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scipy.interpolate bispline equiv to ~ 0 + patsy.bs:patsy.bs
{
"metadata": {
"name": "2013_08_31_tensor_product_splines_and_patsy"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": "!date",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Mon Sep 2 12:12:37 PDT 2013\r\n"
}
],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Matching up splines and bisplines"
},
{
"cell_type": "code",
"collapsed": false,
"input": "import scipy.interpolate",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": "x = linspace(0, 10, 100)\n\nt = [0,0,0] + [0,2,4,6,8,10] + [10,10,10]\nc = zeros_like(t)\nc[0] = 1\nk=3\n\ny = scipy.interpolate.splev(x, [t, c, k])\nplot(x,y, 'k-')",
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 3,
"text": "[<matplotlib.lines.Line2D at 0x2e12990>]"
},
{
"metadata": {},
"output_type": "display_data",
"png": 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paalSUlKUlJSkVatW3fP866+/LofDoeTkZE2aNEk1NTUeD9oVFotFkydP1j/+8Q9Drg8A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\nAcBEKHUAMJH/ByhCojvzkG2aAAAAAElFTkSuQmCC\n",
"text": "<matplotlib.figure.Figure at 0x2d6bdd0>"
}
],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": "x = linspace(0, 10, 100)\ny = linspace(0, 10, 100)\n\ntx = [0,0,0] + [0,2,4,6,8,10] + [10,10,10]\nty = [0,0,0] + [0,2,4,6,8,10] + [10,10,10]\nc = zeros(len(tx)*len(ty))\nc[0] = 1\nkx,ky = 3,3\n\nz = scipy.interpolate.bisplev(x, y, [tx, ty, c, kx, ky])\nplot(x, z, 'k-');",
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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SXV0dqVQqkslkdPbsWSorKyMjIyMqKSmhZcuW0bx58+jUqVPk7OxMV65cIXNz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\nY+3I/wNYc+n9zJmjgQAAAABJRU5ErkJggg==\n",
"text": "<matplotlib.figure.Figure at 0x2d66a10>"
}
],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": "import patsy",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 5
},
{
"cell_type": "code",
"collapsed": false,
