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constants.py
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import numpy as np
alphas_cumprod = np.array([
9.9850e-01, 9.9699e-01, 9.9548e-01, 9.9396e-01, 9.9244e-01, 9.9091e-01,
9.8938e-01, 9.8784e-01, 9.8629e-01, 9.8474e-01, 9.8318e-01, 9.8162e-01,
9.8005e-01, 9.7847e-01, 9.7689e-01, 9.7531e-01, 9.7371e-01, 9.7212e-01,
9.7051e-01, 9.6890e-01, 9.6729e-01, 9.6567e-01, 9.6404e-01, 9.6241e-01,
9.6077e-01, 9.5913e-01, 9.5748e-01, 9.5583e-01, 9.5417e-01, 9.5251e-01,
9.5084e-01, 9.4916e-01, 9.4748e-01, 9.4580e-01, 9.4411e-01, 9.4241e-01,
9.4071e-01, 9.3900e-01, 9.3729e-01, 9.3557e-01, 9.3385e-01, 9.3212e-01,
9.3039e-01, 9.2865e-01, 9.2691e-01, 9.2516e-01, 9.2340e-01, 9.2164e-01,
9.1988e-01, 9.1811e-01, 9.1634e-01, 9.1456e-01, 9.1277e-01, 9.1099e-01,
9.0919e-01, 9.0739e-01, 9.0559e-01, 9.0378e-01, 9.0197e-01, 9.0015e-01,
8.9833e-01, 8.9650e-01, 8.9467e-01, 8.9283e-01, 8.9099e-01, 8.8914e-01,
8.8729e-01, 8.8543e-01, 8.8357e-01, 8.8171e-01, 8.7984e-01, 8.7796e-01,
8.7608e-01, 8.7420e-01, 8.7231e-01, 8.7042e-01, 8.6853e-01, 8.6662e-01,
8.6472e-01, 8.6281e-01, 8.6090e-01, 8.5898e-01, 8.5706e-01, 8.5513e-01,
8.5320e-01, 8.5127e-01, 8.4933e-01, 8.4738e-01, 8.4544e-01, 8.4349e-01,
8.4153e-01, 8.3957e-01, 8.3761e-01, 8.3564e-01, 8.3367e-01, 8.3170e-01,
8.2972e-01, 8.2774e-01, 8.2576e-01, 8.2377e-01, 8.2177e-01, 8.1978e-01,
8.1778e-01, 8.1577e-01, 8.1377e-01, 8.1175e-01, 8.0974e-01, 8.0772e-01,
8.0570e-01, 8.0368e-01, 8.0165e-01, 7.9962e-01, 7.9758e-01, 7.9555e-01,
7.9351e-01, 7.9146e-01, 7.8941e-01, 7.8736e-01, 7.8531e-01, 7.8325e-01,
7.8120e-01, 7.7913e-01, 7.7707e-01, 7.7500e-01, 7.7293e-01, 7.7085e-01,
7.6878e-01, 7.6670e-01, 7.6462e-01, 7.6253e-01, 7.6044e-01, 7.5835e-01,
7.5626e-01, 7.5417e-01, 7.5207e-01, 7.4997e-01, 7.4787e-01, 7.4576e-01,
7.4365e-01, 7.4154e-01, 7.3943e-01, 7.3732e-01, 7.3520e-01, 7.3308e-01,
7.3096e-01, 7.2884e-01, 7.2671e-01, 7.2459e-01, 7.2246e-01, 7.2033e-01,
7.1819e-01, 7.1606e-01, 7.1392e-01, 7.1179e-01, 7.0965e-01, 7.0750e-01,
7.0536e-01, 7.0322e-01, 7.0107e-01, 6.9892e-01, 6.9677e-01, 6.9462e-01,
6.9247e-01, 6.9031e-01, 6.8816e-01, 6.8600e-01, 6.8384e-01, 6.8169e-01,
6.7952e-01, 6.7736e-01, 6.7520e-01, 6.7304e-01, 6.7087e-01, 6.6871e-01,
6.6654e-01, 6.6437e-01, 6.6220e-01, 6.6003e-01, 6.5786e-01, 6.5569e-01,
6.5352e-01, 6.5135e-01, 6.4918e-01, 6.4700e-01, 6.4483e-01, 6.4265e-01,
