lec_2_v2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d84f8022",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 253,
   "id": "5d3452b7",
   "metadata": {},
   "outputs": [],
   "source": [
    "torch.set_printoptions(precision=2, linewidth=140, sci_mode=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5207e11a",
   "metadata": {},
   "source": [
    "#### mean-shift algo\n",
    "<br/>\n",
    "<li> goal: cluster the nearby data points using \"mean shift algo\" </li>\n",
    "<li> algo: </li>\n",
    "<div>\n",
    "    \n",
    "        1) find distance between each data point to every other data points.\n",
    "        \n",
    "        2) use weight function to penalize or reduce the weights for the distant data points.\n",
    "        \n",
    "        3) take the weighter avg of all the distance, and update this weighter distance for the point.\n",
    "        \n",
    "        4) repeat this for all points\n",
    "        \n",
    "        5) do this some number of iteration again and again\n",
    "    \n",
    "    \n",
    "    \n",
    "<div>\n",
    "<li> intution: </li>\n",
    "<div>\n",
    "    \n",
    "        when we do the weighted avg of the distance for each point against each other points, close points\n",
    "        tend to move closer together, and distant points move further away at each iteration. so after certain\n",
    "        number of iteration it will create group of distinct clusters which are composed of closer data points.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60084e30",
   "metadata": {},
   "source": [
    "#### synthetic data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 332,
   "id": "db8b0104",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_clusters = 6 \n",
    "n_samples = 250\n",
    "dim = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 333,
   "id": "8be5db61",
   "metadata": {},
   "outputs": [],
   "source": [
    "centroids = torch.randn(n_clusters, dim)*70 - 35"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 334,
   "id": "5f2db477",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.return_types.max(\n",
       " values=tensor([34.82, -0.20]),\n",
       " indices=tensor([3, 3])),\n",
       " torch.return_types.min(\n",
       " values=tensor([ -99.35, -117.06]),\n",
       " indices=tensor([0, 5])),\n",
       " tensor([-32.40, -30.12]),\n",
       " tensor([52.13, 45.10]))"
      ]
     },
     "execution_count": 334,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "centroids.max(dim=0), centroids.min(dim=0), centroids.mean(dim=0), centroids.std(dim=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 335,
   "id": "0094010c",
   "metadata": {},
   "outputs": [],
   "source": [
    "from torch.distributions.multivariate_normal import MultivariateNormal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 336,
   "id": "e15df14c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sample(m):\n",
    "    return MultivariateNormal(loc=m, covariance_matrix=torch.diag(torch.tensor([5., 5.]))).sample((n_samples,))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 337,
   "id": "1f0164cd",
   "metadata": {},
   "outputs": [],
   "source": [
    "slices = [sample(c) for c in centroids]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 338,
   "id": "64555ccb",
   "metadata": {},
   "outputs": [],
   "source": [
    "slices = torch.cat(slices)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 339,
   "id": "a5921feb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1500, 2])"
      ]
     },
     "execution_count": 339,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "slices.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 340,
   "id": "df900003",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_data(centroids, data, n_samples, ax=None):\n",
    "    if not ax:\n",
    "        _, ax = plt.subplots(figsize=(20, 8))\n",
    "       \n",
    "    for i, c in enumerate(centroids):\n",
    "        sample = data[i*n_samples:(i+1)*n_samples]\n",
    "        ax.scatter(sample[:,0], sample[:,1], s=10)\n",
    "        ax.plot(*c, marker='x', markersize=10, color='k', mew=5)\n",
    "        ax.plot(*c, marker='x', markersize=5, color='m', mew=2)        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 341,
   "id": "aa383293",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1440x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_data(centroids, slices, n_samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30216cd9",
   "metadata": {},
   "source": [
    "#### algo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 342,
   "id": "e91cc060",
   "metadata": {},
   "outputs": [],
   "source": [
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 343,
   "id": "4f25050b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# distance weighting function\n",
    "def gaussian_kernel(d, bw):\n",
    "    return torch.exp(-0.5*((d/bw))**2) / (bw*math.sqrt(2*math.pi))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 344,
   "id": "d0a95584",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_func(f):\n",
    "    x = torch.linspace(0, 10, 100)\n",
    "    plt.plot(x, f(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 345,
   "id": "f319de0e",
   "metadata": {},
   "outputs": [],
   "source": [
    "from functools import partial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 346,
   "id": "353e0e01",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_func(partial(gaussian_kernel, bw=2.5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 347,
   "id": "d8437d4e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# distance weighting function\n",
    "def tri(d, i):\n",
    "    return (-d+i).clamp_min(0)/i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 348,
   "id": "12e05987",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_func(partial(tri, i=3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 349,
   "id": "64389961",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = slices.clone()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 350,
   "id": "ad2e58ce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([-103.10,   -6.25])"
      ]
     },
     "execution_count": 350,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = X[0]\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 351,
   "id": "cb8f8eb0",
   "metadata": {},
   "outputs": [],
   "source": [
    "dist = ((x.view(1, -1) - X)**2).sum(1).sqrt()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 352,
   "id": "91ea1ca9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1500])"
      ]
     },
