From 12960c05a6122ec987256dc0155c412528e784af Mon Sep 17 00:00:00 2001 From: Balakrishna Sandeep Haridasu <32479204+Sandeepharidasu@users.noreply.github.com> Date: Tue, 30 May 2023 13:57:15 +0000 Subject: [PATCH 01/22] before split --- Notebooks/Validation_kernel.ipynb | 26 +++++++++----------------- 1 file changed, 9 insertions(+), 17 deletions(-) diff --git a/Notebooks/Validation_kernel.ipynb b/Notebooks/Validation_kernel.ipynb index 5ae2690..fcbf7c3 100644 --- a/Notebooks/Validation_kernel.ipynb +++ b/Notebooks/Validation_kernel.ipynb @@ -435,7 +435,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 21, "metadata": {}, "outputs": [], "source": [ @@ -535,7 +535,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 18, "metadata": {}, "outputs": [], "source": [ @@ -544,7 +544,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 22, "metadata": {}, "outputs": [], "source": [ @@ -589,20 +589,12 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 26, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[0.84397473]\n" - ] - } - ], + "outputs": [], "source": [ - "l1 = np.linspace(0.01, 10, 20)\n", - "l2 = np.linspace(0.01, 10, 20)\n", + "l1 = np.linspace(0.01, 20, 80)\n", + "l2 = np.linspace(0.01, 20, 80)\n", "apprange = np.linspace(-10, 10, 100) # Adjust the range as needed\n", "interpolator = KcMM_v1(l1, l2, tau_values=apprange)\n", "\n", @@ -618,12 +610,12 @@ }, { "cell_type": "code", - "execution_count": 118, + "execution_count": 25, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", 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" ] From 8feee04a70c14e7e343ed41e81369f1c06860bf1 Mon Sep 17 00:00:00 2001 From: Balakrishna Sandeep Haridasu <32479204+Sandeepharidasu@users.noreply.github.com> Date: Tue, 20 Jun 2023 05:43:19 +0000 Subject: [PATCH 02/22] Some kernel modifications --- Notebooks/Validation_kernel.ipynb | 165 +++++++++- marcia/__init__.py | 2 +- marcia/backend/kernel.py | 30 ++ marcia/kernels.py | 523 +++++++++++++++++------------- 4 files changed, 497 insertions(+), 223 deletions(-) create mode 100644 marcia/backend/kernel.py diff --git a/Notebooks/Validation_kernel.ipynb b/Notebooks/Validation_kernel.ipynb index fcbf7c3..dd48765 100644 --- a/Notebooks/Validation_kernel.ipynb +++ b/Notebooks/Validation_kernel.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -591,7 +591,15 @@ "cell_type": "code", "execution_count": 26, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.85169018]\n" + ] + } + ], "source": [ "l1 = np.linspace(0.01, 20, 80)\n", "l2 = np.linspace(0.01, 20, 80)\n", @@ -610,12 +618,132 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 32, "metadata": {}, "outputs": [ { "data": { - "image/png": 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2xcfHh6CgIEaMGMG2bducFmNdJBkRQjjcgZMlnCr2w2AczpR+F5eMAAzrYjscbd3hvPOUFI2dr6+v246pd/VJtM6gqirV1dW13jOZTNxyyy1MmTKl3u117tyZt99+m3379rFx40aio6O56qqryM/Pd1TI9SLJiBDC4c4kDYM6hWLQXfw/M73aqxhCV7M2/0MsssTXoSZMmMD69euZP38+iqKgKAppaWlYLBYmTZpEhw4d8PLyokuXLsyfP79G3dpGVEaPHs2ECRPq7O+vj2kmTJjA6NGjmTt3LpGRkYSEhPDAAw9gNpvtfaSnp/Poo4/a4ztj48aNDBkyBC8vL6KionjooYcoKyuz34+OjuaFF15g/Pjx+Pv7c88995CWloaiKHzxxRcMHDgQT09PevTowfr162vEuX79evr374+HhweRkZE8+eSTdSYBAJ988gn9+vXDz8+PiIgIbr/9dvLybH8P0tLS7KcZBwUFoSiK/WdUVVXFQw89RKtWrfD09GTw4MHs2LHD3u6ZEZUVK1bQt29fPDw82LhxY60xzJ49m0cffZSePeu/p8/tt9/OiBEjiImJoXv37rzxxhuUlJTw22+/1bsNR5BkRAjhcEuPfo8uYBf9O3o4pL3oVho8wtZg8d3EzvQmtMRXVcFU5p5XPbc8nz9/PomJiUyePJns7Gyys7OJiorCarXStm1bvv76aw4ePMizzz7LU089xVdffeXwH9PatWs5duwYa9euZdGiRSxcuJCFCxcC8M0339C2bVuef/55e3wAx44d4+qrr2bMmDH89ttvfPnll2zcuJGpU6fWaHvu3LnEx8ezZ88ennnmGfv1GTNm8Nhjj7Fnzx4SExMZNWoUp06dAiArK4trr72WSy65hL1797JgwQI+/PBDXnzxxTrfg9ls5oUXXmDv3r189913pKWl2ROOqKgolixZAsDhw4fJzs62J3aPP/44S5YsYdGiRezevZtOnToxcuRICgsLa7T/5JNPMmfOHJKTk+nVq9eF/7DPwWQy8d577xEQEEB8fLxT+qiLnE0jhHCoonIT2coPeLXOxzcwAWjYzqu16RrcGQPBmDSFfLV/PQM6jL34QF3BXA4vtXZP30+dBIPPeYsFBARgMBjw9vYmIiLCfl2r1TJ79mz79x06dGDLli189dVX3HrrrQ4NNSgoiLfffhutVkvXrl257rrrWLNmDZMnTyY4OBitVmsfcTjj5Zdf5o477rCPzMTGxvLWW28xdOhQFixYYD/K/vLLL+exxx6z10tLSwNg6tSpjBkzBoAFCxawcuVKPvzwQx5//HH+85//EBUVxdtvv42iKHTt2pWTJ0/yxBNP8Oyzz6LRnP05/u6777Z/HRMTw1tvvcUll1yC0WjE19eX4OBgAFq1amWfz1FWVsaCBQtYuHAh11xzDQDvv/8+q1ev5sMPP2TGjBn2Np9//nmuvPLKi/xJ1+6HH37g73//O+Xl5URGRrJ69WpCQ0Od0lddZGRECOFQS/fvR+ORb1vSGzvUIW0qikL3wEsA2JqzySFtivN755136Nu3L2FhYfj6+vLee++RkZHh8H66d++OVqu1fx8ZGWl/xFGXvXv3snDhQnx9fe2vkSNHYrVaSU1NtZfr169frfUTExPtX+t0Ovr160dycjIAycnJJCYm1ngkNGjQIIxGIydOnKi1vV27djFq1CjatWuHn58fQ4fa/uyf6+d17NgxzGYzgwYNsl/T6/X079/fHsv53ocjDB8+nKSkJDZv3szVV1/Nrbfeet6fv6PJyIgQwqHOLOkN03fG3+DvsHZv7HIFe7atooh9FJaZCPYxOKxtp9F720Yo3NX3Rfjiiy+YPn06r7/+OomJifj5+fHaa6/VWGmh0WjOOgH3zFyPBoWq19f4XlEUrFbrOesYjUbuvfdeHnroobPutWvXzv61j8/5R4cuVllZGSNHjmTkyJEsXryYsLAwMjIyGDlypMMmzTrzffj4+NCpUyc6derEpZdeSmxsLB9++CEzZ850Wp9/JSMjQgiHOmbcDcCAyIEObXdkzBBQNWgMBaw5mnz+Co2Botgelbjj1YDt9w0GAxaLpca1TZs2MXDgQO6//34SEhLo1KkTx44dq1EmLCzMPocDwGKxsH9/w05nvtD4+vTpw8GDB+2/RP/8MhjOn6hu3brV/nV1dTW7du2iWzfbwYzdunVjy5YtNRKtTZs24efnR9u2bc9q69ChQ5w6dYo5c+YwZMgQunbtetbIwpmY/vw+OnbsiMFgYNOmP0b7zGYzO3bsIC4u7rzvwVmsVitVVa7d00eSESGEw5wuq6JSaxsiv6bToPOUbhhfgy/+mmgA1qfvdmjbLV10dDTbtm0jLS2NgoICrFYrsbGx7Ny5k1WrVpGSksIzzzxTY5UH2OZjLF++nOXLl3Po0CGmTJnilH00oqOj+fXXX8nKyqKgwLbXzBNPPMHmzZuZOnUqSUlJHDlyhKVLl541gbUu77zzDt9++y2HDh3igQce4PTp0/Z5H/fffz+ZmZk8+OCDHDp0iKVLlzJr1iymTZtW63yRdu3aYTAY+Pe//83x48dZtmwZL7zwQo0y7du3R1EUfvjhB/Lz8zEajfj4+DBlyhRmzJjBypUrOXjwIJMnT6a8vJxJkyY1+OeUkZFBUlISGRkZWCwWkpKSSEpKwmg01lq+rKyMp556iq1bt5Kens6uXbu4++67ycrK4pZbbmlw/xdDkhEhhMP8evwYGl0pqBouaX3xE1f/qqN/N1SLF8dPuXYPhOZu+vTpaLVa4uLi7I8Y7r33Xm666SbGjh3LgAEDOHXqFPfff3+NenfffTd33XUX48ePZ+jQocTExNiXsDrS888/T1paGh07diQszLbnTK9evVi/fj0pKSkMGTKEhIQEnn32WVq3rt+E4Tlz5jBnzhzi4+PZuHEjy5Yts0/abNOmDT/++CPbt28nPj6e++67j0mTJvH000/X2lZYWBgLFy7k66+/Ji4ujjlz5jB37twaZdq0acPs2bN58sknCQ8PtydNc+bMYcyYMYwbN44+ffpw9OhRVq1aRVBQUIN/Ts8++ywJCQnMmjULo9FIQkICCQkJ7Ny5014mOjqa5557DrBNUj506BBjxoyhc+fO9hVFGzZsoHv37g3u/2Io6l8f+DVCJSUlBAQEUFxcjL+/455BCyEca8YPn7Py1Ev4Ku3YMn65w9vfkZ7DLQt2EuhtYM8zV17QScDOVFlZSWpqKh06dLCv5hCNS1paGh06dGDPnj3NYlv6higvLyckJIQVK1YwbNgwh7V7rj/39f39LSMjQgiHOX2qE8aUp/lbmxnnL3wB4tu0wqDVUlRuJqOw3Cl9CNFcrV27lssvv9yhiYijSDIihHAIVVVJyixGtfhyRSfnbMpk0Gno1tr26WpPxmmn9CFEc3XdddexfLnjRywdQZIRIYRDnCyupMBYhVaj0L11gNP68Qxdg0/HV/ju6LdO60M0X9HR0aiq2uIe0TR2kowIIRxizZH9eEV9SGT7TXjqteevcIGC/RQ0htMcLTnotD6EEK4lyYgQwiE2ZO5E53sErU+KU/sZHJUAQJHlGGbLuTfGEkI0DZKMCCEc4nCRbaSic4BzN2u6vMPv22IbcvntpGu3rBZCOIdsBy+EuGgWq0qh+SiKFhLb9j5/hYNLYcPrYK7AbLRSkW3bldKzZwKG8e+Aoe6tzCN9I9CpAVQrxfx8dA99o65x0LsQQriLJCNCiIt2KLcQPGzbgo+IOfeBXpbNH6GsfAyNxvaIpTLLg6wNIbabq7fQ9vi1+M36ATx862wj0rMzmVU72JmzF5BkRIimTh7TCCEu2k9H9qAoFrSqL1H+Z5/dcYZl/btkPPYvsjYGova8AyYsR/u31/CO74JHu3CwKpz4NoeSZ66GyuI62+kR2gOAdOMhh78XIYTrSTIihLhoO7KTAAj3iK1zV9Tqn+eT/sRcKk8bqCjxx9z3cYgejPe1d9H+y+/o8OPP+F8xEFSFrO8LKH7qaqiofS+RKzr0x1LRluLiIMqqqp31tsR5pKWloSgKSUlJdZZZt24diqKc88waRVH47rvvHB6fK9XnfYq6STIihLhomUXFqBZP4oJ71Hq/euVcMv75b6qK9Gj9PGj/+f8wREfXKKPodLR+6z0Crh4KqsLJH09T+uxIKC88q72RHQfjXzidqoIR7M+qewRFOFdUVBTZ2dn06FH7//f6ys7O5ppr6v+4beHChQQGBl5Un43BsGHDeOSRR5zW/oEDBxgzZgzR0dEoisK8efPOW2fdunXceOONREZG4uPjQ+/evVm8eLHTYjzjgpKRd955h+joaDw9PRkwYADbt28/Z/l58+bRpUsXvLy8iIqK4tFHH6WysvKCAhZCNC6VZgvZ6YkYU55lat9/nHXfmrKR9GffpapYjy7Ai/ZffoNHbGytbSlaLZFv/IfAUVfiGarirU+B5dNqLRsfZdtYbe+JIoe9F1F/JpMJrVZLREQEOt3FTT+MiIjAw8PDQZHVn8ViwWpt+svDTSZTrdfLy8uJiYlhzpw5RERE1KutzZs306tXL5YsWcJvv/3GxIkTGT9+PD/88IMjQz6b2kBffPGFajAY1I8++kg9cOCAOnnyZDUwMFDNzc2ttfzixYtVDw8PdfHixWpqaqq6atUqNTIyUn300Ufr3WdxcbEKqMXFxQ0NVwjhZDvTCtX2T/yg9n3hJ9Vqtda8abWq+ZMuVQ926aqmXNJLrUpNrVebVqtVrT6ySVVnBajqLH9VPbHrrDLvrD2itn/yW3XSJz9f/JtwkIqKCvXgwYNqRUWFu0NpkJKSEvX2229Xvb291YiICPWNN95Qhw4dqj788MP2Mu3bt1eff/55ddy4caqfn5961113qampqSqg7tmzx15u+fLlamxsrOrp6akOGzZM/fjjj1VAPX36dJ39A+q3336rqqpqb3PJkiXqsGHDVC8vL7VXr17q5s2bVVVV1bVr16pAjdesWbNUVVXVyspK9bHHHlNbt26tent7q/3791fXrl1r7+fjjz9WAwIC1KVLl6rdunVTtVqtmpqaqt51113qjTfeqD733HNqaGio6ufnp957771qVVWVvW5lZaX64IMPqmFhYaqHh4c6aNAgdfv27fb7Z+I68z4LCgrUv//972rr1q1VLy8vtUePHupnn31mL3/XXXed9T5Sf//7sW7dOvWSSy5RDQaDGhERoT7xxBOq2Wy21x06dKj6wAMPqA8//LAaEhKiDhs27Lz/j9u3b6+++eab5y1Xm2uvvVadOHFinffP9ee+vr+/Gzwy8sYbbzB58mQmTpxIXFwc7777Lt7e3nz00Ue1lt+8eTODBg3i9ttvJzo6mquuuorbbrvtvKMpQoimISnD9hglvm3gWfNFrPt/4NR22/1W06ef9WimLoqioO00EHqNBaB62TNnlTF57MS3yyx2lb13EdG7Rrm5vM5XlaWq3mUrqyvrVbahpk2bxqZNm1i2bBmrV69mw4YN7N69+6xyc+fOJT4+nj179vDMM2f/P8nMzOSmm25i1KhRJCUl8Y9//IMnn3yywfEA/POf/2T69OkkJSXRuXNnbrvtNqqrqxk4cCDz5s3D39+f7OxssrOzmT59OgBTp05ly5YtfPHFF/z222/ccsstXH311Rw5csTebnl5Oa+88goffPABBw4coFWrVgCsWbOG5ORk1q1bx+eff84333zD7Nmz7fUef/xxlixZwqJFi9i9ezedOnVi5MiRFBae/RgRbCfZ9u3bl+XLl7N//37uuecexo0bZ//dN3/+fBITE5k8ebL9fURFRZGVlcW1117LJZdcwt69e1mwYAEffvghL774Yo32Fy1ahMFgYNOmTbz77rsX9DOur+LiYoKDg53aR4NGRqqqqlStVmvPYM8YP368esMNN9RaZ/HixWpAQIC6bds2VVVV9dixY2rXrl3Vf/3rX3X2U1lZqRYXF9tfmZmZMjIiRCN1wyfPqXHvXaZO/vbNmjcs1ar6TqJa+UiwmjPlBtVqsTS47er0/WrmlR3Uwz07q9V7vq9xb/OJXWqPhT3UuA8GqHkljWMkoq5PiD0W9qjzNWX1lBplL/n0kjrLTlgxoUbZIZ8PqbVcQ5SUlKh6vV79+uuv7deKiopUb2/vs0ZGRo8eXaPuX0dGZs6cqcbFxdUo88QTT1zQyMgHH3xgv3/gwAEVUJOTk1VV/WOE48/S09NVrVarZmVl1bh+xRVXqDNnzrTXA9SkpKQaZe666y41ODhYLSsrs19bsGCB6uvrq1osFtVoNKp6vV5dvHix/b7JZFJbt26tvvrqq6qqnj0yUpvrrrtOfeyxx+zf/3X0SVVV9amnnlK7dOlSY5TxnXfescdypl5CQkKd/dTmQkdGvvzyS9VgMKj79++vs4wjRkYa9KCvoKAAi8VCeHh4jevh4eEcOlT7Ervbb7+dgoICBg8ejKqqVFdXc9999/HUU0/V2c/LL79cIyMVQjReJ8oPo/EoJCLQUPPGvq8h7wAe4QGEP7wQNA2foqZp0xWTORSLqZRTc5+l1X+vtbfTJ6I7qFo0ujLWHT/MLfHxDng3Lc/x48cxm83079/ffi0gIIAuXbqcVbZfv3PvIZOcnMyAAQNqXEtMTLyguHr1+uPk58jISADy8vLo2rVrreX37duHxWKhc+fONa5XVVUREhJi/95gMNRo+4z4+Hi8vf/YbC8xMRGj0UhmZibFxcWYzWYGDRpkv6/X6+nfvz/Jycm1xmOxWHjppZf46quvyMrKwmQyUVVVVaOP2iQnJ5OYmFhjlHHQoEEYjUZOnDhBu3btAOjbt+8523GEtWvXMnHiRN5//326d+/u1L6cvunZunXreOmll/jPf/7DgAEDOHr0KA8//DAvvPBCrcN8ADNnzmTatD8mrZWUlBAVFeXsUIUQDVRUbqJSk44GGBHzp38cq6uo/uFF2z8wgx8Fr6ALal/Ragl7/J+cePRJCveUE/TrQvTD7gbAQ+uBv6YdJWoqv6bvbtTJyLbbt9V5T6upeajgulvX1VlWo9RM6FaOWXlRcTWUj4+Py/rS6/X2r8/8Yj7XZFOj0YhWq2XXrl1otTV/pr6+f2yg5+XlVefyc0d67bXXmD9/PvPmzaNnz574+PjwyCOP1DnZtKGc/f9i/fr1jBo1ijfffJPx48c7tS9oYDISGhqKVqslNze3xvXc3Nw6Z+o+88wzjBs3jn/8wzbLvmfPnpSVlXHPPffwz3/+E00tn5Y8PDzcMrNaCNEwG44fRaMvAVVDv8ie9uuV37xC6uJqAmIjiXziH1zMP/2+V9+A1ztvUnE0l4L5rxM5+E7Q2UZhYvy7klScSnLh/ot8J87lrT/3p2FXlK1LTEwMer2eHTt22D91FxcXk5KSwmWXXdagtrp168ayZctqXNu6detFx/hXBoMBi8VS41pCQgIWi4W8vDyGDBnS4Db37t1LRUUFXl5egC1uX19foqKiCA0Ntc/PaN++PQBms5kdO3bUuTR306ZN3Hjjjdx5552ALZFKSUkhLu6Ps5tqex/dunVjyZIlqKpqT5o2bdqEn58fbdvWvaGgI61bt47rr7+eV155hXvuucclfTZo3NRgMNC3b1/WrFljv2a1WlmzZk2dQ3Hl5eVnJRxnslZVVRsarxCiEdmcuRcAb6X1H78YK4vJf/9TsCpYA7qiePldVB+KotDqmX8BUHTIQtXyN+33+kbYhtvzTccuqo+WzM/Pj7vuuosZM2awdu1aDhw4wKRJk9BoNA0eQbjvvvs4cuQIM2bM4PDhw3z22WcsXLjQ4TFHR0djNBpZs2YNBQUFlJeX07lzZ+644w7Gjx/PN998Q2pqKtu3b+fll19m+fLl523TZDIxadIkDh48yI8//sisWbOYOnUqGo0GHx8fpkyZwowZM1i5ciUHDx5k8uTJlJeXM2nSpFrbi42NZfXq1WzevJnk5GTuvffesz7IR0dHs23bNtLS0igoKMBqtXL//feTmZnJgw8+yKFDh1i6dCmzZs1i2rRptX54P997SkpKIikpCZPJRFZWFklJSRw9erTOOmvXruW6667joYceYsyYMeTk5JCTk1PnRF1HafBD3GnTpvH++++zaNEikpOTmTJlCmVlZUycOBGA8ePHM3PmTHv5UaNGsWDBAr744gtSU1NZvXo1zzzzDKNGjTprKE0I0bQkFx4GoLV3R/u18k9mYczUggJhs+Y6pB/vAYPwTegIqkL+go/AZFsxMri97dGMRZtNobHqXE2Ic3jjjTdITEzk+uuvZ8SIEQwaNIhu3brh6enZoHbatWvHkiVL+O6774iPj+fdd9/lpZdecni8AwcO5L777mPs2LGEhYXx6quvAvDxxx8zfvx4HnvsMbp06cLo0aNrjPicyxVXXEFsbCyXXXYZY8eO5YYbbuC5556z358zZw5jxoxh3Lhx9OnTh6NHj7Jq1SqCgmp/BPn000/Tp08fRo4cybBhw4iIiGD06NE1ykyfPh2tVktcXBxhYWFkZGTQpk0bfvzxR7Zv3058fDz33XcfkyZN4umnn27wz+nkyZMkJCSQkJBAdnY2c+fOJSEhwf6kAmwbyP056Vy0aBHl5eW8/PLLREZG2l833XRTg/tvkAZPrVVV9d///rfarl071WAwqP3791e3bt1qvzd06FD1rrvusn9vNpvV5557Tu3YsaPq6empRkVFqffff/85Zxz/lewzIkTjdMl749UeC3uoT/78lu1CtUlNv7yzerBLV/Xk1HEO7avy0EH1YNeu6qEenVXzettKi8rqSjVhwQS10ysz1F9Tchza34VoqvuM/JXRaFQDAgJqrGhpzs7sM9ISPfvss+rQoUMvqg2Xr6Y5Y+rUqUydOrXWe+vWravxvU6nY9asWcyaNetCuhJCNFJmi5XS0iAU77YMjLKNUJg3f0VZlu1TVshjjl0R59GlG+0evQavjI/QHP8WLpuEh9aDvt4PsDotl6N55QypfWNXcR579uzh0KFD9O/fn+LiYp5//nkAbrzxRjdHJpxtxYoVvP322+4OQ86mEUJcmNSCMiryrkST/QjXdbJNGCxa/CGg4B0bhiG6g8P79Bk7DY0OSNsAhccB6BZhm5NyKLvU4f21JGc2NBsxYgRlZWVs2LCB0NBQd4clnGz79u01lnW7i9OX9gohmqfk7BIAukT4odEoUJpLye5MQEfg2Nud02lAW+h4OerRNVi3LER73fPERvigMeSRlHcKOHv/CHF+CQkJ7Nq1y91huI0zJtmKhpGRESHEBfntZA5QTdffRyb47UuiR+QTMSIAvzF3Oa3fMsMgjq8I4+T8r8FqoVyzH5+Ob5Cl+wSLVVboCdEUSTIihLgg6/IW49v1WYoNP4Gqwp5P0RpUgibeh+b3vRqcQdf7WkwleoyZKtW7ljKo/e+jIYY8juYXOa1fIYTzSDIihLggp0xpKIqVTiERqJk7oOAw6Lygu3OXAHp06YZXdBCoCsWfvksb30g0qheKYmVj2kGn9i2EcA5JRoQQDXa6rAqzNguAQe16UvTuHFJ/CqVEHQSe/k7vP+DmWwAo2pIK5YUEaG37SOzOlmREiKZIkhEhRINty0xHoysHVaFXUFuKft1PZaEBs7dzD9M6w//vk1F0YCrRUfHdW7TztW26dqT4yHlqCiEaI0lGhBANtjVjHwCeSgTqz59QWaAFDQSMf9Al/Wt9ffG/1HbGR/G3S+nRynaSa35Vqkv6F0I4liQjQogGO3DKtg18hGcHir/6HADfXu3QhYW5LIbAux4AoORQBUO0tl0KTJosSivNLouhpUtLS0NRFJKSkuoss27dOhRFoaioqM4yiqLw3XffOTw+V6rP+xR1k2RECNFgJ8psG4718Ayl+DfbAVqBd052aQxeg4cTdGkEbQcX0jt/F7qSkVTl3sjhnBKXxtGSRUVFkZ2dTY8ePS6qnezsbK655pp6l1+4cCGBgYEX1WdjMGzYsDpP/XWEAwcOMGbMGKKjo1EUhXnz5p23zuHDhxk+fDjh4eF4enoSExPD008/jdns3CRfkhEhRINYrCrFhe0xF8dz7eEMLFVatD5afK8e7dI4FEUh4qmZ+ESY8Dm8gnjvm6ku7cGhHKNL42ipTCYTWq2WiIgIdLqL2z8zIiICDw8PB0VWfxaLBavV6vJ+Hc1kMtV6vby8nJiYGObMmUNERES92tLr9YwfP56ffvqJw4cPM2/ePN5//32nH+kiyYgQokEyCsspL+yDmncHHXfYVq/4J/ZEuchfSBckZigY/MCYw3D/TAAOychIg5WWlnLHHXfg4+NDZGQkb7755lmf2qOjo3nhhRcYP348/v7+3HPPPbU+pvnxxx/p3LkzXl5eDB8+nLS0tPP2/+fHNGfa/Oabbxg+fDje3t7Ex8ezZcsWwPY4ZOLEiRQXF6MoCoqi2E/XraqqYvr06bRp0wYfHx8GDBhQ47y0MyMqy5YtIy4uDg8PDzIyMpgwYQKjR49m9uzZhIWF4e/vz3333Vfjl3xVVRUPPfQQrVq1wtPTk8GDB7Njx44639OpU6e47bbbaNOmDd7e3vTs2ZPPP//cfn/ChAmsX7+e+fPn29/HmZ/V+vXr6d+/Px4eHkRGRvLkk09SXV1trzts2DCmTp3KI488QmhoKCNHjqw1hksuuYTXXnuNv//97/VO9mJiYpg4cSLx8fG0b9+eG264gTvuuIMNGzbUq/6FkmRECNEgh37fBn5AmBnfgBP4ta3A7+bx7glG50Gl70DykvyI37cErW8yO3M3uSeWc7CWl9f9qqqqf9nKynqVbahp06axadMmli1bxurVq9mwYQO7d+8+q9yZ82v27NnDM888c9b9zMxMbrrpJkaNGkVSUhL/+Mc/ePLJJxscD8A///lPpk+fTlJSEp07d+a2226jurqagQMHMm/ePPz9/cnOziY7O5vp06cDtkNct2zZwhdffMFvv/3GLbfcwtVXX82RI3+ssiovL+eVV17hgw8+4MCBA7Rq1QqANWvWkJyczLp16/j888/55ptvmD37j8MeH3/8cZYsWcKiRYvYvXs3nTp1YuTIkRQWFtYaf2VlJX379mX58uXs37+fe+65h3HjxrF9+3YA5s+fT2JiIpMnT7a/j6ioKLKysrj22mu55JJL2Lt3LwsWLODDDz/kxRdfrNH+okWLMBgMbNq0iXffffeCfsb1cfToUVauXMnQoUOd1gcAF3VusIvU9whiIYTzzV6xSY1+eqH65bvPqeosf1V9b7hb48l76j71YJeu6o5r49QeC3uo3f/vatVqtbollrqOUj/YpWudr/R77qlRNrl3Qp1l0+4cV6Ps4UsTay3XECUlJaper1e//vpr+7WioiLV29tbffjhh+3X2rdvr44ePbpG3dTUVBVQ9+zZo6qqqs6cOVONi4urUeaJJ55QAfX06dN1xgCo3377bY02P/jgA/v9AwcOqICanJysqqqqfvzxx2pAQECNNtLT01WtVqtmZWXVuH7FFVeoM2fOtNcD1KSkpBpl7rrrLjU4OFgtKyuzX1uwYIHq6+urWiwW1Wg0qnq9Xl28eLH9vslkUlu3bq2++uqrqqqq6tq1a8/7Pq+77jr1scces38/dOjQGj9jVVXVp556Su3SpUuNP8PvvPOOPZYz9RISEurspzbt27dX33zzzXqXT0xMVD08PFRAveeee+x916auP/eqWv/f3zIyIoRokE253+HbaS57lZW2C12vc2s8vjdPAMAnzYLerII+h/RTcoJvfR0/fhyz2Vzj5NaAgAC6dOlyVtl+/fqds63k5GQGDBhQ41piYuIFxdWr1x+HHkZGRgKQl5dXZ/l9+/ZhsVjo3Lkzvr6+9tf69es5duyYvZzBYKjR9hnx8fF4e3vXiNtoNJKZmcmxY8cwm80MGjTIfl+v19O/f3+Sk5NrjcdisfDCCy/Qs2dPgoOD8fX1ZdWqVWRkZJzzfScnJ5OYmIiiKPZrgwYNwmg0cuLECfu1vn37nrOdi/Xll1+ye/duPvvsM5YvX87cuXOd2p+c2iuEaJC8qjQwqAzflospUIuh6yi3xuPZuz86fz3VJWYSUhW2d65mY/phokMvcWtcf9Zl9zlOxNVqa3zbedPGustqan5+7LTm54sJq8F8fHxc1pder7d/feYX87kmmxqNRrRaLbt27UL7l5+pr6+v/WsvL68av+id5bXXXmP+/PnMmzePnj174uPjwyOPPFLnZNOGcvb/i6ioKADi4uKwWCzcc889PPbYY2f9bB1FRkaEEPVmrKrGpMkiKh/abPLg+MpwrL5Rbo1JURT8Lu0JwPBDtl9WO08ecGdIZ9F4e9f9+svEwnOW9fSsV9mGiImJQa/X15iMWVxcTEpKSoPfZ7du3exzIs7YunVrg9s5H4PBgMViqXEtISEBi8VCXl4enTp1qvGqz0qSvXv3UlFRUSNuX19foqKi6Nixo31+xhlms5kdO3YQFxdXa3ubNm3ixhtv5M477yQ+Pp6YmJizfqa1vY9u3bqxZcsWVFWt0Zafnx9t27Y97/twBqvVitlsdurKI0lGhBD1tiszE42+hP4ptn8ofbq1duoJvfXl97c7AehxzILGqpJS1PBfpC2Vn58fd911FzNmzGDt2rUcOHCASZMmodFoGjyCcN9993HkyBFmzJjB4cOH+eyzz1i4cKHDY46OjsZoNLJmzRoKCgooLy+nc+fO3HHHHYwfP55vvvmG1NRUtm/fzssvv8zy5cvP26bJZGLSpEkcPHiQH3/8kVmzZjF16lQ0Gg0+Pj5MmTKFGTNmsHLlSg4ePMjkyZMpLy9n0qRJtbYXGxvL6tWr2bx5M8nJydx7773k5uae9T62bdtGWloaBQUFWK1W7r//fjIzM3nwwQc5dOgQS5cuZdasWUybNg2NpmG/sk0mE0lJSSQlJWEymcjKyiIpKYmjR4/WWWfx4sV89dVXJCcnc/z4cb766itmzpzJ2LFja4xWOZokI0KIetucsR+AgSm2T0h+I+u/UZUzeQ+5Eo2ngkelQpcTkFsh28I3xBtvvEFiYiLXX389I0aMYNCgQXTr1g3Pv4zEnE+7du1YsmQJ3333HfHx8bz77ru89NJLDo934MCB3HfffYwdO5awsDBeffVVAD7++GPGjx/PY489RpcuXRg9ejQ7duygXbt2523ziiuuIDY2lssuu4yxY8dyww032JcMA8yZM4cxY8Ywbtw4+vTpw9GjR1m1ahVBQUG1tvf000/Tp08fRo4cybBhw4iIiGD06NE1ykyfPh2tVktcXBxhYWFkZGTQpk0bfvzxR7Zv3058fDz33XcfkyZN4umnn27wz+nkyZMkJCSQkJBAdnY2c+fOJSEhgX/84x/2MgsXLqyRdOp0Ol555RX69+9Pr169mD17NlOnTuWDDz5ocP8Noah/HgtqpEpKSggICKC4uBh/f+efCCqEqN3tX73GyZxFLPiPBRSV2A0b0YWGujssAE5OvIGiPYeZd7WOTZ2C2XXXOjz1znm+XZfKykpSU1Pp0KFDg3+RNyZlZWW0adOG119/vc5P/s3JhAkTKCoqavJb0l+IWbNmsX79+hr7sTTUuf7c1/f3t4yMCCHqLaP0mP0RjXeH4EaTiACEP/s87W7M5bqQIjSZt5KSKytq6mvPnj18/vnnHDt2jN27d3PHHXcAcOONN7o5MuFsK1assI8suZOsphFC1IuqqpTm9+D6g+sABd/Lh7k5opq0HXrjG9aZGwsOs8acQ0qukV5tA90dVpMxd+5cDh8+jMFgoG/fvmzYsIHQRpRsCuf464Rjd5FkRAhRL/mlVXQ9VUF4vooVBb8x/zh/JVfreh3qhsNcY9pKUu6d7o6myUhISGDXrnMsP27mnDHJVjSMJCNCiHpJyTUy3GMvsTfmUuF7OYYOMe4O6Szl1i6kLwsn1PsE27uvBLq5OyQhRD3InBEhRL1sP5FCsM9uCjw0+Fx/h7vDqZWh75WolVp8T2lQ8pe5OxwhRD1JMiKEqJekrGW80FrL3OAg6HiFu8OplS4kBGs7226bXTIKKKuqPk8N52gCixSFcBhH/HmXZEQIUS+tDm3l1Q+rGbjbF7wC3R1OnUIG2s5G6ZZuYU9Wlkv7PrNVtqO2/BaiKSj//aToi9kUTeaMCCHOS1VVotMLiM6D4taB7g7nnAJH3UnR52voka6y+dA6Bsfc5bK+dTod3t7e5Ofno9frG7xjphBNiaqqlJeXk5eXR2Bg4EWdWyPJiBDivHKKSumYbjtDI3DocDdHc26evftT5gU+FaDuXAbXui4ZURSFyMhIUlNTSU9Pd1m/QrhTYGBgvc7/ORdJRoQQ53Vgw2dE/356e4eb7nVvMOehaDTkdPSj4/5SQlKOu7x/g8FAbGysPKoRLYJer3fISb6SjAghzqv8V9vKlMxwhW7hkW6O5vxKB13CUt+1nI4u53ZLNWhd+0+dRqNp0tvBC+Fq8kBTCHFe3ikZAGTGBLo3kHoacOdTDOls5Fkll4q0xrHDpBCibpKMCCHOSS3Np026GQCPAde5OZr6iQlrQ5m5Oz6qSvG+Fe4ORwhxHpKMCCHOyXJgFQGRleALfa+9z93h1Fu6dz+MJz2o/mmlu0MRQpyHJCNCiHMyZ26g9aVFbLg6gQ6Rge4Op95OV5vJ/DWEos0lqMYCd4cjhDgHSUaEEHVTVU6n/cJnfr5sC2qHp/7iZ827ytGueioMoK3UUPnL5+4ORwhxDpKMCCHqZE3bxbGCcuaEBHEgdK+7w2mQuMhu7G+vAFC2Rh7VCNGYSTIihKhT2Q+fErrUn9mfWgj3jHZ3OA1yads4kmJsyYhx7zGQ82KEaLQkGRFC1Mm4eQsAqeEKHYM6uTmahukV3pm9HWzJSEUuWFJ3uTkiIURdJBkRQtRKrTJSlnIagL0dFHqHd3VzRA3jrffmdGAY2UGAqlD+42J3hySEqIMkI0KIWpk2f4e5TItZCwfaKwxsF+fukBosxNDO/qimYuc2N0cjhKiLbAcvhKhV2c/fA3CorUKV3kCHgHZujqjhov1iWH7JLrxjjdyrLQRzJehlm3YhGhsZGRFC1KosKRmAfdEKPkprtJqms6z3jL93uZNj+c9wM6BYKuGEbA0vRGMkyYgQ4ixqSS7lGVUAJHtcy+DgCe4N6AL1bRsFFl82WH5/xJT6q3sDEkLUSpIRIcTZUjfQdlAhuh4adnsO4bJ2A90d0QUJ9DYQ5udBSkEbTmwKIueDpe4OSQhRC0lGhBBnUTI24hNhYmuPXlg1WjqH+7o7pAsWGLmBvYHHKc30ouRgMWpFsbtDEkL8hSQjQoizpa7HAiwKqMIQtJ22QQZ3R3ThPNM41CkXixYslVpMm75zd0RCiL+QZEQIUYM17xi5awpIy/UhLzAFj/Dv8TY03WQk2i8Gs04hq7UegLJffnRzREKIv5JkRAhRQ8XqLyk87Ev5tkBUBXyU1miUpvtPRY9WnQHY3c4DgLK9ye4MRwhRi6b7L4wQwinKN60HILOdDygKEV7t3RzRxbm0rW0lzbYOVgDKM6pQS3LdGZIQ4i8kGRFC/EFVKTuQDsCOKNuk1Y6BTetMmr/qFd4ZVIXjbarAAFazhspfvnR3WEKIP5FkRAhhZ834jYo829e/trNto947vLMbI7p4XjovDISiahRKOgTiGWzCmrbD3WEJIf5EkhEhhF35T1+AqqAL0JEbajskLzGqu5ujunjB+ihUiyerxgyhw1UF+Gj2uzskIcSfSDIihLAr27wZgPLY1iiaalD1dAiMcnNUF+/2Dk9hTJlFTvW1oGih8DgUZbo7LCHE7yQZEULYWC1UpWcDcLpLIsaUf9JDeaJJnknzV3ERoYDCvgIrtOmDxaxQ/dsKd4clhPidJCNCCJucfUQNySVmdBnrOl6JavGjT0S8u6NyiNhwPwAyCyvI2R9IyjcRnP78f26OSghxhs7dAQghGonU9SgKePQayMES2+eU2FZ+bg7KMQK8tPi3/xSLLpu8U5eiVw9QdiCDMFUFRXF3eEK0eDIyIoSwOW7bX0TtMIRD5k8xhK0gyL/MzUE5hlajReeZjcZwis2dugJQkQ+WjL1ujkwIAZKMCCEAqk2kvbePE5uCyKcjVt8teISuJyKw+QyeBhtsE3F3aErQB+pBVShfJfuNCNEYSDIihMD82xoq8nWUnvBkuyYARWMGVUfHoHbuDs1h2vl1ACC99Dg+PWxfl2/d4s6QhBC/k2RECEH5z98B4Bnpw44S25JXbyUCnab5jIzEhdo2bztlysR78HAAyg9ng9XqzrCEEEgyIoQAynYmAeDdO47DhUcBCPNo2mfS/FX/Nt0AMGmy0V5+EwCVpxQsx2U3ViHc7YKSkXfeeYfo6Gg8PT0ZMGAA27dvP2f5oqIiHnjgASIjI/Hw8KBz5878+KMc4y1Eo1BdRflx226rPsOvIassDYCYgI5uDMrx+kR2AUCjK+WAqhDUL5DwvsWQsdXNkQkhGpyMfPnll0ybNo1Zs2axe/du4uPjGTlyJHl5ebWWN5lMXHnllaSlpfG///2Pw4cP8/7779OmTZuLDl4IcfHMu1ZhNmpBUfEafgPFlhMAxId3cXNkjuVr8MVgjcRS0Zb9OdlE3HsLwbHlaPPO/WFKCOF8DX4g/MYbbzB58mQmTpwIwLvvvsvy5cv56KOPePLJJ88q/9FHH1FYWMjmzZvR6/UAREdHX1zUQgiHKVuzDACvtn4UoceiKUIDJLbr5t7AnOCqgLl8vj2Twg7+0P0y28W0jbZ5Ixp5ai2EuzTob5/JZGLXrl2MGDHijwY0GkaMGMGWLbXPSl+2bBmJiYk88MADhIeH06NHD1566SUsFkud/VRVVVFSUlLjJYRwDk3xETxDTPj07cnRPCNlR57CL28WXYJj3B2aw3X+fSfWI7lGiOyNqdKf0/tNWI7Ioxoh3KlByUhBQQEWi4Xw8PAa18PDw8nJyam1zvHjx/nf//6HxWLhxx9/5JlnnuH111/nxRdfrLOfl19+mYCAAPsrKqrpH9QlRKNkrsDf9yAdriwg9LGZHMkzAgpdQts1izNp/urMjrJH8kpAqyNzYwg5OwMp++lrN0cmRMvm9HFJq9VKq1ateO+99+jbty9jx47ln//8J++++26ddWbOnElxcbH9lZkpp2sK4RSZ28FiAr9IlNBOHM0zAn+c5dLcePkU4t3hTfICnqOq2oJPr04AlG+XFTVCuFOD5oyEhoai1WrJzc2tcT03N5eIiIha60RGRqLX69Fq//iU1a1bN3JycjCZTBgMhrPqeHh44OHh0ZDQhBAXwLxnFRqzgjZ6CCgKGwo+xbNNGnqfO4HmN2ckNiQCraft36/92TnEDhnB6V8OUJaSD1YLNMPRICGaggaNjBgMBvr27cuaNWvs16xWK2vWrCExMbHWOoMGDeLo0aNY/7SxUEpKCpGRkbUmIkII18n7dJXtBNujPgDkW35D77+fAF+TmyNzDn8Pf3TWIAC2ZCbjfdXNAJiKNVQf+NWdoQnRojX4Mc20adN4//33WbRoEcnJyUyZMoWysjL76prx48czc+ZMe/kpU6ZQWFjIww8/TEpKCsuXL+ell17igQcecNy7EEI0mFpVRnlaKagKhj5DOV1WhVVrm/uVGBXn5uicJ1DfFoD9eYfRhYTiEe4JQPnP37gzLCFatAYv7R07diz5+fk8++yz5OTk0Lt3b1auXGmf1JqRkYHmT0vkoqKiWLVqFY8++ii9evWiTZs2PPzwwzzxxBOOexdCiAYzbV1GdYUWRQteQ65hY1oqitYEqoauoc1vJc0ZbX2iKSjZR2pJKgA+vbpQtXovZTt24e/m2IRoqS7o4ImpU6cyderUWu+tW7furGuJiYls3SpL54RoTMp/se2C7NU+AI2nJztOHgTAkwj0Gr07Q3OquNDOJJVAQVUGAN5Dr6Rw9V7KjxWApRq0zec8HiGaCtnlR4gWqizpAADefeIBOFRgO5Mm1KN5L6W/5PczaiqVk5iqrXhfdQttr6gi+oo8yE5yb3BCtFCSjAjRAqmVJZSn2Zbx+oy4AYDMMttjiw7+zetMmr+6pE1X1KpILOXRHMsvRuvvj9+QRLQGFVJlEqsQ7iDJiBAtkGnjd1iqbPNFPAdeCUBJZRWqVUfPVrFujs65AjwC6GSeReXJ2ziWX2G7GD3E9t+0De4LTIgWTJIRIVogbekBIvoWEXJ5BzQGA8UVZk6nj8F4+HlujbvW3eE5XedwX+D3beGB6qB48n7z48Snv0F181zWLERjJsmIEC2QLn87QbHlhP1jPABHcksBiAzwJsTH252huYTtjBorB3KyAVAiu3Mq2ZfSdAPmpJ/dG5wQLZAkI0K0NJXFf0zU/P3xRMrvIwSdm+k28H9VrkvCt8ss9lS+DYDW3x/P1rbRkrI137kxMiFaJklGhGhhTNu+5/QRT0yaaAhoA8CP6V/j3WE++G90b3Au0iMiCkVjplI5SVW17QRxn962jd7Kdya5MTIhWiZJRoRoYYwrvydnZyA5O/8YBUk3HkbrmY2/t9mNkbnOJa27AqDRl/DbSdujGu/h1wBQfrwIqqvcFZoQLZIkI0K0MGV7DwHgfUkf+7Vii+1k7Pjwrm6JydX8PPzQWYMB2Jzx+34rw0aBomIu02LaucKd4QnR4kgyIkQLopbmU55ZCYDPlX8DIL+0AqvOdpLt4PY93BabqwUb2gGwL/8wABpfX7yibKNF5Wu+d1tcQrREkowI0YJUrl+C1axBowfPfrbJq5vTj6BozKDqiA2Odm+ALtTOtwMAaSXH7Ne8E3qgNVixnjzsrrCEaJHkEAYhWpDyX23LVr07haHobH/9d2Un264prdFqtG6LzdV6hHVhZxGcMmXYr4U++Bhhnt+g6ArBXAF6L/cFKEQLIiMjQrQgZb+lAODd/xL7teRTtmvhnu3dEpO7XBadgLmkO2VFsVSYbCtqNG26o/hHgsUEmdvdHKEQLYckI0K0EGppPhUnbatEfK68yX79dKmCpSqMzkFd3BWaW1zSOg6fokmYTg3laJ5tnxUUBaIHo6pgTVnr3gCFaEEkGRGihVAyN9Pp+lzaXu+NR8KlAKiqSv7J/pQff4yJPSa4N0A3iP19W/iU33egBSgtCOfo963IflcmsQrhKpKMCNFSpG5Aa1Dxu/xyFK1tbkh+aRXFFWY0CnQM83VzgK7XuZUviq6YPSdT7de0nQZQXa6jLM2IWmV0Y3RCtBySjAjRUpw5kfbMCbXAwZwiQCU6xAdPfcuZvHpGvm45vrEvs+nUl/ZrnoNHomjBUqnBtHmpG6MTouWQZESIFkA9nUX6l/nk7fXHGt7Pfn3F8dX4dp6FEvaVG6Nzn7iwjgCcNv+xokbj4YFXdCAAZb/I5mdCuIIkI0K0ABVrvqI8z4OiND+UoAj79ZTCoyhaEwFeejdG5z6D2nUHoFp7kpIKk/26T9/eAJQnHXBHWEK0OJKMCNEClG+0rQzx7hyJovnjr312hW2uRGxQJ7fE5W49W8WCqkHRVrE98495I94jbgCgPL0ctaLYXeEJ0WJIMiJEC1C2z7bLqPeAS+3XVFXFaD0BQN/W3dwSl7vptXo8sY0Ubc/6YxTEK3EEig4sJg1VG751V3hCtBiSjAjRzFnz06nIsW3q5TPyFvv1tMJi0BcAMCiq5ZxJ81ehHrYzag7kH7FfU/R6Avu3JaizEU1+kpsiE6LlkGREiGau4qfPUS0KWh8Nhrh4+/VNackoiopi9aa1X7gbI3SvmADbJNYTZcdrXI94ZDIRfUowGHe7IywhWhRJRoRo5so2rQfAp1tbFEWxX9+dYzuTxk9b83pLM6TtQEynLsNYGFfzRofLbP/N/g3KC10fmBAtiCQjQjRnqopSlI7WYMFn4JAatwpKdFSXdqWTb2/3xNZIXNc5kaq8azmV34nicvMfN/wisAZ2pixXj2n7MvcFKEQLIMmIEM3Z6VTCOmcRO6aQgLum1rxVEEPFiQnc1vkfbgqucfDz1NMm0HY6b0peaY17J7f4kbE2lJKl37khMiFaDklGhGjOjtse0Sjt+qP4BNovW60qR37/xds53M8dkTUqMeGg9T7OtowjNa579x8AQNm+o+4IS4gWQ5IRIZoxy4FfUFX+mP/wu9RTJVRZizHoFNqH+LgnuEakyOt/eLd/jw3Zq2tc97n6VgAqsqux5qe7IzQhWgRJRoRorqxW0v9vO0eXhVNR2bbGrbWpSfh2/hc+MW+i1bTcyatndAy0bfqWVZZa47ohrjc6Hw2qRaHip8/cEZoQLYIkI0I0U9UpW6gq1FBdoUWfcEWNe0lnVtLogt0RWqOTENEVgGJLJqqq2q8rioJ3nC2RK9u43i2xCdESSDIiRDNVvup/AHi08kAXHlnj3tFi2xyItr4dXB5XYzSkvW3TN1WfR3ZxWY17Z1YhlR9Ihz8lKkIIx5FkRIhmqmz7dgB84jufdS+v0vY4omdYV5fG1Fh1CIxCsXqiKBbWpdY8HM/n2tsAqMhXsWTud0d4QjR7kowI0RxZqilLsW317j10ZI1bFaZqTJosAAa16+Xy0BojRVHw09q2hd95smYyom/fkYirQuhwVT6anB3uCE+IZk+SESGaIXPSasylGlBUvK+6uca9HZnpKLoyUBUuaaEH5NUmyicGgMOnD591L+im6/EMqkZJ/9XVYQnRIkgyIkQzVLbadtKsVxtftP4BNe5tzPgNAA/C8dJ7uTy2xuqKqJFUZo+msrDP2TfPLI1O3QBWq2sDE6IFkGREiGbIQ0kluIsR/8sHnHWvoMgT06lBdPK+rJaaLde1nQdhLrqU9Bw/TNU1Ew61dV+KMwM4+Us11Ye3uClCIZovSUaEaG7MlXiZ9hKeUELw5IfOup2dH0RV3ijGxExwfWyNWOsAT/w9dVRbVY7mGWvcU/QenDoSTHGaN+U//c9NEQrRfEkyIkRzk7kNLFXgGwGhNVfSqKpKck4JAN0i/d0RXaOlKArRrUvQB25nQ9rZq2Z84rsAULZtu6tDE6LZk2REiGam4pdvKMsxYG07CJSau6ueKDJSqqag0VbSqZWvmyJsvKp8V+IZ+Q0bT2486573sKsAKDtSAJZqV4cmRLMmyYgQzUzBd+vJWBdKYbLHWffWpe7DO/r/8O30Kh46+ev/Vx0DYgFILz37YDzvK28GRcVcqsG0a6WrQxOiWZN/jYRoRtSSPMrTKwDwueaWs+6f2UPDX9sORZEzaf6qb2R3AIqqzz4UT+sfgFeU7YTjslXfuDQuIZo7SUaEaEYqVn+O1axB6wGelww96/6R0ykARPl0dHVoTcLQaNsmcFZ97lnbwgP49IsHoGxHkivDEqLZk2REiGakbN1PAHh3a42i1Z51P7fKtg18D9kGvlYdg9rZt4Vfn1rLJNarxwBgKSqGymJXhydEsyXJiBDNhapS9ttxAHwGDznrdqW5mirlBACD2/V0aWhNhaIo+GmiANjxl23hAbwGXknsBE/aX14AaWdPchVCXBhJRoRoJiwZ+6jIs50q63vdHWfd35mZYd8Gvn+bOFeH12S0/f0RVm3bwis6Hbqel9u+OfaLK8MSolmTZESIZqJ85WegKhiC9eg7xJ51f2PGPgAMqmwDfy7XtP8b5emTMJ0aVnuBmOEAqCmSjAjhKJKMCNFM+Ppl0GFkHhF3XVHr/ZLiICpzbqS77/UujqxpuaJjbyzlsaTmqpgtZ59DYw3vS/raEFI+LMeSdcgNEQrR/EgyIkRzYKlGSd+IZ1A1PtfdWWuRjHwPzKcTuS76by4OrmlpG+SFr4cOs0XleP7ZK2o0wZGYK72xVmso/3GxGyIUovmRZESI5uDkbqgqBs9AaN37rNuqqpKcbdsGvmuEbAN/Loqi0LZ1GoawFfxyfHetZXx62eaVlG3c4MrQhGi2JBkRohko/uJDsrYEYrT2Bs3ZS3qziksp1m1G53mCWNkG/rysvtvwCF3Pluzaz6HxGf771vCHssFqcWVoQjRLkowI0QyUbthJSbo3FWVhtd5fn3oAr9b/w7v9h3gZzk5WRE0dA20HDKaXnL0tPIDPNbeBomIq1mDeKxNZhbhYkowI0cSpZacpS7Udee/7+6Zcf2XfBl7TXraBr4eEcNvS59O1bAsPoA0KxquNDwBlK752WVxCNFeSjAjRxFWu+QKrWYPGAJ6JV9ZaJuX3beDb+sa4MrQma1gH27bvVl0OeaVnT2IF8Olr2ziubMcel8UlRHMlyYgQTVzZ2lUA+HQJR9Hpai2TW/n7NvCh3VwWV1PWKTgKrB4oGgvrjx+stYzvtbfgE1mJj382mGpPWIQQ9SPJiBBNnDHpCAA+AwfWer/KbKFSyQQgMaqHy+JqyjSKBj9NOwC2Ze2rtYzXZdfS7gZfAjuUQvpmV4YnRLMjyYgQTZgl6zAVObbVHD7Xn70FPMC2zDT7NvCJUbINfH3Zt4UvPFZ7AUWBjsNsXx9d45qghGimJBkRogmr3rUMj4Bq9IE6DLHday2zLtW2V4YHkXjrvV0ZXpN2S+ydGI8+TkVe7fNwAOg0AnO5htLVK10XmBDNkCQjQjRhHmV7iLk6n5gXbquzjLG4HeUZdzMgoPadWUXthnbogmoO5nh+GeWm6lrLmL27cXRZBCdWVGLJ2O/iCIVoPiQZEaKpqq6C4+sA0HS/ts5ih7OrsZR15uqY2s+sEbVr5e9JKz8PrCr23Wv/Sh/dGUOwHlSFsu8XuThCIZoPSUaEaKIsh37BWlEOPq0goletZcwWq/0Xac82Aa4Mr1mIaLMfzzafsPRw3XNCfPt0AcC4YZOrwhKi2ZFkRIgmqui/H5HyTQR5xzuCpva/yrtPZELQj/gFJdMuWOaLNJTBJxO9/wH25Nd+Rg2Az9WjASg7fArVVOGiyIRoXiQZEaKJMu5KRrUq6GJ61lnm5+M78Qhdh0ern9BoZOfVhurVyjYpOLviSJ1lvK+8GUUH1RUaqtZ95arQhGhWLigZeeedd4iOjsbT05MBAwawfXvth0n91RdffIGiKIwePfpCuhVC/M6SlUz5SdukSt8bx9dZbm+ebVJlhGcnl8TV3AyLTgCgUpNBRR2TWDUeHvjEhgJgXLXUZbEJ0Zw0OBn58ssvmTZtGrNmzWL37t3Ex8czcuRI8vLyzlkvLS2N6dOnM2TIkAsOVghhU7Z0IagKhiAdhs51j4xkGG3bwHcPlf1FLsSlbbqDqkXRVvBr6uE6y/kOGQyAcXfdZYQQdWtwMvLGG28wefJkJk6cSFxcHO+++y7e3t589NFHddaxWCzccccdzJ49m5gYORtDiItVtmEjAD6/T56sTbXFihHbQW+Donq7Iqxmx6Az4E1bAH5Nr/sMGt9bJtN6YDFRl2ZBYaqrwhOi2WhQMmIymdi1axcjRoz4owGNhhEjRrBly5Y66z3//PO0atWKSZMm1aufqqoqSkpKaryEEDaquRLj4QIAfK+6oc5yu7MyUXTFqKrC8A69XRRd89PWuzMA+wtqP6MGQB8VQ8CQBLQeKhz92VWhCdFsNCgZKSgowGKxEB4eXuN6eHg4OTk5tdbZuHEjH374Ie+//369+3n55ZcJCAiwv6KiohoSphDNWtX6r6ku16BoVbxH3lpnuTXHdwHgobbCz8PXVeE1Oz3D4lCtOvKMpecuGPv7h7QjPzk/KCGaGaeupiktLWXcuHG8//77hIaG1rvezJkzKS4utr8yMzOdGKUQTYvudBLhCcWEDOuAxtOzznK/5R0CIFwmr16UcT1vwnh4Nvlp11BVbamznKXNEAoO+JL50W7UqnIXRihE01f7eeN1CA0NRavVkpubW+N6bm4uERERZ5U/duwYaWlpjBo1yn7NarXaOtbpOHz4MB07djyrnoeHBx4eHg0JTYgWQ5f7K8FdyuCWe85Zzlw4FGNWW/52bd3zSsT5xYQEEeTtyelyM4dzSunVNrDWckrrnhQk+6NWQ+XaL/G6eqJrAxWiCWvQyIjBYKBv376sWfPHboRWq5U1a9aQmJh4VvmuXbuyb98+kpKS7K8bbriB4cOHk5SUJI9fhGio02lQkAKKFmKG11nMalU5eLIU1RzC0BhZSXMxFEWhx++71+7Pqnv+msbDA58uYQCUrVrmktiEaC4aNDICMG3aNO666y769etH//79mTdvHmVlZUycaPsUMH78eNq0acPLL7+Mp6cnPXr0qFE/MDAQ4KzrQojzK/9xEaZj3vj064HeK7DOcscLyig3WfDUa+gYJvNFLpZX8G68O3zD/44P5PYBs+ss53vZEIwHvsG4J4X6P5gWQjQ4GRk7diz5+fk8++yz5OTk0Lt3b1auXGmf1JqRkYGmjq2phRAXp2jZKor3BhIcEEj4OcotT9mEZ5tPaeORgFZzjcvia67CA3RoS3I4UX7onOV8b5wAC76hItdC9fE96GISXBOgEE1cg5MRgKlTpzJ16tRa761bt+6cdRcuXHghXQrR4qkVJRgPnQI0+F570znLbju5E73/fgx6f9cE18xd1q4332VCOelUmS146LW1ltNHx+IRZqAq30TZNx8RMP3fLo5UiKZJhjCEaCIqVizCUqVBYwDvEWPOWTbNaNsJtGuwzBdxhCHRPUHVoOjK2Jpx9JxlfRN7A1C6YbMLIhOieZBkRIgmonTl9wD49miLYjDUWc5qVSm1pgEwMKqXK0Jr9jx1nniqrQFYn5Z0zrJ+o+9E0VnRmAqgvNAF0QnR9EkyIkRTYLVg3Gvb2t3vqqvPWXRfTjboTwNwRUwfp4fWUrT2jgVgb/7+c5bzvPQKOt8bSusBRZCyygWRCdH0STIiRBNQtXkppmINaFR8/nb3Ocue2XlVZw0j2CvAFeG1CN1DuwNwouzIOcspGg2a7tfavjn8o7PDEqJZkGREiCagcv1SUFR8YoLQBgSds+zuHNsn93CPszcUFBduaPsELFVhlBoDMVus5y7c1ZaMVO1eK7uxClEPkowI0QQE+O8ndnQO4Q9OOG/ZE8WFqFYtXYNk8qojXRlzCbqTT1CePYrDOec+p0aNiCf159YcX+pH5c+fuShCIZouSUaEaOwKjsCpo+i8dHgMve2cRastVnLSLseYMptJ8ecuKxpGo1Ho3c42KrUn4/Q5yyoaDfrWtiMySn/81umxCdHUSTIiRCOnHrStoqHDEPA8974hh3JKqTRb8ffwpHvEubZFExciISoQsLIlPf28Zf1GXAWAcc8xsJ7nsY4QLZwkI0I0clmvfUrazyGUa3qft+zudNtS0t7tgtBoFCdH1vJ4BxzHt/NsthhfO29Z3zGTQFGpKlQw7ZZVNUKciyQjQjRi1oITGI+XU1Hggabz0POW//L4Arw7zCcg9IALomt5hkR3QdFWYdadILvk3PNGtCGt8G5vG8kyfrfYFeEJ0WRJMiJEI1b27XuoFgW9vwaPfudPRk5WHkTrmU37EC8XRNfydAuLRrH6oSgWlh/acd7yfpcNBKB0y15nhyZEkybJiBCNWOkvvwDg27czinLuxy7ZJaWYdScAuK7zpU6PrSVSFIUwfWcANp3Yfd7yvjdPAqD8pBlL2j6nxiZEUybJiBCNlFppxHgwHwC/624+b/kfDm1HUSxorH50DW3v7PBarLjgHgAcKT73TqwAhs49CRkYRNvBhSiZ65wbmBBNmCQjQjRSNQ7Gu+qW85bf/Psn9VD9+UdRxIUb1v4SAIqsR7FY1fOWbzX5DvzaVKE5utLZoQnRZEkyIkQjVfL9NwD49jz3wXhnpPz+ST0uuKdT42rpRnbqh6pqUHTFbM04dv4K3UbZ/puxGYx5zg1OiCZKkhEhGqPqKnw8juHbuhL/0ed/RFNtsVJstR1tf+aTu3AOXw8fQqxDqcq/goMnjeevENiOSo9e5CX5YPzyLecHKEQTJMmIEI3RsV/wCz9N1HWe+I2ZfN7iB3NOUV0Wg2oKZWSnvi4IsGW7vs39mAquJCWrfo/DSnLbcirZj6Lv5VGNELWRZESIxujAd7b/xt0AmvP/Nd1/ooLKk3+nFy/j6+Hj3NgEfc5sC59ZVK/yfmNtJy0bjxix5mc4KywhmixJRoRoZFRTBYXfrcZk1ELc6HrVOXNWSkK7QOcFJux6RwWiaEtJK99GvrHsvOU9Lx2BPkCLalEwfvm2CyIUommRZESIRqZixSJyt3uQuqoVanhCverszDoKWO2f2IVzBfsY8Os0H6+oT1h+eOd5yyuKgn+ibUlwyc9rnR2eEE2OJCNCNDKly/4H/L6KxtPzvOXzS8vID3gB387PExVW7ezwBLbkIkQXC8DGzPMnIwB+t555VFOCtSDTabEJ0RRJMiJEI6KaKinZY/tF5T/qb/Wq80PKDhSNBY2iIzaktTPDE3/SLcg20nH4dP3OAfJMvBK9vwbVosH41TvODE2IJkeSESEakYqVi6gu16DRq/iMvrtedTZm7AIgRBcrm5250FD75mdHsNZj8zNFUfAf2BOthwXLkS3ODk+IJkWSESEaEfsjmh5t0HjV77C7lCLbZmfdZLMzl7o69hJUVQFdETtOpNarTshjTxN7Yy5Bgfug7JSTIxSi6ZBkRIhGwvaIxrbs03/U6HrVsVpViqxHALgsqp+zQhO1CPD0xVNtA8Cqo9vqVUcb1QOldS9QLXDoe2eGJ0STIsmIEI2EecsSLJU06BHNtszjoCtGVRWu6Sw7r7palE83AHbm7Kl/pe6jUVUwbfjKSVEJ0fRIMiJEI2E4vZnOf8ul3ZSBaLzrt3HZ0kMbAPBW2xHg6evM8EQtroseRcXJWyjKSax3HXPYYI4uC+f4+8exFmQ5MTohmg5JRoRoDMyVkPw9Gp2K1zUT610tJz+EqoLL6RN8tRODE3W5pedgrCV9ycgzkFNcWa86ui79UfR62wZon89zboBCNBGSjAjRCFgP/ABVxeDfBtoPqlcdVVXZl+qJKf8q7u51u5MjFLUJ8NLTvXUAANtS6zchVVEU/If0BqB45c/OCk2IJkWSESEagZw5b3J8RRhG3ZB6nUUDcDTPyKkyEx46DfFRAU6OUNSlR/tq9MEb+PrwN/WuE3DXQwAYj1dQfSzJSZEJ0XRIMiKEm1lPnaR0fwFVxXo03a6qd71vD25F53uA3u0NeOi0ToxQnEtQcDae4cvZX7qi3nU8eg3AM9ITVIWS/85zXnBCNBGSjAjhZqWLX8darUHvr8HrivrtugqwOvM7vKI+QRe8znnBifMaEzcUgGrdCY7m59e7XsBVtnrFa7eDev5N04RoziQZEcLNilf8AoD/ZX1Q6vmIRlVVcsy2bcgvj67/Sg7heB2DW6OztEJRVJYc/LXe9fzvmgaKSmWeStW2H5wYoRCNnyQjQrhR9dFdlKVVABAw4aF619uacRR0p1BVDaPj6jfhVThPe59eAGzKqt/mZwC61u0Iv64j7a8owHBqvbNCE6JJkGRECDcqWTQfVAXP1p549Kj/pmVLD20EwFttT4iXTF51t0FtBgCQWb6vQfWC730U7zATyoFvwGJ2RmhCNAmSjAjhLqpK8Trb8fMBI4c3qOrO3B0AdA7o7eioxAW4Ke4yAMy6LI4W5NW/Ysww8GkF5afg6BrnBCdEEyDJiBBuombuILRbAf7RJtv8gfrWU1Vyf58vMry9zBdpDDoGt0ZviQBVw/JDDdgaXqujqtVIsncGkPfaq84LUIhGTpIRIdxE2fcVfq2raHPPFegi2ta73raMY6ArRFU1/E3mizQaV4Y8iTHlOXLyWjeoXnXopRQd9eH0tiysxQ0YVRGiGZFkRAh3qDbB/iW2r3uNbVDVlJM6jEen0776XoK9/J0QnLgQV8b2AFXPtuP124n1DO+rb0Pnq2A1azB+Pt9J0QnRuEkyIoQbVCz/gLytZqrM4dBhaIPqbkstRDWHclX0lU6KTlyISzoEoyhwvKCM3JL6nVMDoGi1BAzuCUDxDyudFZ4QjZokI0K4QeGnn3Aq2Y/C7I6g1dW7nqqq9k/el8YEOys8cQECvPS0jd6Kd4d5fLynYfuG2LeHP1aG+dB2Z4QnRKMmyYgQLladcZDSA6cBCLy7/nuLgG1/EWPAh3iFbCM+KtAJ0YmLERJQhtYzh80N2G8EwCNhEF5R3qAqFH8gE1lFyyPJiBAuVvL+HFSrgke4Ac9BVzeo7neHNqD3P4Bf6F489XIeTWMzqK1tv5GMiobtNwIQdNONABSt249qqv9jHiGaA0lGhHAh1VLN6dW2PUKCRo1EUZQG1d91Zn8R/96ODk04wM3dbfN/LLosDuflNKiu3/hpeASp+Lczou5f6ozwhGi0JBkRwoUqvn8fUxEoOhX/SY83qK6puppc814AroyRJb2NUYegCAyWNgAs/m11g+pqfHzp8OIdtOpVimb/Z84IT4hGS5IRIVyo6LNPAPDvF402KLRBdZcl7wRdKVgN3NqjYStwhOt0CbBt67/x5IYG11X6jAcUOL4OCo87NjAhGjFJRoRwlZJsdOYTaPRWgiY+0ODqS1Ns24WHaHvgpfdwdHTCQW6IvQKA/OrfqDQ38LyZoPaoHYZTmuVByYcvOSE6IRonSUaEcJWkT2kVX0zsg9F4XnZ9g6sfLLIt+UyMlEc0jdnf4gaCuRXm0q5sTs1qcP2S8nhObAgh76uNqOYqJ0QoROMjyYgQrmC1wu7/AqAZMLHBE1dPFhkprwJV1TAufqQzIhQO4qEzMMLvdSqzb2H7sYavivEbNw2NQcVcqlD29b+dEKEQjY8kI0K4QNX6zylLyUH1CIC4Gxtcf+OR01Rk3EMH4+vEtWrvhAiFIw3rEgbAusMNP2tG4+tPwKWxABR9/ZVD4xKisZJkRAgXOPV/C8j4JZT8jF6g92pw/XUptl9qw7u0c3Rowgkuiw1Do1hJKUomJT+3wfUD//EIAKWHSqg+luTY4IRohCQZEcLJqtMPULKvAADfm+9ucP1Ks5kNR9MBGP77J27RuAX5GAiL/QSfDm+zcM+PDa7v2f8KvNp4gqpw+j8vOiFCIRoXSUaEcLKit55DtSh4RnjgdfnfGlz/2wNbUds/h3/0Qnq1DXR4fMI5ugR2B2Bz9sYLqh80dgwAp3/Zh9V42mFxCdEYSTIihBNZjacp/MW2NXjwbWMaPHEV4Psjv6AoKmE+/mg1Da8v3OPGLiMAKLDso9xkanB9//HT0fmA3rOa6vUfOjo8IRoVSUaEcKKS95/HUqGg8wH/u2ZcUBuHSmxLege1HuzI0IST3dBlAFi8UbQV/G//pgbXVzw9iX5pMtFXFWA4/rltRZYQzZQkI0I4iWqxULhkFQBB1wxE8fRscBsHc09g1mUAMK63LOltSvQ6HRGG3gAsP/rLhbUx7B4UzwA4dRSONmx7eSGaEklGhHASy67vUKtMKFqVwAefu6A2Pt37EwAelnbEhrR2YHTCFS5rMwSAlNIdF9aAhy/0GYfFpFC66FUHRiZE4yLJiBBOojv0CTHX5tNhxpXowqMuqI0zkx/jAgc4MjThIuN7X4WqKlTrstibnX5BbVi63sbR78M5sSQL0641Do5QiMZBkhEhnCH3IBxfi6LR4HHj9AtqotxkosBim/x6Y+crHBmdcJH2Qa0IN99Kedo97E2vvqA2tO174BUdBCgUvjPHsQEK0UhIMiKEE5R/9TLWaqDr9RB0YTumbk8roDL3ejTGftzQVUZGmqqbOv0dS0UM6w4VXnAbwXdPBqBoeyaWnFRHhSZEoyHJiBAOZslJI/P/dnB0WTim6FsuuJ2fDpyiurgf10Q8il6nc2CEwpWujAsHYOORAoorGniK7+98bpyIR4gOtVqh6O1ZjgxPiEZBkhEhHKzoraexVivo/AzoL2n46bwA1RYrK/fnAHBtz0hHhidcrHO4H+1bF6CELeHfW7+9oDYUjYagm68DoHDFdtTyEkeGKITbXVAy8s477xAdHY2npycDBgxg+/btdZZ9//33GTJkCEFBQQQFBTFixIhzlheiKbOezuPUjzsBCB57I4rmwvL9L3/bTKnHagL9SknsGOLIEIUbtG+bjiFoG6vSv7/gNgLufRqtN1SXKRS//U8HRieE+zX4X8ovv/ySadOmMWvWLHbv3k18fDwjR44kL6/20ynXrVvHbbfdxtq1a9myZQtRUVFcddVVZGVlXXTwQjQ2RfOewFKpoPdTCLj3mQtu5/Pk/+EZvoLW0ZvQa2UAs6kb3+sGAE6r+8gqvrC5IxpvX0JGDwNFxbT7Z6iucmCEQrhXg/+Ve+ONN5g8eTITJ04kLi6Od999F29vbz766KNayy9evJj777+f3r1707VrVz744AOsVitr1sgSNdG8WEsLObVsCwAhf78OxaPhm5wBVJpNpFduA+DGztc4LD7hPld0jEdniUDRWPi/HRc+OhL0yMt0vEWhVdeTkLTYgREK4V4NSkZMJhO7du1ixIgRfzSg0TBixAi2bNlSrzbKy8sxm80EBwfXWaaqqoqSkpIaLyEau6L5M6n+fev3gPtnX3A7n+5dB1ojWLwZ31uW9DYHiqLQM/AyAH45ceE7qWr8AzFc+7Dtm41vguXCJsQK0dg0KBkpKCjAYrEQHh5e43p4eDg5OTn1auOJJ56gdevWNRKav3r55ZcJCAiwv6KiLmzDKCFcxlyBafc6AEJuuQqNl/cFN/Vtiu3I+XaeA/DSezgiOtEITIi3PaopYj8nLvBRDQB97wKfMKrST1L+v9cdFJ0Q7uXSh9Fz5szhiy++4Ntvv8XzHOd0zJw5k+LiYvsrMzPThVEKcQF2/5eIXjl0uEVD4IMvXnAzlWYTGZVbARgde52johONwOUd49FVR6IoFt7dsfTCG9J7UWK4luMrwsiZ/19Uc8NPBBaisWlQMhIaGopWqyU3N7fG9dzcXCIiIs5Zd+7cucyZM4effvqJXr16nbOsh4cH/v7+NV5CNFrVVbBxHgCeNzyKxsfvgpv6JOkX0JaBxYdxvYc7KEDRWPQKGorVFMTezNMX1Y7P7TPR6KGqUKX045ccFJ0Q7tOgZMRgMNC3b98ak0/PTEZNTEyss96rr77KCy+8wMqVK+nXr9+FRytEI1T+1auYsnPBLxJ633lRba09dhDVqqed56V46g0OilA0Fk8m3kfZscc5dLQrxeUXPt9DGxZJ8FUJABT892tUi8VRIQrhFg1+TDNt2jTef/99Fi1aRHJyMlOmTKGsrIyJEycCMH78eGbOnGkv/8orr/DMM8/w0UcfER0dTU5ODjk5ORiNRse9CyHcRK0sJ3v+Zxxb3gqj342gv7AVNABmi5XklB4YU55mau/7HRilaCy6RYbQNcIfs0Xlp4P1m2dXl+DHX0GjU6kqsGJc9LKDIhTCPRqcjIwdO5a5c+fy7LPP0rt3b5KSkli5cqV9UmtGRgbZ2dn28gsWLMBkMnHzzTcTGRlpf82dO9dx70IINyl6cwamYtB6gNctF3Yg3hlbj5/idLmZYG8/ruzSyUERisbGtqNuNV/t23RR7WjD2xE0wvbIO+/9z1CrKhwQnRDuoaiqqro7iPMpKSkhICCA4uJimT8iGg1rYTZHrxiOpUIhfPwVBD/19kW19+j/NvLtzmJuH9COl/7W00FRisZm94kTjP/pJtBUsfzG1bQPanXBbVnyT3JsxOVYqhQi7r6SoMffcmCkQly8+v7+lq0dhbhAp/71MJYKBX2AQtCjr11UW4XlRn4ufRTvDvMY1FkOxWvO+rRti0ENQVGszNv61UW1pQ1rTeiY4WgNVpSUFVBV6qAohXAtSUaEuADVqfs5teo3AFpNvgPFy+ui2ntj81egqUSvMzOya2dHhCgasUER1wKwPvt7LnZwOnDGXDqO8yawbR5skpER0TRJMiLEBcif/QhqtYJnhAG/u2eev8J5/JRh23eib/DV6LTai25PNG4zBt6GatVh1p7ku4P12726LhovH7TXPWf7ZsvbUHpxE2OFcAdJRoRoqLxk9OWH0OistJr+2AWfzHvGL8d+o0J7HFXVMH3gxS0NFk1Du6BQInT9Afhg7+cX32C3G1Db9KM01cqpWfdcfHtCuJgkI0I01M/PERpXSqfpCfhcP/6im3tnl+3As2ClN3HhbS+6PdE03Nn9VgDSqzaTX1Z8cY0pCpXtJ3FiYzB5K1Iw7V7rgAiFcB1JRoRoiLSNkLISFC3a6y982/czSqsqSDGuA+Dm2Jsvuj3RdIyLH46muhWKxsSCbT9edHteV92OT6w/qAp5Lz7lgAiFcB1JRoSoJ9VURdZDD1CWa4C+EyD04vcCeXvrUtCWo1QHce8lV198kKLJ0Go1XNf6AcqOP8Lew+0d0marp18ERaX0YBFlS/7jkDaFcAVJRoSop9OvPEhJiokTm0Kw9H/UIW0eONqO8szxDA65Cw+93iFtiqbjkUHXopgj2ZV+mpTci1+W6zngSoIGxQCQ89rbWMtKLrpNIVxBkhEh6sF87Dfyv/oVgFZ3Xo22VdRFt5lZWM6mo6exGON4cshtF92eaHpa+XtyRVfbpmefbT/ukDbDXnofrZeKqUilcPZ9DmlTCGeTZESIesh7cgpWs4JnhJ7AaY45yuDrnZmoKgzuFEq7EG+HtCmantF9gvFs/QVL8u+jqPLiz+zStmpD+D1jAShYvpvqIzsvuk0hnE2SESHOw/jV25TsKwRFJfKFF1F0F79DaoWpikXpj2AIW8XoPqEOiFI0VVd2a4/BJxO0RuZt/p9D2vS/dxaBvQNoO7gQ3daXoPGf+iFaOElGhDgHq7GI3NdtEwGDhnTCc8gNDmn339u+xWo4gUfgLq7p0cYhbYqmSa/V0ifINnn5x/QlF70jK4Ci0RD5zmJ826pwbA0cXHrRbQrhTJKMCHEOJW9Nx1SsovNWCXv5fYe0qaoqXx39BIAe/lfhY/B0SLui6Zox8E5Uq44KTRpf7VvvmEZDOsJg20Rr85KZWE/nOqZdIZxAkhEh6pJ3iIDqpbROLCTiofFoQyId0ux/9/xElSYD1apn9rB7HdKmaNq6R7QlSn8ZAO/scUzSC8DgRynOb8fxr6zkPT7Rce0K4WCSjAhRG4sZvr0HxWoi4Ioh+N118efPnPHevg8B6OBxBZ3DIhzWrmjaZg66D1VVOM1vrDm2xzGN6r3QDr0Xa7WG0xtSKfvmXce0K4SDSTIiRC1K5k2lOu038AyEG/4NiuKQdn9M2UYJyaiqhqcHy6iI+MNlHboRwiUAzN36gcPa9b11KoGJtqXoJ/81H0tepsPaFsJRJBkR4i8qfv6KrA/Wc3xFK6oHPw/+jnk8A/D6tv8DoJWSyIB2F7+Dq2heHup3L1V5Izl26HLySiod1m74m5+h94fqMsh9WA5jFI2PJCNC/Im1+BQnn34OVAWfzuHoBt/lsLaziirIODoUU1E/pvWXURFxtjE9+tPL9yZMZk8+3JTqsHY1gaG0fv5pUFSK9+RR8uHFn6skhCNJMiLEn+Q9Ng5TkW31TMT8Txza9ocbUjFXhdLH616u75bg0LZF83Hf0I4AfLY1ncLycoe16331HYRc2R2AnLc+pTr1oMPaFuJiSTIixO+M/1vA6Y22T6ORTz6ANjLaYW0XGqv4fHsGAPcN6+iwdkXzc3nXVrRvnY0l4t88uuo1h7Yd9sp/8WylJTDGiGbDLNkMTTQakowIAZiP7ePki/MBCBrYDt9bH3Ro+w+u+hdq2KfEtinjsljZcVXUTaNRGNHTD613BruLllNQXuywthUvH6IXf0KrPlVojv8EW+VkX9E4SDIihMVM/uMTsVQqeIRqafXmZw5t/tipk/xWshx9wF6u6m1AcdDKHNF8zRg8Bo25FWgqeGrNOw5tW4lKgKv+BYB1xTNUbXDMFvRCXAxJRoRYPYvwrkcJ6Gim7TvvogkIcWjzj66eAxoTenMHHkkc5dC2RfPkqdcxqr1tk7ItBUs4VnjSsR30n0x1hxtJXxNE+oNPYz62z7HtC9FAkoyIlm3/N7D1HbR6ldZz52GIH+zQ5telJnG8ch0AU+MfRa/TOrR90XzNGn4benMH0JiYtnqOYxtXFDSj30RVPLFUKmTdMw61wnGTZYVoKElGRItVue0nCudMs83hG/QIdLveoe2rqsozG15GUVQCrP2Y2G+YQ9sXzZtep2VqvO1smWMV61ifmuTQ9jUBIbaRQL1KRVYVuQ/f6tD2hWgISUZEi2TJyyLroUfI3elFYW4PuPwZh/fx0Z4VFKkHUa1aXrzsCZkrIhpsYr9hBFj7oSgqL2907FJzAEP8EFrPsD0OOv3rMYr/4/i/B0LUhyQjosWxlhs5ceco22m8PioBTy8Erc6hfaiqyv8lfQxAB8NIhnXs6tD2RcugKAovXPY4lVl/59CBYezJOO3wPvzGP0HIyG4AZL/9NWXfL3R4H0KcjyQjokVRLRayJ1xLeUYFGr1K1LxX0LWNdXg/K/bnkHfkdiynruHNq6Y7vH3Rcgzv2I0bY68HNPxreTKqE/YGCXvtc/y6BaBaFXJeeBk155DD+xDiXCQZES1K3sO3UPJbPigqbWdNxXPIjQ7vo6rawpwVh0A18I+e/6BTWJjD+xAty/SruuCl17IzM4f3tq1zePuKwYPWi5YTEOdF1JB8lC9uBWOew/sRoi6SjIgWo/ClByn8ORmA1veNwufmqU7p57nVS8koNBLm58G9l8U4pQ/RskQEeHJLoh6fjq/xTvJMMotzHd6Hxj+E1v9dhaFdFBSlw2e3gqnM4f0IURtJRkTLkPITyqFvQFEJu6E3AQ87dpvtM75N/pUf8mbh3f5dHrsqBh8Px85FES3XY8MHolMDUDVl/GP5TKc8rsE3DO78BryCMe48SOYtl2OtkIREOJ8kI6L5O7oGvhpHUIyRDg9dQsicxU7ppqTSyPNbZwEQ4dWBsf06OKUf0TIFeHnxZL/nUFUNJ807mL/1K+d0FNIRyw0fkbUlCOPhErL+PkISEuF0koyIZs345b8xf3QHVFdCl2vxvOcjFI1z/tjfs/x5qjUFUB3I+9c/J0t5hcPd1vtSunreBMBHh94gvSjbKf1ouw2n7TMPoGhVjIeLyBorCYlwLklGRLNV+umbZM5+h4zVflS3vQpuWQRavVP6+vrAWg4YVwAwrtPjdAyVw/CEc3xw4+NozG1RNeX8Y/mTznlcA/jc+hBRz06xJSQpRWSNvUISEuE0koyIZqn00zc58a//A6uCZ/tQtHcuAp3BKX0VVZbyr+3PAdBKHc6Myxy7k6sQfxbo5cU/L5mNqmrJqd7NvC1fOK0vn7EP/ykhKZaERDiNJCOi2Sn+vxdsiYiq4N8jkNafrkHx9HZaf1OW/wuLphDMwXx4gzyeEc53a3x/4jzHYC7uzVcbfDFWVTutL5+xDxM16357QlL8zE1grnBaf6JlkmRENBuqqlLwzGROvvmZLRHpGeT0RGTb8VPs/C0OS2U4E7o8TnRwsNP6EuLPPhr9JKEVE8k+reGJJb857XEN/P7IZtb9BMRUEuizFRbdAGWnnNafaHkkGRHNg9VK4ZNjyf96IwDBl7Wn9WfrnJqInDhdzv2Ld2OuCuFyv5eZNvhap/UlxF/5euqZN7Y3Oo3C8t9O8sSKr5yekLT+z6coXgFwYjvW90ZQlbTBaf2JlkWSEdH0mSthySQCWI3et5rwv19K+P+tQNE7Z44IQGZxLnd9tphTZSa6t/bntZv7yOMZ4XL9ooOZNSoOz9ZfsSL/RWavf8+5HUYPgkmrUf2jyF5RSNr4yZT94PgD/ETLI8mIaNKq05PhvzfCgW/Q+WiIWfAswc99DE5MDKqqq/j70ink+vybwFZJvDe+H14GrdP6E+JcxiVGE98qDoAlaf/h2+T1zu0wrAvqHd9jrvbHalLIePxfnJ47w6mjMqL5k2RENFmln73FsVF/o+jXveDhD3cuQXPJOKf2qaoq45fOpEQ9AlZPnh95PW0CvZzapxDn898xM/CvHgCKlVlbn+BQQbpT+9OEd6Ddd+vwi/MHq0LOBz9w8o4RWEuKnNqvaL4kGRFNjmoykffwWE48vwCrSaH4ZBjq5LUQM8zpfT+99h0OGlejqgq3tH+SG7rHO71PIc7HQ6/lyzGvozFFoWrKGPfDfRSUn3Zqnxr/ENp8vYlWf0sARaVk90nSrhlC1d7NTu1XNE+SjIgmxZx2mIxRAzm16jcAgge1pd13G1FCOzm97+fXv8eyzP8DIM7z7zx7+d+c3qcQ9dU2MID5w+ejVvtRqZzg+q/Hcaq8yKl9KlodIS9/Rvt/PYTWS6XqVDWZ/5iIemilU/sVzY8kI6JJUFWVogXPc/yGGylPL0OjU2nz0GjCP/gJxSfA6f3/a8OHfJ32bwDacj2f3vyETFgVjc6wTrH8s8881GofjNYTPPTNcqotVqf3633T/cR8/Tne7QxE9itE+WIsLHsIqkqd3rdoHiQZEY1fxWlM744j+63PsJoUPFtpiP7gDfzvf9mpE1XP2Hy0gMW7dgMQyTV8d/uLGHQyYVU0Trcl9OfJhDcxn7yLTfsDeezrvViszp9cquuUQLvl2/C5YZLtwu5FFD96KSWfvOn0vkXTp6hNYAp0SUkJAQEBFBcX4+/v7+5whCsdXgk/PAKl2eTt80cTcykhz3+M4uXrku63Hj/FxI93UGGupm/XXD67YwIeeklEROO3+mAuUz7dRbVV5Zp4A6/clIi/h2v+3pC2EfMnUzj+pQlrtQb/hEjCX/8IXeto1/QvGo36/v6WZEQ0SpVbV5P73EzCu6biGVgNIZ1g9AKI6u+S/lVVZda6D/h6bSsqTDqGdQnj/8b1xUNGREQTsnJ/DlO//gmPqPfw0/vz2Q3/R0xQlEv6tpYWUvDkeE79chRUBY1BJezvVxP02CsoHh4uiUG4X31/f8tjGtGoVOeeIHvyKFInPkh5Whl5vwXAwAfh3g0uS0QqzBX87X/3823GW6itPuOyzqG8e6ckIqLpubpHBE9cG42iWCgjk799N5Y1qdtc0rfGL5hW7/xA9BtP4BmmYDUp5P53FamX96Ps+/+6JAbRdMjIiGgUrMZSTr85k1P/W4OlynbNv5sfrV54A32PwS6LI7M4m7FL76NUPY6qaujr8w8+vOkBdFrJ20XTtfLQQR7f8Ciq4SSoWu6Ne5Kp/f/usv7VqnKKXn+E/C/XY6nSgKLS6YlB6EfPgsB2LotDuJ48phFNg9VC0dtPk7fwOyzltksewRD+6H343PyQSyaonrEubSePrH0Ei6YYtdqbO2KeYebw613WvxDOlJJXwB1LH6HSsBeAwWE389bVT6HX6F0Wg+VECvnPTEE5nUJ47xLQ6KHPeMxxE9HH9HRZHMJ1JBkRjZulGpKXwrpXKNycSe7uQPS+KqE3Dyfg4VdRvPxcForZYmba6tdYl/MlKFYwhfPiwDe4sXsvl8UghCuUVJq45ctZnOQHADpqb2bRTU8R4O26hARAzdiGsvZFSP2VytM6Un8KI6BvO0JmzMYjPtGlsQjnkmRENErVJ1I5/dYsDGW7CAg7AYBVH0iJMpKAh+ag+Aa7NJ7CMhMzv9vOxoon0eiL8Tb148Pr59AjMtylcQjhKharyiPfL2RN9leUp08m3M+fOWN6MbxLK9cHk7qBgpcfJ//XIvslny5BhEy+H+/r7pC9fJoBSUZEo6GqKpVbVnP6/96gZEcaqlXB4G8m5iYLyqX3wqVTwNP5G5f9mcli4pfkfJ7+LpkCYxV6n+NcE+/P69eNQy/zQ0QLsDu9kOlf/8bxgjLASnyvTfxrxCR6tIp1bSCqSsWKjyn4z9sYj5YDtgTEI8xA8N9HEzDpSRRPOf+pqZJkRLidpSCH4g9fpWj5GqryTPbrXhEagm8dhd+kZ1A8fFwak6qqfJT0Hf/Z+xYluQMxnx5I53BfXr+lNz3bujYhEsLdKkwWXlt1mE8OfoZnxFJQNSQEXsPcK6fTyifU5fGYti2n8D9zKdqZjWpR0HlX0+nvGpQ+t0HCOAjp6PKYxMWRZES4h9UCGVth/xJOvP09pWk6ABSNil9Xf4ImTML7+smgcf3ow+rjW5i96RWKrcdsoVZFcmfb+Tx6ZWc8ZSMz0YItP3iAZze+iMljPwCK1ZOro27juaH34a33dnk8loyDnP73LDQFewhunw+AaoWMbTH4Jl6K3x0PYIjt4fK4RMNJMiJcxlpRQdnSjylZ9g0h0Zl4GnIAMJ70IO9ACIEjBhBw9wy07bu7PDZVVfnx6Abm7/iAbPMe2zWrgWjddbx+1UN0CXf9pz8hGiOzxcqr65bz5bH/oHrY5nPprIFc2/4WZg99AJ3WDQl7tQlSVsDuTyhdv5ETG4LstzwjPfEfPhC/2+/H0Mn1/7aI+pFkRDiV+Xgyxm8XYtywkbIjp1Attue8IXGltOqvga6jUHuMgQ5DUdzxjxiQlFnEU+teIdNqWzmgqgqBlkG8cNk0hse6+Lm4EE1EcUUVT676LxsK/ouiL6K6rAOR5dO4e3AHxvRpi5fBPX+fLScOU7JwLiXrt1F+wgTqH5NbPUL1hE8Yic+oCdAqzqVbAohzk2REOJa5Ek7swLxnFZlvLKOqwFzjts7bin9CO/xv/jteV44DncEtYe7NPczmI4X8vE9lV/ppNJ5ZeLd/l1B1EFP6TOTW+ASZoS9EPWQUFvP8usVsS1EpLYoGIMC3itYdl3NL1xu4vedIPHWebomt+shOSj9fQMmv2ynPMoOqEHNNHh4B1eDfljJrL6qqI/C+8iY8EgahuOGxsLCRZERcMFVVMafso+LXH6jYtR2dJZ/QdkfAUoVqhZRvI7BWK3hF6PDt2xXfa27CY+jNKG5KQLJKcnh35zf8nPkjRtIxFfWjKvtm9FqFG+LbcNulrejXLtItsQnR1Bmrqvl6ZyYfbUolV/M9HmE/A6BYvejmP5i748cwIuZStBo3jZik7ads+SL8AtJQ0n6F6kqyNgdSkmGb66L1BO9OYXjF98Rr4BV4Jl6Nxtv182BaKklGRP2VF1K6dDGVe7ZTefgYFRmnsVT8cVvvU02nUXngGw7RQyivbI9h8Gh00e7bFGx92k6+OLCKPQVbKCPdfl1VNXiZ+jGx80zG9GlLuL97PrkJ0dxYrCqf79nB4gNLyDRtQtEX2+9prD5Ee/fhoYRHGdapE1qNm0YfzRWQtpHT//2Y0u0HKD9RiWqpOSqiaFU6T+uEpl1fiOyFmQi0Mb3ReLt2ZV9LIcmIqEFVVaozjlK1ZyOm5CQseZmE9dNB7gEoOcHxlWFUFf1pF0aNimeYFq+OkXj36YPf2H+ghMa65Vms2WpmT/YRThUGsSPtNNtST5HqMRutZ+7v701BY2pPQvDl3Nv3JhKj28mjGCGcqLCskve2r+aH4z9QpOxG0VaiWnUYU54lyMuHgZ1CCQg5ROdW/lzXOZEwnxC3xKmWnqLil/9RvnENFYeOU5FZis7TQszV+fYyqT+FUnlajyFIj0ebIDyi2+HRtQeGXgMw9LgUjZfscXIxJBlpgaxlRjTm0//f3p1HR1Xejx9/3ztr9knIDgmELSB7VWJihbZyRMRWWr+IyCmWUreiVeF4FL/ViD0tLlRtqd+ipxb6O5aq+LNYrcrBBfgqEdlcCIsEE0IgC0lMMllmu/fz/SNkNGQhk2aF53XOHLjP/Tx3nifP3LmfufPMvVB7AmpOUP3a2zR+UYCvog5fjQ8JfHOA1nQh879K0c58aDh9LA1/wIVz7GjCLr0cx3d/iO5K7vM+NCceR9hR9BmfVeRT5D5KjfEVohnUH8kFaf4qyB7/PnGuSi5OyGHBxKv4bsYI9P76NKYoF7Cy2gY2fva/fFR8mC8LxuP2BAAIz3gGi7P5l3UOSSbZOZrxcePIHjaZmRlTGRIW29lme4UE/JiF+7DUHoSyz5HSzzm2rgR/Q/tzSuzRAUbdHAexGRA3kpr8RnRXEraM8VjHTsGaOlzNRzmHXk1Gnn32WZ588knKysqYMmUKa9euZfr0jm/vvmnTJh566CGKiooYM2YMjz/+ONdcc02Xn++CT0ZMAxqroL6Cxt0f4z36JYGyUwROV+KvrCFQ00jA7cfwCePmlwZPXpR8FIv7xLeyek2wR4MjKRJ7eirxC+agp0+BpAl9egVUU0xK6sr4orwIuzGc4iofhZX15FVvpEJ/GzSjTR0xwkiqv5ec9ElcMiKWy0fHEx/p6LM2K4pybgHDZF9xDZ8UVvL/i9dS6T8E9vI2ceJLZITnETLiI8mIj6DOkkdGbCKTkkcyLj6tT69tIkaAwNG9eHd/gPdwPr6i43hPVeOt9BOe4CNtRnVznMCXryVj+r9JPjRdsEZZsMU4CRuVSOINV0BUCkQm0VhUgx6finXYGCyJKRds0tJrycjLL7/M4sWLWbduHVlZWTzzzDNs2rSJI0eOkJjY9t4GO3fuZMaMGaxevZprr72WjRs38vjjj7Nv3z4mTuzaRWsGezIiIoi7DrP2NEZ1OebXpwnLSAKvGzy11P3vbjwFxzHq3Jj1DRjuJgL1HozGAIbHJPP6cjTNBGg1Mas9o+dVYUtJgZg03GUR+L0R2EeOxT5uKrZxl6JF9d7pUr/hp6y+CtMIx90kVNZ72V22h8+r86j2VFLrr6LBOE1A+zqYcDR8dQ+mt/kMjC1uB86ktxDDgc0YRqJjJGNjM8keNpVrxk3FFaaSD0UZTAxT2HuihHcKPuHA6YOcaCjALccJNKbhOXXjmSiTyMxcNP2bX+hpZiRObQjR1gTSwi/i+ynzSYxykBDl4Gt/IakxcQyLiifKEdlrX8lKwI+cPobecBK+LsSsKKB0ww78VW78tT4CjVqrnxdHpHhIn1kdXD7yajJm4EwCogkWh4Yl3IIlwk74iDgS502FMBc4XdR8chwtLAo9Jg6Lawi6Kx7LkCT02ET06Dg0e//8OKAn9FoykpWVxaWXXsqf/vQnAEzTJC0tjbvuuosHHnigTfyCBQtoaGjgzTffDJZddtllTJ06lXXr1vVoZ0JWV4qvuBCzrgbxehCvF/E2Nf/f54GAj6hLxoLhg4CHurx8fKcqEK8P0+tFPF5Mnxfx+hG/n2HXDwN/I/gbKd1SRf1XPkyfYAag5X4LLcbNP4V2ZvL5yTwXdcc7TjDGzCvD6hQIj6P6aAwNp3SscdFY4+OwJadgHZqGNW0UtjGTsSSP7vTqpiKCz/DR6PdhwY5hangDJmX1FZQ2lNPg81Dvb6Le20iDv4l6XyON/iZGhH0XAhE0+AwK6vP4yrMNj9GATxoISCOG1gi6B4CGwjsxPcMAsMVtx5n0djvt0CEQQ3zTYsbHTiMjPoJEl59kl4XLR4whytm3dxFVFKVvmKZwrLKOokoPX52u5+jpSnbW/Q/1RhmmpQrN4m0V76+bgOfkT88sCZHj/jv44QyxoJsRWLRwbFo4Q/TxTI64iUiHlXCHlUON/8RpsxNpiyDCFkaEPYwIWzhR9jDiw+MY5RqF3arjsFpoNGoJt9kIszkIszrO+esgqf8af8FnBIqOEDhZiK41EZmmgbsUqS3nq7+VYzSaGL6278dnJy6HX01GAu2/b4cl+BhxjQ/sEWCP5PhmL6ahozus6HYrmsOO7rCh2e3Yk2IYcvU0sDrA4qAm7yhi6mhOJ5rdgWZ3ojudzf/GxBA2fixY7KDbEM2CFjMUbD076b+rx29rKBv1+Xzs3buXlStXBst0XWfWrFnk5eW1WycvL4/ly5e3Kps9ezabN2/u8Hm8Xi9e7zcvyLq6ulCa2WUVf/kvit6oIKq0/T+DYREmzi8NLh/amUB0cccHycDEfKxnXk9FTfG4Gu18OwkRBL8dvA44YRkKzgg8eiT7RjcQiPXT6NRpcFpxh9lwh1upC7dTE24jMeI31FuGEkCnIv5darS9CCYifoQixPcVcuwD5JhBbN0yMFwYptAQ9g7e8O1nzkIYiGaifesrkIZj92L6mu9Oa4/fiiPhvQ771lBoxfSkAWCLO4wzaV9z1876UCKiYbV6iI50EB9pJzx6Cj6LEOeMJykigZGxaYxPSGdCYhrxkWFqoqmiXGB0XWNMYgxjEmOAJGAUkAWAx29QUHma/Ioivqw6wUl3KUa4C92VxGm3l4r6OmqMaESvR9MDoBmYljpM6vADtbVhHDx44swzCZHjNn6TuJwlUD+GphNLg8uRYx9Bs3iCyyIamlgAC7p3JOFf34bVomHVdWpdTyF6IxoWQEcL09HQ0E9bcJBKmvVeLLdoaECZPEdE42limvxEN/qJbvLhc8KJYSOINzQWu11EDCvC4vFTaQSw+MDuE+w+sBgaBWEW/hJlJdZoYkVVKZ7yljMuvrO7RGWywbahu4gwheVf13D69SQCTe0nVbVDTD5Y4MWKcF91DRKAioX/ImnCzBBHtGeElIxUVlZiGAZJSa1vr56UlMThw4fbrVNWVtZufFlZWYfPs3r1alatWhVK07qltMnKyUgLSREQsDQ/DB38VvBbIGDRqDfH4xMrXux8PqIKR6yfgAV81jMPm4bXCj4bWP1L8GgRNOKg+rKP8M88iccOHjs02ZvjWyZ0uI88Ap7mDNQx9lXsrj1nWtX2BfbJUT8SaM6iHUnF2OOOdtinwqpaxN+cMNkTmnBENQTXtTnsa80Tzay6hk2LhIALDSs6dnTsWDVH8HHp2GEkOdMIt1vxaBbcMhyXM5pYZwxDwmNICHeRHpPAMFcc0U77WUnGoq4OiaIoFzCnzcLElGQmpiQDl3UQNQdvwKC8zk1x7WlOuauoaqyluqkWMSKIuWgs9b4A9R4f+xq+h9dowms2YYiPgHgx8GHixU4cVqcVb8DEFzCD74ctNE3OlAXwmV5qa79JVCJiK9AtDbSnvsnHiaKqb2JHHUWPqYF2puUZZiJvVC6Fqc3L4SOfwuKoCK63GILVsOC1O7D4I/mk7C7GZh8nMuCh1PUpptaI3Q/2ADj8UB2l8360g/CAzqjKi0hJrsDmDVBs8+MTsBmC1QCbAafiLGyMicJhCrdU+bFIgGqvRlLbZvaJkJKRvrJy5cpWZ1Pq6upIS0vr8ec5MOv/seOit6g3Wk+wajmQauhMi7qhpZDCpg+pC5w6sy4YjXZmaWr0T7BoFjQNippG8bW/pPnkgXYm5sy/mgZTZk/EpjcnDSVN1/G1/+LmOE3DolnQNR1d09A1jYvGXYLTGoZFh3JPFNW+H2DRdKy6BYtmwarrWHQLdouNUdnjCbeFY9Gh3j+OJnMJDosdh9WG02IjzO4gzOYg3OYg0ubEbtWxWnSg6xOK4aJu/b0VRVF6gsNqIT3ORXqcC+js1g5/6NL2RASPfzaegJ9Gv5dGn4cGvxdvwI/P8INYcNmT8Jsmpil8WfMkPsOHzwwQMAIETJOAaWBIAJsWTsZlUxBpnjOTX7sMj9GASPPkfRMTwzQRBIceQeaEizCluQ0H3QtpMtwIJqYICDSfUxdsWjgTRl3dPAdRwN/wHg2Blq96mmMApgEW7BxLn8exGc1rjza8R71xOhjTMjtjMqBpFv6S03ycu2lkegij0LNCSkbi4+OxWCyUl7c+eJeXl5Oc3P7PQJOTk0OKB3A4HDgcvT9ZcVHWcBZxRwg1xoYQG8q9T0aGEDsshNi4EGIVRVEuTJqmEWa3Ema3Esu5rytyCVd0edvXc+O5g4JCORaEcowJ5djVP0L6rZHdbufiiy/mvfe+mVtgmibvvfce2dnZ7dbJzs5uFQ+wdevWDuMVRVEURbmwhPw1zfLly7n55pu55JJLmD59Os888wwNDQ0sWbIEgMWLFzN06FBWr14NwN13383MmTP5/e9/z9y5c3nppZfYs2cPzz//fM/2RFEURVGUQSnkZGTBggWcPn2ahx9+mLKyMqZOnco777wTnKRaXFyM/q2flubk5LBx40Z+/etf8+CDDzJmzBg2b97c5WuMKIqiKIpyflOXg1cURVEUpVd09fh9YV6fVlEURVGUAUMlI4qiKIqi9CuVjCiKoiiK0q9UMqIoiqIoSr9SyYiiKIqiKP1KJSOKoiiKovQrlYwoiqIoitKvVDKiKIqiKEq/UsmIoiiKoij9KuTLwfeHlovE1tXV9XNLFEVRFEXpqpbj9rku9j4okhG32w1AWlpaP7dEURRFUZRQud1uYmJiOlw/KO5NY5omp06dIioqCk3Temy7dXV1pKWlceLEifP2njfnex9V/wa/872Pqn+D3/nex97sn4jgdrtJTU1tdRPdsw2KMyO6rjNs2LBe2350dPR5+QL7tvO9j6p/g9/53kfVv8HvfO9jb/WvszMiLdQEVkVRFEVR+pVKRhRFURRF6VcXdDLicDjIzc3F4XD0d1N6zfneR9W/we9876Pq3+B3vvdxIPRvUExgVRRFURTl/HVBnxlRFEVRFKX/qWREURRFUZR+pZIRRVEURVH6lUpGFEVRFEXpV+d9MvLb3/6WnJwcwsPDcblc7cYUFxczd+5cwsPDSUxM5L777iMQCHS63erqahYtWkR0dDQul4ulS5dSX1/fCz3oum3btqFpWruP3bt3d1jve9/7Xpv422+/vQ9bHpoRI0a0ae9jjz3WaR2Px8OyZcsYMmQIkZGRXH/99ZSXl/dRi7uuqKiIpUuXkpGRQVhYGKNGjSI3Nxefz9dpvYE+hs8++ywjRozA6XSSlZXFJ5980mn8pk2bGDduHE6nk0mTJvHWW2/1UUtDs3r1ai699FKioqJITExk3rx5HDlypNM6GzZsaDNWTqezj1ocukceeaRNe8eNG9dpncEyftD++4mmaSxbtqzd+IE+fjt27OCHP/whqampaJrG5s2bW60XER5++GFSUlIICwtj1qxZHD169JzbDXUfDtV5n4z4fD7mz5/PHXfc0e56wzCYO3cuPp+PnTt38re//Y0NGzbw8MMPd7rdRYsWkZ+fz9atW3nzzTfZsWMHt956a290octycnIoLS1t9fjFL35BRkYGl1xySad1b7nlllb1nnjiiT5qdfc8+uijrdp71113dRp/77338sYbb7Bp0ya2b9/OqVOn+MlPftJHre26w4cPY5omzz33HPn5+Tz99NOsW7eOBx988Jx1B+oYvvzyyyxfvpzc3Fz27dvHlClTmD17NhUVFe3G79y5k4ULF7J06VL279/PvHnzmDdvHgcOHOjjlp/b9u3bWbZsGR9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"metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "\n", + "([interpolator([x,1,2]) for x in tau_list])" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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" ] @@ -723,6 +851,33 @@ "MTGP['Interpolate']" ] }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "from marcia.backend import kernel as kernel " + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0.72159661, 0.45008845])" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [] + }, { "cell_type": "code", "execution_count": null, @@ -747,7 +902,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.10.4" }, "orig_nbformat": 4 }, diff --git a/marcia/__init__.py b/marcia/__init__.py index 89deee9..f83e9b7 100644 --- a/marcia/__init__.py +++ b/marcia/__init__.py @@ -5,4 +5,4 @@ from .database import Data from .likelihood import Likelihood from .sampler import Sampler -from .kernels import Kernels +from .kernels import * diff --git a/marcia/backend/kernel.py b/marcia/backend/kernel.py new file mode 100644 index 0000000..37f5575 --- /dev/null +++ b/marcia/backend/kernel.py @@ -0,0 +1,30 @@ +from numba import jit +import numpy as np +from scipy.integrate import odeint + + +# To combine the above functions into a single function, we need to use the following: +@jit(nopython=True) +def gMdef(tau, l1, nu): + if nu == 7/2: + return np.sqrt(2./5.) * 7**(3./4.) * np.exp(- np.sqrt(7.) * np.abs(tau) / l1) * (1./l1**2.)**(1./4.) * np.abs(tau) * (1. + l1 / np.sqrt(7. * tau**2.))/ l1 + else: + A = (nu / (2. * np.pi * l1**2.))**(1./8.) + #* (sp.special.gamma(nu/2. - 1./4.)/sp.special.gamma(nu/2. + 1./4.))**(1./2.) * (sp.special.gamma(nu + 1./2.)/sp.special.gamma(nu))**(1./4.) + B = 2.**(5./4. - nu/2.) + # / sp.special.gamma(nu/2. - 1./4.) + C = (2. * nu)**(1./2.) * tau**2. / l1 + return A,B,C # A**2. * B * C**(nu/2. - 1./4.) * sp.special.kv(nu/2. - 1./4., C) + +@jit(nopython=True) +def gdMdef(tau, l1, nu): + x = np.abs(tau) + l_s = l1 # just renaming + A = 2**(11./8. - nu/4.) * (nu / l_s**2.)**(1./4.) * (np.sqrt(nu) * np.sqrt(x**2.) / l_s)**(3./4. + nu/2.) + D = np.pi**(1./4.) * x + # * sp.special.gamma(1./4. + nu/2.) + return A, D + + + + \ No newline at end of file diff --git a/marcia/kernels.py b/marcia/kernels.py index d6c4c95..6e7e989 100644 --- a/marcia/kernels.py +++ b/marcia/kernels.py @@ -8,9 +8,12 @@ from scipy.interpolate import interp1d from scipy.integrate import quad from scipy.interpolate import RegularGridInterpolator +from multiprocessing import Pool +import itertools from marcia import Data from marcia import GPconfig +from marcia.backend import kernel as kernel class Kernels(object): @@ -20,268 +23,354 @@ class Kernels(object): This initialisation retuns the final covarinace matrices as functions of kernal paramters. """ - def __init__(self, parameters, data, filename = None): - + def __init__(self, data, filename = None): + """ + Initialisation simply takes the data and the filename for the config file, which declares all the GP + configurations. + """ self.clight = 299792458. / 1000. # km/s - self.kernels = ['SE', 'M92', 'M72', 'Mnu', 'dMnu', 'dSE'] # Possible kernel choices - # Here 'Mnu' is a generalised matern kernel with nu as a parameter - # 'dMnu' is the derivative of the generalised matern kernel with nu as a parameter - + # read the config file if filename is None: MTGP = GPconfig.GPConfig('GPconfig.ini').