Skip to content

Instantly share code, notes, and snippets.

Show Gist options
  • Save brandonwillard/d506bc96347201107f564cb6afc81aa6 to your computer and use it in GitHub Desktop.
Save brandonwillard/d506bc96347201107f564cb6afc81aa6 to your computer and use it in GitHub Desktop.
Display the source blob
Display the rendered blob
Raw
{
"cells": [
{
"metadata": {
"trusted": true,
"collapsed": true
},
"cell_type": "code",
"source": "from mpmath import mp, fp\nmp.dps = 5\nfp.dps = 5",
"execution_count": 62,
"outputs": []
},
{
"metadata": {
"collapsed": true,
"trusted": true
},
"cell_type": "code",
"source": "import pandas as pd",
"execution_count": 1,
"outputs": []
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "import seaborn as sns \nsns.set(style=\"darkgrid\")",
"execution_count": 2,
"outputs": []
},
{
"metadata": {
"collapsed": false,
"trusted": true
},
"cell_type": "code",
"source": "%pylab inline\npylab.rcParams['figure.figsize'] = (10.0, 8.0)",
"execution_count": 3,
"outputs": [
{
"output_type": "stream",
"text": "Populating the interactive namespace from numpy and matplotlib\n",
"name": "stdout"
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "# Introduction\n\nIn this notebook we compare different numerical approaches to computing the posterior expectations, $E[Z^n \\mid y, \\sigma, \\tau]$ for $n=1, 0$. These values are then used in the following SURE calculation. "
},
{
"metadata": {
"collapsed": false,
"trusted": true
},
"cell_type": "code",
"source": "def SURE_hs_single(y, E_Z_hs_func, sig=1., tau=1., **kwargs):\n r\"\"\" Compute SURE for a given :math:`E[Z^k]` implementation.\n \n Parameters\n ==========\n y: float\n Observation\n E_Z_hs_func: function\n A function that takes the same inputs as this one and\n returns a pair corresponding to value and computation\n type.\n sig: float\n Error std. dev\n tau: float\n Global shrinkage parameter\n \n Returns\n =======\n tuple (float, str)\n A SURE value and computation type for the given point.\n \"\"\"\n E_1 = E_Z_hs_func(y, sig=sig, tau=tau, n=1, **kwargs)\n E_2 = E_Z_hs_func(y, sig=sig, tau=tau, n=2, **kwargs)\n res = 2. * sig**2 - (y * sig**2 * E_1[0])**2\n res += 2. * (-sig**2 * E_1[0] + y**2 * E_2[0])\n return (res, '{}-{}'.format(E_1[1], E_2[1]))\n\nSURE_hs = np.vectorize(SURE_hs_single, excluded=set([1]), \n otypes=[float, str])",
"execution_count": 4,
"outputs": []
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Since each implementation makes separate computations of $E[Z^n]$ and $E[Z]$ for large $y$, they are all expected to fail when $E[Z^n]$ and $E[Z]$ correspondingly become too large for floating point precision. Although the two quantities are ultimately divided, we should still get overflow errors, so, when we do, we catch the errors and perform the infinite precision calculation. If the inifinite precision calculation fails, which it can given maximum iteration limits, we return `NaN`. In all cases, we label the values by their method of computation."
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## Finite Precision $\\Phi_1$\n\nThis method estimates $E[Z]$ using `mpmath.hyper2d`, which is designed to directly estimate $\\Phi_1$."
},
{
"metadata": {
"trusted": true,
"collapsed": true
},
"cell_type": "code",
"source": "def E_Z_hs_num_single(y, sig=1., tau=1., n=1):\n try:\n # (double) floating point calculations\n res = fp.rf(1., n)/fp.rf(3/2., n)\n res *= fp.hyper2d({'m+n': 0.5, 'm': 1.}, {'m+n': 3/2.+n},\n 1. - 1./tau**2, (y/sig)**2/2.)\n res /= fp.hyper2d({'m+n': 0.5, 'm': 1.}, {'m+n': 3/2.},\n 1. - 1./tau**2, (y/sig)**2/2.)\n return (res, 'fp')\n except:\n pass\n try:\n # If it fails, use the direct infinite precision calculations.\n res = mp.rf(1., n)/mp.rf(3/2., n)\n res *= mp.hyper2d({'m+n': 0.5, 'm': 1.}, {'m+n': 3/2.+n},\n 1. - 1./tau**2, (y/sig)**2/2.)\n res /= mp.hyper2d({'m+n': 0.5, 'm': 1.}, {'m+n': 3/2.},\n 1. - 1./tau**2, (y/sig)**2/2.)\n return (res, 'inf')\n except:\n pass\n return (np.nan, 'failed')",
"execution_count": 5,
"outputs": []
},
{
"metadata": {
"collapsed": false,
"trusted": true
},
"cell_type": "code",
"source": "y_range = pd.Series(np.linspace(-50, 50, 500), name='y')",
"execution_count": 6,
"outputs": []
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "%%time\nSURE_num_vals = SURE_hs(y_range, E_Z_hs_num_single, tau=1)",
"execution_count": 7,
"outputs": [
{
"output_type": "stream",
"text": "CPU times: user 697 ms, sys: 36 ms, total: 733 ms\nWall time: 687 ms\n",
"name": "stdout"
}
]
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "from timeit import timeit\ntimeit(stmt=lambda: SURE_hs(y_range, E_Z_hs_num_single, tau=1),\n number=10)",
"execution_count": 8,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "6.547171115875244"
},
"metadata": {},
"execution_count": 8
}
]
},
{
"metadata": {
"trusted": true,
"collapsed": true
},
"cell_type": "code",
"source": "SURE_num_df = pd.DataFrame(zip(*SURE_num_vals), index=y_range, \n columns=['SURE', 'precision'])",
"execution_count": 9,
"outputs": []
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "ax = SURE_num_df.pivot(columns='precision', values='SURE').plot()\n_ = ax.set_ylabel(\"SURE\")",
"execution_count": 10,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAmAAAAHwCAYAAAAB5dMOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text/plain": "<matplotlib.figure.Figure at 0x7fb4b3f8c410>"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "y_range_tail = pd.Series(np.linspace(37.5, 37.8, 500), name='y')\nSURE_num_tail_vals = SURE_hs(y_range_tail, \n E_Z_hs_num_single, tau=1)\nSURE_num_tail_df = pd.DataFrame(zip(*SURE_num_tail_vals), \n index=y_range_tail, \n columns=['SURE', 'precision'])\nax = SURE_num_tail_df.pivot(columns='precision', values='SURE').plot()\n_ = ax.set_ylabel(\"SURE\")",
"execution_count": 55,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAoIAAAH1CAYAAABiP5/xAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nJUmSCvVfSSiwTQrs4hUAAAAASUVORK5CYII=\n",
"text/plain": "<matplotlib.figure.Figure at 0x7fb4b167c3d0>"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## $F_1(1/\\epsilon)$ Hack\n\nBelow is a computation of $E[Z]$ using finite (double) precision floating point operations and a hack that uses the relationship between the Appell $F_1$ function and the Humbert/Horn $\\Phi_1$ in which $E[Z]$ is defined here. "
},
{
"metadata": {
"trusted": true,
"collapsed": true
},
"cell_type": "code",
"source": "def E_Z_hs_eps_single(y, sig=1., tau=1., n=1, eps=1e-5):\n try:\n # (double) floating point calculations\n res = fp.rf(1., n)/fp.rf(3/2., n)\n res *= fp.appellf1(0.5, 1./eps, 1., 3/2. + n,\n eps * (y/sig)**2/2., 1. - 1./tau**2)\n res /= fp.appellf1(0.5, 1./eps, 1., 3/2.,\n eps * (y/sig)**2/2., 1. - 1./tau**2)\n return (res, 'fp')\n except:\n pass\n try:\n # If it fails, use the direct infinite precision calculations.\n res = mp.rf(1., n)/mp.rf(3/2., n)\n res *= mp.hyper2d({'m+n': 0.5, 'm': 1.}, {'m+n': 3/2.+n},\n 1. - 1./tau**2, (y/sig)**2/2.)\n res /= mp.hyper2d({'m+n': 0.5, 'm': 1.}, {'m+n': 3/2.},\n 1. - 1./tau**2, (y/sig)**2/2.)\n return (res, 'inf')\n except:\n pass\n return (np.nan, 'failed')",
"execution_count": 12,
"outputs": []
},
{
"metadata": {
"collapsed": false,
"trusted": true
},
"cell_type": "code",
"source": "%%time\nSURE_eps_vals = SURE_hs(y_range, E_Z_hs_eps_single, tau=1, eps=1e-15)",
"execution_count": 13,
"outputs": [
{
"output_type": "stream",
"text": "CPU times: user 2.77 s, sys: 24 ms, total: 2.8 s\nWall time: 2.77 s\n",
"name": "stdout"
}
]
},
{
"metadata": {
"trusted": true,
"collapsed": false,
"scrolled": true
},
"cell_type": "code",
"source": "SURE_eps_df = pd.DataFrame(zip(*SURE_eps_vals), index=y_range, \n columns=['SURE', 'precision'])",
"execution_count": 14,
"outputs": []
},
{
"metadata": {
"collapsed": false,
"trusted": true
},
"cell_type": "code",
"source": "ax = SURE_eps_df.pivot(columns='precision', values='SURE').plot()\n_ = ax.set_ylabel(\"SURE\")",
"execution_count": 15,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAmAAAAHwCAYAAAAB5dMOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nZAQwAACAkP0/HsE3+5vNFyIAAAAASUVORK5CYII=\n",
"text/plain": "<matplotlib.figure.Figure at 0x7fb4b3979250>"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "y_range_tail = pd.Series(np.linspace(36.7, 37, 500), name='y')\nSURE_eps_tail_vals = SURE_hs(y_range_tail, \n E_Z_hs_eps_single, tau=1, eps=1e-15)\nSURE_eps_tail_df = pd.DataFrame(zip(*SURE_eps_tail_vals), \n index=y_range_tail, \n columns=['SURE', 'precision'])\nax = SURE_eps_tail_df.pivot(columns='precision', values='SURE').plot()\n_ = ax.set_ylabel(\"SURE\")",
"execution_count": 54,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAoIAAAH1CAYAAABiP5/xAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text/plain": "<matplotlib.figure.Figure at 0x7fb4b17bfa90>"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## Truncation\n\nNext, we try truncating the values of $y$ in the regions where $E[Z]$ fails for floating point calculations. "
},
{
"metadata": {
"collapsed": true,
"trusted": true
},
"cell_type": "code",
