From d420dde884634b819ca544ae8660047b0a3f0d17 Mon Sep 17 00:00:00 2001 From: Shubh Tripathi <65160713+shubh-tripath-i@users.noreply.github.com> Date: Wed, 8 Nov 2023 17:13:14 +0530 Subject: [PATCH] Add files via upload --- Sentiment Analysis with LLMs.ipynb | 2975 ++++++++++++++++++++++++++++ 1 file changed, 2975 insertions(+) create mode 100644 Sentiment Analysis with LLMs.ipynb diff --git a/Sentiment Analysis with LLMs.ipynb b/Sentiment Analysis with LLMs.ipynb new file mode 100644 index 0000000..66bac2f --- /dev/null +++ b/Sentiment Analysis with LLMs.ipynb @@ -0,0 +1,2975 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Vectors" + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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vbKCioCqgRlT7pf5RY0yzR6tZu1InVzdez0ffwkDBkNMIYfTW+InJJdMCs2hzJwsVSzbLNatX1nds6m0L7JLsAx0cHfWd5J0FXEiuWNdVt/fuYx69nre8Gnee9j6665BPsi/Vj0L29fcIcAq0D7IJtqRYhpiFaobJhgtEsOymiURErkd9o36P/hGLjiPGCyVo7HFKjE4qSm7bO5NCs58vVSZN+4BNut/B+Iy8Q9WZHVmj2V9zmfMUDtvnRxzJK2gofHD0zbFfRZzFyiV2J0JLD5adKm892V8xd+rnGeZKibPaVXbnyNWxNYdqS+Bzrrdh4QLxomKj46Woy/lXGpq6r45d+9SCaeW4LnlD46ZFm9utwPaYjpTbqZ0Hug7eyeg+dDfzXvb93Ad5PXkP8x7l9eY+znmS1XeoP30gdXDv07i/ooZ2D0c+ixlJen5w9OiLyrGml/fGn7/6MAleE6cE38hP68yYz/rNnX774b3yfNKH9o8/FzWX4j5d/PxmmX3F8mvKt6bvs2vc6w4/sn92b8ffGKGP3IH8iOpEH8I4YsWxS7jr+AyCAw03zTjtWbpwenUGBEMnYzqTBZGB2E86wmzLwsDymDWbzYQdYm/liOAU4hzhyuHW4f7AU8ZrxvuFr4LfjP+jwDFBDcExob3C/MLtIt4i66IlYkpiveIB4usSRyWlJDukHKVmpFNlRGRGZHN3GOz4Ilcj76lAp9ChGKkkoDSonKaioDKpmq+mrfZBvUzDXGNZ86yWvdZP7QYdd12s7jU9sj5R/7ZBpCG/Yb9RmrGS8axJqakt/N5x0zzKQsrijWWFlYc1q/VTm0JbBzuS3bD9CQdvR2HHd06XnRNdjF0ZXEfdqt2jPQw8aT2HvU7tDPZW8F7bddenwNfLT8JvhdztfzTAN1AxCBU0HFxPSQlxCpUOQ4e9Cr8RUbI7PtI1SoPKG42Kno8Ziu2Ma4yvSMjfk5oYnxSa7L935z63FKf9Dqn2afYHHNKdDrpn7DwUkBmaFZ2dkpOZW5hXcbguv/nInYKBwvGjH4+jiiSKvUqOnLhbulYue9Kv4viph6fXKxXOBlSVnuurQdVq1cXXNza8vyB5MaSx/tLCFZWm/Vd7mzlawlq7b/DdTGl73W7V0dYp33W+W+ru5fsGD0YfJvTyPe7vyxtweio6BIbfj7wZffcSvBKZ3DVVP4OeS3wPPlQtkj/rrqh9d14v2Yj/1v+AGwWjAsDxQwBs/M/jUAdA7nkAxPYAwAbnnnZ0ADipA4SAKYCWuwBkof3n/oDgxJMASIAHSAI1YAbnl2FwTlkMGkEPmAI/IHZIGXKEoqHjUCv0Es75pBEuiFREI2IcyYA0QMYjLyBn4CzNC1WGegFnYj7oc+gPGBVMKuYJlgcbju3AkXAUXCeeEx+LHyQoEooJ6zRkmse06rS1dOx0ufQI+iT6rwyxDCuMiUwQUzaRlVhFUiP1M4ewYFnOsRqzzrBlskux93PEcHJwtnP5c9NwX+Hx4EXyXuDzhDOCAYF8QVshJqGnwsUinqICojNi58WjJTQkIckeqQJpT3h1LsoO7miTq5YvVNinSFFyVNZQ4VOFVCfU2tSPaYRoamvRa41p1+nE6Orq4fQG9JsMrhq2GN0wbje5Y9pj1mc+bDFuOWu1ZL1mi7NjtRd1UHO0ciI7J7uUuLa7zXmQPPW9IndWeg/5EHz1/ZLIrf5fA9WCkoI7QwihzmFV4cu7zSIrohaitWJyYsfjlRKO7FlKck2+t087pT3VMm0qPStDOxNkDeRcyivPLywwO4o8dreooCSg1LBcukLwtEilUpVNdVRtWf2jC6BR9bJNk/u14Jbk68dvXrk12LHSxdttdi/mwemHT3p/9MkM7Hx6eOj2CGmUPHZhfH6Se0ptWm9W/i39u2fzhz/uWOhcMvvU/UVhuXRl9Zv993OrS+saP1J+3t48P7biT4TjLwFUgQlwBSFgHzgGGkA3GAffIBIkB9lAEdARqAl6jgAICTjLT0NcRryG83grZDqyA7mG0kYdQPWi2dGB6GYMHuONacYyYsOwj3DSuHzcMt4Lf48gSyimQdJE0UzSOtM+pDOka6fXor8FZ7EPGO0Zx+E89RfxGEmW9Jg5As48W1l92WjYWtkDOVg57nPu4ZLmmuQu5rHlxfF28e3nNxDACDwWLBLyFZYVXhfpFa0QixI3luCS+CT5UOqsdIqMp6zmDgk5dnm8/LrCguKU0jPlhyo3Vc+rlaof0qBqemoZakvqMOos647qtes3Glw2bDJqMb5p0mHabfbQvN/imeUrq1nrJZs1O5w9q4OYo7qTtbO/y17XUrfr7qMeP7wEd1p4x+w67dPnB5FV/CMC6gJngkUpISGXQ1fDTSOKds9FaVH3RnfEouKs4osTZhLVkw4nz+4zTqlNpU/bc2AWPk/6My2y7ueY5fYedsifKEg5ynvsdlFgCf2J1jL/k6SKe6f3Vqqc/XTuck1snVYD5vzQxXOXkq94XVVppm+Zun715oFbNh3stye76rqp97QeYHuGH9U93t/nNaDzVGSIafjBiPPz6ReJL5nHr0w4Ta5P1U67zzLM9bzLnLf8yLjwbOn055Blla+Ib32rZetBPxW3448EGEC7eQKIAxV4BbiBcHAQnAI3wSi8/wUhCygWqoKGETQII3jndyFxSHvkKeQnlAWqBo1HU9GvME7wbrfBDuHIuO/4IoI6YZrmBK0e7RhdEj0/fQ9DPKMk4xTTKaIfSYL0lfk+SwVrEpsnux6HFCc7Fw03gnudZ5V3nR8IYOE3UB5hWRFtUQexIPH9Eickr8F596Is4w4FOVf5fQpVin1KayoSqu5qheqDmsxa7tpVOgt62vp5Bq+MFI1zTCbNtMyLLD5Z2VlfsKW1C7N/6CjplOP8ztXCrd4D70nxuu8tuuugz7SfIbk6ABnoH3SHIhqSEToXbhXRGMkSlUCdiDGKvRjPnrBvz/skN3ifqqTUpHKkHU5HHUzO+JTpkXU5+1euU17N4dUjjgUXjxKOUY7fK5YqyT2xUOZafqtC9FQBfPb7n+09p1ldU8tUl1g/c97xQluj6KX8yytN3lfvNcu0HGldvGF/8+ItQntgR3snsSvgTvNd1D27+2UPph5KPKL0Vj+e7OPstx84OHj16eshwrDcM4cR6vPDo3Uv7owNvZwZX3q1Pgm9xk5h3mCmwfTqzIfZ8bnHb1vfVb7PnI/4YP1RagG78GqxdSnrk8dnic+fvrQtp60YfcV87f6W8l3z+9LquTWPdcJ68w/yT7qfV365b8R/69vR5v3BCMBprg00cOnTx39/t9n6rvSP3OTfLdi8XTbKxu2y2cI3Dfgf/mXQx+i0F10AAAA4ZVhJZk1NACoAAAAIAAGHaQAEAAAAAQAAABoAAAAAAAKgAgAEAAAAAQAAAcGgAwAEAAAAAQAAAN0AAAAAnnc1YQAAQABJREFUeAHtnQe8FcX1xy9NREUFC4IFxG4Ue4u9V8CSWGLsPRpNbLGhV+xJ1L8t9gSNmmhMEOwtij0xFizYRbE3ULAh7f/9XXbwvGHvfeXue++Wcz6f35s5M7Ozs7+7O2fmzOy+XM7FGXAGqoGB7jTyl2Ceamist9EZcAacAWfAGSiXgS5UsDsYDr4DM8AewMUZcAYyYqBDRvV4Nc6AM5A9A52p8mOwgKlaBnFno5eKLkSmjOZPQS8wHbwEbgL/AS7OgDPgDDgDzkBFM3A1rdMMMEAzQrlGS0lXMo8HX4FwXBzeRl4P4OIMOAPOgDPgDFQsA1vSstiA/aJEa+ci74WUY+I6pL8C5gcuzoAz4Aw4A85ARTIgl+hnwBoxzeKKyTVk2LKKPwluBR+l5N1Bmosz4Aw4A86AM1CxDFxJy6xh+x593pTW7hiV+xZ9U1NOG22ujcqo3oGmjEedAWfAGXAGnIGKYmBzWmONoOJ6XSKW20mw5U6OC6BrM1zsLh2dUs6TnAFnwBlwBpyBdmFALtDFwFpA7wV2Ap8Ca+BGoMcyngRbZu24APrKQO5UW07xtLIkuzgDzoAz4Aw4A23DwIKc5k9gCghG6hvifwNPmzTlxS5R7QgNx4RwI9IkA8AZ4FUQ8myoXaT7ABdnwBlwBpwBZ6BdGNiOs04A1jg1Ft/LtLQj8anR8Q+hvxalhTonkn4jGAxkQF2cAWfAGXAGnIF2YaA3Z/0cBAMVwtdJuw/Eu0NDvtYArYxDCXlp4dfka1a5E5gTuDgDzoAz4Aw4A23CgHZmpu3o1Mn1moI1WnJ17qaMRHRsHtgyik8G84Eg+hJMXEbu1JvBLqAbCKL3Aw8AfwAypm8CrUO6OAPOgDPgDNQ5A1m5B7XBZWug1xK0aeUsEMviJMSG69S4UKJfmlJ2b1N2j5T8o02+jcZl9SUauVRdnAFnwBlwBuqYgXW5dq2VZSF3UYk1cG+kVPrzqIzKL59STkkLAxkrW6dmkUFkdMcCm69vjy4UCphQG3BsuUdMnkedAWfAGXAG6pCBpbhmvYogQ9PY9zmbQs9RFLKGRvFVowMPTSkzd1TGqldF5eUSlWszyCFE4nO+TZo23mgdsDe4CMRltiLNxRlwBpwBZ6BGGVDnfzi4vMj1LUD6ayAYh1Lf51QVendvc3AlWBukyaIkTgehToVnRwV1Hpuv+GpRGatqbS8uv68pIFfuYylldEzcllDPDeZ4jzoDzoAz4AzUEANrcS1y9U0DodPvRzyW2HU5Ii5gdM2kPgGhPunF5FEyQjmFsUt0vShfZTSbKyb9yLD1Ka62W9EGnP+CuFyarnVGXwu07HncGXAGnIEaYkDra3Hnf1zK9Wnzii0XXkbXDPFgoHqC3EvElv0AvZghOTIqq+PsTE87P/XOnq3vSfRi0osMW1bxH0CP6ADpfwbxu4MqrxnhSFBsBkuWizPgDDgDzkCtMPACF2INh2ZJsWxLgi2j+IsgfL3lHHPAASllNzL5NtoHxc5CVW/sEv0HafG517GVmHjazFHH7mfK2Khee9gTnAKOAYOADLuLM+AMOAPOQJ0wMITrlKHQZ8POBKuAWBYmYTKIjVHQrRuzJ+U0+wp5Ci8DxUTuWFvW1qVjtonyVfYlMBeIRbtBbV0hfndc0HVnwBlwBpwBZ0AM9Ab6cHQx0ft7sVELxiWE+qLLoqYCGZ2Qp/BjUMwlenRUVuWtS1THPZtSRmk7ALVf5e2M8X50e361X8bZxRlwBpwBZ8AZKMqA3IO/BVovC3IQEWtQbHwUeZqp6R08K3I/2nKKb2oLmPjSKWWte1VF1wSNGeJwvm8pq+v4EGh97wkgQ2u/HoPq4gw4A86AM+AMzGRAu0S1U1NGIxiTpWZmFdbIppj0kK9Q/3YoTfRuXmy0rk4rmKS9TmjrfTOlbJphtceE+D7JsTK6MoYuzoAz4Aw4A85ASQaWIzcYkRCeaI7QjtHBYBgI+QrDLlGis0m8PjeJEvr/f2lyC4m2XsVXTym4I2mfpZRV+bFga+DiDDgDzoAz4Aw0m4HRHGEN0XMpNWwZlVH5X6aUU9LewNanuFyraaIZZVw2domG4+Ygsj24Dmjt8Uogd2faRhmSXZwBZ8AZcAbqkQEZi4OB/kvCk0AuxmFArzukyckkxoZomaig1v7imdiIqExQtQY3Gdg6nw6ZJuyRUk7HpLlEzWEedQacAWfAGXAG0hlYjWQZEWuAbPzwlMNk8GwZxWUYY7mKBFuulEs0bYZnZ45ad3wqqe89QrsmqXOkuURJdnEGnAFnwBlwBn5kQLOp3RJ1WUKtv1lDFcdlbNZNyttALlBbdrTNTOJbRmVUfq+UckrSGp2tL8QfJv0hYNv5W3T7zqA2y+hcLs6AM9BODHRop/P6aZ2BpjIg4yPjtxXoAn4CrgVpBo7kBvJ3tD0apORy2gxzdpS2PPprJk0u0Y/AgibtPuIyeLHoGXoeDIgzIl1u0g3BzmBVoLalrUmS7OIMFBjQGnBv0AfoXuyUQPdniCvUPfgF+BjovlX4HXBxBpyBGmDgGa4hzK4UPmB0GRa9BN8d7AT0Qrst+wO6OhErS6HYMooPsQWS+FVRuWnoiyV52gFq65VLUy7TuN6gq522PKqLM1D411ZrwMN+4FxwPdD9PQZ8CcL905JQx78K/g1+D/xzeZDg4gxUKgNz0jAZsevAHFEjf4ee1gk8RrpmhlYORonLpn0sOzasL9pKkvgGKXXdQ5rqew8MA1b0sntc74eknQi62YIerzsGNFPrB2SItAatjVyvgKkgvl9bU9cSgQysBnh7A30q0MUZcAbamYG/cH67bjYwas+S6Gkdw4FROalyH40HtrxmYbGkGdYV4kLo6qhsXTauWWaYGdpDl0DRzLCfTfR4XTEgd+U6QAMmvUta7qzO3ndZxifTthtAU5YWKFabohGKizPQFgxotqdXF7R2Jtfi80CuGo2K9X3MIH8lolGqFRkyzbSsyI30rE1I4ucRHh+lywX6tkmTYbW6svLgdEWMaCPLBUaPo6eQcFac6HrdMdCVK5bR2whsDNYDc4Pmylcc8AGQB0GhjU9A18xRz45g46iFNcNFCHsBhSG+KvE+oDGRF+NS8HfwfWOFPd8ZcAaax8AuFB8L4lHsp6TdE6WrI1CnYkUj6vjYQ2wBE18mpezvTH6IyrDaOl8OGSbUiN7u5gzl1Un8EcSuW3OoR2ucAQ3qBgMN2nTPhnujKaEM2qPgMnAoWB/MB1pLNOj7JbgcyPU/HRRrp9bVDwcuzoAzkBEDetCLPXDF0gdF5+6bUofcOMXkOTJs3WkzxjTD+pOUCnuSdjQYCa4AvwYLAZf6Y6Abl7wzuAlMBPYeKxb/mnL3gyFge7A4aG+ZnwbsDZ4Cxdp9L3mLAhdnwBkog4EdOTZ+yDTSvAicBDQLlFsnLpNm4P4TlXsXvZio7rjOpaPC/VLKxO7Q6BBX65ABrTP/HMhtL4MW31exrlne7UCDLLlI5U2oZNGywrXgWxBfy3jSdgcuzoAz0AIG5uYYGTz7YD2N3jOqSx3MlKhcmkv0mKiM6l0RpIkMnj2v4jKMscSGdXRcwPW6ZGAerno3cCv4BsT3ktW1PjcK/AasAvS/IatRetDos0HaoPRvpHevxovyNjsDrcGAFtm3BDsBbVYp9tCnzQJXo3yanEKi7VgUHxwVXAI9XssoNXOTC9TW+XxUn1QZ1h/AnWAfMB9wqU8G5uWyfwGGg++AvXfiuAzfQ+BXYBFQS6JNPW+C+JrvI61LLV2oX4sz0BwG+lH4fPAqiB+Ot0nbGMQSG7bvKdAhLpToMj5fAlv3jSlln4zKvJJSJiSdGJVV3cuGzCTUeTUCdqlPBjpx2bsArffq/rT3XxzXDOkBoI0stf5+nbw4V4GYAy1TFHuGyXJxBmqPAY1y5QpRBxA/EFaX21NlrfwexZb5wmamxK+OymvjgXbgWfktiq1T8QG2gInrtQhbVtegzQAuzoAGP/ICvAPsPRLH5abXDOggsBCoN9mZC/4BWF7+WG8k+PXWLwPLceljgX0ASsUviKg6LuXYUjvjDk4pL5eqlcVQYpfombZAFNcapNZr5LbqFeW5Wn8MaK34YjAJFLuX1enfAw4AC4B6lz0hIH7mNBh1cQZqmgGt88nVaDsKPQhaL5Fb9FQQr5topmdnboPQ7fGK/wIUE60zxuW1FT2Wx0mw5V6PCxh9DhP3aP0ysCmXLpen1vLsvRPi8hJoXXg/4O5xSIjkaPTAlUL1BeLUxRmoWQbkBrE3/afoG0ZXqw7DllF8V1NGLqfYjardmMXkCDLi+jRit4ZVxx6VUm41Zbg4A4aBrsR1j44G8X0VdK1Dy73XF7iUZiBe3ij1LJeuyXOdgXZioDfnPRfoSxXPgH+C7UGaaLYXOgqFl6cU2oq0+NWGW6JyI9BtPYoPjMpI1QaFJ0FcVvpOwEofFI1EhcfAkcDdVpDgUmBAbu88+ASk3U9KewNo0DUPcGkaAx0optm05TR+NptWk5dyBtqYAbk2tSYW774MN3O8lqfm/RXoxWCNomUstW06SE8i14FwvA11TLdQkHDtlHLfkLatKdOd+JWmXGxYbzBlQ3QPIqXWF0M5D+uHgVW51GFgMrD3pI0/SJ4GYcVe6yHLpQQDK5BnXcovozuXJQjzrMpg4HiaYTuCtPjPoqbKMKWJ3J2lRtiqW65UK/ehpJ1zDOkPg89N/vPErze6jlO+P2iQ4JLKgAZUD4G0e0xpevXhz2AAcCmfgfj53Lv8Kr0GZ6B8BvpRxRBwM9AsbV/QDWi2pNmZ7SDkRrS64i+BUjI/mdqkYo+bgL4/kGvJpt+IbmVRlLHAlikW12aaHVLK2pko2UXlHHJWKprrGbXEwOpcjGZ2xe6lj8k7DSwMXLJjoD9V/QAC728R90Fqdvx6Tc1koAvlTwTfgnBThvBV0h5K0qcRykDImC0FngGhXAg3JC1NNiLxPRDKKdTaQG8guQjYPG1miWeSOueHUTl7jOJDgUQbYWKX1kGFnNJ/1iQ71DmO+BEg3lRTugbPrQYGlqCRfwVpgzn9/vIm7Au0McaldRi4gmrF9V1gtdY5hdfqDBRnYBmywuhWxih0/KXCM6Lq5BqKy18ZlZEqoyl3ZCir1yIOB1YGo4T8EB5mCyRxbV7RBpuJIJRT+D+wM7DyFIotM8RmFomnuV1lkG8FvwQ9ihznydXBgHYbnwt0D9p7Q3EZxBFgE+DS+gxoc9oGrX8aP4Mz8CMD/YmeDDTK1UN/EtgliccdQpq+CmVjGUWCLfsZeueo0IVRmYujfKm/iMqoztHKKCJzkK7R40/BgkXKhOsM7du1SLmQ3I9IsZlBqEMbbh4AmiEuDlyqgwF5O44EdjAWflOFuo/XAi7OgDNQwwwcz7XZB38M+vtJ2leEmnmtC/4vSbNlFV8IxLIPCXG5LaNCz0VltMvUSgeUO0Bcj/T9bcEicRlEK51Qfg3i+vraQinxi6JjGjOIql8z0FPA2kDndak8Bn5Gk+I153BvyN0/uPKa7C1yBpyB1mCgH5WGh9+Gcg0pz8pjKLaM4gNtgSQ+H2G89nZ1VE4zJ1vXu+iLJmV6EFoD+G1U9nv0NZKyCrRGsz74DbgRvA70uoTaJkO0O3gB2PMpPgKUkp5kfg3Cceo0FwMaGNwLfgAhr1g4gTL/AnL1Lgdc2pcBeQmeAGm/1yek67eNvRYkuTgDzkAtM/BfLi7uFNRxx7IbCXG5s+JCiX57VFYuJ9u5DIvyVa8M13vgC5N3H3F1XDI4Sr8WbA1sXUugx0Y3bmesy6B3A6XkZDLtceogrcjYy8D+HUwEtmyxuK7vL2BPsAhwaRsGluY0t4K030X33ZmgO3BxBpyBOmTgWK457hyGpvCgNZR4J+YjKeWUtBeI65TxCrISkWkgLmP198kP7tYViHcGxeRsMuyxxeI651VABqyUaHb5MQj1aF2zlNGU+3UbcAWIOQp1pIUvUV6u5h2Ad8KQkLH0pj6tN2sQFfOve+HPYFHg4gw4A3XMQF+uPe4g5O5Lk/NJtGXVkfRKKSgj831U9pqo3G/Rp0RlQt1yVWrTTlNFBkoGqNiandytvwfLgqbIQRQKbVGYb8pBSRmtZ8oNexJ4EKTtOrR1h7i4eBxcADTrXhK4tIwBGT8NLopxr/t7QMuq9qOcAWegFhl4iosKnbFCuffSNnWsE5VT2XhTC0kFGclfW6fcmZpNWlkPRTOzZ8BjSXwrwpbKWhx4JJDBuxDsDhYHzREZsVdBaLvWJMOMtDn1hLJzEtkcnAPkep4KQt2NhZ9SVuujpwLNNHsCl+IM9CFLM79ixm80eeXcX8XP7DnOgDNQ1QwcTevjDtluPrEX905U9mGbaeK/jMqpfnXklS6DaKDl4vKMGzw/9e0ILgFjgD1XU+JvcMyN4CigQYSMbL2LNiyJz9j7EPjUWuy+oCNwcQacAWdgNgY0W4pdiWfOVmpmwh8IQueiUC5RuZ9imZeEuFPK2qDE58xCf4JKwvXp2pbOotISdWj2shcYBsaCcO6mhj9wzP/An8A+4CdAa5q1LrrOE4BcyPqd0vgaR7o8FfXAB5fpUkkMyKXkUl0MqPPXzCKIZhzLBsWEaxJ/2uiK/hpcGqVJ1dre+uA2oN15DwKtfVWqaBaoNgcZTmTnoLRRuDDnkVtXrue1k3hz3aAa0Gj28ybQ76gwxN8mrsFJtckcNHgjMDBBqTXTdygj9/MwoEGCS6szcGWXXO4jrc3jmehMOINwWqJ3SMIZQZ+bcvyeQS9sOpNHI8kvhIpbfMVE/jhWBp4jvSrEjWBV/EwNGvkbNK2jWVkN5XmbkMTVkdpOSOt5G6aUU4c+HkxNyau0JLnKXgCaYUg0s1gdpF2/8ttSNBuVQQzQ79JSN6iu630QG0cZybeA1tPaW9RJrgi0i1i/h8Kfgu6glOi+PAv8FVTyYKvUNZSZl8e4zInxmMb9MSUxKh2TcHoSzmaUkvSSRik2UrHemq7mv2EzGWif9EWZ5LTp4W4E25TuTE62KLVo9mB/O42mT0qp/VzSfmfS1bEuBj40adUW3YcGDzON5sErfLrNJFVMlFF3YXdjMIoKlwfldkT6HT8AMoiCNuZoEKPOJy2cSnpzRO2bD/QAmt0qDPF+xIPB60vc3oeoRUVtuwuMSNDcNhWtuPIyTt+SsdmxtGsBICNkDVHQy70HKumyuf86HMo/7ZBHpuqkqTdw1V1YjTdYM7r1zTVqZqBZSCyaIT0DJgK5Om8B94FqHX13pe2vAXW+El3HCkDXXy3SnYbKjToA6DdbJgl1TZ1Aa4h+/2/BdAMZ0ljvTJqMnQxgFp30q9RzOxgJngTTQJ3IWb24PU/kYg8BMny1Kjcz+zu82mZ/9sdwI2jZqJ74kTT1oqi5a6A/G6VJ3QY8BCZLqXKJXcGXcz2/qvJrCs3XrLEfkGGMsSRpyq90eZ8GvggeADJ8mqXWuZyJ52bqyZBwIKiG37Cpv5dmfzx7p/2zqQdUajk3gpX6y5RuVx+y5RK1o/Xz0LULr1ZFMyitJS2YXKBmNjIWHyV6LQeaIS4BgnEMs0fp/YDWitpSxPlL4OUImnG6pDKQ70fyELA36AyqWeRRYvaX/7yaLyK03Y1gYKL6wlE0eSPwNZDL6VrwIKhVOZ0LO9Vc3LnE5W5ymelu6wkRwgJJGPQQyiWnQZMMqhDiIVSa3JVfggkp0Fqj0j8AKuPSIgbyGrjkwR7ADmJRK14+Y/aH8TvtHxXf0mY00I1gM8iqsKJb0555gDYbVMJOwdakZ2EqfwvoeiXqjPsD74zFhksVMpBfkUZrYLcLqIZ++FbW/nB/noQhrC2pBvJri3G/mpYwoPVPrYMGkdtX7l8XZ6DKGRi6CvuThnIRgyr0QvAAFNb+2ABTm+JGsDZ/11q6qn5czGtAL2FL9HqHXEq1PvvVtbrUDQP5tblUGUN5eCpF/kVDDsN7+2mlNKg12uFGsDVY9TqzZOBvVLa7qfBQ4lca3aPOQA0xkN+AizkDbNKOF/UF5z4C4/f3dmxDm53ajWCbUe0nagEDW3KM3msMoi33K4CpIcFDZ6D2GMhrB/TvwAFA7222pdzGmxwMNE/+pC1P2p7nqvatuu3JnZ+7dRnQbka9B2jlWBQ3gJYRj9cIA3lee+qwE1+a2ZkL2hhot25bCmt/+rZw/qa2PGklnMuNYCX8Ct6GNAZOIXEpkzGCuODiDNQIA3ntcJbRE9bFALaXZ24k5z8EA/gxYd1Je5Fed0T7BTeLAW0ffx6EL2zoXUilvQdcnIEqZqDwaoSMnl6NWLWdL0SvGh2J8buhndvRrqf3mWC70u8nT2FAA7MrQDCAKqKX5N0AigmXKmRg6Bq8BhFmfMtXyAXcziPG7O/kjyqkPe3WDJ8Jthv1fuIiDBxA+jUm7zni+uC0vmbi4gxUAQP5jnwMZj0Mn2Z7Mn76OHqliD4wcRSzv+srpUHt3Q43gu39C/j5LQMLobwKeiaJ0wlZK5ntnwMn2R44A5XCQF5etU2AjB4bXHKLgEqTO2nQwRhAvWvrkjDg7lC/FSqJgfNpTDCAapd2hz6tiIszUHkMXNyVL/htlezoHET77L1bbnPl+XgU3Av0XyjCJwOJNlu+4ojfYPyGNfvIOjjAZ4J18CNXySVuRjsfNG3VWoXWTyaaNI86A+3MQB5j1GFbDJ9cndsB/XeTrOQHKtIzwJda5mAntL7TmT8P/fgyTnA3/7TioFzulA/KqKOmD3UjWNM/b9VcHCPq3AtgWdPiXYnX1NfqzbV5tKoYOKcH/45zIE3eGWwN9A5rVvIdFd2DYf1nLtf1Dv4bmmZtiRT+Me/bKHOFlGaEqudojOifm3FMXRZ1d2hd/uwVd9En0iJrABm9ugGsuF+prhokAzR1x5muzsmbcul2t3K5TMi7gcHrwIxvBvd6/tv0Cgv/mb4lBlAu1AOp9/30ej3VMuAzQcuGx9uDgeU46Wig2aBEHcJKYKwUF2eg7RjIL5F8tUWuzvUBuzwzk8+paSRgxpd7AAMl12cJyS9G5psgPBclys7KknE9hrrt7upZmR5JZ8Bngum8eGrbMKD7bxiwD/pQdDeAkODSFgzk5YHYOQGv4szI8qQfUtnwma7OFR7J5XZtzms+2gxjn4vG2sU3djsz+zvF36dtjKko32eCESGutikDMnhDzBlfIr46mGLSPOoMZMxAfgAVhnf45HXIUrSGh5uzIxjyFAawBVb1jCV5LfY16mmKC3YS52D2d9rVWV5EPdXlM8F6+rUr61o3oDknmSbJPbQPcANoSPFoFgzom5xnrJ18tUXGb6ksajV1jCGO0ZOrM//8j+mn/hhtVmyaDmyKAXyAcnxc4rRxzareCzdgwGeCDehwpY0YmI/zaB2wrznfscTPN7pHnYEyGLilUy43ZkMqkKtzJ7BYGZWlHfoMiTJ8IK8PPGQkBfesjCrtLypfM/vjeTntyqIlPKPJDPhMsMlUecEMGbicuqwBZD0jd0GG9XtVdclAfg4uezPAbG/MYEJ9gSgrmU5FT85c3+uE4Tvl3awqjurJo5cygP8mX7O/dwibIxoIXBgd0B9d11VP8jMu9o/mgme4ETRseLRNGNiLs+xhzvQpcblBZ5g0jzoDTWTggm653KRtZr7KkBvIQfIyZCVTqehhDB9Gb8ZwZnwfZ1Vxej15rU/ulp6X0+zveL4lfwVhS56VeajXDjyLnKbmk2fjwY1gzf/mFXWBy9Cay6IW7Yfeyp1LdEZXq5yB/LxcwA4AV+dEvt7SopfJi3EwmYz7Aet7eqUhP75YwVZIP506O6bU+xCTQ2Z/Q8YyA0zJ9qRyGHAjWA57fmxzGFDHRafS4DNTF6Hf1ZxKvGy9MpBfkCsfBLSxZQsg12dW8g0VcR/qqy1zEv5uUlYVN72e/OqUlcvSCu3q8Dtmf39q4ezP1uXxIgy4ESxCjCdnyoBGtzeB5U2t2kXHA+7iDBRjIN+Hzh/DMIMZX25jUGqtrFglxdInkHE79f+L+u9lxvd9sYJtlD6U89iNiqPQ92fm97bP/lr3F3Aj2Lr8eu0zGTiLYHtDBh8GzvFJqpxcTy7OgGEg3x9FRk9YFwNlDYMp16LoJxw1AjDj642L8ZAKeR0nz3XOej40+zuR2d+lhDNadJV+ULMYcCPYLLq8cAsY2INjTjDHqeP5OXjXpHm0rhnIr8jly+jJ1blqxlS8R33M9gp4jBlfJe6GPCO5ZmZ/hbW/t9p49qfNOJuDnwItW/wPPAUuAxjlRmUwJXT86kC/pdzJb4A7wTWJTlBSViH3ILAS0OssC4OJYDx4EdwB9EF9bVYqJb3JPASsCVYD2nj3BNAar3bWziZZjrJmq9wT6p6BNWDgUcAOvllyGLErZmkeqVMGhnJvTJfhE6ybPAs+1AHT6emrLac+nUWFrVdHfiPq1npka8/+tCv7+ug6ZPCuBsV2pI4hT7/PayBN5idRz3Kx43WMNr0dALjGVOlE6g1g99TchokvoMrgvtMweZamTVLXgYVmpfwY0az6XMAAo2CYZ+W4EZxFhUcyZmAR6lMHpFFdkCuJHBoUD+uJgXxHjNJ6GL5duGp1rH0zvno6yML6HsYv/1LGdbdidfmhzP7ouIeoc25NSTOCmmGt3MhJ1a5lQTyDXpS0x0FTfkfN3vYAt4JY/kzCfnFiCV19ytop+fuSproas2lfUGYBMEsaO2BWQY84A81goCdlHwb2AXsEfQswBbjUBQN5LbdsAmT0tPNRA6OsRCN7dYgYvcJXW97MquK2qyesd7bJ2l+aEdSlfgceBriKc8sBrdVrhmhFs6+RNoH4Q2CTKE2zPT3nC4M9QS8QZAIRuUo1Mwwi/eWgJOEbhPcCrd8yaCq4aDXjtKJXrezvrftKx81jCxGXW/duoNmmZolyj84mukldnIEsGehOZbrxrAF8F/1nwA0gJNS2XNw1l5uwVbKjcxDXqgFRVjKNiuis9SpD4eX197OquH3qaRPjV+rSNEPbBshwBdmciIyQDEeQDYlYI7gx+iYhMwmPJrzQpP2euGaKSyVpPQiPAKckugIZpm/BXFKQt4EMlV2H3B5d64FWVkGxRlDepdgAXkLab4HuGclp4BqwjxQrPhO0bHi8XAbmpAIZwE1MRZ8S10P0uknzaE0xkKcD6kCHNkOuzu2ABkJZiQZOD850dXa5jW+uf5ZVxXVWz15c7/XRNZ+JPiRKk6pnVbOtINcSOTAohNL3N7pmcwNA7DLV/XCrKTeOeF+jK9oRLA10vAzb88BKFxT95vOZRLVFbQjyHJFVg0L4HlCdP5g0RTWjVBsa3J+dlePiDGTAgG5WRui5TUxdXxHfGrgBNKTURvQcRvaTB3ItOwN+4xkaAGUl31GRZiO6n5gF5L/MqmKvpwEDTzXQflQ+J2qNIL91A9mwgTZz92VsAFXk4ajcEui9wUcmXcepf4j7iOVI2yRBfG9Zd63yVgZWbkCJDaDydR/9CzSYDboRFDUu5TKg0ZxuPM0CgsjNIVfG8yHBw2pn4Kxe7FDfcaarc/KmXI0GPlnJRCq6E9BJzY034TjrEsvqHF5PQwbGNlRnaV/Mis2MdDe6vIf9ja6oXKj3RGlBlZFT/xBEBssawZA+PxEGU4U+YwtCGcumyEIUsq5bHfNWiQO1NNNA3Ag2oMOVFjCge0iuiV3NsRqFaYbwuEnzaFUykGf0XvhqC66tKetzCbZDK/eK1NmOmOnq7PFALnfk5HIr9OObxcA7RUprQFJMZKxioyOjGBvGYsfHs8oFKHgdkAFsqj2aYSq3s8KQXMplPpsBbupJQ+UeOgOWAS1o/wPYGeA09D2B3FkuVclA4X/aaRAjrMXML8ur+JDKbgP/ZLPgKMZOul9c2oeB71tw2q85Rr+ZNYRTk7SmVNfVFOpLXP3EciZNUQ2GHgYMjAovuGtdcUkQRLPLIHKdxxIbWpvP+nVDcSPYkA/Xms7AghSV+2ptc4h6y4OBXQw32R6tXAbyA2ibNjLI8K2UcTvHUp/WYsBpTzLzy9SqZtxWr640A9qoNA5Yo3Qm+umlD0vNPYNUawC1hLI/uAtMAkG6hUgSWiMob0IsfeIEoy9u4oWoG8GYEdebwoAeAI3g7OK5Ho4DwF+BS8UzoHfUzmAAU/hqi4zfUhk3+RXqY7ZX+GqLdu8lkg8RD6uXAe3itEZwtSKX0pN01pEL7/BpthjLllHCheg3R2lSVU8x+YqMt4F1xw5GPyflgE6kbROnuxGMGXG9MQZ0w7NxocGLsHKR/Ay4CxQSKlduoRMYsyHtY7Z3+k6Ei2Xc1mdnru/NwPjlX824bq+uchgYSVOsAdsBXd6Dl6ImXoq+B9AeAd0PL4CDgNywmpEtAqykreXtRoE5bCHi3SNdblN5oIKsQ+QX4KaQkISHES4bpTV5ITI+zvX6ZEA3u24sexN+gq5doM8Al4pjID8HTdoMMNsboxGydtNlJXJr4t4svMqAqzP/TlYVez0VzcC1tG4IWDhppWZYcmEeDu4D6h+0L0AGUKJ7cACQkZQBlHwIvgPW1XkkugbSMpjzAN2vfwKxzBclXIF+cJR2PfqKQEs28lL9HBwHZhOfCc5GiSekMKB3cf4Ajojy5BbZGsgd4VIxDFxAxzIJt0/h//ANpFlxp1FOS+XWGgUwel2G53Inf1ROZX5sVTIg43UGuMS0XjM7zRBlcDoCGUYrclueahKmEb8fDDJpcmm+Al4ESwFtvEsT7VC18hyKZp22f9L5T05AMEs+JRaMdyHRjeAsbjxShAGN4G4CP4nyn0bfHnwWpbvaLgzk5+W0mqnj6py4LWGxDqQlrZvMQXRY+kB1Fzq6k75oSSV+TE0xIKPTC5wSXVWXSJc6Ach9+pYUI4cT3wjERm1lU+Zl4o+Aw0yadcWG5GOJ6NyHhISU8HPStAzwuM1zI2jZ8LhlgI0TuaPAuaCrzSAuoyj3wzdRuqttykB+QU6nkbQ2tmwB5gBZiX7bu8E/8Vjdmcv9blJWFXs9NcOAXKKazZ0ONgTx7E8zxr+AP4B3QCzvk7AWuADIY2FF99tVQLO5BYCMm2aYEs0YNwCPSUlEA7VDgdLOA31AEBlh3csylGpTA1FH5+IMxAz0JmEY2CrKkEtDo7cbo3RX24yBPA934eV1Zny5jUHc8ZTTki85+HbAjG9e1maOnq3DKKdyP7amGejJ1f0E9AI/gHeAZn5NHShrk8yyYCHwIngDlPMqzWIcvzoYB14A00GquBFMpaVuE+WWOAb8BswTsfAo+l7g3Sjd1VZnIK+Rr4yesC7I8rnVGsltM12di/ybAfcUdBdnoG4YyPJhqhvSavBC5+aa5PqUu6BHdH3qFE8DcjEUHU1Fx7haNgP5FalCRm8XsGrZ1TWs4D3U4QBXp9xHef9dG/LjWh0x4Eawjn7slEvVrk8tOJ8AGuyYSsq+RrgneCbRPWhVBoaukby8LuO3fManepP6ZPRwdZ72NDO/clxNGTfNq3MG2o8BN4Ltx317nVlrSFrEVkf7cyBffCwfknAmuAa4eyxmJzM9z0J/x/UwfJrt6ffom1nVMyt6kQCj1xHjd6riLs6AMxAx4EYwIqRGVe0a3Byoox0MtPicJl+QKLfnpcA3RaQxVHZavjNVbAL0W2i7dtoghOQWiWZ3muXJ8IEhb7SoFj/IGagjBtwI1s6PrRmednUuCrQzKkCbKrYA84JiMomMC8H5YGKxQp7eUgYu5hWTCey0Lby8Pohaera0ppTjtJ7Hup5cnZ1Z5ztF630uzoAz0EQG3Ag2kahWLNadutUpKrTQ7kyrl4prY4t2dsoQNkdepvCtQDM/vUjqkhkDeX6/Dtti+OTq3A7o98tK5KJmJ6dcndrZmdcOTxdnwBloAQNuBFtAWgsO0SxsGbB0ghBXmLYhheRWE9xlhc5THejrrXaWuqz4HHbWTh7IpcvVuTXQxqOsRO5p3t2Tq3PG7Ri+L7Oq2OtxBuqZATeC2f3681FVMG4ydiGusNgaXHZnT69Ja0SfAc34mDEUtsW7uwwispOzeDl46o6Jq3NT6u2SXd2F/6l2J/X9M5eb+26+//tNhnV7Vc6AMwADbgSbfxuIsxXARkAvLusrBzJ0C4LWlKlU/jXQ+l1aKGP3PvggCRXXLk99vcElUwbyS/DosKml4Opcn6rZ5ZmZfEFNIwEzvp7353JHTs6sZq/IGXAGZmPAjeBslMyW0JmU1YBeK5Dh2wAsAMqR7zlYnxR6M8E4wokgGLc0Q6djXNqNgbwGO3JzCmtl3IyPqI+ZegdmfDNG4erUgMfFGXAG2oABN4Kzk9yNpHVAMHq8x5XTxpPmitZwZOjeAMHYhbhmaf6yMiRUtuQH0L5dgAzfShm39R3q07oshu+0JzGAfj9kTLBX5ww0hQE3gjN3VcqlJaMnrAnmAE0RuRpfBcG4WWMnV6R3bE1hsWLKzOB5OGPt5KstMn5LZdw03SsYPRm//LMZ1+3VOQPOQAsYqEcjqNcI5NZkM0PhK/wrEzZ1TUcbExi1F/6/1aOE/wGa8blULQO3cD+M0eBHsz29vL5YxpfyHPVh9Dph/Ia8knHdXp0z4AyUyUC9GEGt620GNLpXR7cQaIqMp9Bj4BEgo6fRu6/XQEJ1S14z/XA/DCbe1PuhKZet2f9TM9f3Cl9tGduUg7yMM+AMtA8DtWwE1dFtCWT41NH1BI2JdlbK2AWj9zJxd2k2xlpV5F/AWu+kbfg5NeMbCPRKS1YyjYpGAbk62eCSlyvcxRlwBqqAgVo0guvC+0HgZ2DeRn4DreVZo/d2I+U9u6oYyOv33wHI8G0L5gJZiV5deAD8iyXkEbncSV9kVbHX4ww4A23HQK0YwR5Qthc4EKzcCH3PkH9rAm1kcakpBvILcjmDgDwAWwB5BLISrQnfk7zKcCczvolZVez1OAPOQPswUO1GUBtcwqyv2Ceq5M78LwiG7x3iLjXFQL4Phom13oKrc2Mujc0umclX1HQ79TPj644BPNo3QmVGrVfkDLQ/A9VoBLXJ5RfgBLBCCQpHkzcMaJ3mPeBSUwzk+3M5cnMKcoFneS/r6zus7cnV2fvBXO6QKcRdnAFnoAYZyLLjaG165NbaB8j4qQNMk0kk/h1cDZ5OK+Bp1cxAfkVaL6MnV+eqGV/J+9Q3fOY/oF3+sVxuV212cXEGnIEaZ6AajKDcnAeC48HiRX4Pva93DZAB1KfHXGqGgaFrJC+vy/gtn/FlaU2Y2V7hVQZc5v7VljL47cKxuwF9YUnPqXbf3gduBr72DgkulclAJRtBGb/DwbFgkRT65KK6DlwMXkzJ96SqZCDfEaNERzpdsz0Zvr4ZX8ZL1CcXOcYv/0LGdddrdXxlpzAAXTKFAG0m2gI8lZLnSc5AuzNQqUZQ29pl3NIequ9JvxacB3ytDxKqX/KduYZNgIweG1xSBz0kt1jkGsfoFb7aotdiXMpjoBeHrwbuAeuAUaArKCbjyVgaTChWwNOdgfZioNKMYD+IkPEbmEKIRpRXgj+Aj1PyPamqGLiYTnPCVsmOzkE0vWeGzZ9OXY/j3mTGN4N1vvy4DOuu16q6ceGHAA1U1gd6T3Ix8BxYAjQm8uic31ghz3cG2pqBSjGCGkUeB04CetisaI1PhvFC8LnN8Hi1MZCfB8O0LYZJrs7tQPcMr0Du8YeonxlfZ3Z2nvxJhnV7VZAKCeLUDlY0E9wmIQfuc0cDPaP7g1OBfVXlLfRlwAzg4gxUDAOVYAQ3g40rgB6QWG4m4RjwQZzherUwcE4PJg2a2WsGsTXQWm9WItf4vQDD1/X2XO7EenO3aRChwYQGFaeBV0Bryl+ofN+UE1xH2n7AGjg905o5WtkU5WGb4HFnoL0Z0OiuvaQjJ9aDewpQ3MrLKL8GD9lEj1cLA2exZjR1R/pEDN9kdXxdMmz5JOq6K3F13o2rU56CehN5Tm4FWwLFJS+CMwqxpv/Rc7cSWBaoHq2xPw8mgjRhsJFqBC8