__dict__ else: MTGP = GPconfig.GPConfig(filename).__dict__ + + # read the models and the number of tasks self.models = MTGP['models'] - self.nus = MTGP['nus'] - self.n_Tasks = MTGP['n_Tasks'] - self.nmodel = self.n_Tasks + self.nTasks = MTGP['n_Tasks'] + self.nmodel = self.nTasks self.self_scale = MTGP['self_scale'] + # read the nus from the config file + self.nus = MTGP['nus'] + # The data must contain the list/lists of x-axes self.data = data self.ndata = len(data) - self.params = parameters - self.nparams = len(parameters) - - # To do: the self-scaled GP case should be handled outside the class and the parameters should be passed as a list of lists -- rewrite the code to handle this case - if self.self_scale is True and (self.nparams == self.nmodel): - self.ntasks = self.nmodel - 1 - self.model = self.model[:-1] - # Implying that the scale length for all the datasets is set to be the same, we need sigma_f equal to the number of GPs and one l_s - for i in range(self.ntasks-1): - self.params = np.append(self.params, parameters[-1]) - - elif self.self_scale is not True and (self.nparams != 2*self.nmodel): - # We need atleast two paramters per GP task: {sigma_f, l_s} - print('Error: Number of parameters does not match the model specifications') - sys.exit(0) - - # Reshaping the parameters to be a 2D array of shape (2, ntasks) - self.params = np.transpose(np.reshape(self.params, (2, self.ntasks))) - - # To create a dictionary of paramters and datasets - self.data_f = {} - self.sig_f = {} - self.l_s = {} - self.kernel_f = {} + + # To check if the number of datasets is equal to the number of models + if len(self.data) != self.nmodel: + raise ValueError('Error: data length does not match the number of kernels') + + # Here we initialise the interpolated covarince matrix function that can be called with the parameters + # We interpolate between the min and max values of scale lengths and the number of points is set to be 100 + # This is done to speed up the calculation of the covariance matrix + self.CovMat = {} self.CovMat_all = [] + self.data_tau = {} - if len(self.data) != self.ntasks: - print('Error: data length does not match the number of kernels') - sys.exit(0) - else: - for i in range(self.ntasks): - if self.model[i] in self.kernels and len(self.params[i]) == 2: - self.kernel_f[f't_{i}'] = self.model[i] - self.sig_f[f't_{i}'] = self.params[i, 0] - self.l_s[f't_{i}'] = self.params[i, 1] - self.data_f[f't_{i}'] = self.data[i] - + for i in range(self.nmodel): + for j in range(self.nmodel): + self.nu1 = self.nus[i] + self.nu2 = self.nus[j] + # To create the symmetric matrix + if i <= j: + # Set l1 and l2 values from the config file taskwise + l1_values = np.linspace(MTGP[f'Task_{i+1}']['l_min'], MTGP[f'Task_{i+1}']['l_max'], MTGP['KERNEL']['n_points']) + l2_values = np.linspace(MTGP[f'Task_{j+1}']['l_min'], MTGP[f'Task_{j+1}']['l_max'], MTGP['KERNEL']['n_points']) + tau_values = np.linspace(-10, 10, MTGP['KERNEL']['n_points']) + self.CovMat[f't_{i}{j}'] = self.KcMM(l1_values, l2_values, tau_values) + # To create the dictionary of tau values from the for each cross and auto combination of task + self.data_tau[f't_{i}{j}'] = self.data[i][:, None] - self.data[j][None, :] else: - print(self.model[i], self.params[i]) - print('Error: model or parameters not specified correctly') - sys.exit(0) - - # self.kernel = self.initialise_kernel(self.model, self.data) - - def __call__(self, parameters): - """ - This function is called when the class is called. It returns the covariance matrix for the GP model - """ - self.params = parameters - self.CovMat = self.Cov_Mat() - return self.CovMat - - # def initialise_kernel(self, data): - # """ - # Initialises the kernel for the data and the choosen kernels for the joint GP model - # """ - # n_tasks = len(model) - # x = self.data_f - # nu_f = {} - # if nu is not None: - # nu_f[f't_{i}'] = nu[i] + self.data_tau[f't_{j}{i}'] = self.data_tau[f't_{i}{j}'] + self.CovMat[f't_{j}{i}'] = np.transpose(self.CovMat[f't_{i}{j}']) + + - # # for i in range(n_tasks): + def __call__(self, pars): + """ + It returns the covariance matrix for the GP model for the given paramters + """ + # We set the self-scaling in the likelihood function and here simply create the dictionary of parameters - # return 0.0 + self.CovMat_all = np.block([[ pars[i,0]* pars[j,0]*self.CovMat[f't_{i}{j}']([pars[i,1]* pars[j,1], self.data_tau[f't_{i}{j}']]) for i in range(self.nTasks)] for j in range(self.nTasks)]) + return self.CovMat_all + # Define the special fucntions needed for the generalised matern kernel + def _spkv_(self, tau, l1): + return sp.special.kv(2., 3. * np.abs(tau) / l1) + + def _spgamma_(self, x): + return sp.special.gamma(x) - def gMdef(self, tau, nu, sigma1, l_s): + def gMdef(self, tau, nu, l1): """ Defines the basis function for the GP model and returns a vector Finally I define only ine single function for the basis function This is independent of the amplitude paramter sigma_f """ x = np.abs(tau) - if nu == '0.0': - return np.exp(- (x**2.)/(2. * l_s**2.)) - if nu == '9/2': - A = 48 * np.sqrt(3./35.) * (1./l_s**2.)**(5./4.) * x**2. * sp.special.kv(2., 3. * np.abs(x) / l_s) / np.pi - return A - if nu == '7/2': - A = np.sqrt(2./5.) * 7**(3./4.) * np.exp(- np.sqrt(7.) * np.abs(x) / l_s) * (1./l_s**2.)**(1./4.) * np.abs(x) * (1. + l_s / np.sqrt(7. * x**2.))/ l_s - return A - else: - A = (nu / (2. * np.pi * l_s**2.))**(1./8.) * (sp.special.gamma(nu/2. - 1./4.)/sp.special.gamma(nu/2. + 1./4.))**(1./2.) * (sp.special.gamma(nu + 1./2.)/sp.special.gamma(nu))**(1./4.) - B = 2.**(5./4. - nu/2.) / sp.special.gamma(nu/2. - 1./4.) - C = (2. * nu)**(1./2.) * x**2. / l_s - return A**2. * B * C**(nu/2. - 1./4.) * sp.special.kv(nu/2. - 1./4., C) + if nu == '0.0': # Squared Exponential kernel + return np.exp(- (x**2.)/(2. * l1**2.)) + elif nu == 5/2: # Matern 5/2 kernel + return kernel.gMdef(tau, l1, nu) * _spkv_(tau,l1) / np.pi + elif nu == 7/2: # Matern 7/2 kernel + return kernel.gMdef(tau,l1, nu) + else: # Generalised Matern kernel + A, B, C = kernel.gMdef(tau,l1,nu) + A = A * (_spgamma_(nu/2. - 1./4.)/_spgamma_(nu/2. + 1./4.))**(1./2.) * (_spgamma_(nu + 1./2.)/_spgamma_(nu))**(1./4.) + B = B / _spgamma_(nu/2. - 1./4.) + return A**2. * B * C**(nu/2. - 1./4.) * _spkv_(tau,l1) / np.pi + - def gdMdef(self, model, x, l_s, nu = None): + def gdMdef(self, tau, nu, l1): """ Defines the derivative of the basis function for the GP model and returns a vector - Finally I define only ine single function for the basis function - This is independent of the amplitude paramter sigma_f - """ - if model == 'SE': - return - x / l_s**2. * np.exp(- (x**2.)/(2. * l_s**2.)) - if model == 'Mnu': - A = 2**(11./8. - nu/4.) * (nu / l_s**2.)**(1./4.) * (np.sqrt(nu) * np.sqrt(x**2.) / l_s)**(3./4. + nu/2.) - B = sp.special.kv(1./4. * (5. - 2. * nu), np.sqrt(2.) * np.sqrt(nu) * np.sqrt(x**2.) / l_s) - C = np.sqrt(sp.special.gamma(1./2. + nu) / sp.special.gamma(nu)) - D = np.pi**(1./4.) * x * sp.special.gamma(1./4. + nu/2.) - return A * B * C / D - - def gddMdef(self, model, x, l_s, nu = None): - """ - Defines the second derivative of the basis function for the GP model and returns a vector Finally I define only ine single function for the basis function""" - if model == 'SE': - return (x**2. - l_s**2.) / l_s**4. * np.exp(- (x**2.)/(2. * l_s**2.)) - if model == 'Mnu': - A = l_s**2. * np.pi**(1./4.) * sp.special.gamma(1./4. + nu/2.) *2**(+25./8. + nu/4.) - B = (nu / l_s**2.)**(1./4.) * (np.sqrt(nu) * np.sqrt(x**2.) / l_s)**(nu/2.- 1./4.) - C = sp.special.kv(1./4. * (3. + 2. * nu), np.sqrt(2.) * np.sqrt(nu) * np.sqrt(x**2.) / l_s) - D = np.sqrt(sp.special.gamma(1./2. + nu) / sp.special.gamma(nu)) - E = 4. * (l_s**2. * (3. + 4. * (-2. + nu) * nu) + 8. * nu**2. * x**2.) - F = sp.special.kv(1./4. * (7. + 2. * nu), np.sqrt(2.) * np.sqrt(nu) * np.sqrt(x**2.) / l_s) - G = np.sqrt(2. / nu / x**2.) * l_s * (l_s**2. * (- 9. + 2. * nu * (9. + 2. * nu - 4. * nu**2.)) - 32. * nu**2. * x**2.) + B = sp.special.kv(1./4. * (5. - 2. * nu), np.sqrt(2.) * np.sqrt(nu) * np.sqrt(tau**2.) / l1) + C = np.sqrt(_spgamma_(1./2. + nu) / _spgamma_(nu)) + A, D = kernel.gdMdef(tau, l1, nu) + D = D * _spgamma_(1./4. + nu/2.) + return A * B * C / D + + def gMMdef_integrand(self, params): + tau, l1, l2 = params + gMMdef_integrand = lambda u: self.gMdef(u, self.nu1, l1) * self.gMdef(tau - u, self.nu2, l2) + integral, _ = quad(gMMdef_integrand, -np.inf, np.inf, epsabs=1e-8, epsrel=1e-8, limit=100) + return integral + + + def KcMM(self, l1_values, l2_values, tau_values): + integrals = np.zeros((len(tau_values), len(l2_values), len(l1_values))) + params = list(itertools.product(tau_values, l2_values, l1_values)) + with Pool() as pool: + integrals = pool.map(self.gMMdef_integrand, params) + integrals = np.array(integrals).reshape((len(tau_values), len(l2_values), len(l1_values))) + return RegularGridInterpolator((tau_values, l2_values, l1_values), integrals, bounds_error=False, fill_value=None) + + + + # self.kernels = ['SE', 'M92', 'M72', 'Mnu', 'dMnu', 'dSE'] # Possible kernel choices + # # Here 'Mnu' is a generalised matern kernel with nu as a parameter + # # 'dMnu' is the derivative of the generalised matern kernel with nu as a parameter + + # if filename is None: + # MTGP = GPconfig.GPConfig('GPconfig.ini').__dict__ + # else: + # MTGP = GPconfig.GPConfig(filename).__dict__ + # self.models = MTGP['models'] + # self.nus = MTGP['nus'] + # self.n_Tasks = MTGP['n_Tasks'] + # self.nmodel = self.n_Tasks + # self.self_scale = MTGP['self_scale'] + + # # The data must contain the list/lists of x-axes + # self.data = data + # self.ndata = len(data) + # self.params = parameters + # self.nparams = len(parameters) + + # # To do: the self-scaled GP case should be handled outside the class and the parameters should be passed as a list of lists -- rewrite the code to handle this case + # if self.self_scale is True and (self.nparams == self.nmodel): + # self.ntasks = self.nmodel - 1 + # self.model = self.model[:-1] + # # Implying that the scale length for all the datasets is set to be the same, we need sigma_f equal to the number of GPs and one l_s + # for i in range(self.ntasks-1): + # self.params = np.append(self.params, parameters[-1]) + + # elif self.self_scale is not True and (self.nparams != 2*self.nmodel): + # # We need atleast two paramters per GP task: {sigma_f, l_s} + # print('Error: Number of parameters does not match the model specifications') + # sys.exit(0) + + # # Reshaping the parameters to be a 2D array of shape (2, ntasks) + # self.params = np.transpose(np.reshape(self.params, (2, self.ntasks))) + + # # To create a dictionary of paramters and datasets + # self.data_f = {} + # self.sig_f = {} + # self.l_s = {} + # self.kernel_f = {} + # self.CovMat = {} + # self.CovMat_all = [] + + # if len(self.data) != self.ntasks: + # print('Error: data length does not match the number of kernels') + # sys.exit(0) + # else: + # for i in range(self.ntasks): + # if self.model[i] in self.kernels and len(self.params[i]) == 2: + # self.kernel_f[f't_{i}'] = self.model[i] + # self.sig_f[f't_{i}'] = self.params[i, 0] + # self.l_s[f't_{i}'] = self.params[i, 1] + # self.data_f[f't_{i}'] = self.data[i] + + # else: + # print(self.model[i], self.params[i]) + # print('Error: model or parameters not specified correctly') + # sys.exit(0) + + # def __call__(self, parameters): + # """ + # This function is called when the class is called. It returns the covariance matrix for the GP model + # """ + # self.params = parameters + # self.CovMat = self.Cov_Mat() + # return self.CovMat + + # # To define the special fucntions needed for the generalised matern kernel + # def _spkv_(self, tau, l1): + # return sp.special.kv(2., 3. * np.abs(tau) / l1) + # def _spgamma_(self, x): + # return sp.special.gamma(x) + + + + # def gdMdef(self, model, x, l_s, nu = None): + # """ + # Defines the derivative of the basis function for the GP model and returns a vector + # Finally I define only ine single function for the basis function + # This is independent of the amplitude paramter sigma_f + # """ + # if model == 'SE': + # return - x / l_s**2. * np.exp(- (x**2.)/(2. * l_s**2.)) + # if model == 'Mnu': + # A = 2**(11./8. - nu/4.) * (nu / l_s**2.)**(1./4.) * (np.sqrt(nu) * np.sqrt(x**2.) / l_s)**(3./4. + nu/2.) + # B = sp.special.kv(1./4. * (5. - 2. * nu), np.sqrt(2.) * np.sqrt(nu) * np.sqrt(x**2.) / l_s) + # C = np.sqrt(sp.special.gamma(1./2. + nu) / sp.special.gamma(nu)) + # D = np.pi**(1./4.) * x * sp.special.gamma(1./4. + nu/2.) + # return A * B * C / D + + # def gddMdef(self, model, x, l_s, nu = None): + # """ + # Defines the second derivative of the basis function for the GP model and returns a vector + # Finally I define only ine single function for the basis function""" + # if model == 'SE': + # return (x**2. - l_s**2.) / l_s**4. * np.exp(- (x**2.)/(2. * l_s**2.)) + # if model == 'Mnu': + # A = l_s**2. * np.pi**(1./4.) * sp.special.gamma(1./4. + nu/2.) *2**(+25./8. + nu/4.) + # B = (nu / l_s**2.)**(1./4.) * (np.sqrt(nu) * np.sqrt(x**2.) / l_s)**(nu/2.- 1./4.) + # C = sp.special.kv(1./4. * (3. + 2. * nu), np.sqrt(2.) * np.sqrt(nu) * np.sqrt(x**2.) / l_s) + # D = np.sqrt(sp.special.gamma(1./2. + nu) / sp.special.gamma(nu)) + # E = 4. * (l_s**2. * (3. + 4. * (-2. + nu) * nu) + 8. * nu**2. * x**2.) + # F = sp.special.kv(1./4. * (7. + 2. * nu), np.sqrt(2.) * np.sqrt(nu) * np.sqrt(x**2.) / l_s) + # G = np.sqrt(2. / nu / x**2.) * l_s * (l_s**2. * (- 9. + 2. * nu * (9. + 2. * nu - 4. * nu**2.)) - 32. * nu**2. * x**2.) - return A * B * D * ( G * C + E * F) / (E * D**2.) + # return A * B * D * ( G * C + E * F) / (E * D**2.) - def gMMdef(self, tau, u, nu1, sigma1, l1, nu2, sigma2, l2): - gM1 = self.gMdef(u, nu1, sigma1, l1) - gM2 = self.gMdef(tau - u, nu2, sigma2, l2) - return gM1 * gM2 + # def gMMdef(self, tau, u, nu1, sigma1, l1, nu2, sigma2, l2): + # gM1 = self.gMdef(u, nu1, sigma1, l1) + # gM2 = self.gMdef(tau - u, nu2, sigma2, l2) + # return gM1 * gM2 - def KcMM(self, l1_values, l2_values, tau_values): + # def KcMM(self, l1_values, l2_values, tau_values): - integrals = np.zeros((len(tau_values), len(l2_values), len(l1_values))) + # integrals = np.zeros((len(tau_values), len(l2_values), len(l1_values))) - for i, tau in enumerate(tau_values): - for j, l2 in enumerate(l2_values): - for k, l1 in enumerate(l1_values): - integrand = lambda u: self.gMMdef(tau, u, nu1, 1.0, l1, nu2, 1.0, l2) - integral, _ = quad(integrand, -np.inf, np.inf, epsabs=1e-8, epsrel=1e-8, limit=100) - integrals[i, j, k] = integral + # for i, tau in enumerate(tau_values): + # for j, l2 in enumerate(l2_values): + # for k, l1 in enumerate(l1_values): + # integrand = lambda u: self.gMMdef(tau, u, nu1, 1.0, l1, nu2, 1.0, l2) + # integral, _ = quad(integrand, -np.inf, np.inf, epsabs=1e-8, epsrel=1e-8, limit=100) + # integrals[i, j, k] = integral - return RegularGridInterpolator((tau_values, l2_values, l1_values), integrals, bounds_error=False, fill_value=None) + # return RegularGridInterpolator((tau_values, l2_values, l1_values), integrals, bounds_error=False, fill_value=None) - def matern(self, nu, x1, x2, l_s): - """ - Defines the generalised matern kernel https://en.wikipedia.org/wiki/Mat%C3%A9rn_covariance_function - nu is a positive half-integer that determines the differentiability of the function and the smoothness of the resulting Gaussian process sample paths. - nu = 1/2, 3/2, 5/2, ... tend to be used most often in practice. - nu tends to infinity, the matern kernel tends to the squared exponential kernel - nu tends to 0, the matern kernel tends to the absolute exponential kernel - The input x1 and x2 are the x-axes of the data points and l_s is the scale length - """ + # def matern(self, nu, x1, x2, l_s): + # """ + # Defines the generalised matern kernel https://en.wikipedia.org/wiki/Mat%C3%A9rn_covariance_function + # nu is a positive half-integer that determines the differentiability of the function and the smoothness of the resulting Gaussian process sample paths. + # nu = 1/2, 3/2, 5/2, ... tend to be used most often in practice. + # nu tends to infinity, the matern kernel tends to the squared exponential kernel + # nu tends to 0, the matern kernel tends to the absolute exponential kernel + # The input x1 and x2 are the x-axes of the data points and l_s is the scale length + # """ - # This fucntion returns nan when x1 = x2, so we need to replace nan with zero - return np.nan_to_num((2.**(1.-nu)/sp.special.gamma(nu)) * ((np.sqrt(2.*nu) * np.abs(x1-x2))/l_s)**nu * sp.special.kv(nu, (np.sqrt(2.*nu) * np.abs(x1-x2))/l_s)) + np.eye(len(x1)) + # # This fucntion returns nan when x1 = x2, so we need to replace nan with zero + # return np.nan_to_num((2.**(1.-nu)/sp.special.gamma(nu)) * ((np.sqrt(2.*nu) * np.abs(x1-x2))/l_s)**nu * sp.special.kv(nu, (np.sqrt(2.*nu) * np.abs(x1-x2))/l_s)) + np.eye(len(x1)) - def kernel(self, model, params, x1, x2=None): - """ - Defines the kernel function for the GP model and returns the covariance matrix - """ - if x2 is None: - x2 = x1 - if model == 'SE': # Squared Exponential kernel - return params[0]**2. * np.exp(- ((x1[:, None]-x2[None, :])**2.)