"source": "def E_Z_hs_trunc_single(y, sig=1., tau=1., n=1, trunc_val=40.):\n if abs(y/sig) >= trunc_val:\n return (0., 'trunc')\n try:\n res = fp.rf(1., n)/fp.rf(3/2., n)\n res *= fp.hyper2d({'m+n': 0.5, 'm': 1.}, {'m+n': 3/2.+n},\n 1. - 1./tau**2,\n (y/sig)**2/2., maxterms=1e5)\n res /= fp.hyper2d({'m+n': 0.5, 'm': 1.}, {'m+n': 3/2.},\n 1. - 1./tau**2,\n (y/sig)**2/2., maxterms=1e5)\n return (res, 'fp')\n except:\n pass\n try:\n # If it fails, use the infinite precision calculations.\n res = mp.rf(1., n)/mp.rf(3/2., n)\n res *= mp.hyper2d({'m+n': 0.5, 'm': 1.}, {'m+n': 3/2.+n},\n 1. - 1./tau**2, (y/sig)**2/2.)\n res /= mp.hyper2d({'m+n': 0.5, 'm': 1.}, {'m+n': 3/2.},\n 1. - 1./tau**2, (y/sig)**2/2.)\n return (res, 'inf')\n except:\n pass\n return (np.nan, 'failed')",
"execution_count": 17,
"outputs": []
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "%%time\nSURE_trunc_vals = SURE_hs(y_range, E_Z_hs_trunc_single, tau=1)",
"execution_count": 18,
"outputs": [
{
"output_type": "stream",
"text": "CPU times: user 385 ms, sys: 7 ms, total: 392 ms\nWall time: 377 ms\n",
"name": "stdout"
}
]
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "SURE_trunc_df = pd.DataFrame(zip(*SURE_trunc_vals), \n index=y_range, \n columns=['SURE', 'precision'])",
"execution_count": 19,
"outputs": []
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "ax = SURE_trunc_df.pivot(columns='precision', values='SURE').plot()\n_ = ax.set_ylabel(\"SURE\")",
"execution_count": 20,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAmAAAAHwCAYAAAAB5dMOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3XmYXGWd9//POXWqqrfqJUl3QhYI2U5AQNlEERF4mB+O\ny7iM64goiDLKKAhuuMxz4SjooD4uM6KCiIqPKIrwAOIyqKOo4woaBA5JgIQsJJ10p7fqrvX8/qg6\nVd2dXqq6z6n1/brkSnWtd3PM4VPf+z7f23BdVwAAAKgcs9oDAAAAaDYEMAAAgAojgAEAAFQYAQwA\nAKDCCGAAAAAVRgADAACoMCvIN7dt25R0gyRbUlbSPzuO8/Ckxy+XdLGk/fm7LnEcZ2uQYwIAAKi2\nQAOYpJdKch3HOcO27RdIukbSyyc9frKkNzqO80DA4wAAAKgZgU5BOo5zp6S35X9cK2lw2lNOlnSV\nbdu/sm37A0GOBQAAoFYEvgbMcZysbds3S/qcpG9Ne/jbkv5Z0tmSzrBt+0VBjwcAAKDajEptRWTb\ndp+k30s6xnGc8fx9nY7jDOdvv13SEsdxPj7be6TTGdeyQhUZLwAAwCIZsz0Q9CL88yWtdhznE5Im\nJGWUW4wv27Y7JT1k2/ZmSeOSzpH01bneb3AwHuRwq663N6b+/pFqDwMLwLGrbxy/+sbxq1+Nfux6\ne2OzPhb0FOTtkk60bfu/Jd0r6XJJr7Rt++J85esqSb+Q9N+SHnIc50cBjwcAAKDqAq2AOY4Tl/Ta\nOR7/lg5fFwYAANDQaMQKAABQYQQwAACACiOAAQAAVBgBDAAAoMIIYAAAABVGAAMAAKgwAhgAAKhJ\nH/7w+2Z97JZbbtajjz5cwdH4K9A+YAAAAAv1sY/9+6yPnX/+mys3kAAQwAAAgG/uvfdu/fKXv1A8\nHtfw8CG9+c0X66tf/bLWrDlS4XBE733vVbr22n/TyMiwwuGQ3vGOd2vduvW6++47dMcdtyubzeqM\nM87URRe9TS972Xm6884f6/bbb9OPfnSPQiFTmzc/Q5dddqWuueZqnXvueTrppFN07bVXa8+e3cpm\nXb32tW/QOeecq3e+8xJt3LhJjz++XfF4XP/2b5/Q8uUrqv2vp4AABgAAfJVITOhzn/uiBgcH9Na3\nvknZbFYXXvg2bdiwUddf/wWdcsqz9fKX/6Pi8QG95z3v08c/fp1uueUb+uY3v6NwOKwvf/k/NT4+\nLm8v63vvvVtXXvkBbd58jO644/vKZDKFz7rzztvV3b1EH/nIvykej+stbzlfJ598iiTp2GOP07ve\ndaW+8pUv6r/+68d6wxveVI1/HTMigAEAAF8961knSZJ6epYoFotpx44dWrPmSEnS449v05///Ef9\n7Gc/lWWZGhkZ1p49u7V+/XqFw2FJ0iWXXDrl/a666l916623aO/ePTruuBPkum7hsR07ntCpp54m\nSWpra9PatUdr9+5dkqRNm2xJUl/fcg0ODgT7S5eJAAYAAHzlOI9IkgYGDmpsbEw9PT0yzdx1f0cd\ndbTOO+8YnXvueQqFUrr55m9p1arV2rFjh9LptCzL0oc//H5dfvl7JOWC1l133aH3vveDCofDuuKK\nd+pvf9tS+Ky1a9fpwQcf0POff5bi8TE9/vh2rVy5Ov+oUclfuywEMAAA4KuDBw/qssveoXh8VO95\nz1W67rprC49dcMGFuvbaf9Odd96uZHJCF1xwsbq7u/WGN1ygSy99q0zT0POed6aWLeuVF6DWr1+v\nd7zjLWpra1df33Ide+xxuuee/ydJ+od/eIU++cmP6R3vuFjJZFIXXfQ2dXd3yzBqN3xJkjG5jFfr\n+vtH6mewC9DbG1N//0i1h4EF4NjVN45ffeP41ZZ7771bO3fuOGwacSaNfux6e2OzpkD6gAEAAFQY\nU5AAAMA3f//3L6n2EOoCFTAAAIAKI4ABAABUGAEMAACgwghgAAAAFUYAAwAAFZfJZPTGN75Rb3/7\nWzQ6Ojrnc/fs2a03vOFVuuaaqys0uuBxFSQAAKi4/v5+xeNxfelLN8/73L/+9UGdfvrzdemllwU/\nsAohgAEA0OS++7Nt+sOj+319z1M39+k152yY9fFPf/pa7dixQ9ddd41GR0d16NCgRkZG9O53v1fH\nH//MwvP27Xta3/zm15RIJLRq1Srdd99PddRRa7Vjx5OSpI9+9Fr19CzxdeyVwBQkAACouCuv/IDW\nr1+vZct61draqs997np95CMf1ac//ckpz1u+fIXOP//N+ru/e6Fe/vJXSZJOOOFZ+sIXvqxzzvk7\nff3rN1Vj+ItGBQwAgCb3mnM2zFmtCtpJJ50qSTr66HUaGDioLVv+oq985YsyDEOvf/0bZ3j+KZKk\n4447Qfff/8uKjtUvVMAAAEBVOc7DkqTHH9+m3t4+HX/8M/WFL3xZn//8l/Tc5z7vsOc/+ugjkqQt\nW/6io49eV9Gx+oUKGAAAqArDyO1V/dhjji677B1KJCb0/vd/aN7X3XvvXbr11lvU1tamD3/4o0EP\nMxAEMAAAUHErVhyhW2+9VZ/85Kd17rnn6WUve+Wsz52+v+Qll/yLjjzyqKCHGCimIAEAQNV4VbCg\nnl+rqIABAICqufDCt5b1/M9//ksBjaSyqIABAABUGAEMAACgwghgAAAAFUYAAwAAqDACGAAAqLjf\n/e63uu2222Z8bGRkRBdddL6uuOJfpty/detjuvnmG2d9z0wmo3e+8xK9/e1v0ejoqK/j9RtXQQIA\ngIo77bTnqrc3pv7+kcMe2759q1auXKWPfWzqvpAbN27Sxo2bZn3P/v5+jY+P68Ybv+H7eP1GAAMA\noMndvu1uPbB/i6/veWLf8XrlhpfM+vi9996tBx/8g3bseEp9fcu1e/cuHXvscbrssiv1uc99SgcP\nHtRNN31FF130tsJrHnjgT7rjju/r6quv0ete9wqdcMKztHPnDi1ZslQf+9gn9elPX6tdu3bqU5+6\nVu95z1W+/j5+YwoSAABUza5dO/XBD/5v3XDD1/Xb396vkZFhvetdV+qkk06ZEr48XiPWvXv36G1v\ne4e+9KWbNDg4oEcffVhXXvkBrV27rubDl0QFDEADuOmeR9QatfT6czdW9HN/+oen9NfHD+qyV50g\nK8T3WdSvV254yZzVqiCtWrVGLS0tkqRly3qVSCSnPP6+971bExPjWrdug17wgrML93d3d2vZsl5J\nUl/fciWTU19X6whgAOrajqdHdP+WvZKk1/2vDRXdpuTb922VJP35sX49+5jlFftcoJFM/jvruu5h\nj//7v/+fwu0HHvjTvO8303vUIr6yAahr//3g7sLtgeFExT43my2e5H/xwO45nglgNtO/MJX3Bar4\n3Mmvq5e9Io16SYqS1N8/Uj+DXYDZrgZB7ePYVUcmm9W/fPZXSiQzkqR3v+aZOn7d0rLfZyHHb/+h\ncX3gS78t/Hzd20/X0q6Wsj8bi8ffv/rV6Meutzc2axqkAgagbg2NJpVIZmR6i3IPjFXss/fkPytk\n5j57/2C8Yp8NoP4RwADUrcGR3JTjM45eIknac7ByAcwLe95nD4xUbvoTQP0jgAGoW14A23xUt0zD\n0J4DlatCeRWwY9cumTIWACgFAQxA3RoYnpAk9XW3qq+nVXsrWQEbiCtkGrLXdEsigAEoDwEMQN3y\npv16Yi3qiUU1NpFWOpOtyGcPjyXV1RHRsu7cwnsCGIByEMAA1K3BQgCLqi2aa2s4nkhX5LPjE2m1\nRS21RS1FwyENjExU5HMBNAYCGIC6NTiSUMg01NUeUVtLLoDFJ4IPYFnX1XgirbaWsAzDUE8sWtEe\nZEAjSCaTuu222wL9jOHhYf30pz8K9DMWigAGoG4NjEyouyMi0zSKAawCFbCJRFquVKi69cSiGh1P\nKZXOBP7ZQKM4ePCAvve97wX6Gdu2Pab77/9loJ+xUGxFBKAuZbOuDo0ktW5lp6RiGBqbSAX+2V6V\nzQt9S2JRSbmKXF9PW+CfD/it/7ZbNfLHP/j6nrFTTlXvq1836+Pf+MbXtG3bNp155rN1yinP1vj4\nuD7wgY/ommuu1pe//DVJ0iWXXKirr75WP/zh/9PevXs0ODigffue1rvedYVOPfU5+vWvf6Wbb75B\nkrRp02a9970fnPIZ3/zm17R9+zbdddcd2rLlLxoaOqTh4WG9/vVv1H33/URXX32NJOllLztPd975\nY11zzdUKh8Pau3evBgYO6kMf+t/auNHW3XffoTvuuF3ZbFZnnHHmjJuEl4sKGIC6NDSWVNZ11Z0P\nP20tYUmVmYIcmxbAejqLAQxAad70pou0YcMGXXjhW7V27dG6/vqvKhqNzrqtUCQS0ac+9Xm9611X\n6jvf+b/KZDL67Gev06c+9XndcMM3tGrVGu3fv2/KZ1xwwUU66aRT9NKXvlySdPLJz9b1139VsVhs\n2pZFxdsrVqzUZz7zBf3jP75Gd975Aw0ODuqWW76h66//qm666RalUilNTCx+zScVMAB1aSSelCR1\ntUckqaJrwLxpTq/q1tmWG8NwPPjqGxCE3le/bs5qVdCOPPKoGe/PZotXNW/caEuSli9frmQyqaGh\nQ4rFYurqyrWC+ad/eqN2796ld77zEhmGofPOe5FWrlxV0udIxZ0ON23KfU5f33Jt2fIX7dmzW+vX\nr1c4nPuSd8klly7od5yOChiAujQ6ngs7sdbcSbG9gmvA4vlpzvZ81a2jLTxlTADmZxhGIWAZRi6O\nRCIRDQ4OyHVdjYyMaO/ePVOeP1lPzxKNjo5qZCS3l+RnP/spjYwM6wtf+LI+//kv6cUv/geZpinX\nLYY40/Q+J6qDBw9Ikp5+eq+Gh4dn/ZxVq1Zrx44dSqdz55YPf/j9OnDgwKJ/fypgAOqSF3ba8wGs\nLVq5Kcjpa8A68mMYzVflAMyvp2eJ0um0Eoni1P2SJUt16qmn6eKLL9DKlau0evWaWV9vGIauuOL9\neu97L1MoFNLGjbY2bz52ynNWrVqt7du367bbbp1y/+bNx6ijo0OXXHKhjjpq7WGVssm6u7v1hjdc\noEsvfatM09Dpp5+pZcuWLfC3njR+13Xnf1aN6O8fqZ/BLkCj7wrfyDh2lfezP+/SLT95TJf8wzN0\n2rHLtfvAmD5y4+901rNW6oIXbi7rvco9fj/+/U5952fb9M5XHq8TN/XqyaeH9dGb/6i/O2WNXn/u\nxnJ/FSwSf//qV6Mfu97emDHbY0xBAqhLo/n1Vt70XyWnIKcvwi9UwMapgAEoDQEMQF3ypiA7Wrwp\nSK8NRfABbLwQwPJrwAoBrDJd+AHUPwIYgLpUWISfr4CFLVNWyKjQVZC5z/ZCXzQckhUyqYABKBkB\nDEBdmr4I3zAMtbWEC1coBmn6FKRhGOpotbgKEkDJCGAA6tLoeEoRy1Q0HCrc1xa1KtOGIpGWaRhq\niRQ/u6M1whQkgJIRwADUpdHxVKH65WlvsRSfSCvoq7vjE2m1tVhT+gV1tFoaT6SVzmTneCUA5BDA\nANSl0fFUYfG7p7XFUibrKpkKNgTFJ1KF9V8ebyyVuAgAQP0jgAGoO+lMVhPJzGEBzAtFQU9Djicy\naomGptzXkd+OiGasAEpBAANQdwotKKYFsEh+PVgynQnss13XVTKVUUt4WgBrtaaMDQDmQgADUHem\nN2H1RK18AAtwCjKdycpVMex5OlrzFTACGIASEMAA1J3pTVg9kUjulJZIBVcBS+TD3eEBjAoYgNIF\nuhm3bdumpBsk2ZKykv7ZcZyHJz3+UkkfkZSS9DXHcW4McjwAGoO30N3bfshTrIAFF8C8946Gp35/\nbW+p3GbgAOpf0BWwl0pyHcc5Q7mgdY33gG3blqTPSDpX0lmS3mbbdm/A4wHQAMYmpjZh9RTWgAU4\nBelV16ZXwLwANlqBRrAA6l+gAcxxnDslvS3/41pJg5MePkbSVsdxhh3HSUm6X9KZQY4HQGOIT+tE\n7/GqUkFOQXrhLjotgHljoQIGoBSBTkFKkuM4Wdu2b5b0ckmvmvRQp6ShST+PSOoKejwA6l+hAjZ9\nDVg4+CnIYgVs+hRk5TYDB1D/Ag9gkuQ4zptt2+6T9Hvbto9xHGdc0rByIcwTk3Rorvfp6WmTZYXm\nekrd6+2NVXsIWCCOXeVk8x3oVx/RNeXfe+/SEUlSOBou+3iU+vynDo5Lknq62qa8prunTZKUzrj8\nf6EK+Hdev5r12AW9CP98Sasdx/mEpAlJGeUW40vSI5I22LbdLSmu3PTjdXO93+BgPMDRVl9vb0z9\n/SPVHgYWgGNXWQfz54LEeHLKv/eJ8YQkaeBQvKzjUc7x239gVJKUTqYPe00kbGpweIL/L1QYf//q\nV6Mfu7nCZdCL8G+XdKJt2/8t6V5Jl0t6pW3bFzuOk5Z0haSfSPq1pBsdx9kb8HgANIDZ1oBFKngV\n5PQpSCk3JTrGInwAJQi0AuY4TlzSa+d4/B5J9wQ5BgCNZ2wiLStkKGJNDUHRSC6ABdoHLD3zVZBS\nLhAODicC+2wAjYNGrADqzthESu0tYRn5tWAeL5AF2YYimfT6gB0ewNpbwhpPpJXNuoF9PoDGQAAD\nUHfiE+nDph+lYigK9CrItNcJf6YpSEuugt8MHED9I4ABqCuu6yo+kT6sBYVUnBYMtg/Y7BWwYi8w\n1oEBmBsBDEBdmUhmlHXduStg6Qp0wp+hJY4XCukFBmA+BDAAdaXYhPXwABb2OuEng++EP9sUpEQ3\nfADzI4ABqCvFFhSHT0GahqGwZSqZrtYUpFcBYwoSwNwIYADqije9N1MFTMoFo2psxj15TExBApgP\nAQxAXRkbn3kfSE8kbAa7CD8982bcUrECxiJ8APMhgAGoK16Lh5kW4UteBSzYzbgNQ7JCxmGPtbdS\nAQNQGgIYgLpSqIC1zlIBs0KFXl1BSKYyioRDhzWBlSZdBTlOBQzA3AhgAOrKaH56r2O2ABY2lUxm\n5LrBdKNPpLIzTj9Kk/uAUQEDMDcCGIC6MjY+/yJ8V1I6E0wVLJnKHLYHpact6k1BUgEDMDcCGIC6\nUugDNmsFzOuGH1wAm60CZoVMtURCVMAAzIsABqCuFK+CnK0C5m3IHcxC/EQqO2MLCk97i0UFDMC8\nCGAA6srYRFqt0ZBC5synryD3g8xmXaUz2ULIm0lbS5irIAHMiwAGoK6MTaRm7QEmTdoPMoApyLma\nsHraWyxNJDPKZIO7EhNA/SOAAagrY+PpOQNYOL9APhVAK4pUfmH/bIvwpWIrCtaBAZgLAQxA3Uil\ns0qkMoWGpzMpBjD/pyDT+VAXniOAtbEdEYASEMAA1A1vi5+SKmABtKFIlRDA2tmQG0AJCGAA6sao\ntxH3LC0oJCkcCnAK0gtgodnXgNGMFUApCGAA6obXgqJjjilIqwJrwCzr8G2IPF44pAIGYC4EMAB1\no9gDrMoVsDmnIPNrwMapgAGYHQEMQN0YrZU1YKH5F+HHqYABmAMBDEDdKOwDWdJVkEFWwObqA+ZN\nQVIBAzA7AhiAujFWTgUswDVgJU1BUgEDMAcCGIC6MVb1qyBzvcXmDGDeInzWgAGYAwEMQN0oXAU5\ny0bcUnF6sFprwFqjlgyjuF4NAGZCAANQN7xpvbZqTUGWcBWkaRhqbwkXwiIAzIQABqBujI2nFQ2H\n5gxAlVgDZs3x+ZLU0RrWKAEMwBwIYADqxthEas4rIKXq9wGTcgFsbDwt13V9HwOAxkAAA1A3xiZS\n6phj+lGqfh8wKXclZNZ1NZ5gIT