{ "cells": [ { "attachments": {}, "cell_type": "markdown", "id": "4bd147b8", "metadata": {}, "source": [ "# Using _egobox_ surrogate model _Gpx_" ] }, { "attachments": {}, "cell_type": "markdown", "id": "3141794e", "metadata": {}, "source": [ "## Installation" ] }, { "cell_type": "code", "execution_count": null, "id": "33b7dcca", "metadata": {}, "outputs": [], "source": [ "%pip install egobox" ] }, { "attachments": {}, "cell_type": "markdown", "id": "0fa96b71", "metadata": {}, "source": [ "We import _egobox_ as _egx_ for short" ] }, { "cell_type": "code", "execution_count": 2, "id": "d502466d-906e-4b64-9968-ea5b642fbadf", "metadata": {}, "outputs": [], "source": [ "import egobox as egx" ] }, { "attachments": {}, "cell_type": "markdown", "id": "c8e65173-d594-4a1d-8bfb-f5e3a480ce47", "metadata": { "tags": [] }, "source": [ "# Example 1 : Gpx basics" ] }, { "attachments": {}, "cell_type": "markdown", "id": "358adf9c-0447-4b16-b3dc-02eb881a7d96", "metadata": { "tags": [] }, "source": [ "### Training " ] }, { "attachments": {}, "cell_type": "markdown", "id": "d72fd25e-803b-435e-ae81-9aa7175494bc", "metadata": {}, "source": [ "#### Training data definition" ] }, { "cell_type": "code", "execution_count": 3, "id": "f4de436a-8319-47f5-bb5a-e68d02419752", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "xt = np.array([[0.0, 1.0, 2.0, 3.0, 4.0]]).T\n", "yt = np.array([[0.0, 1.0, 1.5, 0.9, 1.0]]).T" ] }, { "attachments": {}, "cell_type": "markdown", "id": "465167dc-424b-4b73-8e1d-28dc6e5e3044", "metadata": {}, "source": [ "#### Building the surrogate" ] }, { "cell_type": "code", "execution_count": 4, "id": "41bca9a8-bc79-4122-a650-64dd4c37203c", "metadata": {}, "outputs": [], "source": [ "gpx = egx.Gpx.builder().fit(xt, yt)" ] }, { "attachments": {}, "cell_type": "markdown", "id": "a302fb72-aff9-4d92-949f-f77832ab78d6", "metadata": { "tags": [] }, "source": [ "### Prediction" ] }, { "attachments": {}, "cell_type": "markdown", "id": "b4419c24-cb8e-4dd0-893b-8b6b23ad3218", "metadata": {}, "source": [ "#### Using the surrogate for estimation" ] }, { "cell_type": "code", "execution_count": 5, "id": "47d51b54-41df-4b78-b10f-f996ec8bf5a2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimal theta = [1.67830276]\n", "GP variance = 0.30493880450870275\n", "Reduced likelihood = 0.5781740714671411\n" ] } ], "source": [ "# number of x locations to estimate\n", "num = 100\n", "\n", "# x should have 2D shape (nsamples, nx)\n", "x = np.linspace(0.0, 4.0, num).reshape((-1, 1))\n", "\n", "# estimated values\n", "y = gpx.predict(x)\n", "# estimated variances\n", "s2 = gpx.predict_var(x)\n", "\n", "# Print hyperparameters\n", "print(f\"Optimal theta = {gpx.thetas()[0]}\")\n", "print(f\"GP variance = {gpx.variances()[0]}\")\n", "print(f\"Reduced likelihood = {gpx.likelihoods()[0]}\")" ] }, { "attachments": {}, "cell_type": "markdown", "id": "4c44d3ba-4540-4e3f-8eb8-35eac1a6c3df", "metadata": {}, "source": [ "#### Plotting results" ] }, { "cell_type": "code", "execution_count": 6, "id": "782b0849-ef74-4267-999b-d714065323e7", "metadata": {}, "outputs": [ { "data": { "image/png": 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CBKvAf/c6hu3bt5OWlgaAXq9n/PjxrFq1yv24y+Vi1apVTJ482V8hCuER/uj9iSrfyOCVl7ftr6M1UHrCLRSe9BjO8Hifx9JbWo3CtRPa4j10ivNOdSD/z/4AT7X+Hqeiw1T2NYM//wOmws/9E2gvlZSU+K9nUIgg5tchMIvF4u69AcjLy2P79u3Ex8eTnZ3NggULKCkp4bXXXgNg0aJFDBgwgOOOO46WlhZefPFFvvzySz7//Jc3rPnz5zNnzhwmTJjAxIkTWbRoEVarlblz5/r8+oTwlObmZt8ee6GqJOz/N6k7nkHBRXPsMIom3hMwE5x76twTssjKyuL+T3ZR1vDL4aWxRgNRE/7IwZhzydz8MBH1e8jadB+RlVsoG/tXVF24H6PuvvLyclwul2z1IUQP+DUB2rx5c4eNDdvn4cyZM4elS5dSVlZGYWGh+3G73c7NN99MSUkJRqOR0aNH88UXX3So48ILL6Sqqoq7776b8vJyxo4dy/Lly4+YGC1EMKmpqfFZW4qrlbStTxCf/wkAdbnnUHrCLajawNwn51gyMjKIi4sjLQ3OPC6VTXm1VDa2kBSlJ1VrpclqwcZgDpz2Asm7l5K0eynx+Z9grN1F4a8eDJqkr7KyEq1WS0JCgr9DESIoBMw+QIFE9gESgcThcPDTTz/5pC1tSx3ZG/5GZM33qGgoH309NUMu9Mlmhp6m1WrJycnBaDzyXLB2NpuNffv2dbgvsmIzmZvuI8xWi1MbQen4W2nInuHtcD0mMzOzx4e+CtFf9Pt9gIQIJb7a9DDMUsKgr64lsuZ7nLpICk56jJqhFwVl8qPX6xk0aFCXyQ+0LYA4PFmwpkzgwBlLsSSNR+tsJmvT/aRtewpcvp+A3hvFxcU0Njb6OwwhAp4kQEIEMFVVfZIAGcx5DFz9Z/TWUuyR6Rw87QUsacG5cMBoNDJo0CD0+u4N2XU2b8YRnkD+KU9TMfIqABIOfEDuNzejsQfHJqmFhYUBe1iuEIFCEiAhApjFYvH60vfwup8YsPp6wlqqaYkZwMFTn8MWk+vVNr0lJiaG3NxctFrtsQv/TK/XEx/fyao2RUvVyCspmLwQpzaCqMrNDPryWvSNhUeWDTDt+wTJjtFCHJ0kQEIEMG/3/hirtjNgzY3o7A00xY0gb+oSHBGJXm3TWxISEsjKyurVOVlJSUlHPWS0MeMU8qY9hz0iBYOliEFfXktkxaa+hut1LpeLgoICnM7g2OFaCF+TBEiIANXa2urVuRyRFZvJ/WY+WkcT1sQTyD9lMU6DyWvteVNKSgqpqam9Pik9LCysy9VTLbFDOHD6izTFH4+2tZHcb24htuB/vQ3XZ+x2O8XFxX49PkWIQCUJkBABqr6+3mt1G6u/J2f97WicNhpTJ5P/6ydxhUV6rT1vSktL67IHp7sSExO7rMMZHk/e1GeozzoDRXWS+d2DJOx5q09t+kJjYyNVVVX+DkOIgCMJkBAByJuTn8Pr9pDzzS1onC00pkyicPLDqFqDV9rytszMTI/te6PT6UhM7Hr4T9XqKZ54N9VDLgYgbecSUnc8A6rLIzF4S2VlpawME+IwkgAJEYCsViutra0er9dgziP36/loHVasiWN+Tn6Cc4PD7Oxsj+93k5iYeOw5RIqG8jE3UDbq+rbn7HuHzE33o7g8/3p5UlFRkUyKFuIQkgAJEYC80fsTZikhd+08dPZ6muKGU3DS40Fz1MPhcnJyvLJJqVarPWYvULuaYZdQfOJdqIqW2KKVZK9fgOIM3ATD5XJRWFiIyxXYvVVC+IokQEIEGIfDgdns2f1mtC21DPh63s9L3QdScPJTQTnnR1EUcnJyiI6O9lobCQkJ3V5JVp8zk4KTHsOlNRBdvoGcdbejOFqO/UQ/sdlslJeX+zsMIQKCJEBCBBhPT35WnDZy1t+O3lqKLTKD/F8/HZSrvXyR/EDPeoEALKm/ouCkJ37eK+i7tg0TW61ejLBvamtrZT6QEEgCJERAUVXVswefqi4yNz2AsXYXDn0MBSc/EZT7/LQnP1FRUT5prye9QADW5HFtiaUuksjq7eR+PR9Nq8WLEfZNcXGxV+aYCRFMJAESIoA0Nzd79IMp5Yd/Yir5Cpeio3DyQuzR2R6r21cURSE3N9dnyQ/0vBcIoDlxFHmnLMYRFo2x9gdy196Exh6YPS1Op1P2BxIhTxIgIQJIXV2dx+qKy/sPSXveAKB0wgKaksZ6rG5fae/5iYz0/XylnvYCAbTEjyB/6jM49LEY634i95v5ATscZrVaPdvbKESQkQRIiADhcrloaGjwSF2RFZtJ3/oEAJUj5lKfM9Mj9fpadna2T3t+DtWbXiBo2zU675TFOPQxGGt3te255AjMg0nLy8tpaQncSdtCeJMkQEIEiMbGRo8sUQ6zlpO18W4U1Ul91hlU/nyiebDxxYTnY+lNLxCALXYw+b9ehDMsmsia78led1vArg6ToTARqiQBEiJAeGL4S3HayP72bz8fbjqckgkLoI9HRPhDdna235Mf6H0vEEBL3DDyf/0UTp2RqKpt5Ky/IyD3CWppaaG6utrfYQjhc5IACREAHA4HFksfVw2pKunbniKibg8OvYmiXz0UlEdcZGVleWWTw97qbS8QQHP8SPJPfsq9RD7r27vA5fBwhH1XWVkpu0SLkCMJkBABwBN7/8Tl/Ye4/E9Q0VA06T5aI1P7HpiPZWZmYjIF1h5FfekFgrbVYQUnP45LoyembB2Z3z0YcGeHqaoqQ2Ei5EgCJEQA6OvwV0TNj6RtewqAiuP/iDXlRE+E5VMZGRkeP9vLU/rSCwTQlHQChZMfch+bkbb9aQiwZKO5udlrB/AKEYgkARLCz1paWvo0/KC11ZP97Z1oVAcNGVOpHnapB6PzjfT0dOLi4vwdxlFptdo+nzpvSZvSdnYYCgkHPiR514seis5zysvLsdvt/g5DCJ+QBEgIP+vT8JeqkrH5YcKaK7FFZ1My4e9BN+k5NTWV+Ph4f4dxTAkJCSh9/N02ZJ9B2Qk3A5C8eykJe9/xRGgeo6oqJSUlMhQmQoIkQEL4kaqqfRr+it//PjFl63Bp9BRNuj/oDjhNTk7u0/waX9LpdB6JtXbQeVQcdy0Aad8/Q2zB8j7X6UlWq9Xjh/EKEYgkARLCjywWC06ns1fPDa/fS+rOJQCUj76eltghngzN65KSkkhOTvZ3GD3iiV4ggKrhl1M95EIAMjY/TFT5xj7X6UllZWW9/ncpRLCQBEgIP+rt8JfiaCZr4z1oXK2Y006mdtDvPBuYlyUkJARd8gNtvUB9nQsEgKJQPvoG6rPOQFGdZG34O+G1u/ter4c4HA6qqqr8HYYQXiUJkBB+4nK5ej3UkL59EYbGQlojkiiZ8LegmvcTFxdHamqqR3pS/CExMdEzsSsaSk78O5bkCWidzeSuuwW9pbjv9XpIdXW1HJMh+jVJgITwk8bGxl5NNjUVffHzfj8KRRPvwWkIrH1zumIymUhPTw/a5Ac82AsEqJowCic/THPsUHS2enK//ivalsBZil5aWioTokW/JQmQEH7Sm+EvXXOV+5DTqhFzaEo6wcNReU9MTAyZmZlBnfy081gvEOAKi6Tg5CewR6ajt5aSG0CHpzY1NXnsgF4hAo0kQEL4gdPppLGxsWdPUlUyNj+CtrWRprgRVI6Y653gvCA6OpqsrKx+kfxAWy+QJ5fuO8ITyD/5KRz6WCLq95D57T0Bc2SGTIgW/ZUkQEL4QW/m/sTl/Yfoim9xafQUn3gXaHReiMzzoqKi+lXy086TvUAA9ugsCk56tO3IjPL1pG1fFBC7RTudTpkQLfolSYCE8IOeDn+FWUpI3fEM0HbUhT0mxwtReZ7RaCQ7O7tPx0gEqrCwMI9v4NiccDzFk+5p2y364Eck7n3Lo/X3VnV1tRyWKvqd/veuJESAczgcWK3W7j9BdZG5+WG0zmasiWOpGXKB94LzIKPRSG5ubr9Mftp5YxNHc8aplI+5EYDUnf9HTNEXHm+jN8rLy/0dghAe1X/fmYQIUD2dVJqw7z0iq7fj1EZQfOLfQQn8P9uIiAhycnL6dfID3ukFAqgZciHVg88HIPO7BzFWbfd4Gz3V2NiIxWLxdxhCeEz/fncSIgD1JAHSNxaQ8sM/ASgfcyOtkeneCstjIiIiyM3NRavV+jsUn/DWUR7lY26kIf0UNK5Wsjf8DX1jkVfa6YmysjJZFi/6DUmAhPCh1tZWmpq6ucRZdZGx+RE0LjuNKZOoG/D/vBucB4SHh4dU8gOg1+u9c5K9oqV44j00xY1AZ28gZ92taG3+XZJus9n6dnivEAHErwnQ2rVrOffcc90boy1btqzL8h9++CFnnHEGSUlJxMTEMHnyZFasWNGhzL333ouiKB1uw4cP9+JVCNF9Pen9iTv4MZE13+PURlA67raA3+05PDycAQMGhFTy0y4pKckr9aq6cApPehS7MQWDpYjsDQtQnHavtNVd5eXlsixe9At+TYCsVitjxoxhyZIl3Sq/du1azjjjDD777DO2bNnCtGnTOPfcc9m2bVuHcscddxxlZWXu2zfffOON8IXose5+e9Y1VZK68/+AtlVfrZGpXoyq70I5+QEv9gLRtkdQwUlP4NRFElm9g4wtj/h1ebzT6aS6utpv7QvhKX7dSOSss87irLPO6nb5RYsWdfj54Ycf5uOPP+a///0vJ5zwy464Op2O1NTuf2DYbLYOSzx7ez6TEF2x2WzdO1tJVUnf9gRaRxNN8cdRO/i33g+uD0I9+WmXlJREXV2dV+q2mQZSOPlBcr+5hdjCFdiiMqkaeaVX2uqO6upq4uPjCQsL81sMQvRVUM8BcrlcNDY2HrEKY9++faSnpzNw4EAuvfRSCgsLu6xn4cKFmEwm9y0rK8ubYYsQ1d3EOqb4S2LK1uFSdJSMvwOUwE0sIiIiJPn5mV6vJzY21mv1W1MmUnrCLQCk7HoJU+HnXmvrWFRVpaKiwm/tC+EJQZ0APfHEE1gsFi644Jd9USZNmsTSpUtZvnw5zz33HHl5efz617/u8tiBBQsW0NDQ4L4VFfl/tYXof7oz/0drN5O+/WkAqodfjs000Nth9VqorfbqjuTkZK/WXzfw/1E19BIAMjY/jLH6e6+215X6+no5LV4EtaBNgN566y3uu+8+3nvvvQ5vOmeddRbnn38+o0ePZsaMGXz22WfU19fz3nvvHbUug8FATExMh5sQnmS327v1YZH6/bPobHW0ROdSNfwyH0TWO+2bHEry05G3e4EAKkZdh7l9efz6BYRZSrzaXpexSC+QCGJBmQC98847XH311bz33ntMnz69y7KxsbEMHTqU/fv3+yg6IY7UneEvY9V24vI/RUWhZPwdqFq9DyLrucjISEl+uuDtXiAUDUUT76Y5dhg6ez05625DY+/hwboe0tjY2LNdzYUIIEGXAL399tvMnTuXt99+m3POOeeY5S0WCwcOHCAtLc0H0QnRuWOu/nI5SN/2JAB1A/4fzYmjvB9UL0RHR4fEDs994YteIFUXQcFJj9IakUR4Yz7Z397lt9Pjy8vLZXNEEZT8+i5msVjYvn0727dvByAvL4/t27e7Jy0vWLCAyy+/3F3+rbfe4vLLL+fJJ59k0qRJlJeXU15e3mFuxS233MKaNWvIz89n/fr1nHfeeWi1Wi6++GKfXpsQ7boz/JWw/9+Emw/i0MdScfwffRRZz5hMpn57sKmneb0XCHBEJFFw0mM4tRFEVX5H+van/LI8vrm5ucs5lkIEKr++k23evJkTTjjBvYR9/vz5nHDCCdx9991A27brh67geuGFF3A4HFx//fWkpaW5bzfddJO7THFxMRdffDHDhg3jggsuICEhgW+//dZrG5UJcSzHGv7SNVWS/ONLAJSP/jNOg8kXYfVIXFwcmZmZKAG+GWOg8EUvEEBL7FCKJ92LikL8wY9J2Peu19vsjPQCiWCkqPKv9ghmsxmTyURDQ4NMiBZ9duDAAZqbm4/6eNaGOzGVfIU1YTR5py4JuMNOk5KSSE5OluSnh+x2O3v37vVJWwl73yHt+2dQUSic8giN6Sf7pN1Dpaene+VgWCF6oief34H1TitEP9Pa2tpl8hNV/i2mkq9QFS2lJ9wccMlPWloaKSkpkvz0gl6v91lCUDPkQmoHzEJBJXPjvYTX+ybxOlRlZSUul8vn7QrRW4H1bitEP9PV8JfitJG27SkAagafjy12sK/C6pbMzEwSEhL8HUZQ89ZJ8UdQFEpPmI8leQJaZzM5625H1+zb4yocDofXdsIWR+d0OmlqasJisdDY2EhDQwP19fWYzWZsNpsMTXbBr0dhCNHfdbX6K3HPWxisJbSGJ1Lpx2MNDqcoCtnZ2URHR/s7lKDX3gtUW1vr/cY0Ogp/9SADv/oj4Y0FZK+/nbypS1B14d5v+2eVlZXExcXJRHkvUVWVpqYmmpqaaG5uprm5mdbW1mM+LywsDIPBQHR0NDExMXKEyc/kX6kQXtLV8FdYUwVJe14HoHzMjbjCIn0Z2lFptVoGDhwoyY8HJSUl+WwI0aWPpvCkx3DoTRjrfiLzu/tB9d2wlNPppKamxmfthQJVVWlubqa8vJw9e/aQl5dHRUUFZrO5W8kPtL0XWSwWysrK2LNnDwcOHKC6urrbz++vJAESwku6Gv5K2fl/aJw2rIljaMg83YdRHZ1er2fQoEFERET4O5R+JSwszKeTg+1RmRROWYhLE4apZA0pO5/3WdsAVVVVOJ1On7bZH7lcLmpra9m3b587YXE4PLPX06EJVWlpacgmQpIACeElRzv7y1i1ndiiL1BRKBszDwJggnFkZCSDBg1Crw/M3aeDnS97gQCaEsdQMmFBW9t73yQu7z8+a9vlclFd7dv5R/2Jy+WipqaGvXv3Ulpait1u92p7tbW17N27l7KyMo8lWMFCEiAhvMDhcNDU1HTkA6qTtB2LgLYdn1vihvo2sE7ExsaSk5MjR1t4kU6n8/mE8obsGVSOaJtblr71CSIrNvusbU/2VoQKVVX9loyoqkpNTQ179uyhuro6ZCZOSwIkhBccbWfcuLxPiKjfhzMsiorjr/FxVEdKTU0lIyNDJq36QGJios+3E6gceSX1WWegqE6yv/07BnO+T9pVVVV6gXqgpaWFAwcOUFpa6tfEUVVVysvLycvL83rPUyCQdz0hvKCz+T8au5mUH14AoHLkVTgNcb4O65dYNBpycnL88qEcqnQ6ne93pFcUSiYswJowGm2rhZx1t6Jt8c1S9ZqampCdW9JdLpeL8vJy9u/ff8zjcnypqamJ/fv3H/sMwyAnCZAQHuZyubBYLEfcn7zrZXT2elpicqkZ9Fs/RNamfbKzrPTyvYSEBJ8PNapaA4VTHsYWmYHeWkrO+ttQnDbvtyu9QF2yWCzs27cvYH9HLpeL4uJiioqK+u0Gl5IACeFhjY2NR4yh6xsLSDjwIQBlY24CjX+24IqKimLQoEEYDAa/tB/qtFqtTw5KPZzTEEfByY/jCIvGWLuLzE2+WR4vvUBHUlWVyspK8vPzg+J309DQQF5eXr+c0yUJkBAe1tnwV+r3/4eiOjGnnYQ1ZaIfooKUlBSZ7BwA4uLi0Ol8nwDbo3MonPLIz8vjV5Oy8zmftFtVVeWTdoJBa2sreXl5VFZW+juUHmlububgwYP9bl6QJEBCeJCqqkdMgI6s3EJM2TeoipbyUdf7PCatVktubq7Pl2KLzmk0GlJSUvzSdlPS2EOWx79F3MFlXm+ztrY2KHo6vM1isbB///7OV4cGAbvdfsyDnYONJEBCeJDVau04Xq66SP3+WQBqB87CHpPj03giIiIYPHgwUVFRPm1XdC02NtZvey41ZM+gYuTVAKRvfZKosvVebzOUe4Ha50Ll5+cH/QaRTqeTgwcPdjrHMRhJAiSEBx0+/BVbsJyI+r04dZE+P+8rKSmJgQMHyrk/AUhRFL/1AgFUjbiCutxzUHCR/e1dhNfu9mp7tbW1/W74pDtUVaW0tJTy8nJ/h+IxqqpSUFAQtD1Zh5IESAgPUVW1w+7PiqOZlB/+CUDViDk+W/au0+kYMGAAKSkpMuQVwGJiYggP991BpR0oCiXjbqMxZSIaZwu5624lzFrq1SZDrRfI6XSSl5dHXZ1vth3wJVVVyc/PD6il+70hCZAQHtLc3Nyhiztx79uEtVRjN6ZRM/j3PokhOjqawYMHExkZGIeriqNTFIW0tDT/BaDRUfSrB2k2DUZnqyP3m5vR2jo/vsUT6urqQqYXyGazBfV8n+5wuVxBv2GiJEBCeMihw1+65iqS9rwJQPmo61C13l12rigK6enpZGdn+2WFkeidyMhIv+7H5AqLpODkJ7BHpGBoLCR7/R1e3SMoFHqB2ldMhcLE7/ZermC9VkmAhPCAw4e/kne9jMbZQlP88ZgzT/Nq25GRkQwZMoT4+HgZ8gpCqampfm3fEZFEwclP4AyLIrLmezI33Qeqdybr9vdeIKvVysGDB4N+snNPtC/tD8ZrlgRICA+w2Wzub0EGcz5xeZ8AUDb6Bq+d9t4+hJKbmyunuAcxg8FAfHy8X2OwmQZS4N4jaA3p254ELx2I2V97gcxmM/n5+SFzkOih7HY7RUVFQXftkgAJ4QGH7v2T8sPzKLgwp59Cc+Ior7QXGRnJ4MGDSUhIkF6ffiA5Odnvr2NT0gkUT7wHFYX4gx+TtPsVr7TTH3uB6urqKCwsDLoEwJMsFkvQJbeSAAnhAe3DX8bq74kp/RoVDRXH/9Hj7Wg0GjIyMsjNzZXjLPoRnU7nlyMyDmfOnEbZCTcDkLLrJeIOfOSVdoLtg7IrtbW1lJSU+DuMgFBZWdnpTviBShIgIfqotbW1bTmoqpKy8/8AqBvwG2wxuR5tx2QyMXToUOLi4vzeWyA8LyEhISAmsNcOOo/KEXMBSN/2JDElqz3eRn/pBaqpqaG01LvbBwSboqIibDbvH7brCZIACdFH7cNf0aVfE1mzE5fW4NFND/V6Pbm5uWRlZQXEB6TwDo1G4/cJ0e0qR15F7YBZKKhkbryPyMotHm8jUE9B767q6mrKysr8HUbAad8oMRgmRUsCJEQfmc1mcDlI+eF5AKqHXIgjIqnP9SqKQmpqqhxlEUJMJhMRERH+DgMUhdJxN9OQMRWNy072utuJqPnRo00E8xlh1dXV/Wp3Z0+z2+2UlJQE/JwoSYCE6AOXy4XFYiEu/zPCGwtw6E1UD7u0z/W2D3clJiai0cifaaho388pIChaiifeiyV5AlpnMznf3Iyh4YBHmwjGuUCS/HSP2Wymvr7e32F0Sd5ZhegDi8WC4mghedeLQNuRF66w3vfWhIeHM2DAALKysuQMrxAVERFBXJxvjk05FlWrp2DKIzTFH4+utZHctfPQW4o9Vn+w9QJJ8tMzpaWlAT3XSxIgIfrAbDaTcOADwlpqsBtTqR14Xq/q0el0ZGRkMGjQIDnGQpCSkhIwPX+qLoL8kx+n2TSYMFstuWtvQtdU6bH6g2UuUE1NjSQ/PaSqakDvDxQYf2FCBCFVVbFUl5D40+tA28RRVduzDQkVRSE5OVlWd4kOdDqdX0+LP5xLH0P+r5/GFpWFvqmcAWv/gq7ZM4lLMPQC1dbWyoTnXmpubg7YJFcSICF6qampifif3kTX2khLTC71OTN69Py4uDiGDh1KcnJywHzbF4EjPj4+oPZ6cobHk3/KIuzGFAyWInLX3oS2pbbP9aqqGrAfkNC2ZF+WuvdNRUUFzc3N/g7jCPKuK0QvWSvySNj3HgAVx10LirZbz4uOjmbIkCFkZGTIPB9xVAE1IfpnrcZU8k55htaIZMIb8xmw9i9obXV9rre2thaHw+GBCD2roaFBNjn0kKKiIlwul7/D6EASICF6QVVVwr79B1pnM01xI2hMP+WYzzEajQwcOJCcnJyA+mYvAldkZCQmk8nfYXTQGpVB3in/oDU8kXBzHrlr56G1NRz7iV0IxF4gs9lMUVGRv8PoN+x2e8Ct+pMESIhesFcdwLT/Q4C2Iy+6mLtjMBjIyclhwIABGI1GX4Uo+om0tLSAGyK1R2eRN/UftIYnENGwn9yv56G19+0IhJqamoDpBbJYLBQWFvo7jH6nqqqqbdf8ABFYf1VCBDCnS2XDgRo+3l5C1X/vQ+NqxZI0HmvKiZ2WDwsLIzMzk8GDBxMdHS0TnEWv6HQ60tLS/B3GEezROeSfshiHIZaI+r3krrmxT8NhgdILZLVaKSgo8HcY/VZhUTEbDlTz8fYSNhyoweny3woxvyZAa9eu5dxzzyU9PR1FUVi2bNkxn7N69WrGjRuHwWBg8ODBLF269IgyS5YsITc3l/DwcCZNmsSmTZs8H7wIKct/KOPkR7/k4n99yz/e/ZS0wv8CsDJpzhFltVotaWlpDBkyhNjYWEl8RJ/FxsYG5PYItpgBbXOCDPFENOxnwOob+rQ6zN+9QM3NzeTn5wfssu1gt76wiUve3s/F/9rITe9s5+J/fcvJj37J8h/8s8LOrwmQ1WplzJgxLFmypFvl8/LyOOecc5g2bRrbt29n3rx5XH311axYscJd5t1332X+/Pncc889bN26lTFjxjBjxgwqKz23b4UILct/KOO6N7ZS1tDWdftX3ftoFZXPneP569ZE1hc2AR2XtCckJATcsIUIXoqikJGREZDJtM00kLxTl/wyMXrN9YQ1VfSqLlVVqamp8XCE3dPS0kJeXp4kP16yvrCJh9dWUd3U8Yyw8oYWrntjq1+SIEUNkFdbURQ++ugjZs+efdQyt99+O59++ik//PCD+76LLrqI+vp6li9fDsCkSZM48cQTefbZZ4G2owqysrK48cYbueOOO7oVi9lsxmQy0dDQQExMTO8vSgQ9p0vl5Ee/dCc/I5V8PjP8DZeqcJZ9IXvUbBKNWpZdNZrUlGQ5rFR4VVVVFRUVvUsuvC3MWsqANX9B31SG3ZjWNkcosuer2BRFYdiwYT79W7LZbBw8eDAoDvAMRk6XylXLStzJjxYnp2m2sdU1hBpMKECqKZxvbj8NraZvSX5PPr+D6ivqhg0bmD59eof7ZsyYwYYNG4C2WeZbtmzpUEaj0TB9+nR3mc7YbDbMZnOHmxAAm/Jq3ckPtPX+APzXNZk9ajYA1U1OiloMkvwIr0tMTAzYFYStkenknbrk580Syxj41XW9OjvM171AdrudvLw8SX686MdKG9VNTpKo5wbtR6w1zONf+qe4ULsaABUoa2hhU17f95XqiaBKgMrLy4/YHTUlJQWz2ezebdLpdHZapqstzBcuXIjJZHLfsrKyvBK/CD6Vjb8kP2OU/Zyh3YpTVVjs+O1RywnhLYqikJmZ6e8wjqrVmELe1GdpiRlIWEs1A1f/GWPV9h7X0/5e7m2tra3k5eUFzOqzfklVCa/cxjNh/2C94UZuCfs3GUoNtWoUdjp+afT1+2hQJUDesmDBAhoaGtw32ftBtEuODnf//826fwPwofPXHFTTj1pOCG+KiIggOTnZ32EclSMikYOnLsGaMBptq4Xcr/9KdMnaHtXhixVhDoeDvLy8gD+GI1gpThux+Z8y6Isr+O3eWzhX+y1hipMtriHMs/+ZybZnedF5Tofn+Pp9NKj67FNTU48Y/66oqCAmJoaIiAi0Wi1arbbTMqmpqUet12AwBGy3svAfVVUZFKOSaNQyoPlHTtHupFXVstj5S+9P+9j1xAHx/gtUhJykpCQaGxsD8ngB+PnssFMWkfXt3cSUfUP2hr9TOu5W6gb+v27XUVNTQ2JiIlpt93ZY74n25CeQTyoPVrrmKuIPfET8wY/R2esBcGkNLHOezIu209ml5h7xHH+9jwZVD9DkyZNZtWpVh/tWrlzJ5MmTAdDr9YwfP75DGZfLxapVq9xlhOgOq9XK/v37qawo59rxcdwc1tb7857zVIrVtm/f7VP17jl3ZJ8n7gnRE4qikJWVFZCrwtqpWgOFkx+iNvc3KLjI2PooyT+8AGr3jkNwuVxemQvkdDrJz8/HZrN5vO5QFl6/j4zvHmDoZ78n+adX0dnrsUekUD7qz+w5ZxnVE+84avID/nkf9WsPkMViYf/+/e6f8/Ly2L59O/Hx8WRnZ7NgwQJKSkp47bXXAPjTn/7Es88+y2233caVV17Jl19+yXvvvcenn37qrmP+/PnMmTOHCRMmMHHiRBYtWoTVamXu3Lk+vz4RfBwOB2VlZTQ0/LK1/xnhuxmg2Y0dHc86ZrvvTzWFc8+5I5l5fOBtUif6P71eT3p6emCfVaXRUTr+DhzhCST/9CrJP72KwVJE8YS/o+qOPdxRXV1NQkKCx3qBnE4neXl5AbUbcVBTVaLKvyVx3ztEVW52321NGE3NkAswp/8aNG1pxpRs+NspSbywubbDUnh/vo/6NQHavHkz06ZNc/88f/58AObMmcPSpUspKyvrsB35gAED+PTTT/nrX//K4sWLyczM5MUXX2TGjF9O4b7wwgupqqri7rvvpry8nLFjx7J8+fIjJkYLcShVVamvr6esrKzjgX2qSsqPLwDQMGg2N6aNxKmPZHBGMhMHxEvPj/Cr2NhYGhsbA3vlqqJQefy12KMySN/yGKbiLwmzllE45REcEYldPrW9F8gTc57ae34k+ek7xdWKqfBzEve+Tbg5DwBV0dKQcSo1Qy+iOX5kp8+bkm1kUmYEhc1huAzRJEeH+/V9NGD2AQoksg9QaLHb7ZSUlGC1Wo94LKpsA7nrbsGlNbD3rH/jCE9g6NCh6PV6P0QqxJEcDgf79u0LimXcxqrtZG9YgM5upjUimYKTHqUldmiXz9FoNAwbNqxPvUAul4v8/Hyampp6XYcATauF+IMfk7DvPcJa2iapO3VG6gb8P2oGn09r5NHn2h5q0KBBREREeCXGnnx+B9UkaCE8SVVVamtrKS8v73z3V1UledeLANQM+i2O8AQiIyMl+REBRafTkZ2dTV5enr9DOaampLEcPO1fZK+7jfDGAgZ+9SdKx91Gfc7Moz6nr71A7T0/gTphPBjomqtI2Pce8QeXoXW0JZGt4QnUDLmQ2gH/D5c+utt1RUREeC356SlJgERIam1tpbi4uNNen3bRZesx1v2ESxtO9dBLAYiLi/NViEJ0W2RkJKmpqV3udxYo7FGZHJz2T7I23kN0xUYyv3uAiJqdlI+5CVXb+ZeL3s4FkuSnb/TmAhL3vkVs4Qo0rrbtAlqic6kedgkNWWcc9fXqSkJCgqfD7DVJgETIaWhooKSkpONcn8OpKsm7XwKgZtDvcIbHodFoZEhUBKyEhASam5s7TOAPVC59NAUnP07yrqUk7X6FhIPLiKjbQ9GvHux0GKU3vUAy4bn3Imp+IGnPm0SXfo1CW++4NWE01cP+QGPaZFB6t4A80N5DJQESIcPpdFJaWtqtD4josm+IqNuDUxtB9bBLgLYJp3LAqQhU7QemtrS0BMcSb0VL5XFX0RQ/kszv7sdYt5tBq+ZSMuHvNKaffETxnvQCSfLTC6qL6LINJO55g8ia7913m9N/TdXQS2lOHNXnJuLj4wPqPVQSIBESWlpaKCws7N7GZ6pK8q623p/awb/DaYgF2hIgIQKZRqMhOzubAwcOdN3DGUAsaZM5cPrLZH/7dyLq9pCz/nZqB86ibPSNqLpf5oq4XC6qq6uPuaK3tbVV9vnpAcVpb1vRte9tws35ALgUHQ05M6kaegn2mByPtRUfH1gbxkoCJPq9uro6SktLO5/o3Ino0rVE1O/DqYugemhb749OpwuYiXtCdMVgMJCVlUVBQYG/Q+m21sg0Dp76PCk/vEDivreJP/gxkZVbKZ54d4cl1dXV1V3uDm2z2cjPz5fjLbpBYze3reja/2/CWto2nHTqjNQOnE3NkAtwRCR5tL3o6OiAW0AiCZDot1wuF2VlZdTV1XX/SaqL5F0vA1Az+AKcBhMAMTExAb3rrhCHio6OJi0tjbKyMn+H0m2qVk/5mBtoTJtM5ncPYrAUMfCrP1E54gqqh1+GqglDVVUqKqsoaAqjsrGlwz4yzc3N5OfnB8V2AP4UZikhYf+/icv/BK2jbXJ4a0QSNYPPp3bgLFxhUV5pNzGx6z2f/EESINEvtba2UlBQ0OM5ADEla4ho2I9TF0nN0Ivc90dHd3+ZpxCBICEhAYfDQVVVlb9D6RFr8nj2nfEq6dueJLboC1J2vYSpaBWl427li+ahvPDh9iN2Er79jIEMjWjqdi9vyFFVjDXfk7DvXWJKvkahbXi0xTSI6qEX05A1HVUT5rXmDQYDRqPRa/X3liRAot9pbm6moKAAh8PRsyeqLpJ3vwJAzZDzcerbVisoikJkZKSnwxTC65KTk3E4HD3rBQ0ALn0MxZPuozH916RtX0R4Yz4D11xPtGMarY6LgV96KcobWvjr+7v42ylJTMkOvA9Zf1KcdkzFq4jf/z7Gup/c9zem/IqaIRdgSZkIPujZTkxMDMgedEmARL9iNpspKirq1TfBmJI1hDccwKmLpHrIhe77o6KiAmrlghDdpSgK6enpOJ3OwD4u4ygasqZjSZlI8vf/R0L+f7lY9xVnaLfwmONC3ndOxXXIed4vbK5lUmaEHE8D6JoqiT+4jPi8j9HZ6gFwafTU58ykZsgF2GIG+CwWrVaLyWTyWXs9IQmQ6BdUVaWmpqb3G8GpLpJ2LwXaen9c+l/2qpDhLxHMFEUhMzMzaI+CcOpjWJE5jw/3nMDDYS8xVFPCY2H/4irt/1jouJjVrrGAQnWTkx8rbYxOPfYhq/2S6iKq4jviDi4jpmwdito2TNgakUztwNnUDvx/OA2+38g1ISEhYL9ASgIkgp6qqpSXl1NTU9PrOmJK1/4898dIzSG9PyAJkAh+Go2G3NxcCgsLsVgs/g6nx+qanWxWh3OOfSGXa1dwo24ZwzTFLNU/znrnSBY6LmGnOpC65tCbAK1rriYu/1Pi8v6LvumXSe/WxBOoGfy7Diey+0OgLX0/lCRAIqipqkpJSQn19fV9qMRF0q6f5/4M/mXuD7RN3gsL897kQCF8RaPRkJOTQ3FxcVDsFn2ouIi2Ze+t6HjJeQ7/dk7lz7r/MFe7ginaXfxXeydrnKNptc0BdZJP5rX4k+K0EVP6NbEF/yOqfJN7UrMzLJq6nJnUDfh/2EwD/Rxl295pOl3gphmBG5kQx+ByuSgqKqKxsbFP9USXfv1L788hK7+AgNq2XYi+ah8O02q11NbW+jucbjsu2UCiUete/WUmikccl/C64wzmh/2b2Zp1TNV+Dz/cTFPpSKqG/YHG9F/3+siGgKQ6iazagaloJabiL9G2/tKTZ00YTd3A/0dD5mmoWoMfg+wokM796oyiyrrBI5jNZkwmEw0NDfIBGKCcTicFBQV9n9OgqgxaNZeI+n1UDr+cyuP/2OHhgQMHBuTyTSH6QlVVqqqqqKys9Hco3ba+sImH11ahAId/aGUpFTyf9SUjqlegcbXt9m43plGXew71uWfTaux69+iApTqJrNpOTPFXxJSsIcz2S9JqN6ZQnz2T+pyzsEdn+THIzhmNRgYO9H0vVE8+v6UHSAQdT57wHF32jXvX55ohHXt/tFqt7P4s+iVFUUhOTkav11NSUhLw++eEhYVx2bRRZGfXc99/d1HW8Mv+XolGLZdNOB41eyJ7Wq4lYf+/STjwEfqmMlJ2vUjyrpewpEyibsA5NKZO7nC8RiDS2M1EVWwiunwD0eXfuldxATjComnMmEp99plYk04I6B6uQNz48HDSA9QJ6QEKXC6Xi7y8PI8kP229P1cSUb+XqmGXUTHqTx0ejo2NJTMzs+/tCBHAbDYbhYWFAXt2VlxcHKmpqe7jL5wulU15tVQ2tmBwtZCmazpi6bviaMFUspq4vE+IrN7mvt+l0WNJnkBj+q9pTD8JR7j/h2gURwvG2h8xVu8gquI7jLU/uldwwS9JT0PmaViSx/t1QnN36fV6hgwZ4pe9f6QHSPRLLpfLYz0/0N77s/fnM78uOuJxSX5FKDAYDAwaNIjy8vKAmhdkMBjIyMg4Yghaq1GYPKgtcVFVlaKioiP2OFJ14dTnzKQ+ZyZ6SzFxef/FVPwlemspMeXriSlfj7pVoSV2ME0Jo36+jW4bKvPmh7bqRN9YTETDPsLr9mKs+Z6I2t1o1I6btrbEDKAxdTKW1MlYE0cHRdJzqKSkpIDc+PBw0gPUCekBCjwul4uCggKsVqtnKlRVBn15FRF1e6ga9gcqRl13RJERI0Yc9dBFIfojs9lMaWlpz3dR9yBFUUhNTSU+Pr5bH6Iul4t9+/Yd+wBUVcVgPkhM6TdEl36NsW73EUVawxOwxQzAFpWFPTobW3Q2rcZUHAYTzrDoYyciqorG0YTWbiasqQK9tRS9tYywpjIMjQWENxxA4zyyp601Iglr4lisSWOxpPyK1sjUY153oNLpdAwbNsxvCZD0AIl+xeVyUVhY6LnkB4gq30BE3R5c2vBOe38iIyMl+REhJyYmhqioKGpqaqisrPTp3CBFUUhISCAxMbFHS6c1Gg2pqakUFRUdqwFspkFUmQZRNWIOuuZqjDU7MVZ/j7FmJxH1ewlrqSGspYaoys2dVuEIi27bJkPRgKKgogAKiqsVbWsjWrvFvST9aFzacFpMg9p6n+KPx5o0llZjWr9Zuh+ox150RhIgEdDa9/nx6OZtqvrLmV+Dzut0d1Tp+ROhSqPRkJSURFxcHJWVlV4fFtNoNCQmJhIfH9/rPWNiYmIIDw/v0eHHjohEzJnTMGdOA9rm4oQ37MfQWIChsQi9pRBDYyG65mp0rW1bbehaG93/3xWXJozWiGRaI9OwR6bRakzDFpVJS+wQ7FEZoPTPL1cajSagNz48nCRAIqBVVFR4fNO2qIpNGGt34dLoqR56SadlZPdnEep0Oh3p6ekkJibS0NBAXV0ddrvdY/UbjUZMJhOxsbF97m1tHzbLz8/vdR2qLpzmhONpTjj+yAddDrStjehsDWjsjYdMUlZRVBVVo8Opj8YZFo1TH42q0febHp2eCORjLzojCZAIWDU1NVRXV3u2UlUl6efen9qBs3GGH/ltRa/Xo9frPduuEEFKr9eTlJREYmIizc3N1NfX09jYeOw5N4dRFIWIiAhiY2OJiYnx+A7BUVFRREZGenSo3E2jw2mI88tZWsGifQgzmPT4X+CcOXO46qqrOOWUU7wRjxBA20S2srKyYxfsociqrUTW7Gzr/RnWee+PDH8JcSRFUTAaje5VWU6nk5aWFvfN5XIdUd5gMLhver3e63NDUlNTOXDggFfbEJ3ryxCmv/Q42oaGBqZPn05OTg5z585lzpw5ZGRkeCM2EaKampqOPaGxl5J/PvOrbsC5OCKSOi0jw19CHJtWqyUyMpLIyEh/h+IWERHhXgEkfCvYen8AejxYt2zZMkpKSrjuuut49913yc3N5ayzzuL999/vcZeoEIez2+0UFBR4ZfWJsWobkdXbcGnCqBr2h07LaDQaOfpCiCCWkhKkx14EsdjY2KCcNtCr2UpJSUnMnz+fHTt2sHHjRgYPHsxll11Geno6f/3rX9m3b5+n4xQhoH2vH6fTeezCvZC8eykAdbm/wWFM7rRMVFRU0CzhFEIcSa/XB2VvRDBLTu78/TTQ9Wm6dllZGStXrmTlypVotVrOPvtsdu7cyciRI3n66ac9FaMIAe3L3b21Hb+x+nuiKjejKlqqj9L7AzL/R4j+ICkpKahWIwWzuLi4oOz9gV4kQK2trXzwwQf85je/IScnh3//+9/MmzeP0tJSXn31Vb744gvee+897r//fm/EK/qpmpoar47bJ7l7f87ucpfVqKgor8UghPANnU4XtL0SwSYpqfO5lMGgx5Og09LScLlcXHzxxWzatImxY8ceUWbatGnExsZ6IDwRCiwWC+Xl5V6rP6J2F9EVG1EVLVXDLjt6uYiIoFvFIIToXEJCArW1tR7du0h0FMy9P9CLBOjpp5/m/PPPJzw8/KhlYmNjycvL61NgIjTY7XYKCwu92kZ770999pm0Rh19xaIMfwnRfyiKQlpaGgUFBf4Opd8K5t4f6MUQ2GWXXdZl8iNEd7Wf8XX4/iGeFF63l5iydahoqBp+eZdlZfm7EP1L++aIwvPi4+ODuvcH+jgJWoi+qKio6NHZPb3RvutzQ9bp2KOzj1pOp9NhMBi8GosQwrfae4GE5wV77w9IAiT8pLGxkZqaGq+2YWg4gKl0LSoKVSPmdFk2JiZGlr8L0Q+Fh4cTFydHWHhSfHw8YWFh/g6jzyQBEj7X2trqtZ2eD9W+7485cxq2mAFdlpXhLyH6r5SUFFkW7yGKovSL3h8IkARoyZIl5ObmEh4ezqRJk9i0adNRy5566qkoinLE7ZxzznGXueKKK454fObMmb64FHEMqqpSVFTk1Xk/AAZzPjHFXwFQOeKKLssqiiLzBITox3Q6newQ7SFJSUn9ovcHAuA0+HfffZf58+fz/PPPM2nSJBYtWsSMGTPYs2dPp/s4fPjhhx2WNdbU1DBmzBjOP//8DuVmzpzJK6+84v5Z5ncEhsrKSpqamrzeTtJPr6KgYk4/BZtpUJdlo6Ki5NuhEP1cfHw8tbW1XttsNRRotVoSExP9HYbH+P1d/6mnnuKaa65h7ty5jBw5kueffx6j0cjLL7/cafn4+HhSU1Pdt5UrV2I0Go9IgAwGQ4dyXY0B22w2zGZzh5vwvKamJqqqqrzejr6xCFPhF8Cxe39Ahr+ECAWKosjB3X3U34YS/XoldrudLVu2MH36dPd9Go2G6dOns2HDhm7V8dJLL3HRRRcdMYSxevVqkpOTGTZsGNddd12XE24XLlyIyWRy37Kysnp3QeKoXC4XxcXFPmkr6afXUHBhTp1CS9ywY5aXBEiI0GA0GmVCdC8ZDIZ+97vzawJUXV2N0+k8Ymw2JSWlWzsDb9q0iR9++IGrr766w/0zZ87ktddeY9WqVTz66KOsWbOGs84666iHbC5YsICGhgb3zRcTdENNRUWFT3ZkDbOWElu4AoCqbvT+GAyGfjOeLYQ4tv7Wi+Erqamp/W6lrN/nAPXFSy+9xKhRo5g4cWKH+y+66CL3/48aNYrRo0czaNAgVq9ezemnn35EPQaDQeYIeZHVavX6kvd2ST+9jqI6aUyZSHPCcccsL7s/CxFadDodaWlplJSU+DuUoBEZGdkvz0n0axqcmJiIVquloqKiw/0VFRWkph79wEpo+1B95513uOqqq47ZzsCBA0lMTGT//v19ilf0nNPp9NnQV1hTObH5nwFQNWJut54jCZAQoSc2NpaIiAh/hxE0+mPvD/g5AdLr9YwfP55Vq1a573O5XKxatYrJkyd3+dx///vf2Gw2/vCHPxyzneLiYmpqamRHUD8oLy+ntbXVJ20l7nkTjerAkjSOpsTRxyyv1WrlWBchQpBMiO6+/pws+n0gdP78+fzrX//i1VdfZffu3Vx33XVYrVbmzm37Bn/55ZezYMGCI5730ksvMXv2bBISEjrcb7FYuPXWW/n222/Jz89n1apVzJo1i8GDBzNjxgyfXJNoY7FYqKur80lbuuYq4vL+C/Ss96c/fqsRQhxbeHh4p1utiF9oNJpjjsYEM7/PAbrwwgupqqri7rvvpry8nLFjx7J8+XL3xOjCwsIjJqzt2bOHb775hs8///yI+rRaLd9//z2vvvoq9fX1pKenc+aZZ/LAAw/IPB8fcrlcPh1jT9zzJhpXK9aE0ViTTujWc2T1lxChLSkpiYaGBtkb6CjS0tLQ6fyeJniNoqqq6u8gAo3ZbMZkMtHQ0CBzRHqpvLyc6upqn7Slball2P9+j8ZpI//kp7CkTurW80aMGIFWq/VydEKIQNbS0iLzQzthNBoZMGBA0PWS9+Tz2+9DYKL/aWlp8VnyA5C49y00ThtN8SOxpEw89hNoW9UgyY8QQobCOpeenh50yU9PSQIkPEpVVZ8OfWltdSQc+AiAyhFzoZt/sNKzJ4Rol5SUJFMkDpGUlBQSC0QkARIeVVtbS3Nzs8/aS9z7DhpnC81xw7Ckdr1y8FAy/0cI0U5RFDIzM/0dRkDQ6XT95rT3Y5EESHhMa2trt3bw9hStrYH4Ax8APev90ev16PV6b4YmhAgyERERMhQGZGRkhMxO2aFxlcInysrK8OWc+oR976J1NNNsGkxj2sndfp4MfwkhOpOUlHTEuZKhJC4uLqR6xyUBEh5hsVgwm80+a09jN5Ow/30AqkZ2v/cHZPhLCNG59qGwUFwgERYWFnKbBUsCJPpMVVVKS0t92mbC/vfROqy0xAzEnH5Kt5+n0WgwGo1ejEwIEczCwsLIysrydxg+l5WVFTJDX+1C62qFV9TW1vrkpPd2mlYLifveA6ByxBWgdP+fsez+LIQ4lqioqJCZCAyQnJwckl8MJQESfeJwOI44zNbbEva/j7a1kZboXMyZp/bouTL8JYTojuTk5H57BtahIiIiQirZO5QkQKJPKioqcLlcPmtP02olYe87AFSNmANKz8bqo6KivBGWEKKfURSFrKysfj0fqH3OU6j2iksCJHqtubnZZ4edtkvY/z661kZs0dk0ZJ3eo+fK7s9CiJ7Q6/Xk5OT4OwyvyczMDOkNICUBEr3ij4nPmlYrCfvaen8qh1/R494fWf4uhOgpo9HYLydFJyUlYTKZ/B2GX0kCJHrFbDb7dMdngPgDH6Kzm7FFZfW49wdk/o8QondMJlO/2iQxOjq6X11Pb0kCJHrM5XL5dMdnAI2jicS9bwM/z/3R6Hr0fIPBILs/CyF6rb/0mBgMhpCe93MoSYBEj9XW1tLa2urTNuMPfITO3oAtKpP6rDN6/HwZ/hJC9IWiKGRkZAT1yjCNRkNOTo7MhfyZJECiR5xOJ5WVlT5tU3E0k7j3LQCqhl/e494fkOEvIUTfaTQacnNzg/ak9JycHOkJP4QkQKJHqqqqfLrsHSD+4DJ0tnrskenUZ8/o8fO1Wm1Qf2sTQgQOrVbLgAEDgu49JScnJ6TPOeuMJECi2+x2OzU1NT5tU3G0kLTnTQAqh/d87g/I7s9CCM/SarXk5uYGRRKkKAo5OTnSC94JSYBEt1VWVvr0tHeA+IMfobPVtfX+5MzsVR3yhy+E8LRgSIIURSE7O1veA49CEiDRLS0tLdTX1/u0TcXRTNKeN4De9/6A7P4shPCO9iQoEIeWpOfn2CQBEt3i62Xv8PPKr/a5P73s/YmKigq5E46FEL7TngQlJib6OxS39pjky1/XeveVWoQUq9WKxWLxaZuKo5mkvT/P/RlxRa97f2T5uxDC2xRFITU1lYiICIqLi30+VeBQERERZGdnExYW5rcYgoUkQKJLqqr6/LR3gIQDH6Kz1WOLzOjVyq920v0rhPAVk8mEwWCgoKDA53ulASQkJJCamiqLPrpJxgZEl6xWK01NTT5tU+NoInHPz/v+9KH3JyIiQr4FCSF8Kjw8nMGDB5OQkOCzNttPrk9LS5PkpwekB0gclb96f+L3f4jOXt+263P2mb2uR4a/hBD+oNVqSUtLIy4ujrKyMqxWq9faio+PJzk5GZ1OPs57Sn5j4qgsFovPDzzVtFp/2fW5D70/IMNfQgj/Cg8PJzc3l8bGRsrKyjw6LBYTE0NKSgoGg8FjdYYaSYBEp/zW+3Pgw5/P/Mrq1Zlf7cLCwuSNQQjhd4qiEBMTQ3R0NFarlfr6ehoaGno1UVqr1RITE0NcXBxGo9EL0YYWSYBEpxobG2lpafFpm4f2/lSOmNun3h+TySRj4UKIgKEoClFRUURFRZGenk5DQwNWq5WWlhbsdnunRwwpikJYWBgxMTHExMQQEREh72seJAmQOILfVn7texed3UxLdC4N2dP7VJcMfwkhApVGoyEuLo64uDj3fQ6HA7vdjqIo6HQ6tFqt7GHmZZIAiSOYzWZsNptP29TYzSTuexeAypFXgqLtfV0ajXQPCyGCik6nk4nMPibppejAX70/iXvfQdtqocU0CHPmtD7VJYefCiGEOBZJgEQHjY2N2O12n7aptdWTsP89ACpGXgVK3/5ZyvJ3IYQQxyIJkHDzW+/PnjfROpppjh1GY/opfaqrfaKhEEII0RVJgISbxWLx+dwfXUsNCQc+AKDiuKuhj0NXcvipEEKI7giIT4olS5aQm5tLeHg4kyZNYtOmTUctu3TpUhRF6XALDw/vUEZVVe6++27S0tKIiIhg+vTp7Nu3z9uXEdRUVaWystLn7Sb+9Doap42m+JFYUif3uT4Z/hJCCNEdfk+A3n33XebPn88999zD1q1bGTNmDDNmzOjywzgmJoaysjL3raCgoMPjjz32GP/4xz94/vnn2bhxI5GRkcyYMcPn+9oEE6vV6vNdn3XNVcQf/BiAiuOu6XPvD8jydyGEEN3j9wToqaee4pprrmHu3LmMHDmS559/HqPRyMsvv3zU5yiKQmpqqvuWkpLifkxVVRYtWsSdd97JrFmzGD16NK+99hqlpaUsW7bMB1cUnPzR+5O8+xU0LjvWxLFYk0/sc31Go1GWkQohhOgWvyZAdrudLVu2MH36L5veaTQapk+fzoYNG476PIvFQk5ODllZWcyaNYsff/zR/VheXh7l5eUd6jSZTEyaNOmoddpsNsxmc4dbKPHHie96SzFxeZ8AUHH8tR7p/TGZTH2uQwghRGjwawJUXV2N0+ns0IMDkJKSQnl5eafPGTZsGC+//DIff/wxb7zxBi6XiylTplBcXAzgfl5P6ly4cCEmk8l9y8rK6uulBZWqqiqft5m86yUU1Ulj6mSaEsd4pE4Z/hJCCNFdfh8C66nJkydz+eWXM3bsWKZOncqHH35IUlIS//znP3td54IFC2hoaHDfioqKPBhxYGtubsZisfi0TUPDAUyFKwGoOO5aj9QZHh6OXq/3SF1CCCH6P78mQImJiWi12iP2nqmoqCA1NbVbdYSFhXHCCSewf/9+APfzelKnwWBwHzbXfgsV/uj9SfnxXyioNGSeRkvcUI/UKcNfQgghesKvCZBer2f8+PGsWrXKfZ/L5WLVqlVMnty9JdFOp5OdO3eSlpYGwIABA0hNTe1Qp9lsZuPGjd2uM1TY7Xafz3eKqPmRmNKvUdFQMfJqj9UbSkmrEEKIvvP7kpn58+czZ84cJkyYwMSJE1m0aBFWq5W5c+cCcPnll5ORkcHChQsBuP/++/nVr37F4MGDqa+v5/HHH6egoICrr277MFUUhXnz5vHggw8yZMgQBgwYwF133UV6ejqzZ8/212UGpOrqap+3mfLjCwDU556FPSbHI3Xq9XoMBoNH6hJCCBEa/J4AXXjhhVRVVXH33XdTXl7O2LFjWb58uXsSc2FhYYedfevq6rjmmmsoLy8nLi6O8ePHs379ekaOHOkuc9ttt2G1Wrn22mupr6/n5JNPZvny5UdsmBjKHA4HdXV1Pm0zsnILUZWbcSk6Kkdc6bF6ZfhLCCFETymqqqr+DiLQmM1mTCYTDQ0N/XZopbKy0rd7/6gqA7+6FmPtLmoG/56ysX/1WNWDBg0iIiLCY/UJIYQITj35/A66VWCi71wul8+Hv2JK12Cs3YVTG0HV8Ms9Vq9Op5OePSGEED0mCVAIqqurw+Vy+a5Bl4OUH9q2KagZehGO8ASPVW0ymVA8sImiEEKI0CIJUIhRVdXnvT9x+Z9haCzEoY+leujFHq27vw5RCiGE8C5JgEKM2WymtbXVZ+0pjhaSd70IQNWIObjCIj1Wt0ajwWg0eqw+IYQQoUMSoBCiqqrPNz5M2P8eYS012I1p1A6c7dG6ZfhLCCFEb0kCFEKamppoaWnxWXtaWwNJe94EoOK4a1C1nj2qQpa/CyGE6C1JgEKIr+f+JP30OtpWC82mwTRkn+HRujUaDZGRnhtOE0IIEVokAQoRdrudxsZGn7UX1lRO/IEPAKg4/k+gePafmgx/CSGE6AtJgEJETU2NT9tL+eEFNC47lqQTsKT+yuP1y/CXEEKIvpAEKAQ4nU5qa2t91l543U/EFq4AoHz0DeDhnhoZ/hJCCNFXkgCFgLq6Onx24omqkvr9swDUZ8+gJW64x5uQ4S8hhBB9JQlQP+frjQ+jy74hqmobLo2eiuOv9UobMvwlhBCiryQB6ufMZjMOh8M3jbkcpO78PwBqhlxAqzHV403I8JcQQghPkASon/Nl70983n/cR15UDb/MK23I8JcQQghPkASoH2tubqa5udknbWlaLST/+BIAlSOvxBUW5ZV2ZPhLCCGEJ0gC1I/5svcn6afX0dnrsUVnUztwllfakOEvIYQQniIJUD/lcDhoaGjwSVth1lIS9r0HQPmoP4NG55V2ZPhLCCGEp0gC1E/5ct+f1O+X/Lzp4Xga0072WjsxMTFeq1sIIURokQSoH1JV1WcJUGTlVkwlq1HRUDb2Jo9vethOo9EQFeWdeUVCCCFCjyRA/ZDPlr6rTlJ3LAagdtBsbKZBXmsqNjZWhr+EEEJ4jCRA/ZCvzv2Ky/svEQ37cYRFUznyaq+2FRsb69X6hRBChBZJgPqZlpYWmpqavN6Oxt5Iyg//AqBy5FU4Dd5bnq7T6YiIiPBa/UIIIUKPJED9jK96f5J3v4LOXk9LdC61g87zalsy/CWEEMLTJAHqR5xOJ/X19V5vR99YQML+9wEoH/MXry17byfDX0IIITxNEqB+xCenvqsq6dueRlGdmNNOwpI6yavN6fV6wsPDvdqGEEKI0CMJUD+hqqpPhr9iSlYTVfkdLo2+rffHy+Li4rzehhBCiNAjCVA/YbFYaG1t9WobGkcTaTv+AUD1sD9gj8r0ansgZ38JIYTwDkmA+glfbHyYtPtVwporsUemUzX8D15vLyIiAr1e7/V2hBBChB5JgPoBu91OY2OjV9swmPNJ3Ps2AGVj5qFqDV5tD2TysxBCCO+RBKgfqKur824DqkratqfcE58b00/ybns/k+EvIYQQ3iIJUJDzxblfMcWriKragkujp2zsPK+21S4yMhKdzrvL64UQQoQuSYCCnNlsxul0eq1+TauFtB3PAFA1/HJaI9O91tahZPWXEEIIb5IEKMh5u/cnZefzhLVUY4vKpHrYJV5tq52iKMTExPikLSGEEKFJEqAgZrPZsFqtXqvfWP09CQc/AqB03G0+mfgMbZOfNRr5pymEEMJ7AuJTZsmSJeTm5hIeHs6kSZPYtGnTUcv+61//4te//jVxcXHExcUxffr0I8pfccUVKIrS4TZz5kxvX4bPebP3R3G1kr71UQDqcs/Bmjzea20dToa/hBBCeJvfE6B3332X+fPnc88997B161bGjBnDjBkzqKys7LT86tWrufjii/nqq6/YsGEDWVlZnHnmmZSUlHQoN3PmTMrKyty3t99+2xeX4zMul8urq78S97xJuDkfhyGW8tE3eK2dw4WFhcnJ70IIIbzO7wnQU089xTXXXMPcuXMZOXIkzz//PEajkZdffrnT8m+++SZ//vOfGTt2LMOHD+fFF1/E5XKxatWqDuUMBgOpqanuW3/rVWhoaMDlcnmlbn1jAUm7lwJte/449b6bjxMXFycnvwshhPA6vyZAdrudLVu2MH36dPd9Go2G6dOns2HDhm7V0dTURGtrK/Hx8R3uX716NcnJyQwbNozrrruuy3OybDYbZrO5wy3QeW34S1XJ2PI4GlcrjSm/oiFr+rGf40Gy+aEQQghf8GsCVF1djdPpJCUlpcP9KSkplJeXd6uO22+/nfT09A5J1MyZM3nttddYtWoVjz76KGvWrOGss8466nLxhQsXYjKZ3LesrKzeX5QPtLS00Nzc7JW64/L/S2T1NlzacErH3Qw+7I2JjIyUoy+EEEL4RFDvNPfII4/wzjvvsHr1asLDw933X3TRRe7/HzVqFKNHj2bQoEGsXr2a008//Yh6FixYwPz5890/m83mgE6CvNX7E9ZUTurPe/5UHHeNz/b8adffhimFEEIELr/2ACUmJqLVaqmoqOhwf0VFBampqV0+94knnuCRRx7h888/Z/To0V2WHThwIImJiezfv7/Txw0GAzExMR1ugcrlclFfX+/5ilWVjM2PoHU0YU0YRc2Q8z3fRhdk7x8hhBC+5NcESK/XM378+A4TmNsnNE+ePPmoz3vsscd44IEHWL58ORMmTDhmO8XFxdTU1JCWluaRuP3JW5Of4/L+Q1Tld7g0ekom/A0Urcfb6Irs/SOEEMKX/P6JM3/+fP71r3/x6quvsnv3bq677jqsVitz584F4PLLL2fBggXu8o8++ih33XUXL7/8Mrm5uZSXl1NeXo7FYgHAYrFw66238u2335Kfn8+qVauYNWsWgwcPZsaMGX65Rk/yxvBXmLWM1O9/Hvo6/o/Yo7M93saxyORnIYQQvuT3OUAXXnghVVVV3H333ZSXlzN27FiWL1/unhhdWFjYoWfgueeew2638/vf/75DPffccw/33nsvWq2W77//nldffZX6+nrS09M588wzeeCBBzAYfLOTsbd4ZfKz6iJj80K0jmasCaN9PvQFbT2BRqPR5+0KIYQIXYqqqqq/gwg0ZrMZk8lEQ0NDQM1LKSsr63I5f2/EH/iI9G1P4NIa2H/Ga9ijMj1af3ekpqaSmJjo83aF8DSn00lra6u/wxCi3woLC0OrPfoUjZ58fvu9B0h0jzd2ftY3FpHy/RIAyo+/zi/Jj6IosvpLBD1VVSkvL/fOAgUhRAexsbGkpqb2edNcSYCChNls9ujkZ8XVSuame9E6m7EknUDt4N95rO6eMJlMXWbzQgSD9uQnOTkZo9Eou5kL4QWqqtLU1OQ+KquvC5skAQoSnh76Sv7xRYx1P+EIi6b4xLtB8c98+MN38BYi2DidTnfyk5CQ4O9whOjX2s+KrKysJDk5uU9foP2+Ckwcm81m8+jk58jKLSTueROA0vG34zAme6zunjAYDHLwqQh67XN+ZCK/EL7R/rfW1/l2kgAFAU/O/dHazWR+9wAKKrW5v8GcOc1jdfdUfHy8DBWIfkP+LQvhG576W5MEKMB5dPKzqpK+5THCmquwRWVRPvYmz9TbC4qiyN4/Qggh/EYSoADX2Nh41ENceyou/7+YSr5CVbQUTbwHl85/XfaxsbEy+VmIwzhdKhsO1PDx9hI2HKjB6Qq+XUpyc3NZtGhRt8uvXr0aRVH8soJu6dKl8kUshMkk6ADnqd6f8Pq9pG17GoCK466lJX6ER+rtLZn8LERHy38o477/7qKsocV9X5opnHvOHcnM4z1/jM+xhhHaN5ftqe+++47IyMhul58yZQplZWWYTKYet+UPubm5zJs3j3nz5vk7FNFHkgAFMLvd7j7ioy809kayN/wdjcuOOXUK1cMu8UB0vRceHi6Tn4U4xPIfyrjuja0c3t9T3tDCdW9s5bk/jPN4ElRWVub+/3fffZe7776bPXv2uO+Liopy/7+qqjidTnS6Y39kJCUl9SgOvV5/zMOvhfAGGQILYB7pElZVMjc/hN5ait2YSsnEu/y25L2dLBUW4hdOl8p9/911RPIDuO+777+7PD4clpqa6r6ZTCYURXH//NNPPxEdHc3//vc/xo8fj8Fg4JtvvuHAgQPMmjWLlJQUoqKiOPHEE/niiy861Hv4EJiiKLz44oucd955GI1GhgwZwn/+8x/344cPgbUPS61YsYIRI0YQFRXFzJkzOyRsDoeDv/zlL8TGxpKQkMDtt9/OnDlzmD17dpfXvHTpUrKzszEajZx33nlHbC9yrOs79dRTKSgo4K9//SuKorh70Wpqarj44ovJyMjAaDQyatQo3n777Z68HMIPJAEKUKqqeuTg08S9bxFT+jUuTRiFv3oQp96/R3totdqg6eoWwhc25dV2GPY6nAqUNbSwKc/zByEfyx133MEjjzzC7t27GT16NBaLhbPPPptVq1axbds2Zs6cybnnnkthYWGX9dx3331ccMEFfP/995x99tlceumlXb6/NTU18cQTT/D666+zdu1aCgsLueWWW9yPP/roo7z55pu88sorrFu3DrPZzLJly7qMYePGjVx11VXccMMNbN++nWnTpvHggw92KHOs6/vwww/JzMzk/vvvp6yszJ2UtbS0MH78eD799FN++OEHrr32Wi677DI2bdrUZUzCv2QILEBZrVYcDkef6jBWbSflh38CUDbmJr/P+4G23p9DD7cVItRVNh49+elNOU+6//77OeOMM9w/x8fHM2bMGPfPDzzwAB999BH/+c9/uOGGG45azxVXXMHFF18MwMMPP8w//vEPNm3axMyZMzst39rayvPPP8+gQYMAuOGGG7j//vvdjz/zzDMsWLCA8847D4Bnn32Wzz77rMtrWbx4MTNnzuS2224DYOjQoaxfv57ly5e7y4wZM6bL64uPj0er1RIdHd1h2C4jI6NDgnbjjTeyYsUK3nvvPSZOnNhlXMJ/5JMoQPW190fXXEXWxrtRVCf12TOoGzjbM4H1gaIoMvlZiMMkR4d7tJwnTZgwocPPFouFW265hREjRhAbG0tUVBS7d+8+Zg/Q6NGj3f8fGRlJTEyM+ziDzhiNRnfyA21HHrSXb2hooKKiokNiodVqGT9+fJcx7N69m0mTJnW4b/LkyR65PqfTyQMPPMCoUaOIj48nKiqKFStWHPN5wr+kBygAORwOzGZzr5+vOFrIWX87YS01tMQMoGTcrRAAm7TFxsZ2axKlEKFk4oB40kzhlDe0dDoPSAFSTeFMHOD7Lw+Hr+a65ZZbWLlyJU888QSDBw8mIiKC3//+99jt9i7rCQsL6/Czoihdnm3YWXlV9f6WAL29vscff5zFixezaNEiRo0aRWRkJPPmzTvm84R/SQ9QAOrT5GfVReZ3DxJRtweH3kTBlEdRdYGx4komPwtxJK1G4Z5zRwJtyc6h2n++59yRaDX+/xKzbt06rrjiCs477zxGjRpFamoq+fn5Po3BZDKRkpLCd999577P6XSydevWLp83YsQINm7c2OG+b7/9tsPP3bk+vV5/xN5s69atY9asWfzhD39gzJgxDBw4kL179/bi6oQvSQIUYFRV7dPeP8m7XsZU8hUuRUfh5IdpjcrwYHS9FxUVRXi477vwhQgGM49P47k/jCPV1PFvJNUU7pUl8L01ZMgQPvzwQ7Zv386OHTu45JJLuuzJ8ZYbb7yRhQsX8vHHH7Nnzx5uuukm6urqutzb6C9/+QvLly/niSeeYN++fTz77LMd5v9A964vNzeXtWvXUlJSQnV1tft5K1euZP369ezevZs//vGPVFRUeP7ChUdJAhRgWlpasNlsvXquqegLkne/AkDpuFtpShrrwcj6JjEx0d8hCBHQZh6fxje3n8bb1/yKxReN5e1rfsU3t58WMMkPwFNPPUVcXBxTpkzh3HPPZcaMGYwbN87ncdx+++1cfPHFXH755UyePJmoqChmzJjR5ZesX/3qV/zrX/9i8eLFjBkzhs8//5w777yzQ5nuXN/9999Pfn4+gwYNcu95dOeddzJu3DhmzJjBqaeeSmpq6jGX5Av/U1RfDKwGGbPZjMlkoqGhgZgY3y4bLy0t7dUE6IjaXQxYfT0al53qIRdTPuboKzJ8zWAwMHjwYDksUvRLLS0t5OXlMWDAAOnl9BOXy8WIESO44IILeOCBB/wdjvCyrv7mevL5LTNSA4jL5erV/B99YyE562517/RcPvo6zwfXB4mJiZL8CCE8pqCggM8//5ypU6dis9l49tlnycvL45JL/LvLvQguMgQWQMxmc4/H03XNVeR+/Vd0tnqaY4dRPOleUALnkFHZ+FAI4WkajYalS5dy4oknctJJJ7Fz506++OILRozw/15nInhID1AA6enkZ43dTO7X89E3lWOLyiT/5CdxhXX/EEJfSEpKko0PhRAelZWVxbp16/wdhghy8skUIOx2O1artdvlFUcLOetuI9x8kNbwBPJ/vQhneJwXI+w5rVYrGx8KIYQISJIABYiezP1RXK1kfXsXkTU7cYZFk//rp2mNDJyVIu2k90cIIUSgkk+