6.4048e-01, 6.3830e-01, 6.3613e-01, 6.3395e-01, 6.3178e-01, 6.2960e-01,
6.2742e-01, 6.2524e-01, 6.2307e-01, 6.2089e-01, 6.1871e-01, 6.1653e-01,
6.1436e-01, 6.1218e-01, 6.1000e-01, 6.0782e-01, 6.0565e-01, 6.0347e-01,
6.0129e-01, 5.9912e-01, 5.9694e-01, 5.9476e-01, 5.9259e-01, 5.9041e-01,
5.8824e-01, 5.8607e-01, 5.8389e-01, 5.8172e-01, 5.7955e-01, 5.7738e-01,
5.7521e-01, 5.7304e-01, 5.7087e-01, 5.6870e-01, 5.6653e-01, 5.6437e-01,
5.6220e-01, 5.6004e-01, 5.5787e-01, 5.5571e-01, 5.5355e-01, 5.5139e-01,
5.4923e-01, 5.4707e-01, 5.4492e-01, 5.4276e-01, 5.4061e-01, 5.3846e-01,
5.3631e-01, 5.3416e-01, 5.3201e-01, 5.2987e-01, 5.2772e-01, 5.2558e-01,
5.2344e-01, 5.2130e-01, 5.1916e-01, 5.1703e-01, 5.1489e-01, 5.1276e-01,
5.1063e-01, 5.0850e-01, 5.0638e-01, 5.0425e-01, 5.0213e-01, 5.0001e-01,
4.9789e-01, 4.9578e-01, 4.9367e-01, 4.9155e-01, 4.8945e-01, 4.8734e-01,
4.8524e-01, 4.8313e-01, 4.8104e-01, 4.7894e-01, 4.7685e-01, 4.7475e-01,
4.7266e-01, 4.7058e-01, 4.6849e-01, 4.6641e-01, 4.6434e-01, 4.6226e-01,
4.6019e-01, 4.5812e-01, 4.5605e-01, 4.5399e-01, 4.5193e-01, 4.4987e-01,
4.4781e-01, 4.4576e-01, 4.4371e-01, 4.4167e-01, 4.3962e-01, 4.3759e-01,
4.3555e-01, 4.3352e-01, 4.3149e-01, 4.2946e-01, 4.2744e-01, 4.2542e-01,
4.2340e-01, 4.2139e-01, 4.1938e-01, 4.1737e-01, 4.1537e-01, 4.1337e-01,
4.1138e-01, 4.0939e-01, 4.0740e-01, 4.0542e-01, 4.0344e-01, 4.0146e-01,
3.9949e-01, 3.9752e-01, 3.9555e-01, 3.9359e-01, 3.9164e-01, 3.8968e-01,
3.8773e-01, 3.8579e-01, 3.8385e-01, 3.8191e-01, 3.7998e-01, 3.7805e-01,
3.7612e-01, 3.7420e-01, 3.7229e-01, 3.7038e-01, 3.6847e-01, 3.6656e-01,
3.6467e-01, 3.6277e-01, 3.6088e-01, 3.5899e-01, 3.5711e-01, 3.5524e-01,
3.5336e-01, 3.5150e-01, 3.4963e-01, 3.4777e-01, 3.4592e-01, 3.4407e-01,
3.4222e-01, 3.4038e-01, 3.3855e-01, 3.3672e-01, 3.3489e-01, 3.3307e-01,
3.3125e-01, 3.2944e-01, 3.2763e-01, 3.2583e-01, 3.2403e-01, 3.2224e-01,
3.2045e-01, 3.1867e-01, 3.1689e-01, 3.1512e-01, 3.1335e-01, 3.1158e-01,
3.0983e-01, 3.0807e-01, 3.0633e-01, 3.0458e-01, 3.0285e-01, 3.0111e-01,
2.9939e-01, 2.9766e-01, 2.9595e-01, 2.9423e-01, 2.9253e-01, 2.9083e-01,
2.8913e-01, 2.8744e-01, 2.8575e-01, 2.8407e-01, 2.8240e-01, 2.8073e-01,
2.7906e-01, 2.7741e-01, 2.7575e-01, 2.7410e-01, 2.7246e-01, 2.7082e-01,
2.6919e-01, 2.6757e-01, 2.6594e-01, 2.6433e-01, 2.6272e-01, 2.6111e-01,
2.5952e-01, 2.5792e-01, 2.5634e-01, 2.5475e-01, 2.5318e-01, 2.5161e-01,
2.5004e-01, 2.4848e-01, 2.4693e-01, 2.4538e-01, 2.4383e-01, 2.4230e-01,
