensor([10, 20, 30])\n",
    "a * b\n",
    "\n",
    "# b is broadcast along the inner-most dimension in a"
   ],
   "execution_count": 103,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor([[[ 10,  40,  90],\n         [ 40, 100, 180],\n         [ 70, 160, 270]],\n\n        [[110, 240, 390],\n         [140, 300, 480],\n         [170, 360, 570]]])"
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "rafEJLP4QrXO",
    "outputId": "28d3816d-416e-4c8e-effc-d310d4d6dca3",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 153
    },
    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.580243Z",
     "start_time": "2023-11-23T09:26:22.414630Z"
    }
   },
   "source": [
    "# Broadcasting in torch: what is the output and why?\n",
    "a = torch.tensor([\n",
    "    [\n",
    "        [1, 2, 3],\n",
    "        [4, 5, 6],\n",
    "        [7, 8, 9]\n",
    "    ], [\n",
    "        [11, 12, 13],\n",
    "        [14, 15, 16],\n",
    "        [17, 18, 19]\n",
    "    ]])\n",
    "b = torch.tensor([[10], [20], [30]])\n",
    "a * b\n",
    "\n",
    "# b is broadcast along the second dimension in a"
   ],
   "execution_count": 104,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor([[[ 10,  20,  30],\n         [ 80, 100, 120],\n         [210, 240, 270]],\n\n        [[110, 120, 130],\n         [280, 300, 320],\n         [510, 540, 570]]])"
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "oPDDtULvQ0up",
    "outputId": "7804393c-d311-43fa-cde6-1af5cf8fd2cf",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 153
    },
    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.580280Z",
     "start_time": "2023-11-23T09:26:22.417531Z"
    }
   },
   "source": [],
   "execution_count": 104,
   "outputs": []
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "f2G27sVbRFxc",
    "outputId": "54e9d3b2-72a5-4f6c-8419-a9f284fab483",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 153
    },
    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.580363Z",
     "start_time": "2023-11-23T09:26:22.419114Z"
    }
   },
   "source": [
    "# Broadcasting in torch: what is the output and why?\n",
    "a = torch.tensor([\n",
    "    [\n",
    "        [1, 2, 3],\n",
    "        [4, 5, 6],\n",
    "        [7, 8, 9]\n",
    "    ], [\n",
    "        [11, 12, 13],\n",
    "        [14, 15, 16],\n",
    "        [17, 18, 19]\n",
    "    ]])\n",
    "b = torch.tensor([[10], [20], [30]])\n",
    "torch.matmul(a, b)\n",
    "\n",
    "# a is multiplied by a \"column-vector\" b twice"
   ],
   "execution_count": 105,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor([[[ 140],\n         [ 320],\n         [ 500]],\n\n        [[ 740],\n         [ 920],\n         [1100]]])"
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "2a1smQOCRuLl",
    "outputId": "92706735-ab40-44a3-892b-a0f5c74ca693",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 153
    },
    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.580465Z",
     "start_time": "2023-11-23T09:26:22.423210Z"
    }
   },
   "source": [
    "# Broadcasting in torch: what is the output and why?\n",
    "a = torch.tensor([\n",
    "    [\n",
    "        [1, 2, 3],\n",
    "        [4, 5, 6],\n",
    "        [7, 8, 9]\n",
    "    ], [\n",
    "        [11, 12, 13],\n",
    "        [14, 15, 16],\n",
    "        [17, 18, 19]\n",
    "    ]])\n",
    "b = torch.full((3, 1), 10)\n",
    "\n",
    "torch.matmul(a, b)\n",
    "\n",
    "# a is multiplied by a \"column-vector\" b twice"
   ],
   "execution_count": 106,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor([[[ 60],\n         [150],\n         [240]],\n\n        [[360],\n         [450],\n         [540]]])"
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "LExsCozMS93P",
    "outputId": "317f4ce0-55d6-4de5-8796-5d19f44d12d8",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.580564Z",
     "start_time": "2023-11-23T09:26:22.427131Z"
    }
   },
   "source": [
    "# Which operator (for Python 3.5+) is for matrix multiplication\n",
    "# and is implemented in torch?\n",
    "a = torch.tensor([\n",
    "                    [1, 2]\n",
    "                ])\n",
    "b = torch.tensor([\n",
    "                    [3],\n",
    "                    [4]\n",
    "                ])\n",
    "\n",
    "# at-sign\n",
    "a @ b"
   ],
   "execution_count": 107,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor([[11]])"
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "arfKnUgg5q12",
    "outputId": "bef2bd99-7673-4291-8bc5-2eb0a5e90b6f",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.580650Z",
     "start_time": "2023-11-23T09:26:22.430509Z"
    }
   },
   "source": [
    "# What is the result and why?\n",
    "t = torch.tensor([[1, 5, 3],\n",
    "                 [4, 2, 6]])\n",
    "torch.max(t)\n",
    "\n",
    "# If no dimension provided, reduces to a scalar\n",
    "# among all dimensions; returns the max value"
   ],
   "execution_count": 108,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor(6)"
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "tzV-dezu6N_N",
    "outputId": "ceb40c78-9766-4d74-d1f5-9255b96b18ea",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.580745Z",
     "start_time": "2023-11-23T09:26:22.433397Z"
    }
   },
   "source": [
    "# What is the result and why?\n",
    "t = torch.tensor([[1, 5, 3],\n",
    "                 [4, 2, 6]])\n",
    "torch.max(t, dim=0)\n",
    "\n",
    "# Max values along the first axis"