nANCTg08Vp52sDXcSU74el0ZPwUmPYTMNOvYTfUx6f4QQQgQymQMUALp78KnitHVIfgqnLKQpcfQxn+cP0vsjhBAikEkCFAC6M/lZcdrIXv83oiu+/bnn51GsKYF5yrD0/gghhAh0kgD5mdPpPObBp+2Hm0ZVbsalDafgpMewJnd98rE/Se+PEEKIQCefUn7W0NDQ5SnHWruZ3G/mE1W5Gac2gvyTnwzo5Ed6f4QQh7viiis6HA1x6qmnMm/evD7V6Yk6RGiTBMjPupr8HGYpYeBXfySyegdOXSQFv34qoM736kxiYqL0/ggRJK644goURUFRFPR6PYMHD+b+++/v1pzEvvjwww+7fWTF6tWrURTliJWyPalDiM7IEJgftbS00NLS0uljEbW7yFl3GzpbHfaIFApOfjwgV3sdSqfTkZCQ4O8whBA9MHPmTF555RVsNhufffYZ119/PWFhYSxYsKBDObvdjl6v90ibnugllp5m0VfyVd2Pjrb3T3Tp1wxYcwM6Wx3NsUM4eNo/Az75AUhLS5PeHyEAVBXsVt/fenG2tcFgIDU1lZycHK677jqmT5/Of/7zH/ew1UMPPUR6ejrDhg0DoKioiAsuuIDY2Fji4+OZNWsW+fn57vqcTifz588nNjaWhIQEbrvttiOG+Q8fvrLZbNx+++1kZWW5D09+6aWXyM/PZ9q0aQDExcWhKApXXHFFp3XU1dVx+eWXExcXh9Fo5KyzzmLfvn3ux5cuXUpsbCwrVqxgxIgRREVFMXPmTMrKynr8OxP9g/QA+Ymqqkeu/lJdJO1+leRdL6Gg0pj6K4om3R9wx1t0JiIi4pgn7woRMlqb4OF037f7t1LQ9+39IiIigpqaGgBWrVpFTEwMK1euBKC1tZUZM2YwefJkvv76a3Q6HQ8++CAzZ87k+++/R6/X8+STT7J06VJefvllRowYwZNPPslHH33EaaeddtQ2L7/8cjZs2MA//vEPxowZQ15eHtXV1WRlZfHBBx/wu9/9jj179hATE0NERESndVxxxRXs27eP//znP8TExHD77bdz9tlns2vXLsLCwgBoamriiSee4PXXX0ej0fCHP/yBW265hTfffLNPvzMRnCQB8hOLxYLT6XT/rLXVkbnpfqIrNgFQO3AWpWPngyY4XqL09HQ58V2IIKaqKqtWrWLFihXceOONVFVVERkZyYsvvuge+nrjjTdwuVy8+OKL7r/3V155hdjYWFavXs2ZZ57JokWLWLBgAb/97W8BeP7551mxYsVR2927dy/vvfceK1euZPr06QAMHDjQ/Xj7UFdycjKxsbGd1tGe+Kxbt44pU6YA8Oabb5KVlcWyZcs4//zzgbYE7vnnn2fQoLYe9RtuuIH777+/t78yEeSC49O1n3C6VDbl1VLZ2ALNDeRGqmg1CsbqHWRtvIew5ipcWgOlJ9xCfe7Z/g6322JjY4/6rUyIkBRmbOuN8Ue7PfTJJ58QFRVFa2srLpeLSy65hHvvvZfrr7+eUaNGdZj3s2PHDvbv3090dHSHOlpaWjhw4AANDQ2UlZUxadIk92M6nY4JEyYcdbXr9u3b0Wq1TJ06tcext9u9ezc6na5DuwkJCQwbNozdu3e77zMaje7kB9qG7SsrK3vdrghukgD5yPIfyrjvv7soa/hl0nNKBDyTsZLjSl5DUZ20ROdQ9KsHsZkGdlFTYFEUhZSUFH+HIURgUZQ+D0X5yrRp03juuefQ6/Wkp6ej0/3ysRAZ2fEaLBYL48eP73TIKCkpqVft+/LLU/tQWDtFUbrchkT0bwExY3XJkiXk5uYSHh7OpEmT2LRpU5fl//3vfzN8+HDCw8MZNWoUn332WYfHVVXl7rvvJi0tjYiICKZPn95hMpyvLf+hjOve2Noh+TlOyeMl59+YWPwKiuqkPusMDp7+YlAlP9D2pnf4m4oQInhERkYyePBgsrOzOyQ/nRk3bhz79u0jOTmZwYMHd7iZTCZMJhNpaWls3LjR/RyHw8GWLVuOWueoUaNwuVysWbOm08fbe6AOnTJwuBEjRuBwODq0W1NTw549exg5cmSX1yRCl98ToHfffZf58+dzzz33sHXrVsaMGcOMGTOO2i25fv16Lr74Yq666iq2bdvG7NmzmT17Nj/88IO7zGOPPcY//vEPnn/+eTZu3EhkZCQzZsw46pJzb3K6VO777y7av2OEY+MO3Vt8rL+L4zX51KuR3KP8mYIJd+PS9bz72p90Oh2JiYn+DkMI4SOXXnopiYmJzJo1i6+//pq8vDxWr17NX/7yF4qLiwG46aabeOSRR1i2bBk//fQTf/7zn4+64hUgNzeXOXPmcOWVV7Js2TJ3ne+99x4AOTk5KIrCJ598QlVVFRaL5Yg6hgwZwqxZs7jmmmv45ptv2LFjB3/4wx/IyMhg1qxZXvldiODn9wToqaee4pprrmHu3LmMHDmS559/HqPRyMsvv9xp+cWLFzNz5kxuvfVWRowYwQMPPMC4ceN49tlngbben0WLFnHnnXcya9YsRo8ezWuvvUZpaSnLli3rtE6bzYbZbO5w85RNebXunp/Jmh9Zrr+DP+k+Qae4+I9zMtNtT/Bq88n8WGX3WJu+kpmZKcvehQghRqORtWvXkp2dzW9/+1tGjBjBVVddRUtLi3sV6M0338xll13GnDlzmDx5MtHR0Zx33nld1vvcc8/x+9//nj//+c8MHz6ca665BqvVCkBGRgb33Xcfd9xxBykpKdxwww2d1vHKK68wfvx4fvOb3zB58mRUVeWzzz6THmpxVIrqxwFQu92O0Wjk/fff77BN+pw5c6ivr+fjjz8+4jnZ2dnMnz+/w/4P99xzD8uWLWPHjh0cPHiQQYMGsW3bNsaOHesuM3XqVMaOHcvixYuPqPPee+/lvvvuO+L+hoaGPi/t/nh7CTe9sx2AO3Rv8SfdJ5Sq8dzZeiVfusa5y916UiJTBwTHnAFo25MjIyPD32EI4XctLS3k5eUxYMAAwsPD/R2OEP1eV39zZrMZk8nUrc9vv359r66uxul0HjGJNiUlhfLy8k6fU15e3mX59v/2pM4FCxbQ0NDgvhUVFfXqejqTHP3Li7PI8TsWO87jTNtjHZIfgLgIrcfa9DadTkdqaqq/wxBCCCF6TVaB0bYTqsFg8ErdEwfEk2YKp7yhhRYMPO04/4gyiUYtxyV7p31vyMzMRKsNnoRNCCGEOJxfe4ASExPRarVUVFR0uL+iouKoPQypqaldlm//b0/q9CatRuGec9tWIRxtm8BrJ8Sj1QTHJoLx8fFERUX5OwwhhBCiT/yaAOn1esaPH8+qVavc97lcLlatWsXkyZM7fc7kyZM7lAdYuXKlu/yAAQNITU3tUMZsNrNx48aj1ultM49P47k/jCPV1HGsMtGo5W+nJDElOzhWf4WFhcnQlxBCiH7B70Ng8+fPZ86cOUyYMIGJEyeyaNEirFYrc+fOBdrOiMnIyGDhwoVA2xLLqVOn8uSTT3LOOefwzjvvsHnzZl544QWgbWOrefPm8eCDDzJkyBAGDBjAXXfdRXp6eoeJ1r428/g0zhiZ6t4JOjk6nKFxGspKS/wWU0/Jqi8hhBD9hd8ToAsvvJCqqiruvvtuysvLGTt2LMuXL3dPYi4sLOzwoTtlyhTeeust7rzzTv72t78xZMgQli1bxvHHH+8uc9ttt2G1Wrn22mupr6/n5JNPZvny5X5foaHVKEwelNDhvuYma5d7ZASKtLS0I3aFFUIIIYKVX5fBB6qeLKPrK5fLxYEDB7DZbF5tpy9kybsQRyfL4IXwrX6xDF6ARqMhNzc3YDfrMhqNpKen+zsMIYQQwqMkAQoAYWFh5ObmBtzS8rCwMLKzs1GU4FihJoQQQnSXJEABwmAwkJubGzDJhqIo5OTkHPNwRCHE0dntdpqbm31ys9sD+zgdVVW59tpriY+PR1EUtm/fzqmnntphV//O5ObmsmjRIp/EGOpC7Xctn24BJCIigpycHPLz8/0ah6Io5ObmynwGIfrAbrezb98+fDXNUlEUhgwZ4j49vbvKy8t56KGH+PTTTykpKSE5OZmxY8cyb948Tj/9dI/Ft3z5cpYuXcrq1asZOHAgiYmJfPjhhwE7/N8T+fn5DBgw4IgjmLpy7733smzZMrZv3+7V2DyptbWVhQsX8uqrr1JSUsKwYcN49NFHmTlzprtMY2Mjd911Fx999BGVlZWccMIJLF68mBNPPNFd5oknnuCxxx4D4Pbbb+fmm292P7Zx40b+/Oc/s3HjRq9/AZcEKMBERUWRlZXl0eM4ekKr1ZKbm0tERIRf2heiv3A6nT5LfqCth8XpdPboOfn5+Zx00knExsby+OOPM2rUKFpbW1mxYgXXX389P/30k8fiO3DgAGlpaUyZMsV9X3x8vMfqD1V2u73HSW9v3Xnnnbzxxhv861//Yvjw4axYsYLzzjuP9evXc8IJJwBw9dVX88MPP/D666+Tnp7OG2+8wfTp09m1axcZGRl8//333H333XzyySeoqspvfvMbzjzzTEaNGoXD4eBPf/oTL7zwgk9GH2QILACZTCYGDhzo8zlBOp2OgQMHSvIjRIj485//jKIobNq0id/97ncMHTqU4447jvnz5/Ptt9+6yxUWFjJr1iyioqKIiYnhggsu6LDb/r333svYsWN5/fXXyc3NxWQycdFFF9HY2AjAFVdcwY033khhYaG7hxk4YgissrKSc889l4iICAYMGMCbb755RMz19fVcffXVJCUlERMTw2mnncaOHTu6HQu0rb597LHHGDx4MAaDgezsbB566CH340VFRVxwwQXExsYSHx/PrFmzetQzv3r1ahRFYdWqVUyYMAGj0ciUKVPYs2cPAEuXLuW+++5jx44dKIqCoigsXbq0R9f34osvuldBvfDCC6Snp+NyuTrEMWvWLK688kqgLQGdNWsWKSkpREVFceKJJ/LFF190+5oAXn/9df72t79x9tlnM3DgQK677jrOPvtsnnzySQCam5v54IMPeOyxxzjllFMYPHgw9957L4MHD+a5554D4KeffmL06NGcdtppnH766YwePdqdaD/++OOccsopHXqLvEkSoABlNBoZNGiQ184oO5zBYPBpe0II/6qtrWX58uVcf/31ne7xFRsbC7QlC7NmzaK2tpY1a9awcuVKDh48yIUXXtih/IEDB1i2bBmffPIJn3zyCWvWrOGRRx4BYPHixdx///1kZmZSVlbGd99912lMV1xxBUVFRXz11Ve8//77/N///R+VlZUdypx//vlUVlbyv//9jy1btjBu3DhOP/10amtruxULtB2A/cgjj3DXXXexa9cu3nrrLffec62trcyYMYPo6Gi+/vpr1q1bR1RUFDNnzuzxPKu///3vPPnkk2zevBmdTudORi688EJuvvlmjjvuOMrKyigrK3P/Prtzffv37+eDDz7gww8/ZPv27Zx//vnU1NTw1Vdfucu0v76XXnopABaLhbPPPptVq1axbds2Zs6cybnnnkthYWG3r8dmsx0xNSIiIoJvvvkGAIfDgdPp7LLMqFGj2Lt3L4WFhRQUFLB3716OP/54Dhw4wCuvvMKDDz7Y7Xj6SobAApher2fQoEEUFxdjNpu91k50dDQZGRky4VmIELJ//35UVWX48OFdllu1ahU7d+4kLy+PrKwsAF577TWOO+44vvvuO/e3dZfLxdKlS4mOjgbgsssuY9WqVTz00EOYTCaio6PRarVHPU5n7969/O9//2PTpk3uOl966SVGjBjhLvPNN9+wadMmKisr3V/WnnjiCZYtW8b777/Ptddee8xYGhsbWbx4Mc8++yxz5swBYNCgQZx88skAvPvuu7hcLl588UX3opRXXnmF2NhYVq9ezZlnntnt3/FDDz3E1KlTAbjjjjs455xzaGlpISIigqioKHQ6XYffR3evz26389prr5GUlOR+7llnncVbb73lnrf1/vvvk5iYyLRp0wAYM2YMY8aMcZd/4IEH+Oijj/jPf/7DDTfc0K3rmTFjBk899RSnnHIKgwYNYtWqVXz44Yfuodfo6GgmT57MAw88wIgRI0hJSeHtt99mw4YNDB48GIARI0bw8MMPc8YZZwCwcOFCRowYwfTp03nsscdYsWIF9957L2FhYSxevJhTTjml27/vnpJPvACn0WjIysqitraWioqKI7o4+0Kn05Genu71zR6FEIGnu/OTdu/eTVZWljv5ARg5ciSxsbHs3r3bnazk5ua6Ew5o2z3+8N6bY7Wj0+kYP368+77hw4e7e6IAduzYgcViISHhsB31m5s5cOCA++euYtm9ezc2m+2oE7x37NjB/v37Ozwf2jbfO7SN7hg9enSHGKBtmC87O/uobXfn+nJycjokPwCXXnop11xzDf/3f/+HwWDgzTff5KKLLnKfpGCxWLj33nv59NNPKSsrw+Fw0Nzc3KMeoMWLF3PNNdcwfPhwFEVh0KBBzJ07l5dfftld5vXXX+fKK68kIyMDrVbLuHHjuPjii9myZYu7zJ/+9Cf+9Kc/uX9+9dVX3cnTsGHD+O677yguLuaiiy4iLy/PayMTkgAFAUVRSEhIIDY2lqqqKqqrq/tcZ3x8PCkpKQG395AQwjeGDBmCoigem+h8+GouRVE8+oUN2j7E09LSWL169RGPHZoodRXLseY4WiwWxo8f3+n8o8OTjmM5NI723qSufifdvb7OhizPPfdcVFXl008/5cQTT+Trr7/m6aefdj9+yy23sHLlSp544gkGDx5MREQEv//973s0rJeUlMSyZctoaWmhpqaG9PR07rjjDgYOHOguM2jQINasWYPVasVsNpOWlsaFF17Yocyhqqurue+++1i7di0bN25k6NChDBkyhCFDhtDa2srevXsZNWpUt2PsCUmAgkh793F8fDyVlZU9PkNMo9FgMpmIj4+Xic5ChLj4+HhmzJjBkiVL+Mtf/nLEh2p9fT2xsbGMGDGCoqIiioqK3L1Au3btor6+npEjR3osnuHDh+NwONiyZYu7V2nPnj0d3ufGjRtHeXk5Op3OPZG6p4YMGUJERASrVq3i6quvPuLxcePG8e6775KcnOzV3nG9Xn/Eqr2+XF94eDi//e1vefPNN9m/fz/Dhg1j3Lhx7sfXrVvHFVdcwXnnnQe0JVu93XIlPDycjIwMWltb+eCDD7jggguOKBMZGUlkZCR1dXWsWLHCvez9cH/961/561//SmZmJt999x2tra3ux9rnFHmLTIIOQnq9nszMTEaMGEFOTg6JiYlH3bNHq9USFxdHTk4OI0aMICMjQ5IfIQQAS5Yswel0MnHiRD744AP27dvH7t27+cc//sHkyZMBmD59OqNGjeLSSy9l69atbNq0icsvv5ypU6cyYcIEj8UybNgwZs6cyR//+Ec2btzIli1buPrqqzu8X02fPp3Jkycze/ZsPv/8c/Lz81m/fj1///vf2bx5c7faCQ8P5/bbb+e2227jtdde48CBA3z77be89NJLQNtQUmJiIrNmzeLrr78mLy+P1atX85e//IXi4mKPXW9ubi55eXls376d6upqbDZbn6/v0ksv5dNPP+Xll192T35uN2TIEPek6R07dnDJJZf0uIdu48aNfPjhhxw8eJCvv/6amTNn4nK5uO2229xlVqxYwfLly8nLy2PlypVMmzaN4cOHM3fu3CPqW7lyJXv37uX6668H4MQTT+Snn37if//7Hy+88AJarZZhw4b1KMaekB6gIKbVaomOjnaPVbfvO6IoChqNJmB2lRYiFGm1WhRF8elGiD0d0h44cCBbt27loYce4uabb6asrIykpCTGjx/vXrasKAoff/wxN954I6eccgoajYaZM2fyzDPPePwaXnnlFa6++mqmTp1KSkoKDz74IHfddZf7cUVR+Oyzz/j73//O3LlzqaqqIjU1lVNOOcW9iqs77rrrLnQ6HXfffTelpaWkpaW556QYjUbWrl3L7bffzm9/+1saGxvJyMjg9NNP92iP0O9+9zs+/PBDpk2bRn19Pa+88gpXXHFFn67vtNNOIz4+nj179nDJJZd0eOypp57iyiuvZMqUKSQmJnL77bf3eHFNS0sLd955JwcPHiQqKoqzzz6b119/vcPwXENDAwsWLKC4uJj4+Hh+97vf8dBDDx0xLNnc3MwNN9zAu+++656nlJmZyTPPPMPcuXMxGAy8+uqrXv3CLqfBd8KXp8ELIYJbVydT2+12r3bhH0qr1fpsQzwh/MlTp8FLD5AQQniJJCRCBC6ZAySEEEKIkCMJkBBCCCFCjiRAQgghhAg5kgAJIYQHyHoSIXzDU39rkgAJIUQftC/vbWpq8nMkQoSG9r+1w5fW95SsAhNCiD7QarXExsa6z5oyGo2yB5cQXqCqKk1NTVRWVhIbG9vno5wkARJCiD5qP9G7J4d/CiF6JzY21v031xeSAAkhRB8pikJaWhrJyckdzjISQnhWWFiYxw7xlgRICCE8RKvVeuzNWQjhXTIJWgghhBAhRxIgIYQQQoQcSYCEEEIIEXJkDlAn2jdZMpvNfo5ECCGEEN3V/rndnc0SJQHqRGNjIwBZWVl+jkQIIYQQPdXY2IjJZOqyjKLK/u1HcLlclJaWEh0d7fENzcxmM1lZWRQVFRETE+PRugOBXF/w6+/XKNcX/Pr7Ncr19Z6qqjQ2NpKeno5G0/UsH+kB6oRGoyEzM9OrbcTExPTLf9jt5PqCX3+/Rrm+4Nffr1Gur3eO1fPTTiZBCyGEECLkSAIkhBBCiJAjCZCPGQwG7rnnHgwGg79D8Qq5vuDX369Rri/49fdrlOvzDZkELYQQQoiQIz1AQgghhAg5kgAJIYQQIuRIAiSEEEKIkCMJkBBCCCFCjiRAXrBkyRJyc3MJDw9n0qRJbNq0qcvy//73vxk+fDjh4eGMGjWKzz77zEeR9k5Prm/p0qUoitLhFh4e7sNoe2bt2rWce+65pKenoygKy5YtO+ZzVq9ezbhx4zAYDAwePJilS5d6Pc7e6un1rV69+ojXT1EUysvLfRNwDy1cuJATTzyR6OhokpOTmT17Nnv27Dnm84Llb7A31xdsf4PPPfcco0ePdm+SN3nyZP73v/91+Zxgef2g59cXbK/f4R555BEURWHevHldlvPHaygJkIe9++67zJ8/n3vuuYetW7cyZswYZsyYQWVlZafl169fz8UXX8xVV13Ftm3bmD17NrNnz+aHH37wceTd09Prg7bdPsvKyty3goICH0bcM1arlTFjxrBkyZJulc/Ly+Occ85h2rRpbN++nXnz5nH11VezYsUKL0faOz29vnZ79uzp8BomJyd7KcK+WbNmDddffz3ffvstK1eupLW1lTPPPBOr1XrU5wTT32Bvrg+C628wMzOTRx55hC1btrB582ZOO+00Zs2axY8//thp+WB6/aDn1wfB9fod6rvvvuOf//wno0eP7rKc315DVXjUxIkT1euvv979s9PpVNPT09WFCxd2Wv6CCy5QzznnnA73TZo0Sf3jH//o1Th7q6fX98orr6gmk8lH0XkWoH700UddlrntttvU4447rsN9F154oTpjxgwvRuYZ3bm+r776SgXUuro6n8TkaZWVlSqgrlmz5qhlgu1v8FDdub5g/htsFxcXp7744oudPhbMr1+7rq4vWF+/xsZGdciQIerKlSvVqVOnqjfddNNRy/rrNZQeIA+y2+1s2bKF6dOnu+/TaDRMnz6dDRs2dPqcDRs2dCgPMGPGjKOW96feXB+AxWIhJyeHrKysY37TCTbB9Pr1xdixY0lLS+OMM85g3bp1/g6n2xoaGgCIj48/aplgfg27c30QvH+DTqeTd955B6vVyuTJkzstE8yvX3euD4Lz9bv++us555xzjnhtOuOv11ASIA+qrq7G6XSSkpLS4f6UlJSjzpkoLy/vUXl/6s31DRs2jJdffpmPP/6YN954A5fLxZQpUyguLvZFyF53tNfPbDbT3Nzsp6g8Jy0tjeeff54PPviADz74gKysLE499VS2bt3q79COyeVyMW/ePE466SSOP/74o5YLpr/BQ3X3+oLxb3Dnzp1ERUVhMBj405/+xEcffcTIkSM7LRuMr19Pri8YX7933nmHrVu3snDhwm6V99drKKfBC6+aPHlyh282U6ZMYcSIEfzzn//kgQce8GNkojuGDRvGsGHD3D9PmTKFAwcO8PTTT/P666/7MbJju/766/nhhx/45ptv/B2KV3T3+oLxb3DYsGFs376dhoYG3n//febMmcOaNWuOmiQEm55cX7C9fkVFRdx0002sXLky4CdrSwLkQYmJiWi1WioqKjrcX1FRQWpqaqfPSU1N7VF5f+rN9R0uLCyME044gf3793sjRJ872usXExNDRESEn6LyrokTJwZ8UnHDDTfwySefsHbtWjIzM7ssG0x/g+16cn2HC4a/Qb1ez+DBgwEYP3483333HYsXL+af//znEWWD8fXryfUdLtBfvy1btlBZWcm4cePc9zmdTtauXcuzzz6LzWZDq9V2eI6/XkMZAvMgvV7P+PHjWbVqlfs+l8vFqlWrjjq+O3ny5A7lAVauXNnleLC/9Ob6Dud0Otm5cydpaWneCtOngun185Tt27cH7Ounqio33HADH330EV9++SUDBgw45nOC6TXszfUdLhj/Bl0uFzabrdPHgun1O5quru9wgf76nX766ezcuZPt27e7bxMmTODSSy9l+/btRyQ/4MfX0KtTrEPQO++8oxoMBnXp0qXqrl271GuvvVaNjY1Vy8vLVVVV1csuu0y944473OXXrVun6nQ69YknnlB3796t3nPPPWpYWJi6c+dOf11Cl3p6fffdd5+6YsUK9cCBA+qWLVvUiy66SA0PD1d//PFHf11ClxobG9Vt27ap27ZtUwH1qaeeUrdt26YWFBSoqqqqd9xxh3rZZZe5yx88eFA1Go3qrbfequ7evVtdsmSJqtVq1eXLl/vrErrU0+t7+umn1WXLlqn79u1Td+7cqd50002qRqNRv/jiC39dQpeuu+461WQyqatXr1bLysrct6amJneZYP4b7M31Bdvf4B133KGuWbNGzcvLU7///nv1jjvuUBVFUT///HNVVYP79VPVnl9fsL1+nTl8FVigvIaSAHnBM888o2ZnZ6t6vV6dOHGi+u2337ofmzp1qjpnzpwO5d977z116NChql6vV4877jj1008/9XHEPdOT65s3b567bEpKinr22WerW7du9UPU3dO+7PvwW/s1zZkzR506deoRzxk7dqyq1+vVgQMHqq+88orP4+6unl7fo48+qg4aNEgNDw9X4+Pj1VNPPVX98ssv/RN8N3R2bUCH1ySY/wZ7c33B9jd45ZVXqjk5Oaper1eTkpLU008/3Z0cqGpwv36q2vPrC7bXrzOHJ0CB8hoqqqqq3u1jEkIIIYQILDIHSAghhBAhRxIgIYQQQoQcSYCEEEIIEXIkARJCCCFEyJEESAghhBAhRxIgIYQQQoQcSYCEEEIIEXIkARJCCCFEyJEESAghhBAhRxIgIYQQQoQcSYCEEEIIEXIkARJC9HtVVVWkpqby8MMPu+9bv349er2eVatW+TEyIYS/yGGoQoiQ8NlnnzF79mzWr1/PsGHDGDt2LLNmzeKpp57yd2hCCD+QBEgIETKuv/56vvjiCyZMmMDOnTv57rvvMBgM/g5LCOEHkgAJIUJGc3Mzxx9/PEVFRWzZsoVRo0b5OyQhhJ/IHCAhRMg4cOAApaWluFwu8vPz/R2OEMKPpAdICBES7HY7EydOZOzYsQwbNoxFixaxc+dOkpOT/R2aEMIPJAESQoSEW2+9lffff58dO3YQFRXF1KlTMZlMfPLJJ/4OTQjhBzIEJoTo91avXs2iRYt4/fXXiYmJQaPR8Prrr/P111/z3HPP+Ts8IYQfSA+QEEIIIUKO9AAJIYQQIuRIAiSEEEKIkCMJkBBCCCFCjiRAQgghhAg5kgAJIYQQIuRIAiSEEEKIkCMJkBBCCCFCjiRAQgghhAg5kgAJIYQQIuRIAiSEEEKIkCMJkBBCCCFCzv8H+4udsfCfdbcAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "def plot_gp(xt, yt, x, y, s2):\n", " fig, axs = plt.subplots(1)\n", " \n", " # training data\n", " axs.plot(xt, yt, \"o\")\n", " \n", " # gp mean\n", " axs.plot(x, y)\n", " \n", " # 99% confidence interval\n", " axs.fill_between(\n", " np.ravel(x),\n", " np.ravel(y - 3 * np.sqrt(s2)),\n", " np.ravel(y + 3 * np.sqrt(s2)),\n", " color=\"lightgrey\",\n", " )\n", " \n", " # legend\n", " axs.set_xlabel(\"x\")\n", " axs.set_ylabel(\"y\")\n", " axs.legend(\n", " [\"Training data\", \"Prediction\", \"Confidence Interval 99%\"],\n", " loc=\"lower right\",\n", " )\n", " return axs\n", "\n", "plot_gp(xt, yt, x, y, s2)\n", "plt.show()" ] }, { "attachments": {}, "cell_type": "markdown", "id": "81c877a9-85b0-43f0-89d3-a9bd78940e80", "metadata": { "tags": [] }, "source": [ "### Sampling" ] }, { "attachments": {}, "cell_type": "markdown", "id": "e9771aff-1fdb-4cc0-b6c4-620abd209513", "metadata": {}, "source": [ "#### Sampling the conditionned Gaussian process" ] }, { "cell_type": "code", "execution_count": 7, "id": "c6b11bc9-777d-45c7-ba9b-6fac8cc0f33e", "metadata": {}, "outputs": [], "source": [ "# number fo trajectories to sample\n", "n_traj = 30\n", "\n", "trajs = gpx.sample(x, n_traj)" ] }, { "attachments": {}, "cell_type": "markdown", "id": "432580a5-e386-4fb2-900c-eb557c39aa73", "metadata": {}, "source": [ "#### Plotting trajectories" ] }, { "cell_type": "code", "execution_count": 8, "id": "7f7475e5-2653-47d5-8cfe-adf1178a44fa", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "axs = plot_gp(xt, yt, x, y, s2)\n", "\n", "for i in range(n_traj):\n", " axs.plot(x, trajs[:, i])\n", "\n", "plt.show()" ] }, { "attachments": {}, "cell_type": "markdown", "id": "a7f6a424-1da4-4816-b95f-47d46fa418c2", "metadata": {}, "source": [ "## Example 2 : Gpx trend and correlation models customization, saving and loading" ] }, { "attachments": {}, "cell_type": "markdown", "id": "8a910ef7-33b0-4033-998b-6317760e3ac7", "metadata": {}, "source": [ "### Test function\n", "\n", "$$f : \\left\\{ \\begin{array}{c} [-10, 10] \\rightarrow \\mathbb{R} \\\\ x \\mapsto x^2 \\sin(x) \\ \\end{array} \\right.$$" ] }, { "cell_type": "code", "execution_count": 9, "id": "ad996348-9dd9-4068-8a45-8455520ad859", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "def f(x):\n", " return x**2 * np.sin(x)" ] }, { "attachments": {}, "cell_type": "markdown", "id": "2fe7b4b2-6ac9-465c-8436-3e7429aa4747", "metadata": { "tags": [] }, "source": [ "### Training" ] }, { "attachments": {}, "cell_type": "markdown", "id": "87fe0c9f-cd81-4494-be24-a3aab057a69e", "metadata": {}, "source": [ "$f$ is approximated with _Gpx_ at points $-8.5$, $-4.0$, $-3.0$, $-1.0$, $4.0$ and $7.5$. " ] }, { "cell_type": "code", "execution_count": 10, "id": "9ef79902-15e1-4ef3-a671-3f14a89d470e", "metadata": {}, "outputs": [], "source": [ "xt = np.array([[-8.5, -4.0, -3.0, -1.0, 4.0, 7.5]]).T\n", "yt = f(xt)" ] }, { "attachments": {}, "cell_type": "markdown", "id": "8a2f08c8-1c1d-4e10-a157-012a46eafe17", "metadata": {}, "source": [ "To show features of _Gpx_, below, we build the surrogate asking for best GP regression by testing constant, linear or quadratic trend with either squared_exponential or matern52. The quality of the surrogate is assessed by cross validation." ] }, { "cell_type": "code", "execution_count": 11, "id": "99e498c1-9ce5-4f07-a92b-c7bb0cb679f9", "metadata": {}, "outputs": [], "source": [ "gpx_builder = egx.Gpx.builder(regr_spec=egx.RegressionSpec.ALL, \n", " corr_spec=egx.CorrelationSpec.SQUARED_EXPONENTIAL | egx.CorrelationSpec.MATERN52)\n", "gpx = gpx_builder.fit(xt, yt)" ] }, { "attachments": {}, "cell_type": "markdown", "id": "77456008-7572-4138-b307-b6d77522bd8d", "metadata": {}, "source": [ "We can get string representations of the trained GP" ] }, { "cell_type": "code", "execution_count": 12, "id": "7f58b435-8c3d-4d8a-844f-79c829f10983", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Gpx string: Mixture[Smooth](Linear_SquaredExponentialGP(mean=LinearMean, corr=SquaredExponential, theta=[14.452882749810662], variance=441.2141000495963, likelihood=3.031768565015306))\n", "Gpx stringified JSON serialization {\"recombination\":{\"Smooth\":null},\"experts\":[{\"type\":\"GpLinearSquaredExponentialSurrogate\",\"theta\":{\"v\":1,\"dim\":[1],\"data\":[14.452882749810662]},\"likelihood\":3.031768565015306,\"mean\":\"LinearMean\",\"corr\":\"SquaredExponential\",\"inner_params\":{\"sigma2\":441.2141000495963,\"beta\":{\"v\":1,\"dim\":[2,1],\"data\":[-0.07757166517069636,0.7944037509309693]},\"gamma\":{\"v\":1,\"dim\":[6,1],\"data\":[-0.44643171321364306,1.1331405283903964,-0.3878788861969931,0.1553420259776689,-0.8959678802322967,0.4417959252748667]},\"r_chol\":{\"v\":1,\"dim\":[6,6],\"data\":[1.000000000000011,0.0,0.0,0.0,0.0,0.0,0.00015107687965342333,0.9999999885878993,0.0,0.0,0.0,0.0,1.960569341106461e-6,0.647617274864888,0.7619657901065864,0.0,0.0,0.0,2.4359093850121372e-11,0.020038526606141666,0.21382309005204245,0.9766668539538308,0.0,0.0,3.299917901018181e-30,8.401926714807942e-13,7.451627142017255e-10,0.00001964311890039922,0.999999999807085,0.0,4.983282830665148e-49,1.1139381004845755e-25,2.069666987829042e-21,2.387862924959664e-14,0.004882594368483155,0.9999880800650851]},\"ft\":{\"v\":1,\"dim\":[6,2],\"data\":[0.9999999999999889,-1.3292355199392736,0.9998489345307233,-0.5488312520922597,0.462591105466827,-0.02653440727656832,0.9021006879988441,-0.012517047814952423,0.9999822797762914,0.8379965521044357,0.9951293540292918,1.4407467936872096]},\"ft_qr_r\":{\"v\":1,\"dim\":[2,2],\"data\":[2.2400270233067623,0.16524847426703282,0.0,2.1953646732623318]}},\"w_star\":{\"v\":1,\"dim\":[1,1],\"data\":[1.0]},\"xtrain\":{\"data\":{\"v\":1,\"dim\":[6,1],\"data\":[-1.3292355199392882,-0.549032062583619,-0.3756535165045814,-0.028896424346506258,0.8379963060486816,1.4448212173253132]},\"mean\":{\"v\":1,\"dim\":[1],\"data\":[-0.8333333333333334]},\"std\":{\"v\":1,\"dim\":[1],\"data\":[5.767726299562651]}},\"ytrain\":{\"data\":{\"v\":1,\"dim\":[6,1],\"data\":[-1.5797826304192275,0.3712640485913234,-0.002705461006250771,0.009275082294565307,-0.3056720463069517,1.5076210068465417]},\"mean\":{\"v\":1,\"dim\":[1],\"data\":[-1.1732910418024691]},\"std\":{\"v\":1,\"dim\":[1],\"data\":[35.77542995914992]}}}],\"gmx\":{\"weights\":{\"v\":1,\"dim\":[1],\"data\":[1.0]},\"means\":{\"v\":1,\"dim\":[1,1],\"data\":[-0.8333333333333334]},\"covariances\":{\"v\":1,\"dim\":[1,1,1],\"data\":[27.722223222222226]},\"precisions\":{\"v\":1,\"dim\":[1,1,1],\"data\":[0.0360721429873776]},\"precisions_chol\":{\"v\":1,\"dim\":[1,1,1],\"data\":[0.18992667792434426]},\"heaviside_factor\":1.0,\"log_det\":{\"v\":1,\"dim\":[1],\"data\":[-1.6611171869637489]}},\"output_dim\":1}\n" ] } ], "source": [ "print(f\"Gpx string: {gpx}\")\n", "print(f\"Gpx stringified JSON serialization {repr(gpx)}\")" ] }, { "attachments": {}, "cell_type": "markdown", "id": "b143465a-1a0f-4cd4-a214-cf436212fd47", "metadata": {}, "source": [ "... and save it in a json file." ] }, { "cell_type": "code", "execution_count": 13, "id": "c7aa44a9-d9d9-4e41-851c-80ca9aa0ebc5", "metadata": {}, "outputs": [], "source": [ "gpx.save(\"gp.json\")" ] }, { "attachments": {}, "cell_type": "markdown", "id": "7319042a-ab3d-43b7-8a12-1bebb0e44a60", "metadata": { "tags": [] }, "source": [ "We can reload it with" ] }, { "cell_type": "code", "execution_count": 14, "id": "f0ffeda5-1939-44af-9754-d523842bc15d", "metadata": { "tags": [] }, "outputs": [], "source": [ "gpx = egx.Gpx.load(\"gp.json\")" ] }, { "attachments": {}, "cell_type": "markdown", "id": "aa750f99-8508-4405-b79d-10b868c5d6be", "metadata": { "tags": [] }, "source": [ "### Prediction" ] }, { "cell_type": "code", "execution_count": 15, "id": "cd4b168f-79f5-4153-a8f8-1d3ff7fab14a", "metadata": { "tags": [] }, "outputs": [], "source": [ "x_min, x_max = -10, 10\n", "n_plot = 500\n", "\n", "# x must have (nsamples, nx) shape\n", "x = np.linspace(x_min, x_max, n_plot).reshape(-1, 1)\n", "\n", "y = gpx.predict(x)\n", "s2 = gpx.predict_var(x)" ] }, { "cell_type": "code", "execution_count": 16, "id": "dd5d170f-c274-4acc-be25-4fe8faba3722", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_gp(xt, yt, x, y, s2)\n", "plt.show()" ] }, { "attachments": {}, "cell_type": "markdown", "id": "4eaf76ed-5a6b-4b11-8944-f622a47a2264", "metadata": { "tags": [] }, "source": [ "### Sampling" ] }, { "attachments": {}, "cell_type": "markdown", "id": "1e5ce606-a320-470e-a1e9-d5e75866b6fd", "metadata": {}, "source": [ "#### Sampling the conditionned Gaussian process" ] }, { "cell_type": "code", "execution_count": 17, "id": "2cde3d09-2e38-414b-901f-0c92cb4ed08f", "metadata": {}, "outputs": [], "source": [ "# number fo trajectories to sample\n", "n_traj = 10\n", "\n", "trajs = gpx.sample(x, n_traj)" ] }, { "attachments": {}, "cell_type": "markdown", "id": "960f9d9c-b5cb-4db3-80a3-f4d7b48810e3", "metadata": {}, "source": [ "#### Plotting trajectories" ] }, { "cell_type": "code", "execution_count": 18, "id": "42ebdbc8-b9d7-48c8-abf8-49825139ce07", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "axs = plot_gp(xt, yt, x, y, s2)\n", "\n", "for i in range(n_traj):\n", " axs.plot(x, trajs[:, i])\n", "\n", "plt.show()" ] }, { "attachments": {}, "cell_type": "markdown", "id": "0781134f-ccae-4fd0-a0de-835f2cc30ead", "metadata": {}, "source": [ "## Example 3 : Clustering" ] }, { "attachments": {}, "cell_type": "markdown", "id": "3015e350-d8b5-4f89-872e-f0e5eb094d7b", "metadata": {}, "source": [ "### Test function\n", "\n", "We are going to use a test function with three modes to show clustering feature" ] }, { "cell_type": "code", "execution_count": 19, "id": "33133e72-262e-445d-ab97-525c693e66e3", "metadata": {}, "outputs": [], "source": [ "def function_3modes(x):\n", " y = np.zeros(x.shape)\n", " y[x < 0.4] = x[x < 0.4] ** 2\n", " y[(x >= 0.4) & (x < 0.8)] = 3 * x[(x >= 0.4) & (x < 0.8)] + 1\n", " y[x >= 0.8] = np.sin(10 * x[x >= 0.8])\n", " return y" ] }, { "attachments": {}, "cell_type": "markdown", "id": "b39b12aa-c2c6-4f64-8e27-5078ae5c9ee5", "metadata": { "tags": [] }, "source": [ "### Training " ] }, { "attachments": {}, "cell_type": "markdown", "id": "1c597ff9-bfa8-433e-8800-d5f20533f140", "metadata": {}, "source": [ "#### Training data definition" ] }, { "cell_type": "code", "execution_count": 20, "id": "b31cb879-19ae-4054-b18d-39ffda55a24b", "metadata": {}, "outputs": [], "source": [ "np.random.seed(42) # results may differ depending on training data, set seed here for reproducibility\n", "xt = np.random.sample(60).reshape((-1, 1))\n", "yt = function_3modes(xt)" ] }, { "attachments": {}, "cell_type": "markdown", "id": "c4dbc652-7bf1-4bd1-a348-bcf0c19df50f", "metadata": {}, "source": [ "#### Building the surrogate" ] }, { "cell_type": "code", "execution_count": 21, "id": "412e4c38-7361-4ce2-88bb-533797b048dd", "metadata": {}, "outputs": [], "source": [ "gpx = egx.Gpx.builder(n_clusters=3).fit(xt, yt)" ] }, { "cell_type": "code", "execution_count": 22, "id": "ce2d2c7c-bf96-468c-bb4f-f358e477825d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mixture[Smooth(0.1)](Constant_SquaredExponentialGP(mean=ConstantMean, corr=SquaredExponential, theta=[0.02798142256558686], variance=0.02638828606423465, likelihood=278.2517956877343), Constant_SquaredExponentialGP(mean=ConstantMean, corr=SquaredExponential, theta=[0.007994050570374143], variance=1.3952667945423496, likelihood=192.53772467321363), Constant_SquaredExponentialGP(mean=ConstantMean, corr=SquaredExponential, theta=[0.030545446402999624], variance=0.9814282111121166, likelihood=89.03789739740697))\n" ] } ], "source": [ "print(gpx)" ] }, { "attachments": {}, "cell_type": "markdown", "id": "caf365bb-f2b5-4dfd-98b2-7f78b4d2b854", "metadata": {}, "source": [ "We see that 3 experts are smoothly recombined with an heasviside factor of 0.1 automatically adjusted to improve the overall surrogate quality." ] }, { "attachments": {}, "cell_type": "markdown", "id": "fb9cb31d-2b01-41f3-b4cb-acf625635db5", "metadata": {}, "source": [ "### Plotting" ] }, { "cell_type": "code", "execution_count": 23, "id": "e5e4db6f-d0a2-43fb-9095-6ad6ee56d7c6", "metadata": { "tags": [] }, "outputs": [], "source": [ "x_min, x_max = 0, 1\n", "n_plot = 500\n", "\n", "# x must have (nsamples, nx) shape\n", "x = np.linspace(x_min, x_max, n_plot).reshape(-1, 1)\n", "\n", "y = gpx.predict(x)\n", "s2 = gpx.predict_var(x)" ] }, { "cell_type": "code", "execution_count": 24, "id": "933f231a-71eb-4728-9245-ce4331a8abd9", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_gp(xt, yt, x, y, s2)\n", "plt.show()" ] }, { "attachments": {}, "cell_type": "markdown", "id": "7a3f976c-6260-41a3-97b7-7513abf2beb0", "metadata": {}, "source": [ "We can check it is better than one cluster (the