/(2. * params[1]**2.)) - if model == 'M92': # Matern 9/2 kernel - mat_nu = 9./2. - return params[0]**2. * self.matern(mat_nu, x1[:, None], x2[None, :], params[1]) - if model == 'M72': # Matern 7/2 kernel - mat_nu = 7./2. - return params[0]**2. * self.matern(mat_nu, x1[:, None], x2[None, :], params[1]) - - def derivative_kernel(self, model1, model2, params1, params2, x1, x2=None): - """ - Defines the derivatives of cross kernel function for the GP model and returns a matrix - """ - dK = {} - if x2 is None: - x2 = x1 - if model1 == 'SE' and model2 == 'SE': - # product of the sigmas - sig1sig2 = params1[0] * params2[0] - # product of the scale lengths - l1l2 = params1[1] * params2[1] - # quadrature of length scales - l1l2_quad = params1[1]**2. + params2[1]**2. - # difference between x1 and x2 - x1x2 = x1[:, None]-x2[None, :] - - # derivativve wrt x1 and derivative wrt x2 - dK['dK_dx1'] = - 2 * sig1sig2 * x1x2 * np.exp(- (x1x2**2.)/(l1l2_quad)) * np.sqrt(2. * l1l2) / np.sqrt(l1l2_quad**3.) - dK['dK_dx2'] = - dK['dK_dx1'] - # derivative wrt x1 and x2, double derivative wrt x1 and double derivative wrt x2 - dK['d2K_dx1dx2'] = 2 * sig1sig2 * (1. - 2 * (x1x2**2.)/(l1l2_quad)) * np.exp(- (x1x2**2.)/(l1l2_quad)) * np.sqrt(2. * l1l2) / np.sqrt(l1l2_quad**3.) - dK['d2K_dx1dx1'] = dK['d2K_dx2dx2'] = - dK['d2K_dx1dx2'] - # double derivative wrt x1 and derivative wrt x2, derivative wrt x1 and double derivative wrt x2 - dK['d3K_dx1dx1dx2'] = - 4 * sig1sig2 * x1x2 * (3. - 2 * (x1x2**2.)/(l1l2_quad)) * np.exp(- (x1x2**2.)/(l1l2_quad)) * np.sqrt(2. * l1l2) / np.sqrt(l1l2_quad**5.) - dK['d3K_dx1dx2dx2'] = - dK['d3K_dx1dx1dx2'] - # double derivate wrt x1 and double derivative wrt x2 - dK['d4K_dx1dx1dx2dx2'] = 4 * sig1sig2 * (3. - 12 * (x1x2**2.)/(l1l2_quad) + 4 * (x1x2**4.)/(l1l2_quad**2.)) * np.exp(- (x1x2**2.)/(l1l2_quad)) * np.sqrt(2. * l1l2) / np.sqrt(l1l2_quad**5.) + # def kernel(self, model, params, x1, x2=None): + # """ + # Defines the kernel function for the GP model and returns the covariance matrix + # """ + # if x2 is None: + # x2 = x1 + # if model == 'SE': # Squared Exponential kernel + # return params[0]**2. * np.exp(- ((x1[:, None]-x2[None, :])**2.)/(2. * params[1]**2.)) + # if model == 'M92': # Matern 9/2 kernel + # mat_nu = 9./2. + # return params[0]**2. * self.matern(mat_nu, x1[:, None], x2[None, :], params[1]) + # if model == 'M72': # Matern 7/2 kernel + # mat_nu = 7./2. + # return params[0]**2. * self.matern(mat_nu, x1[:, None], x2[None, :], params[1]) - else: - # We need to define the general case for the derivatives of the cross kernel function using the basis functions - print('Error: Derivative for generalised cross kernel not defined') - sys.exit(0) + # def derivative_kernel(self, model1, model2, params1, params2, x1, x2=None): + # """ + # Defines the derivatives of cross kernel function for the GP model and returns a matrix + # """ + # dK = {} + # if x2 is None: + # x2 = x1 + # if model1 == 'SE' and model2 == 'SE': + # # product of the sigmas + # sig1sig2 = params1[0] * params2[0] + # # product of the scale lengths + # l1l2 = params1[1] * params2[1] + # # quadrature of length scales + # l1l2_quad = params1[1]**2. + params2[1]**2. + # # difference between x1 and x2 + # x1x2 = x1[:, None]-x2[None, :] + + # # derivativve wrt x1 and derivative wrt x2 + # dK['dK_dx1'] = - 2 * sig1sig2 * x1x2 * np.exp(- (x1x2**2.)/(l1l2_quad)) * np.sqrt(2. * l1l2) / np.sqrt(l1l2_quad**3.) + # dK['dK_dx2'] = - dK['dK_dx1'] + # # derivative wrt x1 and x2, double derivative wrt x1 and double derivative wrt x2 + # dK['d2K_dx1dx2'] = 2 * sig1sig2 * (1. - 2 * (x1x2**2.)/(l1l2_quad)) * np.exp(- (x1x2**2.)/(l1l2_quad)) * np.sqrt(2. * l1l2) / np.sqrt(l1l2_quad**3.) + # dK['d2K_dx1dx1'] = dK['d2K_dx2dx2'] = - dK['d2K_dx1dx2'] + # # double derivative wrt x1 and derivative wrt x2, derivative wrt x1 and double derivative wrt x2 + # dK['d3K_dx1dx1dx2'] = - 4 * sig1sig2 * x1x2 * (3. - 2 * (x1x2**2.)/(l1l2_quad)) * np.exp(- (x1x2**2.)/(l1l2_quad)) * np.sqrt(2. * l1l2) / np.sqrt(l1l2_quad**5.) + # dK['d3K_dx1dx2dx2'] = - dK['d3K_dx1dx1dx2'] + # # double derivate wrt x1 and double derivative wrt x2 + # dK['d4K_dx1dx1dx2dx2'] = 4 * sig1sig2 * (3. - 12 * (x1x2**2.)/(l1l2_quad) + 4 * (x1x2**4.)/(l1l2_quad**2.)) * np.exp(- (x1x2**2.)/(l1l2_quad)) * np.sqrt(2. * l1l2) / np.sqrt(l1l2_quad**5.) + + # else: + # # We need to define the general case for the derivatives of the cross kernel function using the basis functions + # print('Error: Derivative for generalised cross kernel not defined') + # sys.exit(0) - return dK + # return dK - def cross_kernel(self, model1, model2, params1, params2, x1, x2): - """ - Defines the cross kernel function for the GP model and returns the covariance matrix - """ - # product of the sigmas - sig1sig2 = params1[0] * params2[0] - # product of the scale lengths - l1l2 = params1[1] * params2[1] - # quadrature of length scales - l1l2_quad = params1[1]**2. + params2[1]**2. - # difference between x1 and x2 - x1x2 = x1[:, None]-x2[None, :] - - if model1 == 'SE' and model2 == 'SE': # Squared Exponential kernel - # This fucntion boils down to the SE kernel function when the scale lengths are equal for both the datasets - return sig1sig2 * np.exp(- (x1x2**2.)/(l1l2_quad)) * np.sqrt(2. * l1l2 / l1l2_quad) - else: - print('Error: Cross kernel not defined') - sys.exit(0) + # def cross_kernel(self, model1, model2, params1, params2, x1, x2): + # """ + # Defines the cross kernel function for the GP model and returns the covariance matrix + # """ + # # product of the sigmas + # sig1sig2 = params1[0] * params2[0] + # # product of the scale lengths + # l1l2 = params1[1] * params2[1] + # # quadrature of length scales + # l1l2_quad = params1[1]**2. + params2[1]**2. + # # difference between x1 and x2 + # x1x2 = x1[:, None]-x2[None, :] - def Cov_Mat(self): - """ - Defines the covariance matrix for the GP model and returns the covariance matrix - """ - # To create a dictionary of covariance matrices for each task + # if model1 == 'SE' and model2 == 'SE': # Squared Exponential kernel + # # This fucntion boils down to the SE kernel function when the scale lengths are equal for both the datasets + # return sig1sig2 * np.exp(- (x1x2**2.)/(l1l2_quad)) * np.sqrt(2. * l1l2 / l1l2_quad) + # else: + # print('Error: Cross kernel not defined') + # sys.exit(0) + + # def Cov_Mat(self): + # """ + # Defines the covariance matrix for the GP model and returns the covariance matrix + # """ + # # To create a dictionary of covariance matrices for each task - for i in range(self.ntasks): - for j in range(self.ntasks): - if i == j: - self.CovMat[f't_{i}{j}'] = self.kernel(self.kernel_f[f't_{i}'], self.params[i], self.data_f[f't_{i}']) - elif i < j: - self.CovMat[f't_{i}{j}'] = np.transpose(self.cross_kernel(self.kernel_f[f't_{i}'], self.kernel_f[f't_{j}'], self.params[i], self.params[j], self.data_f[f't_{i}'], self.data_f[f't_{j}'])) - else: - self.CovMat[f't_{i}{j}'] = np.transpose(self.CovMat[f't_{j}{i}']) + # for i in range(self.ntasks): + # for j in range(self.ntasks): + # if i == j: + # self.CovMat[f't_{i}{j}'] = self.kernel(self.kernel_f[f't_{i}'], self.params[i], self.data_f[f't_{i}']) + # elif i < j: + # self.CovMat[f't_{i}{j}'] = np.transpose(self.cross_kernel(self.kernel_f[f't_{i}'], self.kernel_f[f't_{j}'], self.params[i], self.params[j], self.data_f[f't_{i}'], self.data_f[f't_{j}'])) + # else: + # self.CovMat[f't_{i}{j}'] = np.transpose(self.CovMat[f't_{j}{i}']) - # To join all the covariance matrices defined above in the dictionaries into one big covariance matrix taking into account the cross correlations between the datasets - self.CovMat_all = np.block([[ self.CovMat[f't_{i}{j}'] for i in range(self.ntasks)] for j in range(self.ntasks)]) + # # To join all the covariance matrices defined above in the dictionaries into one big covariance matrix taking into account the cross correlations between the datasets + # self.CovMat_all = np.block([[ self.CovMat[f't_{i}{j}'] for i in range(self.ntasks)] for j in range(self.ntasks)]) - return self.CovMat_all + # return self.CovMat_all \ No newline at end of file From 36a8b3584fe298a8b26fa46abcdaf8d3cf3f4775 Mon Sep 17 00:00:00 2001 From: Balakrishna Sandeep Haridasu <32479204+Sandeepharidasu@users.noreply.github.com> Date: Wed, 21 Jun 2023 05:57:49 +0000 Subject: [PATCH 03/22] initiali likelihood added --- Notebooks/Validation_kernel.ipynb | 56 +++++++++++++------- Notebooks/data.ipynb | 2 +- marcia/likelihood_GP.py | 87 +++++++++++++++++++++++++++++++ 3 files changed, 125 insertions(+), 20 deletions(-) create mode 100644 marcia/likelihood_GP.py diff --git a/Notebooks/Validation_kernel.ipynb b/Notebooks/Validation_kernel.ipynb index dd48765..17ef166 100644 --- a/Notebooks/Validation_kernel.ipynb +++ b/Notebooks/Validation_kernel.ipynb @@ -2,9 +2,18 @@ "cells": [ { "cell_type": "code", - "execution_count": 2, + "execution_count": 3, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The autoreload extension is already loaded. To reload it, use:\n", + " %reload_ext autoreload\n" + ] + } + ], "source": [ "import sys\n", "sys.path.append('../')\n", @@ -189,7 +198,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 12, "metadata": {}, "outputs": [ { @@ -208,26 +217,34 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "{'x0': array([0.0708, 0.09 , 0.12 , 0.17 , 0.1791, 0.1993, 0.2 , 0.27 ,\n", - " 0.28 , 0.3519, 0.4 , 0.48 , 0.5929, 0.6797, 0.7812, 0.8754,\n", - " 0.88 , 0.9 , 1.037 , 1.3 , 1.363 , 1.43 , 1.53 , 1.75 ,\n", - " 1.965 , 0.3802, 0.4004, 0.4247, 0.4497, 0.4783, 0.47 ]),\n", - " 'x1': array([0.07, 0.2 , 0.35, 0.55, 0.9 , 1.5 ])}" + "array([[ 3.873024e+02, 0.000000e+00, 0.000000e+00, ..., 0.000000e+00,\n", + " 0.000000e+00, 0.000000e+00],\n", + " [ 0.000000e+00, 1.440000e+02, 0.000000e+00, ..., 0.000000e+00,\n", + " 0.000000e+00, 0.000000e+00],\n", + " [ 0.000000e+00, 0.000000e+00, 6.864400e+02, ..., 0.000000e+00,\n", + " 0.000000e+00, 0.000000e+00],\n", + " ...,\n", + " [ 0.000000e+00, 0.000000e+00, 0.000000e+00, ..., 1.089000e-03,\n", + " -1.054560e-03, 9.361500e-04],\n", + " [ 0.000000e+00, 0.000000e+00, 0.000000e+00, ..., -4.247100e-04,\n", + " 2.704000e-03, -1.185790e-03],\n", + " [ 0.000000e+00, 0.000000e+00, 0.000000e+00, ..., 1.633500e-04,\n", + " -5.137600e-04, 6.241000e-03]])" ] }, - "execution_count": 8, + "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "d2.x" + "cov2" ] }, { @@ -784,7 +801,7 @@ }, { "cell_type": "code", - "execution_count": 58, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -804,7 +821,7 @@ }, { "cell_type": "code", - "execution_count": 59, + "execution_count": 5, "metadata": {}, "outputs": [], "source": [ @@ -813,7 +830,7 @@ }, { "cell_type": "code", - "execution_count": 60, + "execution_count": 6, "metadata": {}, "outputs": [ { @@ -822,7 +839,7 @@ "['M92', 'SE']" ] }, - "execution_count": 60, + "execution_count": 6, "metadata": {}, "output_type": "execute_result" } @@ -833,22 +850,23 @@ }, { "cell_type": "code", - "execution_count": 61, + "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "True" + "0.001" ] }, - "execution_count": 61, + "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "MTGP['Interpolate']" + "# exttrac teh l_min and l_max values for each task \n", + "MTGP['Task_1']['l_min']" ] }, { diff --git a/Notebooks/data.ipynb b/Notebooks/data.ipynb index e68096d..b00098a 100644 --- a/Notebooks/data.ipynb +++ b/Notebooks/data.ipynb @@ -412,7 +412,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.10.4" }, "orig_nbformat": 4 }, diff --git a/marcia/likelihood_GP.py b/marcia/likelihood_GP.py new file mode 100644 index 0000000..2de130c --- /dev/null +++ b/marcia/likelihood_GP.py @@ -0,0 +1,87 @@ +import numpy as np +from marcia import Data +from marcia import GPconfig +from marcia import Cosmology as cosmo +from marcia import kernels as kern + + +class Likelihood_GP(object): + # This contains the generalized likelihood for the GP and MTGP + def __init__(self, model,parameters,data,GP_filename=None, cosmo_filename=None): + + # Read form the GP config file + # read the config file + if GP_filename is None: + MTGP = GP_filename.GPConfig('GPconfig.ini').__dict__ + else: + MTGP = GP_filename.GPConfig(GP_filename).__dict__ + + # read the models and the number of tasks + self.models = MTGP['models'] + self.nTasks = MTGP['n_Tasks'] + self.nmodel = self.nTasks + self.self_scale = MTGP['self_scale'] + # To define the priors for the GP hyperparameters using the the GPconfig file + self.priors = [] + for i in range(self.nTasks): + self.priors.append([MTGP[f'Task_{i}']['sigma_f_min'], MTGP[f'Task_{i}']['sigma_f_max']]) + self.priors.append([MTGP[f'Task_{i}']['l_min'], MTGP[f'Task_{i}']['l_max']]) + + self.priors = np.array(self.priors) + + # validate the number of models and data + if len(self.models) != len(data): + raise ValueError('The number of models and the number of data are not equal') + + # read the data and set the data covarince matrix + self.d = Data(data) + self.x, self.y, self.cov = self.d() + self.D_covmat = self.cov + + # intialize the kernals from Kernel class + self.GP_kernels = kern.Kernels(list(data.x.values())) + + + def logPrior(self, theta): + # if self.priors[0][0] < theta[0] < self.priors[0][1] and self.priors[1][0] < theta[1] < self.priors[1][1]: + # logPrior is independent of data for the most of it, unless otherwise some strange functions are defined + #if all((np.array(theta)-self.priors[:, 0])>0) and all((self.priors[:, 1]-np.array(theta))>0): + if all(self.priors[i][0] < theta[i] < self.priors[i][1] for i in range(len(theta))): + return 0.0 + return -np.inf + + def logLike(self,theta): + chi2 = self.chisq(theta) + return -0.5*chi2 + + def logProb(self, theta): + lp = self.logPrior(theta) + if not np.isfinite(lp): + return -np.inf + return lp + self.logLike(theta) + + def chisq(self,theta): + # We define the GP likelihood here + chi2 = 0 + # To call the GP class to get the covariance matrix + GP_covmat = self.GP_kernels(theta) + Total_covmat = GP_covmat + self.D_covmat + + # To perform cholesky decomposition + L = np.linalg.cholesky(Total_covmat) + L_inv = np.linalg.inv(L) + y_inv = np.dot(L_inv, self.y) + + # To calculate the log determinant + log_det = 2*np.sum(np.log(np.diag(L))) + + # To calculate the chi2 + chi2 = np.dot(y_inv.T, y_inv) + log_det + + return chi2 + + + + + + From cffc076a80d1160e86d76cf8618a91b1120cd65c Mon Sep 17 00:00:00 2001 From: Balakrishna Sandeep Haridasu <32479204+Sandeepharidasu@users.noreply.github.com> Date: Wed, 21 Jun 2023 06:02:16 +0000 Subject: [PATCH 04/22] intrinsic scatter option in GPconfig --- marcia/GPconfig.ini | 6 +++++- marcia/GPconfig.py | 7 +++++++ 2 files changed, 12 insertions(+), 1 deletion(-) diff --git a/marcia/GPconfig.ini b/marcia/GPconfig.ini index 801b4f7..db6b513 100644 --- a/marcia/GPconfig.ini +++ b/marcia/GPconfig.ini @@ -8,7 +8,7 @@ method = cubic n_points = 1000 [Task_1] -model = M92 +model = SE nu = 0.0 l_min = 0.001 l_max = 10.0 @@ -23,3 +23,7 @@ l_max = 10.0 sigma_f_min = 0.001 sigma_f_max = 10.0 +[INTRINSIC_SCATTER] +sigma_int = 0.1 +offset = 0.0001 + diff --git a/marcia/GPconfig.py b/marcia/GPconfig.py index d0552fb..edd7f2c 100644 --- a/marcia/GPconfig.py +++ b/marcia/GPconfig.py @@ -37,6 +37,13 @@ config.set(Task, 'sigma_f_min', '0.001') config.set(Task, 'sigma_f_max', '10.0') +# if necessary to include a intrinsic scatter or an offset to the covariance matrix +config['INTRINSIC_SCATTER'] = {'sigma_int': True, 'offset': True} +if config['INTRINSIC_SCATTER']['sigma_int']: + config['INTRINSIC_SCATTER']['sigma_int'] = '0.1' +if config['INTRINSIC_SCATTER']['offset']: + config['INTRINSIC_SCATTER']['offset'] = '0.0001' + # Write the configparser object to a file with open(filename, 'w') as configfile: config.write(configfile) From 6bf3991d66f8b0ff3d3769e5e2bb659558d5b1ce Mon Sep 17 00:00:00 2001 From: Balakrishna Sandeep Haridasu <32479204+Sandeepharidasu@users.noreply.github.com> Date: Wed, 21 Jun 2023 06:16:09 +0000 Subject: [PATCH 05/22] to include set theta function --- marcia/likelihood_GP.py | 21 +++++++++++++++++++++ 1 file changed, 21 insertions(+) diff --git a/marcia/likelihood_GP.py b/marcia/likelihood_GP.py index 2de130c..88d1c55 100644 --- a/marcia/likelihood_GP.py +++ b/marcia/likelihood_GP.py @@ -21,6 +21,8 @@ def __init__(self, model,parameters,data,GP_filename=None, cosmo_filename=None): self.nTasks = MTGP['n_Tasks'] self.nmodel = self.nTasks self.self_scale = MTGP['self_scale'] + self.scatter = MTGP['INTRINSIC_SCATTER']['sigma_int'] + # To define the priors for the GP hyperparameters using the the GPconfig file self.priors = [] for i in range(self.nTasks): @@ -41,6 +43,25 @@ def __init__(self, model,parameters,data,GP_filename=None, cosmo_filename=None): # intialize the kernals from Kernel class self.GP_kernels = kern.Kernels(list(data.x.values())) + # def set_theta(self, theta): + # # To reorganise the theta values for the GP