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@jgomezdans
Forked from anonymous/NDVI_smoothing.ipynb
Created February 21, 2013 18:37
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{
"metadata": {
"name": "NDVI_smoothing"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np\n",
"%pylab inline\n",
"plt.rcParams['figure.dpi'] = 2*plt.rcParams['figure.dpi']\n",
"plt.rcParams['savefig.dpi'] = 2 * plt.rcParams['savefig.dpi']"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n",
"For more information, type 'help(pylab)'.\n"
]
}
],
"prompt_number": 115
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Experiments smoothing univariate time series"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"J G\u00f3mez-Dans (NCEO & UCL)\n",
"j.gomez-dans@ucl.ac.uk"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"The fundamental problem"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The fundamental problem we are trying to solve with EO-LDAS (and indeed most other inversion approaches) is to *infer the state of the land surface, given all available observations, as well as any other relevant information*. This leads quite naturally to Bayes' Rule, that states\n",
"\n",
"$$\n",
"p(\\theta|y) \\propto p(\\theta)\\cdot p(y|\\theta)\n",
"$$\n",
"\n",
"In other words, the *distribution* of $\\theta$ (the variable of interest) **conditioned** by $y$ (the observations or evidence) is proportional to the product of whatever information we might have had of $\\theta$ to start with (from previous experiments, expert knowledge, etc.) times the probability of the observations given the true parameters (the likelihood function)."
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Defining the prior"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The prior distribution is an assessment of what we know before we even start the experiments. Typically, it can include realistic parameter boundaries (for example, weight cannot be less than 0!), typical values, etc. A common approach is to use a Gaussian distribution, controlled by two parameters: the mean($\\mu_p$) and the standard deviation ($\\sigma_p$). $\\mu_p$ controls the typical location of the magnitude, whereas $\\sigma_p$ informs us of how certain/uncertain we are about it. A Gaussian pdf is\n",
"$$\n",
"p(x) = \\frac{1}{\\sqrt{2\\pi}\\sigma_P}\\exp\\left[-\\frac{1}{2}\\frac{(x-\\mu_p)^2}{\\sigma_p^2}\\right]\n",
"$$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def gauss ( x, mu, sigma ):\n",
" c1 = 1./(np.sqrt ( 2.*np.pi)*sigma)\n",
" c2 = -0.5*( x - mu )**2/sigma**2\n",
" return c1*np.exp(c2)\n",
"x = np.arange(-10,10,0.02)\n",
"plt.plot ( x, gauss(x,0, 1), '-r', label=r'$\\sigma=1$')\n",
"plt.plot ( x, gauss(x,0, 2), '-g', label=r'$\\sigma=2$')\n",
"plt.plot ( x, gauss(x,0, 10), '-b', label=r'$\\sigma=10$')\n",
"plt.plot ( x, gauss(x,0, 0.5), '-k', label=r'$\\sigma=0.5$')\n",
"plt.plot ( x, gauss(x,0, 0.025), '-y', label=r'$\\sigma=0.025$')\n",
"plt.ylim(0,2)\n",
"plt.legend(loc='best')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 116,
"text": [
"<matplotlib.legend.Legend at 0x2af331f3a4d0>"
]
},
{
"output_type": "display_data",
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33HKLRo4cqRdffFE//vijl6r0bwR1AAAASJLKysq0a9cuzZ8/X4MGDVJubq5KSkoqPf/b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\nTkSuQmCC\n"
}
],
"prompt_number": 116
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"x = np.arange(-10,10,0.02)\n",
"plt.plot ( x, gauss(x,-5, 1), '-r', label=r'$\\sigma=1\\;\\mu=-5$')\n",
"plt.plot ( x, gauss(x,0, 2), '-g', label=r'$\\sigma=2\\;\\mu=2$')\n",
"plt.plot ( x, gauss(x,3, 10), '-b', label=r'$\\sigma=10\\;\\mu=10$')\n",
"plt.ylim(0,0.5)\n",
"plt.legend(loc='best')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 117,
"text": [
"<matplotlib.legend.Legend at 0x15f17d90>"
]
},
{
"output_type": "display_data",
"png": 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GOhITE2ulruuvv95hs9kcn3766VmPf/bZZw673e4YPHiww+FwOGbMmOGYM2dO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\nsmMKZsVMTZ+aTOk6hb4N+9r364sQZSRBvQxsMagXNepIwdbt260reNv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JSm7x4sWMHj2a\nDh06UKVKFfR6PYMHD77jfQ4fPszAgQOpV68eAQEBdOvWrURZtCTs+oJH6enpvPrqq+h0OoKCgggJ\nCeHs2bPFXlRm8uTJvPXWW4SEhNC7d28yMzP5/fffWbFiBXPmzGHQoEFW+gmEI2vevDl9+vS5ZX2T\nJk00qEY4ktjYWCIiIjh+/DidO3emY8eOREVF8eGHH7JlyxZWrFiBr6+v1mUKB+br68srr7xyy3ov\nLy8NqhGO5L333uPgwYN4e3tTvXp1oqOj75grN2zYwOOPP47JZKJ79+5Uq1aN1atX8/zzz7Nv3z4+\n//xzywpS7FhOTo6yZs0aJT4+XlEURZk0aZKi0+mUOXPm3PY+//zzj6LT6ZSwsDDl/Pnz+esPHjyo\n+Pr6Kt7e3kpqamqF1y4c1+nTpxWdTqcMHTpU61KEgxo0aJCi0+mU9957r9D65557TtHpdMrbb7+t\nUWVCKEpYWJhSq1YtrcsQDmrTpk3KyZMnFUVRlM2bNys6nU4ZPHhwkfsajUYlLCxMcXV1VTZu3Ji/\n/urVq0qLFi0UnU6n/PHHHxbVY9ddX5ydnenWrRtBQUElvs+0adMAeP3117nrrrvy1zdt2pShQ4eS\nnp7ON998U+61CiGELbhw4QKLFi2iWrVqjBs3rtC2jz/+GCcnJ2bOnElWlly+XAjheDp27EidOnWA\n4i+kuXTpUuLi4ujVqxedOnXKX+/t7U1kZCQAU6dOtageuw7qZbFu3Tp0Ol2RXQ4ee+wxANavX2/t\nsoQDOn/+PLNmzeLjjz9m0aJFREdHa12ScACbNm3CaDTSq1evW77O9ff3p3379iQlJbFv3z6NKhQC\nsrKy+PHHH/noo4/47rvv2Llzp9YlCXGLdevWARSZKSMiInBzc2PDhg0WPYZd91Evi/Pnz2MwGKhe\nvfot22rWrAnAuXPnrF2WcEDr16+/5UNhv379mDp1aqFve4QoT3mvb+Hh4UVuDwsLA9TXSiG0oNPp\niI+P55lnnim0vmXLlnzxxRe0adNGo8qEKOxOr6cuLi4EBQURFxdHUlISAQEBZXoMh2pRv3LlCllZ\nWfj7+xe5PTAwEJCgLiqWp6cnEydOZO/evaSkpHDixAk+/PBDmjdvzi+//MJjjz2G0WjUukxRSeUF\n8Nu9acjroNDa0KFD2bhxIwkJCSQlJTF79my6d+/O3r17iYiIIC4uTusShQDU11OdTnfH11NFUSx6\nPdU8qN9pGKaipuKGyBHCGix53gYGBhIZGUnz5s2pUqUKderU4c0332Tr1q34+PiwZ88e5s2bp+FP\nJ4QQ2pk4cSIdO3YkMDAQf39/hg0bxqpVq+jcuTOpqam89dZbWpcohNVo3vWlbt26eHh4lHj/0NDQ\nMj+Wv78/bm5uXLlypcjtly5dAiiyW4wQBVXE89bT05MhQ4YwY8YM9uzZw/PPP29JiUIUKe+5mJSU\nVOR2eR0Utuqll15i48aN7NmzR+tShADU19PDhw/f8fVUp9NZ9HqqeVC3tJN9aYWGhnLq1CnOnj1L\njRo1Cm2LjY0F5A1KFK+inrf33HMPcCMsCVHe8l73Tp8+XeR2eR0UtkpeH4WtyXudPH36NO3bty+0\nLTs7m4SEBFxcXMrcPx1soOuLtXXr1g1FUVi+fPkt25YtWwZA165drV2WEAB8/fXXgDpcqBAVoVOn\nTjg7O7Nq1SrMZnOhbZcvX2br1q0EBgbSokULjSoUomjy+ihsTbdu3QCKzJRr1qwhKyuLhx9+2KLH\ncLig/sorr6DT6fj000+5cOFC/vpDhw4xb948vL29pcuBqFC7du0iNze30LqcnBzmz5/Prl27cHFx\noW/fvhpVJyq7kJAQ+vfvT2JiIh988EGhbWPHjsVkMjFy5EhcXV01qlA4sqNHjxbZPXX37t3Mnj0b\ngAEDBli7LCGK1LdvX8LCwli5ciUbN27MX3/16lUiIyPR6XS8+uqrFj2GTiluNHcb99FHH+WPP71/\n/34OHjzIAw88QN26dQHo0KEDzz33XKH7TJ48mXHjxhEUFESPHj3Iyspi1apVZGVlMWfOHAYOHGj1\nn0M4jo4dO3L06FE6duxIaGgoly5dYsWKFaSlpWEwGJg2bRqjRo3SukxRicXFxREREUF0dDSdOnWi\nadOm7Nixgz179tCuXTtWrlyJj4+P1mUKBxQZGclHH31Ely5dCAsLQ6/Xs2LFCs6ePYtOp6N///4s\nXLhQ6zJFJbZ8+fL8FvL4+HjWrVtH7dq187u2BAYG8sknn+Tv/8cff/D444+Tm5tLjx49CAwMZM2a\nNZw5c4ZRo0bx2WefWVSP3Qf1Tp068eeff95y4Q5FUdDpdAwZMoS5c+fecr/ly5czZ84c/vrrL1xd\nXWndujVjxoy5pY+REOVt7ty5LFu2LP8EFIPBQHh4OM2bN+e///0vDRo00LpE4QBSU1OZMGECUVFR\nxMTE0LhxYzp37sykSZNwdnbWujzhoLZs2cLMmTPZt28f8fHxZGdnU7NmTe6++25efPFFIiIitC5R\nVHLvvPMO77zzTpG5EtRR306dOlVo25EjR3j//ffZs2cPycnJtGrViieffJJhw4ZZXI/dB3UhhBBC\nCCEqI4froy6EEEIIIYQ9kKAuhBBCCCGEDZKgLoQQQgghhA2SoC6EEEIIIYQNkqAuhBBCCCGEDZKg\nLoQQQgghhA2SoC6EEEIIIYQNkqAuhBBCCCGEDZKgLoQQQgghhA2SoC6EEEIIIYQNkqAuhBBCCCGE\nDZKgLoQQQgghhA2SoC6EEEIIIYQNkqAuhBBCCCGEDfp/JGfgTSFRb9kAAAAASUVORK5CYII=\n"
}
],
"prompt_number": 117
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"The likelihood function"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The likelihood function matches the parameter to the observations. Again we will use Gaussian distributions for this. The likelihood basically states the probability of measurement $y$ given a value of the parameter $x$. So if the mapping between $x$ and $y$ is $x=y$, the only difference is given by additive noise, with a Gaussian distribution:\n",
"$$\n",
"y = x + \\epsilon\n",
"$$\n",
"\n",
"$$\n",
"\\epsilon \\sim \\mathcal{N}(\\mu, \\sigma_{obs})\n",
"$$"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Combining prior and likelihood"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"From Bayes' Theorem, we have that the *posterior distribution* of $x$ is the product of prior and likelihood:\n",
"\n",
"$$ \n",
"p(x|y) = \\frac{1}{\\sqrt{2\\pi}\\sigma_P}\\exp\\left[-\\frac{1}{2}\\frac{(x-\\mu_p)^2}{\\sigma_p^2}\\right]\\cdot \\frac{1}{\\sqrt{2\\pi}\\sigma_{obs}}\\exp\\left[-\\frac{1}{2}\\frac{(x-\\mu_{obs})^2}{\\sigma_{obs}^2}\\right]\n",
"$$\n",
"\n",
"Ignoring the constants...\n",
"$$ \n",
"p(x|y) \\propto \\exp\\left[-\\frac{1}{2}\\frac{(x-\\mu_p)^2}{\\sigma_p^2}\\right]\\cdot \\exp\\left[-\\frac{1}{2}\\frac{(x-\\mu_{obs})^2}{\\sigma_{obs}^2}\\right]\n",
"$$\n",
"\n",
"It is useful to work in terms of logarithms...\n",
"$$\n",
"\\log(p(x|y)) \\propto \\left[-\\frac{1}{2}\\frac{(x-\\mu_p)^2}{\\sigma_p^2}\\right] + \\left[-\\frac{1}{2}\\frac{(x-\\mu_{obs})^2}{\\sigma_{obs}^2}\\right]\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's assume that the prior distribution is centred at -5 with a standard deviation of 1, and that the likelihood is centered at 0 with a standard distribution of 2. What does this mean? It basically means that before we even do anything, we are quite sure that the value will be quite close to -5. It also means that the evidence (suggesting a value of 0 with a standard deviation of 2) is of little information content, compared to the prior:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"prior = gauss(x,-5, 1)\n",
"likelihood = gauss(x,0, 2)\n",
"posterior = prior * likelihood\n",
"plt.subplot(2,1,1)\n",
"plt.plot ( x, prior, '-r', label=\"Prior\")\n",
"plt.plot ( x, likelihood, '-g', label=\"Likelihood\")\n",
"plt.plot ( x, posterior, '-b', label=\"Posterior\")\n",
"plt.axvline ( x[posterior.argmax()])\n",
"plt.legend(loc='best')\n",
"plt.subplot(2,1,2)\n",
"plt.plot ( x, np.log(prior), '-r', label=\"Prior\")\n",
"plt.plot ( x, np.log(likelihood), '-g', label=\"Likelihood\")\n",
"plt.plot ( x,np.log(likelihood) + np.log(prior) , '-b', label=\"Posterior\")\n",
"plt.axvline ( x[posterior.argmax()])\n",
"plt.legend(loc='best')\n",
"print \"Maximum a posteriori: \", x[posterior.argmax()]\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Maximum a posteriori: -4.0\n"
]
},
{
"output_type": "display_data",
"png": 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WHEOxz58/nw8//JD09HQA7OzsuHDhAnFxcWzcuJE333yTr776qkhjTEpKIigo\niHPnzmFnZ0d6ejpHjhzhyJEj7N69m6ioqFz7q6pKcHAwn3zyif745cuX5/Dhwxw+fJgffviBJUuW\n8Nprr+Uq78aNGwwaNIht27YBYGVlhY2NDbt372b37t2sW7eO0NBQXnjhhVz7Hj58mO7du+snqH3m\nmWfYtm0bW7du5cSJE9SuXbvA16a4kpoAIYpCRgboZqUu7UmAzBcghBDFUkJCAm3atOHkyZO0b9+e\niIiIHAnA//73P/7973/j6OjI+PHjiYqKIi0tjWPHjvHhhx/i7OzMkiVLWL16dZHFpKoqPXv2pFKl\nSsTExHDnzh3++OMP3nzzTWxtbdmzZw/r1q3Ltd/KlSv55JNPUBSF8ePHk5ycTFpaGmfOnKFDhw6k\npaUxaNAgYmNjc+37/vvvs23bNsqXL8/KlSu5efMmaWlp7N69G3d3d86dO0fv3r3JyMjIsV96ejq9\ne/fmr7/+wtPTk3379pGWlsaNGzf44osv+PbbbwuVIBVbqngiQJVLJfK1Z4+qgqo2aGDpSEwvI0NV\nHR2153vhgqqq2rfyERGibJHvxoIbMmSIqiiK6ufnZ9T2K1asyHN7Nzc3VVEUdffu3aqqqurp06fV\nWrVqqYqiqL169VLT09NzbH/37l21Vq1aqkajUVeuXGmwvIULF6qKoqhVq1ZVs7Ky9MsvXryoKoqi\najSaXPtMnTpVVRRFHTp0aK51iqKoiqKoHh4e6sOHD3OtDwgIUBVFUf39/XMsv3//vlq7dm1VURT1\n3XffzbVfRkaG+tJLL6mKoqg9e/bMse73339XNRqNqtFo1A0bNuTaNykpSbW3t1cVRVEXLFiQY92i\nRYtURVHUihUrqlevXs2179dff60/J0Pnm5eCflbM9dmS5kBCFIWy0hQItP0d2reHn37SnveoUZaO\nSAhRQinTis9Y6+pUyw+3WVhHjx7F39+f69evM3DgQH1fgkdt2LCBpKQkGjVqxKBBgwweZ8iQIQQH\nB5OSksLFixepV69ekcQ3YcIEbG1tcy338/MjPDyc+Pj4HMt/+eUXEhMTsbW1ZeLEibn2s7a2Jjg4\nmN69e7N582Zu375NxYoVAfjuu+9QVZXGjRvTs2fPXPvWqFGDESNGsHDhQlatWsW7776rX