     "execution_count": 352,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dist.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 353,
   "id": "8e0de8d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0.00, 5.61, 8.41, 2.33, 1.23, 3.60, 6.29, 2.49])"
      ]
     },
     "execution_count": 353,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dist[:8]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 354,
   "id": "32badb5c",
   "metadata": {},
   "outputs": [],
   "source": [
    "weights = gaussian_kernel(dist, 2.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 355,
   "id": "f216f790",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1500])"
      ]
     },
     "execution_count": 355,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weights.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 356,
   "id": "577ae2b0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0.16, 0.01, 0.00, 0.10, 0.14, 0.06, 0.01, 0.10])"
      ]
     },
     "execution_count": 356,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weights[:8]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 357,
   "id": "71a40ccd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1500, 1])"
      ]
     },
     "execution_count": 357,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weights.view(-1, 1).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 358,
   "id": "dcecf59d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([-101.07,   -6.66])"
      ]
     },
     "execution_count": 358,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(weights.view(-1, 1) * X).sum(0)/weights.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 359,
   "id": "07a5e44d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(10.88)"
      ]
     },
     "execution_count": 359,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weights.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 360,
   "id": "babd8a17",
   "metadata": {},
   "outputs": [],
   "source": [
    "def one_update(X):\n",
    "    for i, x in enumerate(X):\n",
    "        dist = ((x.view(1, -1)-X)**2).sum(1).sqrt()\n",
    "        weights = gaussian_kernel(dist, 2.5)\n",
    "        X[i] = (weights.view(-1, 1)*X).sum(0)/weights.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 363,
   "id": "e170e722",
   "metadata": {},
   "outputs": [],
   "source": [
    "def mean_shift(data):\n",
    "    X = data.clone()\n",
    "    for it in range(10):\n",
    "        one_update(X)\n",
    "        \n",
    "    plot_data(centroids+2, X, n_samples=n_samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 364,
   "id": "f1b5b767",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.53 s, sys: 8.1 ms, total: 1.53 s\n",
      "Wall time: 1.53 s\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1440x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%time mean_shift(slices)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "204f0ca7",
   "metadata": {},
   "source": [
    "#### GPU batched algo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 468,
   "id": "77129f53",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([5, 2]), torch.Size([1500, 2]))"
      ]
     },
     "execution_count": 468,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bs = 5\n",
    "X = slices.clone()\n",
    "x = X[:bs]\n",
    "x.shape, X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 481,
   "id": "86398b41",
   "metadata": {},
   "outputs": [],
   "source": [
    "def dist_b(a, b):\n",
    "    return ((a[None] - b[:,None])**2).sum(2).sqrt()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 482,
   "id": "588779e5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([5, 1500])"
      ]
     },
     "execution_count": 482,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dist_b(X, x).shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c617bc50",
   "metadata": {},
   "source": [
    "<code>\n",
    "\n",
    "rule-1:\n",
    "      X = (1, 1500, 2)\n",
    "      x = (5, 1, 2)\n",
    "rule-2:\n",
    "      X = (1, 1500, 2) => (5, 1500, 2) \n",
    "      x = (5, 1, 2) => (5, 1500, 2)\n",
    "rule-3:\n",
    "     * both shape matches so we can perform the broadcasting rue\n",
    "    \n",
    "</code>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 483,
   "id": "3d765f10",
   "metadata": {},
   "outputs": [],
   "source": [
    "weight = gaussian_kernel(dist_b(X, x), 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 485,
   "id": "ec8d62c4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([5, 1500]), torch.Size([1500, 2]))"
      ]
     },
     "execution_count": 485,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weight.shape, X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "791488b3",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "919c21da",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "caf02903",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a11c5695",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b3687c77",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9c3e5386",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4b386293",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "b7b66f78",
   "metadata": {},
   "source": [
    "#### broadcasting test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 404,
   "id": "9447d082",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 407,
   "id": "01cc3c1e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((3,), (3,))"
      ]
     },
     "execution_count": 407,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([\n",
    "    0, 1, 2\n",
    "])\n",
    "b = np.array([\n",
    "    5, 5, 5\n",
    "])\n",
    "a.shape, b.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 406,
   "id": "72ca81d8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 6, 7])"
      ]
     },
     "execution_count": 406,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 408,
   "id": "82fcc170",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 6, 7])"
      ]
     },
     "execution_count": 408,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a + 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 413,
   "id": "26cac2dd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 1., 1.],\n",
       "       [1., 1., 1.],\n",
       "       [1., 1., 1.]])"
      ]
     },
     "execution_count": 413,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M = np.ones((3, 3))\n",
    "M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 415,
   "id": "e2fd410b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 2., 3.],\n",
       "       [1., 2., 3.],\n",
       "       [1., 2., 3.]])"