j3RpAHau02AjKWD8MXJyBimGgQzu1ZBHOexNQB2lFD18eXAKmApeqYSDPulDhqy3q6LRmFA9syrmS8Rw8cqarswfb7o/UelS9y7MQoM0pQUYTaeq7k30oexQ4CDBTbyCaXf8DyJ35DrAiQ/kZsG7sH9DnAtNALI+QsKFJlEdncRAbTFPEo85A2zLQHkZwcy7xRsBsoYHowTsS+KaXBrRUspLXDILZXgFrZdxS3QfDgWYfDzM2qtdBkQxPmtE/mfQzgZWlUbT2Vkr2J/NPQPWWkm/IPBTcEBX6G/ruUZqMr4xwLPuQMCxKXA/9qSjNVWeg3Rjo3IZnlsHV6FKwswQ94EcDPZguFc9AfgBN1GxPxk+utCzlXSrD6HX8J+8JPonhm55l5VVYl4zQfOC8lLZrcCAjqI0oI4B0uTNLydlknliqgMmbm/h1QM+nBqhBdJ7YCGq2l2YEmb3ntGGpCwiieycYwR2I85GC3Kch00NnoK0ZaKuZoM6jNYLDogt8G31X8EyU7mrFMDCD3+6MtZOvtqgDWyrjpr1GfRg9fbXlVL8PfiRXgwwZH3EC/6nyU1L/A6al5jZM3B71joZJhff2riBNv0FfoJlbf2DlKxQNdt5PEmUcPwPdEl3BzSA2jCH7XiJbBYVQz3y4h+4nvgV4B+g6ZBAVPgu+Ay7OQKsz0BZGsJgBvI2r2w982epX6SdoJgO3dMrlxmh0r454J6D3wbKU52eu783A+OXHZFlxjdS1Edch4zEn0PqZDFSpWd785A8E+r1+DYLBIloQeV7eBfZ3fAF9UzAeBJGB06xy85CQhFcTHmzS9OwONrpmo4uANGOs4640ZRVdDXAPFAbFf1JCJHJ9vwisYXwVvd49AxFNrmbBgAxUa4rqj2eAeqhPAL9vzRN73c1lID8HR2wGNNtTB7cQyEr0m8sFJlcayGs24JLOwLwky2DJsAU5ksglQTGhXKWahel3Cy7Ho4hfDKxoxvi4TSC+KhgdpUmdC+j3sWv236L3BhOBZC9wfSH24x+14aEf1VmxhYl9BDrOSpnpxh2CLsP5QZQXiumesf3TJPSngQxjwMfEXZyBshiwN1lZFaUcXMwAHk7Zy1PKe1KbM3BBt1xu0jYzX2UozCTUqWYlmhU8Qj/GbK/w1ZYPs6q4Dup5i2vsb67zYeKbgr5A62h6fsKsSAZrSRBkFJFNgpKEpxKebtL0Wyxq9Dh6PAnnRYnbot+TpMlAax0vGF4lXwo0C00TtWkjk/EK8RUT/VHCDUxec6K6rjOac4CXdQZiBjrHCRnqGo0eZurTyM4NoCGkfaJ5zTTUke7MwF4dm0b+WYm2yz+QuDpxq+XlJnNpPgPDOeQYc9iGxJ8FciNKNIN7rBCb+THwY5O4ApXV7EtGKoh0KzKcpeRGMmMjuCZpwQh+SfzfYGsQhPupsLtbz3ksDIQaGMEV0JcGbwLltcQIcn/lzgYuzkBZDLSWEdyVVh1hWuYG0JDR9tH8gpxzEJCrcwsg12dW8i0V3Q3+Be7A8AWXWVb112M9milZ6YQSDKDSZXCCERTv1gjK7TgYaB0vSPcQScLlIj1W5aLUAEb3TZCeIZKEMl7WCPZBXxc8meTbQG38P/A8UFzHygBKpF9YiDX9j659dyBvg4szUBYDrWEEF6dF8UK4zwDL+placnCeTqnw8ro6zI2BOtKs5CsqwuAVXJ1s4MjLELqUz4AM2Mtg+UaqWsfka61VRsu6NzXYsUYwGJxwmNZ75UIdGxJSwtgIfh+VuQ39cmDvK503zQi+T7r6BbUzSA8ig4Duz+lA194UET8DQdyephzrZZyB2RjI2gjqRr4BzG/OdClxPSwurc5Avj+nUKciMCrX6w2ZyWfUhAtKH6ie8SCGT65Pl2wZkDF4AxQzgteQNww8AYLIyyL3qfW8bIauZ/BLIHlmZtDg76/Rjm6Q8qMyJ9FlflQLsZciXffDY0ADrCC6744NShTKAPYCOwIZy01Bc/uf9zhGs89wXURdnIHyGGjuTdjY2U6gwEamkB6c44zu0cwZyGuDgTofdSyrZly9Oi51sLivVnyUVzrd/dRygvWsqeNfG6wO5gbvgsfBDUAGUCL3oGY6afIYiSofi46xRrALuur4a1LwfsKPgHZ4BjmYyCUgbTZ4KOl2hvcd+l0gFu6LghGcSvgwUDt0ndKDLEFE96ewPmjqjI+iDWQ82lZA96SLM5AZA1nOFNakVXKF6CGQTAZrgReluGTJwNA16DNDx1Js1tDSE77FgXRm+mrLkP8y89NMw6XlDMiYHAWOAVo3SxM9I/uD/4EFwK/AbeABsDAIMpLI4KCYUOf4GCxo0pi1F2ZdIWkIkaFBScL3CWUsn0909Qd7Ay1ndE3SFFwB7Ca3kCWjKsN0O5CRCrIsEd2fuwD1C6VEHgU8C7kBQPzEfZLuP7k+Nbt9Crg4A5kyEN9w5VSuB2EHU4Ee/IuN7tEWM5Bn9NxxPQyfOhV1Ln1bXFX6gVpnwegVvtoyOr2Ip7aAgXk5RjMozYAaExkRlXvVFJQxOtjoMgYLga9NWoheTeTAoBCqrIziN0na/ITPgiUT3QbPociILgOWthnEPwHyNqh9pWQAmcHwrVSqIHmaWd4DNJO8A3wF8uA0YEUGUDPkQSBtJmrLetwZaBEDWRlBPTyvgVDfw8Q1ctNN7NIiBvKdOWwToI5lJ7AIyFKYdRTW9+iI8q9nWbHXVWCAgUvhNYKNm8HHDZTdy5TXLOteoyu6K/hHlCZ1WxAbirjsKpR5AswFmiIyfHqO0wZGetbl6QkDs9h4ktVAJqLJ4P0L3A2+BVZWRnnBJIS+Y1/SrjfpHnUGMmVAHW0WciSVBAOo+s4D4SaW7tIkBi7GBTWBjk//h68w+u3ZpMOaVkgj6seBOiGQH9e0w7xUCxk4kOOsAdTzcDb4PZBBkOtvFJDx0EzsJKDZkZWHUL4EmsUF0b2RZgTlUtSMar5QkFAGypaVMVObbgDLgVKic+8P3jGFOhLfEKgNwmKglHxB5gige+5+8AMoJi+S8QYQHxL1J78DbgDFhkurMWANV0tPoofufTBPUsGrhHKf6KF3aZSBPLx1YBQ/Qx3WdqB7o4c0vYA2KNCZ6VWGzrflcifLteXSNgy8wGk0uwlyGZEjgpKEMiI/BTJUxZ6X68jTOl2QSUTkEp0cEkwo47an0eU2lUs0LquZ4L5gMFgPzA00SHoF/BcMA48BSRewGdD9qfILg1LyEZnDAfdcwchPK1U4yjsH/YQk7ULCo6N8V52BzBnIwggeQ6v+aFp2GPErjO7R2Rg4pwf90kCSNZreGsw5W5GWJ3zPofdh+Bh9zzGS/5wzoeVV+ZEwMAc4CMgArA66AQ0mNKuWYUvbrNGH9A+AFRmbtLK2TFpc52UA00B2SklTAaVr1mVlEMrtNqFIXJtrgsHSNeq+1P2p+9TORFFnk3dI0Xll+J4ExQw6WSVF7lUZ4ZvAL0FL6+FQF2egaQxkYQStC0Mdrka3sb+/aa2p6VJn9WLn+I481+pYNgUaYWclGvHfBdQJEeal15PYDjzL696dys4C/UtUeiV5RwLr6pPBeyI6ph/6u1FaU1QNkD4DwdOiY/Q7/0wRRLNC5UtkvD4HmukFuY7IvkEpEXYnb3ugGd+2QLPDUvIqmWqHjN+zpQo2M+9ayh8KpjTzOC/uDLSIgc4tOurHgzRCXPpHtfAf490AziIkvwQzMkbncnVOWZ9kralkJRpwMNMrfLXlfgyfZoD1JMymZ31xRDO0JYHcv1nJr6no4iZUdghl1JbdTFm5FmNZnoSWGEH9rpoJamYUZCARGYpFwHFALtXR4DtwN5AhC6KyxQYJPcnTTHNnsCXoCkrJ82TK8AmvlCpYRt4BZRzrhzoDzWagXCO4UnTG/0V6Har5ZblodSoC7p1MPTofUycdYmFX50MYviw7faquGlGHrZmvvX83Rn+wGVegAcmGYDkwEcjQhIHEKsT/AKy8jDISaAa/O5DHI8iuREaBPyUJn4YME65D/F6j2+h8KBuBZYAGlQq3A2E2dD1xawTlor0cBDmGyN6JIgPFwKvgltQsTQhuTqKFF+Z3JJShFGeWQ9QGopv3KaA6VO9Y4OIM1BQDHcq8ml9x/GWmjtWJP2f0OonmB3Ch6lRk+OKBQbkcaPYwHKgTwsWWT5tllHuOSj5exkZGQkYoiHQZGhmDIDJAhwelkVBG5i9As/MgWsf7KFF0D68aMgjlojsYBO57Er8TrAuCjCeyFPgySdCApVcSV/AGkMGVYYllaxLuMYlyrXY1ugy27gNreE12wVguSsJnQC5R8aPzB+lHRPemoFljqedeBvMRoPttOPgQuDgDNctAqVFgUy56ZVNoKvExRq/hqL7Jecba9InqVGT81PllKa9RmUbfIF+Ps+sluXateYlbeC7MoLROFeQrIg8Cm6aZVDGZiwyV7QsuANcBrdtZmZwoPyG0BvA79CNBMIAqNh7sC2SYOwGJDKPKDZWC3A/s7E2GV224C8QyT5QwMdJ17v2ADGU4Xygiw/cboFCi9grLg3B/rk68lMjoik8ZvhHgc+DiDNQFA1kawddhLHQkNUjeLXQ+YzbkwuhYTpe7qdiovKXXPnrm+p5cnafaWU9L66vm4w6n8ceYC9ic+PwgzLKUBU+5VcBtSXwUYSwLk3A52AbIEH4PngaxASRplit0DSlGXiL+rdEV1YxOBmYSULuC7EMkGMFriVsjqDLngyfBBCmJaMa3f1CSMO1aHiBP1yFj2BuMBY+CvwNdl2RVoIGD2rYiKCW6JhlV8XgH0MDCxRmoOwY6lHnFckktlNRxK+HPy6yvwg7Py922GVDHMhiEayVatsgt9p+Z63v6XNmQt8qusXYqkJF6IrqcvdH/atK6EJ8KxGMQBioN1r80yPsE9AwFCMeBJRL9A8IxQOW2AJpxHQd+D4K8S6QfWA3IuBQzMGrLKLA7CDOp/xJfC1hR2hDwLJAxvQSobitqy4M2oUhcz+86IBi+/kXKheSJRGTwZPjuBrFxJ8nFGagvBvTwlyNyuwRRp1QDckE3BviMuAuvMgzkgubL8KKmUZdG77idOg/P5U5RJ+wyOwNPkaS1qD4mS8bHGsEpSZ4GJhqgKH8pIMMSRIZpJNg3JBAGA/hv4nK5TjB5itrZpvS+QLOufiAWeT40Q5MbUef5Alj5FYpmfvY5Wxv9XlsoistAqW3FpBMZGwFd705Aa4GlRG0aAdRGtVWuTxdnwBlIGLAPZ0tI0QMWOpUFWlJBZRyTn5d27ADoWCZq3WauDNuVrLcUXmWgM8qHWUKGp6i5qjS7Y5DQYKPL1uhzg29AEM2AbgYyDEHWIPJMUAhlVPY1eoheSSQ2gMqTwYuln0nQ+TWLUr2aVU0CVtQWDXYk/wP7geuBZm2NyT8o8Aug67cij8TmQNcrg78gKCUaQMhNLMM3CoT2EHVxBpwBy0C5RnC8qWwBE6+CaF4dySCgjmULoI4mK0nWW7S+15WO8oSvsqq4juqRkdHaYBBm6IXXBmQogmiW1TEoSagZkjWC96HLUHVP8kMwOkSiUHVqlmk9G1pzuxXIqGgWZz0gO6JrrW4ZsDTQLHY3EOQGIh+BP4MwYAx5IXyWyNlA1xwMoAZiqlfXowHafKCUyHjreEHXEOoh6uIMOAPFGGjK6LTYsUrXKHzXpMBnhAsn8QoN8n0YkO+UuDo3ppF2BlFumydSgWYG6ijZcJCXIXRpOQP6bT4Gdtbzd/Q9oiqfQF/PpL1GfHmjK/o3oLU6KxuiPGYTTHwk8YFGn0x8WaD1xFheIGFlk3ga8aFGD9HORAaBTUE/IMP6CngQaLYmmRfI4GlgJgPYmEfiVcrofpPhexa4OAPOQDMZ0INZjnxhDu5JXEa1wkag+f60aecE66UosfEAAAymSURBVNI8tTEr+ZyKcHEWOiHWW/Jyfbq0nIE5OXQRoJmb7i1xewAIsj2RrkBGKYiMgDWCy6H/BLwcChDKSOxudEVXAcWM4HnkDVShRHTOi4AGfGEtUllLAZ3Lyr+tYuJan1Q7BCsy8rpG3aNbgMY8Es9RRnXoumVEXZwBZ6AMBso1gk9x7vnB+ASqz3YSqO0h+RU5qzoVjahXzbgF2swyfOauzhUeoV/09ZbyCO7I4fuAPAjuQt1Dd4MPgZXuKFsCzbiDyCD8MShJqN/eGsG70L8DcqkGkcG5LChR+Dj6Y2ADky63p1yrF4BxQIb3XKD2B5EB1HGNCR6JwqYW3Z8bAc16i4kGlXrOguEbW6ygpzsDzkDzGchyVtT8s2d6xNA1kpfX1QEun2nVudzb1Jd0Qqf9BwNYYbPdjK+27aqT+/wesFozTjmMsvtF5Z9Ft3WMRo8HPwxccjJkQbTBZQFgZ5UhT6FmlAxymuzi/4iyMqxjQJr0J1H3poBHouRGGQ2sdG7N9tTueDBAkosz4AxkwUAVG8E8I/COjManazStjqVvFoSYOtSZqRPC+OWfN+kezYYB3XsygFtF1X2N/haQm3DRKE/qeNALyL0Y5BQiZwQlCZcmVD1B9iJyfVCScFtCtaGYDCDjYdCjWIEk/QXCweCdRA9BczwScqU/CHTPjQBytbs4A85AKzNQZUYw3xk+NgEyejuBRUCW8gyVYfQ60RENeS3Lir2u2Rg4mpTzo9Rh6EqfAOQi3BtcBfS7W5FL9AGTsALxeAZ2PGl/MGXmJ/4p6GLSLif+K6OnRfuTeA7QYMu