2.4077e-01, 2.3924e-01, 2.3772e-01, 2.3620e-01, 2.3470e-01, 2.3319e-01,
2.3170e-01, 2.3020e-01, 2.2872e-01, 2.2724e-01, 2.2576e-01, 2.2429e-01,
2.2283e-01, 2.2137e-01, 2.1992e-01, 2.1848e-01, 2.1704e-01, 2.1560e-01,
2.1418e-01, 2.1275e-01, 2.1134e-01, 2.0993e-01, 2.0852e-01, 2.0712e-01,
2.0573e-01, 2.0434e-01, 2.0296e-01, 2.0158e-01, 2.0021e-01, 1.9885e-01,
1.9749e-01, 1.9614e-01, 1.9479e-01, 1.9345e-01, 1.9212e-01, 1.9079e-01,
1.8947e-01, 1.8815e-01, 1.8684e-01, 1.8553e-01, 1.8423e-01, 1.8294e-01,
1.8165e-01, 1.8037e-01, 1.7910e-01, 1.7783e-01, 1.7656e-01, 1.7530e-01,
1.7405e-01, 1.7280e-01, 1.7156e-01, 1.7033e-01, 1.6910e-01, 1.6788e-01,
1.6666e-01, 1.6545e-01, 1.6424e-01, 1.6304e-01, 1.6185e-01, 1.6066e-01,
1.5948e-01, 1.5830e-01, 1.5713e-01, 1.5597e-01, 1.5481e-01, 1.5366e-01,
1.5251e-01, 1.5137e-01, 1.5023e-01, 1.4910e-01, 1.4798e-01, 1.4686e-01,
1.4575e-01, 1.4464e-01, 1.4354e-01, 1.4244e-01, 1.4136e-01, 1.4027e-01,
1.3919e-01, 1.3812e-01, 1.3705e-01, 1.3599e-01, 1.3494e-01, 1.3389e-01,
1.3285e-01, 1.3181e-01, 1.3078e-01, 1.2975e-01, 1.2873e-01, 1.2771e-01,
1.2670e-01, 1.2570e-01, 1.2470e-01, 1.2371e-01, 1.2272e-01, 1.2174e-01,
1.2076e-01, 1.1979e-01, 1.1883e-01, 1.1787e-01, 1.1691e-01, 1.1597e-01,
1.1502e-01, 1.1409e-01, 1.1315e-01, 1.1223e-01, 1.1131e-01, 1.1039e-01,
1.0948e-01, 1.0858e-01, 1.0768e-01, 1.0678e-01, 1.0589e-01, 1.0501e-01,
1.0413e-01, 1.0326e-01, 1.0239e-01, 1.0153e-01, 1.0068e-01, 9.9825e-02,
9.8979e-02, 9.8138e-02, 9.7303e-02, 9.6473e-02, 9.5648e-02, 9.4828e-02,
9.4014e-02, 9.3204e-02, 9.2400e-02, 9.1601e-02, 9.0807e-02, 9.0018e-02,
8.9235e-02, 8.8456e-02, 8.7683e-02, 8.6914e-02, 8.6151e-02, 8.5392e-02,
8.4639e-02, 8.3890e-02, 8.3147e-02, 8.2408e-02, 8.1674e-02, 8.0946e-02,
8.0222e-02, 7.9503e-02, 7.8789e-02, 7.8080e-02, 7.7375e-02, 7.6676e-02,
7.5981e-02, 7.5291e-02, 7.4606e-02, 7.3926e-02, 7.3250e-02, 7.2579e-02,
7.1912e-02, 7.1251e-02, 7.0594e-02, 6.9941e-02, 6.9294e-02, 6.8651e-02,
6.8012e-02, 6.7378e-02, 6.6749e-02, 6.6124e-02, 6.5503e-02, 6.4888e-02,
6.4276e-02, 6.3669e-02, 6.3067e-02, 6.2469e-02, 6.1875e-02, 6.1286e-02,
6.0701e-02, 6.0120e-02, 5.9544e-02, 5.8972e-02, 5.8404e-02, 5.7841e-02,
5.7281e-02, 5.6726e-02, 5.6176e-02, 5.5629e-02, 5.5087e-02, 5.4548e-02,
5.4014e-02, 5.3484e-02, 5.2958e-02, 5.2437e-02, 5.1919e-02, 5.1405e-02,
5.0895e-02, 5.0390e-02, 4.9888e-02, 4.9390e-02, 4.8896e-02, 4.8406e-02,
4.7920e-02, 4.7438e-02, 4.6960e-02, 4.6485e-02, 4.6014e-02, 4.5547e-02,