   ],
   "execution_count": 109,
   "outputs": [
    {
     "data": {
      "text/plain": "torch.return_types.max(\nvalues=tensor([4, 5, 6]),\nindices=tensor([1, 0, 1]))"
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "F1Q1Il2F6oAk",
    "outputId": "2f568809-568a-4325-9c33-87be7d2535f6",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.580842Z",
     "start_time": "2023-11-23T09:26:22.437159Z"
    }
   },
   "source": [
    "# What is the result and why?\n",
    "t = torch.tensor([[1, 5, 3],\n",
    "                 [4, 2, 6]])\n",
    "torch.max(t, dim=1)\n",
    "\n",
    "# Max values along the second axis"
   ],
   "execution_count": 110,
   "outputs": [
    {
     "data": {
      "text/plain": "torch.return_types.max(\nvalues=tensor([5, 6]),\nindices=tensor([1, 2]))"
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "2i3ofUeN7Awj",
    "outputId": "3560d6fc-87fb-4bc9-f37f-bda4d92f60ae",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.580942Z",
     "start_time": "2023-11-23T09:26:22.440334Z"
    }
   },
   "source": [
    "# What is the result and why?\n",
    "t = torch.tensor([[1, 0, 0],\n",
    "                 [4, 2, 6]], dtype=torch.float64)\n",
    "torch.mean(t, dim=1)\n",
    "\n",
    "# Mean value along the second axis"
   ],
   "execution_count": 111,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor([0.3333, 4.0000], dtype=torch.float64)"
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "_GZOBmmd7hGX",
    "outputId": "c0ccfa39-5fcc-480a-d307-aebc23307725",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.581085Z",
     "start_time": "2023-11-23T09:26:22.444075Z"
    }
   },
   "source": [
    "# What is the result and why?\n",
    "t = torch.tensor([1, 0, 0])\n",
    "torch.mean(t, dtype=torch.float)\n",
    "\n",
    "# Mean value but the method has an aggressive type inference\n",
    "# from the input tensor, thus integers end up as integers!!"
   ],
   "execution_count": 112,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor(0.3333)"
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "WU70gwlS8BRg",
    "outputId": "72ce844b-13b5-4eb8-e474-24a10938aaa0",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 68
    },
    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.581206Z",
     "start_time": "2023-11-23T09:26:22.447382Z"
    }
   },
   "source": [
    "# What is the result and why (incl. shape)?\n",
    "x = torch.tensor([[1, 1, 1],\n",
    "                 [1, 1, 1]])\n",
    "torch.sum(x, dim=1, keepdim=True)\n",
    "\n",
    "# sum along the second axis, but the dimensions are kept"
   ],
   "execution_count": 113,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor([[3],\n        [3]])"
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "vQciiIOo81kn",
    "outputId": "3cc89b4c-1862-4da3-fb89-c166e002855b",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.581357Z",
     "start_time": "2023-11-23T09:26:22.450955Z"
    }
   },
   "source": [
    "# What is the result and why?\n",
    "x = torch.tensor([[1, 2, 3],\n",
    "                 [1, 1, 1]], dtype=torch.float64)\n",
    "torch.linalg.vector_norm(x, ord=2, dim=1)\n",
    "\n",
    "# length of the vector; distance from the origin to the point X\n",
    "# [sqrt(14), sqrt(3)]"
   ],
   "execution_count": 114,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor([3.7417, 1.7321], dtype=torch.float64)"
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "sGgWPJOd9xk5",
    "outputId": "1ee69bd2-39a9-4bbf-eb84-f92ca740971f",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.581574Z",
     "start_time": "2023-11-23T09:26:22.454559Z"
    }
   },
   "source": [
    "# What is the result and why?\n",
    "x = torch.tensor([[1, 2, 3],\n",
    "                 [1, 1, 1]], dtype=torch.float64)\n",
    "torch.linalg.vector_norm(x, ord=2)\n",
    "\n",
    "# length of the vector; distance from the origin to the point X\n",
    "# No axis given!\n",
    "# sqrt(17) -- it reduces all cells, so first all squared, summed\n",
    "# up, and sqrted"
   ],
   "execution_count": 115,
   "outputs": [
    {
     "data": {
      "text/plain": "tensor(4.1231, dtype=torch.float64)"
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "kbReE8Vu_jJn",
    "outputId": "046ba6be-c20a-4605-881d-d63312822bbc",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 136
    },
    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.581639Z",
     "start_time": "2023-11-23T09:26:22.457506Z"
    }
   },
   "source": [],
   "execution_count": 115,
   "outputs": []
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "sgIHZZNw_4_O",
    "outputId": "62a743bd-38e4-40db-eb6d-2853e3914e94",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.581684Z",
     "start_time": "2023-11-23T09:26:22.459848Z"
    }
   },
   "source": [],
   "execution_count": 115,
   "outputs": []
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "q_JFSsB15WEc",
    "outputId": "bb99e4c0-7bbd-42cf-959b-f70dba052bc1",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "ExecuteTime": {
     "end_time": "2023-11-23T09:26:24.581727Z",
     "start_time": "2023-11-23T09:26:22.461969Z"
    }
   },
   "source": [],
   "execution_count": 115,
   "outputs": []
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "3A0LBpz7Azgi",
    "outputId": "73420d3a-bc51-423a-e535-3d4a03ed676c",
    "colab": {
     "base_uri": "https://localhost:8080/",
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