hyperparameters in accordanace with the GPconfig file + # # theta contains no self-scale: [sigma_f_1, l_1, sigma_f_2, l_2, ...] + # # or [sigma_f_1, sigma_f_2, ..., l] if self_scale is True + # # and possibly with intrinsic scatter at the end [..., sigma_int] + + # if self.self_scale == False and len(theta) != 2*self.nTasks and self.scatter == False: + # raise ValueError('The number of hyperparameters does not match the number of tasks') + # elif self.self_scale == False and len(theta) != 2*self.nTasks+1 and self.scatter == True: + + # params = [] + # for i in range(self.nTasks): + # params.append(theta[2*i]) + # params.append(theta[2*i+1]) + # params = np.array(params) + + + # return params + def logPrior(self, theta): # if self.priors[0][0] < theta[0] < self.priors[0][1] and self.priors[1][0] < theta[1] < self.priors[1][1]: From 42fa4e8922ad5b8fb03dabda01085e02b6f62a9f Mon Sep 17 00:00:00 2001 From: Balakrishna Sandeep Haridasu <32479204+Sandeepharidasu@users.noreply.github.com> Date: Thu, 29 Jun 2023 13:19:12 +0000 Subject: [PATCH 06/22] config update --- marcia/GPconfig.ini | 2 +- marcia/GPconfig.py | 14 +++++++++----- 2 files changed, 10 insertions(+), 6 deletions(-) diff --git a/marcia/GPconfig.ini b/marcia/GPconfig.ini index db6b513..d618111 100644 --- a/marcia/GPconfig.ini +++ b/marcia/GPconfig.ini @@ -5,7 +5,7 @@ self_scale = True [KERNEL] interpolate = True method = cubic -n_points = 1000 +n_points = 100 [Task_1] model = SE diff --git a/marcia/GPconfig.py b/marcia/GPconfig.py index edd7f2c..dae4113 100644 --- a/marcia/GPconfig.py +++ b/marcia/GPconfig.py @@ -21,7 +21,7 @@ # self scale implies all the tasks have the same length scale paramter. config['GENERAL'] = {'n_Tasks': n_Tasks, 'self_scale': True} -config['KERNEL'] = {'Interpolate': True, 'Method': 'cubic', 'n_points': 1000 } +config['KERNEL'] = {'Interpolate': True, 'Method': 'cubic', 'n_points': 100 } # Set the configuration for each task: Need not be a loop, can be done manually as well @@ -65,8 +65,15 @@ def __init__(self, filename): # Set the number of tasks self.n_Tasks = config.getint('GENERAL', 'n_Tasks') + # Set the self_scale parameter self.self_scale = config.getboolean('GENERAL', 'self_scale') + + # Set the interpolation parameters + self.Interpolate = config.getboolean('KERNEL', 'Interpolate') + self.Method = config.get('KERNEL', 'Method') + self.n_points = config.getint('KERNEL', 'n_points') + # Set the configuration for each task for i in range(self.n_Tasks): Task = 'Task_' + str(i+1) @@ -84,7 +91,4 @@ def __init__(self, filename): # Create the GPparams class self.__dict__[Task] = {'model': model, 'nu': nu, 'l_min': l_min, 'l_max': l_max, 'sigma_f_min': sigma_f_min, 'sigma_f_max': sigma_f_max} - # Set the interpolation parameters - self.Interpolate = config.getboolean('KERNEL', 'Interpolate') - self.Method = config.get('KERNEL', 'Method') - self.n_points = config.getint('KERNEL', 'n_points') + From f5fa447f576c93b289c3b0d67afc42ac05e9c4e9 Mon Sep 17 00:00:00 2001 From: Balakrishna Sandeep Haridasu <32479204+Sandeepharidasu@users.noreply.github.com> Date: Fri, 30 Jun 2023 05:45:54 +0000 Subject: [PATCH 07/22] update mean function in likelihood --- marcia/likelihood_GP.py | 59 +++++++++++++++++++++++++---------------- 1 file changed, 36 insertions(+), 23 deletions(-) diff --git a/marcia/likelihood_GP.py b/marcia/likelihood_GP.py index 88d1c55..7c6491d 100644 --- a/marcia/likelihood_GP.py +++ b/marcia/likelihood_GP.py @@ -1,13 +1,14 @@ import numpy as np from marcia import Data from marcia import GPconfig +from marcia import CosmoConfig from marcia import Cosmology as cosmo from marcia import kernels as kern class Likelihood_GP(object): # This contains the generalized likelihood for the GP and MTGP - def __init__(self, model,parameters,data,GP_filename=None, cosmo_filename=None): + def __init__(self, data, GP_filename=None, cosmo_filename=None): # Read form the GP config file # read the config file @@ -15,7 +16,22 @@ def __init__(self, model,parameters,data,GP_filename=None, cosmo_filename=None): MTGP = GP_filename.GPConfig('GPconfig.ini').__dict__ else: MTGP = GP_filename.GPConfig(GP_filename).__dict__ - + + # To read the cosmology file and inculde a comological mean function in the GP + if cosmo_filename is None: + cosmo = cosmo_filename.CosmoConfig('cosmology.ini').__dict__ + else: + cosmo = cosmo_filename.CosmoConfig(cosmo_filename).__dict__ + + # To include the cosmological mean function in the GP + if cosmo['sample'] == False: + self.cosmo = cosmo['model'] + elif cosmo['sample'] == True: + # Yet to define the cosmological mean function for the sampled cosmology with paramters sampled amongside the GP hyperparameters + pass + else: + self.mean = [0.0] * len(np.flatten(data.x.values()) ) + # read the models and the number of tasks self.models = MTGP['models'] self.nTasks = MTGP['n_Tasks'] @@ -41,32 +57,28 @@ def __init__(self, model,parameters,data,GP_filename=None, cosmo_filename=None): self.D_covmat = self.cov # intialize the kernals from Kernel class - self.GP_kernels = kern.Kernels(list(data.x.values())) - - # def set_theta(self, theta): - # # To reorganise the theta values for the GP hyperparameters in accordanace with the GPconfig file - # # theta contains no self-scale: [sigma_f_1, l_1, sigma_f_2, l_2, ...] - # # or [sigma_f_1, sigma_f_2, ..., l] if self_scale is True - # # and possibly with intrinsic scatter at the end [..., sigma_int] + self.GP_kernels = kern.Kernels(list(data.x.values())) - # if self.self_scale == False and len(theta) != 2*self.nTasks and self.scatter == False: - # raise ValueError('The number of hyperparameters does not match the number of tasks') - # elif self.self_scale == False and len(theta) != 2*self.nTasks+1 and self.scatter == True: + def set_theta(self, theta): + # To reorganise the theta values for the GP hyperparameters in accordanace with the GPconfig file + # theta contains no self-scale: [sigma_f_1, l_1, sigma_f_2, l_2, ...] + # or [sigma_f_1, sigma_f_2, ..., l] if self_scale is True + # and possibly with intrinsic scatter at the end [..., sigma_int] - # params = [] - # for i in range(self.nTasks): - # params.append(theta[2*i]) - # params.append(theta[2*i+1]) - # params = np.array(params) + if self.self_scale == False and len(theta) != 2*self.nTasks and self.scatter == False: + raise ValueError('The number of hyperparameters does not match the number of tasks') + elif self.self_scale == False and len(theta) != 2*self.nTasks+1 and self.scatter == True: + params = [] + for i in range(self.nTasks): + params.append(theta[2*i]) + params.append(theta[2*i+1]) + params = np.array(params) - # return params + return params def logPrior(self, theta): - # if self.priors[0][0] < theta[0] < self.priors[0][1] and self.priors[1][0] < theta[1] < self.priors[1][1]: - # logPrior is independent of data for the most of it, unless otherwise some strange functions are defined - #if all((np.array(theta)-self.priors[:, 0])>0) and all((self.priors[:, 1]-np.array(theta))>0): if all(self.priors[i][0] < theta[i] < self.priors[i][1] for i in range(len(theta))): return 0.0 return -np.inf @@ -91,13 +103,14 @@ def chisq(self,theta): # To perform cholesky decomposition L = np.linalg.cholesky(Total_covmat) L_inv = np.linalg.inv(L) - y_inv = np.dot(L_inv, self.y) + y = self.y - self.mean + y_inv = np.dot(L_inv, y) # To calculate the log determinant log_det = 2*np.sum(np.log(np.diag(L))) # To calculate the chi2 - chi2 = np.dot(y_inv.T, y_inv) + log_det + chi2 = np.dot(y_inv.T, y) + log_det return chi2 From f77e5ec237ec9c31d10de8f4049e6f5758f440f7 Mon Sep 17 00:00:00 2001 From: Balakrishna Sandeep Haridasu <32479204+Sandeepharidasu@users.noreply.github.com> Date: Fri, 30 Jun 2023 05:46:34 +0000 Subject: [PATCH 08/22] added new cosmoconfig for GP (To be completed) --- marcia/CosmoConfig.py | 26 ++++++++++++++++++++++++++ 1 file changed, 26 insertions(+) create mode 100644 marcia/CosmoConfig.py diff --git a/marcia/CosmoConfig.py b/marcia/CosmoConfig.py new file mode 100644 index 0000000..1158350 --- /dev/null +++ b/marcia/CosmoConfig.py @@ -0,0 +1,26 @@ +import os +import toml +import numpy as np +import configparser + +# 1.) This is anexample file on how to create the config file +# 2.) We read the config file and create the comsoconfig class +# 3.) We define the functions to read the config file elsewhere in the code + +# Create a configparser object +config = configparser.ConfigParser() + +# This is the model name +model = 'LCDM' +sample = False +# To set the name of the file to be written,can be changed to any name however called correctly in the code +filename = 'cosmology.ini' + +# If utilising a constant cosmological mean then the following paramters are required +config['GENERAL'] = {'model': model, 'sample': sample} + + + + + + From 3cc2185f9556e555bfccbfce6dcb61b9b9fd19d7 Mon Sep 17 00:00:00 2001 From: Balakrishna Sandeep Haridasu <32479204+Sandeepharidasu@users.noreply.github.com> Date: Sat, 1 Jul 2023 08:04:23 +0000 Subject: [PATCH 09/22] update GPconfig --- marcia/GPconfig.py | 13 ++++++++++++- 1 file changed, 12 insertions(+), 1 deletion(-) diff --git a/marcia/GPconfig.py b/marcia/GPconfig.py index dae4113..c5d1a0f 100644 --- a/marcia/GPconfig.py +++ b/marcia/GPconfig.py @@ -17,12 +17,15 @@ # To set the name of the file to be written,can be changed to any name however called correctly in the code filename = 'GPconfig.ini' -# Set the number of tasks in the GENERAL section # self scale implies all the tasks have the same length scale paramter. config['GENERAL'] = {'n_Tasks': n_Tasks, 'self_scale': True} config['KERNEL'] = {'Interpolate': True, 'Method': 'cubic', 'n_points': 100 } +config['COSMO'] = {'cosmo_model': 'LCDM', 'sample': False} # 'LCDM' or 'wCDM', if sample is False then the mean is fixed to the fiducial cosmology + +config['ANALYSIS'] = {'method': 'optimise'} # 'optimise' or 'mcmc' + # Set the configuration for each task: Need not be a loop, can be done manually as well for i in range(n_Tasks): @@ -74,6 +77,14 @@ def __init__(self, filename): self.Method = config.get('KERNEL', 'Method') self.n_points = config.getint('KERNEL', 'n_points') + # Set the cosmology part + self.cosmo_model = config.get('COSMO', 'cosmo_model') + self.sample = config.getboolean('COSMO', 'sample') + + # Set the analysis part + self.method = config.get('ANALYSIS', 'method') + + # Set the configuration for each task for i in range(self.n_Tasks): Task = 'Task_' + str(i+1) From d2377c34b615b744c1dc16e70651bc50fbdbac87 Mon Sep 17 00:00:00 2001 From: Balakrishna Sandeep Haridasu <32479204+Sandeepharidasu@users.noreply.github.com> Date: Sat, 1 Jul 2023 08:27:26 +0000 Subject: [PATCH 10/22] update kernels and backend --- marcia/Archive/kernels.py | 376 ++++++++++++++++++++++++++++++++++++++ marcia/backend/kernel.py | 5 +- marcia/kernels.py | 321 +++++++++----------------------- 3 files changed, 470 insertions(+), 232 deletions(-) create mode 100644 marcia/Archive/kernels.py diff --git a/marcia/Archive/kernels.py b/marcia/Archive/kernels.py new file mode 100644 index 0000000..d348936 --- /dev/null +++ b/marcia/Archive/kernels.py @@ -0,0 +1,376 @@ +import sys +import cmath +import numpy as np +import scipy as sp +import scipy.constants as const +import time +import configparser +from scipy.interpolate import interp1d +from scipy.integrate import quad +from scipy.interpolate import RegularGridInterpolator +from multiprocessing import Pool +import itertools + +from marcia import Data +from marcia import GPconfig +from marcia.backend import kernel as kernel + + +class Kernels(object): + """ + General Gaussian process modelling that all the specific kernels must be inherited from. + Inputs would be the appropriate amplitude and scaling parameters needed for the particular model. + This initialisation retuns the final covarinace matrices as functions of kernal paramters. + """ + + def __init__(self, data, filename = None): + """ + Initialisation simply takes the data and the filename for the config file, which declares all the GP + configurations. + """ + self.clight = 299792458. / 1000. # km/s + + # read the config file + if filename is None: + MTGP = GPconfig.GPConfig('GPconfig.ini').__dict__ + else: + MTGP = GPconfig.GPConfig(filename).__dict__ + + # read the models and the number of tasks + self.models = MTGP['models'] + self.nTasks = MTGP['n_Tasks'] + self.nmodel = self.nTasks + self.self_scale = MTGP['self_scale'] + + # read the nus from the config file + self.nus = MTGP['nus'] + + # The data must contain the list/lists of x-axes + self.data = data + self.ndata = len(data) + + # To check if the number of datasets is equal to the number of models + if len(self.data) != self.nmodel: + raise ValueError(f'Error: data length is {len(self.data)} and does not match the number of kernels {self.nmodel}') + + # Here we initialise the interpolated covarince matrix function that can be called with the parameters + # We interpolate between the min and max values of scale lengths and the number of points is set to be 100 + # This is done to speed up the calculation of the covariance matrix + + self.CovMat = {} + self.CovMat_all = [] + self.data_tau = {} + + for i in range(self.nmodel): + for j in range(self.nmodel): + self.nu1 = self.nus[i] + self.nu2 = self.nus[j] + # To create the symmetric matrix + if i <= j: + # Set l1 and l2 values from the config file taskwise + l1_values = np.linspace(MTGP[f'Task_{i+1}']['l_min'], MTGP[f'Task_{i+1}']['l_max'], MTGP['n_points']) + l2_values = np.linspace(MTGP[f'Task_{j+1}']['l_min'], MTGP[f'Task_{j+1}']['l_max'], MTGP['n_points']) + tau_values = np.linspace(-10, 10, MTGP['n_points']) + self.CovMat[f't_{i}{j}'] = self.KcMM(l1_values, l2_values, tau_values) + # To create the dictionary of tau values from the for each cross and auto combination of task + self.data_tau[f't_{i}{j}'] = self.data[i][:, None] - self.data[j][None, :] + else: + self.data_tau[f't_{j}{i}'] = self.data_tau[f't_{i}{j}'] + self.CovMat[f't_{j}{i}'] = np.transpose(self.CovMat[f't_{i}{j}']) + + + + def __call__(self, pars): + """ + It returns the covariance matrix for the GP model for the given paramters + """ + # We set the self-scaling in the likelihood function and here simply create the dictionary of parameters + + self.CovMat_all = np.block([[ pars[i,0]* pars[j,0]*self.CovMat[f't_{i}{j}']([pars[i,1]* pars[j,1], self.data_tau[f't_{i}{j}']]) for i in range(self.nTasks)] for j in range(self.nTasks)]) + return self.CovMat_all + + # Define the special fucntions needed for the generalised matern kernel + def _spkv_(self, tau, l1): + return sp.special.kv(2., 3. * np.abs(tau) / l1) + + def _spgamma_(self, x): + return sp.special.gamma(x) + + def gMdef(self, tau, nu, l1): + """ + Defines the basis function for the GP model and returns a vector + Finally I define only ine single function for the basis function + This is independent of the amplitude paramter sigma_f + """ + x = np.abs(tau) + if nu == '0.0': # Squared Exponential kernel + return np.exp(- (x**2.)/(2. * l1**2.)) + elif nu == 5/2: # Matern 5/2 kernel + return kernel.gMdef(tau, l1, nu) * _spkv_(tau,l1) / np.pi + elif nu == 7/2: # Matern 7/2 kernel + return kernel.gMdef(tau,l1, nu) + else: # Generalised Matern kernel + A, B, C = kernel.gMdef(tau,l1,nu) + A = A * (_spgamma_(nu/2. - 1./4.)/_spgamma_(nu/2. + 1./4.))**(1./2.) * (_spgamma_(nu + 1./2.)/_spgamma_(nu))**(1./4.) + B = B / _spgamma_(nu/2. - 1./4.) + return A**2. * B * C**(nu/2. - 1./4.) * _spkv_(tau,l1) / np.pi + + + def gdMdef(self, tau, nu, l1): + """ + Defines the derivative of the basis function for the GP model and returns a vector + Finally I define only ine single function for the basis function""" + B = sp.special.kv(1./4. * (5. - 2. * nu), np.sqrt(2.) * np.sqrt(nu) * np.sqrt(tau**2.) / l1) + C = np.sqrt(_spgamma_(1./2. + nu) / _spgamma_(nu)) + A, D = kernel.gdMdef(tau, l1, nu) + D = D * _spgamma_(1./4. + nu/2.) + return A * B * C / D + + def gMMdef_integrand(self, params): + tau, l1, l2 = params + gMMdef_integrand = lambda u: self.gMdef(u, self.nu1, l1) * self.gMdef(tau - u, self.nu2, l2) + integral, _ = quad(gMMdef_integrand, -np.inf, np.inf, epsabs=1e-8, epsrel=1e-8, limit=100) + return integral + + + def KcMM(self, l1_values, l2_values, tau_values): + integrals = np.zeros((len(tau_values), len(l2_values), len(l1_values))) + params = list(itertools.product(tau_values, l2_values, l1_values)) + with Pool() as pool: + integrals = pool.map(self.gMMdef_integrand, params) + integrals = np.array(integrals).reshape((len(tau_values), len(l2_values), len(l1_values))) + return RegularGridInterpolator((tau_values, l2_values, l1_values), integrals, bounds_error=False, fill_value=None) + + + + # self.kernels = ['SE', 'M92', 'M72', 'Mnu', 'dMnu', 'dSE'] # Possible kernel choices + # # Here 'Mnu' is a generalised matern kernel with nu as a parameter + # # 'dMnu' is the derivative of the generalised matern kernel with nu as a parameter + + # if filename is None: + # MTGP = GPconfig.GPConfig('GPconfig.ini').__dict__ + # else: + # MTGP = GPconfig.GPConfig(filename).