{
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  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "65b5bd15",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "bafde0b2",
   "metadata": {},
   "outputs": [],
   "source": [
    "freqs = 1.0 / (10000 ** (torch.arange(0, 6, 2).float() / 6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5312d72e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([1.0000, 0.0464, 0.0022])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "freqs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "8551e607",
   "metadata": {},
   "outputs": [],
   "source": [
    "t = torch.arange(10).float()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "cd26f2a2",
   "metadata": {},
   "outputs": [],
   "source": [
    "angles = torch.outer(t, freqs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "fbe2659f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0.0000e+00, 0.0000e+00, 0.0000e+00],\n",
       "        [1.0000e+00, 4.6416e-02, 2.1544e-03],\n",
       "        [2.0000e+00, 9.2832e-02, 4.3089e-03],\n",
       "        [3.0000e+00, 1.3925e-01, 6.4633e-03],\n",
       "        [4.0000e+00, 1.8566e-01, 8.6177e-03],\n",
       "        [5.0000e+00, 2.3208e-01, 1.0772e-02],\n",
       "        [6.0000e+00, 2.7850e-01, 1.2927e-02],\n",
       "        [7.0000e+00, 3.2491e-01, 1.5081e-02],\n",
       "        [8.0000e+00, 3.7133e-01, 1.7235e-02],\n",
       "        [9.0000e+00, 4.1774e-01, 1.9390e-02]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "angles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9c9c2c6c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([[ 1.0000,  1.0000,  1.0000],\n",
       "         [ 0.5403,  0.9989,  1.0000],\n",
       "         [-0.4161,  0.9957,  1.0000],\n",
       "         [-0.9900,  0.9903,  1.0000],\n",
       "         [-0.6536,  0.9828,  1.0000],\n",
       "         [ 0.2837,  0.9732,  0.9999],\n",
       "         [ 0.9602,  0.9615,  0.9999],\n",
       "         [ 0.7539,  0.9477,  0.9999],\n",
       "         [-0.1455,  0.9318,  0.9999],\n",
       "         [-0.9111,  0.9140,  0.9998]]),\n",
       " tensor([[ 0.0000,  0.0000,  0.0000],\n",
       "         [ 0.8415,  0.0464,  0.0022],\n",
       "         [ 0.9093,  0.0927,  0.0043],\n",
       "         [ 0.1411,  0.1388,  0.0065],\n",
       "         [-0.7568,  0.1846,  0.0086],\n",
       "         [-0.9589,  0.2300,  0.0108],\n",
       "         [-0.2794,  0.2749,  0.0129],\n",
       "         [ 0.6570,  0.3192,  0.0151],\n",
       "         [ 0.9894,  0.3629,  0.0172],\n",
       "         [ 0.4121,  0.4057,  0.0194]]))"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "angles.cos(), angles.sin()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ccec4526",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[[0., 0., 0., 0.],\n",
       "         [0., 0., 0., 0.]],\n",
       "\n",
       "        [[0., 0., 0., 0.],\n",
       "         [0., 0., 0., 0.]],\n",
       "\n",
       "        [[0., 0., 0., 0.],\n",
       "         [0., 0., 0., 0.]],\n",
       "\n",
       "        [[0., 0., 0., 0.],\n",
       "         [0., 0., 0., 0.]],\n",
       "\n",
       "        [[0., 0., 0., 0.],\n",
       "         [0., 0., 0., 0.]],\n",
       "\n",
       "        [[0., 0., 0., 0.],\n",
       "         [0., 0., 0., 0.]]])"
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     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "torch.zeros(6, 2, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fa05b2dc",
   "metadata": {},
   "outputs": [],
   "source": []
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