diff --git a/bayesian/normalizing_flows/change_of_variables.ipynb b/bayesian/normalizing_flows/change_of_variables.ipynb index 5c1051b..005d28d 100644 --- a/bayesian/normalizing_flows/change_of_variables.ipynb +++ b/bayesian/normalizing_flows/change_of_variables.ipynb @@ -28,24 +28,31 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 17, "metadata": {}, "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.0\n" + ] + }, { "data": { "text/plain": [ - "1.0" + "[]" ] }, - "execution_count": 2, + "execution_count": 17, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": "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\n", + "image/png": "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\n", "text/plain": [ - "
" + "
" ] }, "metadata": { @@ -58,10 +65,12 @@ "x = np.linspace(0.01, 2, num=100)\n", "\n", "base = stats.norm(1, 0.1)\n", + "print(np.trapz(base.pdf(x), x))\n", "\n", - "plt.plot(x, base.pdf(x))\n", - "\n", - "np.trapz(base.pdf(x), x)" + "plt.figure(figsize=(16, 4))\n", + "plt.xlabel(r'$x$')\n", + "plt.ylabel(r'$p(x)$')\n", + "plt.plot(x, base.pdf(x))" ] }, { @@ -75,24 +84,31 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 26, "metadata": {}, "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "5.641895835477563\n" + ] + }, { "data": { "text/plain": [ - "5.641895835477563" + "" ] }, - "execution_count": 3, + "execution_count": 26, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": "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\n", + "image/png": "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\n", "text/plain": [ - "
" + "
" ] }, "metadata": { @@ -105,10 +121,15 @@ "def f(x):\n", " return x**2\n", "\n", + "y = f(x)\n", "transformed = f(base.pdf(x))\n", - "plt.plot(f(x), transformed)\n", + "print(np.trapz(transformed, y))\n", "\n", - "np.trapz(transformed, f(x))" + "plt.figure(figsize=(16, 4))\n", + "plt.xlim(0, 2)\n", + "plt.plot(y, transformed, label=r'$P(y)$')\n", + "plt.plot(x, base.pdf(x), label='$P(x)$', ls='-.')\n", + "plt.legend()" ] }, { @@ -144,24 +165,31 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 27, "metadata": {}, "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.9987379589284238\n" + ] + }, { "data": { "text/plain": [ - "0.9987379589284238" + "" ] }, - "execution_count": 4, + "execution_count": 27, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": "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\n", + "image/png": "iVBORw0KGgoAAAANSUhEUgAAA60AAAD4CAYAAAAHDgAGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAgAElEQVR4nOzdd3SUVf7H8fdNpyQEQqgJhJrQQSIgShOpoiJ2sa6Kvazoupbd1S0/190V17YiuooF1BW7UlUQEEVaIPQOCQRIAqSQPnN/f0xEwAABMnkyM5/XOXPIzNw8zyd79ph85977vcZai4iIiIiIiEhNFOR0ABEREREREZHjUdEqIiIiIiIiNZaKVhEREREREamxVLSKiIiIiIhIjaWiVURERERERGqsEKdu3LBhQ5uQkODU7UVERERERMSLli1blmWtjT3T6zhWtCYkJLB06VKnbi8iIiIiIiJeZIzZURXX0fJgERERERERqbFUtIqIiIiIiEiNpaJVREREREREaizH9rSKiIiIiIgEgtLSUtLT0ykqKnI6ildEREQQFxdHaGioV65f6aLVGBMMLAV2WWtHHfOeAZ4HRgIFwE3W2uVVGVRERERERMQXpaenExkZSUJCAp7SyX9Ya8nOziY9PZ1WrVp55R6nsjz4fmDdcd4bAbQrf4wDXjnDXCIiIiIiIn6hqKiImJgYvytYAYwxxMTEeHUWuVJFqzEmDrgQeP04Qy4B3rYePwLRxpimVZRRRERERETEp/ljwfozb/9slZ1p/TfwO8B9nPebA2lHPE8vf+0oxphxxpilxpilmZmZpxRURETE5xTs/+Vra53LISIi4sNOWrQaY0YB+6y1y040rILXfvXb2Vo7yVqbbK1Njo2NPYWYIiIiPmbbAniuk+dfgPn/gpd7w2d3w7K3YO9acLuczSgiIuIDKtOI6VzgYmPMSCACiDLGvGutve6IMelA/BHP44DdVRdTRETER7jKIDgEmp8FXa+CmDae12NaQ3RLWD8dVrzreS08yjOuzflwzj0QFOxcbhERkRrqpDOt1tpHrbVx1toE4Grg22MKVoDPgRuMRx8gx1qbUfVxRUREaihXGSyYAK/2h5ICCKsDF/0bopp53u98GYz9H/xuK9y7HEZPhC5XwKFsmPNH+PIBLSEWERGvevXVV2nSpAndu3endevWTJ48GYDCwkIGDBiAy1XxCqCSkhL69+9PWVlZNab9xal0Dz6KMeYOY8wd5U+nA1uBzcBrwF1VkE1ERMQ37F0Drw+Gb57yzKiWnaCDojGe2dfu18CoCXDnQuj3ECx/G1KmVl9mEREJOKtWreLJJ58kJSWFadOmMX78eADeeOMNxowZQ3BwxSt+wsLCGDx4MB988EF1xj3slIpWa+28n89otdZOtNZOLP/aWmvvtta2sdZ2sdYu9UZYERGRGsVVCvOegVcHQE46XDEZrnoXajc4teuc/4Rn5rXrlV6JKSIiApCamkqHDh0AiIuLOzyzOmXKFC655BJSU1M599xzD49fvnw5559/PgCjR49mypQp1R+ayu1pFRERkWMd3AnvXQt7U6Hz5TDiH1An5vSuZYxn5hUgPxN2LIROl1ZdVhERqTGe+mINa3fnVuk1OzaL4k8XdTrpuNTUVJKSkrDW8sILLzBq1ChKSkrYunUrCQkJuN1utmzZgsvlIjg4mPHjx/Pss88C0LlzZ5YsWVKluStLRauIiMipcrvgo9vg4A64eiokXVh11/7uGVj5HrQ8D+qq076IiFSNtLQ08vPzGTZsGKGhofTq1YuXX36ZrKwsoqOjAQgKCqJTp06sWbOGTZs20aJFC8466ywAgoODCQsLIy8vj8jIyGrNrqJVRETkVC16EdJ+hEsnVW3BCjD0L9DjOhWsIiJ+qjIzot6watUqBg8ezMyZM4963e12U1T0Sy+GPn368