6AmRHAANSFdCar8URmzisgpWIAS1e5AiaJaUgAsyKAAagL8Xw1\nqX2OKyClyWvAMr6PoZQ+YFKxFcUorSgAzIIABqAuFPaBnKcCFjINGar+GjCJChiA2RHAANSFwjZE\n86wBMwxDYcsMZA1YusQ1YF4Aoxs+gNkQwADUhcJG3PNcBSnlKlRUwADUMgIYgLpQmIKcpwIm5fp0\nVWsvSGnydkQEMAAzI4ABqAuFfSBLCGDhUDBTkFTAAPiFAAagLhT2gazmFGQmK9MwFDIJYAAWhwAG\noC54C9pLqoAFuAZsvuqXVAyJTEECmA0BDEBdGInnK2Bt1Qtg6RIDWNgKKRoOFcYMANMRwADUhZF4\nUlJxem8u4ZCpTNZVNuvvXoylVsAkKdYW1ggVMACzIIABqAsj8ZTaWyxZ8/TgknIVKMn//SBTmey8\nPcA8ne0RDY8l2ZAbwIwIYADqwnA8qc72SEnPLW5H5HMAK6MC1tkWUSbLhtwAZkYAA1DzsllXo/GU\nYiVMP0rBBjCrjClISRpmHRiAGRDAANS80fGUXEmxUitg+WlC36cgy6mA5cc6PJb0dQwAGgMBDEDN\n8xbgd7ZVbwoyk80q67olrwGL5cfKlZAAZkIAA1DzvGm8WAktKKRiAEv7GMBK7YLv8cbqhUcAmIwA\nBqDmFSpgVVyEX24A86p1wwQwADMggAGoed46qlipU5DeGrB0xrcxLLgCNsYUJIDDEcAA1DxvCrKz\nzClIPxfhe+9VTh8wiQoYgJkRwADUPG8KstQKmNesNZnyfwqy1DYUXsd+1oABmAkBDEDN864kLHUN\nmBeS0ln/Ali6zAqYFTLV3mLRBwzAjAhgAGre0FhCIdNQW4tV0vOtkCFJSqf92wbIe69StkLyeNsR\nAcB0BDAANe/QSFJdHRGZhlHS870qVTqANWBeuCtFd0dUo+Mp3zvyA6h/BDAANc11XR0aTai7I1ry\na6wAAlimEMBKP216Yx4aTfg2DgCNgQAGoKaNjqeUyboLDGD+TUGmFhLAYrk1a4dGmYYEMBUBDEBN\n88JLd0dpC/AlybJy04R+tqHwwlypfcAkqbs9FxoPUQEDMA0BDEBN88JLWRUwM3dqy/gawHLvFSpn\nDVgsN+ZBAhiAaQhgAGraoZEFBLAAGrF6+0qW2oZCKlbtqIABmI4ABqCmFSpgsdKnIAtXQfrZhmIR\ni/APjbAGDMBUBDAANa24Bqz0Cpg3TehvI1avD1g5bSiogAGYGQEMQE1byBqwYgXM/zVg5VTAwlZI\n7S0WAQzAYQhgAGraodFkYVufUgXRB6zQhqKMqyClXHAcog0FgGkIYABq2sDIhLo7IjJK7IIvTdqK\nyMc+YIUpSLP0cUhSTyyqeCKt8UTat7EAqH8EMAA1K5XOaGg0qWVdLWW9rrAZdwBtKMqtgC3Nj/3g\n8IRvYwFQ/0qv6ZfJtm1L0k2S1kqKSPq44zh3TXr8ckkXS9qfv+sSx3G2BjUeAPVnYDi3dmppuQEs\nVBttKCRpaWc+gA1NaHVvh2/jAVDfAgtgks6XdMBxnAts2+6R9KCkuyY9frKkNzqO80CAYwBQxw7k\nq0ZeiCmVNwWZ8XMKMpt7r1C5AYwKGIAZBBnAvivptvxtU1Jq2uMnS7rKtu0jJN3jOM4nAhwLgDp0\ncCgfwMqsgIVMU4YRVAWsvDVgkytgAOAJbA2Y4zhxx3HGbNuOKRfEPjTtKd+W9M+SzpZ0hm3bLwpq\nLADq04F8aFnW1Vr2a8Mhs+ptKCQV1q9RAQMwWZAVMNm2vUbS7ZL+w3Gc70x7+HOO4wznn3ePpBMl\n/XCu9+vpaZNlhQIZa63o7Y1VewhYII6d/8byVw5uOnqpepe2l/XasGVKhlHycZnveaH8uWd5X2dh\nj8dSLFnaoZBpaCie4v8jAeLfbf1q1mMX5CL85ZJ+LOlSx3F+Pu2xTkkP2ba9WdK4pHMkfXW+9xwc\njAcx1JrR2xtTf/9ItYeBBeDYBWP3/lEZktxUuux/vyHT0ESitNeVcvzG4rleXkOH4kpNlNfXqycW\n1dMHx/j/SED4+1e/Gv3YzRUug6yAXSWpW9JHbNv+V0mupBsktTuOc6Nt21dJ+oWkCUn3OY7zowDH\nAqAOHRyaUHcsWva0n5RrFxFEI9awVd4aMCk3DfnozkNKpbO5yhyAphdYAHMc53JJl8/x+LckfSuo\nzwdQ39KZrAZHElq3qnNBr7dMU8l0xr/x5NeTlXsVpOStYTukA0PjOqLMqVQAjYmvYgBqUv+hcWVd\nVyt62hb0+lwFzM82FFmFTENmGR35PcuX5C4i2Dc47tt4ANQ3AhiAmrRvIBdWvPBSLitk+NyGwl3Q\nVKgkLc+HyH0Djb2OFUDpCGAAatK+/EU3yxdaAQuZyvi8FZFVZg8wz/IlBDAAUxHAANQkL6ysWLLw\nAJbOuHJdf6YhcwFsYafMvp5cFe9pAhiAPAIYgJrkhRUvvJTL61jv1zqwxQSwaDikJZ1R1oABKCCA\nAahJ+wbHtaQzqkh4Yc2XvasV/WpFkcq4shbRQmJ5T5sGRxJKJP27MhNA/SKAAag5iWRGgyOJBa//\nknJbEUn+BbDMItaASZPWgTV4Q2kApSGAAag5ew6OSZJWLqJnllet8msKMrWIKUhJOmJpLoDtPjDm\ny3gA1DcCGICas2v/qCRpVd8iApjprQHzpwKWTruFqtpCrOntkCTt6h/1ZTwA6hsBDEDN2dWfqxKt\nzoeWhShWwBYfwLJZV1nXXdQU5Oq+3O+yu58KGAACGIAa5FWJVi1bRAUsX61KpRcfwLwQt5gpyI7W\nsLo6IlTAAEgigAGoQbv7R7Wsq0Wt0YVvV+tVqzLZxa8B8yOASbmK3sBwQvGJ1KLHBKC+EcAA1JSh\nsaSG46lFTT9KflfA3Px7LnwKUpq8DoxpSKDZEcAA1JSn9o1IKq6ZWig/21AUKmCL6AMmSWvyv9OO\n/O8IoHkRwADUlMf3DkuS1h3Ruaj3CfnYCT/l0xTk2iNikqQn878jgOZFAANQU57YkwsnR+fDykL5\nWwHzpiAXd8pcvqRNrVFLj++lAgY0OwIYgJrhuq6e2DuspZ1RdXVEF/VefrahSKe9Ctji1oCZhqGj\nj4hp30CchfhAkyOAAagZA8MJDcdTWrvI6UepWK3ycw3YYhqxeo7O/25PPE0VDGhmBDAANWP7niFJ\ni1//JRWrVX6sAfMCWMjHAPb47qFFvxeA+kUAA1AznKcOSZI2rule9HsF0YYivMgpSEnauLpLkvRY\n/ncF0JwIYABqxmM7DykSNrV2xeIW4EvFAJbxYQoy5VMbCkmKtUW0alm7tu4e8m2fSgD1hwAGoCaM\nxJPafWB2bDf+AAAgAElEQVRMG1Z1LfpqQ2lSBcyHkOOFOMv055S56chuJVNZPck6MKBpEcAA1ARv\nSs72YfpRKk4X+toHzIcKmFT8HZ2dg768H4D6QwADUBP+9sSAJGnzUT2+vF/Iz6sg0/5sReTZfGTu\nd/R+ZwDNhwAGoOpc19WWxw+qLWpp3crFXwEpSWE/+4Bl/emE7+lsj+ioFTFt3TWk8UTal/cEUF8I\nYACqbs/BuA4OJ3TcuiUK+bTOqtgHzIc2FGn/+oB5jl+3VJmsq0d2MA0JNCMCGICq27L9oKRcKPFL\nsQ9Y7WxFNNkJ+d/1r/nfHUBzIYABqLo/P9Yvw/A7gOUrYL70AfNnK6LJ1q3sVEdrWA9uO6BsdvFV\nOgD1hQAGoKoGRxLatntI9ppudbZHfHvfQgDzIdwUA5h/p0zTNHTSpl4NjyW1dRdNWYFmQwADUFV/\ncvZLkk62+3x938IUpA8VML/bUHhO2dwrSfqj0+/r+wKofQQwAFX1u0f2yZB00qZeX9/X30as/rah\n8Gw+skftLZb+8Oh+ZbJ0xQeaCQEMQNU8PRDX9t3DOvboJeqJRX1970C2IvJxCtJ7v9OOXa7hsSQ9\nwYAmQwADUDW/3rJXkvS841f4/t5etSpVo20oPM87/ghJ0v1bnvb9vQHULgIYgKpIZ7K6f8tetUZD\nOmmjv9OPkmQYhqyQ4WsbipDPU5CStHZFTKuWteuBx/o1NJb0/f0B1CYCGICq+PNj/RoaTep5xx+h\nSDgUyGeEQqZPASy4CphhGDrrxFXKZF398i97fH9/ALWJAAagKu770y5J0jknrQ7sM8Ih059O+AFd\nBek5/bgVaomE9IsHdvsSGAHUPgIYgIrbtmtIW3cN6bh1S7RiSVtgn2OFDJ8aseavgvRpm6TpWqOW\nnn/CSg2OJPSbh1gLBjQDAhiAirvnt09Kkl78nKMC/RwrZBY20l6MYgXM/zVgnheedqSskKm7f/Mk\nVTCgCRDAAFTU9t1D+sv2g9qwqkub1nQH+llWyPStEathyLeNwmfSE4vqrGet1IGhCapgQBMggAGo\nGNd19Z2fbZMkveqs9TKM4CpKUi6A+dWGIogF+NP9/XOOogoGNAkCGICK+ZPTr227h3TSpt7Aq19S\nbg2YH41Y0xlXoQoEsMlVsJ/lL1IA0JgIYAAqIp3J6nu/2K6QaehVZ62vyGdalunLVkTpTFbhAHqA\nzeQlz1ur9hZLP7j/CQ0MT1TkMwFUHgEMQEXc/Zsntf/QuM46cVWgVz5OFg6Zcl0tep/FdCYbWAuK\n6TrbInr12RuUSGZ0631bK/KZACqPAAYgcE8+Pay7f7NDSzujeuWZ6yr2uV7n+sX2AktnsoG1oJjJ\nGSccoQ2ruvRHp18PbjtQsc8FUDkEMACBSqUzuvHuR5R1XV34omPUGrUq9tnewvnFLmhPZ9yKVcAk\nyTQMXXCerZBp6Gs/fESDI4mKfTaAyiCAAQjUrfdt054DYzrnpFU6du2Sin625QWwRbaiSGWyhc29\nK2V1X4dec84GjcRTuuGuvymbXfzVnABqBwEMQGB+8cBu/fyB3Vrd265Xn7Wh4p9v+TQFmclkC2Gu\nks49ebVO2tSrR3ce0g9+9XjFPx9AcAhgAALh7BzUt376mDpaw3rXP56gaCSYDbfnYvkwBem6bm4K\nsgoBzDAMXfiizVrW1aJ7fruDzbqBBkIAA+C7J/YO6/Pf/6sk6dJXHKdl3a1VGYe3bmsxrSi86lml\n2lBM194S1rtf80x1tIb1jR85LMoHGgQBDICvdu4b0We+86Amkhm95SXHyD6yp2pj8a5czCxiCtKr\nnlWiEetsjljarstefYKskKHr73hIf91OCAPqHQEMgG+27jqk6779gOITaV30omP0nGNXVHU83ubZ\ni6uA5V5bia2I5rJ+ZZf+5R+PlyHpC9/fot8/sq+q4wGwOAQwAL74w6P7dd23H9R4IqOLXnyMnnf8\nEdUeUrENxSKugvSmICvZhmI2xx29VFe89lkKW6a+fOffdO/vdsh1uToSqEfVP6MAqGvpTFa3/WKb\nrr/jIVkhQ5e/5oSaCF9ScdowvYhO+F4FzDKrswZsuk1ruvW+fzpRXR0R3fbz7brhroeVSGWqPSwA\nZapcR0QADefAoXF95e6HtW3XkPp6WnXpK47Xmr6Oag+roFgBW/wasFqogHnWrujUv775VP3nD7bo\nfx7epyefHtFbX3qsjj6is9pDA1AiAhiAsmWzru770y59/5fblUxl9exj+vSmF26uaJf7UhT7gC28\nApbKT19Wow3FXLo7onrf60/S936xXT/941P6+Df+pBc990i9+LlrFQ1XvuUHgPLU1tkSQM1zdg7q\n1vu2ace+EbW3WLrgPFvPfcYKGUZtTNFN5kcfsEy+A32lO+GXImyZev25G/XMDUt10w8f0d2/2aH/\n+ds+vfacjTpp07KaPCYAcghgAEryxN5h3fXrJwt9qJ77jOV67Tkb1dkeqfLIZucFsMVcBVmrFbDJ\njl27RB+7+DTd9esn9ZM/PKX//MEWrV0R08ufv07Hr1tCEANqEAEMwKxc19WjOw/ph799Un97clCS\ntHF1l157zkatW1n76428NhSL2YqoVtpQzKclYunVZ2/QGSccoTt+9YT+8Oh+ffa2v2j9yk6d9+wj\n9ayNy2o6RALNZs4AZtv2Vx3HeUv+9pscx/n6pMfudxznjKAHCKDyRsdT+s1DT+uXf9mjPQfGJEnH\nru3Ri5+7VpuP7K6biorXiHUxU5BeeAvV4BTkTI5Y2q63v/w4vWT/qO68/wn9+bF+ffGOh9QTi+qs\nZ63UGSesVE8sWu1hAk1vvgrYiZNuXybp65N+bvd/OACqZSKZ1l+3H9QfHt2vv2w7qHQmKytk6NnH\n9OnvTl2j9Su7qj3EsnlXLi4ugNVHBWy6NX0d+pdXHq+9B8f0sz/t1v0P7dUPfvWE7vjVE9p8VI9O\nO3a5TrF71dYSrvZQgaY0XwAzZrktSXT/A+pc/6Fx/e2JAW15/KD+9sSAkvn1TkcsbdOZz1yp049b\noVhb7a7xmo8/jVhrrw1FOY5Y2q43/H+b9MoXrNP/PLxPv33oaT2yY1CP7BjUN3/saOPqLp2wfpmO\nX79UK5e21U11E6h38wUwd5bbAOrQwPCEtu0e0tanhvTQEwe1b3C88NiKJW06dXOfTt3cp1W97Q3x\nH+JiGwof+oDVWQVsutaopbNPXKWzT1yl/kPj+t3D+/TA1n49uvOQHt15SN/9+TYt62rR5iN7tHF1\nlzat6VZfT2tD/P8AqEXzBbCIbdtrlOuY7932/jbW79dioAkMx5N6av+onto3qif2Dmv7niENDCcK\nj0cjIT1rwzIdt26Jjjt6ifp62qo42mD40YaisBVRnawBK0Vvd6tecvpaveT0tRoaS+qhxw/qr9tz\nVdD7t+zV/Vv2SpI628Jav6pLRy6P6cjlHTpqeUw9sSihDPDBfAGsQ9IvJ/38y9meCKDyXNfV0FhS\n+wbi2j84rr0Dce3aP6qn9o9qaCw55bmdbWGduHGZNqzq0vpVXVq3srPuqzrzaZY2FIvR1R7R844/\nQs87/ghls652HxjTY08d0tZdh7R115Ae2HpAD2w9UHh+R2tYRy7v0BFL27ViSZtWLGnT8iWtWtLZ\nIpNgBpRszgDmOM7a2R6zbZtWy0DAsq6r0XhKgyMJDYxM5P4cTmj/YFz7Bse1f3B8xn0Al3ZG9cz1\nS7VmeYdW93Zo7YqYerubbzrJq1plFjEFmWmQKchSmKahNX0dWtPXof918upCwN+5b0Q79o1q574R\n7dw3ooefHNTD+bYknrBlqq+nVct72rS0s0VLOqNa4v0Za1FXR4SABkwyXxuKVkkXSDroOM73Jt3/\nIknXSXpGsMMDGo/ruoon0hqJpzQ8ltRIPKWReDL/T0rD8aQOjSY1mA9cs61fioRN9XW3aXlPq/qW\n5P7Dt7ynVav7OtTOlW2SigvnF1UBa6IANp1hGOruiKq7I6oT1i8r3D+eSOvpgbj2DcT1dP6ffQPj\nenowrt39YzO+V8g01BOLqjsWVVdbRLH2iDrbwupsj6izLaJY/nasLaL2Fqvpviyg+cw3Bfl1SUdJ\n6rJtu0/SXZJukPRcSZ+c64W2bVuSbpK0Vrn1Yh93HOeuSY+/VNJHJKUkfc1xnBsX+DsAFZN1XSVT\nGSVSWSWS6dyfqYx2Hoxr774RxRNpxSdSiifSGp9I53+e+ufYeKqwvc1sDEmdHRGt6YtpSSyqnlhU\nPZ25P5fEWtTb3arujgj/kZpH2Mc1YOEGWgO2WK1RS0cf0XnY5t+u62p4LKmBkYQGhic0MJzQweEJ\nDYwkNDg8oYPDE9q+e0juPAVJw5DaopbaW8JqbbHU3mKpLWqprSWstmk/t0YtrRhJanwsoZZISNFI\nSNFw7h/T5Jihds0XwE6VtFHSEkn3SHqfpB9JeqPjOP3zvPZ8SQccx7nAtu0eSQ8qF+C8cPYZSSdL\nGpf0a9u27yzhPQFJuRN91nWVzrhKZ7JKpbNKp7NK5W+nMlN/TmdcpdKZSbcnP5Z/TdoLVhklUvl/\nJt9OZZRMLew/5CHTUHuLpdaopd6uFsXy3/hjbbkqQKwtolh7WLHWYiWgGSsufgsVAtjir4IMcTzm\nZRiGujqi6uqIHhbOPNmsq9GJlEbGkhoeS2o4X/UdiSc1PJarCo+OpwpfZg4dSBTao5QrYpmKhEOF\nYNYSDhV+DlumwpapiFW8HQ6ZCofzf0563Jr8uGUqkv85ZJqyQoZCIVMh08jdNk2CH0oyXwA75DhO\nWtL+/BWQ73Ac5/YS3/u7km7L3zaVq3R5jpG01XGcYSnXVV/SmZK+X/LIG4zrukplUkplUnKVCxeu\nXLnT/5x0uyXUosSElEhllHVzJ7ZcMMndzrquXDdXtSk8lnWVleTmH89mlX/e1Nflnp9/revmn6/D\nb3vvOcNnZjKuMtmsMtlptws/5++bfHvK49lpz536/KBZISP3TToSUkdrWEs6W9SS/zkSzp3Mo+GQ\nIhFTvUva5aYzam2x1BbNfUvPfUPP/Rm2TKpVVeBVrfzoAxau0z5gtcY0DXW25aYdV/WW9ppUOjul\nuhyf8P7J/RwKWxo4FFcyldFEcuoXp4n87UMjCU0kMxU5dxiGiuHMzAU077aVD2uhkCnLLD4eChmy\nzNyfIdOQaRoyjfw/hZ9VuN97juHd9h4zJ70m/2fINPJjOvyx4vur8HmGkQvTpmHIyN9vGN6fk28X\n/7RCpjraTMUzudY2hszcY8q/ZpY/s+7C/27Wu3L6gO0rI3zJcZy4JNm2HVMuiH1o0sOdkoYm/Twi\nqf7abPvohoe+qb/0P1TWaywjrJE/nill6n+9j2kYCoVyJ4IpJyXTUDhiKhQyC8857PFJ306tWf6c\n+TlG/rGQrFDufVoilqLh3LfmcipQvb0x9fePBPhvCAvhSxuKtNeGggBWLWHLVJcVUdcsG7+X8/cv\nnclqIpmZWgVPZ5XMV8gL/2SyU39OZ6bcl0xni18U85V474uid7v4p6tMJld9TyRTuZ/zXygXU52t\nLa6WnvZbxd3hsl61pmul3n/SZU35BbWcPmChaX3A5DjOzrlenH/+7ZL+w3Gc70x6aFi5EOaJSTo0\n32Aff/+V8z2lbp28aaXc5xyjVCqT++ZR+JZg5v/UYd8cWowOJY8/UpmMCt9epn9rMc3it