6LWWEHwUXArlng3dgdeJhYNaYR+JbysoIc88V6viK0MUZcAbakIEqMIIXd6VPZLZQeHl9ENz0zJCf6dT1xMz1vU50RKe8m2HdXlVpBl4nexlTBDdz4YPW00yaovuDa6O0K9APi9JkBGUMg6i+dYOShDI4W5u0j4hrthkMmMmaLdqdlLVBNzARaMAkl6qeoZ+CnRP0IywlOlZGk4FWwQDKELo4A85AOzFQoUYwPw99y7b0TRpRbwfUAWUlGsE/DNQJ3Yar82NCl7ZlQAOZL6JTHoGetlFF9+jLwBo4/WYyXhrEBDmTyMlBIZRhWwK8b9IOIq6ZpZUNUB63CU2Ia2a6MdD9qXXG3qCUyLU5Euie0wz2B+DiDDgDFcBA7GZqxyadw7rL5IE0QCNqRusz5sywMdr8cB+Q24nOKD8+w7q9quYzICMYy1txQqLLmP0fuNLkL0Jcs6/HTJoMjDWCMp5ymV9iyjDoKXxQ27o1db81xQjikShsfJHhk0diAVBKPiRTm1p0z40C8QyXJBdnwBlobwba2QiexQaHqYyk5eqcvClkdMmQEG2wuGumq3PGnRg+6S6VwYDciLH0ixOMzu83m8gYWSP4HPpYsKQpqTKXGP0z4jpGs7ggMpTHBCUK50bHI1EYmO1A2D3Kj1WdX0ZPeBLIgLs4A85ABTPQDkYwj4uq8NUWOqgp68NNxwz50YaK24FmBcz88t9nWLdXlR0DMkaanWt2FWT1EEkJPyDtE6BdoUE0g/ttUJJQxscaNLk6FwI6XxDdGzKCz4NgsEKewvmBDB73Z2H9sBthKXmFTNWjemWIXZwBZ6CKGJDLqA0kvywnUaclrJXxCdU5ys1FR9T7oVzukCkZ1+/VtQ4D/6Zazf6DjCeyGPguJETh6+jLRGm6l/5n0tYjzkanBnIw2tUmBbd74ZWHt02aDCUeicL9uTlhYx4JGbtg+GQEXZwBZ6BKGWjFmWB+AJxoNC3Dt1LG/IyjvuFMIhl9T3+cGd/0jOv36lqfAe3UtEawJ/qe4JqUU+s+7ZeSrvvLGsGn0LUW1ycpK3fkCkk8BPIWCDK4coWqDs0Y7TohagNRPapbsz0Zv7HAxRlwBmqAgQxngvom5xlsIZ8uo6eOZamM+dFMIBl9523Hl/FpvLo2YkCbW94DdiD2OfoaQIMcK8ei/MEmJHHdE8tF6f+HvjLQvcJAqcHXVnRP6t7UParXHUrd/9rI8giQ4YvrIcnFGXAGaoGBUp1AM67v9O3ZA3AFB2h0naW8QGXJ6Dv/UpYVe10VwcBfaMW+UUvkpjwJyPB0BweC04HWD18E8irY+1YGr9S9ofJhYCbvRCn5gcwHgAzoCCCj7OIMOAM1zIAdhZdxmR1wQc3IwgDK7fRfQCdU+GpLsW3zZbTVD60gBk6kLXJJzmfa1J/4341uoyo/BKwDtHZ4L+gIYlmThDDjWzbOjHS9rC7XrAzf7WAicHEGnIE6YcCOqMu85LzWSfq1oBK5nR5NXmVg9J9/vwV1+CHVy8CWNJ1XWRq4RdOu5gYS9wJ4HQpfbbmb8BsgkSHUTmPN+IQlQCmRobsDyMsgAyhD6OIMOAN1yEBGM8ECc3Jf/baJHMrt9G9AJzQHbqeT7Bb2JlbhxWqEgfu5ji3AjWDRlGuaTNo54Nwk784k1L0rA6oZn3Z29gKlRK7NkUCGTy5P3YMuzoAzUOcMZDgTHLohm2K0kaCYyH2VuJ3mxO10wlfFCnp6XTLQhaveCmiH6DJAuzzHgYvAm0AyJ1AZzfYGgR6glKgODc7k6hwF5HVwcQacAWdgFgMZGsG8XFIfgYVn1T5zfYWRewdG3zNwX+Xd7WTI8WiTGJiHUvp+rGZ8CqWXErnlZfQ049NrDVpndnEGnAFnIJWBDI2g6s9fxR+N0nFxBrdT3t1OkOHSLAY0wxsIZPg089MMsJS8QmYwfM+VKuh5zoAz4Ay0IgP6CPYtnVrxBF517TIgD8IhQDs+NXDSDK4UniX/ZBC/DE+SizPgDDgDzoAzUF0MnEJzSxk9fRXoCXAMWBK4OAPOgDPgDDgDNcPAilxJbASnkvYgOBz0AS7OgDPgDDgDzkDNMqC1Pb0SodcgDgALAhdnwBlwBpwBZ6AuGBjAVc5bF1fqF+kMOAPOgDPgDDgDzoAz4Aw4A86AM+AMOAPOgDPgDDgDzoAz4Aw4A86AM+AMOAPOgDPgDDgDzoAz4Aw4A86AM+AMtBYDGX82rVnN7EXpbuYI/Vuc+L9J6L8K6MPKQb4iMiEoHjoDzoAz4Aw4A63BgF5c5r9CtKro81j25Wh9+zGWN0iwZf4YF3DdGXAGnAFnwBloKQP6zw9W9OHii8BosIrN8Lgz4Aw4A86AM1BrDNh/qquPF58J/CsdtfYr+/U4A86AM+AMpDJgjeCllLB66gEZJmpt7xNTn6/1GTI86gw4A86AM9D6DLSl0YuvZvc4wXVnwBlwBpwBZ6AtGcjKCOp7j4sB1fcF+BzoQ8guzoAz4Aw4A85ARTPwKq0T7C5MxT9O0pW3J4hlPRJuAHptIT52CmkPgf1BsdcwriEvnFvhJSAW3x0aM+K6M+AMOAPOQKYMxAYsTT8iOuNv0NPKpaXdTtm0/zbvr0hEpLrqDDgDzoAz0LYMxK9INOXsgyh0YVMKJmV2IDyoGeW9qDPgDDgDzoAz0CYMaA3v5uRMuxJa1+Wz6HJHSl6fGRT+nmjiio4DF4MnQF/wU3AYsOuN26NfAVycAWfAGXAGnIGKZEDreNadGbtA1WhtgBkGngPfg+lgIxDLXSTYul6OC6C7OzSFFE9yBpwBZ8AZaDsG7GytKWedSKF9k4I6dnEwNtFtcCfKtiZBX6JxcQacAWfAGXAGKoqB5hpB2/ipKMEAzkN8fbBJgjUJrcxtFY87A86AM+AMOAOVwEA5RnBZLkCbXrTep49t2//2gNpA5DZ1cQacAWfAGXAGKoqBlhhBHXMV2K/IlWgtUP8SaWGTrzQXZ8AZcAacAWegohho7isSKj8CxAZQRu/PQDtMZfyOB1Z8JmjZ8Lgz4Aw4A85ARTBQaiZoX5cIjV2DyHZBSUK9MvF7YA2ddpFa8ZmgZcPjzoAz4Aw4AxXBgJ0J/hC1aI5Il7pVlDYO/XxgDaCKWFeodHse6S7OgDPgDDgDzkC7M2CN07dRa+LZnLL7R2UWQu8epS2KrpflraTVZfM97gw4A86AM+AMtDkDpYzgUbRGH7W+C4TPnuk/zlvphnItWAf0BkeCB8ECwIrcrnPZBI87A86AM+AMOAOVxMA/aYzW7tLwx6ShSxDqhfm0Mo2lxbNI/2JMQqoHzoAz4Aw4A+3DgJ0JXk0T4rW90Cr9r0DJOHA4mCaliLxPutYO34jyd450V50BZ8AZcAacgXZlwP6LozdpyePgJ0DuzLBzVOn/Av8BkhfAcLA46Ank5tSmGrlKbwa7gTFABnVu8G6CKYRyrQZZhYjSQv7TxB8KmUkoN+sEEMo8Svx/SZ4HzoAz4Aw4A85AWQz8P+fE39x5CyQdAAAAAElFTkSuQmCC" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A vector is an essential concept in mathematics and physics. It's like an arrow with a specific length (magnitude) and direction. Imagine a straight arrow in space. That arrow is a vector.\n", + "\n", + "Components of a Vector:\n", + "\n", + "Magnitude: This is just a fancy word for the vector's length or size. Imagine measuring the length of the arrow from its tail to its tip.\n", + "\n", + "Direction: Think of this as the way the arrow points. Does it go up, down, left, right, or at some angle?\n", + "\n", + "![image.png](attachment:image.png)\n", + "\n", + "Vector Notation:\n", + "Mathematically, we write vectors like this: v = (x, y) for 2-d.\n", + "\n", + "For 3-D, v = (x, y, z),\n", + "\n", + "For N-D, v = (x, y, z, a,....)" + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In most standard vector representations, the tail of the vector is considered as the origin (0, 0). This means that the coordinates of the vector's endpoint are relative to the origin.\n", + "\n", + "\n", + "The coordinate (2, 3) in coordinate system is represented as:" + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The above point (2, 3) in vector space will be represented by movement from origin. It means you move 2 units to the right (along the x-axis) and 3 units up (along the y-axis) from the origin (0, 0).\n" + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Word Embedding \n", + "\n", + "Word embeddings are a way to represent words as vectors in a multi-dimensional space, typically in high-dimensional numerical form. These vectors capture semantic and syntactic information about words, allowing us to perform various natural language processing (NLP) tasks, such as text classification, sentiment analysis, machine translation, and more. \n", + "\n", + "king = [0.1 0.05 0.2 .... 150 such number] \n", + "\n", + "You can perform vector operations on word embeddings. \n", + "\n", + "king - men + women = queen\n" + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "code_folding": [] + }, + "outputs": [], + "source": [ + "#Loading OpenAI key\n", + "\n", + "with open(\"openai_key\", \"r\") as file:\n", + " openai_key = file.read()" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{\r\n", + " \"object\": \"list\",\r\n", + " \"data\": [\r\n", + " {\r\n", + " \"object\": \"embedding\",\r\n", + " \"index\": 0,\r\n", + " \"embedding\": [\r\n", + " 0.006479884,\r\n", + " 0.012256625,\r\n", + " -0.01229533,\r\n", + " -0.02647431,\r\n", + " -0.010624559,\r\n", + " 0.0026174346,\r\n", + " -0.013101687,\r\n", + " -0.03929861,\r\n", + " 0.0013409716,\r\n", + " -0.029802952,\r\n", + " 0.009450503,\r\n", + " 0.017559228,\r\n", + " -0.027996711,\r\n", + " 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-0.02171358,\r\n", + " 0.024848694,\r\n", + " 0.015920712,\r\n", + " 0.04894909,\r\n", + " -0.032228474,\r\n", + " -0.014527326,\r\n", + " 0.02737743,\r\n", + " -0.012856554,\r\n", + " -0.017868869,\r\n", + " -0.015985219,\r\n", + " -0.0076958705\r\n", + " ]\r\n", + " }\r\n", + " ],\r\n", + " \"model\": \"text-embedding-ada-002-v2\",\r\n", + " \"usage\": {\r\n", + " \"prompt_tokens\": 