P333/Of//znV2OLi4uJiIiolrxHOu1GTCIiIoHLeroBe2MPamgtaNbd8/XSN2HHoqq/h4iIBJzU1FS6dev2q9fr16+Py+U6XLj26dOHJ554gksvvZTmzZsfHpednU1sbCyhoaHVlvlnKlpFRERO1Xm/hcv+69mL6i2lRfDDyzD1KshY6b37iIhIQEhNTaVr164Vvjd06FAWLlwIQFJSEuHh4TzyyCNHjZk7dy4jR470es6KqGgVERGprEUvwsZZnq+9WbAChEbA9Z9AeBS8MwayNnv3fiIi4temTJnC2LFjK3zvnnvu4a233gLg+eef5+mnn6ZOnTpHjZk6dSrjxo3zes6KqGgVERGpjLISWPUBrP2s+u4ZHQ83lN/vnUuhOK/67i0iIgGjR48eDBw4kHbt2lFYWMiNN9541PslJSWMHj2axMRER/IZa60jN05OTrZLl+o4VxER8SFlxZ6zWcPrVu99dy6GN4ZC/4c9Z7qKiIhPWbdu3eHzUf1VRT+jMWaZtTb5TK+tmVYREZGTSZ0GRbkQEl79BStAi96exk+LXoKcXdV/fxEREQepaBURETmRrfPgo1s8+1mdNPiPYF0w92/O5hAREalmKlpFRESOpygHPr0bYtp5OgY7qX4C9L4dUqZCxipns4iIiFSjEKcDiIiI1Fgzfg95GXDLHAir7XQa6Dfeszw4tAZkERERqSYqWkVERCqy7ktYORX6/w7iejqdxqNWfbjiTadTiIiIVCstDxYRETnWoSz44n5o0tXTsbemObAdZj0OrjKnk4iIiHidilYREZFjLXwOCg/Apa9CSJjTaX4tYxUs+S/sTXU6iYiIiNdpebCIiMiRDmXD0jegyxXQuKPTaSrW4SJ4YBXUbeR0EhEREa876UyrMSbCGPOTMWalMWaNMeapCsYMNMbkGGNSyh9/9E5cERERL9vyLZQVOd8t+ESM8RSs1kLWJqfTiIiIj3j11Vdp0qQJ3bt3p3Xr1kyePBmAwsJCBgwYgMvlqvD7SkpK6N+/P2VlzmxLqczy4GLgfGttN6A7MNwY06eCcQustd3LH3+u0pQiIiLVpesV8MBqaJTkdJKT++4fMLEf5O52OomIiPiAVatW8eSTT5KSksK0adMYP348AG+88QZjxowhODi4wu8LCwtj8ODBfPDBB9UZ97CTLg+21logv/xpaPnDejOUiIiII4rzIDwS6jV3OknldLsKFvwLvv0bjH7Z6TQiIlJZb1548jHth8G59/0yvvu10GOsZxvL/244euzNX1XqtqmpqVx55ZUAxMXFHZ5ZnTJlClOnTgVg0KBBPPbYYwwZMoQnnniC3NxcXnjhBUaPHs2jjz7K2LFjK/czVqFKNWIyxgQbY1KAfcAca+3iCoadU76EeIYxptNxrjPOGLPUGLM0MzPzDGKLiIhUsdJCeDEZFkxwOknl1U+A3rdDyhRPcyYREZETSE1NJSkpCWstL7zwAqNGjaKkpIStW7eSkJAAwFNPPcXf/vY3pkyZwooVK3juuecA6Ny5M0uWLHEkd6UaMVlrXUB3Y0w08IkxprO1dvURQ5YDLa21+caYkcCnQLsKrjMJmASQnJys2VoREak53GWeT7BbnON0klPTbzyseBdmPwE3fObZ7yoiIjVbJWdGKxxfJ+bUvx9IS0sjPz+fYcOGERoaSq9evXj55ZfJysoiOjr68Lj+/ftjrWXChAnMmzfv8JLh4OBgwsLCyMvLIzIy8pTvfyZOqXuwtfagMWYeMBxYfcTruUd8Pd0Y8x9jTENrbVaVJRUREfGm8EgY7IN9BGvVhwGPwMzfw+avod0QpxOJiEgNtGrVKgYPHszMmTOPet3tdlNUVHT4eWpqKhkZGTRs2PBXxWlxcTERERHVkvdIlekeHFs+w4oxphZwAbD+mDFNjPF8tGuM6VV+3eyqjysiIuIFm76GDTM93Xh9UfItUL8VzP4DuN1OpxERkRooNTWVbt26/er1+vXr43K5KCoqIiMjg7Fjx/LZZ59Rp04dZs2adXhcdnY2sbGxhIaGVmdsoHJ7WpsCc40xq4AlePa0fmmMucMYc0f5mMuB1caYlcALwNXlDZxERERqNrfLM0v57V+dTnL6QsJg0OOQuc4z2yoiInKM1NRUunbtWuF7Q4cOZfbs2YwZM4Znn32WDh068Ic//IEnn3zy8Ji5c+cycuTIakp7NONUbZmcnGyXLl3qyL1FREQOW/uZpwvj5W9C5zFOpzl9rlL4dxdo1BGu/9jpNCIicoR169bRoUMHp2Mc14oVK5gwYQLvvPPOcceMGTOGp59+msTExArfr+hnNMYss9Ymn2m+U9rTKiIi4leshQXPQoM20PESp9OcmeBQGPA7KM73/FxqyCQiIpXUo0cPBg0ahMvlqvCs1pKSEkaPHn3cgtXbVLSKiEjg2vwNZKyEi1+CoIoPVPcpyb9xOoGIiPio3/zm+L9DwsLCuOGGG477vrdV6pxWERERv7TgWYiKg65XOZ2k6pQVw8r3oSjH6SQiIiJVQkWriIgEph2LYOciOPc+TyMjf7FvHXxyO6z51OkkIiJyBH/uU+vtn03Lg0VEJDAtmAC1G0KP651OUrWadYdb5kDc2U4nERGRchEREWRnZxMTE4Pxs54D1lqys7O9en6rilYREQk8GSth8xwY/EcIq+10mqoX38vpBCIicoS4uDjS09PJzMx0OopXREREEBcX57Xrq2gVEZHAE9MORvwDul3tdBLvWficpzi/YrLTSUREAl5oaCitWrVyOobP0p5WEREJPGG1offtEFHP6STe4y6DNZ9A5gank4iIiJwRFa0iIhJYfvgPLH/b6RTe1/NmCA6HnyY5nUREROSMqGgVEZHAYS1snAFb5zmdxPvqNIQul0PKe1B40Ok0IiIip01Fq4iIBA5j4IbP4eKXnE5SPXqNg9JDkDLF6SQiIiKnTUWriIgEjpICT+Hqjx2DK9KsO7Q4x7NE2O1yOo2IiMhpUdEqIiKBYd96+Gdb2PS100mqV+/b4cB22DTb6SQiIiKnRUWriIgEhuVvgasEmnZzOkn1ShoFkc1g8atOJxERETktKlpFRMT/lRZBylTocBHUjXU6TfUKDoWzb4Gtcz0zriIiIj4mxOkAIiIiXrfucyg6CD1vcjqJM5J/A+2HQf0Ep5OIiIicspPOtBpjIowxPxljVhpj1hhjnqpgjDHGvGCM2WyMWWWMOcs7cUVERE7DssnQoDUk9HM6iTNqN4AmXZxOISIicloqszy4GDjfWtsN6A4MN8b0OWbMCKBd+WMc8EqVphQRETldmRthx/dw1o0QFMC7YspK4ONx2tsqIiI+56S/va1HfvnT0PKHPWbYJcDb5WN/BKKNMU2rNqqIiMhpWDYZgkKh+1inkzgrJAwKD0JJ/snHioiI1CCV2tNqjAkGlgFtgZettYuPGdIcSDvieXr5axnHXGccnplYWrRocZqRRUREKqm0CFZOhQ6jAq8BU0Wu/cBzTq2IiIgPqdQ6KWuty1rbHYgDehljOh8zpKLfgMfOxmKtnWStTbbWJsfG6o8HERHxsp2LoPBA4DZgOpYxYC1kb3E6iYiISKWd0uYea+1BYB4w/Ji30oH4I57HAbvPKJmIiMiZanM+3LcCEvo7naTmmPd3eKWvZ6mwiIiID6hM9+BYY0x0+de1gAuA9ccM+xy4obyLcB8gx1qbgYiIiFNs+YKfBq0DuwHTsRJHQFkRrP7I6SQiIiKVUpnf4k2BucaYVcASYI619ktjzB3GmDvKx0wHtgKbgdeAu7ySVkREpLK+fhL+d+Mvxat4NO0GjTvDinedTiIiIlIpJ23EZK1dBfSo4PWJR3xtgburNpqIiMgZiIjynE+qxkNHMwZ6XAczfw9710DjTk4nEhEROSGtlxIREf/UbzyMes7pFDVTlys9xwCtmOJ0EhERkZNS0SoiIv4nbQm4XU6nqLnqxHj2tq56H8pKnE4jIiJyQipaRUTEv2Rthv9eAD9NcjpJzdbjeijIhk2znE4iIiJyQipaRUTEvyyfDEEh0GmM00lqtjbnQ2RTNWQSEZEaT0WriIj4j7JiSJkKiSMhsrHTaWq24BDodrWnGVNpodNpREREjktFq4iI+I/1X3mWvPa80ekkvqHfQ3BfCoTWcjqJiIjIcZ30yBsRERGfkTIVouKg9SCnk/iG8Lqef11lEBSs44FERKRG0kyriIj4h9wM2PINdLvKU4BJ5exeAc91grSfnE4iIiJSIRWtIiLiH1L/B9YN3a51OolviWkH8b0gJMzpJCIiIhXS8mAREfF91nqWBsf3hoZtnU7jW8LrwlXvOJ1CRETkuDTTKiIivu9QFrhKoNs1TifxXQd2QMZKp1OIiIj8imZaRUTE99WNhXuXg9vldBLfZC28exnUbQQ3T3c6jYiIyFE00yoiIr7NVQqlRZ7Ot8H6LPa0GAPdr4Ed30P2FqfTiIiIHEVFq4iI+Lb1X8GziZC50ekkvq3bNWCCIGWK00lERESOoqJVRER8W/2W0PkyiGnjdBLfFtUM2l4AKe9pmbWIiNQoKlpFRMS3NesBoybobNaq0H0s5O2GLXOdTiIiInLYSYtWY0y8MWauMWadMWaNMeb+CsYMNMbkGGNSyh9/9E5cERGRI2xfCPvWOZ3CfySOgFoNYIWOwBERkZqjMh0ryoDx1trlxphIYJkxZo61du0x4xZYa0dVfUQREZEKWAvTH4bQ2nDbN06n8Q8h4dD1KljyOhTsh9oNnE4kIiJy8plWa22GtXZ5+dd5wDqgubeDiYiInFBGCuxbC92vdTqJf+l+LbhLYfVHTicREREBTnFPqzEmAegBLK7g7XOMMSuNMTOMMZ2O8/3jjDFLjTFLMzMzTzmsiIjIYSlTITgcOo9xOol/adoV4npB4QGnk4iIiACVWx4MgDGmLvAR8IC1NveYt5cDLa21+caYkcCnQLtjr2GtnQRMAkhOTrannVpERAJbWTGkfghJF0Kt+k6n8T+3zPac3SoiIlIDVGqm1RgTiqdgnWKt/fjY9621udba/PKvpwOhxpiGVZpURETkZxtneWYCu491Ool/+rlgPZTlbA4REREq1z3YAP8F1llrJxxnTJPycRhjepVfN7sqg4qIiByWMhXqNoE2g5xO4r9mPgav9AVXmdNJREQkwFVmefC5wPVAqjEmpfy1x4AWANbaicDlwJ3GmDKgELjaWqvlvyIiUvXy98Gm2dD3Hp3N6k2JI6B+S3CXQXCldxOJiIhUuZP+FrLWLgROuLHFWvsS8FJVhRIRETmu1A/BuqCbugZ7Vat+noeIiIjDTql7sIiIiONcpdDmfGiU5HQS/1ecB8vfVidhERFxlIpWERHxLec9ANd/4nSKwJC9BT6/V2e2ioiIo1S0ioiI7ziYBmqZUH2adoNGnSDlPaeTiIhIAFPRKiIivqGsBCYNgBm/czpJ4DAGul8Lu5ZC5gan04iISIBS0SoiIj7CwpA/Q5crnA4SWLpeCSbYc8yQiIiIA1S0ioiIbwgJhx7XQXwvp5MElrqNoN1QWPUBuF1OpxERkQCkolVERGq+vL3ww8vqYuuU7tdCXgZsnet0EhERCUAqWkVEpOZb+R7MegwOZTmdJDC1Hwa16muJsIiIOEJFq4iI1GzWQsoUiO8DDds5nSYwhYR79hKv+xIKDzqdRkREAoyKVhERqdnSl0DWRugx1ukkga37tdCit2a7RUSk2oU4HUBEROSEVrwDobWh06VOJwlszXrAjV84nUJERAKQZlpFRKTmKjkEqz/xFKzhkU6nEYD8fZCf6XQKEREJICpaRUSk5lr7OZTkQXctDa4RinLguc7w48tOJxERkQCi5cEiIlJzrXgXGrSGln2dTiIAEfXgwmehRR+nk4iISABR0SoiIjXT/q2wYyGc/wcwxuk08rOzrnc6gYiIBBgtDxYRkZqprBgSR0K3a5xOIsfaNh8WT3I6hYiIBIiTFq3GmHhjzFxjzDpjzBpjzP0VjDHGmBeMMZuNMauMMWd5J66IiASMRh3gmvegXnOnk8ix1n4Gc/4AhQecTiIiIgGgMjOtZcB4a20HoA9wtzGm4zFjRgDtyh/jgFeqNKWIiASW7C1wYLvTKeR4zroRyopg1f+cTiIiIgHgpHtarbUZQEb513nGmHVAc2DtEcMuAd621lrgR2NMtDGmafn3ioiInJpv/wrbvoPxGyG45rVfsNZyoKCUjJxCMg4WkZFbRMbBQjJyijyv5RRRWuamcb0ImtaLoElULc+/Pz+vF0GjyAjCQnx0l07Trp5zW5e9Bb3Gac+xiIh41Sn9JWCMSQB6AIuPeas5kHbE8/Ty144qWo0x4/DMxNKiRYtTSyoiIoFjyJ8ha4MjBau1lpzCUnYfLGJPbqHn35widpcXqHtyPYVpUan7qO8LCTI0jvIUpV3jogkNMuzJLWJ9Rh5z12dSWOo6arwx0LBueHlR+3Mxe3Rx2zgqgojQ4Or88SvvrBvhywcgfSnEn+10GhER8WOV/mvAGFMX+Ah4wFqbe+zbFXyL/dUL1k4CJgEkJyf/6n0REREAouM9j2qSV1TKt+v3MT01g4WbsjhUcnSBGRxkaBwZTtPoWnRqFsUFHRrRtLzAbBpdi2b1IoipG05wUMUzjtZacovK2FM+E+v511MMZ+QWsT37ED9szSavqOxX3xtXvxaDkxoxpGMTerduQGhwDZmd7XI5zHoclk9W0SoiIl5VqaLVGBOKp2CdYq39uIIh6cCRf13EAbvPPJ6IiASc6b+DpJHQeqBXb5NTWMrXa/cyY3UG8zdmUeJy0zgqnNE9mtOqYR2aRZcXpfVqERt5/IK0Mowx1KsVSr1aoSQ2iTzuuEPFZezJLTpc1GYcLGRl+kHeX5LGWz/sIDIihEGJjRjSsTEDE2OJjAg97UxnLDwSulwGqdNg2NMQEeVcFhER8WsnLVqNMQb4L7DOWjvhOMM+B+4xxrwP9AZytJ9VREROWcYq+OlViGnjlaL1wKES5qzdy/TVGXy/OYtSl6VZvQiuP6clI7s0oUd8fYLOoDg9U3XCQ2gTW5c2sXWPer2gpIwFm7KYs3Yv367fx+crdxMabDinTUOGdGjEBR0b07RereoP3PMmWP42pH4IZ99S/fcXEZGAYDy9k04wwJjzgAVAKvDzBp7HgBYA1tqJ5YXtS8BwoAC42Vq79ETXTU5OtkuXnnCIiIgEmhmPwNI3YPwGqN2gSi6ZnV/M7LV7mZ6awaIt2bjclrj6tbiwS1NGdGlKt7h6GB9qJORyW5btOMCctXuYs3Yv27MLAOjSvB5DOzZmSKfGJDaOrJ6fyVqY2A+CguD2+d6/n4iI+BRjzDJrbfIZX+dkRau3qGgVEZGjlBXDs0nQegBcMfmMLrUvr4hZa/YyIzWDH7dm47aQEFObkV2aMrJLUzo1i/KpQvV4rLVs3pfP7LV7mbN2LylpBwGIb1CLIR2aMKRjY85OqE+IN/fBpk6Dgzuh7301stOziIg4R0WriIj4lzWfwoc3wnUfQdsLTvnbs/OL+WLlbqav3sOS7fuxFlrH1vHMqHZuSoem1TT76KB9uUV8vW4fc9bu4fst2ZSUuYmuHcr5iY0Y2qkxgzs0rjmNnERExO+paBUREf/y7uWwby08kApBlT/m5WBBCZPmb+XN77dTWOoisXEkI7o0YWSXprRrVNfvC9XjOVRcxvyNmZ59sBv2cbCglGb1IrilX2uuPjueOuFVOCtaVgzrvoD2wyG87snHi4hIQKiqolXreERExHm5u2HLN3Deg5UuWPOKSnlj4XZeX7CV/JIyRnVtxj2D2p6wO28gqRMewojyfbtlLjfzN2Xy6ndb+cuXa3nx203ccE4CN/VNoEGdsDO/2e4U+OgWuPRV6Hb1mV9PRETkCCpaRUTEecsme5r69Bh70qEFJWW8/cMOJn63hYMFpQzt2JgHh7YnqYmOXDmekOAgzk9qzPlJjVm+8wAT523hhW82MWn+Fq5KjufWfq2Jb1D79G8Q3wtumg4tzqm60CIiIuW0PFhERJxVVgL/7gxNusJ10447rKjUxXs/7eTluVvIyi9mQPtYxg9tT9e46GoM6z8278tn0vwtfLJiF24LF3Vtyu0D2tChqYp/ERGpGtrTKiIi/qG0yHPWZ+OOkHDer992uflwaTovfruJjJwierdqwEPDEjk7oWqOxAl0GTmFvLFwG1MX7+RQiYuBibHcOaANvVo1OPX9wN/8BUwQnP+4d8KKiIhPUdEqIiJ+zeW2fJayi39/vYmd+wvo0SKah4Ym0rdNTMA2V/KmnIJS3vlxO29+v53sQyX0aBHNHQPaMKRDY4KCKvm/90e3wsbZMH49hJ3BcmMREfELKlpFRMT3ZW6AHYs8zXtCawHgdltmrN7DhDkb2JJ5iI5No3hoWHsGJTZSsVoNikpdfLgsnUnzt5C2v5A2sXW4fUAbRndvTljISY7L2bYA3hoFoydC92uqJ7CIiNRYKlpFRMT3zXsGFk6AB9dha9Xnm3X7eHbORtZl5NKuUV0eHNKeYZ2aVH6mT6pMmcvN9NV7mDhvC2szcmkSFcEt57Ximt4tqHu843KshRd7Qp1YuGVW9QYWEZEaR0WriIj4PmvhwDaW5Ebz16/