5TiN578\nt5vCNyzJmOF24XWTviUZ0qSfJ3+mCt/GvM+3TO+bXj4w5b/dFUNW8WeujkIQfAlgWW8RPv8fbQRW\nyFRHa+2E6cnLKTIZV+lsNjeb4P2Tn53IZHOzD5nCfZOfU5yB8J7n3c7NWqj4uuwMr532Orcww5Eb\n35TZkGmPebMlMqSuvudoWPsnzdho2ixONvcaucr9z9WzHzioJ777nmofhsD03vSVWR9bTB8wV9K6\n2V5o2/ZyST+WdKnjOD+f9vAjkjbYtt0tKa7c9ON184xFpmmqUf87bS8/Wi88603VHgYWobc3Vu0h\nYAamacgwzXmPz2yPh6xcx52+3ph6l7IFbq3i7199emLX13VwUp+5ZrLgPmAluEpSt6SP2Lb9r8oF\nthsktTuOc6Nt21dI+olyFbUbHcfZO98brr123oxW95jGqk9MQdYuK2QoPpGa8/jMdfxGx3K7BwwP\njSuUbd71KrWMv3/16+gL36SOl7yy2sOoivn6gF0w7a6spEFJv3EcZ3CGlxQ4jnO5pMvnePwe5a6s\nBIDAWKZZaKa6EJkG3IoIQPXNNwV59rSfDUl9km6ybfv1juP8LJhhAYA/LMtUahELnZu5ESuA4Mw3\nBXnhTPfbtr1Z0s2SnhPAmADAN+GQsag2FBnaUAAIwILOKI7jPCqp1eexAIDvQiGzcCXjQnjVsxDN\nNQH4aEEBLL8RN5txA6h54ZC56EasVshoyj5FAIIz3yL8M2e4u1u5Dbp/FMiIAMBHVshc9FZEbEME\nwG/zLcK/Wrn2Ed5Xv6ykAUn/pVxLCQCoaVbIWPRm3GECGACfzXlWcRznbEn/R9LF+dv/odzar5Wa\n1BEfAGqVFTILXcAXIp3O0oICgO/mDGC2bV8p6V8lRW3bPkHSLZLuUK5D/qeCHx4ALI6Vv3pxob3A\n0tksLSgA+G6+s8oFkl7gOM7Dkv5J0v9zHOdGSVdKOi/owQHAYln5qxcXug4sVwEjgAHw13xnFddx\nnHj+9tnKL7x3HKdRtm8H0OC8ClhqgRWwVMYlgAHw3XyL8NP5DbM7JJ2o3N6Nsm37KEnpgMcGAIvm\nLaBfaCuKTIY1YAD8N9/Xuk9IelDS/yi/YbZt26+RdJ+kfw96cACwWKF8eEpnF1a4T2WyhSoaAPhl\nvq2Ivmfb9m8kLXMc56/5u0eVuyryF0EPDgAWazEVsEw2K9cVbSgA+G6+KUg5jrNH0p5JP/8w0BEB\ngI+89VsL6QXmLdwPMQUJwGd8rQPQ0IoBrPwpSC+0UQED4DfOKgAammV5bSgWUAHLT1tyFSQAv3FW\nAdDQvPC0kDYUXtWMqyAB+I0ABqCheQFsIZ3wvaoZFTAAfuOsAqChFSpg6fLXgHlVM9pQAPAbZxUA\nDS0cWvgasIw3BWlyqgTgL84qABpaaBFtKIoVMNaAAfAXAQxAQwsvIoBlaEMBICCcVQA0NG/91kL6\ngHkVsBABDIDPOKsAaGiWuZg+YLnQRgUMgN84qwBoaMUK2MLbULAVEQC/EcAANLRiG4qFBzAqYAD8\nxlkFQEPzuthnsovoA0YAA+AzzioAGtpiKmAZtiICEBACGICGFi5sRUQFDEDt4KwCoKF5C+gXthk3\nWxEBCAZnFQANbTGNWNNMQQIICAEMQENbzFZE6TRXQQIIBmcVAA0tvIhO+GnWgAEICGcVAA3Nmz5c\n3BQkp0oA/uKsAqChWYtaA+ZVwFgDBsBfBDAADS3k7QW5gD5gKa6CBBAQzioAGpphGLJCplILWAOW\n8QKYyakSgL84qwBoeFbIKISpcnihjQoYAL9xVgHQ8HIVsMW0oWANGAB/EcAANLywZS5sEX4295oQ\nV0EC8BlnFQANL2QaC+sDRiNWAAHhrAKg4S28AubKMCTTZAoSgL8IYAAanhVaYABLZ6l+AQgEZxYA\nDc8KLXAKMpOlCz6AQHBmAdDwrJCpdDor1y0vhKUzLl3wAQSCAAag4VkhU66kTLbcAJalBxiAQHBm\nAdDwvGnETJnTkCmmIAEEhDMLgIbnTSOW24w1k3EJYAACwZkFQMML56cRy70SMlcBYw0YAP8RwAA0\nvJC5sABGGwoAQeHMAqDhha1cFaucVhSu6yqTddmGCEAgOLMAaHjeOi5va6FSeGGNjbgBBIEABqDh\nFQJYtpwAlp3yWgDwE2cWAA2vWAErfQqSAAYgSJxZADS8hbSh8KYgacQKIAicWQA0vGIj1tIDWKpQ\nAWMNGAD/EcAANDwvgJVTAcswBQkgQJxZADS8YiPW0teApdIEMADB4cwCoOGFQl4fsIW0oeA0CcB/\nnFkANLzwgvqA5Z4bYg0YgAAQwAA0vEIbirIqYLnnUgEDEATOLAAanhUqfysi77lUwAAEgQAGoOFR\nAQNQazizAGh4XjPV8hqxZqe8FgD8xJkFQMOzzIVMQdKGAkBwOLMAaHiWtZApyPxWRKwBAxAAAhiA\nhreQNhQ0YgUQJCvoD7Bt+zRJn3Ac5+xp918u6WJJ+/N3XeI4ztagxwOg+YS8AJYtfQqSrYgABCnQ\nAGbb9nslvVHS6AwPnyzpjY7jPBDkGAAg7LWhKKcCRgADEKCgzyzbJL1ilsdOlnSVbdu/sm37AwGP\nA0ATW1gbCm8rItaAAfBfoAHMcZwfSErP8vC3Jf2zpLMlnWHb9ouCHAuA5rWYPmAhKmAAAhD4GrA5\nfM5xnGFJsm37HkknSvrhXC/o6WmTZYUqMbaq6e2NVXsIWCCOXe1q60hJksxQaNbjNP3+cCR3euxd\n1sGxrQMco/rVrMeuUgFsSg3ftu1OSQ/Ztr1Z0rikcyR9db43GRyMBzO6GtHbG1N//0i1h4EF4NjV\ntlQ6I0kaG0/OeJxmOn4jIwlJ0ujIBMe2xvH3r341+rGbK1xWKoC5kmTb9usltTuOc6Nt21dJ+oWk\nCUn3OY7zowqNBUCT8aYRM+VMQWa9RfisAQPgv8ADmOM4OySdnr/97Un3f0vSt4L+fAAwDUMh0yhv\nKyL6gAEIEGcWAE3BCplKp0vvA0YbCgBB4swCoClYIWNhbSjYjBtAADizAGgKYcssbC9UCu+5YSpg\nAALAmQVAUwhbZnlrwLwpSItF+AD8RwAD0BSsUPkVsNzifU6TAPzHmQVAUyi3ApZKZ1n/BSAwnF0A\nNIWwZZa1GXc6QwADEBzOLgCaQjhkKpN1lc2W1ooilc7ShBVAYAhgAJqCla9mlToNmaICBiBAnF0A\nNAWvnUSpvcBya8BCQQ4JQBMjgAFoCl41q9QrIVMZpiABBIcABqApeBWwUgNYmqsgAQSIswuApuCF\nqVKmILNZV5msSxd8AIHh7AKgKVhlVMC8hfqsAQMQFAIYgKZQzhow7zmsAQMQFAIYgKZglXEVZLpQ\nAeMUCSAYnF0ANIWFVMAIYACCwtkFQFNYUABjET6AgHB2AdAUCovwy5iCtKiAAQgIZxcATYEpSAC1\nhLMLgKZQTh+wwiJ8piABBISzC4CmUE4nfCpgAILG2QVAU/DWc5WyBoxF+ACCxtkFQFMoTEGW0Qmf\nRfgAgsLZBUBTCJdxFSQVMABB4+wCoCmUdRUknfABBIyzC4Cm4FWz0ml33uemC3tBcooEEAzOLgCa\nQnERfmbe51IBAxA0zi4AmgJtKADUEs4uAJpCYQ1YpoQpyAxTkACCxdkFQFOwQmW0oaACBiBgnF0A\nNIXiVZAlrAEjgAEIGGcXAE3BChmSypuCpA8YgKBwdgHQFAzDkBUyWYQPoCZwdgHQNMJWeQGMrYgA\nBIWzC4CmEbbMwvTiXNL5aUqmIAEEhbMLgKYRDhklVsByC/WZggQQFM4uAJqGZYXK2ow7ZBpBDwlA\nkyKAAWga4VIX4WeyilimDIMABiAYBDAATSMSNpVMzd8HLJnKMv0IIFCcYQA0jYhlKpN1lc3O3Qss\nmc4oEg5VaFQAmhEBDEDTCFu5UJWcpxt+Mk0FDECwOMMAaBqRfKhKzrMOLJXKFp4LAEHgDAOgaUTC\n+f0gU3MHsGQ6yxQkgEARwAA0jVKmILOuq3SGChiAYHGGAdA0vFA1VyuK4j6QVMAABIcABqBphMPz\nrwHz2lRQAQMQJM4wAJpGJF/VSs3RC6xQAQtzegQQHM4wAJpGKVdBeo9RAQMQJM4wAJpGuJQAlvI2\n4mYNGIDgEMAANA2vtcRc2xGlqIABqADOMACaRriEqyCThasgOT0CCA5nGABNo5Q1YKl8jzAasQII\nEgEMQNPw1nWl5mjEmkxRAQMQPM4wAJpG1OsDNsdWRF6X/CgVMAABIoABaBrFChhrwABUF2cYAE2j\nuAZsjqsgU1wFCSB4nGEANI2StiJK0wcMQPAIYACaRqSEKUj6gAGoBM4wAJpGoRP+HI1Yk+wFCaAC\nOMMAaBol9QErrAFjChJAcAhgAJpGoRP+nBWwfCNWpiABBIgzDICmYRiGwpY5zyJ82lAACB5nGABN\nJWKZc/cBS7EVEYDgEcAANJVcBWyOPmBUwABUAGcYAE0lEg4xBQmg6gI/w9i2fZpt2z+f4f6X2rb9\ne9u2f23b9sVBjwMApPwU5Bx7QabSGYUtU6ZhVHBUAJpNoAHMtu33SrpBUnTa/Zakz0g6V9JZkt5m\n23ZvkGMBACnX4X6+ChhXQAIIWtBnmW2SXjHD/cdI2uo4zrDjOClJ90s6M+CxAIAilql0Jqus6874\neCqVZfoRQOACPcs4jvMDSekZHuqUNDTp5xFJXUGOBQCk4tWNs01DJtIZmrACCJxVpc8dVi6EeWKS\nDs33op6eNlkNfmLs7Y1VewhYII5dfejsyK2I6OhsVXesuDrCO36pdFZLOls4nnWG41W/mvXYVSqA\nTV/N+oikDbZtd0uKKzf9eN18bzI4GA9gaLWjtzem/v6Rag8DC8CxqyNurvK1++khpSZaJRWPn+u6\nGk+kFTINjmcd4e9f/Wr0YzdXuKxUAHMlybbt10tqdxznRtu2r5D0E+XC2Y2O4+yt0FgANLGWcO60\nl0ge3gsslc7KdaUWmrACCFjgAcxxnB2STs/f/vak+++RdE/Qnw8Ak0UiuaWviRn2g/TuixLAAASM\nS30ANBWvujVTBcy7LxohgAEIFgEMQFOJRnKF/4kZAthEigAGoDIIYACaSks+XCVSh3fIKVTAmIIE\nEDACGICmEgl7a8AO7wPmrQFjET6AoBHAADSVua6CZA0YgEohgAFoKl64mkgePgU5wVWQACqEAAag\nqXhrwJJzTEFSAQMQNAIYgKbi7QU5MVMfsCRrwABUBgEMQFMp9gGb4ypIKmAAAkYAA9BUimvA5ugD\nRqbCg2UAAAh3SURBVAUMQMAIYACaSnEN2BxbEVEBAxAwAhiApmKFTIVMgzVgAKqKAAag6UTDoTn7\ngEWogAEIGAEMQNOJRkKF6cbJ6IQPoFIIYACaTktk5grYRCojw5DCFqdGAMHiLAOg6UTCoVnXgEXD\nIRmGUYVRAWgmBDAATaclHFIylVXWdafcn0hmuAISQEUQwAA0negsrSgSqQzrvwBUBAEMQNOJFrrh\nTw1gE6kMTVgBVAQBDEDTmakbvuu6SiYztKAAUBEEMABNpy1qSZLiieJ+kOOJjNxJjwFAkAhgAJpO\nW0s+gE0UA1h8IiVJam8hgAEIHgEMQNNpbwlLksbyoSt3OxfG2vKPAUCQCGAAmk47FTAAVUYAA9B0\n2uaogLVTAQNQAQQwAE3Hq3KNTa6AJbwpSCpgAIJHAAPQdIqL8CdXwLwpSCpgAIJHAAPQdIqL8IsV\nsLFxKmAAKocABqDpzNmGopUKGIDgEcAANB0rZCoaCc2yCJ8KGIDgEcAANKX2Fqsw7SjRhgJAZRHA\nADSltmhY8cTUCljYMhW22AsSQPAIYACaUnuLpfFERtmsKym3HowF+AAqhQAGoCkVFuLn+3+NTaRo\nQQGgYghgAJqSd7Xj2ERK2ayreCLN+i8AFUMAA9CUJu8HGU+k5bo0YQVQOQQwAE2pI18BG4knNTyW\nkMQVkAAqhwAGoCkt7WyRJB0YmtD+gXjuvq6Wag4JQBPh6x6AptTb3SpJ6j80rq6D8Sn3AUDQCGAA\nmpIXtg4cmlBH+9iU+wAgaAQwAE0p1hZWJGyq/9C4WvLrwQhgACqFAAagKRmGod7uVvUPjSscCSls\nmerqiFR7WACaBIvwATSt3q5WjScy2r5rSMu6WmQaRrWHBKBJEMAANK3JU45MPwKoJAIYgKbV290y\n6TYBDEDlsAYMQNM6YcMy/f7R/TIMQ88+pq/awwHQRAhgAJpWX3erPnj+yertjam/f6TawwHQRJiC\nBAAAqDACGAAAQIURwAAAACqMAAYAAFBhBDAAAIAKI4ABAABUGAEMAACgwghgAAAAFUYAAwAAqDAC\nGAAAQIURwAAAACqMAAYAAFBhBDAAAIAKI4ABAABUGAEMAACgwghgAAAAFUYAAwAAqDACGAAAQIUR\nwAAAACqMAAYAAFBhVpBvbtu2IemLkp4paULSxY7jPD7p8c9Kep6kkfxdL3McZ+SwNwIAAGgggQYw\nSS+XFHUc53Tbtk+T9Jn8fZ6TJZ3nOM5AwOMAAACoGUFPQZ4h6UeS5DjO7ySd4j2Qr45tlPQV27bv\nt237woDHAgAAUBOCDmCdkoYm/Zy2bdv7zHZJn5d0vqQXSnqHbdvHBTweAACAqgt6CnJYUmzSz6bj\nONn87bikzzuOMyFJtm3/TLm1Yg/N9ma9vTEjqIHWit7e2PxPQk3i2NU3jl994/jVr2Y9dkFXwH4t\n6UWSZNv2cyRtmfTYJkm/tm3bsG07rNx05Z8DHg8AAEDVGa7rBvbmk66CPCF/14WSXixpq+M4d9u2\nfaWk10pKSvqG4zhfCWwwAAAANSLQAAYAAIDD0YgVAACgwghgAAAAFUYAAwAAqLCg21CgRLZtb5b0\nP5L6HMdJ5q8a/ayklKSfOo7z0aoOEDOybbtT0i3K9bwLS7rCcZzfcfzqw3zbpaG22LZtSbpJ0lpJ\nEUkfl/SwpJslZSU95DjOpdUaH0pj23afpD9KOldSRk16/KiA1QDbtmOSPqXcfwA810t6neM4z5d0\nmm3bz6zK4DCfKyT9l+M4Zyl3le8X8/dz/OpDYbs0SVcpt10aatf5kg44jnOmcg28/0O5Y/ZBx3Fe\nIMm0bftl1Rwg5pYP0V9Srheo1MTHjwBWG76i3Mk/LhUCWcRxnCfzj/9YuW8KqD2fkfTl/O2wpHGO\nX12Zdbs01KTvSvpI/nZIUlrSSY7j/Cp/373i71qt+5RyX1D3SDLUxMePKcgKsm37IknvljS598dO\nSd92HGdLfjpEyk1nDU96zoikoyszSsxm2vEz8n9e6DjOn2zbXiHpm5LeJY5fPZlxu7RJO3aghjiO\nM/lL6m2SPqTcf9A9I5K6qjA0lMC27TdL2u84zk9t2/5g/u7JhaCmOn4EsApyHOcm5dYvFNi2/Zik\nt9i2fbGkFZJ+Iumlyv2HwROTdKhS48TMZjp+kmTb9vGS/q+kKx3HuT//HweOX32Ya7s01CDbttdI\n/397dwgiVRiFYfjVYrUsiwbF4gG7VVlhWIwilgXDNk0WEQ0aDTbRJog7ySCKSdgggpoMaxDkq2LY\nKJhEcA33Lmxasfx3lv990ty5MBw43JmP/wwcXgKPkzyvqgd7bvusLbZ14E9VzRj+dzkHlvbc76p/\njiAnluR0kgtJVoBtYJbkJ/Crqk6Np2KrwPt9P0iTqKozDGORtSSbAPbvQNlvXZoWTFUtM4z0byXZ\nGN/eqqpz4+uL+KwtrCTnk6yMv3efgavAm1775wnYYtkdbQFcYzhVOQxsJvk0WVXaz33gCPBwDFs/\nklwCrmP/DoJXwKyqPo7X61MWo3+6AxwF7lbVPYbvzBvAo3Gn8FfgxYT16f/dBJ702D9XEUmSJDXm\nCFKSJKkxA5gkSVJjBjBJkqTGDGCSJEmNGcAkSZIaM4BJkiQ1ZgCTJElqzAAmSZLUmAFMUpeqaj7u\nYN29fltVZ6esSVI/DGCSevWUYRcdVXUSWHJllKRWDGCSupTkHXCsqk4wBLH5tBVJ6onLuCX1bANY\nA64AqxPXIqkjBjBJPdsAPgBfkmxPXYykfjiClNStJN+Bb8CziUuR1BkDmKRuVdVxYBl4PXUtkvpi\nAJPUpaq6DGwBt5P8nroeSX05tLOzM3UNkiRJXfEETJIkqTEDmCRJUmMGMEmSpMYMYJIkSY0ZwCRJ\nkhozgEmSJDX2Fxm1lul+BYgyAAAAAElFTkSuQmCC\n",
"text/plain": "<matplotlib.figure.Figure at 0x7fb4b3874350>"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "y_range_tail = pd.Series(np.linspace(36, 42, 500), name='y')\nSURE_trunc_tail_vals = SURE_hs(y_range_tail, \n E_Z_hs_trunc_single, tau=1)\nSURE_trunc_tail_df = pd.DataFrame(zip(*SURE_trunc_tail_vals), \n index=y_range_tail, \n columns=['SURE', 'precision'])\nax = SURE_trunc_tail_df.pivot(columns='precision', values='SURE').plot()\n_ = ax.set_ylabel(\"SURE\")",
"execution_count": 34,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAnAAAAH1CAYAAAB2hsNVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRK5CYII=\n",
"text/plain": "<matplotlib.figure.Figure at 0x7fb4b3a68d50>"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## Quadrature\n\nThis case simply uses finite precision numeric quadrature to estimate $E[Z]$."