"input": "print patsy.bs.__doc__",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "bs(x, df=None, knots=None, degree=3, include_intercept=False, lower_bound=None, upper_bound=None)\n\n Generates a B-spline basis for ``x``, allowing non-linear fits. The usual\n usage is something like::\n\n y ~ 1 + bs(x, 4)\n\n to fit ``y`` as a smooth function of ``x``, with 4 degrees of freedom\n given to the smooth.\n\n :arg df: The number of degrees of freedom to use for this spline. The\n return value will have this many columns. You must specify at least one\n of ``df`` and ``knots``.\n :arg knots: The interior knots to use for the spline. If unspecified, then\n equally spaced quantiles of the input data are used. You must specify at\n least one of ``df`` and ``knots``.\n :arg degree: The degree of the spline to use.\n :arg include_intercept: If ``True``, then the resulting\n spline basis will span the intercept term (i.e., the constant\n function). If ``False`` (the default) then this will not be the case,\n which is useful for avoiding overspecification in models that include\n multiple spline terms and/or an intercept term.\n :arg lower_bound: The lower exterior knot location.\n :arg upper_bound: The upper exterior knot location.\n\n A spline with ``degree=0`` is piecewise constant with breakpoints at each\n knot, and the default knot positions are quantiles of the input. So if you\n find yourself in the situation of wanting to quantize a continuous\n variable into equal-sized bins with a constant effect across each bin, you\n can use ``bs(x, num_bins, degree=0)``.\n\n Similarly, a spline with ``degree=1`` is piecewise linear with breakpoints\n at each knot.\n\n The default is ``degree=3``, which gives a cubic b-spline.\n\n This is a stateful transform (for details see\n :ref:`stateful-transforms`). If ``knots``, ``lower_bound``, or\n ``upper_bound`` are not specified, they will be calculated from the data\n and then the chosen values will be remembered and re-used for prediction\n from the fitted model.\n\n Using this function requires scipy be installed.\n\n .. note:: This function is very similar to the R function of the same\n name. In cases where both return output at all (e.g., R's ``bs`` will\n raise an error if ``degree=0``, while patsy's will not), they should\n produce identical output given identical input and parameter settings.\n\n .. warning:: I'm not sure on what the proper handling of points outside\n the lower/upper bounds is, so for now attempting to evaluate a spline\n basis at such points produces an error. Patches gratefully accepted.\n\n .. versionadded:: 0.2.0\n \n"
}
],
"prompt_number": 6
},
{
"cell_type": "code",
"collapsed": false,