6cbhWno\n0KG4uLjk2jcoKIiQkBAuX75ckNMvtqQ5kBBFQZcE6MbRL+2kSZAQQhQLe/bswc/Pj+vXrzN69GhW\nr16dKwGbLoIFAAAgAElEQVQAOHPmDAAXL16kRo0aVK9ePdfrX//6F+np6aiqqt/+aSmKYrDtPYCv\nry8Af/75Z47l58+fB8DT0zPP+QfatWunf/9oJ2HdvvnNoqzb98KFCwbLzWtfGxsbWrZsmedxSxqz\n1QSkpqYyefJkoqOjiYuLo1GjRvj5+TF16lSD2eHjbty4wfr16wkPD+fEiRMkJyfj5ORE/fr1GTNm\nDL179861z6PTXBsSGBjI999//1TnJQQpKXDkCNjagomnbi82dEnArl3akYJ48mdYCCEeV5KfvhcX\nU6ZMAbQ3tl988UWe2509exaAe/fucf/+/XyPqSgK169fL7IYa9SoYXC5k5MTAA8ePMixXHdTn9ck\naQAODg44Ojpy69Yt4uLi8Pb2Nnpf3bq0tDRSUlJwdnbm1q1bpKamoihKvp1/S1PHYLMkAQkJCXTq\n1InY2Fjatm2Lr68v0dHRzJ49mz179hAWFkalSpXyPUZoaCijR4+mWrVqtGjRgp49e3Lw4EF++eUX\noqKiGDZsGEuXLjW4r5eXl8EqocaNGxfJ+YkyLiJC2yS+TRuwt7d0NOZRpw489xycPg379wNlJPkR\nQohi5rXXXuOHH35g165dLF68mFF5NNHUjQZU2NF/LOFpEpGUlJQijKR0MksSMGnSJGJjY5kxYwaT\nJk3SLx8xYgTLly9n3rx5TJ8+Pd9j/Otf/+L777+nb9++WFlZ6ZdfuHCBxo0bs3z5cvr06UPnzp1z\n7evl5aXPlIUocmWpP8Cj/P21ScDPPyNJgBBCmJ+iKIwaNYrmzZszbtw4xowZQ7ly5QyO2f/cc8+x\nadMmfZOX4uzZZ58F4MiRI6Smphp8UHz79m1u3bqFoij67QHq1avHb7/9RkRERJ7HT0hIALS1Cc7O\nzgA4OjpSqVIlUlNTuXTpEs2aNTO476VLlwp9XsWNyfsEJCcnExoaStWqVQkODs6xbu7cuVhbW7N4\n8eJcVUGPa9u2LYGBgTkSAAAPDw99B5dff/21aIMX4klUFXSTq5TFJAD+SYKEEEKYlXYgGXjvvfeY\nM2cOqqoycuRIvvvuu1zbNmzYENDeWN+8edOscRaU7qY+KyuLSN3w24/ZtWuX/v2jHZg9PT0B+O23\n3/KsSdDt+3jHZ92+e/fuNbhfRkYGBw4cMOYUSgSTJwFRUVFkZmYSEBCQayIIJycnWrduTUpKCseO\nHSt0GVWrVgXIs29BUlISS5YsYe7cuYSGhhZZZxch+OMPSE6G6tWhSRNLR2NeL78M5crB0aOWjkQI\nIcq8CRMmMG3aNLKzswkKCuLHH3/Msb5Hjx7UqFFD30czP5ZuSuPr66tve79ly5Zc6zMyMvj4448B\n6NmzJw4ODvp1AwYMQKPRkJ2dTXh4eK59k5KS9M3Hg4KCcqzT1aAsX77c4DVYtWpVqRkZCMyQBCQm\nJgLg7u5ucL2bmxug/UcpjIcPH7Ju3ToURaFt27YGt9m5cydvvfUWH3zwAa+99hoNGzYkMDCQ5OTk\nQpUphN6jowIVYEbHUqF8eW0iIIQQokAyMjK4fv06KSkpeb4yMzOfeJzHH65OnjyZSZMmkZWVxYAB\nA9i0aZN+nYODAwsXLgTgyy+/pFevXvz+++/6vgLJycns3LmTfv36WXwEnHLlyjFt2jRAO2znhAkT\n9DP4xsbG0rVrV44cOYK1tTWzZ8/OsW/jxo0ZOHAgAG+99RarVq3izp07ZGRksGfPHlq3bs39+/fx\n8PDgrbfeyrHv8OHDqV27NmlpabRu3ZqDBw+SmZnJrVu3+OqrrxgzZoy++VBpYPIkQHdzn9dF043D\nqksWCuqdd94hNjaW119/nTZt2uRYZ29vz5QpUzh69CipqamcO3eO2bNn4+XlxY8//kivXr2M+pAJ\nkaey2h9Ap6yetxBCPIXo6GhcXFyoWrVqnq/o6OgnHkfXHOhRM2bM4D//+Q+ZmZkEBgaydetW/bre\nvXvz5Zdf4uDgwKZNm/Dy8sLe3h57e3tq1aqFv78/69atIzs7u8jO1VCMxhgyZAgTJ05EURQ+/fRT\natSogb29Pc899xwRERFUrFiRNWvW8K9//SvXvvPnz6dLly7cv3+foUOH4ujoiIODA76+viQkJODp\n6clPP/2EtXXOrrE2NjasX78eV1dXzp49S8uWLXFwcKBy5cqMGTOGAQMGMHr06EKdT3FUoucJWLBg\nAd988w0NGzY0OCyWi4sLISEheHl5UbFiRerVq8fEiRPZu3cvjo6OxMTEsGLFCqPLUxQlz1dISEgR\nnpkoEe7dgz17tDUAHTpYOhrLkCRACCGMpntyn9/9xOOv/I6V1/q5c+fy7rvvkp6eTt++fXN0kh01\nahR//PEH77zzDn5+fjg7O2NtbU2DBg3o2rUrixcv5uDBgwU6pyfFWRiKojB79mx27Nihb8VhbW3N\nSy+9xMiRIzl69CiBgYEG961cuTJbtmzhq6++IiAggNq1a1OhQgV8fX0JDg7m2LFjec5d8OKLL3Lo\n0CFGjhxJ48aNqVChAl27dmXevHksXbr0iedrrJCQkAL/mxc1RS1simakTz75hA8//JDp06fz0Ucf\n5Vo/dOhQVq1aRWhoKH379jX6uAsXLuS9996jUaNGREZGGpzZLT/vvfceCxcuZMSIEXz99df5bqv7\nBzHxpRIlzfbt0LkzvPgiHD5s6WgsQ1WhVi2U5CT9r0KIskG+G4UwTkE/K+b6bJm8JkDXsePixYsG\n1+uGaapVq5bRx1ywYAHvvfceTZo0ISoqqsAJAKDPAK9du1bgfYUA/hkVqKzMEmyIopTt8xdCCCFK\nKJMnAX5+ftjY2BAeHp6rjdn169fZu3cvLi4u+pnenuS///0v48aNw9vbm6ioqEJ30NA9/W9S1kZ0\nEUWnrPcH0Cnr5y+EEEKUQCZPAlxdXenXrx9Xr17VD+ekM2HCBLKyshg1ahTlypUDIDMzkzNnznDh\nwoVcx5o1axYTJ06kWbNmREZG6qebzsvBgwfJyMjIsSw9PZ3vvvuOgwcPYmtrS+/evZ/yDEWZ9Oef\ncOoUVKgAFh5FweIe7Q9x967l4hBCCCGE0UzeJwC0s6t16tSJM2fO4OfnR5MmTdi/fz8xMTH4+Piw\nZcsWHB0dAYiPj8fDwwM3N7ccTYhWrVrF0KFDsbKyYuzYsVSsWDFXOXXr1mXIkCH63319fTl16hS+\nvr7UrFmTa9euERYWRlpaGlZWVixYsIAxY8Y8MX5p9yhyWbYMRoyA7t3hkSHYyipdPyY1fCt06WLZ\nYIQQZiHfjUIYp7j2CbB+8iZPr06dOuzfv5+PPvqI6OhoVqxYQaNGjQgODmbq1KnY2Njk2ufx3tHx\n8fEAZGdns2DBAoPl+Pr65kgCBg8ezIYNG4iJiWHbtm1YWVlRt25dvLy8+OCDD2jQoEHRnaQoW8rq\nLMFP8vPPkgQIIYQQJYBZagJKOnnaIXLIygIXF7h5E86dg7+nNy/L9DUB9RuAzMgtRJkg341CGKe4\n1gSU6HkChLCIw4e1CYCHhyQAj4uNhb9H/BJCCCFE8SVJgBAFJaMC5U/XVEoIIYQQxZYkAUIUlPQH\nyJ8uSRJCCCFEsSV9Aowg7R6F3q1bUKWKthH89etgYJSqskjfJwAFHB0hJQWszTLugBDCQuS7UQjj\nSJ8AIUqDXbu0HYNbtZIEwBBPT22idOiQpSMRQgghRD4kCRCiILZv1/6UpkCGdeyo/SlNgoQQQohi\nTZIAIYylqtIp+El010WSACGEEKJYkz4BRpB2jwLQjn//3HPaOQL++gs0kkPr6PsEpN0BJydtk6lr\n17TvhRClknw3CmEc6RMgREmnawrUsaMkAHmpUAF8fCA7W9t/QgghhBDFktzJCGEsaQpkHGkSJIQQ\nQhR7ZksCUlNTGTt2LE2bNsXR0ZFWrVoxadIk0tPTjdr/xo0bLF26lF69evHss89Svnx5atWqRbt2\n7Vi/fn2++548eZLXX38dT09PnJ2d8ff3Z9myZUVxWqKsuH8fdu/Wvtd1fhWGPZoESDMBIYQQBeTr\n64tGo2HVqlWWDqVUM0sSkJCQQMuWLVm0aBFOTk4MHz6crKwsZs+eTbt27UhNTX3iMUJDQ3njjTc4\ncOAAjRs3ZvTo0dStW5dffvmFvn37MmLECIP7RURE4OPjw+bNm/Hy8iIwMJBz584xcuRI3n777aI+\nVVFa7d2rTQS8vaFaNUtHU7y98IK230RiIpw+belohBCi2AgKCkKj0eR61apVi1deeYWQkBDu3Llj\nsfgWLFjAtGnTSEhIsFgMj9K1jRcmoprBgAEDVEVR1JkzZ+ZYPnz4cFVRFHXy5MlPPMauXbvUH374\nQc3MzMyxPC4uTn3mmWdURVHUrVu35liXmZmpurm5qeXKlVMjIyP1y2/fvq16e3uriqKou3btemLZ\ngGqmSyWKq3HjVBVU9YMPLB1JsaR95P/IggEDtAvmz7dYTEII05LvxoIbMmSIqiiKamtrq7q6uqqu\nrq6qi4uLqiiK/lW9enX1yJEjFonPzc1NVRRF3b17t0XK1xk8eLD63HPPqRs3brRoHEWloJ8Vc322\nTF4TkJycTGhoKFWrViU4ODjHurlz52Jtbc3ixYt58OBBvsdp27YtgYGBWFlZ5Vju4eHBoEGDAPj1\n119zrFu/fj2XLl0iICAAPz8//XIHBwdCQkIAmD9/fmFPTZQl0h+gYKRfgBBC5MnHx4fk5GSSk5O5\nevUqhw8f5t1338XBwYErV64QFBRERkaGRWIrDk/fV61axalTp+jRo4elQynVTJ4EREVFkZmZSUBA\nQK4/LCcnJ1q3bk1KSgrHjh0rdBlVq1YFwNbWNsfyHTt2ANCzZ89c+3Tq1Ak7OzsiIiIKXa4oIxIT\n4Y8/tCPftGpl6WhKBl2/id274QkJvhBClHVNmzZl/vz5jBo1CtD2Zdy2bZtFYlFVVYZ9LSNMngQk\nJiYC4O7ubnC9m5sbAElJSYU6/sOHD1m3bh2KotC2bVujy7a1taVatWqkp6eTkpJSqLJFGaF7mt22\nLTyWaIo8VKsGXl7afhR791o6GiGEKBECAwP1708/0qcqIyODTz75hE6dOuHq6kr16tXx9/dnzpw5\nZGZm5nm8Y8eOMWDAABo0aIC9vT2Ojo54enrSs2dPvv76a/3NfkhICBqNhkuXLgHg5+eXo8/Co60p\ndDIzM5k/fz7du3fHzc2NypUr4+Pjw8SJE0lLSzMYj67D7+rVq7l//z4zZ86ka9euODs7U7ly5Vzb\n5dUxuDDXQ3eOQ4cOBWDlypX0798fDw8PNBoNv/32W57XsbSyNnUBupt7Z2dng+tdXFyAf27YC+qd\nd94hNjaWAQMG0KZNm1xlK4qSb9kJCQkkJibmuY0Q0hSokPz94fhx7fXr0MHS0QgzylazuZN+BwUF\njaJBo2iws7YrFs0MhCjOvL29KV++PPfu3dPfFyUkJBAYGMihQ4cAsLGxQVEUdu7cyc6dO9mwYQOh\noaH6h6o669ato1+/fvrfra2tsbKy4sKFC8TFxbF582aCgoKwtbXFwcGBatWqce3aNbKzs3FycsrR\nuqJKlSo5jn3hwgUGDBjAwYMHAW0TIltbW/bv38/+/fv54Ycf+Omnn2jWrJnB87x37x49evQgIiIC\nKysr7O3t0RiYf8fQ/xmFvR6Pmjx5MrNmzUJRFCpWrIiiKGXy/yeTJwGmtGDBAr755hsaNmzIF198\nYelwRGmUmQm6JmOSBBRMx47wySfwd7M8UbpcTrvMoaRDnEk5w7kb5zh/4zyJtxO5+eAmN+/fRCVn\ncwJrjTUu5V1wsXehhkMNGjg3oEGVBjzn8hxNXZtSwbaChc5EiOJj37593Lt3D/inFcOQIUM4dOgQ\nVapUYcWKFXT4+6HKzp07CQoKIiYmhoEDB7L3kVrXrKwshg8fDkD37t2ZMGECTZs2xc7OjtTUVA4e\nPMiaNWv0N77//ve/+fe//427uzuXLl1i/fr1vPzyywZjzMzMpFu3bpw+fZqOHTvSt29funTpgqOj\nI5s3b2bVqlXs2LGDQYMG8fvvv2NjY5PrGMHBwVhbW7N+/Xo6duxI+fLluXDhglHXqDDX41GbNm0i\nLS2NOXPmMGzYMJydnUlJSaFcuXJGlV+amDwJqFmzJkCeTW6uXbsGQK1atQp03IULFzJu3DgaNWpE\nZGQkjo6OBss+efJkvmUrimJ02flliVOnTtV3NhalSEwM3LwJzz4L9epZOpqSxccHypeHEycgORlq\n1LB0ROIpJN5OZNu5bURcjOBA4gEu3bqU7/b2NvYoikK2mk1WdhYPsx5y+c5lLt+5zO9Xfmf7+e36\nba0UK16o/gI+tX1oV7cd7T3aY29rb+pTEqLYWbt2LaC932jUqBHh4eHs2bMHjUbDjh078Pb21m8b\nEBDAzp07adasGdHR0WzatEnfkfbMmTOkpaVRrlw5Fi1apL8XA6hUqRL+/v74F/LB1ldffcXp06d5\n9tlnCQ8PzzFgS//+/enbty916tQhNjaWJUuWGByO/datW8TExNC0aVP9Mg8PjyeWXdjr8ajU1FQ+\n++wz3n//ff0yS7QGCQkJYdq0aWYv91EmTwJq164NwMWLFw2u141FW5AkYMGCBYwbN44mTZqwa9eu\nPP/xdMe8ePEirVu3zrHu4cOHXLlyBVtbW6P/8aWjTBkkTYEKr1w58POD8HBtbUBQkKUjEgUUmxLL\ndye+Y1PsJn6/8nuOdQ62DjSv2Zznqz3Ps07P4unkiVslN5yecaKSXSWsNTm/Xh5kPiDlXgrX7l7j\n0q1LnEk5w+mU05y4eoLf/vqNo5ePcvTyUT4/9Dl21na0q9uOHvV78GqjV6lkV8mcpy3MqDi1wLDU\nV3xmZiY7d+5k9erVbNy4EYCXXnqJjh078vrrrwPQuXPnHDe8Ot7e3nTr1k3/BF5301urVi1sbW3J\nyMggNTU1RxLwtBYuXAjAzJkzc43YCNrmOW+88QYzZszQN9l5XMeOHXMkAMZas2YNUPDr8ajKlSvz\n1ltvFbjsohYSEpLnw2NzNU0yeRLg5+eHjY0N4eHhZGdn52jzdf36dfbu3YuLi4vBf0xD/vvf/zJx\n4kS8vb3ZuXMnTk5OeW6rmxl448aN+mFEdbZv386DBw8ICAgo3ImJskGSgKfj769NAn7+WZKAEiL1\nQSqrf1vNmt/XcDj5sH65vY09Hep1oFO9TrRxa0MD5wZoFOPHlrCztqNWxVrUqlgLb1dvevDPl/Od\n9DscSjrE3oS9bDu/jYNJBwk/F074uXDGbhtLzwY9GfLCEDrW64iVJvdNhxAlzS+//GKwDTyAp6cn\nq1atQqPRcP78eUDbUTYv7dq1Y/PmzTma0zg6OtKjRw9+/PFHunbtytixY+ncuTMNGzZ8qrjT09P1\nD3XHjh3LO++8k+d2kLNz86Py6ivwJIW9Ho9q2LAhdnZ2hSq/tDF5EuDq6kq/fv347rvv+Pjjj/no\no4/06yZMmEBWVhajRo3St8XKzMzk/Pnz2Nra5qoamjVrFpMnT6ZZs2bs3LnTYBOgR/Xu3Rs3Nze2\nbNlCZGSkfvSg27dvExISgqIoOaqDhMjhxg04dAhsbLRPtEXB6ZKnnTshKwsMPDUSxcOpa6f44tAX\nrP5tNXcz7gLap/19G/alf+P+vOz2MuWsTdNmtoJtBdrWbUvbum2Z6juVv+78xZazW1j7x1p2XdjF\n2j/WsvaPtXhU9uCd5u8w1HsoFctVNEkswrzKagW7jY2NvrOtRqPB1dUVDw8PfH19eeONN/RP2OPi\n4gCoU6dOnsfSrdNtq/PRRx9x9OhR4uLiGD9+POPHj8fJyYmuXbvSv39/OnXqVOC44+LiyM7OBvJu\n5q2jKArXr183uE7XSqQw5UPhrsfTll0amaVj8KxZszhy5AhTpkwhKiqKJk2asH//fmJiYvDx8WHc\nuHH6bRMTE2nYsCFubm45mhCtWrWKyZMnY2VlRevWrQ1O8lW3bl2GDBmi/12j0bB06VL69OlDt27d\n6NKlCy4uLmzfvp34+HjGjBljcNgrIQBth+DsbHjlFe0cAaLgPD3B3R3i4+HYMSjk0x9hOoeTDzNt\n9zS2nN2iX9a2blveaPoG3et35xmbZ8weU/UK1RnRdAQjmo7g0q1LfPv7tyw7towLNy/w3s/vMTlq\nMm82e5PxrcZT1b6q2eMT4mn5+PgQGRlp9PaFGcq8SZMmnDx5kq1btxIWFsbu3buJj49nzZo1rFmz\nhsDAQL7//vsCHVP3hF9RFJKTk6lWrVqB4wKe+kn80wztLrUA/zD5PAGgzcr279/PmDFjuHnzJitW\nrMDKyorg4OA8O/U+3h4qPj4egOzsbBYsWMD06dNzvQyNJ9uuXTuio6Pp0aMHx48fJzQ0FE9PT5Yu\nXcrnn39ukvMVpcTWrdqfhXhaIv6mKP9MHCazBxcrMUkxBPwvgJe+eYktZ7dQ3qY8o5qN4uRbJ9k1\neBeBjQMtkgA8ro5jHYLbBHP27bNsCNzAy24vk5aexqf7PqXu/6vLhJ0TuHb3mqXDFMIk6v09IEV+\nE5vq+lbWMzB4Rbly5ejVqxfLly8nLi6Os2fP6h+8rl27lj/++KNA8dSvX19/f6ZrmmNOT3s9RE5m\nSQJA2z7t888/5+jRo9y6dYt9+/Yxc+bMXENHubu7k52dnast19SpU8nOziYrK4vs7GyDr7yy6kaN\nGvG///2Pc+fOkZKSws8//8ywYcNMdq6iFMjOBt1sjV27WjaWkk7XJEiSgGIh7kYcvdf2pvnS5oSf\nC6e8TXkm+Ezg4rsX+arrVzSq2sjSIRpkpbGiZ4Oe7A7aTczIGLr9qxv3Mu7x333/pe7/q8usPbO4\nn3Hf0mEKUaQ8PT0BbR+CvAYn2bVrF2DcTW+9evX49NNPadWqFQDLli3LsV53T6Zr8vM4Ozs76tat\ni6qq/GyB/9OL+nqUdWZLAoQoUQ4fhqtXwc0NnrIjVZnXrp22L8C+fZCaauloyqxbD24xfud4nlv0\nHBvObKC8TXkm+kwk/t14Pmn/SYlqVtOsRjM2999MzMgYunp25W7GXT6K+ogGixrww8kfZCQ3UWoM\nHjwY0A5raWjc+6NHjxIWFoaiKAQ9MviCrtlOXqytta3BH2+zX716dSD/5ja6kXXmzZunf+puSFZW\nFqlF/H9+Ya+HMEySACEM2fJ3++iuXYvXGHYlkaMjtGmj7RgstQFmp6oqK46twPNzTz7d9ykZ2RkM\neWEI58aeY077ObjYu1g6xEJrVqMZW17fQuTgSF6o9gKXbl2i/0/9ab2ida4hTYUoiTp37szLL7+M\nqqr07t2bsLAwHjx4wP379wkLC6Pj380tfXx86Natm36/rVu30rhxYz7//HPOnj3Lw4cPUVWVU6dO\n8fHHH7Nnzx4URaFdu3Y5ytM9aV+9enWeHWvfe+89vLy8uHfvHi+++CIrV67k6tWrANy/f5+TJ08y\nb948nn32WTZt2lQsrofIgyqeCFDlUpUxTZuqKqhqeLilIykRtGN85LPBp59qNxg40GwxCVU9m3JW\n9VvppxKCSghq6+Wt1ZikGEuHZRKZWZnqN0e+Uav+t6pKCKr1dGv1w4gP1Xvp9ywdWqkl340FN2TI\nEFVRFNXPz8/ofRISEtQWLVqoiqKoiqKo1tbWqo2Njf73Fi1aqPHx8Tn22bhxo369oiiqRqNR7e3t\nc/w+YMCAXGUdPXpU1Wg0+u2qVaumurm5qa+99lqumNq3b5+jDAcHh1xlrl69Osd+r7zyiqooirpq\n1ap8zzm/7QpzPVRVVadOnaoqiqIOHTo037JNoaCfFXN9tqQmQIjHXb4MR4/CM8/I0KBFRTcfx9at\n2hoBYVIZWRnM3jubJl81ISo+CufyzqzptYY9QXtoVqN0jtBkpbFiRNMRnH37LKNfGk1Wdhazf53N\n84ufJ+pilKXDEwLQDnpS0Img6tSpw6+//sqcOXPw9/fHxcWFKlWq0LFjR2bPnk10dDRubm459mnb\nti1r1qxhyJAhPP/881SpUoXs7GyeffZZunbtSlhYGN9++22usry9vYmMjKRDhw7UqVOHGzdu8Oef\nf3LlypVcMe3cuZNVq1bx6quv0rhxY7Kzs6lRowbNmzfnnXfeYffu3QwcOLBQ55/fdoW5HgUpuyxR\n/s44RD50fzRyqcqIZctgxAhtU6AtW568vdC3mMrzI6Kq2uFC4+Lg11/Bx8dssZU1p6+dZuCGgRy9\nfBSAIS8M4dOOn+Jc3riZ0UuLfX/u442wN/jjmnb0k7ebv83c9nOLxYhHpYV8NwphnIJ+Vsz12ZKa\nACEeFx6u/SmjAhUdRfmnNkASK5NQVZUvDn1B06+bcvTyUdwrubNz0E5W9lxZ5hIAgFa1W3H0zaNM\n952OtcaaLw59wYtfv6hPjoQQoqyTmgAjyNOOMuThQ3B2hjt3ICEB8pmVUPzjiTUBoJ18rUMHaNIE\nfpdOm0UpOS2ZYZuG8XOctuN1kFcQ/6/T/5NZdf929PJRBq4fyOmU01hrrJnuO50JPhOw0sgM1k9D\nvhuFME5xrQmQJMAI8h9dGSI3qoViVBKQng5VqmgTrPh47fCr4qmFnw1nyMYhXL9/HadnnPg64Gv6\nNOxj6bCKnfsZ95kYMZHPD2kniWxTpw3f9/memhVrWjiykku+G4UwTnFNAqQ5kBCPkqZApmNr+8/E\nYbrrLAotMzuTD3d9SMD3AVy/f52O9Tpy4q0TkgDk4RmbZ1jYeSHbB2zHtYIrey/txXuJNxEX8p55\nVAghSjNJAoR4lCQBpiX9AorE5bTLtF/dnjm/zkGjaJjdbjbbBmyjhkMNS4dW7Pk/68/xUcdp79Ge\na/eu0XFNR6b9Mo2sbBm1SghRtkhzICNIlWcZcfYs1K8PlStrZwv+e0ZF8WRGNQcCuHIFqleHcuXg\n+nWwtzd5bKVN1MUo+v/Unyt3r1C9QnV+6PMDr7i/YumwSpys7Cxm7pnJtN3