4.5084e-02, 4.4625e-02, 4.4169e-02, 4.3717e-02, 4.3269e-02, 4.2825e-02,
4.2384e-02, 4.1947e-02, 4.1513e-02, 4.1083e-02, 4.0657e-02, 4.0234e-02,
3.9814e-02, 3.9399e-02, 3.8986e-02, 3.8578e-02, 3.8172e-02, 3.7770e-02,
3.7372e-02, 3.6977e-02, 3.6585e-02, 3.6197e-02, 3.5812e-02, 3.5430e-02,
3.5052e-02, 3.4676e-02, 3.4305e-02, 3.3936e-02, 3.3571e-02, 3.3208e-02,
3.2849e-02, 3.2494e-02, 3.2141e-02, 3.1791e-02, 3.1445e-02, 3.1102e-02,
3.0761e-02, 3.0424e-02, 3.0090e-02, 2.9759e-02, 2.9431e-02, 2.9105e-02,
2.8783e-02, 2.8464e-02, 2.8147e-02, 2.7834e-02, 2.7523e-02, 2.7215e-02,
2.6910e-02, 2.6608e-02, 2.6309e-02, 2.6012e-02, 2.5719e-02, 2.5428e-02,
2.5139e-02, 2.4854e-02, 2.4571e-02, 2.4291e-02, 2.4013e-02, 2.3738e-02,
2.3466e-02, 2.3196e-02, 2.2929e-02, 2.2664e-02, 2.2402e-02, 2.2143e-02,
2.1886e-02, 2.1631e-02, 2.1379e-02, 2.1130e-02, 2.0882e-02, 2.0638e-02,
2.0395e-02, 2.0155e-02, 1.9918e-02, 1.9683e-02, 1.9450e-02, 1.9219e-02,
1.8991e-02, 1.8765e-02, 1.8541e-02, 1.8320e-02, 1.8100e-02, 1.7883e-02,
1.7668e-02, 1.7456e-02, 1.7245e-02, 1.7037e-02, 1.6830e-02, 1.6626e-02,
1.6424e-02, 1.6224e-02, 1.6026e-02, 1.5830e-02, 1.5636e-02, 1.5445e-02,
1.5255e-02, 1.5067e-02, 1.4881e-02, 1.4697e-02, 1.4515e-02, 1.4335e-02,
1.4157e-02, 1.3980e-02, 1.3806e-02, 1.3633e-02, 1.3463e-02, 1.3294e-02,
1.3126e-02, 1.2961e-02, 1.2798e-02, 1.2636e-02, 1.2476e-02, 1.2317e-02,
1.2161e-02, 1.2006e-02, 1.1853e-02, 1.1701e-02, 1.1551e-02, 1.1403e-02,
1.1257e-02, 1.1112e-02, 1.0968e-02, 1.0826e-02, 1.0686e-02, 1.0548e-02,
1.0410e-02, 1.0275e-02, 1.0141e-02, 1.0008e-02, 9.8773e-03, 9.7477e-03,
9.6196e-03, 9.4930e-03, 9.3678e-03, 9.2440e-03, 9.1216e-03, 9.0007e-03,
8.8811e-03, 8.7629e-03, 8.6460e-03, 8.5305e-03, 8.4164e-03, 8.3036e-03,
8.1920e-03, 8.0818e-03, 7.9729e-03, 7.8652e-03, 7.7588e-03, 7.6537e-03,
7.5498e-03, 7.4471e-03, 7.3456e-03, 7.2454e-03, 7.1463e-03, 7.0484e-03,
6.9517e-03, 6.8561e-03, 6.7617e-03, 6.6684e-03, 6.5762e-03, 6.4852e-03,
6.3952e-03, 6.3064e-03, 6.2186e-03, 6.1319e-03, 6.0462e-03, 5.9616e-03,
5.8780e-03, 5.7955e-03, 5.7140e-03, 5.6334e-03, 5.5539e-03, 5.4754e-03,
5.3978e-03, 5.3212e-03, 5.2455e-03, 5.1708e-03, 5.0970e-03, 5.0242e-03,
4.9523e-03, 4.8812e-03, 4.8111e-03, 4.7419e-03, 4.6735e-03, 4.6060e-03,
4.5394e-03, 4.4736e-03, 4.4086e-03, 4.3445e-03, 4.2812e-03, 4.2188e-03,
4.1571e-03, 4.0962e-03, 4.0361e-03, 3.9768e-03, 3.9183e-03, 3.8605e-03,
3.8035e-03, 3.7472e-03, 3.6916e-03, 3.6368e-03, 3.5827e-03, 3.5294e-03,