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "from functools import partial\n\ndef E_Z_hs_quad_single(y, sig=1., tau=1., n=1):\n x_ = 1. - 1./tau**2\n y_ = (y/sig)**2/2.\n \n def phi_1_integrand_num(t, n_=0):\n res = t**(-0.5) * (1.-t)**(3/2.+n_-1.5)\n res *= fp.exp(y_ * t) / (1.-x_*t) \n return res\n\n try:\n res = fp.rf(1., n)/fp.rf(3/2., n)\n res *= fp.gamma(3/2.+n)/fp.gamma(1+n)/fp.gamma(3/2.)\n res *= fp.quad(partial(phi_1_integrand_num, n_=n), \n [0, 1])\n res /= fp.quad(partial(phi_1_integrand_num, n_=0), \n [0, 1])\n return (res, 'fp')\n except:\n pass\n try:\n # If it fails, use the infinite precision calculations.\n res = mp.rf(1., n)/mp.rf(3/2., n)\n res *= mp.hyper2d({'m+n': 0.5, 'm': 1.}, {'m+n': 3/2.+n},\n x_, y_)\n res /= mp.hyper2d({'m+n': 0.5, 'm': 1.}, {'m+n': 3/2.},\n x_, y_)\n return (res, 'inf')\n except:\n pass\n return (np.nan, 'failed')",
"execution_count": 45,
"outputs": []
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "%%time\nSURE_quad_vals = SURE_hs(y_range, E_Z_hs_quad_single, tau=1)",
"execution_count": 46,
"outputs": [
{
"output_type": "stream",
"text": "CPU times: user 1.85 s, sys: 7 ms, total: 1.85 s\nWall time: 1.84 s\n",
"name": "stdout"
}
]
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "from timeit import timeit\ntimeit(stmt=lambda: SURE_hs(y_range, E_Z_hs_quad_single, tau=1),\n number=5)",
"execution_count": 56,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "8.96604609489441"
},
"metadata": {},
"execution_count": 56
}
]
},
{
"metadata": {
"trusted": true,
"collapsed": true
},
"cell_type": "code",
"source": "SURE_quad_df = pd.DataFrame(zip(*SURE_quad_vals), \n index=y_range, \n columns=['SURE', 'precision'])",
"execution_count": 47,
"outputs": []
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "ax = SURE_quad_df.pivot(columns='precision', values='SURE').plot()\n_ = ax.set_ylabel(\"SURE\")",
"execution_count": 48,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAmAAAAHwCAYAAAAB5dMOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAft/oLE5tXfM/84AAAAASUVORK5CYII=\n",
"text/plain": "<matplotlib.figure.Figure at 0x7fb4b2282e90>"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "y_range_tail = pd.Series(np.linspace(37.55, 37.8, 500), name='y')\nSURE_quad_tail_vals = SURE_hs(y_range_tail, \n E_Z_hs_quad_single, tau=1)\nSURE_quad_tail_df = pd.DataFrame(zip(*SURE_quad_tail_vals), \n index=y_range_tail, \n columns=['SURE', 'precision'])\nax = SURE_quad_tail_df.pivot(columns='precision', values='SURE').plot()\n_ = ax.set_ylabel(\"SURE\")",
"execution_count": 60,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAoIAAAH1CAYAAABiP5/xAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3XlgVOW5x/HvZIEECIsQUFFkkxcVAVnVutcFq21Ru1j3\n3dZba6120Squ6O1t9ba217ZWcLe2tYpVilqrVqEKqKAg8IoiUASRJcgSEkKS+8ckNlogBDKZTOb7\n+YdkzjtznsMr8ZfnnPecRHV1NZIkSco+OekuQJIkSelhEJQkScpSBkFJkqQsZRCUJEnKUgZBSZKk\nLGUQlCRJylJ56S6gOQshtAceBNoD+cAVMcZXPzPmQuAioAIYG2OcGELoDDwMFABLgXNjjGUhhJ8D\nnwPW1bz9yyTn4B1gVs1rj8cYfxlCuAL4BlAJ3BpjnJDCQ5UkSVnIILht3wOeizHeEULoB/weGFq7\nMYTQDbgUGAK0ASaHEJ4FxgAPxRjvDyH8ELgY+EXNe4+LMa6u8xmfBx6OMV5W57UOwHeA3kARMBMw\nCEqSpEblqeHPCCFcF0K4uObb24Hf1nydD2z8zPARwOQY4+YY41pgPjAIOAR4umbMJODoEEIC2Bu4\nK4QwOYRwbs32ocCwEMKLIYQ/1ITLDcBCkiGwHcmuoCRJUqOyI1gjhPA14FvAXsCmEMLXSZ7q/XsI\nYVfgAZJdurraAx/X+X4d0IFkgPv4M6+1Ae4gGS7zgBdCCNOBucBrMcbnQwinAb8ieUp4CTCHZFi/\ntZEPV5IkyY5grRjjH2OMRwL3AbfHGI+qCYH7A38DfhRjnPyZt60lGQZrtQdKal4vqnmtCFgDlAJ3\nxBjLYozrgedJdg9fAF6sGfs4cABwPLAryVDaAzgphDCsMY9XkiTJILgNIYR9gT8Cp8UYn93CkGnA\nISGEVjXX9fUHZgNTgBNqxhwPvAwEYEoIIRFCyCe5aOQN4G7glJqxRwOvAauBjTHGihjjJpJBsmMq\njlGSJGWvRHV1dco+vOa6uDtJdr7KgAtijAvqbG/Iitv/GFvnc74LdI0xXl3ntTbAs8B5McZ3drD+\nCcBAktfrJYA1McaTQgiXA/NjjE+FEM4nuRgkUVPXhBBCV5KdxXbASpJBcmPNSuCvA5uA+2OMd4UQ\negLja3a5oebvaHkI4XpgFMnrAyfHGH+4I8cgSZK0NakOgicBX4wxnhdCGAlcFWMcXbOtG8lTrp+s\nuCW5cOJnwOt1VtyWAY9sZWwuyY7acODPtUEwhDAU+A3QHThiR4OgJElSS5bqU8OfrJ6NMU4F6l7n\ntr0rbo/ZytiBJLuG9wJjP7PfVsBoYF4KjkmSJKlFSPWq4c+uqt0cQsiJMVZtYdu2VtwWfWbseqBD\njHEN8FwI4ey6O40xvgKfnJqu1+bNldUlJaXbfVBqXjp1aoPzl5mcu8zm/GU25y9zFRcXbVe+2R6p\n7gjWXT0LUBsCa7dtz4rbki2MrV2J2yjy8nIb66OUBs5f5nLuMpvzl9mcP0Hqg+AU4AsAIYQD+fdj\n1KBhK26nb2WsJEmSdlCqg+DjQHkIYQpwG3B5COHyEMKJMcblJG+wPBl4Dri65lYpY4FTQwgvAwcC\nv9rG2PqkbiWMJElShkvpquEMUr1ixbp016AdVFxchPOXmZy7zOb8ZTbnL3Nl0jWCkiRJaqYMgpIk\nSVnKIChJkpSlDIKSJElZyiAoSZKUpQyCkiRJ23DNNT/Y6rYHH7yXefPmNGE1jcvbxyR5+5gM5i0Q\nMpdzl9mcv8zm/GWuxrx9TKqfNSxJktTkJk16ipdeepHS0lLWrl3DOedcwLhxv2XPPXuQn9+K73//\nKm699SbWrVsLwGWXXUnv3n146qkJTJjwGFVVVRxyyGGcd95FfPnLx/HEE8/w2GN/4umnJ5Kbm0P/\n/vtx2WVXcMstN3D00ccxZMgwbr31BpYu/YCqqmq+/vXTOeqoo7n00ovZe+9+LFjwHqWlpdx003/T\nrduuaf7b+TeDoCRJapHKy8v4xS/upKRkNRdeeDZVVVWce+5F9O27N7/+9S8ZNmwEo0efwpIl/+KW\nW25g7Nif8uCD9/PAA38gPz+f3/72/9i4cSOQbMBNmvQUV1zxI/r334cJE/5MZWXlJ/t64onH6Nhx\nF6699iZKS0s5//wzGDp0GAD77juA73znCu66606ee+4ZTj/97HT8dWyRQVCSJLVIgwcPAaBTp10o\nKipi0aJF7LlnDwAWLHiXN954jeef/xvV1dWsW7eWpUs/oE+fPuTn5wNw8cX/9anPu+qqMTzyyIMs\nW7aUAQMGUvfyukWL3mf48JEAtGnThp49e/HBB0sA6NcvANC1azdKSlan9qAbyCAoSZJapBjnArB6\n9So2bNhAp06dyMlJrpPda69eHHfcPhx99HGUlJTw1FNP0L37HixatIjNmzeTl5fHNdf8kO9+90og\nGfiefHIC3//+1eTn5/O9713K22/P+mRfPXv2ZubMGRx66BGUlm5gwYL32H33PWq2NtolfY3OIChJ\nklqkVatWcdlll1Baup4rr7yKn/701k+2nXXWudx660088cRjlJaWct55F9GxY0dOP/0s/uu/LiQn\nJ8HnPncYXboUUxvk+vTpwyWXnE+bNm3p2rUb++47gIkT/wLAl750Ej/5yc1ccskFbNq06ZPPSySa\nbwgEVw3XctVwBnPlW+Zy7jKb85fZWvr8TZr0FIsXL/qP07stQWOuGvY+gpIkSVnKU8OSJKnFOf74\nE9NdQkawIyhJkpSlDIKSJElZyiAoSZKUpQyCkiRJWcogKEmStB0qKyu59NKL+da3zmf9+vXbHLt0\n6QecfvpXuOWWG5qouh3jqmFJkqTtsGLFCjZu3Mjdd99f79i33prJwQcfyn/912VNUNmOMwhKkqSM\n88fn32X6vI8a9TOH9+/K147qu9Xtt912K0uWLOanP72F9evXs2ZNCevWrePyy7/P/vsP+mTc8uUf\n8sAD91BeXk737t35+9//xl579WTRooUA3HjjrXTqtEuj1r6jPDUsSZK0Ha644kfstVcvunQpprCw\nkF/84tdce+2N3HbbTz41rlu3XTnjjHM45phRjB79FQAGDhzML3/5W4466hjuu298OsrfIjuCkiQp\n43ztqL7b7N6l2pAhwwHo1as3q1evYtasN7nrrjtJJBJ84xtnbmH8MAAGDBjI5MkvNWmt22JHEPB5\ny5IkqSFinAPAggXvUlzclf33H8Qvf/lb7rjjNxx00Of+Y/y8eXMBmDXrTXr16t2ktW6LHUHg3Jue\n5WtH9mV4/67pLkWSJDVjiUQCgHfeiVx22SWUl5fxwx/+uN73TZr0JI888iBt2rThmmtuTHWZ280g\nCKzbsIlfT5jN6/t05fRj+lHUplW6S5IkSc3Mrrvuxm9+M57x4+/i6KOP48tfPnmrYz/7rOOLL/42\nPXrsleoSG8xTw8AdVx5Jn+7tmTb3I669eypvvLMi3SVJkqRmqrYrmKrxTSnh9XEAVC9fvpZnp/+L\nx15awObKKg7crxunHd2PdoX56a5N9SguLmLFinXpLkM7wLnLbM5fZnP+MldxcVGjJUtPDdfIyUkw\namQP9u/TmfET5/Dq28uZu6iEs0f1Z3DfLukuT5IkqdF5avgzundpy9VnDuWUw3uzvrSCOx59i3ET\n51BaVpHu0iRJkhqVHcEtyM3J4YSDejKoTxfGTZzLlFkfMmdhCece358BvTunuzxJkqRGYUdwG/bo\n2o4fnzWU0Yf0Yu2GTdz+xze5d9I8NpZvTndpkiRJO80gWI+83By+dEgvrj17GHsUt+OlN5cyZtxU\n5ixcne7SJElSE5s69RWefHLCFretW7eO8847g+9979ufen3+/He49967t/qZlZWVXHrpxXzrW+ez\nfv36Rq23Pp4a3k49uhUx5pxhPDllIRNfWcTPHpnJkQd056tH9qGglX+NkiRlg5EjD9rqtvfem8/u\nu3fn5ps//ezhvffux95799vq+1asWMHGjRu5++77G63O7WWCaYC83BxOOqw3g/dOXjv4wowPmLVg\nFeefsA+hR6d0lydJUtZ47N2nmPHRrEb9zAO67s/JfU/c5phJk57i1Vf/yfLlH9K1azc++GAJ++47\ngMsuu4Jf/OJnrFq1ivHj7+K88y765D0zZrzOhAl/5oYbbuHUU09i4MDBLF68iF126czNN/+E2267\nlSVLFvOzn93KlVde1ajHVB9PDe+AXru157pzhvOFA/di1doyfvLwDB7+2zuUb6pMd2mSJKkJLFmy\nmKuvvo7f/e4+XnllMuvWreU737mCIUOGfSoE1qq9qfSyZUu56KJL+M1vxlNSspp58+ZwxRU/omfP\n3k0eAsGO4A7Lz8vhK0f04YB+XRj31Fyee30Jb9V0B/feo2O6y5MkqUU7ue+J9XbvUql79z0pKCgA\noEuXYsrLN31q+w9+cDllZRvp3bsvhx9+5Cevd+zYkS5digHo2rUbmzZ9+n1NzSC4k/rs3oHrzx3O\nhJff55lpi/nvB9/g2BF7ctKhvWmVn5vu8iRJUgrUfWzclp7S9j//87+ffD1jxuv1fl66nvTmqeFG\n0Co/l68d1ZcfnTGE4k6FPDPtX1x/z3TeW/pxukuTJEmN7LPPDm7Ys4T/Pbbu+9L1PGKfNZxU3VjP\nWyyvqOTP/3iP515bQiIBo0b2YPQhvcjPszuYKj4vM3M5d5nN+ctszl/myphnDYcQEsCdwCCgDLgg\nxrigzvYLgYuACmBsjHFiCKEz8DBQACwFzo0xlm1pbJ3P+S7QNcZ4dc33XwSurRl7T4xx6zfvaWSt\n83M57eh+DO1XzLiJc5n06mLefDd57WCv3do3VRmSJEn1SvWp4dFA6xjjwcBVwO21G0II3YBLgYOA\nUcCtIYR8YAzwUIzxcGAmcPHWxoYQCkIIDwLfqvO5eTX7ORo4ArgohFCc4uP8D6FHJ248fwRHDunO\n0pUbGHv/6zz20gI2V1Y1dSmSJElblOogeAjwNECMcSowrM62EcDkGOPmGONaYD7JzuEn7wEmAcds\nZexAkl3De4GxdT53H2B+jHFtjLECmAwclprD27aCVnmceWzgylMH06moFU/9cyE33vsai5fbipck\nSemX6iDYHqi7YmJzCCFnK9vWAR2Aojqvb+k1gPVAhxjjmhjjc9S98nLrn5s2+/bchRvPH8nhg3dn\nyYr13HTfa/xl8vt2ByVJUlql+vYxa0mGuFo5McaqOtvqXjTXHiip857ymj9LtjC2CFizjX1u79hP\nFBcX1Tdkp1155nCOGv4Rv/zjDCZMfp+33l/N5d8YQk+vHdxpTTF/Sg3nLrM5f5nN+VOqg+AU4ETg\n0RDCgUDdZ8FMA24OIbQCCoH+wOya95wA3AccD7wMTAfGbmHslswF+oYQOgKlJE8L/7S+Qptq5dSe\nnQu5/tzhPPL3d5k8axnfvf1FRh/ai1Eje5Cb4918doQr3zKXc5fZnL/M5vxlrsYM8KlOHo8D5SGE\nKcBtwOUhhMtDCCfGGJcDd5C8hu854OoY4yaS1/udGkJ4GTgQ+NU2xv6HGONm4HvAsyRD5d0xxmUp\nPcoGalOQz3kn7MNlXxlIuzb5/PkfC7jlgdf5YOWGdJcmSZKyiPcRTGq0+wg21IayCh7+2zu88vZy\n8nJzOOmwXhw3vAc5Oem5sWQm8rfazOXcZTbnL7M5f5mrMe8j6LnINGtbkM+FX9yPb5+8P21a5/Kn\nF97j1odeZ9kqu4OSJCm1DILNxJB+xdx0wUhG7NOV9z5Yy/X3TOfZaYupsmMrSZJSxCDYjBS1acU3\nvzyAS0YPoHV+Lo88/y7/89AbLC8pTXdpkiSpBTIINkPD+nfl5gtGMrRfMe8s+Zjrxk/j768vsTso\nSZIalUGwmWrfthWXnDSAi7+0H/m5OTz0t3f42e9nsHLNxnSXJkmSWgiDYDOWSCQYuW83br5gJIP7\ndmHe4jVcO34aL874AFd7S5KknWUQzAAd2rXm0lP254IT9yE3keD+ZyK3/2Emqz4uS3dpkiQpgxkE\nM0QikeDgAbtx0wUjGdinM28vLOHacVN56c2ldgclSdIOMQhmmE5FrbnsKwM59wv9SSTg3knz+Pmf\n3qJkXXm6S5MkSRnGIJiBEokEhw7cnRvPG8l+PTsxa8Eqrrl7KlNmLbM7KEmStptBMIN17lDA974+\nmLNGBaqqqxk3cS6//PMsPl5vd1CSJNXPIJjhEokERwzuzk3njaB/j47MfHcl19w9lVfnfGh3UJIk\nbZNBsIXo0rGQK79xAGcc24+Kyiru+ssc7nx8Nms3bEp3aZIkqZnKS3cBajw5iQRHDdmDAb12YfzE\nubz+zgriv9Zw5nGB4f27prs8SZLUzNgRbIG6dmrDD04fwjc+vzebKir59YTZ/OaJ2awrtTsoSZL+\nzY5gC5WTSHDM8D3Zv09nxk2cw7S5HzFvUQlnjerPkH7F6S5PkiQ1A3YEW7hdd2nDVacP5WtH9qW0\nvJJfPTaLu558m/UbK9JdmiRJSjM7glkgJyfBqJE9GFjTHXz17eXMXVTC2aP6M7hvl3SXJ0mS0sSO\nYBbZvUtbrj5zKKcc3psNGyu449G3GDdxDqVldgclScpGdgSzTG5ODicc1JNBfbsw7qm5TJn1IXMW\nlnDO8f3Zv3fndJcnSZKakB3BLLVHcTt+fNZQRh/ai7UbNvG/f3yTeyfNY2P55nSXJkmSmohBMIvl\n5ebwpc/14tqzh7Fn13a89OZSxoybypyFq9NdmiRJagIGQdGjWxHXnj2MLx7ck5J1m/jZIzN54JlI\n2Sa7g5IktWQGQQHJ7uBJh/XmmrOH0r1LW16Y8QFjxk0jLi5Jd2mSJClFDIL6lJ67tmfMOcM54aC9\nWLW2jJ88PIOH//YO5Zsq012aJElqZAZB/Yf8vBxOObwPV585lN06t+G515dw3T3TmL9kTbpLkyRJ\njcggqK3qs3sHrjtnOKNG9GBFyUb++8E3+MPz89lUYXdQkqSWwCCobWqVn8vXjurLVWcMpWunQp6Z\n9i+uv2c67y39ON2lSZKknWQQ1Hbpu0cHrj9vBMcM25Plq0u55YHX+dOL71Kx2e6gJEmZyiCo7dY6\nP5dvHL03PzjtALp0KGDSq4u54d7XeH/Z2nSXJkmSdoBBUA0WenTihvNGcNSQ7ixduYGx97/OYy8t\nYHNlVbpLkyRJDWAQ1A4paJXHGccGvn/qYDoVteapfy7kxntfY9GH69JdmiRJ2k4GQe2UfXruwo3n\nj+DwwbuzZMV6br7/NZ6Y/L7dQUmSMoBBUDutsHUeZ4/qz/e+Poj2bVvxxOT3ufn+11jy0fp0lyZJ\nkrbBIKhGM6BXZ246fySHDNyNxcvXc8O903nqnwuprLI7KElSc2QQVKNqU5DHeV/Yh+9+dSBFbfJ5\n7KUF3PLA63ywckO6S5MkSZ9hEFRKDOzThZsuGMlB++3K+8vWccM905k0dRFVVdXpLk2SJNUwCCpl\n2hbkc+EX9+XSk/enTUEef3rhPW596HWWrbI7KElSc2AQVMod0K+Ymy8YyYh9uvLeB2u5/p7pPDtt\nsd1BSZLSzCCoJtGuMJ9vfnkAl4weQOv8XB55/l1+8vAbLC8pTXdpkiRlLYOgmtSw/l25+YKRDA3F\nzF/yMdeNn8bfX19CVbXdQUmSmppBUE2ufdtWXDJ6AN/88n7k5+bw0N/e4We/n8GKNRvTXZokSVkl\nL5UfHkJIAHcCg4Ay4IIY44I62y8ELgIqgLExxokhhM7Aw0ABsBQ4N8ZY1sCxPwROBT4GfhpjnJjK\n41TDJRIJRuzTjbBnR+5/JjJj/krGjJ/G14/sy+GDdyeRSKS7REmSWrxUdwRHA61jjAcDVwG3124I\nIXQDLgUOAkYBt4YQ8oExwEMxxsOBmcDFDRj7zRDCAJIhcARwHHBjCKEgxcepHdShXWu+ffL+XHji\nvuQmEtz/TOS2P8xk1cdl6S5NkqQWL9VB8BDgaYAY41RgWJ1tI4DJMcbNMca1wHySncNP3gNMAo5p\nwNijgf7AizHGihhjec3Ygak7RO2sRCLBQQN25aYLRjKwT2fmLCzh2nFTeenNpVR77aAkSSmT6iDY\nnuTp2VqbQwg5W9m2DugAFNV5fUuvbWtse2AWcFgIoW3NqeODgbaNdUBKnU5FrbnsKwM59wv9SSTg\n3knz+Pmf3qJkXXm6S5MkqUVK6TWCwFqSYa1WToyxqs629nW2tQdK6rynvObPkgaMXRNjjCGE/yPZ\nKVwMvAqsrK/Q4uKi+oaoiZz8+fYcOqQHv/zjDGa8s4Ix46Zy0Un7c+TQPbd67aDzl7mcu8zm/GU2\n50+pDoJTgBOBR0MIB5Ls1tWaBtwcQmgFFJI8pTu75j0nAPcBxwMvA9OBsdszNoTQBSiKMR4aQmgP\nPFMzdptWrFi380erRvXtkwbw0ptLeeT5d/nf38/ghen/4qxRgY7tWn9qXHFxkfOXoZy7zOb8ZTbn\nL3M1ZoBPpPIarDqrhmuv0TuXZHCbH2N8KoRwPnAxkCC5EnhCCKEryWDXjmQn77QY48YGjv0NMIRk\np/CqGOPkekqt9h9D87VyzUbumTSPuYtKaFuQx2nH9OPAfbt90h30h1nmcu4ym/OX2Zy/zFVcXNRo\nt9ZIaRDMIAbBZq6qupp/zPiAP77wHuUVlRywdxfOOi7QoV1rf5hlMOcuszl/mc35y1yNGQRTfWpY\nahQ5iQRHDtmDAb07c89f5zJj/kre+dcaTj+2Hyce1i7d5UmSlJF8sogySnHHQq78xgGcfkw/Kiqr\nuOsvc7j1vums3bAp3aVJkpRx7Agq4+QkEnx+6B7s33sXxk+cyyuzljHr3ZWccWw/RuzTLd3lSZKU\nMewIKmN17dSGH5w+hAtHD2BTRSW/eeJt7pwwm7WldgclSdoedgSV0XISCb50aB96d23HuL/O5bV5\nHxEXl3DmsYFh/bumuzxJkpo1O4JqEbrt0oYfnTaEU4/qS9mmSu6cMJvfPDGbdXYHJUnaKjuCajFy\nchIcO6IH+/fpzPi/zmXa3I+Yt6iEM4/rz9BQnO7yJElqduwIqsXZrXNbrjp9KF87si+l5ZX83+Oz\nuOsvb7N+Y0W6S5MkqVmxI6gWKScnwaiRPRjUtzPjJs7l1TnLmbuohLNGBQ7Y2+6gJElgR1At3G6d\n23LVGUP46hF92FBWwS//PIvfPTmHDWV2ByVJsiOoFi83J4fjD9yLgX27MH7iHF55+0PmLFrN2aP6\nM7hvl3SXJ0lS2tgRVNbo3qUtV585lFMO78360gruePQtxj01h1K7g5KkLGVHUFklNyeHEw7qyaC+\nXRg3cS5TZn/InEUlnD2qPwP7dE53eZIkNSk7gspKexS348dnDuWkQ3uxdsMmfv6nNxn/17mUlm1O\nd2mSJDUZg6CyVl5uDl/8XC/GnDOcHl3bMfmtZVw7biqz31+V7tIkSWoSBkFlvT27tuOas4cx+pBk\nd/D2P7zJvZPmsbHc7qAkqWUzCEoku4NfOqQX1549jD2K2/HSm0sZM24qby9cne7SJElKGYOgVEeP\nbkWMOWcYX/pcT0rWbeK2R2Zy/9N2ByVJLZNBUPqMvNwcRh/au6Y72JYXZy5lzLhpzLU7KElqYQyC\n0lbstWsR1549nBMP3ouSdeX89JGZPPBspGyT3UFJUstgEJS2IT8vh5MP68OPzxrK7l3a8sIbHzBm\n3DTi4pJ0lyZJ0k4zCErboddu7bnunOGccNBerFpbxk8ensFDf3uH8k2V6S5NkqQdZhCUtlN+Xg6n\nHN6HH585jN06t+Hvry/huvHTeOdfa9JdmiRJO8QgKDVQ793bc/25wzl+ZA9WfLyRnzz0Br9/bj7l\nFXYHJUmZxSAo7YD8vFy+emRfrj5jKN12acPfXvsX14+fxvwldgclSZnDICjthD7dO3D9ucM5bsSe\nfFSykf9+8A0e+ft8NtkdlCRlAIOgtJNa5efy9aP25kdnDKFrp0Kenf4vrrtnOu9+8HG6S5MkaZsM\nglIj2XuPjlx/3giOHb4nH60u5dYHX+ePL7xLxWa7g5Kk5skgKDWi1vm5nPr5vfnh6UMo7lDI01MX\nc/0903lvqd1BSVLzYxCUUqDfnh254bwRHD10D5atKuWWB17n0Rffo2JzVbpLkyTpEwZBKUVat8rl\ntGP68cPTDqBLhwL++uoibrh3Ou8vW5vu0iRJAgyCUsqFHp244bwRHDWkO0tXbmDs/a/z53/YHZQk\npZ9BUGoCBa3yOOPYwPe/cQC7tG/NxFcWceN901n04bp0lyZJymIGQakJ7bNXsjt4xAHd+WDFBm66\n7zUef2kBmyvtDkqSmp5BUGpiha3zOOu4wBWnDqZTUSue/OdCbrz3NRYvtzsoSWpaBkEpTfbruQs3\nnj+SwwfvzpIV67npvtd4YvL7dgclSU3GICilUWHrPM4e1Z/vfX0QHdq14onJ73PzfXYHJUlNwyAo\nNQMDenXmxvNGcujA3Vj8UbI7+JcpdgclSallEJSaiTYFeZz7hX347lcH0b5tKya8/D5j73+dJSvW\np7s0SVILZRCUmpmBfTpz0/kj+Nz+u7Jo+TpuuGc6T/1zIZVVdgclSY3LICg1Q20K8jn/hH257CsD\nadcmn8deWsDY+1/ng5Ub0l2aJKkFSVRXV6fsw0MICeBOYBBQBlwQY1xQZ/uFwEVABTA2xjgxhNAZ\neBgoAJYC58YYyxo49grgG0AlcGuMcUI9pVavWOHF+ZmquLiIljx/G8oq+P1z8/nn7A/Jy00w+tDe\nHDdiT3JzMv/3uJY+dy2d85fZnL/MVVxclGisz0r1/0lGA61jjAcDVwG3124IIXQDLgUOAkYBt4YQ\n8oExwEMxxsOBmcDFDRzbAfgOMBI4Dvh5io9RSqm2BflccOK+fOeUgbQtyOfRF9/jlgfeYKndQUnS\nTkp1EDwEeBogxjgVGFZn2whgcoxxc4xxLTCfZOfwk/cAk4BjGjD2aGADsBAoAtqR7ApKGW/w3l24\n6YKRHLhfN95ftpbr75nOpKmLqKpKXVdfktSypToItgc+rvP95hBCzla2rQM6kAxwH2/jtfrGAiwB\n5gCvAXfdMBvPAAAgAElEQVQ0xoFIzUG7wnwu+uJ+fPvk/WnTOpc/vfAetz70OstW2R2UJDVcXoo/\nfy3JsFYrJ8ZYVWdb+zrb2gMldd5TXvNnSQPGrgGOB3YF9gISwLMhhCkxxte2VWhxcdG2NquZy7b5\nO664iAMHdeeux2fx0swPuOGe6Zz5hX344qF9yM1ptEtHmkS2zV1L4/xlNudPqQ6CU4ATgUdDCAcC\ns+psmwbcHEJoBRQC/YHZNe85AbiPZKh7GZgOjN3OsSXAxhhjBUAIYQ3Qsb5CvWA2c2XzBc/njAoM\n6NmJB56NjPvL2/zjjSWc/4V96LZLm3SXtl2yee5aAucvszl/masxA3xTrRoeWPPSuSSD2/wY41Mh\nhPOBi0l27sbGGCeEELqSDHbtgJXAaTHGjQ0cez3JRSWVJK8t/GE9pbpqOIP5wwzWlm7ioWffYfq8\nj2iVl8Mph/fh88P2ICfRvLuDzl1mc/4ym/OXuRpz1XBKg2AGMQhmMH+Y/dv0eR/xwDOR9Rsr6LdH\nB849YR+6dWq+3UHnLrM5f5nN+ctcmXT7GElNaHj/rtx8wUiGhmLeWfIx142fxnOv/Ysqf+GTJG2B\nQVBqYdq3bcUlowdw8Zf2Iz83h4efm89PH57BR2s2prs0SVIzYxCUWqBEIsHIfbtx8wUjOWDvLsR/\nreG6cdN4/o0ldgclSZ8wCEotWId2rfn2yftz0Rf3JS83wYPPvsNtj8xkpd1BSRIGQanFSyQSHLjf\nrtx0wUgG9+3C3EUlXDt+Gi/O+AAXi0lSdjMISlmiY7vWXHrK/lxw4j7kJhLc/0zktj/MZOXHdgcl\nKVsZBKUskkgkOHjAbtx0wUgG9unMnIUljBk3jX/MtDsoSdnIIChloU5FrbnsKwM57wv7kEgkuO/p\nyP/+8U1Wry1Ld2mSpCZkEJSyVCKR4JCBu3HT+SMY0HsXZr+/mmvHTeWlN5faHZSkLGEQlLLcLu0L\nuPyrgzj3+P4A3DtpHv/7J7uDkpQNDIKSSCQSHDpod246fyT79dqF2QtWc+24aUx+a5ndQUlqwQyC\nkj6xS/sCvve1QZw9KlBdXc34v87lF4++Rcm68nSXJklKAYOgpE9JJBIcPrg7N54/gn326sRb763i\n2run8s/ZdgclqaUxCEraoi4dCrny1MGceVygsqqau5+ayy//PIs16+0OSlJLYRCUtFWJRIIjD0h2\nB/v36MjMd1dy7d1TeeXtD+0OSlILYBCUVK/ijoVc+Y0DOOPYflRUVvG7J+fwq8dm8fGGTekuTZK0\nE/LSXYCkzJCTSHDUkD0Y0Lsz90ycy4z5K5m/ZCqnH9OPEft0JZFIpLtESVID2RGU1CBdOxby/dMO\n4LSj92ZTRSW//cvb3DlhNmvtDkpSxrEjKKnBchIJjh62J/v36cz4iXN5Pa4gLl7DmccFhvfvmu7y\nJEnbyY6gpB3WrVMbfnj6EE79fLI7+OsJs5PdwVK7g5KUCewIStopOYkExw7fk0F9OjPur3N5bd5H\nzFtUYndQkjKAHUFJjaLbLm340WlDOPWovpTXdAd/bXdQkpo1O4KSGk1OToJjR/RgYN8ujJ84l+nz\nPmLe4hLOPDYwzO6gJDU7dgQlNbpdd2nDj04fwteP6kvZpkrunDCb3zwxm3V2ByWpWbEjKCklcnIS\nHDeiBwP7dGb8X+cybe5HzF1kd1CSmhM7gpJSarfObbnq9KF87Ui7g5LU3NgRlJRyOTkJRo3swaC+\nyfsOTpubXFn87a8Npu+uRekuT5Kylh1BSU1mt85tueqMZHewtLySW+6dzm//8jbrN1akuzRJykp2\nBCU1qbrdwfuffYepc5Yzd+FqzjyuP0NDcbrLk6SsYkdQUlrs1rktP/n2oXz1yD6Ullfyf4/P4i67\ng5LUpOwISkqb3JwEx4/ci0F9ujD+r3N5dc5y5iwq4ezjAgf0szsoSalmR1BS2u3epS1XnTGErx7R\nh9KyzfzysVnc9aTdQUlKNTuCkpqF3Jwcjj9wLwb17cK4iXN59e3lzFlod1CSUsmOoKRmZfcubbn6\nzCF85Yg+lJZV8MvHZvE7u4OSlBJ2BCU1O7k5OXyhpjs4fuIcXqntDo7qz+C9u6S7PElqMewISmq2\nundpy9VnDuWUw3uzoayCO/78Fr97cg4byuwOSlJjsCMoqVnLzcnhhIN6Mrjm2sFX3v6QOYtWJ7uD\nfe0OStLOsCMoKSN0L27Hj8+q6Q5urOCOR9/i7qfsDkrSzrAjKClj1HYHa1cW/3P2h8xZmOwODrI7\nKEkNZkdQUsbZo7gd15w1lJMP68260gp+8ehbjHtqDqV2ByWpQewISspIuTk5nHhwTwbvnewOTpn9\nIW8vXM05x/dnYB+7g5K0PewISspoexS348dnDuWkmu7gz//0FuMm2h2UpO2R0o5gCCEB3AkMAsqA\nC2KMC+psvxC4CKgAxsYYJ4YQOgMPAwXAUuDcGGPZ9o4FAvBzoBpIAAcCX44xPpvKY5WUPnm5OXzx\n4J4cUHPt4JRZH35y38GBfTqnuzxJarZS