TUFHpWK8j3/b6tkRP\nnlG7ZZkAACAASURBVGZu8t0ohHHKfHOg1NRUxo4dS9OmTXF0dKRVq1ZMmjTpiVNbP2rdunWMHTuW\nNm3aULFiRTQaDYMGDcpz+/j4eDQaTZ6v/v37F8WpidJCVwvQqZMkAKZSrRo0b67tgL1rl6WjKVFU\nVWXBgQW0X9OeK3ev0LZuW46/eVwSgEKy0lgx1XcqPw/8GZfyLuyI20Gzb5px/K/jlg5NCCHMwix3\nOgkJCXTq1InY2Fjatm2Lr68v0dHRzJ49mz179hAWFkalSpWeeJyZM2fy+++/4+DgQK1atThz5oxR\nEz94eXnRs2fPXMsbN25cqPMRpdTGjdqf3btbNo7SLiAADh3SNgmSa22Uh5kPGRU+ipXHVwLwYesP\nmeE3Q0a3KQId6nXg2JvH6PtjXw4kHqDVslas7LmSfo36WTq0EkMmYBKihDL5nMSqqg4YMEBVFEWd\nOXNmjuXDhw9XFUVRJ0+ebNRxoqKi1PPnz6uqqqq//PKLqiiKOmjQoDy3v3jxYpFMEY1MjV76Xb2q\nqhqNqtrYqGpqqqWjKXG0DYGM3PjoUe3Grq6qmpVl0rhKg+Tbyer/Lf0/lRDUZ2Y+o649udbSIZVK\nDzIeqEM3DlUJQSUEddKuSWpWtvx95qdLly7670d5yUte+b+6dOli9GdLt4+pmbxPQHJyMu7u7jg5\nOXH58uUcTwxu3LhB9erVqVSpEpcuXcLOzs7o4/7yyy+0bduWgQMHsnr1aoPbxMfH4+HhQVBQEMuX\nLy/0OUi7xzJgxQoYNkw7es327ZaOpsQxuk+AbqM6dSAxEQ4cgBYtTBpbSRaTFEPPtT1JTkumjmMd\nNr22Ca/qXpYOq9RSVZWFBxfy7x3/JkvNotu/uvFt729lvgUhhFmVmj4BUVFRZGZmEhAQkKvK0MnJ\nidatW5OSksKxY8dMFkNSUhJLlixh7ty5hIaGcubMGZOVJUooXVOgXr0sG0dZoCj/XOcNGywbSzG2\n7tQ62qxoQ3JaMm3qtCFmZIwkACamKArv/t+7bB+4ncp2lQk7G0bLZS2JT423dGhCCFHkTJ4EJCYm\nAuDu7m5wvdvfEwYlJSWZLIadO3fy1ltv8cEHH/Daa6/RsGFDAgMDSU5ONlmZogS5exd27NC+lzbq\n5vFoEiA1bLl8fvBz+v3Yj4dZD3njxTeIGBxBVfuqlg6rzGjv0Z6YkTE0dGnIqWunaLG0BYeSDlk6\nLCGEKFImTwJ0N/fOzs4G17u4aIdj0yULRcne3p4pU6Zw9OhRUlNTOXfuHLNnz8bLy4sff/yRXr16\nkZmZWeTlihLm55/hwQP4v/8DV1dLR1M2tGmjnT347Fk4fdrS0RQbqqoSvCuYd7a/g4rK7HazWdx1\nMbZWtpYOrcyp51SPfcP20d6jPVfvXsV3pS8bTkvNlRCi9CjVk4W5uLgQEhKCl5cXFStWpF69ekyc\nOJG9e/fi6OhITEwMK1asMPp4iqLk+QoJCTHdiQjT0jUFMjCClDARa2vo1k37XpoEAZCRlcHQTUOZ\n/etsrBQrVvRYwQetP5CRVyzI0c6Rra9vZbj3cO5n3qdPaB/m7Z8n/cOEEE8tJCQkz3tKczF5ElCz\nZk0AUlJSDK6/9v/Zu/P4KOrzgeOf2c1mc18kkJBAYkChhmCA4gFYSTw4xAsU5LAIakul2Np6ISih\ntUitRetRT/BoUQv8AAWEIgIVA2LkEAMGgZAEEgJJyJ1sNrs7vz+GzbkhAZLdTfK8eX1fMzuzO/Ms\n2Wy+z3yPyc8HICoqqr1DqeXr68v06dMBSE1NbfXrVFVttkgS0EHV1NTdvVaSAOeydwlavdq1cbiB\ncnM5d3xyBx98/wE+Bh/WTV7H/Qn3uzosARj0Bt657R0WJS1CReWPm//Ibzf+FotNWpGFEBcvOTm5\n2Tqls7R7EtCrVy8Ajh8/7nB/VlYW4NwkAOCqq64C6pIQ0UXt2AFFRdC/v3a3YOE8N9+s3TF47144\n9z3QFeVX5JP0QRIbj24k1CeUbdO3MebyMa4OS9SjKApzr5/LJxM+wag38s/Uf3LHJ3dQYa5wdWhC\nCHHR2j0JSExMxGAwsGHDBmw2W4N9hYWF7Nixg7CwMAYNGtTeoTTw9ttvAxAfH+/U8wo3I12BXMfb\nG8acq+zafw5dTEZRBsOWDSM1N5XLgi5j58ydXB15tavDEs2YNGASX/7yS7p5d+PzI5+T9GES+RVy\nIUkI0TG1exIQERHBxIkTOXPmDIsWLWqw74knnsBqtTJr1iyMRiMAFouF9PR0MjIyLvncu3fvpqam\npsE2s9nM8uXL2b17N56enowfP/6SzyM6KJutriuKJAGu0YWnCt17ai/Dlg7j6NmjDAofxM4HdnJ5\nt8tdHZZowfDew9n5wE5igmL4Nudbhi8bzvEixy3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y7PZl+Hr6ujo0IcQlkpYAIS6GfQaq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o2j36MdOph5MoKbW3pQ0LGjqqcihBBFlEwMvk9QUBD16tXL1Hq/atUqnn76aUqWLElUVBR290w6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\nMUwCiIiIiIhMzP8D3D9kVYJ6PaYAAAAASUVORK5CYII=\n"
}
],
"prompt_number": 118
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"prior = gauss(x,-5, 5)\n",
"likelihood = gauss(x,0, 1)\n",
"posterior = prior * likelihood\n",
"plt.subplot(2,1,1)\n",
"plt.plot ( x, prior, '-r', label=\"Prior\")\n",
"plt.plot ( x, likelihood, '-g', label=\"Likelihood\")\n",
"plt.plot ( x, posterior, '-b', label=\"Posterior\")\n",
"plt.axvline ( x[posterior.argmax()])\n",
"plt.legend(loc='best')\n",
"plt.subplot(2,1,2)\n",
"plt.plot ( x, np.log(prior), '-r', label=\"Prior\")\n",
"plt.plot ( x, np.log(likelihood), '-g', label=\"Likelihood\")\n",
"plt.plot ( x,np.log(likelihood) + np.log(prior) , '-b', label=\"Posterior\")\n",
"plt.axvline ( x[posterior.argmax()])\n",
"plt.legend(loc='best')\n",
"print \"Maximum a posteriori: \", x[posterior.argmax()]"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Maximum a posteriori: -0.2\n"
]
},
{
"output_type": "display_data",
"png": 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vue/foT/NLJpxLPMYGfkZxg5HiEpVNTFs2bIlnTt3pkOHDuW2qyZQFuXg4ECX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\n"
}
],
"prompt_number": 119
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Exercise"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Calculate the form of the posterior from the equation that defines the log posterior above"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Multivariate distributions"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The previous examples were univariate. What if the problem you try to solve is multidimensional? The pdf equivalent for an $n-$dimensional problem is the multivariate Gaussian distribution. Here, we define the probability of a vector $\\mathbf{x}$ as being a function of a mean vector $\\mathbf{\\mu}$ and a *covariance matrix* $\\mathbf{C}$\n",
"$$\n",
"p(\\mathbf{x}) \\propto \\exp\\left[-\\frac{1}{2}\\left(\\mathbf{x} - \\mathbf{\\mu}\\right)^{T}\\mathbf{C}^{-1}\\left(\\mathbf{x} - \\mathbf{\\mu}\\right) \\right]\n",
"$$"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"DA & Smoothing"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Unfortunately, in most real life problems, the observations only have limited information content, and it is not possible to retrieve all the parameters that we want to find out about purely from analysing the observations. We tend to call these problems *ill-posed* (although this is a more general term). A way around this situation is to add extra constraints from prior information (See e.g. Combal B. et al. Retrieval of canopy biophysical variables from bidirectional reflectance: Using prior information to solve the ill-posed inverse problem //Remote sensing of environment. \u2013 2003. \u2013 \u0422. 84. \u2013 \u2116. 1. \u2013 \u0421. 1-15.). Apart from setting expected distributions of parameters, as we've seen above, we usually also know a lot about e.g. the temporal evolution of things. For example, leaves usually evolve smoothly. So a solution that is very jagged is less likely than one that is smooth. This is the reason one of the first tasks people do to use LAI data from satellites is smoothing. A better way is to enforce smoothness as we solve the problem.\n",