"input": "X = array(patsy.dmatrix(\"\"\"0+bs(x,knots=[0,2,4,6,8,10],\n lower_bound=0,\n upper_bound=10,\n degree=3,include_intercept=True)\"\"\", {'x':x}))\nplot(x, X)\naxis([-1,11,-.1,1.1])\n\nprint X.shape",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "(100, 10)\n"
},
{
"metadata": {},
"output_type": "display_data",
"png": 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6dtVG7t64AaQVpiEpNMnoHBpt4oQkhSYhozgD6noFcOaMNrHGVgQHa82JLVsa\nXZar1fgiLw/zHWx1N/BkYCC6+/pitVhrmd7xdS+MdaxgLMIVcBE2PAySdRLU1YlRWLgfAgHLp2MO\nJChoADgcLoqLfwAA5OXlYfXq1fjkk08cLJmWjh07omfPnth+XwhtSYk2zWLSJNvtzTBA377AiRNA\nWlEakkON+/6pz9sJ8XH3QZh3GKQnfgJiYrQK1pZMnQps3dqoYNU2mQy9/f3R2hbuGgtZ06oVNkgk\nkCgUKNxTCG4MFwG9W4bV3UD0nGjkfZWH3KxViIgYDze3EEeLxBpa63shcnKWgBCC999/H2+88QZa\nt27taNHuMGvWLHzyySdQ3/NZ2LFDmx8XauMHoCeeuEd5hxlX3tTn7aQkhyWj8v+Oav+ituahh7Tv\nzN9/BwCoCcE6sRizBGY0QrYD0Vwu3oyKwsJb2RCtEDl18SlL4cZyEfgqg4L8nRAIZjpaHNYJChoI\nADh9+gv88ssvmGdJST4b8uijjyI0NBRHbofQEqK1ayZOtP3evXtr+4inFZpheVOft/ORHJoMjzMX\n7KO8AeD114HbiQo/FBcj0t0dPf397bO3GbwXHY2Cw8Wo92EQ0LdlWd0NuL5+GPjrSbgqbZ/Nam8Y\nhkFMzPt4//0PMG/ePPj5+TlapEYwDINZs2ZhzZo1AIALF7S+6N69bb93XBzAeMiRV5WPVkHGa9FT\nn7eT0j6oHaKu3AJ69bLPhiNGAL/9BlJUhNUikdNZ3Q34u7hgyj5XHBrNabZx3YZQqcpRpPgGAQWT\nkbclz9Hi2IS0tFBkZ1djxIj2jhZFJy+99BIKCgpw9uxZfP211q6xx1uNYYCOfdMRykmEK8d4/SDa\njMFJ6VrqjkIfDhARYZ8NAwKAQYNw5vBhlKhUGBTinL7Wsv8rQ4jaBYcfrsep8nJHi8M6UulnCA5+\nHvH/ewzitWKTKw42FwghmDt3HubPH4+CgjWOFkcnLi4umD59Olas+AwHDwJjx9pv74gOaXAtNS1R\nibpNnJTW16T4U6CCWmNd1xuzeP11rK+qwrs8Hlyc1KoVLRMhdl4MlsTH4b3sbJMKHjUX1OoaSCQb\nER39Hnwe8oFPZx+z6n03B77//nsolUq8+eYGyOVpFtf7tjXjx4/Hn3+GoGvXGkTascKwa2Qaym4a\nDxMEqNvEafE4cwHX2gbiVtktu+0pfeQR/NGmDcZIJHbb0xwqzlWgLrcOYcPD8Fp4OCpUKvxaVuZo\nsVhDJttFBgxmAAAgAElEQVQGP78e8PbWfnij34uGeLXY7G47zopGo8HChQuxdOlSuLpyIRDMhEi0\nwtFi6cTb2xv+/tPh73/Arvvmq9OAomTk5hofS0MFnRFCgJMnUd69I9IK0+y27VcyGYZXVcHPjFKx\n9kS8SgzBTAEYVwYuDINFsbH4UChsEdY3ISqIxWsQHf3enWv+vfzhFuKG4h+sb5brDOzfvx++vr53\nEnIiIyeivDwFtbWWN2O2FTdvAvX1Apw8Oc9owSo2SStKQ89WyThxwvhYGirojFy/Dvj6Irzdw3fT\n5G2MUqPBl3l5eOvhh7V5ugqFXfY1lZr0GlScqUDEhLtnAK+EhqJOo8GxUvMb+TobhYUH4OHBh7//\no3euMQyD6PeiIVopavZfUGq1GosWLcKSJUvuHDS7uPggKmoya53m2WTnTmDUKFd06dIBBw7Yx/qW\n18tRUF2A53q0Mkl5U5+3M3LyJPDEE0gOTb6bJm9jDhcXI8HTE+1bt9YWKz52zC77mop4rRi8qTy4\neN2t98BhGCxuAdY3IQRi8cpGVncDwYOCoa5So/yv5n04u3fvXoSGhuKpp55qdJ3H+x8KC79DfX2B\ngyRrikaj7Qw