WsTLtIC1javPbC9pzUbdmBKtYdZy1lvmbspg4bws/bM0mKiKEm/omcFv/1kRGhP76G75/Hub8Ee5aDI2Sqj+wiIjUGCpaRUTEt1lLfomLf8xcz9s/7KBpvQjuH9yOy3rGERp8kmWo4oiVaQd5Zd4WZq7ZQ8O6YYwfmsiVyfFHf7iQnwkTOkCvcTD8/5wLKyIijlPRKiIivsta8l7sx5u5yTx3aAg39U3g4WGJ1A7T8eG+YGXaQf7y5VqW7jhAUpNI/jiqI33bNvxlwP9uhG3fwYPrITTCuaAiIuKoqipa9VG2iIhUq5yCUiZNfoPI/akcCqnHh7efw58u6qSC1Yd0i4/mwzvO4eVrzyK/uIxrX1/MrW8tZVvWIc+AnjdB4QFY/6WjOUVExD+oaBURkWoze80ehjz3HQnbplIQEs1v7/8dyTpv1ScZY7iwa1O+fnAAvxueyI9bsxn63Hf85cu15DTpC9EtYembTscUERE/oI+1RUTE67Lzi3nyi7V8sXI3/RoVMqRsOabP/VCrjtPR5AxFhAZz1z9QCAUAACAASURBVMC2XNEznglzNvDG99v4eHk6/+r+MAN6dtUfGiIicsZOOtNqjHnDGLPPGLP6OO8PNMbkGGNSyh9/rPqYIiLii6y1fL5yN0Oem8/M1Rk8OKQ9k7uswQAk/8bpeFKFYiPDeXpMV766tx9JTaK4ZVEDhn9wkHkb9jkdTUREfFxllgdPBoafZMwCa2338sefzzyWiIj4ur25Rdz29jLue28F8Q1q89V9/bhvQAuCV7wN7YdDdAunI4oXdGwWxdTbejPp+p40LM0g+92buX/SdDbtzXM6moiI+KiTrtqx1s43xiR4P4qIiPgDay0fLk3nL1+tpaTMzRMXduDmc1t5jkVZ9T8oyIKzb3U6pniRMYahnZowsFEv7Kvj+XZ3CsOfh7G9W/DABe1pUCfM6YgiIuJDqmqryTnGmJXAbuAha+2aigYZY8YB4wBatNAn7CIi/iZtfwGPfZLKgk1Z9G7VgGcu60pCwyP2rf70GjRoA60HORdSqk1YbGt4ZAt/KQki5uuNTFm8k09W7OL+we244ZwEwkLUD1JERE6uUue0ls+0fmmt7VzBe1GA21qbb4wZCTxvrW13smvqnFYREf/hdlveXbyDv89YjwEeHdmBa3u1ICjI/DIoewu8eBYM/zv0udOxrOIAayF/L5sK6vDXr9bx3cZMEmJq89jIDgzp2BhjzMmvISIiPqeqzmk946K1grHbgWRrbdaJxqloFRHxD2n7Cxj/v5X8tH0/A9rH8n9jutA8ulbFg7M2Qd3GEBFVvSHFWZ/eDTu+h3uXQVAwczfs429frWPzvnz6tonhqYs70a5xpNMpRUSkilVV0XrG63KMMU1M+Uekxphe5dfMPtPriohIzffVqgxGvrCAdXty+dcV3Zh889nHL1gBGrZTwRqI2g2BA9tgw3QABiU2Ysb9/fjzJZ1YszuXEc8v4O8z1lNQUuZwUBERqYkqc+TNe8APQKIxJt0Yc4sx5g5jzB3lQy4HVpfvaX0BuNpWZvpWRER8VmGJi0c/TuXuqctp26gu0+/rx+U9446/zPPHifDBdVBaVL1BpWZIGuXpFr3opcMvhQYHccM5CXw7fgBjzmrOxO+2MGTCfGat2YP+jBARkSNVpnvwNSd5/yXgpRONERER/7FhTx73vrecTfvyuXNgGx4c0p7Q4JN8Bmrd4HZDaET1hJSaJTgE+twFM38P6Ush7peVYjF1w/nH5d24IjmeJz5Zze3vLGNwUiOevLgT8Q1qOxhaRERqikrtafUG7WkVEfEt1lqm/rSTP3+xlsiIUJ67qhv92sU6HUt8RXEeTOgEbc+HKyZXOKTU5Wby99t57uuNuNyWe89vy239WxMeEly9WUVEpErUmD2tIiLi/3IKS7lrynIe/2Q1vVvHMOP+fpUrWK2FLXM9s6wS2MIjIfkmWPsZHNhR4ZDQ4CBu69+ab8YPYHCHRvxr9kZGPL+A7zefsLejiIj4ORWtIiJyQst2HGDk8wuYs3Yvj41MYvJNZxMbGV65b978DbwzGtZ87N2Q4ht63Q4mCBa/esJhTevV4j9jezL55rNxuS1jX1/Mfe+tYF+u9kSLiAQiFa0iIlIhl9vy8tzNXPnqDwQHGabd2Zdx/dscffbqiVgL8/8BUXHQ4WLvhhXfUK85dBoDy9+GopyTDh+Y2IhZD/Tn/sHtmLl6D4Of/Y7J32+jzKWZexGRQKKiVUREfmVfbhE3vLGYf87awIjOTfjyvvPoHh99ahfZvgDSFsN5D0BImHeCiu85524Ir+s5s7cSIkKD+e2Q9sz6bX+6t4jmyS/WcsnL37Ni5wEvBxURkZpCjZhEROQoczfs46H/reRQSRlPXdyJK5Pjj3+UzYlMHuUpTO5fqa7BcjRXmaej8Cmy1jI9dQ9//nIN+/KKufrsFjwyPJHo2vpQRESkJqqqRkyn/htDRET8UkmZm3/OWs9rC7aR1CSSD67tQ9tGkad3sZ0/emZah/2fClb5teAQcJVCXobn/NZKMsZwYdemDEiM5d9zNvLmou3MWrOHR0ckcdlZcZVfui4iIj5Fy4NFRITtWYe4fOIiXluwjev7tOTTu889/YIV4Lt/QO2G0PPmqgsp/mXK5fDBdZ69z6eobngIT4zqyBf3nEdCTG0enraKqyb9wPo9uV4IKiIiTtNMq4hIgPt85W4e+ziVIAMTr+vJ8M5NzuyC6ctgyzdwwZMQVrsqIoo/6nPXGV+iY7Mopt3Rl2nL0nl6xjoufGEhvzk3gfsvaE/dcP2JIyLiL7SnVUQkQBWVuvjzl2uZungnPVvW54VretA8utaZX3jq1bDzB/jtas/ZnCLV4MChEp6ZuZ73l6TRKDKcxy/swMXdmp3efmwREakSVbWnVcuDRUQC0NbMfC79zyKmLt7JHQPa8P64PlVTsFoLbQfD+U+oYJWTK8qF2X/wzM6fofp1wvj7ZV355K6+NI6K4P73U7h60o9s3JtXBUFFRMRJmmkVEQkwn6Xs4rGPUwkLCWLCld0ZlNTI6UgSqIrz4IUe0DARbvoSqmhW1OW2vL9kJ/+YuYH84jJu7pvA/Re0IzIitEquLyIilaOZVhEROSVFpS4e/TiV+99PoUPTKKbf369qC9bMDbD0TSgrqbprin8Lj4QBj8COhbD56yq7bHCQYWzvlsx9aCBXJsfx3++3MfjZ7/gsZRdOfVgvIiKnT0WriEgA2JKZz+iXv+e9n3Zy58A2vDeuD03rVcFy4COlfgizHvfMnolU1lk3Qv1WMOdP4HZV6aUb1Anj6TFd+eSuc2lST0uGRUR8lZYHi4j4uU9X7OKxT1IJDwliwlXdGZTopeXA1sL+rRDTxjvXF/+VOg0+ugUufRW6Xe2VW/y8ZPifszaQV6QlwyIi1aGqlgeraBUR8VNFpS6e+mIN7/2UxtkJnu7AVT67+rOSAh1vI6fP7YbXBkLBAbh3KYSEe+1W+w+V8M9Zni7DsXXVZVhExJuqbU+rMeYNY8w+Y8zq47xvjDEvGGM2G2NWGWPOOtNQIiJyZjbv+3k5cBp3DWzDe7d5YTnwzw5sh2eTYP1X3rm++L+gILjgKcjZCUv+69VbHW/J8IY9WjIsIlJTVWZP62Rg+AneHwG0K3+MA14581giInK6Pl2xi4tfWsi+vGIm33w2vxueREiwF1sYLPw3lBVCsx7eu4f4vzaDoPUgmP9PKMrx+u26x0fzyV3n8n+XdmHD3jxGvrCAv3y5lryiUq/fW0RETs1J/4qx1s4H9p9gyCXA29bjRyDaGNO0qgKKiEjlFJa4eGTaKh74IIXOzeox/b5+DPTW/tWfHdwJKVOgx/UQ1cy79xL/d8GTUHgANs6qltsFBxmu7d2CueMHcmVyPG98v43zn/2OT1eoy7CISE1SFR+9NwfSjnieXv7arxhjxhljlhpjlmZmZlbBrUVEBH5ZDvzB0jTuHtSGqbf1pkm9CO/feOajEBQC/R70/r3E/zXrDvcug65XVutt69cJ4+kxXfj0rnNpVi+CBz5I4SotGRYRqTGqomitqHNBhR9PWmsnWWuTrbXJsbGxVXBrEZHAZq3lf0vTuPilhWTmF/PWb3rx8DAvLwf+2aY5sP5L6P8w1Ivz/v0kMPzcffpQVrXfulv5kuGnx3RhY/mS4T9+tpqs/OJqzyIiIr+oir9q0oH4I57HAbur4LoiInICBwtKuHvqcn43bRVd4zzLgQe0r6YPBEuLYPrDENMOzrmneu4pgSN1GkzoCFmbq/3WQUGGa3p5lgxf0yueKYt3MvCf83jp200UllTtObIiIlI5VVG0fg7cUN5FuA+QY63NqILriojIcSzaksWI5xcwe81eHhmexJRb+1TPcuDDAV6AA9tg5D8gJKz67iuBodUA6HUb1KrvWIT6dcL46+guzP5tf/q2ieFfszcy8F9z+WDJTlxu7XcVEalOJz2n1RjzHjAQaAjsBf4EhAJYaycaz8FmL+HpMFwA3GytPekBrDqnVUTk1JWUuZkwZyOvzt9Cq5g6PH91D7rE1aveEAe2w8u9of1wuPKt6r23iEOWbN/P/01fx4qdB2nfuC6/H5HEoMRGOt9VROQEquqc1pMWrd6iolVE5NRsyczn/vdXsHpXLtf0iucPozpSOyyk+oMc3AmzHofhf4d6FfbdE6kaO36AtZ96/r9WA4pDay0zV+/hmZnr2Z5dwDmtY3h0ZBJd46KdjiYiUiOpaBURCRDWWt5fksafv1hLeGgQfx/TleGdmzgdS8T7Fk+CGQ/D2I+g3QVOpzms1OXmvZ928vzXm8g+VMLF3Zrx8LBE4hvUdjqaiEiNoqJVRCQA7D9Uwu8/WsXstXs5t20ME67sTuOoaty7eqTSQpj5ezjvt1A/wZkMEljKSuDlsyGkFtz+HYSEO53oKHlFpUyav5XXFmzF5bbccE4C9wxqS/062uctIgJVV7RWw5kIIiJyOhZsymT4v+czd8M+Hh/ZgXd+09u5ghUgY5Wnq+uBHc5lkMASEgbDn4HMdTDv706n+ZXIiFDGD01k3kODuOysON78fhv9/zmXid9toahUnYZFRKqKZlpFRGqY4jIX/5y5gdcXbqNNbB1euKYHnZpVc7Ol4ynYD7UbOJ1CAs1nd0PKVPjNbIg/2+k0x7Vxbx7PzFjPN+v30axeBOOHJnJpj+YEBTm/H1dExAlaHiwi4oc27c3jvvdTWJeRy3V9WvD4yI7UCgt2NpS1sG0+tOpfI5rhSAAqyoVX+nqWB9++AMJq9t7RRVuy+PuM9axKz6FD0ygeG5lEv3bVdIayiEgNouXBIiJ+xFrLOz9sZ9SLC9mbW8TrNyTz19FdnC9YATbMgLcvhtUfOZ1EAlVEFIz+D2Rvhq+fdDrNSfVt05BP7zqXF67pQX5xKdf/9yeu/+9i1u7OdTqaiIhP0kyriIjDdh0s5IlPUpm7IZP+7WP51xVdaRTp4N7VI5UUeM5kDasDdyyA4FCnE0kgm/EILJ4IN3wGrQc6naZSistcvPvjTl78dhM5haWM6tqMOwe0oWOzKKejiYh4XVXNtDpwwJ+IiAC43Ja3Fm3nX7M3YC386aKO3HhOQs3a/7ZwAuTshJu+UsEqzhv8J9id4ukq7CPCQ4K55bxWXN4zjonfbeHtRdv5YuVuBibGcueANvRq1QCjZfciIiekmVYREQesy8jl9x+nsjLtIAPax/LX0Z1r3hmPe1bDa4Og06UwZpLTaUQ8rPXpvdU5BaW8u3gHbyzcRvahEs5qEc2dA9syOKlRzfrASkSkCqgRk4iIDyoqdfH8N5t4bf5W6tUK5Y8XdeTibs1q3kxL4QGYNBDKiuH2+VC3kdOJRH7hdsEPL0HDREgc7nSa01JU6uLDpWm8On8r6QcKadeoLncMaMPF3ZsRGqyWIyLiH1S0ioj4mEWbs3jsk1S2Zxdwec84Hh/Zgfp1wpyO9WtuN7x/DWz+Bm6eDvG9nE4kcrSyEnjtfIhLhov+7XSaM1LmcvNVagavzNvC+j15NI+uxa39WnHV2fHUDtMuLhHxbSpaRUR8xIFDJfzf9HV8uCydljG1efrSLvRt29DpWMc37xmY938w8l/Q6zan04hUrPAARET79FLhI1lrmbchk1fmbeGn7fupXzuUm/q24sa+LYmuXQM/3BIRqQQVrSIiNZy1ls9X7ubPX6zlYGEp4/q35v7B7YgIrQHH2ByPqxTeHAEN2sClE/2mIBA/lr0FDmyHtoOdTlJllm7fz8TvtvD1un3UDgvmml4tuLVfK5rWq+V0NBGRU6KiVUSkBkvbX8AfPlvNvA2ZdIurx9NjuvrOERdlxWDdEKo/kMUHvHUxZKyEu36EqKZOp6lSG/bk8ep3W/hs5W6CDIzu3pzbB7ShbaO6TkcTEakUFa0iIjVQmcvN5EXbeXb2RoyBh4YmcmPfBIJrelfQkgL49q8w4GGoVd/pNCKVl70FXjnXs/f6uo/88mim9AMFvL5gG+8v2UlxmZuhHRtz58C2dI+PdjqaiMgJqWgVEalhVu/K4dGPU0ndlcOgxFj+MrozcfVr2DE2x7N1Hky5Eq55z6+WWUqAWPEufHY3dL0KRk+EIP/svpudX8xbi7bz1g87yCks5ZzWMdwxsA392jbUcTkiUiNVa9FqjBkOPA8EA69ba/9+zPsDgc+AbeUvfWyt/fOJrqmiVUT8RfqBAibM2cgnK3YRUyeMP13UiVFdm9a8Y2xOJjfD75ZXSgCZ/0/PaoE+d8Owv/n1fuz84jLe/2knry3Yyt7cYuIb1OLys+K5rGdz3/mgTEQCQrUVrcaYYGAjMARIB5YA11hr1x4xZiDwkLV2VGVvrKJVRHzd/kMlvDx3M+/8sAMM3NQ3gbsHtqVebR9anpj2E+RlQMdLnE4icmashRmPwE+vwgVPwnm/dTqR1xWXuZiRuocPl6Xx/eZsjIG+bWK4omc8wzo1oVZYDW76JiIBoaqK1socANYL2Gyt3Vp+4/eBS4C1J/wuERE/VVBSxn8XbGPS/K0cKinj8p5xPHBBe5pF+1jjory98L8bICQC2g+HkHCnE4mcPmNg+N+hIBu+fhLqxEKP65xO5VXhIcGM7tGc0T2ak36ggI+W7WLa8jQe+CCFyPAQRnVryuU94zmrRbTvrfwQETlCZYrW5kDaEc/Tgd4VjDvHGLMS2I1n1nXNsQOMMeOAcQAtWrQ49bQiIg4qdbl5/6edPP/NZrLyixnasTEPD0ukXeNIp6OdurJimPYbKDwIt36tglX8Q1AQjH4FCvfD5/dBXC+Ibe90qmoRV78291/QjnvPb8vibfv5cFkan67YzXs/pdEmtg6X94xnzFnNaRwV4XRUEZFTVpnlwVcAw6y1t5Y/vx7oZa2994gxUYDbWptvjBkJPG+tbXei62p5sIj4Crfb8lVqBv+avYEd2QX0atWAR4Yn0bOlj3bZLc6D98fCtu9gzOvQ9QqnE4lUreJ82DgTulzudBJH5RWVMj01gw+XprN0xwGCDAxoH8sVyfEM7tCI8BAtHxYR76rOPa3nAE9aa4eVP38UwFr79Am+ZzuQbK3NOt4YFa0i4gsWbMrkmZnrWb0rl6QmkTwyPImBibG+u9SuYD9MuRx2p8AlL0P3a5xOJOJdu5ZBcDg06ex0Ekdtzcxn2rJ0Pl6+iz25RUTXDmV09+Zc3jOOzs3rOR1PRPxUdRatIXgaMQ0GduFpxHTtkct/jTFNgL3WWmuM6QVMA1raE1xcRauI1GSr0g/yzMz1fL85m+bRtRg/tD2XdG9e889bPZHc3fDOpbB/G1zxJiRd6HQiEe9yu+A/fTxnD/9mll93FK4sl9uyYFMmHy5LZ86avZS43HRoGsUVPeMY3aM5DeqEOR1RRPxIdR95MxL4N54jb96w1v7NGHMHgLV2ojHmHuBOoAwoBB601i460TVVtIpITbR5Xz7Pfb2Rr1Zl0KBOGPcMasvYPi18fxld9hZ4Z7RnpvWa96BVf6cTiVSPzA0QUQ8imzidpMY5WFDC5yt38+HSdFJ35RAabBic1JjLe8ZxXruGRIT6+H/3RMRx1Vq0eoOKVhGpKdxuy3cbM3lz0Xbmb8ykdlgwt/ZrzW39WhEZ4UPH15zIjh/go1vgqnegeU+n04hUP7cbZj8BZ98CMW2cTlPjrN+Ty4dL0/l0xS6yD5UQERpE3zYNGZQYy8DERsQ30PmvInLqVLSKiJyh3KJSpi1N5+0ftrM9u4DGUeFc17sl1/RuQcO6ftJNN28vRDb2fF1WrC7BEriyt8DrF4C7DC6dqOXxx1HqcvP95izmbcjk2/X72Lm/AIB2jeoyKKkRAxNjOTuhAaHBQQ4nFRFfoKJVROQ0bd6Xx1uLdvDR8nQKSlz0bFmfm/omMLxzE//6Q2x3Crw5Ei56Xh2CRQAO7vScTbx7BfQbD4MehyAtgT0eay1bsw4xd/0+5m3IZPG2bEpdlsjwEM5r15BBiZ4itpGO0RGR41DRKiJyCtxuy9wN+5i8aDsLNmURFhzERd2acVPfBLrE+WnnzLIS+PpPcN5voW4jp9OI1AylRTDjd7D8LWg9EC57A+rEOJ3KJ+QXl5XPwu5j7vpM9uQWAdC5eRSDEhsxKKkR3eKifbthnYhUKRWtIiKVkFNYyodL03j7hx3s3O9ZAnx9n5Zc3cuPlgAfqSgXvnsG+t6rxjMiJ7L8bfjqIagTC1e+DXHa630qrLWsy8hj7oZ9zNuwj2U7DuC2UL92KAPaxzIoqRH928VSX92IRQKailYRkRPYtDePt37YzsfLd1FQ4iK5ZX1uOjeBYZ38bAnwkTbOgi9/6znaZvQrOoNV5GR2r4APboD8PTDiH9DzJh2Lc5oOFpQwf1MW89bvY97GTPYfKiHIQI8W9Q83c+rYNIogzcKKBBQVrSIix9i0N48Zq/cwPTWD9XvyCAsJ4uLyJcCdm/vpEmCAQ1kw8/eQ+iHEdoCLX4T4s51OJeIbCvbDR7dCST7cNB2CQ5xO5PNcbsuq9IPM3ZDJvA37WJWeA0BkeAhd4urRLT6abnHR9GgRTWPthxXxaypaRSTgWWtZszuXmav3MGN1BlsyDwGQ3LI+wzs34dIezYnxxyXAP7MWUqfBzEc8y4L7PwTnPQghWo4nckrcLijOhVr14cAOyEiBDhdr1rWK7MsrYsHGLFakHWBlWg7rMnIpc3v+/mwSFUG3eE8h2z0ums5x9Yjyl6PGRERFq4gEJmstKWkHywvVPezcX0CQgd6tYhjRpQnDOjUJjE/uc9Lhywdh0yxongyXvASNOjidSsT3zfkTLJ4I96/UvnAvKSp1sTYjl5VpB0lJO8jKtINsz/YcrWMMtImtS7e4aLqXF7NJTaIIC/HTbR0ifk5Fq4gEDJfbsmzHAWaszmDm6j1k5BQREmQ4t21DRnRuwpCOjf17RvVYRTnw767gKoHz/wC9b9exHSJVxe2CPaugWQ/PaoY5f4SOo9WoycsOFpSwMj2HleVF7Mr0g2TllwAQFhxEx2ZRdI+P9szKxkWTEFNH+2NFfICKVhHxa3tzi1iyfT+LtmQze81esvKLCQsJon+7WEZ0bsIFHRpTr3YALSHL3Q0bpsPZt3qer5gCCedC/QRHY4n4tZxd8Go/KMiGDhd5PiSKTXQ6VUCw1rLrYCEr03JYme6ZkU1Nz6Gw1AVAVEQI3eKj6dy8Hm1i69KqYW1aNaxL/dqhGC3rFqkxVLSKiN+w1rIlM58l2w+wZPt+lmzfT9r+QgBqhwUzMDGW4Z2bcn5SI+qGB1CTFGs9j6Ag+PEVmPko3LsMYto4nUwkcBTnwQ//gUUvQukh6HYt9B8PDVo7nSzglLncbM7ML19W7JmV3bA3D5f7l79loyJCaBVbl1YxniI2oWFtWpf/G6m9siLVTkWriPiskjI3q3fnsGTbfpZsP8CyHfs5UFAKQMO6YSS3bEByQn3OTmhAx2ZR/ntEzfGUFsHqjzz76nrdBmfd4PnD+VAWNGjldDqRwHQoGxZOgJ9eA1exZy955zHQ6VKIauZ0uoBVUuYm/UAB27IOHX5szz7EtsxD7M4pOmpsw7rh5TOydUhoWIfW5f8mxNQhIlRbLES8QUWriPgEt9uzxGvj3jxW7DzIku37SUk7SHGZG4BWDeuQ3NJToJ7dqgEJMbUDc2mXqxTSl3jOWl3xjmc5YmwSDHocOl7sdDoR+Vnubs/xUqs/goyVUK8FPLDK00GotAhCA6ARnI8oLHGxY/8htv9/e3ceHldZL3D8+5stk2QmS7M1SZd0SXcqlApFEAEBC1fohVZAubjhRUQUBcHleuEC+tTlXtT6KCiFq7gUUVwQiojKLiLQi5RaCqGlQGmzNG32ySznvX+8J5nJNMlMIWlmyO/zPOc55z3n9545OW/OvPO+Z2vrYUdbLzvaunm5rZftbT20dfcPia0rDdJQWcwsd5hZUUxNSQFV4QIqQwWTr/NUqTGijValVE6JJRx27u2lqaWLppZuXmzppqmlm5dau4nEbAPV6xGW1JWwvGEKb28o58iZU6gKT6IHKKVrexGa/gzbH4CXH7XviRQPzDvNPlxp1vH6yg2lcllbE3S8AnNOgkQcvr0Ell8I77pyordMZdAVifFyWy873LOyL+/tYXtbDztau+mMxIfEisCUogBV4QKqS4JUhQqoLimgOlxAdTg4OF0VLqAoMIluYVEqC2PVaNUjSymVNWMMnX1xdu3vo6m1m6bmLppau3mxuZuX9/YQSyQ7werLCplbHWLF7Aoaq0PMrQ6xsLaE4sl0T2q63nZ49e8wf6VN338NbLsHymfB0nNhzonQ8E4oLJvY7VRKZadyrh0A4hE4/HyoX2bTe56DDe+3Tx2ud4fawyFQNHHbqwaFg34Om1bKYdNKh8w3xrCvN8Yr7b20dEZo6eqntavfHdv0i81dtHb1D75rNlWowDfYgB2pgVtW6Ccc9BP0eybnlUVKvQF6plUpBdjXyrR197OnI8LujgjNnanjPpo7+9nd0Td41hTAIzCzopg5VSEaa0LMdcdzqkKTt3FqDHQ3Q+vz0LrNDu+8Akrr4fHvwX1fgsufh5JaaNkKvqDep6rUW1HzFnjoG7Brkz0bCyBeqF5kG7bTltvp6kXakM1DjmPY1xultbuflk7bqG3piiQbuJ3JdE80Mew6/F6hJOgnHPRRUuhPTgf9lBT6CAf9lATdcWHqtI0PBXz62h+V8w7p5cEishL4DuAF1htjvpa2XNzlpwO9wIeNMZtGW6c2WpUaP5FYgs6+GPv7YnT0xejoTZnui9llvVE6+mLs643R7PYmJ9J6jf1eoTocpLY0SE1pkNqSIFNL7WBfMTDJHl5hjL2E1+O3963t2wnb7rWN1O5m2NtkG6uRjmSeYCl84A6YscLG97RB3eH6XlWlJpPuFtt43fUU7HraDgPfExc9aN8Ju/X38PSP4OyboWiKvX0g0gnhGigsB3+R3i6Qp3r64ylnbCNuPRynlEOYwAAAEFJJREFUKxKjM5I6HaezL0ZXJE5nJEbvCI3dASL2zG5qYzcY8BL0eSgMeAn6vBQGvBT4PYPTg8v8XgqGmRf0eQkGPAT9Xgr9Xr2XV71ph+zyYBHxAt8DTgFeA54UkbuMMf9MCTsNaHSHo4Eb3bFSk4IxhoRjSAyMHYPjQNxxSJjktONANOEQSxmicTM0nTDE4gPTDn3RBH0xd4jaoTeWIBJN0BtNmR+z6a5IbPAhR8MRgXCBj7KiAKWFfsqK/Mypqhy2YTqlKJA/vbjGgHHAiYOTcMdx+4AjX4G95NZJ2AenhGvtmc7+Ltj+EER7INoF/d12XtQdDwxHfhgW/yvs2Wzf2XjuT+07G/c2wR8+Dx4fFFfbV2AsWWMfoFQ13w6hmuQPzfKZdlBKTS6hantbwMCtAcbA3pfsd0jlPDsv3m87tQrCNv3ED+DJm5Pr8AZs4zV9OOM74PXDSw/A/lfgyA/Z+F2bbMPYX2gHb8B2uHndweMHX8B2rA1skzaKx0VxgY9ZBT5mVRYfVL5YwqHbbcB2uQ3azpTGbWfEbez2DcTYTumWWIKI+7shEnOIxBKj/i4YjdcjBH22Eev3evD7BL/Hg9/rwecVO88r+Dwe/D4Pfo8cuMzrIeD14PPIYIzP6xlc7vd68HrEDiJ4PILXAx5Jm+emPYPzOGCe1yPJfCnr8IggwtAxIClpj4AgiAcEDsgjuDGSHKtDJ5vr944Cmowx2wFE5HZgFZDaaF0F3Gbsadu/iUiZiNQaY3aPtNIXmrs45YaHBtPL40/z8citGTfmhuCn2OpbMBh/ddGX2e2p5eToXzg3emfG/OnxlxV/k14pYnX/b1kZuz9j/tT4d8ce5JLQtwG4MPJjVsT/PmreGP4h8XMS2/lS8bUAXN63joWJbaPmb5XKIfF+Yny98AoAruu9nlpnz6j5m7yzh8Tv8tTxg+CFGOC7PZ+j0PSNmv8p3zJuCl4IbvxjvhXcXrAGv4lyY89nR80L8Cf/iWwIrMZvotzUezl3+s9kY+BUqp1W1vZdmzH/r/xnstFv478WuZb1gQt4zHc0jYmX+GLkWxnz3+T/Nx71HMU85yX+M/Yd1vouYbPM52hnE5fFfwTAcNcdDMy7xlzM/5lGjjXPcJXnJ1wc/xw7TQ2r5CE+7v19xs//WOxzvGJqONvzMBf7fs/7otfSTREXeu/hXO+DGfOf51yPEwjzUbmH08zDfLZ8HYV+Lx/r/zHL+h63X6pewRsCT+qXtoD4C2j9wJ8pLfRT8uj1SPNmuOA3dsW//aR9am3LKB9eWp8Sf4ltCK52f0z97H3QviNtb2F/AA2oOxzWuMf3T86Girlw+jds+sbjoL/Dzeq+l3RgbBw7PW8lnLnOxn/rMDhsNZz8X7ax+fUG2xg1o/RIr7gEVq6195zdfCKcfC0c9xl79uMX5w+NFQ8EwlAQsj8eAyH79wKUzYBTrrONUoCZx8KV2+0PR4/2RiulsiQy9H5YgMPW2GHAOy6Fue+231N9+w4c9r9qL0H2uD/lnrvTPthtoNH64Fp48Y+jb0e4Fq543k7//BzbaL7oAZtef7Jdv3jt96LHY8fiAcSOa5fC+b+08T9dYzsDz/yuTd98kn0Kuv2DUxrEktwHs46H97r19y2nwuwT4cQvguPA97M497FkNZzwBTd+hX1F2FH/Dl3N8OMzMudPjb/tTDjhi7aDsnkL/OqjmfOnx//L/0DDcbYz9N6rMudPjz/nNtvZuflX8PA38QPl7jCsc26DqsWD8Xx4IxRX2A6Pp4b+pjbYDnbH2LExsP2MO+jxllG++VaqX9jAgyffRSTmMO+f65i+5/4hsY4xtpqOg8HgGOHq+vXEHMOq9v9lfnQL/1G6lnjC4RPd32NJ/DlbjbufCwxJt5lSPhD7MgBf8d1CmfRwaezTANzo/xZz5PVRd90LZvqQ+BZTxjXxjwDwi8B1lNOFAzh2kw/wuLNoSPxjiSWsS5yN4HBf4POjfjbA3YljWJc4G484/MH/eX7qvIefO6dQJfu5zffVA+LTm7cbWMkdnEqF7Gc913Ej5/AnOYZGdvJ18+1hPzN1HT/0nsdfPMcwx+zkq4kb+Ib3Ip7xLOFIZzNXJNaPuN0D6/hvv41flniWy+Pr+XLgSnZ6pnNy4hE+FPtlxr//6oKreMU7nZPij/DB6B1cVvhVOqSEs2N3c2bsvoz534hsGq31wKsp6dc48CzqcDH1wJBGq4hcBFwEUFI3m8aa0OCyir4K2vdnvq+rZko58YLQYPz0ylJC/hDhnmraOzPnT4+fVR0m6ikk2FlDe0/m/Knx+3pnDf4Nnv21tPeNnj8u/iHxPdE4jdU2Hd87jfZodNT8Pd7yIfGGOI0VNt3bOoP2eOGo+aOB6UPi8VXTWG7THXsa6DP9o2VHgnXMLw8PxhcUTmV+aRifE6W9OfNL1guKprKgtASfidK+ZzahkqksCJVQEo/T3pI5f0nJVBaHSwnH4+xrnk1VeTVLikqZ2l/B/rbZyXpwhPwzyqdydGgKNf1ddLXOYWHVVMoLK2noraO7be4BHcyCDJl3fN1MFhbNYHpPB/HmeayeOZvughrm7t8NrQvcXji31w5bH6dOX7loCf3FdUxr7SD86g7WHb0cbzBE7c7dVO1qd3vubO9dau/eQC/jprNWQqAY/rEPmnq4e/U77YY9sRl2jl52eP3MqHDvmSqth3hKB0X5THtmcTSh6pT4hmQjDuxZgkDyWB66I93pysbkrJrFUFKfTE870r4mQoTkDxsZ2IH2h1HdEcn4JWdBnfugE2/ANkg9Pnu5rcfn/rhy0+K1ZxJqDrPxviC8/3b7owCgdBp8/GG7/QG3keovHPlsQ2EZHHtZMu0P6ustlFLjo7zBDtk6/ZsQS/luf89aOO5y+30f7YVE1L36JGq/w524vQplwJI1EOtJphefBdOPtp2Hxkl2DqZ2LJZNT8bXHWEva05N93cl4yGlM9Mdl6f8bqpeOPR9tzWLM//N4dqh+Yur7LTXb9OZpMZXzU8+BM8XTNYTo0mPD7hnUgtC2eVPjx8oj8Ky7PKnxw/cdlJceUB+t2YltXt1QW25zdvVAL2Lee9Sd/8786Bg9BMhINxyztvt5JPPwp4AvzvjWJt+5O+wOzBiTgPMDZaxdeVKYo6D97EtEOng8eNOIuEYSh5+BG/nqxjMkIauHds1hEIz2XDEChxjmPH024gGyrhlwXISjqHuySX4Yl1u3uQ67Ifb9SwtWcxXZi/BAFM2L2RF6SLK6xfhOA6+zQuT/7KD2UwybWBp+Tw+XdMITgKzbT5HVs4lNGU2BbEOEjvmpXxeciL1xMiC8gbWlE8jGAvT/0ojSysbCIXrKO936NvVOJhxpJs4506ph1A1Ff1RuvfMZVFVHaWFVUzrraW7bc6QfT1cAcytnEqwsIJpfTV0tM1mYU01Nf4p1HbX0rE/82/yxqpKKgJl1HTX0NExm8VTy+n1hintrGN/V0p+A7Al4/qykfGeVhF5H/AeY8zH3PQFwFHGmE+lxNwDrDXGPOqm/wxcZYx5eqT16j2tSimllFJKKfXWNVb3tGZzPdtrQEpXGtOA9HP22cQopZRSSimllFIHJZtG65NAo4jMEpEAcB5wV1rMXcAHxVoBdIx2P6tSSimllFJKKZWNjPe0GmPiInIpcB/2lTe3GmO2iMjF7vKbgI3Y1900YV9585Hx22SllFJKKaWUUpNFNg9iwhizEdswTZ13U8q0AT45tpumlFJKKaWUUmqy03c0KKWUUkoppZTKWdpoVUoppZRSSimVs7TRqpRSSimllFIqZ2mjVSmllFJKKaVUzhL7DKUJ+GCRLmDbhHy4GguVQNtEb4R6Q7Ts8puWX37T8stfWnb5Tcsvf2nZ5bf5xpjwm11JVk8PHifbjDHLJ/Dz1ZsgIk9p+eUnLbv8puWX37T88peWXX7T8stfWnb5TUSeGov16OXBSimllFJKKaVyljZalVJKKaWUUkrlrIlstP5wAj9bvXlafvlLyy6/afnlNy2//KVll9+0/PKXll1+G5Pym7AHMSmllFJKKaWUUpno5cFKKaWUUkoppXKWNlqVUkoppZRSSuWscWm0ishKEdkmIk0i8oVhlouIrHOXPysiy7LNq8ZXFmV3vltmz4rIX0XkbSnLXhaRzSLyzFg93lodnCzK7wQR6XDL6BkRuTrbvGp8ZVF2V6aU23MikhCRKe4yPfYmmIjcKiItIvLcCMu13stRWZSd1ns5LIvy03ovR2VRdlrv5TARmS4iD4jIVhHZIiKXDRMzdnWfMWZMB8ALvATMBgLAP4BFaTGnA/cCAqwAnsg2rw7jN2RZdu8Ayt3p0wbKzk2/DFRO9N8xWYcsy+8E4O43kleHiS27tPgzgL+kpPXYm/gyPB5YBjw3wnKt93J0yKLstN7L4SGL8tN6L0eHTGWXFqv1Xo4NQC2wzJ0OAy+MZ5tvPM60HgU0GWO2G2OiwO3AqrSYVcBtxvobUCYitVnmVeMn4/43xvzVGLPPTf4NmHaIt1GN7M0cP3rsTayD3f/vBzYcki1TWTHGPAy0jxKi9V6OylR2Wu/ltiyOvZHosTfBDrLstN7LMcaY3caYTe50F7AVqE8LG7O6bzwarfXAqynp1zjwDxgpJpu8avwc7P6/ENt7MsAAfxSRp0XkonHYPjW6bMvvGBH5h4jcKyKLDzKvGh9Z738RKQJWAnemzNZjL/dpvffWoPVeftJ6L49pvZf7RKQBOAJ4Im3RmNV9vje7kcOQYealv1dnpJhs8qrxk/X+F5ETsZX3cSmzjzXGvC4i1cD9IvK824umDo1sym8TMNMY0y0ipwO/BRqzzKvGz8Hs/zOAx4wxqb3TeuzlPq338pzWe3lL6738p/VeDhORELZD4TPGmM70xcNkeUN133icaX0NmJ6Snga8nmVMNnnV+Mlq/4vIUmA9sMoYs3dgvjHmdXfcAvwGe+pfHToZy88Y02mM6XanNwJ+EanMJq8aVwez/88j7RIpPfbygtZ7eUzrvfyl9d5bgtZ7OUpE/NgG68+MMb8eJmTM6r7xaLQ+CTSKyCwRCWD/0e5Ki7kL+KD7RKkVQIcxZneWedX4ybj/RWQG8GvgAmPMCynzi0UkPDANnAoM+zQ4NW6yKb+pIiLu9FHY74C92eRV4yqr/S8ipcC7gN+lzNNjLz9ovZentN7Lb1rv5Tet93KXe1zdAmw1xtwwQtiY1X1jfnmwMSYuIpcC92GfDHWrMWaLiFzsLr8J2Ih9mlQT0At8ZLS8Y72NanhZlt3VQAXwfbcOiBtjlgM1wG/ceT7g58aYP0zAnzFpZVl+a4BPiEgc6APOM/YxbnrsTaAsyw7gLOCPxpielOx67OUAEdmAfUpppYi8BlwD+EHrvVyXRdlpvZfDsig/rfdyVBZlB1rv5bJjgQuAzSLyjDvvS8AMGPu6T9zHDiullFJKKaWUUjlnPC4PVkoppZRSSimlxoQ2WpVSSimllFJK5SxttCqllFJKKaWUylnaaFVKKaWUUkoplbO00aqUUkoppZRSKmdpo1UppZRSSimlVM7SRqtSSimllFJKqZz1/09N9TDETuz3AAAAAElFTkSuQmCC\n", "text/plain": [ - "
" + "