"\n",
"Smoothness is characterised by small derivatives (or discrete differences). So one constraint could be that the discrete differences of the parameter as it evolves in time are as small as possible, while still fitting the observations and any other prior laws. Equivalently, we are effectively stating that the evolution of the value of the parameter from one time step to the next should be as small as possible or, in other words: the value tomorrow should be the same as the value today, but with some added uncertainty:\n",
"$$\n",
"x_{t+1} = x_{t} + \\epsilon_{t}\n",
"$$\n",
"If $\\epsilon_t=0$, then $\\mathbf{x}=C$, a constant!, so we know that $\\epsilon_{t} > 0$. We can assume that $\\epsilon_{t} \\sim \\mathcal{N}(0, \\sigma_{m})$, so \n",
"$$\n",
"\\log(p(\\mathbf{x}))\\propto\\gamma \\left(\\Delta\\cdot\\mathbf{x}\\right)^{T}\\mathbf{I}\\left(\\Delta\\cdot\\mathbf{x}\\right)\n",
"$$\n",
"So by inspection, $\\gamma=\\sigma_{m}^{-2}$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"x = np.arange(1,366 )\n",
"y_smooth = (1-np.cos(np.pi*x/366.)**2)\n",
"y_noisy = y_smooth + np.random.randn(365)*0.15\n",
"plt.plot(x,y_noisy, '-g', lw=0.5)\n",
"plt.plot(x,y_smooth, '-r',lw=1.4)\n",
"\n",
"deriv_smooth = np.diff ( y_smooth )\n",
"deriv_noisy = np.diff ( y_noisy )\n",
"print \"RMS of derivative of smooth function:\", np.sqrt(np.mean(deriv_smooth**2))\n",
"print \"RMS of derivative of noisy function:\", np.sqrt(np.mean(deriv_noisy**2))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"RMS of derivative of smooth function: 0.00608608666688\n",
"RMS of derivative of noisy function: 0.205829440075\n"
]
},
{
"output_type": "display_data",
"png": 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lBAFq/p4ATdeg6Rp8nuzvJTIB6dOBqkPVtmtquoZOqdNVs3BMimWMCBVBS8gfsmUdiIho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jjKvcZMAOBcBCSyCdsuFbEDdSTzSkBLpMW5+Hj1VeDii/M/33mnFq6zwDM8BoQBRzsQ2dWq1A60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\nLIu8dcWdbgAAAABJRU5ErkJggg==\n"
}
],
"prompt_number": 120
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the previous code snippet, we show that the typical (RMS-sense) 1st order difference for a smooth function is much less than that of a non-smooth function. "
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Towards variational data assimilation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We have seen above that the MAP (maximum *a posteriori*) estimate of the parameters is obtained by the maximum value of the posterior, or likewise, the minimum value of minus the log posterior. We have also seen how the likelihood and prior terms look like. Let's put them all together for a univeriate time series, $\\mathbf{x}$\n",
"\n",
"$$\n",
"J_{obs} = -\\frac{1}{2}\\left(\\mathbf{x}-\\mathbf{x}_o\\right)^{T} \\mathbf{C_o}^{-1} \\left( \\mathbf{x} - \\mathbf{x}_o\\right)\n",
"$$\n",
"\n",
"$$\n",
"J_{prior} = -\\frac{1}{2}\\left(\\mathbf{x} - \\mathbf{x}_{p}\\right)^{T}\\mathbf{C_p}^{-1}\\left(\\mathbf{x} - \\mathbf{x}_p\\right) \n",
"$$\n",
"\n",
"$$\n",
"J_{model} = -\\frac{1}{2}\\left(\\Delta\\mathbf{x}\\right)^{T}\\mathbf{C_m}^{-1}\\left(\\Delta\\mathbf{x}\\right) \n",
"$$\n",
"\n",
"The posterior is made up of the sum of the previous three terms:\n",
"$$\n",
"J = J_{obs} + J_{prior} + J_{model},\n",
"$$\n",
"and the MAP estimate will then just be minimum value of $-J$. We can solve for this efficiently using gradient descent methods, that use the derivative to locate the minimum value of the function, and are implemented in a number of computer languages and software packages. For that we can either calculate the derivatives analytically, or approximate them numerically. The former is a better approach, and can either be done \"by hand\", or by using automatic differentiation tools. We shall use approximations in this example."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the next code snippet, we introduce an implementation of the above cost function, called `cost_function`. The function takes as its first input $x$, and the other inputs are the other terms defined above. It returns the value of $J$ above. \n",
"\n",
"In the same snippet, we shall also create some synthetic data to play with. `y_smooth` is the ideal true function, to which we add noise (with a standard deviation of 0.15) to create `y_noisy`. We also simulate missing observations by creating `obs_mask`, a random 0/1 array. The prior is set to 0.5 for all values of x with a standard deviation of 1 (this is an uninformative prior). $\\sigma_{obs}$ is set to the value of the noise figure we added, so in this case, 0.15."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import scipy.optimize\n",
"def cost_function ( x, y, x_prior, sigma_obs, sigma_prior, gamma, obs_mask ):\n",
" \"\"\"\n",
" Variational cost function with a weak constraint\n",
"\n",
" Parameters\n",
" -----------\n",
" x: The current estimate of the state\n",
" y: The observations vector\n",
" x_prior: The prior estimate of the state\n",
" sigma_obs: Observational uncertainty (standard deviation)\n",
" sigma_prior: Prior uncertainty (standard deviation)\n",
" gamma: Inverse of the model term variance\n",
" \"\"\"\n",
" I = np.identity(x.shape[0])\n",
" D1 = np.matrix(I - np.roll(I,1))\n",
" D1a = D1*D1.T\n",