      ]
     },
     "execution_count": 415,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M + a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 420,
   "id": "06c8ee37",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((3, 3), (3,))"
      ]
     },
     "execution_count": 420,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M.shape, a.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1abbd211",
   "metadata": {},
   "source": [
    "<code>3, 3\n",
    "   3  =>  3, 3\n",
    "          3, 3</code>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 430,
   "id": "5edb052c",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.arange(3)\n",
    "b = np.arange(3)[:,np.newaxis]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 432,
   "id": "1f732ab7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((3,), (3, 1))"
      ]
     },
     "execution_count": 432,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.shape, b.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 433,
   "id": "c328d06f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2],\n",
       "       [1, 2, 3],\n",
       "       [2, 3, 4]])"
      ]
     },
     "execution_count": 433,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 434,
   "id": "1f00d92e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0, 1, 2]),\n",
       " array([[0],\n",
       "        [1],\n",
       "        [2]]))"
      ]
     },
     "execution_count": 434,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a, b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 440,
   "id": "4c27991e",
   "metadata": {},
   "outputs": [],
   "source": [
    "M = np.ones((2, 3))\n",
    "a = np.arange(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 441,
   "id": "777fbd79",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((2, 3), (3,))"
      ]
     },
     "execution_count": 441,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M.shape, a.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 442,
   "id": "f9d990fd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 1., 1.],\n",
       "       [1., 1., 1.]])"
      ]
     },
     "execution_count": 442,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 443,
   "id": "1f9b1df5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2])"
      ]
     },
     "execution_count": 443,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6748826",
   "metadata": {},
   "source": [
    "<code>\n",
    "rule 1: array has less dim so pad with 1 at leading left side\n",
    "        a = (3,) => (1, 3)\n",
    "\n",
    "rule 3: compare each dim of a and M and copy the deficient dim with the same value\n",
    "        M = (2, 3)\n",
    "        a = (1, 3) => (2, 3) * here 1st dim is deficient so it got filled up with the second dim\n",
    "</code>  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 446,
   "id": "08633530",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[1., 2., 3.],\n",
       "        [1., 2., 3.]]),\n",
       " (2, 3))"
      ]
     },
     "execution_count": 446,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(M + a), (M + a).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 451,
   "id": "653eec5b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((3, 1), (3,))"
      ]
     },
     "execution_count": 451,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(3).reshape(3, 1)\n",
    "b = np.arange(3)\n",
    "a.shape, b.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9df5df2c",
   "metadata": {},
   "source": [
    "<code>\n",
    "\n",
    "rule-1:\n",
    "    (3, 1)\n",
    "    (3,) => (1, 3)\n",
    "\n",
    "rule-2:\n",
    "    (3, 1) => (3, 3) * here column got copied\n",
    "    (1, 3) => (3, 3) * here rwo got copied\n",
    "    \n",
    "</code>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 452,
   "id": "ce5e04e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[0, 1, 2],\n",
       "        [1, 2, 3],\n",
       "        [2, 3, 4]]),\n",
       " (3, 3))"
      ]
     },
     "execution_count": 452,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(a+b), (a+b).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 453,
   "id": "6e6a321b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((3,), (3, 2))"
      ]
     },
     "execution_count": 453,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M = np.ones((3, 2))\n",
    "a = np.arange(3)\n",
    "a.shape, M.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e3a6621",
   "metadata": {},
   "source": [
    "<code>\n",
    "    \n",
    "rule-1:\n",
    "    (3, 2)\n",
    "    (3,) => (1, 3)\n",
    "    \n",
    "rule-2:\n",
    "    (3, 2)\n",
    "    (1, 3) \n",
    " \n",
    "rule-3:\n",
    "    * both shapes are not matching\n",
    "    * both are not compatible, because first dim fine, but second dim not matching so, you can't do the broadcasting\n",
    "\n",
    "</code>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 457,
   "id": "3375b20d",
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "operands could not be broadcast together with shapes (3,) (3,2) ",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[457], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m a \u001b[38;5;241m+\u001b[39m M\n",
      "\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (3,) (3,2) "
     ]
    }
   ],
   "source": [
    "a + M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 458,
   "id": "3e58daf6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# use braoadcasting for mean centering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 460,
   "id": "651b8710",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 3)"
      ]
     },
     "execution_count": 460,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = np.random.random((10, 3))\n",
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 461,
   "id": "a9e31a21",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.53842755, 0.74584377, 0.33992809])"
      ]
     },
     "execution_count": 461,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean = X.mean(0)\n",
    "mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 463,
   "id": "ff9e8f52",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((3,), (10, 3))"
      ]
     },
     "execution_count": 463,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean.shape, X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 466,
   "id": "cc3ee0fb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-3.33066907e-17, -1.77635684e-16, -4.44089210e-17])"
      ]
     },
     "execution_count": 466,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(X - mean).mean(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f1839a7f",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "python_main",
   "language": "python",
   "name": "python_main"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}