5,\r\n", + " \"total_tokens\": 5\r\n", + " }\r\n", + "}\r\n" + ] + } + ], + "source": [ + "import os\n", + "os.environ[\"OPENAI_KEY\"] = openai_key\n", + "\n", + "#Getting embedding from command line\n", + "\n", + "!curl https://api.openai.com/v1/embeddings \\\n", + " -H \"Content-Type: application/json\" \\\n", + " -H \"Authorization: Bearer $OPENAI_KEY\" \\\n", + " -d '{ \"input\": \"This product is really good\", \"model\": \"text-embedding-ada-002\"}'" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import urllib.request\n", + "import json\n", + "import math\n", + "\n", + "# Define the endpoint URL\n", + "url = 'https://api.openai.com/v1/embeddings'\n", + "\n", + "# Create a function to make the API request\n", + "def get_openai_embedding(prompt):\n", + " headers = {\n", + " 'Authorization': f'Bearer {openai_key}',\n", + " 'Content-Type': 'application/json',\n", + " }\n", + " data = {\n", + " \"input\": prompt, \n", + " \"model\": \"text-embedding-ada-002\"\n", + " }\n", + " \n", + " # Encode the data and make the POST request\n", + " data = json.dumps(data).encode('utf-8')\n", + " req = urllib.request.Request(url, data=data, headers=headers, method='POST')\n", + " \n", + " try:\n", + " response = urllib.request.urlopen(req)\n", + " response_data = json.loads(response.read().decode('utf-8'))\n", + " return np.array(response_data['data'][0]['embedding'])\n", + " except urllib.error.HTTPError as e:\n", + " print(f\"HTTP Error: {e}\")\n", + " return None\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([-0.01601839, -0.00278705, -0.00439459, ..., 0.00317546,\n", + " 0.01289842, -0.00163133])" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "embedding = get_openai_embedding(\"How are you\")\n", + "embedding" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Visualizing words" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "from mpl_toolkits.mplot3d import Axes3D" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "code_folding": [ + 2 + ] + }, + "outputs": [], + "source": [ + "from sklearn.decomposition import PCA\n", + "\n", + "def visualize_pca_2d(embeddings, words):\n", + " pca_2d = PCA(n_components=2)\n", + " embeddings_2d = pca_2d.fit_transform(embeddings)\n", + "\n", + " # Create a 2D scatter plot\n", + " plt.figure(figsize=(10, 6))\n", + " plt.scatter(embeddings_2d[:, 0], embeddings_2d[:, 1], marker='o')\n", + " for i, word in enumerate(words):\n", + " plt.annotate(word, (embeddings_2d[i, 0], embeddings_2d[i, 1]))\n", + "\n", + " plt.xlabel(\"Principal Component 1\")\n", + " plt.ylabel(\"Principal Component 2\")\n", + " plt.title(\"2D Visualization of Word Embeddings\")\n", + " plt.grid(True)\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "words = ['cat', 'dog', 'bike', 'kitten', 'puppy', 'bicycle', 'aeroplane', 'helicopter', 'cow', 'wolf', 'lion', 'fighter jet']\n", + "embeddings = []\n", + "for i in words:\n", + " embeddings.append(get_openai_embedding(i))\n", + "visualize_pca_2d(embeddings, words)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Pythagorean Theorem" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.\n", + "\n", + "In mathematical terms, if we have a right-angled triangle with sides of lengths 'a' and 'b' and a hypotenuse of length 'c', the Pythagorean Theorem can be expressed as: ${c^2 = a^2 + b^2}$" + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "${c^2 = a^2 + b^2}$\n", + "\n", + "${5^2 = 4^2 + 3^2}$\n", + "\n", + "25 = 16 + 9\n", + "\n", + "25 = 25" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Let's extend the theorem to calculating distance between any two points in 2 dimension:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Step 1: Two Points - Define the Points\n", + "Imagine two points in a 2-D space. These points can represent anything from physical locations to abstract quantities." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "point1 = (1, 2)\n", + "point2 = (4, 6)" + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Step 2: Connecting a Line - Calculate Differences and Hypotenuse\n", + "To measure the distance between these points, connect them with a straight line. This line represents the shortest path between the two points, equivalent to the hypotenuse of a right-angled triangle." + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Length of side1 is 3 units\n", + "Length of side2 is 4 units\n" + ] + } + ], + "source": [ + "# Calculate the differences in coordinates\n", + "side1 = point2[0] - point1[0]\n", + "side2 = point2[1] - point1[1]\n", + "print(f\"Length of side1 is {side1} units\")\n", + "print(f\"Length of side2 is {side2} units\")" + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Apply pythogorean theorem to calculate length of the hypotenuse, i.e., distance between two points" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The length of the hypotenuse, i.e., distance between two points is 5.0 units\n" + ] + } + ], + "source": [ + "hypotenuse_square = side1**2 + side2**2\n", + "distance_2d = math.sqrt(hypotenuse_square)\n", + "print(f\"The length of the hypotenuse, i.e., distance between two points is {distance_2d} units\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So for two dimension, we can also represent the distance as:\n", + "\n", + "point1 = (1, 2)\n", + "\n", + "point2 = (4, 6)\n", + "\n", + "distance = hypotenuse\n", + "\n", + "distance = $\\sqrt{hypotenuse^2}$\n", + "\n", + "distance = $\\sqrt{side1^2 + side2^2}$\n", + "\n", + "distance = $\\sqrt{(point2[0] - point1[0])^2 + (point2[1] - point1[1])^2}$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Distance between 2D points: 5.0\n" + ] + } + ], + "source": [ + "distance_2d = ((point2[0] - point1[0])**2 + (point2[1] - point1[1])**2)**0.5\n", + "\n", + "print(\"Distance between 2D points:\", distance_2d)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, let's represent them in terms of x and y:-\n", + "\n", + "point1 = (1, 2)\n", + "\n", + "point2 = (4, 6)\n", + "\n", + "${x_2}$ = point2[0] = 4\n", + "\n", + "${x_1}$ = point1[0] = 1\n", + "\n", + "${y_2}$ = point2[1] = 6\n", + "\n", + "${y_1}$ = point1[1] = 2\n", + "\n", + "distance =$\\sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}$\n", + "\n", + "distance =$\\sqrt{(4 – 1)^2 + (6 – 2)^2}$\n", + "\n", + "distance = $\\sqrt{9 + 16}$\n", + "\n", + "distance =$\\sqrt{25}$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is called euclidean distance. " + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Let's extend pythogorean theorem to 3-dimension" + ] + }, + { + "attachments": { + "Screenshot%202023-11-08%20at%2012.01.24%20PM.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![Screenshot%202023-11-08%20at%2012.01.24%20PM.png](attachment:Screenshot%202023-11-08%20at%2012.01.24%20PM.