" j_obs = 0.5*np.sum((x[obs_mask]-y)**2/sigma_obs**2)\n",
" j_prior = np.sum((x-x_prior)**2/sigma_prior**2)\n",
" j_model = 0.5*gamma*(np.sum(np.array(D1a.dot(x))**2))\n",
" return j_obs + j_prior + j_model\n",
"\n",
"x = np.arange(1,366, 5 )\n",
"y_smooth = (1-np.cos(np.pi*x/366.)**2)\n",
"y_noisy = y_smooth + np.random.randn(x.shape[0])*0.15\n",
"obs_mask = np.random.rand(x.shape[0])\n",
"obs_mask = np.where ( obs_mask>0.7, True, False )\n",
"x_prior = np.ones_like(x)*0.5\n",
"sigma_prior = 1.0\n",
"gamma = 100\n",
"sigma_obs = 0.15\n"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 121
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, we want to solve the problem. We use `scipy.optimize.fming_bfgs` to minimise `cost_function`. We start from the prior estimates. The loop sweeps over the value of gamma, to demonstrate its effect:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.plot(x[obs_mask],y_noisy[obs_mask], '-sg', lw=0.5)\n",
"for gamma in np.logspace(0,4,5):\n",
" retval = scipy.optimize.fmin_bfgs ( cost_function, x_prior, args=(y_noisy[obs_mask], x_prior, sigma_obs, sigma_prior, gamma, obs_mask), disp=1, retall=1, fprime=None)\n",
" plt.plot(x,retval[0], '-',lw=1.4, label=\"%4g\"%gamma)\n",
"plt.plot ( x, x_prior, '-k', label=\"Prior\")\n",
"plt.legend(loc='best')\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Optimization terminated successfully.\n",
" Current function value: 4.369565\n",
" Iterations: 50\n",
" Function evaluations: 5475\n",
" Gradient evaluations: 73\n",
"Optimization terminated successfully."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Current function value: 7.151652\n",
" Iterations: 76\n",
" Function evaluations: 7200\n",
" Gradient evaluations: 96\n",
"Optimization terminated successfully."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Current function value: 11.060388\n",
" Iterations: 80\n",
" Function evaluations: 6975\n",
" Gradient evaluations: 93\n",
"Optimization terminated successfully."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Current function value: 14.717567\n",
" Iterations: 79\n",
" Function evaluations: 6600\n",
" Gradient evaluations: 88\n",
"Warning: Desired error not necessarily achieveddue to precision loss"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Current function value: 17.879170\n",
" Iterations: 100\n",
" Function evaluations: 44428\n",
" Gradient evaluations: 590\n"
]
},
{
"output_type": "pyout",
"prompt_number": 122,
"text": [
"<matplotlib.legend.Legend at 0x15ab6890>"
]
},
{
"output_type": "display_data",
"png": 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89uell5cXv//+O++99x69evXCy8uLRo0aMXjwYH799VdGjhyZL6/5ZowfPz5H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\nOeu8efPm7Ny5k6FDh/L5559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HH+eHH37gwoULxMbGMnXqVMaNG4dhGIwaNQrnLMbzBAUF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ZSPc6zs6iInYWFZFXsUvxqbTz9KSrvz9d/P0578Sffn609dRvLFsKJQAn6fVtrwaf0zO6Jysz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\nAHSCBgAAAABJRU5ErkJggg==\n"
}
],
"prompt_number": 122
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the previous plot, look at the effect of $\\gamma$: For low $\\gamma$ (eg blue and green lines), we have a very good fit to the observations (green squares), but then the estimates drift to the original prior, as (i) the observations don't constrain them, and (ii) the smoothness term is very small. As $\\gamma$ becomes more important, we have a gradually smoother solution, that starts departing from the observed points, as the optimizer is balancing fit to the observations with fit to the \"process model\"."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can see how the effect of noise in the observations (ie information content in the observations) affects the inference problem:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"x = np.arange(1,366, 5 )\n",
"y_smooth = (1-np.cos(np.pi*x/366.)**2)\n",
"y_noisy1 = y_smooth + np.random.randn(x.shape[0])*0.15\n",
"y_noisy2 = y_smooth + np.random.randn(x.shape[0])*0.5\n",
"obs_mask1 = np.random.rand(x.shape[0])\n",
"obs_mask1 = np.where ( obs_mask1>0.7, True, False )\n",
"obs_mask2 = np.random.rand(x.shape[0])\n",
"obs_mask2 = np.where ( obs_mask2>0.7, True, False )\n",
"\n",
"x_prior = np.ones_like(x)*0.5\n",
"sigma_prior = 1.0\n",
"gamma = 100\n",
"\n",
"plt.subplot(2,1,1)\n",
"sigma_obs = 0.15\n",
"plt.plot(x[obs_mask],y_noisy[obs_mask], '-sg', lw=0.5)\n",
"for gamma in np.logspace(0,4,5):\n",
" retval = scipy.optimize.fmin_bfgs ( cost_function, x_prior, args=(y_noisy1[obs_mask1], x_prior, sigma_obs, sigma_prior, gamma, obs_mask1), disp=1, retall=1, fprime=None)\n",
" plt.plot(x,retval[0], '-',lw=1.4, label=\"%4g\"%gamma)\n",
"plt.plot ( x, x_prior, '-k', label=\"Prior\")\n",
"plt.subplot(2,1,2)\n",
"sigma_obs = 0.5\n",
"plt.plot(x[obs_mask],y_noisy[obs_mask], '-sg', lw=0.5)\n",
"for gamma in np.logspace(0,4,5):\n",
" retval = scipy.optimize.fmin_bfgs ( cost_function, x_prior, args=(y_noisy2[obs_mask2], x_prior, sigma_obs, sigma_prior, gamma, obs_mask2), disp=1, retall=1, fprime=None)\n",
" plt.plot(x,retval[0], '-',lw=1.4, label=\"%4g\"%gamma)\n",
"plt.plot ( x, x_prior, '-k', label=\"Prior\")\n",
"\n",
"#plt.legend(loc='best')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Optimization terminated successfully.\n",
" Current function value: 7.029514\n",
" Iterations: 49\n",
" Function evaluations: 5400\n",
" Gradient evaluations: 72\n",
"Optimization terminated successfully."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Current function value: 12.298023\n",
" Iterations: 80\n",
" Function evaluations: 7200\n",