__dict__ + # self.models = MTGP['models'] + # self.nus = MTGP['nus'] + # self.n_Tasks = MTGP['n_Tasks'] + # self.nmodel = self.n_Tasks + # self.self_scale = MTGP['self_scale'] + + # # The data must contain the list/lists of x-axes + # self.data = data + # self.ndata = len(data) + # self.params = parameters + # self.nparams = len(parameters) + + # # To do: the self-scaled GP case should be handled outside the class and the parameters should be passed as a list of lists -- rewrite the code to handle this case + # if self.self_scale is True and (self.nparams == self.nmodel): + # self.ntasks = self.nmodel - 1 + # self.model = self.model[:-1] + # # Implying that the scale length for all the datasets is set to be the same, we need sigma_f equal to the number of GPs and one l_s + # for i in range(self.ntasks-1): + # self.params = np.append(self.params, parameters[-1]) + + # elif self.self_scale is not True and (self.nparams != 2*self.nmodel): + # # We need atleast two paramters per GP task: {sigma_f, l_s} + # print('Error: Number of parameters does not match the model specifications') + # sys.exit(0) + + # # Reshaping the parameters to be a 2D array of shape (2, ntasks) + # self.params = np.transpose(np.reshape(self.params, (2, self.ntasks))) + + # # To create a dictionary of paramters and datasets + # self.data_f = {} + # self.sig_f = {} + # self.l_s = {} + # self.kernel_f = {} + # self.CovMat = {} + # self.CovMat_all = [] + + # if len(self.data) != self.ntasks: + # print('Error: data length does not match the number of kernels') + # sys.exit(0) + # else: + # for i in range(self.ntasks): + # if self.model[i] in self.kernels and len(self.params[i]) == 2: + # self.kernel_f[f't_{i}'] = self.model[i] + # self.sig_f[f't_{i}'] = self.params[i, 0] + # self.l_s[f't_{i}'] = self.params[i, 1] + # self.data_f[f't_{i}'] = self.data[i] + + # else: + # print(self.model[i], self.params[i]) + # print('Error: model or parameters not specified correctly') + # sys.exit(0) + + # def __call__(self, parameters): + # """ + # This function is called when the class is called. It returns the covariance matrix for the GP model + # """ + # self.params = parameters + # self.CovMat = self.Cov_Mat() + # return self.CovMat + + # # To define the special fucntions needed for the generalised matern kernel + # def _spkv_(self, tau, l1): + # return sp.special.kv(2., 3. * np.abs(tau) / l1) + # def _spgamma_(self, x): + # return sp.special.gamma(x) + + + + # def gdMdef(self, model, x, l_s, nu = None): + # """ + # Defines the derivative of the basis function for the GP model and returns a vector + # Finally I define only ine single function for the basis function + # This is independent of the amplitude paramter sigma_f + # """ + # if model == 'SE': + # return - x / l_s**2. * np.exp(- (x**2.)/(2. * l_s**2.)) + # if model == 'Mnu': + # A = 2**(11./8. - nu/4.) * (nu / l_s**2.)**(1./4.) * (np.sqrt(nu) * np.sqrt(x**2.) / l_s)**(3./4. + nu/2.) + # B = sp.special.kv(1./4. * (5. - 2. * nu), np.sqrt(2.) * np.sqrt(nu) * np.sqrt(x**2.) / l_s) + # C = np.sqrt(sp.special.gamma(1./2. + nu) / sp.special.gamma(nu)) + # D = np.pi**(1./4.) * x * sp.special.gamma(1./4. + nu/2.) + # return A * B * C / D + + # def gddMdef(self, model, x, l_s, nu = None): + # """ + # Defines the second derivative of the basis function for the GP model and returns a vector + # Finally I define only ine single function for the basis function""" + # if model == 'SE': + # return (x**2. - l_s**2.) / l_s**4. * np.exp(- (x**2.)/(2. * l_s**2.)) + # if model == 'Mnu': + # A = l_s**2. * np.pi**(1./4.) * sp.special.gamma(1./4. + nu/2.) *2**(+25./8. + nu/4.) + # B = (nu / l_s**2.)**(1./4.) * (np.sqrt(nu) * np.sqrt(x**2.) / l_s)**(nu/2.- 1./4.) + # C = sp.special.kv(1./4. * (3. + 2. * nu), np.sqrt(2.) * np.sqrt(nu) * np.sqrt(x**2.) / l_s) + # D = np.sqrt(sp.special.gamma(1./2. + nu) / sp.special.gamma(nu)) + # E = 4. * (l_s**2. * (3. + 4. * (-2. + nu) * nu) + 8. * nu**2. * x**2.) + # F = sp.special.kv(1./4. * (7. + 2. * nu), np.sqrt(2.) * np.sqrt(nu) * np.sqrt(x**2.) / l_s) + # G = np.sqrt(2. / nu / x**2.) * l_s * (l_s**2. * (- 9. + 2. * nu * (9. + 2. * nu - 4. * nu**2.)) - 32. * nu**2. * x**2.) + + # return A * B * D * ( G * C + E * F) / (E * D**2.) + + # def gMMdef(self, tau, u, nu1, sigma1, l1, nu2, sigma2, l2): + # gM1 = self.gMdef(u, nu1, sigma1, l1) + # gM2 = self.gMdef(tau - u, nu2, sigma2, l2) + # return gM1 * gM2 + + # def KcMM(self, l1_values, l2_values, tau_values): + + # integrals = np.zeros((len(tau_values), len(l2_values), len(l1_values))) + + # for i, tau in enumerate(tau_values): + # for j, l2 in enumerate(l2_values): + # for k, l1 in enumerate(l1_values): + # integrand = lambda u: self.gMMdef(tau, u, nu1, 1.0, l1, nu2, 1.0, l2) + # integral, _ = quad(integrand, -np.inf, np.inf, epsabs=1e-8, epsrel=1e-8, limit=100) + # integrals[i, j, k] = integral + + # return RegularGridInterpolator((tau_values, l2_values, l1_values), integrals, bounds_error=False, fill_value=None) + + # def matern(self, nu, x1, x2, l_s): + # """ + # Defines the generalised matern kernel https://en.wikipedia.org/wiki/Mat%C3%A9rn_covariance_function + # nu is a positive half-integer that determines the differentiability of the function and the smoothness of the resulting Gaussian process sample paths. + # nu = 1/2, 3/2, 5/2, ... tend to be used most often in practice. + # nu tends to infinity, the matern kernel tends to the squared exponential kernel + # nu tends to 0, the matern kernel tends to the absolute exponential kernel + # The input x1 and x2 are the x-axes of the data points and l_s is the scale length + # """ + + # # This fucntion returns nan when x1 = x2, so we need to replace nan with zero + # return np.nan_to_num((2.**(1.-nu)/sp.special.gamma(nu)) * ((np.sqrt(2.*nu) * np.abs(x1-x2))/l_s)**nu * sp.special.kv(nu, (np.sqrt(2.*nu) * np.abs(x1-x2))/l_s)) + np.eye(len(x1)) + + + # def kernel(self, model, params, x1, x2=None): + # """ + # Defines the kernel function for the GP model and returns the covariance matrix + # """ + # if x2 is None: + # x2 = x1 + # if model == 'SE': # Squared Exponential kernel + # return params[0]**2. * np.exp(- ((x1[:, None]-x2[None, :])**2.)/(2. * params[1]**2.)) + # if model == 'M92': # Matern 9/2 kernel + # mat_nu = 9./2. + # return params[0]**2. * self.matern(mat_nu, x1[:, None], x2[None, :], params[1]) + # if model == 'M72': # Matern 7/2 kernel + # mat_nu = 7./2. + # return params[0]**2. * self.matern(mat_nu, x1[:, None], x2[None, :], params[1]) + + # def derivative_kernel(self, model1, model2, params1, params2, x1, x2=None): + # """ + # Defines the derivatives of cross kernel function for the GP model and returns a matrix + # """ + # dK = {} + # if x2 is None: + # x2 = x1 + # if model1 == 'SE' and model2 == 'SE': + # # product of the sigmas + # sig1sig2 = params1[0] * params2[0] + # # product of the scale lengths + # l1l2 = params1[1] * params2[1] + # # quadrature of length scales + # l1l2_quad = params1[1]**2. + params2[1]**2. + # # difference between x1 and x2 + # x1x2 = x1[:, None]-x2[None, :] + + # # derivativve wrt x1 and derivative wrt x2 + # dK['dK_dx1'] = - 2 * sig1sig2 * x1x2 * np.exp(- (x1x2**2.)/(l1l2_quad)) * np.sqrt(2. * l1l2) / np.sqrt(l1l2_quad**3.) + # dK['dK_dx2'] = - dK['dK_dx1'] + # # derivative wrt x1 and x2, double derivative wrt x1 and double derivative wrt x2 + # dK['d2K_dx1dx2'] = 2 * sig1sig2 * (1. - 2 * (x1x2**2.)/(l1l2_quad)) * np.exp(- (x1x2**2.)/(l1l2_quad)) * np.sqrt(2. * l1l2) / np.sqrt(l1l2_quad**3.) + # dK['d2K_dx1dx1'] = dK['d2K_dx2dx2'] = - dK['d2K_dx1dx2'] + # # double derivative wrt x1 and derivative wrt x2, derivative wrt x1 and double derivative wrt x2 + # dK['d3K_dx1dx1dx2'] = - 4 * sig1sig2 * x1x2 * (3. - 2 * (x1x2**2.)/(l1l2_quad)) * np.exp(- (x1x2**2.)/(l1l2_quad)) * np.sqrt(2. * l1l2) / np.sqrt(l1l2_quad**5.) + # dK['d3K_dx1dx2dx2'] = - dK['d3K_dx1dx1dx2'] + # # double derivate wrt x1 and double derivative wrt x2 + # dK['d4K_dx1dx1dx2dx2'] = 4 * sig1sig2 * (3. - 12 * (x1x2**2.)/(l1l2_quad) + 4 * (x1x2**4.)/(l1l2_quad**2.)) * np.exp(- (x1x2**2.)/(l1l2_quad)) * np.sqrt(2. * l1l2) / np.sqrt(l1l2_quad**5.) + + # else: + # # We need to define the general case for the derivatives of the cross kernel function using the basis functions + # print('Error: Derivative for generalised cross kernel not defined') + # sys.exit(0) + + # return dK + + # def cross_kernel(self, model1, model2, params1, params2, x1, x2): + # """ + # Defines the cross kernel function for the GP model and returns the covariance matrix + # """ + # # product of the sigmas + # sig1sig2 = params1[0] * params2[0] + # # product of the scale lengths + # l1l2 = params1[1] * params2[1] + # # quadrature of length scales + # l1l2_quad = params1[1]**2. + params2[1]**2. + # # difference between x1 and x2 + # x1x2 = x1[:, None]-x2[None, :] + + # if model1 == 'SE' and model2 == 'SE': # Squared Exponential kernel + # # This fucntion boils down to the SE kernel function when the scale lengths are equal for both the datasets + # return sig1sig2 * np.exp(- (x1x2**2.)/(l1l2_quad)) * np.sqrt(2. * l1l2 / l1l2_quad) + # else: + # print('Error: Cross kernel not defined') + # sys.exit(0) + + # def Cov_Mat(self): + # """ + # Defines the covariance matrix for the GP model and returns the covariance matrix + # """ + # # To create a dictionary of covariance matrices for each task + + # for i in range(self.ntasks): + # for j in range(self.ntasks): + # if i == j: + # self.CovMat[f't_{i}{j}'] = self.kernel(self.kernel_f[f't_{i}'], self.params[i], self.data_f[f't_{i}']) + # elif i < j: + # self.CovMat[f't_{i}{j}'] = np.transpose(self.cross_kernel(self.kernel_f[f't_{i}'], self.kernel_f[f't_{j}'], self.params[i], self.params[j], self.data_f[f't_{i}'], self.data_f[f't_{j}'])) + # else: + # self.CovMat[f't_{i}{j}'] = np.transpose(self.CovMat[f't_{j}{i}']) + + # # To join all the covariance matrices defined above in the dictionaries into one big covariance matrix taking into account the cross correlations between the datasets + # self.CovMat_all = np.block([[ self.CovMat[f't_{i}{j}'] for i in range(self.ntasks)] for j in range(self.ntasks)]) + + # return self.CovMat_all + \ No newline at end of file diff --git a/marcia/backend/kernel.py b/marcia/backend/kernel.py index 37f5575..5d5fe98 100644 --- a/marcia/backend/kernel.py +++ b/marcia/backend/kernel.py @@ -7,14 +7,15 @@ @jit(nopython=True) def gMdef(tau, l1, nu): if nu == 7/2: - return np.sqrt(2./5.) * 7**(3./4.) * np.exp(- np.sqrt(7.) * np.abs(tau) / l1) * (1./l1**2.)**(1./4.) * np.abs(tau) * (1. + l1 / np.sqrt(7. * tau**2.))/ l1 + result = np.sqrt(2./5.) * 7**(3./4.) * np.exp(- np.sqrt(7.) * np.abs(tau) / l1) * (1./l1**2.)**(1./4.) * np.abs(tau) * (1. + l1 / np.sqrt(7. * tau**2.))/ l1 else: A = (nu / (2. * np.pi * l1**2.))**(1./8.) #* (sp.special.gamma(nu/2. - 1./4.)/sp.special.gamma(nu/2. + 1./4.))**(1./2.) * (sp.special.gamma(nu + 1./2.)/sp.special.gamma(nu))**(1./4.) B = 2.**(5./4. - nu/2.) # / sp.special.gamma(nu/2. - 1./4.) C = (2. * nu)**(1./2.) * tau**2. / l1 - return A,B,C # A**2. * B * C**(nu/2. - 1./4.) * sp.special.kv(nu/2. - 1./4., C) + result = A,B,C # A**2. * B * C**(nu/2. - 1./4.) * sp.special.kv(nu/2. - 1./4., C) + return result @jit(nopython=True) def gdMdef(tau, l1, nu): diff --git a/marcia/kernels.py b/marcia/kernels.py index 6e7e989..d3b887d 100644 --- a/marcia/kernels.py +++ b/marcia/kernels.py @@ -48,10 +48,21 @@ def __init__(self, data, filename = None): # The data must contain the list/lists of x-axes self.data = data self.ndata = len(data) + + # To print a few details of the run when the class is initialised + print(f'Number of tasks: {self.nTasks}') + print(f'Number of datasets: {self.ndata}') + # print the chosen kernels + print(f'Kernels: {self.models}') + + # To define kernels in a dictionary + self.kernel_f = {} + for i in range(self.nTasks): + self.kernel_f[f't_{i}'] = self.models[i] # To check if the number of datasets is equal to the number of models if len(self.data) != self.nmodel: - raise ValueError('Error: data length does not match the number of kernels') + raise ValueError(f'Error: data length is {len(self.data)} and does not match the number of kernels {self.nmodel}') # Here we initialise the interpolated covarince matrix function that can be called with the parameters # We interpolate between the min and max values of scale lengths and the number of points is set to be 100 @@ -66,11 +77,15 @@ def __init__(self, data, filename = None): self.nu1 = self.nus[i] self.nu2 = self.nus[j] # To create the symmetric matrix - if i <= j: + if i == j: + # for these we have simply the auto covariance matrix + self.data_tau[f't_{i}{j}'] = self.data[i][:, None] - self.data[j][None, :] + self.CovMat[f't_{i}{j}'] = self.kernel(self.models[i], self.data[i], self.data[j]) + if i < j: # Set l1 and l2 values from the config file taskwise - l1_values = np.linspace(MTGP[f'Task_{i+1}']['l_min'], MTGP[f'Task_{i+1}']['l_max'], MTGP['KERNEL']['n_points']) - l2_values = np.linspace(MTGP[f'Task_{j+1}']['l_min'], MTGP[f'Task_{j+1}']['l_max'], MTGP['KERNEL']['n_points']) - tau_values = np.linspace(-10, 10, MTGP['KERNEL']['n_points']) + l1_values = np.linspace(MTGP[f'Task_{i+1}']['l_min'], MTGP[f'Task_{i+1}']['l_max'], MTGP['n_points']) + l2_values = np.linspace(MTGP[f'Task_{j+1}']['l_min'], MTGP[f'Task_{j+1}']['l_max'], MTGP['n_points']) + tau_values = np.linspace(-10, 10, MTGP['n_points']) self.CovMat[f't_{i}{j}'] = self.KcMM(l1_values, l2_values, tau_values) # To create the dictionary of tau values from the for each cross and auto combination of task self.data_tau[f't_{i}{j}'] = self.data[i][:, None] - self.data[j][None, :] @@ -103,7 +118,7 @@ def gMdef(self, tau, nu, l1): This is independent of the amplitude paramter sigma_f """ x = np.abs(tau) - if nu == '0.0': # Squared Exponential kernel + if nu == 0.0: # Squared Exponential kernel return np.exp(- (x**2.)/(2. * l1**2.)) elif nu == 5/2: # Matern 5/2 kernel return kernel.gMdef(tau, l1, nu) * _spkv_(tau,l1) / np.pi @@ -134,243 +149,89 @@ def gMMdef_integrand(self, params): def KcMM(self, l1_values, l2_values, tau_values): + """ + Defines the cross kernel function for the GP model and returns the covariance matrix + """ integrals = np.zeros((len(tau_values), len(l2_values), len(l1_values))) params = list(itertools.product(tau_values, l2_values, l1_values)) with Pool() as pool: integrals = pool.map(self.gMMdef_integrand, params) integrals = np.array(integrals).reshape((len(tau_values), len(l2_values), len(l1_values))) return RegularGridInterpolator((tau_values, l2_values, l1_values), integrals, bounds_error=False, fill_value=None) - - - - # self.kernels = ['SE', 'M92', 'M72', 'Mnu', 'dMnu', 'dSE'] # Possible kernel choices - # # Here 'Mnu' is a generalised matern kernel with nu as a parameter - # # 'dMnu' is the derivative of the generalised matern kernel with nu as a parameter - - # if filename is None: - # MTGP = GPconfig.GPConfig('GPconfig.ini').__dict__ - # else: - # MTGP = GPconfig.GPConfig(filename).__dict__ - # self.models = MTGP['models'] - # self.nus = MTGP['nus'] - # self.n_Tasks = MTGP['n_Tasks'] - # self.nmodel = self.n_Tasks - # self.self_scale = MTGP['self_scale'] - - # # The data must contain the list/lists of x-axes - # self.data = data - # self.ndata = len(data) - # self.params = parameters - # self.nparams = len(parameters) - - # # To do: the self-scaled GP case should be handled outside the class and the parameters should be passed as a list of lists -- rewrite the code to handle this case - # if self.self_scale is True and (self.nparams == self.nmodel): - # self.ntasks = self.nmodel - 1 - # self.model = self.model[:-1] - # # Implying that the scale length for all the datasets is set to be the same, we need sigma_f equal to the number of GPs and one l_s - # for i in range(self.ntasks-1): - # self.params = np.append(self.params, parameters[-1]) - - # elif self.self_scale is not True and (self.nparams != 2*self.nmodel): - # # We need atleast two paramters per GP task: {sigma_f, l_s} - # print('Error: Number of parameters does not match the model specifications') - # sys.exit(0) - - # # Reshaping the parameters to be a 2D array of shape (2, ntasks) - # self.params = np.transpose(np.reshape(self.params, (2, self.ntasks))) - - # # To create a dictionary of paramters and datasets - # self.data_f = {} - # self.sig_f = {} - # self.l_s = {} - # self.kernel_f = {} - # self.CovMat = {} - # self.CovMat_all = [] - - # if len(self.data) != self.ntasks: - # print('Error: data length does not match the number of kernels') - # sys.exit(0) - # else: - # for i in range(self.ntasks): - # if self.model[i] in self.kernels and len(self.params[i]) == 2: - # self.kernel_f[f't_{i}'] = self.model[i] - # self.sig_f[f't_{i}'] = self.params[i, 0] - # self.l_s[f't_{i}'] = self.params[i, 1] - # self.data_f[f't_{i}'] = self.data[i] - - # else: - # print(self.model[i], self.params[i]) - # print('Error: model or parameters not specified correctly') - # sys.exit(0) - - # def __call__(self, parameters): - # """ - # This function is called when the class is called. It returns the covariance matrix for the GP model - # """ - # self.params = parameters - # self.CovMat = self.Cov_Mat() - # return self.CovMat - - # # To define the special fucntions needed for the generalised matern kernel - # def _spkv_(self, tau, l1): - # return sp.special.kv(2., 3. * np.abs(tau) / l1) - # def _spgamma_(self, x): - # return sp.special.gamma(x) - - - - # def gdMdef(self, model, x, l_s, nu = None): - # """ - # Defines the derivative of the basis function for the GP model and returns a vector - # Finally I define only ine single function for the basis function - # This is independent of the amplitude paramter sigma_f - # """ - # if model == 'SE': - # return - x / l_s**2. * np.exp(- (x**2.)/(2. * l_s**2.)) - # if model == 'Mnu': - # A = 2**(11./8. - nu/4.) * (nu / l_s**2.)**(1./4.) * (np.sqrt(nu) * np.sqrt(x**2.) / l_s)**(3./4. + nu/2.) - # B = sp.special.kv(1./4. * (5. - 2. * nu), np.sqrt(2.) * np.sqrt(nu) * np.sqrt(x**2.) / l_s) - # C = np.sqrt(sp.special.gamma(1./2. + nu) / sp.special.gamma(nu)) - # D = np.pi**(1./4.) * x * sp.special.gamma(1./4. + nu/2.) - # return A * B * C / D - - # def gddMdef(self, model, x, l_s, nu = None): - # """ - # Defines the second derivative of the basis function for the GP model and returns a vector - # Finally I define only ine single function for the basis function""" - # if model == 'SE': - # return (x**2. - l_s**2.) / l_s**4. * np.exp(- (x**2.)/(2. * l_s**2.)) - # if model == 'Mnu': - # A = l_s**2. * np.pi**(1./4.) * sp.special.gamma(1./4. + nu/2.) *2**(+25./8. + nu/4.) - # B = (nu / l_s**2.)**(1./4.) * (np.sqrt(nu) * np.sqrt(x**2.) / l_s)**(nu/2.- 1./4.) - # C = sp.special.kv(1./4. * (3. + 2. * nu), np.sqrt(2.) * np.sqrt(nu) * np.sqrt(x**2.) / l_s) - # D = np.sqrt(sp.special.gamma(1./2. + nu) / sp.special.gamma(nu)) - # E = 4. * (l_s**2. * (3. + 4. * (-2. + nu) * nu) + 8. * nu**2. * x**2.) - # F = sp.special.kv(1./4. * (7. + 2. * nu), np.sqrt(2.) * np.sqrt(nu) * np.sqrt(x**2.) / l_s) - # G = np.sqrt(2. / nu / x**2.) * l_s * (l_s**2. * (- 9. + 2. * nu * (9. + 2. * nu - 4. * nu**2.)) - 32. * nu**2. * x**2.) - - # return A * B * D * ( G * C + E * F) / (E * D**2.) - - # def gMMdef(self, tau, u, nu1, sigma1, l1, nu2, sigma2, l2): - # gM1 = self.gMdef(u, nu1, sigma1, l1) - # gM2 = self.gMdef(tau - u, nu2, sigma2, l2) - # return gM1 * gM2 - - # def KcMM(self, l1_values, l2_values, tau_values): - # integrals = np.zeros((len(tau_values), len(l2_values), len(l1_values))) - # for i, tau in enumerate(tau_values): - # for j, l2 in enumerate(l2_values): - # for k, l1 in enumerate(l1_values): - # integrand = lambda u: self.gMMdef(tau, u, nu1, 1.0, l1, nu2, 1.0, l2) - # integral, _ = quad(integrand, -np.inf, np.inf, epsabs=1e-8, epsrel=1e-8, limit=100) - # integrals[i, j, k] = integral - - # return RegularGridInterpolator((tau_values, l2_values, l1_values), integrals, bounds_error=False, fill_value=None) - - # def matern(self, nu, x1, x2, l_s): - # """ - # Defines the generalised matern kernel https://en.wikipedia.org/wiki/Mat%C3%A9rn_covariance_function - # nu is a positive half-integer that determines the differentiability of the function and the smoothness of the resulting Gaussian process sample paths. - # nu = 1/2, 3/2, 5/2, ... tend to be used most often in practice. - # nu tends to infinity, the matern kernel tends to the squared exponential kernel - # nu tends to 0, the matern kernel tends to the absolute exponential kernel - # The input x1 and x2 are the x-axes of the data points and l_s is the scale length - # """ + def matern(self, nu, x1, x2, l_s): + """ + Defines the generalised matern kernel https://en.wikipedia.org/wiki/Mat%C3%A9rn_covariance_function + nu is a positive half-integer that determines the differentiability of the function and the smoothness of the resulting Gaussian process sample paths. + nu = 1/2, 3/2, 5/2, ... tend to be used most often in practice. + nu tends to infinity, the matern kernel tends to the squared exponential kernel + nu tends to 0, the matern kernel tends to the absolute exponential kernel + The input x1 and x2 are the x-axes of the data points and l_s is the scale length + """ - # # This fucntion returns nan when x1 = x2, so we need to replace nan with zero - # return np.nan_to_num((2.**(1.-nu)/sp.special.gamma(nu)) * ((np.sqrt(2.*nu) * np.abs(x1-x2))/l_s)**nu * sp.special.kv(nu, (np.sqrt(2.*nu) * np.abs(x1-x2))/l_s)) + np.eye(len(x1)) + # This fucntion returns nan when x1 = x2, so we need to replace nan with zero + return np.nan_to_num((2.**(1.-nu)/sp.special.gamma(nu)) * ((np.sqrt(2.*nu) * np.abs(x1-x2))/l_s)**nu * sp.special.kv(nu, (np.sqrt(2.*nu) * np.abs(x1-x2))/l_s)) + np.eye(len(x1)) - # def kernel(self, model, params, x1, x2=None): - # """ - # Defines the kernel function for the GP model and returns the covariance matrix - # """ - # if x2 is None: - # x2 = x1 - # if model == 'SE': # Squared Exponential kernel - # return params[0]**2. * np.exp(- ((x1[:, None]-x2[None, :])**2.)/(2. * params[1]**2.)) - # if model == 'M92': # Matern 9/2 kernel - # mat_nu = 9./2. - # return params[0]**2. * self.matern(mat_nu, x1[:, None], x2[None, :], params[1]) - # if model == 'M72': # Matern 7/2 kernel - # mat_nu = 7./2. - # return params[0]**2. * self.matern(mat_nu, x1[:, None], x2[None, :], params[1]) - - # def derivative_kernel(self, model1, model2, params1, params2, x1, x2=None): - # """ - # Defines the derivatives of cross kernel function for the GP model and returns a matrix - # """ - # dK = {} - # if x2 is None: - # x2 = x1 - # if model1 == 'SE' and model2 == 'SE': - # # product of the sigmas - # sig1sig2 = params1[0] * params2[0] - # # product of the scale lengths - # l1l2 = params1[1] * params2[1] - # # quadrature of length scales - # l1l2_quad = params1[1]**2. + params2[1]**2. - # # difference between x1 and x2 - # x1x2 = x1[:, None]-x2[None, :] - - # # derivativve wrt x1 and derivative wrt x2 - # dK['dK_dx1'] = - 2 * sig1sig2 * x1x2 * np.exp(- (x1x2**2.)/(l1l2_quad)) * np.sqrt(2. * l1l2) / np.sqrt(l1l2_quad**3.) - # dK['dK_dx2'] = - dK['dK_dx1'] - # # derivative wrt x1 and x2, double derivative wrt x1 and double derivative wrt x2 - # dK['d2K_dx1dx2'] = 2 * sig1sig2 * (1. - 2 * (x1x2**2.)/(l1l2_quad)) * np.exp(- (x1x2**2.)/(l1l2_quad)) * np.sqrt(2. * l1l2) / np.sqrt(l1l2_quad**3.) - # dK['d2K_dx1dx1'] = dK['d2K_dx2dx2'] = - dK['d2K_dx1dx2'] - # # double derivative wrt x1 and derivative wrt x2, derivative wrt x1 and double derivative wrt x2 - # dK['d3K_dx1dx1dx2'] = - 4 * sig1sig2 * x1x2 * (3. - 2 * (x1x2**2.)/(l1l2_quad)) * np.exp(- (x1x2**2.)/(l1l2_quad)) * np.sqrt(2. * l1l2) / np.sqrt(l1l2_quad**5.) - # dK['d3K_dx1dx2dx2'] = - dK['d3K_dx1dx1dx2'] - # # double derivate wrt x1 and double derivative wrt x2 - # dK['d4K_dx1dx1dx2dx2'] = 4 * sig1sig2 * (3. - 12 * (x1x2**2.)/(l1l2_quad) + 4 * (x1x2**4.)/(l1l2_quad**2.)) * np.exp(- (x1x2**2.)/(l1l2_quad)) * np.sqrt(2. * l1l2) / np.sqrt(l1l2_quad**5.) - - # else: - # # We need to define the general case for the derivatives of the cross kernel function using the basis functions - # print('Error: Derivative for generalised cross kernel not defined') - # sys.exit(0) - - # return dK - - # def cross_kernel(self, model1, model2, params1, params2, x1, x2): - # """ - # Defines the cross kernel function for the GP model and returns the covariance matrix - # """ - # # product of the sigmas - # sig1sig2 = params1[0] * params2[0] - # # product of the scale lengths - # l1l2 = params1[1] * params2[1] - # # quadrature of length scales - # l1l2_quad = params1[1]**2. + params2[1]**2. - # # difference between x1 and x2 - # x1x2 = x1[:, None]-x2[None, :] - - # if model1 == 'SE' and model2 == 'SE': # Squared Exponential kernel - # # This fucntion boils down to the SE kernel function when the scale lengths are equal for both the datasets - # return sig1sig2 * np.exp(- (x1x2**2.)/(l1l2_quad)) * np.sqrt(2. * l1l2 / l1l2_quad) - # else: - # print('Error: Cross kernel not defined') - # sys.exit(0) + def kernel(self, model, params, x1, x2=None): + """ + Defines the kernel function for the GP model and returns the covariance matrix + """ + if x2 is None: + x2 = x1 + if model == 'SE': # Squared Exponential kernel + return params[0]**2. * np.exp(- ((x1[:, None]-x2[None, :])**2.)/(2. * params[1]**2.)) + if model == 'M92': # Matern 9/2 kernel + mat_nu = 9./2. + return params[0]**2. * self.matern(mat_nu, x1[:, None], x2[None, :], params[1]) + if model == 'M72': # Matern 7/2 kernel + mat_nu = 7./2. + return params[0]**2. * self.matern(mat_nu, x1[:, None], x2[None, :], params[1]) + if model == 'M52': # Matern 5/2 kernel + mat_nu = 5./2. + return params[0]**2. * self.matern(mat_nu, x1[:, None], x2[None, :], params[1]) + if model == 'M32': # Matern 3/2 kernel + mat_nu = 3./2. + return params[0]**2. * self.matern(mat_nu, x1[:, None], x2[None, :], params[1]) + + def cross_kernel(self, model1, model2, params1, params2, x1, x2): + """ + Defines the cross kernel function for the GP model and returns the covariance matrix + """ + # product of the sigmas + sig1sig2 = params1[0] * params2[0] + # product of the scale lengths + l1l2 = params1[1] * params2[1] + # quadrature of length scales + l1l2_quad = params1[1]**2. + params2[1]**2. + # difference between x1 and x2 + x1x2 = x1[:, None]-x2[None, :] + + if model1 == 'SE' and model2 == 'SE': # Squared Exponential kernel + # This fucntion boils down to the SE kernel function when the scale lengths are equal for both the datasets + return sig1sig2 * np.exp(- (x1x2**2.)/(l1l2_quad)) * np.sqrt(2. * l1l2 / l1l2_quad) + else: + print('Error: Cross kernel not defined') + sys.exit(0) - # def Cov_Mat(self): - # """ - # Defines the covariance matrix for the GP model and returns the covariance matrix - # """ - # # To create a dictionary of covariance matrices for each task + def Cov_Mat(self): + """ + Defines the covariance matrix for the GP model and returns the covariance matrix + """ + # To create a dictionary of covariance matrices for each task - # for i in range(self.ntasks): - # for j in range(self.ntasks): - # if i == j: - # self.CovMat[f't_{i}{j}'] = self.kernel(self.kernel_f[f't_{i}'], self.params[i], self.data_f[f't_{i}']) - # elif i < j: - # self.CovMat[f't_{i}{j}'] = np.transpose(self.cross_kernel(self.kernel_f[f't_{i}'], self.kernel_f[f't_{j}'], self.params[i], self.params[j], self.data_f[f't_{i}'], self.data_f[f't_{j}'])) - # else: - # self.CovMat[f't_{i}{j}'] = np.transpose(self.CovMat[f't_{j}{i}']) + for i in range(self.nTasks): + for j in range(self.nTasks): + if i == j: + self.CovMat[f't_{i}{j}'] = self.kernel(self.kernel_f[f't_{i}'], self.params[i], self.data_f[f't_{i}']) + elif i < j: + self.CovMat[f't_{i}{j}'] = np.transpose(self.cross_kernel(self.kernel_f[f't_{i}'], self.kernel_f[f't_{j}'], self.params[i], self.params[j], self.data_f[f't_{i}'], self.data_f[f't_{j}'])) + else: + self.CovMat[f't_{i}{j}'] = np.transpose(self.CovMat[f't_{j}{i}']) - # # To join all the covariance matrices defined above in the dictionaries into one big covariance matrix taking into account the cross correlations between the datasets - # self.CovMat_all = np.block([[ self.CovMat[f't_{i}{j}'] for i in range(self.ntasks)] for j in range(self.ntasks)]) + # To join all the covariance matrices defined above in the dictionaries into one big covariance matrix taking into account the cross correlations between the datasets + self.CovMat_all = np.block([[ self.CovMat[f't_{i}{j}'] for i in range(self.nTasks)] for j in range(self.nTasks)]) - # return self.CovMat_all + return self.CovMat_all \ No newline at end of file From f0e8adda30306cb1da0771b747bc476d0523b241 Mon Sep 17 00:00:00 2001 From: Balakrishna Sandeep Haridasu <32479204+Sandeepharidasu@users.noreply.github.com> Date: Sat, 1 Jul 2023 08:39:18 +0000 Subject: [PATCH 11/22] update kernels.py --- marcia/kernels.py | 26 +++++++++++++++----------- 1 file changed, 15 insertions(+), 11 deletions(-) diff --git a/marcia/kernels.py b/marcia/kernels.py index d3b887d..055cc16 100644 --- a/marcia/kernels.py +++ b/marcia/kernels.py @@ -55,10 +55,12 @@ def __init__(self, data, filename = None): # print the chosen kernels print(f'Kernels: {self.models}') - # To define kernels in a dictionary + # To define kernels and data in a dictionary self.kernel_f = {} + self.data_f = {} for i in range(self.nTasks): self.kernel_f[f't_{i}'] = self.models[i] + self.data_f[f't_{i}'] = self.data[i] # To check if the number of datasets is equal to the number of models if len(self.data) != self.nmodel: @@ -121,14 +123,14 @@ def gMdef(self, tau, nu, l1): if nu == 0.0: # Squared Exponential kernel return np.exp(- (x**2.)/(2. * l1**2.)) elif nu == 5/2: # Matern 5/2 kernel - return kernel.gMdef(tau, l1, nu) * _spkv_(tau,l1) / np.pi + return kernel.gMdef(tau, l1, nu) * self._spkv_(tau,l1) / np.pi elif nu == 7/2: # Matern 7/2 kernel return kernel.gMdef(tau,l1, nu) else: # Generalised Matern kernel A, B, C = kernel.gMdef(tau,l1,nu) - A = A * (_spgamma_(nu/2. - 1./4.)/_spgamma_(nu/2. + 1./4.))**(1./2.) * (_spgamma_(nu + 1./2.)/_spgamma_(nu))**(1./4.) - B = B / _spgamma_(nu/2. - 1./4.) - return A**2. * B * C**(nu/2. - 1./4.) * _spkv_(tau,l1) / np.pi + A = A * (self._spgamma_(nu/2. - 1./4.)/self._spgamma_(nu/2. + 1./4.))**(1./2.) * (self._spgamma_(nu + 1./2.)/self._spgamma_(nu))**(1./4.) + B = B / self._spgamma_(nu/2. - 1./4.) + return A**2. * B * C**(nu/2. - 1./4.) * self._spkv_(tau,l1) / np.pi def gdMdef(self, tau, nu, l1): @@ -136,9 +138,9 @@ def gdMdef(self, tau, nu, l1): Defines the derivative of the basis function for the GP model and returns a vector Finally I define only ine single function for the basis function""" B = sp.special.kv(1./4. * (5. - 2. * nu), np.sqrt(2.) * np.sqrt(nu) * np.sqrt(tau**2.) / l1) - C = np.sqrt(_spgamma_(1./2. + nu) / _spgamma_(nu)) + C = np.sqrt(self._spgamma_(1./2. + nu) / self._spgamma_(nu)) A, D = kernel.gdMdef(tau, l1, nu) - D = D * _spgamma_(1./4. + nu/2.) + D = D * self._spgamma_(1./4. + nu/2.) return A * B * C / D def gMMdef_integrand(self, params): @@ -174,7 +176,7 @@ def matern(self, nu, x1, x2, l_s): return np.nan_to_num((2.**(1.-nu)/sp.special.gamma(nu)) * ((np.sqrt(2.*nu) * np.abs(x1-x2))/l_s)**nu * sp.special.kv(nu, (np.sqrt(2.*nu) * np.abs(x1-x2))/l_s)) + np.eye(len(x1)) - def kernel(self, model, params, x1, x2=None): + def kernel(self, model, params, x1, x2=None, mat_nu=None): """ Defines the kernel function for the GP model and returns the covariance matrix """ @@ -194,6 +196,8 @@ def kernel(self, model, params, x1, x2=None): if model == 'M32': # Matern 3/2 kernel mat_nu = 3./2. return params[0]**2. * self.matern(mat_nu, x1[:, None], x2[None, :], params[1]) + if model == 'matern' and mat_nu is not None: + return params[0]**2. * self.matern(mat_nu, x1[:, None], x2[None, :], params[1]) def cross_kernel(self, model1, model2, params1, params2, x1, x2): """ @@ -215,7 +219,7 @@ def cross_kernel(self, model1, model2, params1, params2, x1, x2): print('Error: Cross kernel not defined') sys.exit(0) - def Cov_Mat(self): + def Cov_Mat(self, params): """ Defines the covariance matrix for the GP model and returns the covariance matrix """ @@ -224,9 +228,9 @@ def Cov_Mat(self): for i in range(self.nTasks): for j in range(self.nTasks): if i == j: - self.CovMat[f't_{i}{j}'] = self.kernel(self.kernel_f[f't_{i}'], self.params[i], self.data_f[f't_{i}']) + self.CovMat[f't_{i}{j}'] = self.kernel(self.kernel_f[f't_{i}'], params[i], self.data_f[f't_{i}']) elif i < j: - self.CovMat[f't_{i}{j}'] = np.transpose(self.cross_kernel(self.kernel_f[f't_{i}'], self.kernel_f[f't_{j}'], self.params[i], self.params[j], self.data_f[f't_{i}'], self.data_f[f't_{j}'])) + self.CovMat[f't_{i}{j}'] = np.transpose(self.cross_kernel(self.kernel_f[f't_{i}'], self.kernel_f[f't_{j}'], params[i], params[j], self.data_f[f't_{i}'], self.data_f[f't_{j}'])) else: self.CovMat[f't_{i}{j}'] = np.transpose(self.CovMat[f't_{j}{i}']) From f8c265763a1764580b14a6c836fb3e20525a60fc Mon Sep 17 00:00:00 2001 From: Balakrishna Sandeep Haridasu <32479204+Sandeepharidasu@users.noreply.github.com> Date: Sat, 1 Jul 2023 10:42:18 +0000 Subject: [PATCH 12/22] some changes to the kernel --- Notebooks/GPconfig.ini | 13 +- Notebooks/KcMM_v1.pck | Bin 0 -> 8002815 bytes Notebooks/Validation_kernel.ipynb | 336 ++++++++++++------------------ marcia/likelihood_GP.py | 15 -- 4 files changed, 141 insertions(+), 223 deletions(-) create mode 100644 Notebooks/KcMM_v1.pck diff --git a/Notebooks/GPconfig.ini b/Notebooks/GPconfig.ini index 50a1c12..e7927ee 100644 --- a/Notebooks/GPconfig.ini +++ b/Notebooks/GPconfig.ini @@ -5,7 +5,14 @@ self_scale = True [KERNEL] interpolate = True method = cubic -n_points = 1000 +n_points = 100 + +[COSMO] +cosmo_model = LCDM +sample = False + +[ANALYSIS] +method = optimise [Task_1] model = SE @@ -23,3 +30,7 @@ l_max = 10.0 sigma_f_min = 0.001 sigma_f_max = 10.0 +[INTRINSIC_SCATTER] +sigma_int = 0.1 +offset = 0.0001 + diff --git a/Notebooks/KcMM_v1.pck b/Notebooks/KcMM_v1.pck new file mode 100644 index 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