default)." ] }, { "cell_type": "code", "execution_count": 25, "id": "531c5590-3504-48ab-a53e-1eb004f62330", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gpx = egx.Gpx.builder().fit(xt, yt)\n", "y = gpx.predict(x)\n", "s2 = gpx.predict_var(x)\n", "plot_gp(xt, yt, x, y, s2)\n", "plt.show()" ] }, { "attachments": {}, "cell_type": "markdown", "id": "7920a0e3-37f6-4ff0-bdf0-bb9cbf550962", "metadata": {}, "source": [ "We can also let _Gpx_ find the best number of clusters" ] }, { "cell_type": "code", "execution_count": 26, "id": "6c0f2a73-03d8-482a-8824-c46c8ef51aee", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mixture[Hard](Constant_SquaredExponentialGP(mean=ConstantMean, corr=SquaredExponential, theta=[0.02798142256558686], variance=0.02638828606423465, likelihood=278.2517956877343), Constant_SquaredExponentialGP(mean=ConstantMean, corr=SquaredExponential, theta=[0.007994050570374143], variance=1.3952667945423496, likelihood=192.53772467321363), Constant_SquaredExponentialGP(mean=ConstantMean, corr=SquaredExponential, theta=[0.030545446402999624], variance=0.9814282111121166, likelihood=89.03789739740697))\n" ] }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gpx = egx.Gpx.builder(n_clusters=0).fit(xt, yt)\n", "print(gpx)\n", "y = gpx.predict(x)\n", "s2 = gpx.predict_var(x)\n", "plot_gp(xt, yt, x, y, s2)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "4e550286", "metadata": {}, "source": [ "## Gpx API" ] }, { "cell_type": "code", "execution_count": 27, "id": "c3db4c30", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Help on GpMix in module builtins object:\n", "\n", "class GpMix(object)\n", " | GpMix(n_clusters=1, regr_spec=Ellipsis, corr_spec=Ellipsis, recombination=Ellipsis, theta_init=None, theta_bounds=None, kpls_dim=None, n_start=10, seed=None)\n", " | \n", " | Gaussian processes mixture builder\n", " | \n", " | n_clusters (int >= 0)\n", " | Number of clusters used by the mixture of surrogate experts.\n", " | When set to 0, the number of cluster is determined automatically and refreshed every\n", " | 10-points addition (should say 'tentative addition' because addition may fail for some points\n", " | but failures are counted anyway).\n", " | \n", " | regr_spec (RegressionSpec flags, an int in [1, 7]):\n", " | Specification of regression models used in mixture.\n", " | Can be RegressionSpec.CONSTANT (1), RegressionSpec.LINEAR (2), RegressionSpec.QUADRATIC (4) or\n", " | any bit-wise union of these values (e.g. RegressionSpec.CONSTANT | RegressionSpec.LINEAR)\n", " | \n", " | corr_spec (CorrelationSpec flags, an int in [1, 15]):\n", " | Specification of correlation models used in mixture.\n", " | Can be CorrelationSpec.SQUARED_EXPONENTIAL (1), CorrelationSpec.ABSOLUTE_EXPONENTIAL (2),\n", " | CorrelationSpec.MATERN32 (4), CorrelationSpec.MATERN52 (8) or\n", " | any bit-wise union of these values (e.g. CorrelationSpec.MATERN32 | CorrelationSpec.MATERN52)\n", " | \n", " | recombination (Recombination.Smooth or Recombination.Hard)\n", " | Specify how the various experts predictions are recombined\n", " | * Smooth: prediction is a combination of experts prediction wrt their responsabilities,\n", " | the heaviside factor which controls steepness of the change between experts regions is optimized\n", " | to get best mixture quality.\n", " | * Hard: prediction is taken from the expert with highest responsability\n", " | resulting in a model with discontinuities.\n", " | \n", " | theta_init ([nx] where nx is the dimension of inputs x)\n", " | Initial guess for GP theta hyperparameters.\n", " | When None the default is 1e-2 for all components\n", " | \n", " | theta_bounds ([[lower_1, upper_1], ..., [lower_nx, upper_nx]] where nx is the dimension of inputs x)\n", " | Space search when optimizing theta GP hyperparameters\n", " | When None the default is [1e-6, 1e2] for all components\n", " | \n", " | kpls_dim (0 < int < nx where nx is the dimension of inputs x)\n", " | Number of components to be used when PLS projection is used (a.k.a KPLS method).\n", " | This is used to address high-dimensional problems typically when nx > 9.\n", " | \n", " | n_start (int >= 0)\n", " | Number of internal GP hyperpameters optimization restart (multistart)\n", " | \n", " | seed (int >= 0)\n", " | Random generator seed to allow computation reproducibility.\n", " | \n", " | Methods defined here:\n", " | \n", " | fit(self, /, xt, yt)\n", " | Fit the parameters of the model using the training dataset to build a trained model\n", " | \n", " | Parameters\n", " | xt (array[nsamples, nx]): input samples\n", " | yt (array[nsamples, 1]): output samples\n", " | \n", " | Returns Gpx object\n", " | the fitted Gaussian process mixture\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", "\n" ] } ], "source": [ "help(egx.Gpx.builder())" ] }, { "cell_type": "code", "execution_count": 28, "id": "284f975e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Help on class Gpx in module builtins:\n", "\n", "class Gpx(object)\n", " | A trained Gaussian processes mixture\n", " | \n", " | Methods defined here:\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | likelihoods(self, /)\n", " | Get reduced likelihood values gotten when fitting the GP experts\n", " | \n", " | Maybe used to compare various parameterization\n", " | \n", " | Returns\n", " | likelihood as an array[n_clusters]\n", " | \n", " | predict(self, /, x)\n", " | Predict output values at nsamples points.\n", " | \n", " | Parameters\n", " | x (array[nsamples, nx])\n", " | input values\n", " | \n", " | Returns\n", " | the output values at nsamples x points (array[nsamples, 1])\n", " | \n", " | predict_gradients(self, /, x)\n", " | Predict surrogate output derivatives at nsamples points.\n", " | \n", " | Parameters\n", " | x (array[nsamples, nx])\n", " | input values\n", " | \n", " | Returns\n", " | the output derivatives at nsamples x points (array[nsamples, nx]) wrt inputs\n", " | The ith column is the partial derivative value wrt to the ith component of x at the given samples.\n", " | \n", " | predict_var(self, /, x)\n", " | Predict variances at nsample points.\n", " | \n", " | Parameters\n", " | x (array[nsamples, nx])\n", " | input values\n", " | \n", " | Returns\n", " | the variances of the output values at nsamples input points (array[nsamples, 1])\n", " | \n", " | predict_var_gradients(self, /, x)\n", " | Predict variance derivatives at nsamples points.\n", " | \n", " | Parameters\n", " | x (array[nsamples, nx])\n", " | input values\n", " | \n", " | Returns\n", " | the variance derivatives at nsamples x points (array[nsamples, nx]) wrt inputs\n", " | The ith column is the partial derivative value wrt to the ith component of x at the given samples.\n", " | \n", " | sample(self, /, x, n_traj)\n", " | Sample gaussian process trajectories.\n", " | \n", " | Parameters\n", " | x (array[nsamples, nx])\n", " | locations of the sampled trajectories\n", " | n_traj number of trajectories to generate\n", " | \n", " | Returns\n", " | the trajectories as an array[nsamples, n_traj]\n", " | \n", " | save(self, /, filename)\n", " | Save Gaussian processes mixture in a json file.\n", " | \n", " | Parameters\n", " | filename (string)\n", " | json file generated in the current directory\n", " | \n", " | thetas(self, /)\n", " | Get optimized thetas hyperparameters (ie once GP experts are fitted)\n", " | \n", " | Returns\n", " | thetas as an array[n_clusters, nx or kpls_dim]\n", " | \n", " | variances(self, /)\n", " | Get GP expert variance (ie posterior GP variance)\n", " | \n", " | Returns\n", " | variances as an array[n_clusters]\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | builder(n_clusters=1, regr_spec=Ellipsis, corr_spec=Ellipsis, recombination=Ellipsis, theta_init=None, theta_bounds=None, kpls_dim=None, n_start=10, seed=None)\n", " | Get Gaussian processes mixture builder aka `GpMix`\n", " | \n", " | See `GpMix` constructor\n", " | \n", " | load(filename)\n", " | Load Gaussian processes mixture from a json file.\n", " | \n", " | Parameters\n", " | filename (string)\n", " | json filepath generated by saving a trained Gaussian processes mixture\n", "\n" ] } ], "source": [ "help(egx.Gpx)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.5" } }, "nbformat": 4, "nbformat_minor": 5 }