3.4767e-03, 3.4247e-03, 3.3734e-03, 3.3228e-03, 3.2729e-03, 3.2236e-03,
3.1750e-03, 3.1271e-03, 3.0798e-03, 3.0331e-03, 2.9871e-03, 2.9416e-03,
2.8968e-03, 2.8526e-03, 2.8090e-03, 2.7660e-03, 2.7236e-03, 2.6818e-03,
2.6405e-03, 2.5998e-03, 2.5597e-03, 2.5201e-03, 2.4810e-03, 2.4425e-03,
2.4046e-03, 2.3671e-03, 2.3302e-03, 2.2938e-03, 2.2579e-03, 2.2225e-03,
2.1876e-03, 2.1532e-03, 2.1193e-03, 2.0859e-03, 2.0529e-03, 2.0204e-03,
1.9884e-03, 1.9568e-03, 1.9257e-03, 1.8950e-03, 1.8647e-03, 1.8349e-03,
1.8055e-03, 1.7766e-03, 1.7480e-03, 1.7199e-03, 1.6921e-03, 1.6648e-03,
1.6379e-03, 1.6114e-03, 1.5852e-03, 1.5594e-03, 1.5340e-03, 1.5090e-03,
1.4844e-03, 1.4601e-03, 1.4362e-03, 1.4126e-03, 1.3894e-03, 1.3665e-03,
1.3439e-03, 1.3217e-03, 1.2999e-03, 1.2783e-03, 1.2571e-03, 1.2362e-03,
1.2156e-03, 1.1953e-03, 1.1753e-03, 1.1557e-03, 1.1363e-03, 1.1172e-03,
1.0984e-03, 1.0799e-03, 1.0617e-03, 1.0437e-03, 1.0261e-03, 1.0087e-03,
9.9154e-04, 9.7468e-04, 9.5807e-04, 9.4172e-04, 9.2563e-04, 9.0978e-04,
8.9418e-04, 8.7882e-04, 8.6371e-04, 8.4883e-04, 8.3418e-04, 8.1976e-04,
8.0557e-04, 7.9160e-04, 7.7785e-04, 7.6432e-04, 7.5101e-04, 7.3790e-04,
7.2501e-04, 7.1232e-04, 6.9983e-04, 6.8754e-04, 6.7545e-04, 6.6355e-04,
6.5184e-04, 6.4032e-04, 6.2899e-04, 6.1784e-04, 6.0687e-04, 5.9608e-04,
5.8546e-04, 5.7502e-04, 5.6475e-04, 5.5464e-04, 5.4470e-04, 5.3492e-04,
5.2531e-04, 5.1585e-04, 5.0655e-04, 4.9740e-04, 4.8840e-04, 4.7955e-04,
4.7085e-04, 4.6229e-04, 4.5387e-04, 4.4560e-04, 4.3746e-04, 4.2946e-04,
4.2160e-04, 4.1386e-04, 4.0626e-04, 3.9878e-04, 3.9143e-04, 3.8421e-04,
3.7711e-04, 3.7012e-04, 3.6326e-04, 3.5651e-04, 3.4988e-04, 3.4337e-04,
3.3696e-04, 3.3066e-04, 3.2447e-04, 3.1839e-04, 3.1242e-04, 3.0654e-04,
3.0077e-04, 2.9510e-04, 2.8953e-04, 2.8405e-04, 2.7867e-04, 2.7338e-04,
2.6819e-04, 2.6308e-04, 2.5807e-04, 2.5314e-04, 2.4830e-04, 2.4355e-04,
2.3888e-04, 2.3429e-04, 2.2979e-04, 2.2536e-04, 2.2101e-04, 2.1674e-04,
2.1255e-04, 2.0843e-04, 2.0439e-04, 2.0041e-04, 1.9651e-04, 1.9268e-04,
1.8892e-04, 1.8522e-04, 1.8160e-04, 1.7804e-04, 1.7454e-04, 1.7111e-04,
1.6774e-04, 1.6443e-04, 1.6118e-04, 1.5799e-04, 1.5486e-04, 1.5178e-04,
1.4877e-04, 1.4581e-04, 1.4290e-04, 1.4005e-04, 1.3725e-04, 1.3450e-04,
1.3180e-04, 1.2915e-04, 1.2656e-04, 1.2401e-04, 1.2151e-04, 1.1905e-04,
1.1664e-04, 1.1428e-04, 1.1196e-04, 1.0968e-04, 1.0745e-04, 1.0526e-04,
1.0311e-04, 1.0101e-04, 9.8939e-05, 9.6911e-05
])