" Gradient evaluations: 96\n",
"Optimization terminated successfully."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Current function value: 17.501796\n",
" Iterations: 80\n",
" Function evaluations: 6825\n",
" Gradient evaluations: 91\n",
"Optimization terminated successfully."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Current function value: 19.945407\n",
" Iterations: 78\n",
" Function evaluations: 6450\n",
" Gradient evaluations: 86\n",
"Warning: Desired error not necessarily achieveddue to precision loss"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Current function value: 23.007590\n",
" Iterations: 112\n",
" Function evaluations: 63521\n",
" Gradient evaluations: 844\n",
"Optimization terminated successfully."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Current function value: 7.181692\n",
" Iterations: 19\n",
" Function evaluations: 2925\n",
" Gradient evaluations: 39\n",
"Optimization terminated successfully."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Current function value: 8.727650\n",
" Iterations: 69\n",
" Function evaluations: 6075\n",
" Gradient evaluations: 81\n",
"Optimization terminated successfully."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Current function value: 9.727234\n",
" Iterations: 82\n",
" Function evaluations: 6750\n",
" Gradient evaluations: 90\n",
"Warning: Desired error not necessarily achieveddue to precision loss"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Current function value: 10.377622\n",
" Iterations: 85\n",
" Function evaluations: 20293\n",
" Gradient evaluations: 270\n",
"Optimization terminated successfully."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Current function value: 10.983200\n",
" Iterations: 79\n",
" Function evaluations: 6300\n",
" Gradient evaluations: 84\n"
]
},
{
"output_type": "pyout",
"prompt_number": 123,
"text": [
"[<matplotlib.lines.Line2D at 0x164e1510>]"
]
},
{
"output_type": "display_data",
"png": 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6OhMCAvg9ZyI/AI+rmUxfFEml61XQZebf3sTVBKeRTjiNcGLLMZPcJ+j3N9AL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ZbKUFWVR9Y9Qs+mPZn1wKxbX1AOFy9qY50B2reHv/+umr7tirIQ0AYStL53AU/dyKTP8T5YqoV/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\nMZUHASdPQtOmahiQv78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fcX+VvPjvfTiuW8zZk75Us8SCEEIIcd1Zd3wdk9dPpp5bPT7o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\nnwAAAABJRU5ErkJggg==\n"
}
],
"prompt_number": 123
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can also see the effect of having an informative prior, maybe from some climatology or something. We will assume that the prior mean is `y_smooth`, with a standard deviation of 0.3, and we will use the same noisy observations as the bottom panel in the previous plot:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"sigma_prior = 0.4\n",
"x_prior = y_smooth + np.random.randn ( y_smooth.shape[0] ) *0.1\n",
"sigma_obs = 0.5\n",
"plt.plot(x[obs_mask],y_noisy[obs_mask], '-sg', lw=0.5)\n",
"for gamma in np.logspace(0,4,5):\n",
" retval = scipy.optimize.fmin_bfgs ( cost_function, x_prior*0 + 0.5, args=(y_noisy2[obs_mask2], x_prior, sigma_obs, sigma_prior, gamma, obs_mask2), disp=1, retall=1, fprime=None)\n",
" plt.plot(x,retval[0], '-',lw=1.4, label=\"%4g\"%gamma)\n",
"plt.plot ( x, x_prior, '-k', label=\"Prior\")\n",
"plt.legend(loc='best')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Optimization terminated successfully.\n",
" Current function value: 6.436259\n",
" Iterations: 10\n",
" Function evaluations: 1575\n",
" Gradient evaluations: 21\n",
"Optimization terminated successfully."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Current function value: 8.884793\n",
" Iterations: 25\n",
" Function evaluations: 3825\n",
" Gradient evaluations: 51\n",
"Optimization terminated successfully."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Current function value: 10.348134\n",
" Iterations: 85\n",
" Function evaluations: 7275\n",
" Gradient evaluations: 97\n",
"Optimization terminated successfully."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Current function value: 11.116676\n",
" Iterations: 81\n",
" Function evaluations: 6600\n",
" Gradient evaluations: 88\n",
"Optimization terminated successfully."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Current function value: 13.668361\n",
" Iterations: 82\n",
" Function evaluations: 7072\n",
" Gradient evaluations: 94\n"
]
},
{
"output_type": "pyout",
"prompt_number": 127,
"text": [
"<matplotlib.legend.Legend at 0x16b21f10>"
]
},
{
"output_type": "display_data",
"png": 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gIjWVQ3FxHIqP51BcHEfj44n5d5eWtm3ht98Y+NNUWPIRrZmK3mDEI/I2lSIi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\n3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tITPuEJEAh0S3kiICkpiV9//RWZTMb48eOrZG+g70D2RO4ht/Dh6/CbeJlovQE3uMHL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\nQXwAAAAASUVORK5CYII=\n"
}
],
"prompt_number": 127
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Exercise"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The optimisation routine works by minimising `cost_function`, but it approximates the partial derivatives of `cost_function` with respect to `x` numerically. These derivatives are easy to calculate, so the exercise is to write some code that calculates them. \n",
"\n",
"**Hint**\n",
"You can find expressions in the [EO-LDAS paper](http://www.sciencedirect.com/science/article/pii/S0034425712000788)!"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
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