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Distance 'e' would be the distance between point 1 & point 2. We could determine it using Pythagora's theorem as seen previously, but we first need to find the value of 'd' using values 'a' and 'b'.\n", + "\n", + "For triangle abd\n", + "\n", + "${d^2 = a^2 + b^2}$\n", + "\n", + "For triangle ecd\n", + "\n", + "${e^2 = d^2 + c^2}$\n", + "\n", + "substituting ${d^2}$ in the above equation\n", + "\n", + "${e^2 = a^2 + b^2 + c^2}$\n", + "\n", + "e = $\\sqrt{a^2+b^2 + c^2}$" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "# Define two 3D points\n", + "point1 = (1, 2, 3)\n", + "point2 = (4, 6, 8)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Distance between 3D points: 7.0710678118654755\n" + ] + } + ], + "source": [ + "# Calculate the differences in coordinates\n", + "delta_x = point2[0] - point1[0]\n", + "delta_y = point2[1] - point1[1]\n", + "delta_z = point2[2] - point1[2]\n", + "\n", + "distance_3d = (delta_x**2 + delta_y**2 + delta_z**2)**0.5\n", + "print(\"Distance between 3D points:\", distance_3d)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Again, we can represent the distance as:\n", + "\n", + "point1 = (1, 2, 3)\n", + "\n", + "point2 = (4, 6, 8)\n", + "\n", + "distance = hypotenuse\n", + "\n", + "distance = $\\sqrt{hypotenuse^2}$\n", + "\n", + "distance = $\\sqrt{\\Delta x^2 + \\Delta y^2 + \\Delta z^2}$\n", + "\n", + "distance = $\\sqrt{(point2[0] - point1[0])^2 + (point2[1] - point1[1])^2 + (point2[2] - point1[2])^2}$" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Distance between 3D points: 7.0710678118654755\n" + ] + } + ], + "source": [ + "distance_3d = ((point2[0] - point1[0])**2 + (point2[1] - point1[1])**2 + (point2[2] - point1[2])**2)**0.5\n", + "\n", + "print(\"Distance between 3D points:\", distance_3d)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So euclidean distance for 3-D becomes as:\n", + "\n", + "distance =$\\sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2 + (z_2 – z_1)^2}$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Let's extend it to n-dimension" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [], + "source": [ + "# Calculate the Euclidean distance\n", + "def calculate_distance(point1, point2):\n", + " distance_nd = sum((x - y) ** 2 for x, y in zip(point2, point1))**0.5\n", + " return distance_nd" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "9.539392014169456" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "point1 = (1, 2, 3, 4, 7, 4)\n", + "point2 = (4, 6, 8, 10, 8, 6)\n", + "calculate_distance(point1, point2)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So, Euclidean distance for n-d becomes as\n", + "\n", + "distance =$\\sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2 + (z_2 – z_1)^2 + (a_2 – a_1)^2 + ............}$\n", + "\n", + "where x, y, z, a ....., each represent a dimension/axis.\n", + "\n", + "Or we can say that,\n", + "\n", + "For two points p and q in n-dimension, \n", + "\n", + "d(p, q) =$\\sqrt{(q_1 – p_1)^2 + (q_2 – p_2)^2 + (q_3 – p_3)^2 + (q_4 – p_4)^2 + ............}$\n", + "\n", + "which comes as,\n", + "\n", + "distance =$\\sqrt{\\sum_{i=1}^{n} (q_i - p_i)^2 }$\n", + "\n", + "where i represents a dimension and n total number of dimensions." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Let's use calculate_distance() to calculate distance between two embeddings" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "cat = get_openai_embedding('cat')\n", + "dog = get_openai_embedding('dog')\n", + "car = get_openai_embedding('car')\n", + "bike = get_openai_embedding('bike')" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Distance between 'cat' and 'dog': 0.52\n", + "Distance between 'cat' and 'car': 0.56\n", + "Distance between 'cat' and 'bike': 0.61\n", + "Distance between 'bike' and 'car': 0.54\n", + "Distance between 'bike' and 'dog': 0.57\n", + "'cat' is closer to 'dog' than to 'car' or 'bike'.\n", + "'bike' is closer to 'car' than to 'dog' or 'cat'.\n" + ] + } + ], + "source": [ + "# Calculate distances between embeddings\n", + "distance_cat_dog = calculate_distance(cat, dog)\n", + "distance_cat_car = calculate_distance(cat, car)\n", + "distance_cat_bike = calculate_distance(cat, bike)\n", + "distance_bike_car = calculate_distance(bike, car)\n", + "distance_bike_dog = calculate_distance(bike, dog)\n", + "\n", + "# Display distances\n", + "print(f\"Distance between 'cat' and 'dog': {distance_cat_dog:.2f}\")\n", + "print(f\"Distance between 'cat' and 'car': {distance_cat_car:.2f}\")\n", + "print(f\"Distance between 'cat' and 'bike': {distance_cat_bike:.2f}\")\n", + "print(f\"Distance between 'bike' and 'car': {distance_bike_car:.2f}\")\n", + "print(f\"Distance between 'bike' and 'dog': {distance_bike_dog:.2f}\")\n", + "\n", + "# Compare distances\n", + "if distance_cat_dog < distance_cat_car and distance_cat_dog < distance_cat_bike:\n", + " print(\"'cat' is closer to 'dog' than to 'car' or 'bike'.\")\n", + "\n", + "if distance_bike_car < distance_bike_dog and distance_bike_car < distance_cat_bike:\n", + " print(\"'bike' is closer to 'car' than to 'dog' or 'cat'.\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Sentiment Analysis" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [], + "source": [ + "embeddings_good_review = get_openai_embedding('The product is amazing')\n", + "embeddings_bad_review = get_openai_embedding('The product is not good')\n", + "embd_positive = get_openai_embedding('positive')\n", + "embd_neg = get_openai_embedding('negative')" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "sent_embeddings = np.array([embeddings_good_review, embeddings_bad_review, embd_positive, embd_neg])\n", + "visualize_pca_2d(sent_embeddings, words = ['The product is amazing', 'The product is not good',\n", + " 'positive', 'negative'])" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.6663293078646436" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "calculate_distance(embeddings_good_review, embd_positive)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.6326785842898347" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "calculate_distance(embeddings_bad_review, embd_neg)" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(0.6871655141231023, 0.6326785842898347)" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "calculate_distance(embeddings_bad_review, embd_positive), calculate_distance(embeddings_bad_review, embd_neg)" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [], + "source": [ + "def is_positive(review):\n", + " embed_review = get_openai_embedding(review)\n", + " dist_pos = calculate_distance(embed_review, embd_positive)\n", + " dist_neg = calculate_distance(embed_review, embd_neg)\n", + " if dist_pos < dist_neg:\n", + " print(\"It is a positive review\")\n", + " return True\n", + " else:\n", + " print(\"It is a negative review\")\n", + " return False" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "It is a negative review\n" + ] + }, + { + "data": { + "text/plain": [ + "False" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "is_positive(\"Camera quality is too worst. Don't buy this if you want good photos. We can get this quality pictures with 5000 rupees android phone. I am totally disappointed because I expected range of iPhone camera quality but not this.. Waste of money.\")" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.9999999589647395" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sum(embd_positive*embd_positive)" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.0000000130911129" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sum(embd_neg*embd_neg)" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "It is a positive review\n" + ] + }, + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "is_positive(\"Worth to buy it. If you are managed money buy then buy it it never feels you waste of money. Performance. Hand in feel. Camera quality at flagship level\")" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "It is a negative review\n" + ] + }, + { + "data": { + "text/plain": [ + "False" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "is_positive(\"At first it seemed like a great product but my expected were changed completed.\")" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "It is a positive review\n" + ] + }, + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "is_positive(\"At first, it seemed like a bad product but it met my expectations.\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Dot product between two vectors" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The dot product, also known as the scalar product, is a mathematical operation between two vectors. Given two vectors A and B in a multi-dimensional space, the dot product is calculated by multiplying their corresponding components and then summing up those products. Mathematically, the dot product of two vectors A and B is represented as A · B and is calculated as follows:\n", + "\n", + "A = (A1, A2, A3, ......, An)\n", + "\n", + "B = (B1, B2, B3, ......, Bn\n", + "\n", + "A · B = A1 * B1 + A2 * B2 + A3 * B3 + ... + An * Bn\n", + "\n", + "So suppose two vectors are\n", + "\n", + "A = (1,2,3)\n", + "\n", + "B = (4,5,6)\n", + "\n", + "A.B = (A[0] * B[0]) + (A[1] * B[1]) + (A[2] * B[2])\n", + "\n", + "A.B = (1 * 4) + (2 * 5) + (3 * 6)\n", + "\n", + "A.B = 32" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### What the Dot Product Represents?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The dot product represents the similarity or alignment between those vectors. It provides a way to quantify how much two vectors point in the same direction, and it's often used to determine the similarity or dissimilarity between vectors in various contexts." + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.dot([0, 1], [1,0])" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [], + "source": [ + "def is_positive2(review):\n", + " embed_review = get_openai_embedding(review)\n", + " dist_pos = np.dot(embed_review, embd_positive)\n", + " dist_neg = np.dot(embed_review, embd_neg)\n", + " if dist_pos > dist_neg:\n", + " print(\"It is a positive review\")\n", + " return True\n", + " else:\n", + " print(\"It is a negative review\")\n", + " return False" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "It is a positive review\n" + ] + }, + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "is_positive2(\"ye product kaafi achha hai\")" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "It is a negative review\n" + ] + }, + { + "data": { + "text/plain": [ + "False" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "is_positive2(\"ye product kaafi kharaab hai\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's visualize both vectors and their dot product projection" + ] + }, + { + "attachments": { + "download.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![download.png](attachment:download.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, we know that cos(θ) = adjacent side / hypotenuse\n", + "\n", + "In the context of the dot product, the adjacent side is (A · B), and the hypotenuse is (|A| * |B|). Therefore, we have:" + ] + }, + { + "attachments": { + "download%20copy.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![download%20copy.png](attachment:download%20copy.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That makes cos θ = (A · B) / (|A| * |B|)\n", + "\n", + "This is called as cosine similarity\n", + "\n", + "If the vectors are exactly the same, the cosine similarity is 1 (cos 0° = 1).\n", + "\n", + "If the vectors are orthogonal (perpendicular), the cosine similarity is 0 (cos 90° = 0).\n", + "\n", + "If the vectors are in opposite directions, the cosine similarity is -1 (cos 180° = -1).\n", + "\n", + "Values in between indicate different degrees of similarity." + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [], + "source": [ + "def cosine_similarity(A, B):\n", + " dot_product = np.dot(A, B)\n", + "\n", + " # Calculate the magnitudes |A| and |B|\n", + " magnitude_A = np.linalg.norm(A)\n", + " magnitude_B = np.linalg.norm(B)\n", + "\n", + " # Calculate the cosine similarity\n", + " cosine_similarity = dot_product / (magnitude_A * magnitude_B)\n", + " return cosine_similarity" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [], + "source": [ + "def is_positive3(review):\n", + " embed_review = get_openai_embedding(review)\n", + " dist_pos = cosine_similarity(embed_review, embd_positive)\n", + " dist_neg = cosine_similarity(embed_review, embd_neg)\n", + " if dist_pos > dist_neg:\n", + " print(\"It is a positive review\")\n", + " return True\n", + " else:\n", + " print(\"It is a negative review\")\n", + " return False" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "It is a positive review\n" + ] + }, + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "is_positive3(\"Useful product\")" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "It is a negative review\n" + ] + }, + { + "data": { + "text/plain": [ + "False" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "is_positive3(\"Useless product\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Comparison of similarity metrics" + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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" 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