" ] }, "metadata": { @@ -181,14 +209,14 @@ "\n", "y = f(x)\n", "px = base.pdf(x)\n", - "\n", "transformed = px * f_i_prime(f_i(y))\n", + "print(np.trapz(transformed, y))\n", "\n", - "plt.plot(x, px)\n", - "plt.plot(y, transformed)\n", + "plt.figure(figsize=(16, 4))\n", "plt.xlim(0, 2)\n", - "\n", - "np.trapz(transformed, y)" + "plt.plot(y, transformed, label=r'$P(y)$')\n", + "plt.plot(x, base.pdf(x), label='$P(x)$', ls='-.')\n", + "plt.legend()\n" ] }, { @@ -235,7 +263,6 @@ "\n", "y = f(x)\n", "px = base.pdf(x)\n", - "\n", "transformed = px * f_i_prime(f_i(y))\n", "\n", "plt.plot(x, px)\n", @@ -271,40 +298,50 @@ "$$ \n", "\\begin{eqnarray}\n", "P(y)&=&P(f^{-1}(y)) \\cdot \\left| \\det \\frac{\\partial{ f(y)^{-1} }}{\\partial{y}} \\right| \\\\\n", - "P(y)&=&P(f^{-1}(y)) \\cdot \\left| \\det \\mathbf{J}_{f^{-1}(y)} \\right| \\\\\n", + "&=&P(f^{-1}(y)) \\cdot \\left| \\det \\mathbf{J}_{f^{-1}(y)} \\right| \\\\\n", "\\end{eqnarray}\n", "$$\n", "\n", "The geometric meaning of the determinant is a scaling factor. $\\det A$ tells us how much an n-dimensional volume is scaled by applying the transformation of $A$." ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$Q(z') = Q(z) \\left| \\det \\frac{\\partial{f^{-1}}}{\\partial{z}} \\right| $$\n", + "\n", + "$$ f(x) $$" + ] + }, { "cell_type": "code", - "execution_count": 259, + "execution_count": 39, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ + "0.9905751293230018\n", "(50, 50, 2)\n" ] }, { "data": { "text/plain": [ - "" + "0.9905751293230018" ] }, - "execution_count": 259, + "execution_count": 39, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": "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\n", + "image/png": "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\n", "text/plain": [ - "
" + "
" ] }, "metadata": { @@ -323,9 +360,12 @@ "\n", "# field of all possible events X\n", "x_field = np.concatenate([x1_s[..., None], x2_s[..., None]], axis=-1)\n", - "print(x_field.shape)\n", "\n", - "plt.contourf(x1_s, x2_s, base.pdf(x_field))" + "print(np.trapz(np.trapz(base.pdf(x_field), x_field[:, 0, 1], axis=0), x_field[0, :, 0]))\n", + "\n", + "plt.figure(figsize=(8, 8))\n", + "plt.contourf(x1_s, x2_s, base.pdf(x_field))\n", + "np.trapz(np.trapz(base.pdf(x_field), x_field[:, 0, 1], axis=0), x_field[0, :, 0])" ] }, { @@ -347,18 +387,9 @@ }, { "cell_type": "code", - "execution_count": 275, + "execution_count": 35, "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/opt/miniconda3/lib/python3.7/site-packages/ipykernel_launcher.py:7: UserWarning: To copy construct from a tensor, it is recommended to use sourceTensor.clone().detach() or sourceTensor.clone().detach().requires_grad_(True), rather than torch.tensor(sourceTensor).\n", - " import sys\n" - ] - } - ], + "outputs": [], "source": [ "def f(x1, x2):\n", " return torch.exp(x1 / 3), x2**2\n", @@ -373,7 +404,7 @@ }, { "cell_type": "code", - "execution_count": 276, + "execution_count": 36, "metadata": {}, "outputs": [], "source": [ @@ -401,32 +432,32 @@ }, { "cell_type": "code", - "execution_count": 277, + "execution_count": 37, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "/opt/miniconda3/lib/python3.7/site-packages/ipykernel_launcher.py:5: UserWarning: To copy construct from a tensor, it is recommended to use sourceTensor.clone().detach() or sourceTensor.clone().detach().requires_grad_(True), rather than torch.tensor(sourceTensor).\n", - " \"\"\"\n" + "/opt/miniconda3/lib/python3.7/site-packages/ipykernel_launcher.py:6: UserWarning: To copy construct from a tensor, it is recommended to use sourceTensor.clone().detach() or sourceTensor.clone().detach().requires_grad_(True), rather than torch.tensor(sourceTensor).\n", + " \n" ] }, { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 277, + "execution_count": 37, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": "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\n", + "image/png": "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\n", "text/plain": [ - "
" + "
" ] }, "metadata": { @@ -438,7 +469,11 @@ "source": [ "px = base.pdf(x_field)\n", "transformed = px * np.abs(create_det_jac(y_field))\n", - "plt.contourf(y_field[..., 0], y_field[..., 1], transformed)" + "\n", + "plt.figure(figsize=(8, 8))\n", + "plt.contourf(y_field[..., 0], y_field[..., 1], transformed)\n", + "\n", + "print(np.trapz(np.trapz(transformed, y_field[:, 0, 1], axis=0), y_field[0, :, 0]))" ] }, {