3REcDbSOMR4MXAXcXrshhNANuBQ4CBgF3BpCyAfGAA/F\nGA8HZgIXN2DsN2OMb8YYj4wxHgX8H/CoIVDKDnt0Ta4sPunQXqzdsImf/+lNxk+ca3dQkrYi1UHw\nEOBpgBjjVGBYnW0jgMkxxs0xxrXAfJKdw0/eA0wCjmnA2M/XfngIoQ1wA3BZag5NUnOUl5vDFz/X\nizHnDKdHt3ZMnrWMa8dN4633VqW7NElqdlIdBNsDH9f5fnMIIWcr29YBHYCiOq9v6bX6xtY6H/hj\njHH1zh+GpEyzZ9d2XHPWMEbX7Q7+dS6lZZvTXZokNRupXjW8lmRYq5UTY6yqs619nW3tgZI67ymv\n+bOkAWPX1BlzOnDK9hZaXFxU/yA1W85f5kr13J0/eiBHjdiLn/9+BpPfWsa8RSVc+rUDGNK/a0r3\nmy38t5fZnD+lOghOAU4EHg0hHAjMqrNtGnBzCKEVUAj0B2bXvOcE4D7geOBlYDowdjvHEkJoD7SK\nMX6wvYWuWLFux49SaVVcXOT8Zaimmrt2+Tn86PQD+Osri3jynwu57nevcOjA3fj6UXvTpsC7aO0o\n/+1lNucvczVmgE/1qeHHgfIQwhTgNuDyEMLlIYQTY4zLgTuAycBzwNUxxk3AWODUEMLLJFf8/qoh\nY2v22w9YmOJjk5RB8nJz+NIhvbj27GH06NqOl99axrXjpjJ7gdcOSspeierq6nTX0BxU+1tR5vK3\n2syVrrnbXFnFxFcW8dQ/F1JZVc1hg5LdwcLWdgcbwn97mc35y1zFxUWJxvosbygtKevk5ebw5Zru\n4J5d2/HSmzXdwfftDkrKLgZBSVmrR7cirj17GF/6XE8+Xr+J2//wJvdOmsfGclcWS8oOBkFJWS0v\nN4fRh/bmmrOGsUdxO156cyljxk3l7fe985Skls8gKEnAXrsWMeacZHdwzfpN3PaHmdz3tN1BSS2b\nQVCSany6O9iWf8ys6Q4utDsoqWUyCErSZyS7g8P54sE9KVm3idsemcn9dgcltUAGQUnagrzcHE46\nrDfXnp3sDr44cyljxk1jjt1BSS2IQVCStqG2O3jiwT0pWVfOzx6Zyf3PRLuDkloEg6Ak1SMvN4eT\nD+vNNWcPpXtxW16c8QFjxk1jrt1BSRlum0EwhDCuztdnf2bb5FQVJUnNUc9d2zPm7OGcePBelKwr\n56ePzOSBZyJlm+wOSspM9XUED6jz9WWf2da2kWuRpGYvPy+Hkw/rw4/PGkr3Lm15obY7uKgk3aVJ\nUoPVFwQTW/kawIcUS8pavXZrz5hzhnPCQXuxem05P/39DB541u6gpMxSXxCs3srXkpT18vNyOOXw\nZHdw9y5teeGNZHdwnt1BSRkir57trUIIe5IMjLVf13YGW6W0MknKEL12a8915wznL1Pe56+vLuJ/\nfj+Do4Z05ytH9KGgVX0/ZiUpfer7CdUOeKnO9y9tbaAkZbPa7uCQfsWMmziX59/4gLfeW8X5J+xD\n6NEp3eVJ0hYlqqt37IxvCCE3xljZyPWkS/WKFevSXYN2UHFxEc5fZmqpc1exuZInJi9k0tRFVFfD\n54fswVeO6EPrVrk09GduIvHZy7Obj5Y6f9nC+ctcxcVFjfaDYZsdwRBCIXAWsCrG+Gid178A/BTY\nr7EKkaSWIj8vl68cUdsdnMPf31jCWwtWMuTg9by88u9Ub+cl14V5Bfxg2KV0bVOc4oolZav6Tg3f\nB+wFdAghdAWeBH4HHAT8JMW1SVJG6717e64/dzgTJr/P01MX88obG9h7UB+qq6vqfe/H5Wv5aONK\nlqxfZhCUlDL1BcHhwN7ALsBE4AfA08CZMcYVKa5NkjJefl4uXz2iLyP36cbG8s3bfb3gq8te44G5\nf6Rsc1mKK5SUzeoLgmtijJuBj2pWDF8SY3ysCeqSpBalR7eiBo0vzCsEoHTzxlSUI0lAw+4juNwQ\nKElNozCvAMCOoKSUash9BHM/cx9BYoyLU1mcJGWr2iC40SAoKYV25j6C1UDvRq9IkmQQlNQkthkE\nY4w9m6gOSVIdBZ4altQE6ruP4FmfeakKKAH+GWP0YZqSlCKFuXYEJaVefaeGj/zM9wmgKzA+hPCN\nGOPzqSlLkrJbbk4urXLy2VhpEJSUOvWdGj53S6+HEPoD9wIHpqAmSRLJW8jYEZSUSvXdPmaLYozz\ngMJGrkWSVEdhXgEbvY+gpBTaoSAYQsgFchu5FklSHckgWEZ19fY9m1iSGqq+xSKHbeHljsBZJB81\nJ0lKkYK8Aqqqq6ioqqBVbqt0lyOpBapvscgNJO8XWHsT6SpgNfAc8LsU1iVJWa/uvQQNgpJSYZun\nhmOMRwL/C1xQ8/WvSF4buDt1njAiSWp83lRaUqptMwiGEK4AxgCtQwgDgQeBCSSfOPKz1JcnSdmr\nwCAoKcXqWyxyFnB4jHEOcBrwlxjj3cAVwHGpLk6SslmbvOTNGXy6iKRUqe8aweoYY2nN10cCdwLE\nGKtDCCktTJKyXW1HcHV5Ces2rU/5/lrntvJaRCnL1BcEN4cQOpI8FXwA8CxACGEvYHOKa5OkrFbb\nEXx43p95mD+nfH/5OXlcM/JKuhTukvJ9SWoe6guC/w3MrBl3d4xxWQjha8AtJFcUS5JSZN/OgYN2\nG94kp4Y/2riSD9YvY3npRwZBKYvU94i5R0MI/wS6xBjfqnl5PclVxC+mujhJymbt8ttyxj5fbZJ9\nvfzBKzwSH2djhU8ykbJJfR1BYoxLgaV1vv9rSiuSJDW5wtyaFcqVLkyRsskOPWJOktSyeKsaKTsZ\nBCVJFNYsTDEIStnFIChJ+uQpJt6zUMou9V4juDNCCAmS9x4cBJSRXGSyoM72C4GLgApgbIxxYgih\nM/AwUEDy2sRzY4xlDRx7PMknogC8HmP8diqPU5IynY+zk7JTqjuCo4HWMcaDgauA22s3hBC6AZcC\nBwGjgFtDCPkkA9xDMcbDSd665uIGjm0H/A9wQozxIGBhTWCUJG2F1whK2SnVQfAQ4GmAGONUYFid\nbSOAyTHGzTHGtcB8kp3DT94DTAKOaeDYg4FZwO0hhJeA5THGVak7REnKfK1zW5EgwcbN3j5GyiYp\nPTUMtAc+rvP95hBCToyxagvb1gEdgKI6r2/ptW2NbQ90AY4gGRRLgZdDCK/EGN/dVqHFxUUNPTY1\nI85f5nLumo/C/AIqqGjQnDh/mc35U6qD4FqSYa1WbQis3da+zrb2QEmd95TX/FnSgLFrgJXA9Bjj\nCoCaruBgYJtBcMWKdQ0/OjULxcVFzl+Gcu6al9Y5rVlXtmG758T5y2zOX+ZqzACf6lPDU4AvAIQQ\nDiR5yrbWNOCQEEKrEEIHoD8wu+Y9J9SMOR54GZjegLEzgAEhhF1CCHnAgcCc1B2iJLUMhXkFlHlD\naSmrpDoIPg6UhxCmALcBl4cQLg8hnBhjXA7cAUwGngOujjFuAsYCp4YQXiYZ4n7VwLErSC5MeRZ4\nBXg0xmgQlKR6FOYVUra5nKrqqvoHS2oREtXV1emuoTmotj2euTy9kbmcu+bl12/ew+xVc/nZYTd+\ncjuZbXH+Mpvzl7mKi4sSjfVZ3lBakgR4U2kpGxkEJUnAv4NgqbeQkbKGQVCSBHhTaSkbpfr2MZKk\nDFHbEVy24UPa5repd3x5q/Ws3rBhp/ZZkNuaTgUdd+ozJO04g6AkCYC2ecnw90h8vEn3e+XQ/6JX\nh72adJ+SkgyCkiQABnUdwEcbV1JeuWm7xhcW5LOxrGKH97e8dAXvlLzLR6UrDYJSmhgEJUkAtMtv\ny0l9T6h/YI2dvf3IGx+9xTsl73pNopRGLhaRJKVFoYtTpLQzCEqS0uKTIFjp7WqkdDEISpLSojDX\nG1hL6WYQlCSlRUFeIeCpYSmdDIKSpLTwGkEp/QyCkqS0yM/JIzeRaxCU0sggKElKi0QiQWFegUFQ\nSiODoCQpbQrzCijb7KphKV0MgpKktLEjKKWXQVCSlDYFeYVsqqqgsqoy3aVIWckgKElKm3/fVNqu\noJQOBkFJUtp4U2kpvQyCkqS0qe0IlrpgREoLg6AkKW0K8uwISulkEJQkpY1PF5HSKy/dBUiSsldt\nEFy0dglt8tqkfH9t89uwe7tdU74fKVMYBCVJadMuvy0Azyx6nmcWPd8k+/zhsO/Qo/0eTbIvqbkz\nCEqS0mafXfpxct8T2dgEi0UWrVvCnFWRlWWrDYJSDYOgJClt8nPz+XyPw5pkX68ue405q6ILU6Q6\nXCwiScoKLkyR/pNBUJKUFQyC0n8yCEqSskJhXiHgPQulugyCkqSs4FNMpP9kEJQkZQWfYiL9J4Og\nJCkrFOZ6jaD0WQZBSVJWyM3JpVVOPhsrDYJSLYOgJClrFOYV2BGU6jAISpKyRkFeodcISnUYBCVJ\nWaO2I1hdXZ3uUqRmwSAoScoahXkFVFZXUlFVke5SpGbBIChJyho+XUT6NIOgJClrGASlTzMISpKy\nRoFBUPoUg6AkKWsU5vq8YamuvFR+eAghAdwJDALKgAtijAvqbL8QuAioAMbGGCeGEDoDDwMFwFLg\n3BhjWQPH/hz4HLCuZldfjjHWfi1JylK1p4bnlrxDeWV5k+yzdV5rQqe+5CTsvaj5SWkQBEYDrWOM\nB4cQRgK317xGCKEbcCkwBGgDTA4hPAuMAR6KMd4fQvghcHEI4ZHtHQv8AhgKHBdjXJ3i45MkZZD2\nrYsA+Pvil/h7E+73mwPPYf8u+zbhHqXtk+ogeAjwNECMcWoIYVidbSOAyTHGzcDaEMJ8kp3DQ4Cx\nNWMmAbcAC7Zz7NgQwh3A3sBdIYRdgXExxntSeZCSpMywf5d9OaP/Vylrom7gv9Z9wNQPX2dN+cdN\nsj+poVIdBNsDdf/r3xxCyIkxVm1h2zqgA1BU5/UtvVbf2DbAHSS7j3nACyGE6THG2Y14XJKkDJSf\nk8dBuw9vsv3NXjmXqR++7uIUNVupDoJrSYa1WrUhsHZb+zrb2gMldd5TXvNnSQPGrgFKgTtijGUA\nIYTnSXYPtxkEi4uLtrVZzZzzl7mcu8zm/G3bbuwCQKJVVbP8u2qONalppToITgFOBB4NIRwIzKqz\nbRpwcwihFVAI9CcZ1qYAJwD3AccDLwPTSZ723Z6xAfhDCGFwzfEdAtxbX6ErVriWJFMVFxc5fxnK\nuctszl/9ytcnH2W3eu3aZvd35fxlrsYM8KlewvQ4UB5CmALcBlweQrg8hHBijHE5yVO4k4HngKtj\njJtIXvN3agjhZeBA4FcNHDsPuB+YCrwA3BdjnJvi45Qk6T/UrlIu3bwxzZVIW5bwwdsAVPtbUeby\nt9rM5dxlNuevfhs3l3HlS2MY0Lk/3xp0XrrL+RTnL3MVFxclGuuzvKmRJEkp0jq3FQkSLhZRs2UQ\nlCQpRXISORTktTYIqtkyCEqSlEIFuQUGQTVbBkFJklKoMK+AskqDoJong6AkSSlUmFdI2eZyqqqr\n6h8sNTGDoCRJKVSYV0A11ZQ30WPtpIYwCEqSlEK19xL0OkE1RwZBSZJSyCCo5swgKElSChUYBNWM\nGQQlSUqh2o5gmUFQzZBBUJKkFPLUsJqzvHQXIElSS1aYVwjA26vmNcnK4cK8Qg7ouj85CXs9qp9B\nUJKkFOrYugMA05fPYPryGU2yz2/nXcA+nfs1yb6U2QyCkiSlUO8Oe3HJoPMprShN+b7mr1nAlKVT\nWbtpXcr3pZbBIChJUgrlJHLYr3Nokn3l5uQyZelUr0fUdvMCAkmSWoh/L0zZmOZKlCkMgpIktRCu\nUFZDGQQlSWohCnMNgmoYg6AkSS1EQc2tajZWGgS1fQyCkiS1ED7FRA1lEJQkqYXIz8kjN5HrqWFt\nN4OgJEktRCKRoDCvwCCo7WYQlCSpBUkGQW8fo+1jEJQkqQWxI6iGMAhKktSCFOQVUlFVQWVVZbpL\nUQYwCEqS1IJ4U2k1hEFQkqQWxJtKqyEMgpIktSCfdAQrXTCi+hkEJUlqQQq8qbQawCAoSVIL0sZr\nBNUAeekuQJIkNZ7a5w1P/3AGyzYs3+q4titas2FDeaPss3Vuaw7efQStc1s1yuep6RgEJUlqQXYp\n6AjAjBWzmLFiVpPtt01eISN3G9pk+1PjMAhKktSChE59+f6wb9d7arhjhzas+bh0p/e38OPFPPX+\ns6yv2LDTn6WmZxCUJKkFSSQS9Gzfo95xxcVFrMhdt9P7y03kAvhYuwzlYhFJkrTDvIF1ZjMISpKk\nHWYQzGwGQUmStMO8b2FmMwhKkqQd5iPtMptBUJIk7bDcnFxa5eSzsdIgmIkMgpIkaacU5hXaEcxQ\nBkFJkrRTCvMKvH1MhjIISpKknZIMgmVUV1enuxQ1UEpvKB1CSAB3AoOAMuCCGOOCOtsvBC4CKoCx\nMcaJIYTOwMNAAbAUODfGWNaQsXX2PRGYEGO8K5XHKUlSNivIK6CquoqKqgpa+bzhjJLqjuBooHWM\n8WDgKuD22g0hhG7ApcBBwCjg1hBCPjAGeCjGeDgwE7i4AWO/WWffNwMdU3x8kiRlPe8lmLlSHQQP\nAZ4GiDFOBYbV2TYCmBxj3BxjXAvMJ9k5/OQ9wCTgmAaM/TxACOEUoLLONkmSlCIGwcyV6iDYHvi4\nzvebQwg5W9m2DugAFNV5fUuvbXNsCGE/4DTgOiDRaEciSZK2qMAgmLFSeo0gsJZkWKuVE2OsqrOt\nfZ1t7YGSOu8pr/mzpAFjPwbOBHYHngd6AuUhhIUxxme3VWhxcdG2NquZc/4yl3OX2Zy/zNZY81e8\nInklVut2Cf+byDCpDoJTgBOBR0MIBwKz6mybBtwcQmgFFAL9gdk17zkBuA84HngZmA6M3Y6xL8UY\nf1q7gxDCdcCy+kIgwIoV63buSJU2xcVFzl+Gcu4ym/OX2Rpz/irLkyfglq1cze65/jeRao0ZtlN9\navhxkh25KcBtwOUhhMtDCCfGGJcDdwCTgeeAq2OMm4CxwKkhhJeBA4FfNWRsio9HkiR9Ru1j5nze\ncOZJeM8fAKr9rTZz2ZXIXM5dZnP+Mltjzt9bK97mt7Puo2/HXuxZ1L1RPnNbCnILOLrH4RTktU75\nvpqj4uKiRlsDkepTw5IkqYUrbtMFgHfXvM+7a95vkn3u1rYbQ7sNapJ9tWQGQUmStFN2a9uNGw+6\nitLNpSnf19xV7/DEgklsqEj9vrKBQVCSJO20zoWd6EynlO/n4/K1gNcjNhafNSxJkjJGYV4hABsr\nDYKNwSAoSZIyhk8xaVwGQUmSlDH+HQQ3prmSlsEgKEmSMkbt4+y8RrBxGAQlSVLGaJ3bigQJTw03\nEoOgJEnKGDmJHAryCgyCjcQgKEmSMkqhQbDRGAQlSVJGKcwroMzbx/x/e3cfZFd913H8vdlN9m5g\nN2HSbQx0aplavq06xk4qAxgbRTAt0ClaOypTpmBT0tZhLI4dSa3gQynGUka01ocihY5QZ3xALA9R\nKwJJmrbYFkvA+RalmZSiBkJooiQh2V3/OGezt5kky7295+7ee96vmUxyz/mdnN/Jd27OZ3/n4dcR\nBkFJktRTGoMNDhw+yOTU5Fx3pecZBCVJUk8ZGWowxRQHJw7OdVd6nkFQkiT1FF8q3TkGQUmS1FOO\nTDNnEPyuGQQlSVJPcUSwcwyCkiSpp4w4u0jHGAQlSVJPaTgi2DFDc90BSZKkVkyPCD7w1FYe251d\n2eeiwYVcePr5LBke68r+usUgKEmSesqKk5azYGABO/buZMfenV3b72knr2DNK87p2v66wSAoSZJ6\nymknr2Dj6ms4OPFiV/b3n89/g089/hleOLS/K/vrJoOgJEnqOYsXLmbxwsVd2dfLFi8DYP9E/wVB\nHxaRJEk6gZHB/n1K2SAoSZJ0Ao0+foG1QVCSJOkE+vkF1gZBSZKkE1i4YIihgUGDoCRJUt0MDAzQ\nGGoYBCVJkupoZKjBgcM+NSxJklQ7I44ISpIk1VNjaIQXJw8xMTkx113pKIOgJEnSLI48OTzRX6OC\nBkFJkqRZ9OtLpQ2CkiRJsxhZ2J/vEjQISpIkzWJ6RHB/nz05bBCUJEmaRb/OLmIQlCRJmkW/zjds\nEJQkSZpFv44IDs11ByRJkua76SD40FOf5/HdWfn+hgcX8fYz3sqS4bFK92MQlCRJmsX3nPRyRoYa\n7Nr/LLv2P9uVfX7/suCcU8+sdB8GQUmSpFksHV7CxtXXMjE1Wfm+Hn32cW557PauXIY2CEqSJL0E\ngwsGGWSw8v2MLjoJ6M79iJUGwYgYAD4BrAQOAOsy88mm9e8GrgAOAddl5j0RsQy4A2gATwOXZ+aB\nFtv+EvBOYBL4WGb+VZXHKUmS1CmNoe7NYlL1U8MXA8OZeQ6wAbhxekVELAeuBM4G3gRcHxELgWuA\n2zNzDfAIsL7FtsuA9cBZwHnAxyo+RkmSpI5Z3MVX1VQdBFcDmwAy84vAG5rWnQlsyczDmbkXeIJi\n5BepD/4AAAmQSURBVPDINsB9wPkttD0vM3cDP5yZk8AKoL9eAS5JkvpaY6h7s5hUHQTHgG83fT4c\nEQuOs24fsAQYbVp+rGWztSUzJ8vLw58H/qJTByNJklS1mensevweQWAvRVibtqAcqZte1/xynDFg\nT9M2B8vf97TQ9vnpBpn5RxHxp8CmiHgoMx88UUfHx0dPtFrznPXrXdaut1m/3mb95q/hwUUcGnix\n8hpVHQS3AhcBfx0RZwGPNq37EvDhiFgEjACvBbaX21wI3Aa8GdgMPAxc91LaRsQZwPWZ+TZggiIk\nzvqs9zPP7PuuD1ZzY3x81Pr1KGvX26xfb7N+81tjcJh9B144Zo06GQ6rvjR8J3AwIrZSPLRxVURc\nFREXZeb/AH8AbAE+B3wwM18ErgN+PiI2Uzzw8fEW234deCQitpXtt2Xm5oqPU5IkqWMaQyNdeWp4\nYGpqqvKd9IApfyrqXf5U27usXW+zfr3N+s1vH/3Xj/PNfd/iph//CAMDA9+xbnx8dOA4m7Ws6hFB\nSZIktWhkqMHE1ASHJg9Xuh+DoCRJ0jwz0qVXyBgEJUmS5pmZIFjtfYIGQUmSpHmmYRCUJEmqp5HB\nYpq5qp8cNghKkiTNM0cuDU8YBCVJkmqlWw+LVD2ziCRJklo0fY/gvd/4HFu+9YXvWHfDBR/q2H4M\ngpIkSfPMK0dP45Thpfzf4Rd4ocJRQYOgJEnSPHNKYykf/tEPVr4f7xGUJEmqKYOgJElSTRkEJUmS\nasogKEmSVFMGQUmSpJoyCEqSJNWUQVCSJKmmDIKSJEk1ZRCUJEmqKYOgJElSTRkEJUmSasogKEmS\nVFMGQUmSpJoyCEqSJNWUQVCSJKmmDIKSJEk1ZRCUJEmqKYOgJElSTRkEJUmSasogKEmSVFMGQUmS\npJoyCEqSJNWUQVCSJKmmDIKSJEk1ZRCUJEmqKYOgJElSTRkEJUmSasogKEmSVFMGQUmSpJoyCEqS\nJNWUQVCSJKmmDIKSJEk1NVTlXx4RA8AngJXAAWBdZj7ZtP7dwBXAIeC6zLwnIpYBdwAN4Gng8sw8\n0GLbq4CfA6aAezPzd6o8TkmSpF5U9YjgxcBwZp4DbABunF4REcuBK4GzgTcB10fEQuAa4PbMXAM8\nAqxvse3pwC9k5lmZeTawNiJ+sOLjlCRJ6jlVB8HVwCaAzPwi8IamdWcCWzLzcGbuBZ6gGDk8sg1w\nH3B+C23PA3ZShMVpCylGIyVJktSk6iA4Bny76fPhiFhwnHX7gCXAaNPyYy07YdvMnMjM5wAi4qPA\nVzLzPzp2RJIkSX2i0nsEgb0UYW3agsycbFo31rRuDNjTtM3B8vc9LbR9HiAihoFbKELi+15CPwfG\nx0dnb6V5y/r1LmvX26xfb7N+qnpEcCtwAUBEnAU82rTuS8DqiFgUEUuA1wLby20uLNu8GdgMPNxC\nW4C/Bx7JzPdl5lRVBydJktTLBqamqstJTU8N/1C56HKK4PZEZt4dEe8C1gMDFE8C/11EvBy4DTgZ\neBa4JDP3v9S2wFqKJ4m/ULadAjaU9yhKkiSpVGkQlCRJ0vzlC6UlSZJqyiAoSZJUUwZBSZKkmjII\nSpIk1VTV7xGcE+VLqz8JBDAJvBf4ELCc4kniVwHbMvOSo7Z7Cvh6+XFbZv56RLwfWAfsKpevz8wn\nKj+IGmunfuU2NwKrgGHgNzPz3vK1Rb9PMUf1P2Xmb3fxUGqnw7W7GLiBYrYggGszc/oVUapAm/X7\nNYrZnKaAU4DlmXlqRLwF+A2K796nMvPmLh5KLXW4fp77uqjN2o0Bf0nx5pQDwDsyc1er572+DILA\nW4CpzFwdEWsoXjdzMUBELAXuB97fvEFEvBr4cma+9ai/axVwaWZ+tQv9VqHl+gGXAkOZ+WMRcSrw\ns+XyPwZ+OjN3RMQ9EbEyM/+tS8dRR52s3SrgA5l5Z5f6rjbql5kbgY1lm88CvxoRQ8yE+/3A1oi4\nKzOf6d6h1FJH6leu8tzXXe3833kZ8LXMvDoi1gEfKH+1dN7ry0vDmXkXcEX58VUUs5BM+y3gDzNz\n11GbrQJeERH3R8TdEfGapuUbImJzRFxdZb9VaLN+a4GnI+Ju4M+Az0bEKLAoM3eUbf6BYj5qVaRT\ntSuXrwJ+MSIeiogbmqanVEXarB8AEfEzwHOZ+c/A6yjeF7s3Mw8BW4A3VtZxAR2tH3ju66o2a/co\nM7OujQGH2jnv9e1/rJk5GRG3AjcBtwNExDhwLnDrMTZ5GvhIZp4LXD+9DfAZ4D3AT1DMbnJBtT0X\ntFW/lwGvzsyLgN8r24xRTEM4bXqOalWoQ7UD+Efgysx8I8Wlj/dU2nEBbdVv2tUUJyw4/lzyqliH\n6gee+7qujdrtBn4qIh6jGMn9c9o47/VtEATIzMuAM4CbI2KE4pLTHceZdu7LFFPTkZlbgRXl8psy\n87nMPAzcA7y+8o4LaLl+u4G7y+0eAl5DcSJqnqP6yHzUqlYHagfFfWU7yj/fhd+9rmmxfkTE64A9\nmflkuejo+eH97nVRB+oHnvvmRIu1uxbYmJk/QHFl5W9p47vXl0EwIt7RNJR9AJiguPnyPOC+42x2\nLeX194hYCXyzvBFze0QsLqfLO5ciMKpCbdZvCzPzWq8Edmbm/wIHI+L0sn5rmZmPWhXoVO3K5V8r\n7xkE+En87lWuzfpxjPX/DnxfRCyNiEUUl4W3VdBlNelU/Tz3dV+btXuOmZH3Z4DRzNxHi+e9vgyC\nFKn49RHxIMU/4C9n5kGKlN38Ew8Rsam8sfl3gTUR8QDFk4qXZeZeYAPwAPAgsD0zN3XtKOqrnfp9\nElgQEduAP2HmMuJ7mZl7+iuZ+XCXjqGuOlm7dwF3RsS/ACNlO1Wrnfpx9PpyFOlXKC7vbwVuzsz/\n6kL/665T9fPc133t1O4a4J3lNn9D8ZQ3tHjec65hSZKkmurXEUFJkiTNwiAoSZJUUwZBSZKkmjII\nSpIk1ZRBUJIkqaYMgpIkSTVlEJQkSaopg6AkSVJNGQQlqcMi4tMRsa7p8/0R8SNz2SdJOhaDoCR1\n3i3ApQAR8b3AuNMbSpqPDIKS1GGZ+QCwIiJeSREIPz23PZKkYxuavYkkqQ23AZcAbwfWznFfJOmY\nDIKSVI3bgC3A9sz877nujCQdi5eGJakCmfkUsBO4dY67IknHZRCUpApExKnAcuCuue6LJB2PQVCS\nOiwi3gZ8Fbg6Mw/NdX8k6XgGpqam5roPkiRJmgOOCEqSJNWUQVCSJKmmDIKSJEk1ZRCUJEmqKYOg\nJElSTf0/qARHO+schREAAAAASUVORK5CYII=\n",
"text/plain": "<matplotlib.figure.Figure at 0x7fb4b219cad0>"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "# Conclusions and $\\tau$ ranges\n\nThe direct $\\Phi_1$ computation and numeric quadrature appear to do best in terms of accuracy and speed. \n\nAll of the above was computed for only $\\tau=1$, and upon changing this value, some other distinctions between methods begin to appear. In general, the results aren't good for different values of $\\tau$; however, it's possible that the Gordy forms of $\\Phi_1$ would work better.\n\nWe briefly illustrate the effect of varying $\\tau$ below."
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "y_range_tau = pd.Series(np.linspace(-50, 50, 50), name='y')",
"execution_count": 63,
"outputs": []
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "from timeit import default_timer as timer\nE_Z_funcs = [E_Z_hs_num_single, E_Z_hs_trunc_single, E_Z_hs_quad_single]\nSURE_tau_vals = []\n\n# tau < 0.71 is unbearably long and then fails! WTF!\nfor tau in [0.71, 0.8, 1.5, 2.5, 5.]:\n for E_Z_func in E_Z_funcs:\n start = timer()\n SURE_tau_val = SURE_hs(y_range_tau, E_Z_func, tau=tau)\n end = timer()\n print(\"tau={}, {}: {} secs\".format(tau, \n E_Z_func.__name__, \n end-start))\n SURE_tau_val = pd.DataFrame(np.asarray(SURE_tau_val).T, \n index=y_range_tau,\n columns=['SURE', 'precision'])\n SURE_tau_val['type'] = E_Z_func.__name__.split('_')[-2]\n SURE_tau_val['tau'] = tau\n SURE_tau_vals += [SURE_tau_val]",
"execution_count": 64,
"outputs": [
{
"output_type": "stream",
"text": "tau=0.71, E_Z_hs_num_single: 21.9975869656 secs\ntau=0.71, E_Z_hs_trunc_single: 26.5072388649 secs\ntau=0.71, E_Z_hs_quad_single: 6.83068990707 secs\ntau=0.8, E_Z_hs_num_single: 20.6433160305 secs\ntau=0.8, E_Z_hs_trunc_single: 16.3297638893 secs\ntau=0.8, E_Z_hs_quad_single: 7.2850060463 secs\ntau=1.5, E_Z_hs_num_single: 21.7059290409 secs\ntau=1.5, E_Z_hs_trunc_single: 16.9456689358 secs\ntau=1.5, E_Z_hs_quad_single: 6.82405281067 secs\ntau=2.5, E_Z_hs_num_single: 21.0273001194 secs\ntau=2.5, E_Z_hs_trunc_single: 16.8646509647 secs\ntau=2.5, E_Z_hs_quad_single: 7.07303714752 secs\ntau=5.0, E_Z_hs_num_single: 22.6930098534 secs\ntau=5.0, E_Z_hs_trunc_single: 20.5155849457 secs\ntau=5.0, E_Z_hs_quad_single: 6.81652402878 secs\n",
"name": "stdout"
}
]
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "SURE_tau_vals = pd.concat(SURE_tau_vals)\nSURE_tau_vals['precision'] = SURE_tau_vals['precision'].astype(\"category\")\nSURE_tau_vals['type'] = SURE_tau_vals['type'].astype(\"category\")\nSURE_tau_vals['tau'] = SURE_tau_vals['tau'].astype(\"category\")\nSURE_tau_vals['SURE'] = SURE_tau_vals['SURE'].astype(np.float)",
"execution_count": 65,
"outputs": []
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "def pdplot(*args, **kwargs):\n data = kwargs.pop('data')\n ax = plt.gca()\n pdata = data.pivot_table(index=data.index, \n columns='precision', \n values='SURE')\n if not pdata.empty:\n dplt = pdata.plot(ax=ax)\n\n#%pdb\ng = sns.FacetGrid(SURE_tau_vals, col=\"type\", row=\"tau\", sharey='row')\ngp = g.map_dataframe(pdplot, 'y', 'SURE')\nplt.subplots_adjust(top=0.9)\ngp.add_legend()\ngp.fig.tight_layout()",
"execution_count": 67,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "<seaborn.axisgrid.FacetGrid at 0x7fb4b1038f10>"
},
"metadata": {},
"execution_count": 67
},
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAt4AAAQyCAYAAACfwvicAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n2HhLkiRJDbDxliRJkhpg4y1JkiQ14P8BQVMtztdS+OEAAAAASUVORK5CYII=\n",
"text/plain": "<matplotlib.figure.Figure at 0x7fb4b0ecad50>"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Numeric quadrature is the clear winner here; it roughly maintains the same computation time and $y$ range across all these $\\tau$ values. Still, it takes too long and fails at the basic finite precision range (which appears to be $|y| \\approx 36$). Plus, we have to consider actual accuracy, which can't really be assessed with this experiment."
}
],
"metadata": {
"kernelspec": {
"name": "python2",
"display_name": "Python 2",
"language": "python"
},
"language_info": {
"mimetype": "text/x-python",
"nbconvert_exporter": "python",
"name": "python",
"pygments_lexer": "ipython2",
"version": "2.7.12",
"file_extension": ".py",
"codemirror_mode": {
"version": 2,
"name": "ipython"
}
},
"gist_id": "d506bc96347201107f564cb6afc81aa6"
},
"nbformat": 4,
"nbformat_minor": 0
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment