{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Random numbers\n", "Module 4 of Phys212/Biol212 class\n", "### by Ilya Nemenman, Apr 1, 2019" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "['Lock',\n", " 'RandomState',\n", " '__RandomState_ctor',\n", " '__all__',\n", " '__builtins__',\n", " '__cached__',\n", " '__doc__',\n", " '__file__',\n", " '__loader__',\n", " '__name__',\n", " '__package__',\n", " '__path__',\n", " '__spec__',\n", " 'absolute_import',\n", " 'beta',\n", " 'binomial',\n", " 'bytes',\n", " 'chisquare',\n", " 'choice',\n", " 'dirichlet',\n", " 'division',\n", " 'exponential',\n", " 'f',\n", " 'gamma',\n", " 'geometric',\n", " 'get_state',\n", " 'gumbel',\n", " 'hypergeometric',\n", " 'info',\n", " 'laplace',\n", " 'logistic',\n", " 'lognormal',\n", " 'logseries',\n", " 'mtrand',\n", " 'multinomial',\n", " 'multivariate_normal',\n", " 'negative_binomial',\n", " 'noncentral_chisquare',\n", " 'noncentral_f',\n", " 'normal',\n", " 'np',\n", " 'operator',\n", " 'pareto',\n", " 'permutation',\n", " 'poisson',\n", " 'power',\n", " 'print_function',\n", " 'rand',\n", " 'randint',\n", " 'randn',\n", " 'random',\n", " 'random_integers',\n", " 'random_sample',\n", " 'ranf',\n", " 'rayleigh',\n", " 'sample',\n", " 'seed',\n", " 'set_state',\n", " 'shuffle',\n", " 'standard_cauchy',\n", " 'standard_exponential',\n", " 'standard_gamma',\n", " 'standard_normal',\n", " 'standard_t',\n", " 'test',\n", " 'triangular',\n", " 'uniform',\n", " 'vonmises',\n", " 'wald',\n", " 'warnings',\n", " 'weibull',\n", " 'zipf']" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#Initialization\n", "import numpy as np\n", "import numpy.random as nprnd #note the new module we will be using\n", "import matplotlib.pyplot as plt\n", "\n", "%matplotlib inline \n", "dir(nprnd) # see which new functions exist in this new module" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Build-in routines for pseudo-random numbers generation\n", "We will first experiment with the build-in routines for generating uniform standard random numbers (floating point numbers between 0 and 1)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0.28801873 0.24311972 0.33676572 0.98767638 0.16936002]\n", "[0.79537143 0.50058157 0.16132389 0.63208191 0.89001868]\n", "[0.36894902 0.31879187 0.48100471 0.93016291 0.41335068]\n", "[[0.92162918 0.70618748 0.64778434]\n", " [0.61216894 0.75695744 0.37548275]\n", " [0.19277267 0.21060764 0.46856178]\n", " [0.02751982 0.84540123 0.54212513]\n", " [0.2714103 0.36446204 0.35171055]]\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Examples of random number generation using built-in routines. The r1 variable should be pointing at an \n", "# array of 5 random numbers. We do the same calls multiple times to illustrate that the numbers are, indeed,\n", "# seeminly random (or rather pseudo-random)\n", "r1 = nprnd.random(5)\n", "print(r1)\n", "r1 = nprnd.random(5)\n", "print(r1)\n", "r1 = nprnd.random(5)\n", "print(r1)\n", "\n", "# The following command generates a 5x3 matrix of pseudo-random numbers.\n", "r2 = nprnd.random((5, 3))\n", "print(r2)\n", "\n", "# Finally, the following command generates n_rand pseudo-random numbers and histograms them into 50 bins,\n", "# illustrating that the numbers we generate are, indeed, uniformely distributed.\n", "n_rands = int(1e4) # how many random numbers to generate\n", "x = nprnd.random(n_rands)\n", "plt.hist(x, bins=50)\n", "plt.xlabel('number')\n", "plt.ylabel('frequency')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Most pseudo-random generators fail not because they do not distribute the numbers uniformely along the interval $[0,1)$, but rather because they produce correlations among the generated numbers. For example, making a scatter plot of two consecutive generated numbers against each other, $x_{i+1}$ vs $x_i$, may show some structure, indicative of dependence. We can plot the pairs of consecutive random numbers from the built-in generator against each other to see that no structure is visible. In reality, this generator passed a lot more stringent tests, but this is a good beginning." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(x[0:n_rands-1],x[1:n_rands],'o')\n", "plt.xlabel('Random number i')\n", "plt.ylabel('Random number i+1')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Linear congruential random number generator\n", "Most pseudo-random generators in use today have underneath them some version of a linear congruential generator illustrated above. They may have bells ans whistles on top, but the core remains the same. In **your work** part, experiment with the generator by using different multipliers, moduli, and increments. What happens if the multiplier has common divisers witht he modulus? Do the numbers still look reasonably random?" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# simple linear congruential random number generator\n", "def lcrng(seed=10, multiplier=7**5, modulus=2**31-1,increment=0,n_rands=1):\n", " # seed,multiplier,modulus, and incrment are the corresponding parameters of the generation\n", " # the default values of parameters are one particularly good generator, similar in quality \n", " # to the built-in one.\n", " # n_rands -- number of random numbers to be generated\n", " rand_flt = np.zeros(n_rands) # allocate memory for our pseudo-random numbers\n", " rand_flt[0] = seed # seed\n", " \n", " for i in np.arange(1, n_rands): # generate the pseudo-random integres\n", " rand_flt[i] = np.mod(rand_flt[i-1] * multiplier + increment, modulus)\n", " \n", " rand_flt = rand_flt / modulus # transform the pseudo-random integers into pseudo-random standard uniform numbers\n", " return rand_flt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Having defined the generator, we can now check that its default version produces correct spread of numbers over the range $[0,1)$ and shows no correlation between the consecutive samples." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "n_rands = 1000 # we will generate these many numbers\n", "\n", "x = lcrng(n_rands=n_rands)\n", "plt.hist(x, 50) # show the resulting histogram of random numbers\n", "plt.xlabel('number')\n", "plt.ylabel('frequency')\n", "plt.show()\n", "\n", "plt.plot(x[0:n_rands-1],x[1:n_rands],'o')\n", "plt.xlabel('Random number i')\n", "plt.ylabel('Random number i+1')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can explore how choosing the parameters of the generator affects its performance. Make sure to make your own choices, but here's one that we came up with in class, which turned out to be not too good. Notice the patterns of correlation among consecutive random numbers." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = lcrng(seed = 10, multiplier = 77, modulus = 8100, increment = 2, n_rands=n_rands)\n", "plt.hist(x, 50) # show the resulting histogram of random numbers\n", "plt.xlabel('number')\n", "plt.ylabel('frequency')\n", "plt.show()\n", "\n", "plt.plot(x[0:n_rands-1],x[1:n_rands],'o')\n", "plt.xlabel('Random number i')\n", "plt.ylabel('Random number i+1')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Examples of using the standard uniform pseudo-random number to generate other types of pseudo-random numbers\n", "Make sure to run each cell multiple times to convince yourself that the generated numbers indeed change." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# generating integer randoms 1...4\n", "rand4 = np.floor(nprnd.random(1000)*4)\n", "plt.hist(rand4)\n", "plt.xlabel('number')\n", "plt.ylabel('frequency')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# generating integer 1...6 with nonuniform probabilities \n", "p1 = .2\n", "p2 = .3\n", "p3 = .1\n", "p4 = .15\n", "p5 = .1\n", "p6 = 1 - p1 - p2 - p3 - p4 - p5\n", "\n", "rand6 = nprnd.random(1000)\n", "\n", "for i in np.arange(1000):\n", " if rand6[i] < p1:\n", " rand6[i] = 1\n", " elif rand6[i] < p1 + p2:\n", " rand6[i] = 2\n", " elif rand6[i] < p1 + p2 + p3:\n", " rand6[i] = 3\n", " elif rand6[i] < p1 + p2 + p3 + p4:\n", " rand6[i] = 4\n", " elif rand6[i] < p1 + p2 + p3 + p4 + p5:\n", " rand6[i] = 5\n", " else:\n", " rand6[i] = 6\n", "\n", "plt.hist(rand6)\n", "plt.xlabel('number')\n", "plt.ylabel('frequency')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following is a bit more complicated. We discussed in class (see your lecture notes) that $y=-\\log x$, where $x$ is a standard uniform (pseudo)-random number generates a standard exponential (pseudo)-random number. Without repeating the derivation here, let's just verify this. First, we generate exponential random numbers using the built-in function. Second, we compare the built-in functio to our own generator. We also do the comparison on the semi-log plot to illustrate that the bumbers are, indeed, exponentially distributed. The built-in and log-uniform are indistinguishable -- and, indeed, the built-in function does just that -- the log of the uniform number." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "n_rands=int(1e5)\n", "# First, we generate exponential random numbers using the built-in function.\n", "plt.hist(nprnd.exponential(size=n_rands), 30)\n", "plt.xlabel('number')\n", "plt.ylabel('frequency')\n", "plt.show()\n", "# Second, we compare the built-in functio to our own generator. We also do the comparison on the semi-log plot\n", "# to illustrate that the bumbers are, indeed, exponentially distributed. \n", "plt.hist([nprnd.exponential(size=n_rands), -np.log(nprnd.random(n_rands))], 30,log=True)\n", "plt.xlabel('number')\n", "plt.ylabel('frequency')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A uniform random number in a circle\n", "This is not a trivial problem -- and, in fact, some of consulting and data science companies use this during interviews. We will explore multiple different ways of generating such numbers. \n", "\n", "First attempt: We will generate a random $x$ coordinate and a random $y$ coordinate. We will combine the two to fine the angle defined by them. We will then generate a uniform radius between 0 and 1, and we will put the point at this radius and at the chosen angle. \n", "\n", "Second attempt: We generate the random radius and the angle directly, and generate $x$ and $y$ pairs directly from the angle and the radius.\n", "\n", "Third attempt: This is similar to the second, except that the random variable we generate is $r^2$, not $r$, and we then calculate the distance to the point by taking a square root of the pseudo-random generated number.\n", "\n", "Fourth attempt: We generate a random $x$ coordinate between $(-1,1)$, and the same range for the $y$ coordinate. We then reject all of the points that fell outside the unit circle. In this case, we do not know how many pairs of points to generate precisely, because we do not know how many will be rejected. So we make an estimate: the area of a square is 4; the area of the unit circle is $\\pi$. So if i want to generate $\\mbox{n_nands}$ points, I should generate instead about $4 \\mbox{n_rands}/pi$. I then check how many actually got generated, and if not enough were, then more are." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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vvXll2wonKVOz1kAa6Th2AG0z/lDUHEPDVSUhGKAW9t1ajSxrVrrPymZwzYA2AiitRENkyWfJ4hYYr01i/0sn257tw9ct1a5G5kr2dFwxdDHyzoRtM1ff6xc5M/e5totzN2R0zM69LyuFHUFNddGJFUwW5HEM+6xsdLTbaSXq0h7bikL8nY6sc4Uo8KR6Nl0Y81zwN0TF0OXIY2rQJfmcOTfRZPT0vX5Rpg8fk4KLQLH5BHyEtk4QMNBcmeiuJ7abqshlha8ZplPhsa6mJ1t7XJW7GJO64kMmmMyy0xU11g2IimEWQzebGh2v5bKVhk5g8p3duwg4U3SM70rC5Ft5cOhIi41aXO/gsVPK7ab7mJDu83T4ZZ7nyCPoXJSibozY2uO7wpEVRFviZZkARktItM28l6WG+GxBzHye4XAR0iEzbH0zql3g2z6X41dvf14Z6mqqR6yrTGfLrDZdSwXfpDnV/VUFhcS1de9Ud517rluKhwdXObXFdj2fsWA7X2fKIQCv77jJem2fsqiu15npWdEx83kOwHWmHdKEUEQCk2/7bDO5oeEqzpyfUJ5rqkesKrQD+NXUdrmP7+pBdX9XB6+MwTUDOHjsFB4/cLx5PgN49lAVay9fnMn3kmcs2FYWeaPydKsKH8jX6baiVUUiKoZpRF6TjOuHGdKEEELJpJ97USVRzu5NFdcAvUBRVXnzxXhtEtufO4qztSlvpeB6fVcnq0/f2t7p/pdOtikVuS0+YzLEWDD5rLKYcorkaepEVne3ICqGaUKI2YfrhxnSVppXyaieOykTkhJ52X9NAiWUMzVLlIsPXJ2suj5Pm5Nc3qlpzPiOyaKds77RXar2b37mMLbtPhqEKXa6uK2mAzGPYZoQoqCNa0ZqyAzbvDH6queuTTIuWtATLAN4pkSNuDhZAX2f39OIt/fpM9OY8R2TuhyCsfMXsuttsOWa2DLSZejGlkyNkacGg67vZmNWdJAVAxHdCOD3AJQBfJ6Zd6T2fwTATgCi5/4nM3++se9eAA82tj/MzF8K0aZuR4jZh89KIFSYad4Yfd3zjY7VMPxpP+I9HVy4+IF6VrXOVKRz7gKo14TmOjPnmfMTmcxWcg6EbSyEzIswjZlNmup1uvaJ+6cz7E+PuUW9hbbZu3w7eUw/pnE12/wNuRUDEZUB/D6ADwB4E8C3iWi3okTnLmb+ROrcxQC2AliL+nd4qHHu6bztmi642jhDmGTEDEkXTVMU8igZ3XP39SZYt2NfkOiPtCAVBXHSpiqRVS1i30U/mpQCAPSUCDvvuEppkz9zbsKJ+E/kQJj6JF0atGjFrssBMI1JcV76mV0EcGibvQtrLHDBbOaraOW+U91nNvkbQqwYrgHwCjO/BgBE9CSAWwG41G7eAODrzHyqce7XAdwI4IkA7eo4fGZAeez+Kvpr19rGPijCkad67qRMeOfsRAuPTV5O/LQgNT2LfJwL905t8gLfVFrQLqokSMpkXUXIlAudjpfXKZms7chaOc/m7/Ade+uvXNIybnTo622vwaAaX7o2mEJpZ4u/IYRiGADwhvT7TQDXKo67nYh+CcD3AWxi5jc0585YdeszA8pjHuhEdERRoXmq53aZZed9PtcZt+uHrXMcj47XkJRISwoosP7KJS1tA6afQiNLOwSPlEpI2la/ptVjeuxt2jWCg8dOGfMt9r900ng/oK7omNtrMKiixLIEBMwU/5YNIRSDil8sPU6eA/AEM58joo8D+BKA6x3Prd+E6D4A9wHA0qVLs7e2QPj6DbKaBzoRHVGk8kk/9/Ite5zOK2I25lqzOg2T47g2xeid14OtN69UMo0C7ULMNhaKLpfp2o40fHmkZOhWKCrBzQAeP3DcmG9hGh8ENPvNxZdiG//rr1zSkg8i2j5bsqJDKIY3AVwm/X43gBPyAcz8Y+nnHwP4benc96XOfUF1E2Z+DMBjQD3zOU+D88D0gXZqFtGJ+3QyNM/VNhzy+XQlTZMSWU1BsgAw9dPgmgHcrxFCPnw+utnrwWOnsOc7bzWfoa+SYNstK9tyI2T/SW9SwvjEFJjr2dl3X3uZV9bz0HBVSeeehqDZBvQrTN0KRSe4bdTdujeWzgZ38aXYzFzPHqq23I8A3H51ZynUi0QIxfBtAFcQ0XLUo47uAvBr8gFEdAkziyoZtwD4+8bfewH8dyLqb/y+AcADAdpUCGzLy07ZivP6JzrhHPe5t0sUUch+NFFciJrVwIXqcQvnlZGUSy1lInfufRmbdo0o614D9X4ymVkAYNmWPU4BA7rZa9qePjpea9bJBqAswzpWm2run2RuXsNFOaTrctvgYn5UrVBMRHg66m7d2FGNG5fvxzT+dZnoLqasmYLcioGZJ4joE6gL+TKALzDzUSJ6CMBBZt4N4L8S0S0AJgCcAvCRxrmniOi/oa5cAOAh4YjuRtiWlz422jymgaw26bzO8aREGDs/geVb9ng/GwDrvUNx0tj61kZxMTpea4nPP3N+EsAk+ipJG3mdSikIIWOaxQq4CE+fVZooxATYaxkLPPHiG06KYefel52VgoCr+VF+Z32G4kwu1N0COqXr8v2EDOudiYgkeh5YprGFu5B6ySiCiM4FvmR18seqitlXtVn3bPN7SkrzQ/reeW3pLn2riygRMBHg6VYAqip2tvvIMJHf+VQpE22Epp06/LAxfk397/M86faYvg/VOyuXCJMpJaQab6Y2yX6FLN+Vri9CklJ2GpFELzDyRF+kMV2cK3mc4+t27HOKVdc9m25WJ987RCSUS9+afBqVpGycaeuE0BRzm/Bz9Z0ArVFOaWHkmrAn3xdw92OUiZr3zhKJA1wIv3UxP6YnHP98tob0QmRyitHfm6B3Xk8m6m4ALdnO4hl8EDqsdyYhUmJYIFL279dEl7hEX6RhqhVQZGq9K4WGCq5KxXc5Ld87BE2ISzttJU19iswLqPrQp+yk8EmoSl0CaKM06U30n+76K5fgzDk1u6wKd19bjx1xoeZISu2BhEmZmgrMRpeSfsbR8XalIDA6VrPSYbj0se8YSkNVRjYUxUy3Iq4YDHDh4ZczWF1hmuUUmVqfdaYzNFw1OlnTv1XPpqKfSN/b1CeucM0iBvQ25oPHThkTpVzJ69KZsrrMatknoRPMch3rnXtfbnEip6Eqbl8iYIphjEpypeaQo5L6exNsvXll26pRrAaIgE27RrBz78vYvGEFtu0+6r3yMSH9LrPQkZugW0U9ctuqrjcb5UFUDAa48PBnmV3aTANFmZWyJjA98JUjWpu7XCYU0CsfmX5Cd28hvNIQpg4XuCo/U7y+KbokKRE2XnOZs2Ncvo8qfFR2kNqcmi4TlTKRcv8li+z2b51SXVS54Ay25TmI/UqmU4+IJh/TTNrkGTKabi5RbcuIisEA2ywjT4joI7et8grLC4UsCUy2CB55hWNTPrp7Dw1XtSYFU9Gb9DVC8EeZ+n4KwNrLF3tXPNPRmLiGvgL2d2Hyj7iMp80bViiF95nzrcrfhqHhKj751OG2Z3FVCmWiXOy/Ie3/c4lqW0ZUDAbYnG15QkTFUjT0DCc0XBkrt+0+miuayGQDtq3KVMlqOv4ol6gn03ufnGJsf+6o07PJ91IJ/fHaZEv2rE4Bnj5zzhoRJMZjFiI8gcE1A239CLRyQ9lgW2HakDc6LzS9yGynvtAhKgYDdLMPn4FrW4oWGeEQgkbBNbJmdLzWtDuHLDoEmJ37JvOKC//Npl0juH/XSIuit5n6XCgzHhw64iT0XcSnyZ8AtIdJ5hlPo5pn070fFbusqw9BoEQAc77QUhlZqWZUKDoCqVNUJ76IisGAELOPkFz7Dw4dwRMvvtEiZHQrl1AkeL6hkgK+dlgtoVol8c4KlmHjvxE9qeofHZ2FDUPD1TYenaKQFlJ5x6yJ2C4N1RjL0v5ujugJvQKR0c01pKNisCDv7CMU1/6DQ0eUkTKifKG4joBtpeI6U0l/GD7FaUIUHdp2y8pc9xD9PDRctQqudBa7jhOor5IY+88l4xkwFwNyxQJF2GqeMbt5wwpsfuZw2/t952y7n8ElOMMEVURTNyLkCsTFvNgNju2Yx1AwXGK7ZehKHT7x4hvK44G6DXj7c0dbtrnU9k3Hy+vyJwbXXCivOLL1Buy846qWGO5+DYWBzg6resbBNdnKj5psvaKfxfO6QO63bbesbPtASgD+76suMfafSVmViZrPd891S53zHHQQ1dJC5b4MrhnAwnnt88XalPsYc0XvvJ5pF4A+sJUhdTlfHjc682I3OLbjiqFg+CxFTUtLmzMvbff2JQHzmamkZ1A6GgqV8rMtn30Fhc7UJTONrtuxL3PsfLlMmJJmz+Uy4a8Ov6Xsv08+dbh5Dd3qJM1muvbyxcboNBeEnmW+rWFOPT1Wa1k1+GR2q9ANAtAVRWXlq9ANju24YugA5Bm3qaC5SWD7xPID5pVKnhC8vLP9ENnNMlT3/tzG1RjZekPz/q4CKK3Mdu59uc2kIorLqzDJjAe+cgTrr1yiXQl8+cBxrN7+fHO2KcaGLvKqRGiyvZoQQsiKd2uagsjvySezW4VOCMC8s3yBIrPyZYgs8ulGXDF0EUwC+57rlhqzcdPCw7RSyRrS6DPbFx9k+t5FxIXrVho2nv6+SoKF8/VcPFnaNF6bxP6XTuKR21YpY/mB9twPwB4BZwtXzSpk5aQ7F5+H3CfpMabLw1ChE9xCIZ27IcatywprYZeY16JiCIw84Wcm848wPzz+4nGkv72kREonrU5gZg3BczVBmT7ITsWFu/D0y0VtVMhqKhFFenSZzEB7v9lMjjbiv/S7cxmH6T5yEenp95TO7HaJYMuTwOaDkFnLIcatS4SfzozXaUTFEBB5Zyg2gf3w4Co8PLgqd+yzSgjJGbi6a7rOmnQf5P27RtDfmyApUUsWrCtfk88zu/D0A1CuagSyhuoKYWFTLII0Ub6/jrZC15bepIR5PaUWPiLAXvsC8I8qsr2n9Ljq603wztmJtnfdqfDUkKvTEPkMcv/oxkU3+BeAWI8hKHRZzH2VBCNbb3C6RicSXtL3SBefAdQf8OrtzzvVVLCZPZIyYeG8nmZFNFe+Jp9EQ10bCMCjG1crM3x19SV8nMPi+iIk2EexCFOOKTfF5b0tSErKJDzf9wSo60z4IE2xTVRPostaa8Pn2zDVschClRLy25yumiyu9RiCKAYiuhHA76Fewe3zzLwjtf83AHwM9QpuJwH8B2Y+1tg3CUDEEh5n5lts9ytaMWQdAKYP7XMNYTEd7UpfIz0gdbZlWZAMDVeV8e1JibDzQ1e1tMOlsIxLcSDxjDrBXCbCZ++8StkHJiV9bmLKuJpQtcunWE5/bwLmullgQVLC2dqUd76Ci5DIUsBHrhlhO99HUNnGZl5BmOV8F3OifH6ns5CnI+u5Y4qBiMoAvg/gAwDeRL1M593M/D3pmPUAXmTmMSL6dQDvY+aNjX3vMPNFPvcsUjHkGcC2GUoeml6dQL/nuqVehG4+wkQWJLrz+nsTDH+6dTXkMlNWVfXS9b2NOE71bnTX0s2mTe1yfSZXUIMCwgbbmNFVFLRdUwgg0yTBZ0bt8s3krXpmUvSmAALbik/cX/d+fZPwVKu6LCVqi1IaroohRLjqNQBeYebXmPk8gCcB3CofwMz7mXms8fMAgHcHuG8hyBOWZrI35g0n1NE5PH7guFcInm8Uhe08FbeOHEKqQ4mord26vjeF6ureTboNgo7axnMkCubYQnL7KgmSsl8IsYDrXMz2rnT9QoA2jFTQX+vCjB/duBo/tIRVp+HyzeS192vH33itJdHw/l0jWPNQeziw7k2J6+r8LT4JhKrE0S8fOO6cSGq6TsgkRheEcD4PAJDTct8EcK3h+I8C+Jr0ewERHUTdzLSDmYcCtCkz8gzgwTVqdkogv1NJd38GgnAS2YrP9PUmXs8lolV0MzER8y+OBfTPKJhSfSmlxXVdZ/qCBtsnJDdvcpoJjPpMWbyHdC0H03kmWvfaFGPb7qPN53EJMzbB5ZtZVEmU/inX78InQkwIc+DCGLBFFZm+b9dIJhdnvsu1uqEGRIgVg0oZK0ctEX0YwFoAO6XNSxtLm18D8Dkieq/m3PuI6CARHTx5Ul9IJS+QKOmqAAAgAElEQVR0A3VRJXFKlNl680ovCoy87QL8OYlU7bvnuqXaBLWh4SreOdteKtIlGUfMSlWz2/SsUveMoj26GbKpb1wjb0RZz/0vnXReMdqS00xQlchUQXBhbX76cFOw2XIFBvoqzbbpMDpew4NDR/DeB76KZVv24L0PfBX3/PHfeM1UbQlxMk/VmfOK8VNyT+byTaZLvzMbNY1NQbl8Y3lXP7b9ncwUD7FieBPAZdLvdwM4kT6IiN4P4FMAfpmZz4ntzHyi8f9rRPQCgDUAXk2fz8yPAXgMqPsYArRbCVVYWlIinDk/4UQr7UOB4duuTZq60z6rkSzt27n3ZWWRFZdkHDGrduGFMYUE6mb/NqXrYo6RHdg6RlVVaKkpOc2Gixb0tBS6F7Zo5QzfgbBQgFCv+SzaaoKcMDnJjG+9eqrtGFnA2iKiZMjvRZVBDtT7wPW7sL0fFXTJeGLVJT+b7R0K02eIvBfb99oNNSBCKIZvA7iCiJYDqAK4C/XZfxNEtAbAHwG4kZl/JG3vBzDGzOeI6GIA6wD8ToA2aWFz6qgE59j5iTYzimlp58L54+tcGlwzgIPHTrXROWdZjdgyhV2zlW3JOC4OW59azFmUmu1jnWJuWRnpIrQIF2ilVeYl1bsxYXSspnTaZ6X6FmCoaz7ngahbIVOUm7Lw045rH/+UCaasfRVUyXiAOsfjkdtW4ZHbVmkZdSeZsWnXCA4eO6UN9nCZILh8r0XXgHBBbsXAzBNE9AkAe1EPV/0CMx8loocAHGTm3aibji4C8DTVzQEiLPVnAfwREU2hbtbaIUczhYZrAlpacC7XRH8IplIfQaWqNuaaCPfw4Kom6VonuOFFERudTds2g3EpRZke7DalmlYOYsYn/BnpvrF9rPIzmOgz0tvTE4P9L51Unuvad6KwT17oaj7LSMrktQoB3OnBCWgzYen8U6oaDza4rs50glRnv9/+3FH0NnJr+ioJ/vlsra3UrAj2WHv5Yu2EUNwjT1RSUVYHH8ypBLesIXM+MfGm0FbbDDpvSGse+MbEu8SA60xfQGv2sa9iVc2mbr96oG2mnJQIFy3o0UYiyc+QZbYuh7aacljSmd6iXSLRa/2VS4IU9rFxHREuVEnT8TjlhWoM6xIjxfEhEs0A+zgKsSITbZ6u7zQvXMNV5xQlRlanjm5pRwSv6AGfamMCnUqCcXFs6bJgdSsxXSSKLnbcZeWkm/GlK9sB9egbnVKQ49Nt9RpMs34bUR8AoMGQ+vZ4rVnoSLSrOjrurBSE4BftWTivjDPnL/SFrSa0LMwOHjtlNAdlgW6WbjI5qt65i7nXNGNXwacmhw0ziS48K+aUYsjq1NEt7XQkaVkVULodebiXfBTK0HDViRlzilmZ/KUT1guSUluYadop6RuWZwpp9YFcJGbb7qNahZ2UCRv/1WVK6ol0aKsOtUkGUX11sW7HvjZl6dpykXgmBPy6Hftw5rxdSBHac2yEnVylUH0gTxZ0fFs2P4/8ztMZ9roKhb7IW21ORl4ncKgkuCIxp+oxrL9ySVtsratTR4T/yTUVdAPEd7uuHVmT7XwSZMSxLsJB136Tc9FUpyGLAg0VmSHuMTRc1Zo5AABcL6ajeg5VaKsOp8dqWL39+dw5D3LfuM5cGWqh+vDgKrz6yAfxuY2rM9VVqCRlfPbOq/D6jpuwecMKPHuoqhxzLqGm4lm2P3dUWQMjXT3OF6Z+19W7qCSlTPLCVAPiwaEj2LRrJHcSXNGYM4pBOPfkIUcAbr86X31cn5wF3QciYujlpbTJ5m8TCD4KxXUmJZfJTA96kyJUKVR5v+48HfIWh5HvMTRcbVZd06E2xc3Z7Le2XI9HN64GgObH7YPR8Zo2A9cVcma26zzflmchck10JVpV6O9tHbO21Z8tE168c53pz5axboMuB6ZMdcp61Xf8yG0/j0c3rvYqN2ualA0NV53MhnkKV4XCnDAl6V4Iox5NkhW+0QMux/uGeKrgMxM3KZmBvkqbg09l2lI5fosKy0v3YVYjyD+9c87ZESmvLvLyJfm0V5WNvuxdFaNTXwXXFbEw5bg4ptP1mm1jzpQJL3IvioTueSalcGVbmLQJpix4WdC7vrfp9mPMCcVgcg7KLyCLo9clZ0F3vLifbJPNEuIpw+QvUCkUnf1XFXmhqp08XrtQsSxL3wH+YXlyH2YhkgOAcxNTzseKfgtpp7ZBECTKtucs0Ut9lURJ42HL47EpwLTgcvXfqXI+RO7F2ssXo08TsOBS3tSEAcM4F+3KajlwmTD4CvrprsswJxSDi806ZBlAF+juZxpcttA+k79Ap1B8Zu2mWWHWD0ueSQolKQrOuFxPJ0hCQe6LTs7iVKy5NvORaoUhV/bzyeMB/ArK+IwjVc6HmFVvu2UlNj99uC28V1Wh0AdFJo25TBhEf7mYHzudzKbCnPAx6LSvHK3hapc3OZZ84MskKmbwNuoK1QA1lVKU7b82O2oWn4AL8rBJbrtlpTPvkC/S/aZ7ThP7axYkZcLayxe3bbeZ/Wz2cB/fk/CpqBzTusTE9Di6/ep6pnL6W7FNMHZ+6KqW66TrfWSBzzj3hW3CIPrLJuxDtysP5sSKQZctuSC5oBdd7PIhVxU+TKKuMwjdNWXaBxVcZ/tFzbrysEmK/b/x1EhbpmpeTHI9Gsbki8iSRWxDbZKVz25ixhUrLFVSl80fYxJsPua+tJk0a93vPGYdE4q6rikcN73K17Evd1vS3JxQDLqXMl6b8ipSH5IO12TbF74Gn2xgkx/FdUafhUcqb9bq+iuXZI6+kiHi6UPDGg3DxZizVM+uUszCF5El017AJY9Hd33dWDB9K93ABRQSuudRzfy33rxyRjz7nFAMwAUCLh0Znstg1QkqE/OmDjYmUVdh61K+0GXQZeWRMl1PRVuQvocp+1YnsNLXHjs/oWR/7QRqU4x/Phvex6F6dl/F7GL7ziqUbOPFZi7yeY5ug2psuwZfzJRnn1NcSaYC8a/vuMk6Y9blFqicfi52whB0F64Fz23ZlioGWXEN3yWujs9ofk/JeWbtU7JztiHU+DHxN8m8SVmEko13zHVc+j7TdCNv7erpRuRKUiCvbVO3lLcxb+oQwuapm5nJLJeq2Z08UzdFSvgyyOri4Mdrk17CXPeh5Q0ZFWGPRUYy5YXsELZFoKlm7IA5RDuEPdvmkzOxoOpWo52ODMyCbqiu1gnMKcWQ17apWgaGsI/nQVbfiCsWVRLjxyorjb7eBO+cncjN2lkm0oat5unXvkrSDHsMwbKpApF7TWcTbEJx+3Pt/E6CPvpsbcrZtJh1hu4yyQL0Ia8qYap7JpvQ7eQqoxuqq3UCcyJcVSBEyJoI4xMUD7o0/04lqLjQcmQdtDYG2XSY6emxmtHW39+bONFZTDJrw1Z9+jUdRDo6Xq8FfPDYKQSOMG1CpRSy3ksXSjo0XDVSR5ho3dPUK1nDhF3GnfhWdI+fjvjTPZNp/OZ5hiwoKmS72zCnFAOgJsPLA90HIsor5s13sGFwzQBuv3qgGUtfJmryPw0NV7Hmoee9iqz09yZNpfkLSxcZP1aflUglKWPrzSvxyG2rWrJYF84ro69Sv6dLXWgfrqSS5nqPHzgeZFbvijz3UgnFLDw6wrSYNa8hjdD5L6Z7loi035HuGe7fNVLId+fLjzZTEcSUREQ3Avg91Cu4fZ6Zd6T2zwfwZwCuBvBjABuZ+YeNfQ8A+CiASQD/lZn3hmhTHvgsTVXmpXQ93CJtpUPDVTx7qNo030wy49lD9Y9h17ff8IqxZwBna1N4dONqK1//pQ0eJRfIiWJDw9UWOooz5ydRSYBHN652ojEX/efC56Pb3y3hFiUAizTVzZrHNISiS6lVQG/KUgnnvGaRkPkvJj+XeI8qM6bpPJMvIyvt9UyJKsqL3FFJRFQG8H0AHwDwJuo1oO+WS3QS0X8C8PPM/HEiugvArzLzRiL6OQBPALgGwKUAvgHgZ5jZOA3NGpXkghBRB7qIjHTh+RAw3SurrX+gr4J/ePus9nzRHy71d9N9Z4pmAdQCQuUsdYlOytMH3YikRNj5oaus/a5KkFSN36yRQ1lgmmwNDVe9iAFF21yj0+Tx4zJuZlKUkS9co5JCmJKuAfAKM7/GzOcBPAng1tQxtwL4UuPvZwD8CtWLP98K4ElmPsfMrwN4pXG9aUOe5bWAKat5064RLAtoXgpVuCZ9TdP54qNRLauTMjVNQ8K8AKBpVjM56zdvWNFGb5GUSLlMl00ZQLs/oZKUcd17+i1POrNQm2Js230Umzes0NrtRZ+rTDxpOpf1Vy7RmuVC2+pNJlxrBbwUfM2Y8jficl430F5PN0KYkgYAvCH9fhPAtbpjmHmCiN4G8K7G9gOpc6dVTedZXruUeRT7QpmXdNEhttkyAdrSm5daVgzpUEpT/d3tzx3FO2ftCWhNU0da4km/VbNOeSaoMudlQSUpYbzmzr7aSYyO17Bz78v4xfcuxl+/eqotf8ZEjZGOLnv2UBW3Xz2A/S+ddI4cKgJZmEd9zumT6ky4njfboox8EWLFoJq8pKWA7hiXc+sXILqPiA4S0cGTJ7PXULAha9SBHB3hihAzE50z7O5rL0NS1ofD/OJ7F2sLlGzesAJ3X3uZ9lx5NpmeCQLwilSS77lz78vK6l2qCKh0AZS0wvCprpZGtyoFgeroOP7u+Nu457qlzhF2upXw/pdOOkcOFQWfiB4xVnzOeefsRHOcqAIS8rZpNiLEiuFNALIUeTeAE5pj3iSiHgCLAJxyPBcAwMyPAXgMqPsYArRbiay5DllzBfJ+eCZn2NrLF2PTUyNKZ+QPf2ymJhD7dDWBdbNJ336Qbdk653O1sfJwidt3oS+fDRivTWLPd97C8KdvcDrethJ2yYfJky9gOtfmL5DrSsvnqb5TAmMspdiFCe7cxJSTiXW6ooy6Kes7hGL4NoAriGg5gCqAuwD8WuqY3QDuBfA3AO4AsI+ZmYh2A/j/iOh3UXc+XwHgbwO0KTOyRh1kFfAhZia66BCTsE1X1lLh4cFVeHhwlZZawbciXBppp7IpYdCn5KOgL59NjmcVTo/Vmqs2G2yC3zYhUpmiNu0awf27RpzrhOii9MR5uqTDKWa8vuOmlm2671Q33nWZ7mUi3H3tZc5RSUWh27K+cyuGhs/gEwD2oh6u+gVmPkpEDwE4yMy7AfwJgD8noldQXync1Tj3KBE9BeB7ACYA/GdbRFInkIWqQvfh9VUSLJzfg+rouJJTqeiZiWtlrSzXYNSdyvKHZBLuaaSVyOYNK9qKtGSFir48KRMWzuvpajoMX7j6AGyCPy1oF1USEKGZgT52fqJtRi/7y+7fNYJtu49i2y0rnVaR6RWnILn0Gauq79QlUk7GJHPHlYJqZWDro06vJoIkuDHzV5n5Z5j5vcz8mca2TzeUApj5LDN/iJn/JTNfw8yvSed+pnHeCmb+Woj2TAd0tv5tt6zEt7Zcjx/uuMm7sHiR7fJRSKaksnT0ik8Cmqrs40ULwrC0lIlaCh8N9FWw846rclcC6za4CkFdQhpwIWJMUJA8unE1zk1M4fRYrenPsdKP40JmeTqSyTWgo6ixWknK6O9VlwYloGNZ04A+U9sUrdfp7G5gjrGr+iCLhu4mG2Gedukos02zsb5KgpGtNyjPTyf8AfpYcRMjaCUp4fwEe5uI5HuZYve7FSazGKGeHOgzzuTC9apV7IKk5KQIdEibCG1MrKq25fmGXCjffdofql2Af96Rb36PDa55DHNSMdhecrdQ606HojE9O2Amn/ucQUC5PotJcOepliY+IpPi6UZUkjJuv3rAmMXuIyA6QVsuaOxN9wz1Pfky/+oqqHWq/TYqdBV9vy75L91OF3QywW1GwbYsE7TReZPcim5nUTDZOm3Pr9vv8/GqTAEEoDcpWZWCyYQlR9+EQJkIV/zUwiDX0qG/N8Ejt9UDAHbecZX2OJvDX05sU41tV/RVEm1CoQyVibCIesu+38jgmgH0zrObKtPtz5v0Kve/Llw2rRQIaHKeTQdx35yi3QbsL/mBrxzRLts7mfQyXbzveRL8VMf4Rlv4RpsICPLAvzr8ljZpD7CHRtogm8wA4MGhI82Q3jIRrntPP7716qlM106jd16Pk3O2RKSNTkr3v6sZTjV7lR3Lutl3OpKpyBVvlm/ENo5VPo28Sa+2/lfVdGHUQ8UfP3Acfb0JkhK1BGUUHbgy5xSD6SXbYvA7mfQyHbzvIgFINXgvNdg6BVRRSqEUnC3aaZIZu/72DahS00qANvqmXkOiBtectvSET4T0yli2ZY/bxSxQOWdVSm2SWatss+bXMOoze1P9b120DACseej5FqVRRPhlllK7pnGkC7vNE9ln63+T/0hsPz1Wa1LNvD1e64hZec4pBtNLNgndTie9hAgzBdxnbWJmoxqk8rPbZts+tX917VWtMG6/eqDNgZ2GLsw1LfNlofbAV444KwUAGNXYp+V+DpVDkV4JmJhldco260RCpkYfOz+BbbuPYtOukbYxlA4ZNfkwQq94dd+IiDQC2sejLmzXZNryTXqVx4JtFEwyK1cMadQmGQvn97SsVovEnPMxmELidEJXpo3uFEKE7vnYYHUzG/nZ08R1qvoJQKtpztc+aqJukO3UvlDZg7PMpvsUYY/pfg6VWCdWAvL7GlwzgCnN9auN0EYZpjFNqCuANHVKUiKcOT/RQmsyOl5zsuPb+jTkilfnj9KV2gWy+Tt8zkmPBRfouIHS6KQpe86tGGyZzd0QjeTSThf4lErUDbopZqUJQcCWFe072zKtMOR7+4ad5s3SFnh7rNY0k3Qiu1r1vkzmkLS5Zv2VS+qFiaRjkhLhogU9GB2rYeH8Hqy89Cdw4LXTTT/JvJ4SzpzXC3fTzN/WpyHNsapvRNcvJvOSCmkfiigLa/v+QpjubObcTmDOKQbATCEBdE8RjiwZ2AK+pRKzmq58av+awoPFftNHIR+3IGlf7KYddLbn8MnSFpjCBRqOTlFupN+XStgLyEL7waEjyuPkZ6iOjrf0wSSzUSno2iRg6tMizLHpb8Q0YdCZl9IYGq5i8zOHW6LgRsdr2Pz0Ye05AsYiSoB2fNtqRnTalD0nFYMJeYRxN8EUSpcWsqYkNNtgdFkRmPrUJWpDlEqVj1MxoF6zvB/Ll1zUJgx1z5E3QsmGSlLC/J5ybgqONJHds4eqRjOFyJbVKY/JAJQjugmDrk9dZ9x5sf7KJcbKgwKmVY+K5Reo+7BsPhKdYhSC30Xod8MENSqGWQrTzGXZuyotSTNpbn7fDGmZtC4d2WFzfpt8GzKjpssS/a9fPYUPrV2KtZcvNlYLk/eZQlzz4vwk4+xEvuumhYZLP1zaV/EufpOnTTJ8hFoR4ax7vvOW87GmqCbfcwR8Oal0zz3dE9SoGDzRrbQXaehmLr1Jqa3AC9DKze8C1UxfRIPIqxVbDoPJtyFnddryGIC6nXbn3pfbKoTp2lwdHceuv33D6PlziRjRIe/MXBX04BqH79JfNojwyL7eBMxoC5XUfQsuQq0INlGT+VQFk2NeZya0mVZdBP90C30XRMXggW6jxtVhaLiKM+cm2rZXkjLm9ZTa+OoFfJyxqplrujrd/J6S1fnt6ttw9QeYnmHb7nZnvInJVdBRiFXUgg5XdvuJFKGgKc8EaI3DN/FauVKL/J+z9THUO6/HShvj+y3oos/ub7C5Zplw+TATmFY9Jt+Ri51/Jgh+G6Ji8IAta3o6VxImYjSgTq+w9eaVxplkiQjLt+xxar9NiYzXJrUmD1lguUYtudqO07H/Q8NVbNt9NJOpKD1b7zQBn2ArFdDlmajet6pfCcA9110wtdmeRdxLJfTzJi6axk/WCZfrxEZ8C7prDxgo9Ge6wHdFVAweMNkkfWZP8hLcd5muQnr2pprvCHoFk0AwCYI0skT0CMj5D6421/0vuZVzlbOAAWSu7zDQV/FKFvvcxtXejuz+3gSjYzWjqUqeeOiuLa/UNu0awcFjp5rZ2KZ+NREi6tphMwG6Cmfb+AmZHU/SfpcJm26yMtso202IisEDuoEnuP9l6AZ2WoiraAMOHjvVEiFkE9QuDklTXoEKtg8zT0RPetbrsvT2MXPJwjRr0Z/NG1a0KedFlUS58iAAB4+dajGdLZxXtoZ92pSCgM+zM4DHDxzH2ssXt9FWiKI7IgLNF3I7TCZAl0mNy/jxzTPJktWsQjdEBU03cikGIloMYBeAZQB+COBOZj6dOmY1gD8A8JMAJgF8hpl3NfZ9EcAvA3i7cfhHmDm/16wg6AaebnCrBrZNiI/XJpV1lvMkFQGteQUHj51qIX7LQhoofzw685UOAxYHXho227oKebJERVGX9CownSEsIISx3DoXfeTCP+VznNweufJX+jl0Yayu7QX0piqxakn7m4DWSU16/Njup4JKAT1y26ogAt3HTzBTAlJ8kJcSYwuAbzLzFQC+2fidxhiAf8fMKwHcCOBzRNQn7d/MzKsb/7pWKQD61HiZV0bGIsV2F4HlK6htH1Ca8fLZQ9XmPUQ0UZbrDq4ZaKtOZ0NWWg9dfoOu7y/tq2TOFGVWZ42bHLaqKC8TRD/YKt4lJdIeZ6JREGPFFCTgg6RMbbH2Mj2KPDEwUVLIEOPncxtXe9O/6OheAOBbW67H6ztu0kanhcR00eMXjbympFsBvK/x95cAvADgt+QDmPn70t8niOhHAJYAGM1572mBanmu+0JVVEIutnndLN4nqUh8qOm8Ap2gyFuPWu4X17a4wMbhBKhpTDZvWIGDx045OazTKLom9MJ5ZXzmV1vNG9qZc2MMqcwbpgxoMVZC8esslCjABcQ7d3HKu64+XbLjL+2r4My59hrU47VJfPKpw0qyv6KQ1Qnf7auMvIrhXzDzWwDAzG8R0U+ZDiaiawDMA/CqtPkzRPRpNFYczHwuZ5sKR5vw00zBVEycNtuqCJH0yUL2sYnqPlAbzbIrQttnXTmcVNTPKjs6Aeh1sP/r0N+b4GxtSqn4XJE2M5kEbG1Sn2279vLFANrNWIR6FBdgdsj6tPltg7L0MWXq4JMdb6NfF8eoTFihBXIWJ/xMCHu3KgYi+gaAn1bs+pTPjYjoEgB/DuBeZhbB4A8A+AfUlcVjqK82HtKcfx+A+wBg6dKlPrcODleirL7eREvcZYtKMmXvquBqE7Wl7IdAyDhuXXvTobXptq/bsU/5jhjIrBQqSRlbb65HptjoREyC15fIUFBcqISJWDXJyoFRV4prL1+s9YvJ+RmLKgnOnJ8wmspMgt22Cs7L85OVmC7dz0UI5CwcY9NVhMsHVsXAzO/X7SOifySiSxqrhUsA/Ehz3E8C2APgQWY+IF1b5K+fI6I/BfCbhnY8hrrywNq1a6e1bK/LDCkpE945O9FCViYPQtsAKCpJxpft1AdFLI9NxWkA/ccdmqI4nYWcfq60IlcpCxnV0fG2nBGTkLHl0Ojs+kJh2t6LjnAPsI8PkWmtOjcEZX2edymfW4RAdv2eXGo0dJJW24a8pqTdAO4FsKPx/1+mDyCieQD+AsCfMfPTqX1CqRCAQQDfzdmejsAUtir4fc6cm2izVecdhCEEb1GheD6zMZ/nSLdXFZ3kS02dBWnTlaqdKmWhKqojkHaamoSMLjHRJEzEPpdJxv6XTmYW7CLSTUVeGIKyXvcu+3sT9M7rcaaqDl0V0YUrTBznEtrdSVptG/JGJe0A8AEi+gGADzR+g4jWEtHnG8fcCeCXAHyEiEYa/1Y39j1OREcAHAFwMYCHc7anI9AV0fnsnVc1oyF0Ntk8gzBU9IOIBgkZuWGb0QpkeQ65vboiNaoymKZon96k1Ey0KxNh3XsXo2QI88ny0Q6uGcBn77zK2A6gVbHpCsKYCh75FkNSwebLkQvar9uxr+19PTy4qhmZ5loAxxW6723rzSub40LVz+mZe4h+EhgarmLz04ebCmuSuRlBln5mF1NYp2m1bci1YmDmHwP4FcX2gwA+1vj7ywC+rDk/jFG7w3CZdYcqzSnQ7XZJGwe+TNmRhs9zuParmMWqopLKpTpXkByy+3fH3zbmHmT9aMUz2bKMbbN7m8kir3nQlrDmshoMYf40rSZtxHS2Y0KaUbftPtqWPFmbYmzbfdQrY57gnpHdScTM54ywfQShbflZl8GdCovThdiWG9xFobJcfWy6T7z4hvIaU1OMdEtkc0Aa/b35OHIG1wxYFUMI1s4879nUr3kmJXmoXUL75UKaUXUhzartnQj4CI2oGApCaFt+lhVIJ8PidHb0SWbnGgIucI151yXFAfpooUnmtkx2ORIpD2xlQPOaEfLO1k39msW/AfiPv06QVBYV1GGCy2Sm2/IaomIoECEHYZYViM9ML+/A1DFSitwIE7Im0+lgU0QmIT1em0SJ6rkGLgl5rv1297WXaZPtXFYknVDy6X4VfgWdOrMpc9+VRiiSyk6gvzdR1n4QdCoybJOZbsxryOt8nrUYGq5izUPPY9mWPVi2ZQ9Wb39+WtPc047JvkqCBUkJm3aNKJ2BgLv5KYRjW+cg3LxhhVGAhHRSCtgU0XXv6Tc6hKf4AgWEqV0PDh3Bpl0jTv328OAqrHvv4rbtrisSV+d+KMhjQgXxbk1OaZOgV41ZU+Ec18AGk4M8JLbevLKNOyspk/ZdmgI+Ov1uXRBXDArkKQZeJMSMznWG4Wp+8p3ZZXEQhmC9dIUtVPXAa6dx97WXYf9LJ7XHmTKOTTUeTP32+H/815lXZnlCLU331O0zrbrESgpoJxrctGsE9+8awUBfBX2aWbU4Nj1m85BUFlURTtdvIU3FocNoQyAqBgV27s1eDLwTcBXkruYnn4GZxUFYRO6E6aO10Y5MMuPZQ1U8ctsqbWIW4Pb8rucJZDUvZo1yU72v+3eNYPtzR3HTz1+ipXfXPQMBTYepKrtcZlVNSmSsFpces7pxootmk6yVBhUAAB9GSURBVJ89dNSeqt82P3MY23YfbWEpCOE8Dh3BGAJRMSjgkjQ0nXAV5K4C2WdgZv0AQ/pbXGaHqrKiqjabVheuz5+GTIWyqJKAqM6bpet/lZIT9zJlUrv4ZnTtPT1WU2Y62/rFJWFMoDbF6KskWDi/R9vHqjGrGie2CU7oWbeq32qT3FwlhvQDFMlGkBVRMSjgKyw6DR9B7iKQTdz663bsaxFmRYbNuppZbDZZ1wJCJ0bH8ejG1coqb2maadfnBNBChSKbm6qj49j89GEcPHaqyVPU15vgnbMTzfuLmSkYLduePVRt4TcSykIw/Or6y9Re00rpUUVFurSw0hUukvH2eA0jW2/QMrC6fE/TkTfk8p5D5REVsaLOi6gYFNi8YUWbjwG4wI2vQifDzULPMOSBmS66I1eV09EmABc+QN3s1zbDt60CXLlmfAjXSkTYtGsEfb0JztYmMV6rczuaagKbhCEBWJCUmtdRoTbFLdFJKhu8yvQyXpvE/pdONk0Xpv4CzBQiNlzaV7EKq6HhKs6cn3C6FpB/zHY6b8iVUkUQHIagqpluE7UMYs9B0w1Yu3YtHzx4sNB7DA1Xsf25o80Pt6+SYNstamGhsjsX6VwV9yxCEelmdia2UPGsgHrJP7+npBSmwomprUUgHeOyChChsVlGtMv7UgUlCAhlYvJZ5AUBeH3HTQD076mvkuDcxJSzclTV4XAZty41GNLXCjVmddcJ+U248hup+rvobz8PiOgQM6+1HhcVQ37oPpJuzmzUYfmWPV6CTY71dxEWaZiiToALlAGuQkinZISt2zSLtr0v3fOVCPjdO1dn7gNXyO1btmVPkGsmJUAscEyTnzRM46RImodOTsJkRZM2+Yn7LkhKylVft377roohmpICoOhws06aqXxYSeUIFcD/eVXx6ar2+HLNqASHLPCWa4Sqrf16ojkYGVJDgNCaHW3LpHaFbPU6N6E3gaXRKZoH18ptRUQLqhL+0t9h1qzwbkdUDAFQZLiZqy256PoHKqSfz0SPnK56ZlspiGNMpiaVECrSUWmKy1fVP/BZOfRVErw9XtPOwhmt0S8hlEIaPgJWVVY0dCSNT+W2TghilR/AJZR2JiIqhgAoItzMxka6/bmjLcI2VPicONdG+qZ6Pl0/qKqeufgWRNRN2iGuu7/8DKEdlUPDVbxz1uxsFc8i39/FaQ4AI1tvAGA2S6Z/u/oYTCaPNFwT5p49VG0rJ3r71fYZts/Y9AkkmC5B3I2hpiEQFUMAhA43c3F8qT7ykOFzLg7h9H1s/eAan65yZDMuOEpdOIxsz2dqpwo7977cFtKahqjvkL6XuK6L0HcVNLrjtt2iVsKAWxivi4BVCWwG8MSLb2Dt5Yu9svNNcF0F5BHEeZVXN4aahkBUDIEQMtzMZ6aURqgltU7wuFTzcu0H00ely6pVmY+yfNy+78ulX23mHReh7yposihh+XidM9VFwOr6YpK5KfxDZCK7VG7LG90Ugkaj20JNQyBXVBIRLQawC8AyAD8EcCczn1YcN4l6lTYAOM7MtzS2LwfwJIDFAP4OwL9l5vO2+3ZbVFJW6ASaLeLEFgIayvkXMinNF7qoFzlkU9y/E1EqLtFGcuRTp/srC7K2xdYXprDh9Puzta/Idzubogld0amopC0AvsnMO4hoS+P3bymOG2fm1Yrtvw3gUWZ+koj+EMBHAfxBzjbNCOhmKwePnTLmDOgIzIDO2zaLpAvOSwD4yacOKzOCswpDF6f8/5HqfAtCuYPHTuHhwVXNY1T+B1PmcpHIOtO19YXo27xO2aLNNN1IXtctyKsYbgXwvsbfXwLwAtSKoQ1ERACuB/Br0vnbMEcUg06gPfHiG9qZ1qMbVyujIlw/mpDVtEzPEKLeQ14CQGHWSUdxZVVkpuzw5j1TPggG8PiB4027u4xu5OB3hWjfJ586rDSfifcbYuLiqryyJL11I3ldtyCvKWmUmfuk36eZuV9x3ASAEQATAHYw8xARXQzgADP/y8YxlwH4GjP/X7b7zgZTkm8iGQD80LAET38A669c0saroyJh0y3LXZbZecw9SYlw0YIeb3K59DGuCWXCwRvKdLB6+/NWniDT9WeaGcOF6gRoHVOdMpvpTE63Xz1gHPN5TFW2761bHdDBTElE9A0AP63Y9SmP9ixl5hNE9B4A+4joCIB/VhynlZVEdB+A+wBg6dKlHrfuTug4d3SJS+lwRRmq2afMx1MdHTcyaaoGsMsyO4+5pzbFzciqPMXlXfMuQjPmuioF3fVnkhlDt7p55LZVzWxznQO8SOFoC+l+4sU32r4lecxnNVW5fG8zZfWng1UxMPP7dfuI6B+J6BJmfouILgHwI801TjT+f42IXgCwBsCzAPqIqIeZJwC8G8AJQzseA/AYUF8x2NrdTVDNLlQEZEmJsPGay6z0yi7ZoGn41BwA3IR+XnOPjLSScp1tpj9uHd3FpYYVQ9GmA9X1Z5IZw2QyTFcj6xRcQrp1UWLyeMyivFyiBovKxu4U8voYdgO4F8COxv9/mT6AiPoBjDHzuYb5aB2A32FmJqL9AO5APTJJef5Mh2p2oZq9A8BFC3rw8OAqrL18sZHV0jUb1AU6VlQX/n/XGZcPU6XuGU0zsLRD16SsQjnsdTV/09BdP4QNvlOmGt/VTSfa5SKcdatvH+WrehbXVV03rv5ckdfH8C4ATwFYCuA4gA8x8ykiWgvg48z8MSL6RQB/BGAK9RrTn2PmP2mc/x5cCFcdBvBhZj5nu+9M8jH4kKq5hPKFJGmzsaKm+f9tzmpXZaaDsK/ntb/7lrIEspkT0kyrSZmw8V9d1uwzW5GePAI0dCinqS0+70PpTyoTFs7raal8lldR2Hx0Lj4GG3R97JpF3o3+oo6EqzLzjwH8imL7QQAfa/z91wBWpY9p7HsNwDV52tDt8Jk1lIgwNFw1Dto8s5ASgEW9SZugUiWTpfn/TXAt9ykEz6JKgjPnJ1qEqjxbzmt/15kHstaK0N1DfiaXlV36unls8CFLWerKf27bfRTbblnptbrpVOUz0ypUzow3rb5t0PXx/J6SletrptNiRNrtguFb38A2o9FdL50NevrMOYwpCsaoZjGu0UU6ZJnhZ5mhuiSQ6eA7+/NpuyoixYf4LwvyvjMZplWovKp0EbCu0XZZ+0F2OGetJeEKUx8/unH1rI5KioqhYJhC6VRRE4BdKLmYEHwEh04wlIkwxWwd6CZh4MPxD7QXSBJISgQQ2lYZroLA1wSnE7AuZjHTbDKL4Bb3TQcchMp8twlzn2v69LMv55Wq72X+rNDCeaaFFLvAVTGUOtGYuYzBNQN45LZVGOirgFAXlAuSEh4/cNwpasJ2vYG+ilI46hxsqu2bN6xAJSm3bZ9kBuPC8n9ouOp8TYHR8Ro2P31Ye64M8eGnlUJfJcFFC3raKqcJ04kLfE1wumdyjUhREeqZrmuC6Jdqg2aiOjqOM+cn6spSQlbzha1NPgpVN5Z01zWNqzR05H1CwTx7qNrSRz7XVkH1LDPdROSKqBg6gME1A/jWluvx6MbVODcxhdNjet59wP6hiuu9vuOmptli+ZY9WLdjX/ND0H2gY+cn2j6WtLJRCTWTELYJg9oUOwlwndBdOL+eCKeCq8DX9WlfJfH6+F3vN8kcTKjo7PYXLeixThBcYHt/BDgL2PRY6u9N2hSYjBDKXVfr2+faKrhOwmYjoimpg3BdZvf3Jrjp5y+xLot1Zg1RfxgAtu0+2mZysJlgstivh4ar1hoONtOB6b55K4aZTHCAe1SST6a1UNp5TRsh/Qk66Ex4AnnMJ6ZENPn6tn4ymXZM1zYxBsw1RFNSF8J1tnl6rIYvHzhuXRbrZtinx2rNyI+F89sDz2wzKR8zlMDgmgFjdjaQ3SQlhEWeGbhp9ievwGwJWy6mEkK9wpnPdU1YVEm8tmfB4JoBDH/6Bu3+PNFwoh9044MAJxOQaQzoTHe67RFmRMXQQegEn8vgVQlz08cqjs8S+plVCG/esAJJ2fwsgvnU98MPsax3McG5XCPdjnXvXQz5qRnAs4equezbMs5PqH0auu15oBPeITKyVe9XFZ2nm7iYxoDOX1dECdS5gFiop4PQxYO7FuVJC3NbRnFW+uOsHDJiv8kkAbQWdElzI5nuG4p7Jy+zabodq7c/78VD5dtWVdgxAO32PPDNyPZJ0lO9X9349V2h6MxJwj9ieg+hkh5nE6KPocNQDULXwvFpO68tdFLYuTtRyEYFl4Iu0xH2ZwtD9KUn1/lWhA8ga4azS2hsEfZz1/aGyL7Om1Ut+4k27RpR+mJ8w7/zhkZ3MzpVqCfCE7pZr0tsfHrWJq6jczDLH3RRsx+TEHEp6OJ6rZAwmdfSVBfV0XFsfuYwADSpmuU2jinIEAUu7avkWp3YQmP7e8P5GGS4rsxCZF/nzaqWyfx0Ctq0+tAx/6Yx00nxfBEVQxdAJbxdk3XERzwdJSNdqTBMBV1crxUSJvPa9ueOtuVL1CYZ2587CgDY/PThpuCwrfLEajCr8DQJtKRMzciz6UJe6hIxZkXexySzMXLNdj+dOclkNvUxWc1kUjxfRMXQJchrPzfxA+URuCaF4yL0xP+2WWFI7h8bTLNU3azz9FgN23YfVc4mVejvTTC4ZgCbMsxiBUw2+IXzpv/TzUMdnh6XIu/DNKGx3S8LY60r8698n7mAGJU0y5En8UeVcSuHErrOGF0iikIXrhkarmLdjn3KqKOsEU6uxXkqSbk5m88S+itgCo0dHa/lzuzNizwhxL7jcmi4ijPn2s128v2yvFfVMyQlaouumysZzwLR+TzLkSc5Sle+MhQ9toyQ1/Jxig4NV5U+mjT6NBX35Ha6Uo77UJrbksNc+ieUmTFk9I5tXMr36utN8M7ZibbVmkjkDBH5NVeikqLzOQKA23Jf92HoBKGYxYcoNiMQ8lquZqmh4WqLz0CHpETYdstKbRhuf2+iFc46/5FcJ8Bk3hMmQp0gta2oQvluTOU9s0SWmcZl+l660OfeeT1BhLXODDsbFEFWRMUwi6AS8DaBq/vg5/forYxCqfhEPNlmrSGjp1zNUjv3vqxVCjpmWVVxHpsTOC14dPUvTP6UrPb8UL6bPNfxHZcuRIXA3HIGdxq5FAMRLQawC8AyAD8EcCczn04dsx7Ao9KmKwHcxcxDRPRFAL8M4O3Gvo8ws5lwJ0KJrAXbdR+86cNMl/d0EQzptm3aNYL7d420RKGESmBzFaImwTLF3GZqC6W8smajZ1lRhfLdZL1OlnGpc9inMZecwZ1G3hXDFgDfZOYdRLSl8fu35AOYeT+A1UBTkbwC4HnpkM3M/EzOdsx5ZC3Y7isgRLSNgIv9WkeXDOhNG3ns4q5C1BSREkroqJ4j6+x/fk+p+Uyu9vU8kUMhrpNlXLpECs01Z3CnkVcx3ArgfY2/vwTgBaQUQwp3APgaM4/lvG9EClkLtuus6/29Cc7WptqEq2w2cbVf25RP2iShu+7BY6ecczsA+8x+84YVSh9DUiZs3rBCWalN5xtQ3Q9Qlw3V1SI20U6kFd3psVozt8IWdRPCd9PJFYvqXkXUjY7QI1dUEhGNMnOf9Ps0M/cbjt8H4HeZ+a8av78I4F8DOAfgmwC2MPM5231jVFI78lILyHClo3a9pwtVtRwl5VoONQRNQToqSaYs11ULS6OvkuDcRLsSNZUNtVFyy0qp1Ej+0sFWJW86o5J0kW19lQQjW/VsrtORsDkXEKy0JxF9A8BPK3Z9CsCXXBUDEV0C4DsALmXmmrTtHwDMA/AYgFeZ+SHN+fcBuA8Ali5devWxY8csjza3oBP2vUkJ47Wplo/LJKh9yi0u27JHuT0dCuvC+SMrE9e6wenzQsK3FKgPbKHCLv2VRpbaEnnhEha85qHntZFcJprviGIQLFyVmd9vuMk/EtElzPxWQ8j/yHCpOwH8hVAKjWu/1fjzHBH9KYDfNLTjMdSVB9auXTvzki8KxuCaARw8dgqPHzjeIlQFA6fg/DHF7BPgLGSHhqvaGXTa7iybdnTCdv2VS1rOdxXKRUWmFBnxksUub8N4bRLbnzvaYv4rklZE1860WVBXeU+3PaI7kDfzeTeAext/3wvgLw3H3g3gCXlDQ5mAiAjAIIDv5mzPnMb+l04aZ9q1STYmafk4JHX+CQKUdufBNQPYvGEFdNUa9r90svm3jrdfBdFmU6ZzFuj6It2OSlLWktn5lA2V2591pXJ6rKYU1J986nCwfpHh4j/o0/RNjCjqbuRVDDsAfICIfgDgA43fIKK1RPR5cRARLQNwGYD/lTr/cSI6AuAIgIsBPJyzPXMaeWa5vg5J3b0Y+tmpydldHR1vCi4VtcE91y1tpy4oE86cm8CyLXuwadeIcyF4FyWio3u457qlbZQLW29eqTx22y0rnSga0tQjoTHJ7NQvvrDRfQwNV/HO2XYaC+Hcj+he5IpKYuYfA/gVxfaDAD4m/f4hgDZpwcydJ+OfxfAxwaRhSmjzuZepvKdNcenYWQXWXr64jSZBrIBcC+W4RlJlyVkwFRgywdd01N+bGAshmRCSmNAWqaRLIFwYKGM5ojjEzOdZBFv9AxMEKZtrSGhRTJYmwSUri3U79lmFo0oR+WTw+iTc5UnO81nppYsJZZkIhPKf2JSn7j6j4zVrVbWI6UVUDLMItvoHNozXJluc1zYOH8BvRu2quFwK+LjSVtuubdveCbiu9NJMoiYOJQDNGgeq+4WCSSGanqtIp3hEfkTa7VmGwTUD+OydVylt3h+W7OM6uBZmF/f61pbr8fqOm4zZ1TJkk1VJ0xBVAZ+0/2BRxVy9TLd60QlFnZO0EzDRawsQoPRP6J5noK+iHQedsu+bnsuV+j1iehAVwyyEjpf+4cFVTUFu8gWkUR0dz+2wFAJejooqk533Xmf6IYI2ckk8L4A2J/PmDSva7gkA75ydmLbaBvL70qEvRUUiYKqJkLXuRCiI++sQSfC6F7EewxyFKjlJl5cA5M8y1iWM9VUSLJzfozVHmXj7H924WmvKMiVf6XI5ikqW80GW+hmuWcLTlU0cstZGRD7EegwRRrjUCZCRN5pFNzt8e7xmpEYwkbeZ7NsmJ/PbmlyOojKdfZCFrM7UD7KTWlb8RSe/yQhZayOiM4iKYQ5DFxKqq3ucZ+mflZ0zNHlbdXRc65QlwBgt04kZd0ghml41uYb0hkbIWhsRnUFUDBEtGFwzoA2DzBPNklXgZRUqOkVEgDZiixv30ZlhQlRC00FWOosqCRYkJYyO5WMSdcmP6JSdP1StjYjOICqGiDYUsfTPM2vMIlRUz2DyoQjoBKVL/kPWFUVa6YyO11BJynh04+pcwjRrSG+6bXGmP/cQFUNEG4pa+rvYwkPdT/UMLj4EnaC05T/kWVHolM72547m6gPbM9uUfdGrpIjuRVQMEUqEXvqbuPzzOkZ1SiX9DDYqbZWgtBU0EookT01kndI5PZYvQ9i0anKhVw9VLzpi5iEqhojCoZp5bn76MEB1xlcgu2PUZ1brKyhdChoJRZIno9o0s88jhPOu/HRt6oborYhiERVDROFQzTxV5GppuAhVX+4jcY6LoDQ5b9OKJE9t5c0bVhQSCQbkM9/porfKZMqdj5gNiIohonBkFW4uQtV3pu5jItNdQ1XQaP2VS/DlA8fbjpULEMlIC+XepNQsqiSjqLoFListXfRWFh6uiJmFSIkRUTiyCDfXKCjdtRdVktyFe2z1BmTIhYZs21X8T7VJttKDhIRppSWgo+jwoVOJmJmIiiGicKj4fJJSO09SmuvIZWavu/aZ8xPOhXtUGBqu4sy59iIzOmHts3LRmdYWzuvpGK+RS3tNPEwRsxu5TElE9CEA2wD8LIBrGgV6VMfdCOD3AJQBfJ6ZRaW35QCeBLAYwN8B+LfMfD5PmyK6DzrbvmqbryBUXXvs/ERbrQafaJoHh4601c4G6gVytt68UnkNHx9DVnqQkHBpb8xYnrvI62P4LoDbAPyR7gAiKgP4fdRLf74J4NtEtJuZvwfgtwE8ysxPEtEfAvgogD/I2aaILoTOth9CyKSvvXzLHuVxLr6OoeGqUikAQK+h8phPUmAeR3UouLY3ZizPTeQyJTHz3zOzjVT9GgCvMPNrjdXAkwBuJSICcD2AZxrHfQnAYJ72REQAfr6BNEw5CybF4kNx3Q0mmumm5I7obnQiKmkAwBvS7zcBXAvgXQBGmXlC2h5HZURu5KH0MAl/m2JxnV13i4kmrgYidLAqBiL6BoCfVuz6FDP/pcM9VEHPbNiua8d9AO4DgKVLlzrcNmKuIo/gNZHvhZzRR6Ec0c2wKgZmfn/Oe7wJ4DLp97sBnADwTwD6iKinsWoQ23XteAzAY0C9UE/ONkXMcmQVvLrs6HuuWxoFecScQSdMSd8GcEUjAqkK4C4Av8bMTET7AdyBut/hXgAuK5CIiMLQLWaeiIjpRK7SnkT0qwD+XwBLAIwCGGHmDUR0KephqR9sHPdBAJ9DPVz1C8z8mcb29+BCuOowgA8z8znbfWNpz4iIiAh/uJb2jDWfIyIiIuYIXBVDzHyOiIiIiGhBVAwRERERES2IiiEiIiIiogVRMUREREREtGBGOp+J6CSAY56nXYx67kQ3olvb1q3tArq3bd3aLqB729at7QK6t21Z23U5M6uLhEiYkYohC4jooIs3fjrQrW3r1nYB3du2bm0X0L1t69Z2Ad3btqLbFU1JEREREREtiIohIiIiIqIFc0kxPDbdDTCgW9vWre0Curdt3douoHvb1q3tArq3bYW2a874GCIiIiIi3DCXVgwREREREQ6YVYqBiD5EREeJaIqItB57IrqRiF4moleIaIu0fTkRvUhEPyCiXUQ0L2DbFhPR1xvX/joR9SuOWU9EI9K/s0Q02Nj3RSJ6Xdq3ulPtahw3Kd17t7R9uvtsNRH9TeO9f4eINkr7gvaZbtxI++c3+uCVRp8sk/Y90Nj+MhFtyNOODO36DSL6XqN/vklEl0v7lO+1g237CBGdlNrwMWnfvY13/wMiurfD7XpUatP3iWhU2ldYnxHRF4joR0T0Xc1+IqL/0Wj3d4joF6R94fqLmWfNPwA/C2AFgBcArNUcUwbwKoD3AJgH4DCAn2vsewrAXY2//xDArwds2+8A2NL4ewuA37YcvxjAKQC9jd9fBHBHAX3m1C4A72i2T2ufAfgZAFc0/r4UwFsA+kL3mWncSMf8JwB/2Pj7LgC7Gn//XOP4+QCWN65T7mC71kvj6NdFu0zvtYNt+wiA/6k4dzGA1xr/9zf+7u9Uu1LH/xfUWaE70We/BOAXAHxXs/+DAL6GepmQ6wC8WER/zaoVA3d3DepbG9d0vfYdAL7GzGMB26CCb7ua6IY+Y+bvM/MPGn+fAPAj1GngQ0M5bgztfQbArzT66FYATzLzOWZ+HcArjet1pF3MvF8aRwdQL4rVCbj0mQ4bAHydmU8x82kAXwdw4zS1624ATwS6txHM/L9RnxDqcCuAP+M6DqBe7OwSBO6vWaUYHKGqQT2A4mtQ/wtmfgsAGv//lOX4u9A+GD/TWD4+SkTzO9yuBUR0kIgOCPMWuqzPiOga1GeAr0qbQ/WZbtwoj2n0yduo95HLuUW2S8ZHUZ9xCqjeayi4tu32xjt6hohEtceu6LOG2W05gH3S5iL7zAZd24P2VycquAUFdUkNat+2eV7nEgCrAOyVNj8A4B9QF3yPAfgtAA91sF1LmfkE1Ysr7SOiIwD+WXHcdPbZnwO4l5mnGpsz95nqFopt6WctbGwZ4HxtIvowgLUAflna3PZemflV1fkFte05AE8w8zki+jjqK67rHc8tsl0CdwF4hpknpW1F9pkNHRljM04xcJfUoPZtGxH9IxFdwsxvNYTYjwyXuhPAXzBzTbr2W40/zxHRnwL4zU62q2GmATO/RkQvAFgD4Fl0QZ8R0U8C2APgwcbyWlw7c58poBs3qmPeJKIeAItQNwu4nFtku0BE70dd2f4yS1USNe81lJCzto2Zfyz9/GMAvy2d+77UuS90ql0S7gLwn+UNBfeZDbq2B+2vuWhKatagpnoEzV0AdnPdgyNqUAPha1DvblzT5dptNs2GYBR2/UEAyqiFItpFRP3CDENEFwNYB+B73dBnjXf4F6jbXZ9O7QvZZ8pxY2jvHQD2NfpoN4C7qB61tBzAFQD+NkdbvNpFRGsA/BGAW5j5R9J25XsN1C7Xtl0i/bwFwN83/t4L4IZGG/sB3IDWFXSh7Wq0bQXqjty/kbYV3Wc27Abw7xrRSdcBeLsxAQrbX0V516fjH4BfRV1zngPwjwD2NrZfCuCr0nEfBPB91LX8p6Tt70H9g30FwNMA5gds27sAfBPADxr/L25sX4t6fWxx3DIAVQCl1Pn7ABxBXbh9GcBFnWoXgF9s3Ptw4/+PdkufAfgwgBqAEenf6iL6TDVuUDdN3dL4e0GjD15p9Ml7pHM/1TjvZQD/JvC4t7XrG43vQfTPbtt77WDbHgFwtNGG/QCulM79D42+fAXAv+9kuxq/twHYkTqv0D5DfUL4VmNMv4m6T+jjAD7e2E8Afr/R7iOQoi9D9lfMfI6IiIiIaMFcNCVFRERERBgQFUNERERERAuiYoiIiIiIaEFUDBERERERLYiKISIiIiKiBVExRERERES0ICqGiIiIiIgWRMUQEREREdGC/x+a2bdnzObTzgAAAABJRU5ErkJggg==\n", 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "n_rands = int(1e3)\n", "x = 2*nprnd.random(n_rands) - 1 # generate random x between -1 and 1\n", "y = 2*nprnd.random(n_rands) - 1 # generate random y between -1 and 1\n", "r = np.sqrt(x**2+y**2) # calculate radius \n", "# the line below -- we should check that r>0, but we don't now\n", "distance = nprnd.random(n_rands) # generating random distance from the center\n", "x = x/r*distance # the next two lines keep the angle defined by (x,y) and move the \n", "y = y/r*distance # point to the radius defined by the variable distance\n", "plt.plot(x, y, 'o')\n", "plt.show()\n", "\n", "\n", "r = nprnd.random(n_rands) # generate random distance from the center between 0 and 1\n", "phi = 2*np.pi*nprnd.random(n_rands) # generate random angle between 0 and 2*pi\n", "x = r*np.cos(phi) # calculate x\n", "y = r*np.sin(phi) # calculate y\n", "plt.plot(x, y, 'o')\n", "plt.show()\n", "\n", "r2 = nprnd.random(n_rands) # generate random distance to the center, squared\n", "phi = 2*np.pi*nprnd.random(n_rands) # generate random angle\n", "x = np.sqrt(r2)*np.cos(phi)\n", "y = np.sqrt(r2)*np.sin(phi)\n", "plt.plot(x, y, 'o')\n", "plt.show()\n", "\n", "def rnd_circle_rejection(n_rands):\n", " N = int(np.ceil(4/np.pi*n_rands)) # need to generate more points because of possible rejections\n", " x = 2*nprnd.random(N) - 1 # generate random x\n", " y = 2*nprnd.random(N) - 1 # generate random y\n", " ind = (x**2+y**2 < 1) # which points fall in the circle?\n", " x = x[ind]\n", " y = y[ind] \n", " if (np.size(x)n_rands):\n", " x = x[0:n_rands]\n", " y = y[0:n_rands]\n", " \n", " return x, y \n", "\n", "x,y = rnd_circle_rejection(n_rands)\n", "plt.plot(x, y, 'o')\n", "plt.show()\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Which one of the generators is correct? Why is there a cross visible in the first, and a higher central density in the second? \n", "\n", "## Your work:\n", "Which one of of the generators is faster at generating points in a circle?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generating a standard normal number \n", "For this, first we show the build-in routine. Then we do our own generation by first generating a random angle $\\phi$ and then a random exponentially distributed $r^2$, and finally taking $r\\cos\\phi$." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
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CfKa7O3/FS/JLwGbm/t0cAtxaVX869vMY9JLUNoduJKlxBr0kNc6gl6TGGfSS1DiDXpIaZ9BLUuMMeklqnEEvSY37P5RFmiBV+0iHAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# generating gaussian random numbers using built-in function\n", "plt.hist(nprnd.randn(n_rands), 30)\n", "plt.show()\n", "\n", "# and comparing built-in to our own generator\n", "phi = 2 * np.pi * nprnd.random(n_rands)\n", "r = np.sqrt(2 * nprnd.exponential(size=n_rands))\n", "rand_norm = r * np.cos(phi)\n", "plt.hist([nprnd.randn(n_rands), rand_norm], 30)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using random numbers for Monte-Carlo (MC) calculations\n", "Here we will try to integrate a function (estimate area under its curve) based on randomly throwing darts and seeing which proportion has ended up under the curve of the function. \n", "\n", "First we define the function that will be integrated. You can edit this function and plug different expression there, to get integrals of different functions. Then we define the MC integrator itself. Finally we integrate the function using the integrator." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.33081000000000005\n" ] } ], "source": [ "# a function to integrate using the Monte Carlo approach\n", "def to_integr(x):\n", " return x**2\n", " #return np.exp(np.sin(x))\n", "\n", "# Monte Carlo integrator\n", "def mc_integr(func, a, b, fmax, N):\n", " # func -- function to integrate\n", " # a,b -- the x range of the integration\n", " # fmax -- the maximum value of the integrand\n", " # N -- number of random samples used for the integration\n", " # return -- estimate of the area\n", " x = a+(b-a)*nprnd.random(int(N)) # generating random x coordinated\n", " y = fmax*nprnd.random(int(N))\n", " counts_under_curve = np.sum(y <= func(x))\n", " frac_under_curve = counts_under_curve/int(N)\n", " area = (b-a)*fmax*frac_under_curve\n", " return area\n", "\n", "# area using monte carlo integrator\n", "area = mc_integr(to_integr, 0, 1, 3, 100000)\n", "print(area)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Above we integrated the function $x^2$ between 0 and 1. The integral should be 1/3 -- and we got a value slightly different from that. How quickly does the integral converge to its true value? Let's explore this now. We will estimate the area as a function of $N$, the number of random samples. We will do the estimate for each $N$ multiple times and see how quickly the geenrated spread cobverges to the true value." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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96HYZDH8Vtt8Xpo2EhwbAd59GnUwkq4QpHKVm1m3TEzPrCpQmL5JILTVvC+c8A8fdCssWwV2HwYIJsHFD1MlEskKYrWOHA5PLjWt8B5ydvEgiNVe4uJixRUtZXlJKy/zd+UP3Qnp/chPMuhLe/kfQtqRFu6hjimS0aq843P0tdz8A2B/Y3907uPu/kx9NJD6Fi4sZPXUJxSWlOFBcUspls76hcJ/b4YSJ8M2HMKEbvDxWTRNFaiF0ryp3X+3uq5MZRqQ2xhYtpbRs89tRpWUbGPvc+3DAyTDyDdirL8y5ASb2gOWLowkqkuGyqsmh2qrXbctLKh56+/l4oxZw0v1wyt/hh5UwqRc8/wco05CdSDyyqnBoHUfd1jI/L9zxvY4LmiZ2OANe/b9gz49PX01BQpHsEKpwmFkXMzvNzM7a9Eh2MJF4jerdjrzcnM2O5eXmMKp3BYPhefnQ/w44axpsXA8PHAtP/xrW6m6sSHWqnVVlZg8BbYB/AZtuIDswOYm5ROI2oEMBQLlZVXmM6t3u5+MV2r0HjJgPc/4MC+6C94ug719hz6NTklkkE4XpVfUusI9n0FaB2gFQauSLhTD9omDL2v1Pht5jYJvtok4lkhKJ7lX1NrBj7SKJZIBdDoELXobuVwVrPsZ1grenqm2JyBbCFI7mwDtmVmRm0zc9kh1MJBL1G0DP0UEByd8FppwbNE1c/WXUyUTSRpiV49clO4RI2tlhXxjyArw+Plj3Me5QOPpPcNBZYBZ1OpFIhVk5/hLwHv/bwOnd2DGR7JZTH7pcDBe+FnTfnXEJTO4P334SdTKRSFVbOMxsMPAGcBJBW/XXzWxQsoPVhBYASlJs1wbOngF9b4fixUHTxPnj1DRR6qwws6reAn7l7itiz1sAL8T6V6UlzaqSpFlVDE9fDh8UQUHHoGni9ntHnUqk1hI9q6repqIR803I94lkn6YFcNrjcOK98N0nMOFwmHsTrF8XdTKRlAlTAGbFZlSdY2bnAM8AM5MbSySNmUH7QUHTxH0HwNy/wMTuUPxm1MlEUiLM4PgoYCJBW/UDgInufmWyg4mkvW2aw4n3wKmPQWkJ3HMUFF0N636MOplIUlU7xpGJNMYhKbd2FTx/Lbx5PzRrHfTBan141KlEQkvIGIeZvRL7ucbMVpd7rDEzdYITKa9hU+h3ezD7CuDBvjDj0qCgiGSZSguHu3eL/Wzs7k3KPRq7e5PURRTJIK2PCNZ9dLkY/jkZxnWGpbOiTiWSUGHWcTwU5piIxGy1NRx9A5z/AuQ1g0dPhilDgs2jRLJAmFlV+5Z/Ymb1gYOTE0ckixQcDMPmQo/fwTvTgqaJS6aoaaJkvKrGOEab2Rpg//LjG8B/gWkpSyiSyepvBT2uhOHzgkHzfwyBR08JFhKKZKiqxjjGuHtjYOwW4xvbufvoFGYUyXzb7w1DnoPef4GPXwqaJi66DzZujDqZSNzCrOMYbWbNzKyTmR2x6ZGKcCJZpV4OHDYy2HGwoEPQumRyf/jmo6iTicQlzNax5wOXAjsTbB/bGZgP9EputPiZWT+gX9u2baOOIrKZwsXFm29pe/R4BrSfA0XXwPgu0PNq6Dwi6MgrkubCDI5fChwCfObuPYEOwNdJTVVD7j7D3Yc1bdo06igiPytcXMzoqUsoLinFgeKSUkY/9TaFdiSMfB3aHAnP/x7u/RX89z9RxxWpVpjCsdbd1wKYWQN3fw9ol9xYItljbNFSSss2b8FeWraBsUVLoclOcMojMOh+KPkc7j4CXvwLrP8porQi1QtTOJaZWT5QCDxvZtOA5cmNJZI9lpeUVn3cDPYbCBcthP1OhJduCgrIFwtTmFIkvDCD4ye4e4m7Xwf8HrgXGJDsYCLZomV+XrjjW28LAyfCaU/CT2uCW1ezfgfrfkhBSpHwqlrH0ST2c9tND2AJ8ArQKEX5RDLeqN7tyMvN2exYXm4Oo3pXcsd3z6NhxAI4ZAgsGBfsOPjx3OQHFQmpqiuOv8d+vgksquCniIQwoEMBYwa2pyA/DwMK8vMYM7A9AzoUVP6mhk3guFvhnJlQrz5MPh6mXxy0bxeJmNqqi6S7slKYeyO8dgds0wL63gZ7HRd1KskyCd061symmdmpZrZ17aOJSNxy8+BX18PQ2UHheOw0ePJc+D4tZ8VLHRBmVtVtwOHAu2b2pJkNMrOGSc4lIltq2QGGvQi9roH3noZxh8Bbj6tpoqRcmFlVL7n7CGB3gi1kBwMrkh1MRCqQkwtHjILhr8B2e8BTw+CRk6Dki6iTSR0S5ooDM8sDTgSGE6wifzCZoUSkGi3awXmz4Jib4bPX4K7OsPAeNU2UlAgzxvE48C5Bb6pxQBt3vzjZwUSkGvVy4NALgqaJOx8Cz/wGHjgOVn4YdTLJcmGuOO4nKBbD3X2Ou+ufNCLppNlucOZTcPxdsOI/MKErvPJX2LA+6mSSpcIUjpeB0WY2EcDM9jCzvsmNJSJxMYMOp8PIN6DtUfDCdXBPL/hqSdTJJAuFveJYB3SJPV8G3JC0RCJSc413DJomDp4Mq7+EiT1g9p+gbG3UySSLhCkcbdz9ZqAMwN1LAUtqKhGpnX2OD1q2tx8M826Buw+Hz1+POpVkiTCFY11sVpUDmFkbIC17PptZPzObuGrVqqijiERv623hhPFwxj+C1ef39YZnr4Sfvo86mWS4MIXjWmAWsIuZPQLMBn6b1FQ1pI2cRCrQ9qhg5lWnofD63UHTxA9nR51KMliYBYDPAwOBc4BHgY7uPje5sUQkoRo0hmPHwrnPQv0G8PBAKBwBpd9FnUwyUFVt1Q/a9AB2A74k2MBp19gxEck0ux0WrDrv9mt46zEYdyi8Mz3qVJJh6lfxu1tjPxsCHYG3CAbF9wdeB7olN5qIJEVuQzjqWth3AEy7CJ44E/buD8feAo13iDqdZIBKrzjcvae79wQ+Aw5y947ufjDQAdDSVJFMt9MBMHQOHHktvF8E4zrBv/6upolSrTCD43u5+8+riNz9beDA5EUSkZTJyYXDfw0Xvgrb7w2FFwbjH999FnUySWNhCse7ZnaPmfUws+5mNomgd5WIZIvmewS7DR57C3zxRjDz6vW71TRRKhSmcJwL/Ae4FLgMeCd2TESySb16wZTdEfNh187w7G/h/mPg6/ejTiZpRlvHisgvuQezropGw7ofoPuV0PXS4NaWZKWEbh0rInWQGRx4atA0sd2xMOdPMKknfPlW1MkkDahwiEjlGm0Pgx+Ekx+G71fAxJ5B592y0qiTSYSqWschIlmucHExY4uWsryklJb5eYzq3Y4BHQp++cK9+0GrbvDcNcFeH+/OgP53BgsKpc6ptHCY2QxijQ0r4u79k5JIRFKicHExo6cuobRsAwDFJaWMnhrMvK+weOQ1g+PHwX6DYMYlcH8fOGRosJiwQeNURpeIVXWr6haC1eOfAKXApNjje+Dt5EcTkWQaW7T056KxSWnZBsYWLa36jW16woXzofOIYJ/zuw6DD15IYlJJN1WtHH/J3V8COrj7ybHOszPc/TTUbkQk4y0vqXicorLjm2nQCPqMgSHPQe7W8MiJ8NRw+PHbBKeUdBRmcLyFme2+6YmZtQZaJC+SiKRCy/y8uI5XaJdOMHweHPFbWPJk0LbkP0+pbUmWC1M4LgfmmtlcM5sLvEiwGFBEMtio3u3Iy83Z7Fhebg6jereL74PqN4BeV8OwudCkAJ48Bx4/A9Z8laiokmaqnFVlZvWA1cAewF6xw++5e1ruACgi4W0aAA81qyqMHdvD+bNhwTh48S9wZyfo/WfocEawLkSyRrUrx81svrtn1Jw7rRwXidg3H8H0i+GzV2H3HtDv/6BZq4hDSVUSvXL8OTM70Uz/ZBCRkLZrA2c/DcfdBsveDGZeLRgPGzdU/15Je2EKx6+BJ4GfzGy1ma0xs9VJziUima5ePThkCIxcECwenHUV3NcbVrwXdTKppTB7jjd293ruvpW7N4k9b5KKcCKSBZruDKc9AQMnBbew7j4cXroZ1q+LOpnUUKheVWbWzMw6mdkRmx7JDiYiWcQM9h8cNE3cux+8+OegaWLxP6NOJjVQbeEws/OBl4Ei4PrYz+uSG0tEslKjFjDoPjjlUfjxG7jnSHju92qamGHCXHFcChwCfBbbg7wD8HVSU4lIdtvrWBj5OnQ4E177G4zvAp++EnUqCSlM4Vjr7msBzKyBu78HxLlCqObMbICZTTKzaWZ2dKq+V0SSrGFT6P83OGs6+EZ44Dh4+nJYq7k36S5M4VhmZvlAIfC8mU0Dlof5cDO7z8xWmNnbWxzvY2ZLzexDM7uqqs9w90J3HwqcA5wc5ntFJIPs3j1omnjYRfDmA3BXZ3i/KOpUUoW4to41s+5AU2CWu1c7JSI2iP49MNnd94sdywHeB34FLAMWAqcCOcCYLT7iPHdfEXvfrcAj7l7taJoWAIpkqGWLYNpF8PW70H4w9LkRttku6lR1QjwLAKvaj2PbCg4vif1sBFTbBtPdXzazVlsc7gR86O4fx77nMeB4dx8D9K0ghwE3As+GKRoiksF27ggXvAyv3AYv3wIfzYZjbob9TlTbkjRS1a2qN4FFsZ9fE1wlfBD785u1+M4C4Ityz5fFjlXmYuAoYJCZDa/sRWY2zMwWmdmir7/W2L1Ixqq/FfS4KiggzVrBP4bAY6fB6lB3yCUFqtqPo7W7704w/bafuzd39+0Irgqm1uI7K/pnQ1U7Df7N3Q929+HuPqGK1010947u3rFFC3V9F8l4O+wDQ56Ho/8MH70I4w4NxkDUsj1yYQbHD3H3mZueuPuzQPdafOcyYJdyz3cm5GC7iNQx9XKgy0Uw4jXY6QCYcSk82A++/TjqZHVamMKx0syuMbNWZrabmV0NfFOL71wI7GFmrc1sK+AUYHotPk9Est22u8PZM4Iuu1++BXd1gdfuVNPEiIQpHKcS7Pj3FMGU3O1jx6plZo8C84F2ZrbMzIa4+3rgIoJbYO8CT7j7f2oSvoLv62dmE1etWpWIjxORdGIGB58TLBzcvQc8dzXc+yv47zsRB6t74pqOmyk0HVcky7nDf6bCzN/C2lVwxBXQ7dfBwLrUSEKm45b7sD2BK4BW5V/v7r1qGlBEpFbMgim6rXsE7drnjoF3pkH/O2Hng6NOl/WqLRwEe3FMAO4BdENRRNLHNtvBiZOg/aCgXcm9R0HnEdDzathq66jTZa0whWO9u49PehIRkZjCxcXx7YW+Z28YsQBeuBbm3wnvPQ3974DW2gEiGcIMjs8wsxFmtpOZbbvpkfRkNaDBcZHMV7i4mNFTl1BcUooDxSWljJ66hMLFxVW/sWET6PtXOOcZsHrBtN3plwRjIJJQ1Q6Om9knFRz22OLAtKTBcZHM1fXGORSX/HJ/joL8PF69KuTQ6rofg3GP+XdCox2CgtLumAQnzS7xDI6H2Tq2dQWPtC0aIpLZlldQNKo6XqGttoaj/wTnz4a8beHRU2DKefDDygSlrNvCjHFgZvsB+wANNx1z98nJCiUidVfL/LwKrzha5ufF/2EFB8GwufDq/8HLNwetS465ORhMV9PEGguzdey1wB2xR0/gZqB/knOJSB01qnc78nJzNjuWl5vDqN413D+u/lbQfRRcMA+2awNTz4e/nwyrliUgbd0UZnB8EHAk8JW7nwscADRIaioRqbMGdChgzMD2FOTnYQRjG2MGtq96VlUY2+8F5xUFe3x8Og/GdYaF98LGjQnJXZeEGRx/w907mdmbBFcca4C33X3fVASMh5n1A/q1bdt26AcffBB1HBFJV99+EjRM/OQl2K1bsIXtdm2iThWphA6OA4tiW8dOItiH45/AG7XIlzTuPsPdhzVt2jTqKCKSzrZtDWfFVpp/tQTGdwnGQTasjzpZRoh369hWQBN3/3eyAiWCpuOKSGirv4SZVwSLBlt2CIrJjvtFnSrlEnrFYWazN/3Z3T9193+XPyYiktGa7AQnPwwnPRAMmE/sDnP+DOt/ijpZ2qq0cJhZw9gK8eZm1qzcqvFWQMtUBRQRSToz2PcEGPkGtD8pmLo74XD4Ii3vykeuqiuOCwjGNPaK/dz0mAaMS340EZEU23pbOGECnD4F1v0A9x4Nz14V/FnWTOvVAAAIcUlEQVR+FmZW1cXufkeK8iSExjhEpNZ+WgMvXA8LJ0H+rtDvb9CmZ9SpkibRs6q+MrPGsQ++xsymmtlBtUqYJGpyKCIJ06AxHHcLnPss1MuFhwbAtJFQWhJ1ssiFKRy/d/c1ZtYN6A08CKRlm3VNxxWRhNutC1z4KnS7HP71KIw7FN59OupUkQpTODZt3nQcMN7dpwHan1FE6o7cPDjqOhg6Bxq1gMdPhyfOhu9XRJ0sEmEKR7GZ3Q0MBmaaWYOQ7xMRyS4tD4ShL0Kv38PSmTCuE7z1WLAHeh0SpgAMBoqAPu5eAmwLjEpqKhGRdJWTC0dcAcNfheZ7wlMXwCODoOSLqJOlTJj9OH5096nu/kHs+Zfu/lzyo4mIpLEWe8K5s4I27Z/Nh7s6wxuT6kTTRN1yEhGpqXr14NALYMR82PmQoHXJA8fCyuxusppVhUPTcUUkEs12gzOfguPvghXvwPiuMO+2rG2amFWFQ9NxRSQyZtDhdBi5EPbsDbOvh3t6wZdp3RO2RrKqcIiIRK7xDnDyQzB4ctB5d2IPmP1HKFubtK8sXFxM1xvn0PqqZ+h64xwKFxcn7btAhUNEJDn2OR5Gvg4HnALzboUJ3eDzBQn/msLFxYyeuoTiklIcKC4pZfTUJUktHiocIiLJsvW2MOAuOGNq0Kb9vj4w87fw0/cJ+4qxRUspLduw2bHSsg2MLVqasO/YkgqHiEhINb4l1PbIYOZVp2HwxkS46zD4MDHbGi0vKY3reCKocIiIhFDrW0INGsGxN8N5s6B+A3h4IBSOgB+/rVWulvl5cR1PBBUOEZEQEnZLaNfOMPwVOPw3QbuScYfCO9NqnGtU73bk5eZsdiwvN4dRvdvV+DOro8IhIhJCQm8J5TaEI/8Aw+ZC4x3hibPg8TNgzVdxf9SADgWMGdiegvw8DCjIz2PMwPYM6FAQf66Q6iftk0VEskjL/DyKKygStboltNP+QdPE+XfAi2Pgk07QewwceFqwLiSkAR0KklootpRVVxxaOS4iyZK0W0I59YO9Pi58FbbfB6aNgIdOgO8+q93nJlFWFQ6tHBeRZEn6LaHme8A5M+HYW2DZwmDm1et3w8YN1b83xardczwTac9xEcloJZ/D05fDhy/ALodC/zugRfIGuyHxe46LiEgq5e8Kp0+BE+6Gle8Hq85fHgsbyqJOBqhwiIikJ7OgXcnIN2Cv42DODTCxJyz/V9TJVDhERNJao+3hpAfg5EfghxUwqRc8fy2UJW9leHVUOEREMsHefYOmiQeeBq/eHty++uy1SKKocIiIZIq8ZnD8nXBmIWxYB/cfA8/8BtauTmkMFQ4RkUzTpieMWACdR8DCe4Opux88n7KvV+EQEclEW20DfcbAkOeCPz8yCKZeAKUlSf9qFQ4RkUy2SycYPg+O+G2wcLBe8jtJqXCIiGS6+g2g19XBnh8NGiX967KqcKhXlYjUafUbpORrsqpwqFeViEjyZVXhEBGR5FPhEBGRuKhwiIhIXFQ4REQkLiocIiISFxUOERGJS1buAGhmXwObNuxtCmy5sKP8sS1/3xxYmaRoFWVJ1Huqel1lv6vu3FR2rPxznS+dL52v+F6XrudrN3dvEeqV7p7VD2BiVce2/D2wKJVZEvWeql5X2e+qOzdVnKPy50/nS+dL56sOnK/yj7pwq2pGNccq+n2y1OS7wr6nqtdV9rvqzk1lx1J1znS+4qPzFR+drxrKyltVtWFmizzkhu2i8xUvna/46HzFJ1Xnqy5cccRrYtQBMozOV3x0vuKj8xWflJwvXXGIiEhcdMUhIiJxUeEQEZG4qHCIiEhcVDiqYWa7m9m9ZjYl6iyZwMwGmNkkM5tmZkdHnSfdmdneZjbBzKaY2YVR58kEZraNmb1pZn2jzpLuzKyHmc2L/R3rkajPrZOFw8zuM7MVZvb2Fsf7mNlSM/vQzK4CcPeP3X1INEnTQ5znq9DdhwLnACdHEDdycZ6vd919ODAYqJPTTuM5XzFXAk+kNmX6iPN8OfA90BBYlrAQqVhlmG4P4AjgIODtcsdygI+A3YGtgLeAfcr9fkrUuTPsfN0KHBR19kw4X0B/4DXgtKizp/v5Ao4CTiH4h0nfqLNnwPmqF/v9DsAjicpQJ6843P1l4NstDncCPvTgCmMd8BhwfMrDpaF4zpcFbgKedfd/pjprOoj375e7T3f3LsDpqU2aHuI8Xz2BzsBpwFAzq3P/DYvnfLn7xtjvvwMStiF5/UR9UBYoAL4o93wZcKiZbQf8GehgZqPdfUwk6dJPhecLuJjgX4VNzaytu0+IIlwaquzvVw9gIMH/qWdGkCtdVXi+3P0iADM7B1hZ7j+MdV1lf78GAr2BfODORH2ZCsf/WAXH3N2/AYanOkwGqOx8/Q34W6rDZIDKztdcYG5qo2SECs/Xz39wfyB1UTJCZX+/pgJTE/1lde4yrwrLgF3KPd8ZWB5Rlkyg8xUfna/46HzFJ6XnS4XjfxYCe5hZazPbimAAbnrEmdKZzld8dL7io/MVn5SerzpZOMzsUWA+0M7MlpnZEHdfD1wEFAHvAk+4+3+izJkudL7io/MVH52v+KTD+VKTQxERiUudvOIQEZGaU+EQEZG4qHCIiEhcVDhERCQuKhwiIhIXFQ4REYmLCodIkpmZm9mt5Z5fYWbXRRhJpFZUOESS7ydgoJk1jzqISCKocIgk33pgInB51EFEEkGFQyQ1xgGnm1nTqIOI1JYKh0gKuPtqYDJwSdRZRGpLhUMkdW4HhgDbRB1EpDZUOERSxN2/BZ4gKB4iGUuFQyS1bgU0u0oymtqqi4hIXHTFISIicVHhEBGRuKhwiIhIXFQ4REQkLiocIiISFxUOERGJiwqHiIjERYVDRETi8v/8vU0BHFxvMwAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# investigating the dependence of the accuracy of the MC integrator\n", "# on the number of samples\n", "n_trials = 10 # number of area estimated for each N\n", "N = np.logspace(1, 5, 9) # different values of N\n", "areaN = np.zeros((N.size, n_trials)) # array to store the area values\n", "\n", "# for each N and each trial within a fixed value of N, calculate and store the area\n", "for i in np.arange(N.size):\n", " for j in np.arange(n_trials):\n", " areaN[i, j] = mc_integr(to_integr, 0, 1, 3, N[i])\n", "\n", "\n", "# plotting areas as a function of N\n", "plt.semilogx(N, areaN, 'o')\n", "plt.xlabel('N')\n", "plt.ylabel('area')\n", "plt.show()\n", "\n", "# plotting the standard deviation of the area as a function of N\n", "# and comparing to 1/sqrt(N)\n", "plt.loglog(N, np.std(areaN, 1), 'o')\n", "plt.loglog(N, 1/np.sqrt(N))\n", "plt.xlabel('N')\n", "plt.ylabel('standard deviation of the area')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice how the convergence of the estimators to their true value (the decrease of the standard deviation) goes as $1/\\sqrt{N}$. This is usually the case for most MC problems, irrespective of the type of the problem." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.1" } }, "nbformat": 4, "nbformat_minor": 2 }