/erS22uEXX3xhl31vFN9AYnAi+jzhYprlTX3eTsjffwM9ethVeX+el4e3eDztL6NH\na9+9ToIiX4GiQ0XgTeU1uffS7aiYw1Z0nHc0ZWX/B0JUCAp6rsk9hsNAMFsA0UrDNc2dGZVKhcWL\nFzeyuhtwdw9DWNhwSKWWd3Jnm7Nntf0lO3cGnn/+eeTl5eHS/a1ubEBaoTazMjlZW2rI2AMl9Xk7\nI5cvA507o11oO2SWZNr82zVNLkdGTQ1ebggPfOUV4M8/jb977IR0vRThI8PhFtK0KhBz2/e9JDe3\n2VrfYvEqCASzwTC63/rho8IhT5Wj+kq1nSVjhz179oDH4+FJPTV6BIIZyMvbArXaOV7fzp1a+4Vh\ntGGDkydPxueff27zfRtqmnA42vZo99b31gX1eTsb9fXa2pPt28PLzQuRvpG4VWrbiJOv8vPxemQk\n3Dm3/9f7+wP9+wP799t0X1NQVamQvzUf/Bl8vWNeCA4GAfBTSYn9BGOJqqrLqKlJR1jYCL1jOB4c\n8P/H19mswdlRq9X4+OOPsWDBAr1jPD1bIyDgSeTnG26GYA/q6rQtyUaOvHttwoQJOHToECpN7Kdq\nKfcWpHroIePKu1n6vI8fP44OHTogKSkJK1eu1Dvu0KFD4HA4dnnkYY20NCA+XvvcBm2afGphqs22\nq9NosKugAK/fnww0erTWBHEw+VvzEfhUIDzj9BfIYhgGH8TE4KNmaH1LJGvB470NDsfd4LioyVEo\n+akEdWL7RT6wwcGDBxEcHIy+ffsaHCcQzIRE8imIg9t6HTumtXrvTTAODw9Hv379sG/fPpvunVqY\neqcUbOfOBnukAGiGPm+FQoEpU6bg+PHjuHr1Kg4ePIjLOl5lVVUV1q9fjx49ethMUJtw22XSwEMR\nD+G/AiNfwVZwuLgYnX18EHd/9cD+/YGsLOCW/eLM70ej1EDyqQSCWcZT9QeHhECuVuO3ZhT3XVcn\nQknJz4iKMl5r1DXAFRFjIyDdILWDZOyg0WiwdOlSLFiwwGgpAz+/R+DhEW2wVZo9aHCZ3M8bb7xh\ntE2aNZTWlqKstuxOTRNTlHez83lfuHABycnJ4PF4cHV1xbBhw3BMR2TEggULMHfuXHh4eDQva+w+\n5d05ojMu5xv5K1rB1vx8TNSVQubmBgwdCuzZY7O9jVF0sAiecZ7wfdh442MOw2B+M7O+JZL1iIgY\nD1dX0wqA8d/lI/+bfKgqnMva0seRI0fA5XLx7LPPmjReIJgFsXi1w/5+paXAX39pj3zu5+mnn4ZM\nJsOVK1dssvd/sv/QKaITOLfPPZKTgexswEBXtubn85ZIJBDc80zD5/MhuS8j8NKlS5BKpXjuOe3p\nfbMqYPTff42Vd2RnXJbZRnln19biSnX1nYiNJrz2GrB7d+O21naCEALxarFJVncDw8LCUFhfj5Rm\nUPNEpSqHTLYNfP67Js/hxnAR1D8I+V/l21AydiCEYOnSpfjggw9M/vwFBz8PtboaFRUmxMnZgEOH\ntK1idRU6dHFxwYQJE/D17cqbbHM5/zI6R9z93Lu7A4mJQKoBj6kz+rwNltMy9kbQaDSYMWMGvv32\n2zvXDH2TL1q06M7Pffr0QZ8+fUyT0hZoNMCVK9rTitvE+MegVlmLguoChPuwWyL06/x8jA4PhwdH\nz/dljx7aA9T7vlDsQflf5dDUahD0XJDJc1wYBnOjo7FMJMKTgYE2lM568vK+RFDQAHC55lVvFMwW\nIHVQKnjv8MBxc96z/V9//RX19fV44YUXTJ7DMBzw+TMhFq9BQEAf2wmnhz17gLff1n9//Pjx6Nq1\nK1auXAlPlpuUXJZdRr+4fo2uNbhOunXTPceePu+UlBSkpKQYH0gMcPLkSTJw4MA7v69atYosXbr0\nzu/l5eUkJCSExMbGktjYWMLlcklUVBT5999/m6xlZCv7c/MmIdHRTS4/uf1J8kvmL6xupdRoSOSZ\nMyS1utrwwPnzCZk1i9W9TeHKgCtE+qXU7HkKtZoIzp4lFysrbSAVO6jVCnL2LI9UVl6yaP7lJy8T\n2S4Zy1KxS+/evcnu3bvNnqdW15IzZ8JJdXWaDaTSj1hMSGAgIbW1hsf179+f7Nq1i/X9kz5PIpfz\nLze6tn49IZMn659TVltG/Jf7sy6LKejTnQbNiW7duiE1NRVSqRRKpRL79+9v1LzU398fRUVFEAqF\nEAqF6NGjB44ePYouXbpY99VjD+7zdzfQOZJ9v/evpaWI4XKR7O1teOBrrwF792qfCuyE/Loc1Zeq\nETHa/HK47hwOZgoEWG5KZR8HUVS0H56ebeDra9nTjGCmAOK1Yqf17Z89exYSiQRDhw41ey6Hw0VU\n1FuQSOzb1/K774CXXwa4XMPjXn/9ddZdJzXKGgjLhE2aDhs7tHRGt4lB5c3lcrFp0yb0798fnTp1\nwuDBg9GlSxcsXLgQR48etZeMtkGPe6JzBPt+7+0yGcabUis8KQkICQFOnWJ1f0NI1kkQNTUKHK5l\nboGJkZE4XVGB9JoaliWzHkIIxOK1VrU4CxoQBE2tBuUpzunbX758OWbPng1XV+MNBXQRFTUFRUUH\n7Zoyv2eP1k4xxqBBg3D16lXksmgcXCu4hrYhbeHu0jhctFMnrc9bracqtDOGCtrNl2HHrUzj2WcJ\nOXKkyeXUglTSekNr1rYprq8n/qdOkTKl0rQJK1cS8uabrO1vCEW+gpwKOEXqi+qtWmeJUEjG3bjB\nklTsUVr6O7lwoR3RaNRWrZP3VR658twVlqRijytXrpDIyEhSa8z/YISMjMkkO3sBS1IZ5sYNQiIi\nCFGpTBs/depUsnjxYtb233RxE5lwZILOe61aEXL9uu55KrWKMIsY1uQwB32603lPYWyNHrdJm5A2\nyKvKQ6WCnQyvvYWFeC4oCAGmWkbDh2uP4uvrWdnfENLPpQgbHqYzFd4cpvF4+LG4GCI7lvM0hQar\nW18qvKmEjwpH9b/VkN+QsyQZO6xYsQLTp08H15j/wQh8/nTk5W2GWm37p6e9e7VvcRcX42MBYNy4\ncdi+fTs0LLkSL8saR5rciyHXiQtHK7CGOE+3pQdTeefnAyoVwG+aBu7KcUX7sPa4ImMnxnRbfr5p\nLpMGoqO17pNff2Vlf32oa9TI25IH/nT9qfCmEujmhgmRkVjnRI0l5PLrqK6+hPDwkcYHG4HD5SDq\nrShI1jrP68vOzsZvv/2GSZOMJx0Zw8srEX5+PVFQsIMFyfRDiNZlMkJ/dYImdO3aFd7e3jjFkivx\n/jDBezHJ7+1EiToPpvL+7z9tiKCeUEi2/N5Xq6tRqFSir7mhdK+9ZvOEHdm3Mvg/6g+vRC9W1pvO\n52OHTIYSpXO8ucXiteDxpoHDsc4qbYD3Fg9Fh4pQX2D7JyJTWLNmDSZNmsRaR3iBYCbE4nUgNrQs\n//lH+1994Xi6YBjmjvVtLSqNCmlFaegU0Unn/c6dDdc4cbZEnQdTed+4oU2r0gNbyvtbmQxjwsPN\n71E5ZAjwyy9AtW0qvxE1gWSdBPyZ1lvdDUR5eOCV0FB8JnV8Snl9vQzFxT8gKmoKa2u6hbghbHgY\npJ87/vUVFBRg3759eNtQoLSZ+Pv3gqtrAEpKbBeIsGePtgiVuR+HkSNH4vDhw6i28vOQXpwOvh8f\nPu4+Ou8nJWlVgz6cLeLkwVTe6elAmzZ6b7MRLqjUaLC7sBBjLelIHxICPP44cOSIVTLoo+RoCdyC\n3eD/uGmp4qYyWyDA51Ip5PqO7O2EVPoZwsJGwM0tmNV1+dP5yNucB3WNY1/fhg0bMHz4cISHs5dI\nxjDM7ZR523SZV6uBffvMc5k0EBERgV69euHgwYNWyWDIZQJoC2SVlgJVVbrvO1vEyYOpvDMygLZt\n9d7uENYBGSUZUKgsb0/2a1kZ4rlcJHpZ6JZoSJe3AeI12lR4tksZJHp5oXdAALbmOy6lXK2WIy9v\nCwSC6ayv7ZXoBf/H/CHb7rgu85WVldiyZQtmzZrF+tqhoYOhUEhQWXmB9bX/+gvg8QzaTAYZO3Ys\nduywzidv6LASADgcbZr8zZu671OftzOQkWHwXeTp5omEoARcLbhq8RY7ZDLLrO4GBg0CzpwBioos\nX0MHFecqoMhTIORlPTVWrOQ9gQBrxWLU2zHR6F5ksu3w9+8FT8/WNllfMFMAyTqJw7rMb9myBc88\n8wzi4+NZX5thXMHnv2uTPpemxnbr4/nnn8eVK1esivn+J+8fdI3qanBMmzZa9aAL6vN2NOXlgFwO\nREUZHNZT0BPnJOcs2qJMqcSvpaUYGhpq0XwAgI8PMHCgtkExi0jWSsCfzgfjYpsCYt38/JDg6Ym9\nhYU2Wd8QhKghkXxiVVKOMfwe89N2mT9i/1ZwCoUCn3zyCebMmWOzPSIiJqC8/E/U1maztmZdHfDD\nD8CwYZav4eHhgaFDh2KXhS0DlWolLuVfQnded4Pj2rbVelV1QX3ejqbB6jbiMujB64HzkvMWbbG/\nqAjPBAUh0M26+Gm2XSe1t2pRfqIckeN1lKVlkbnR0VglEkFj55Ty4uIf4OYWCj+/R40PthCGYSCY\nJYB4tf1T5nfu3IlOnTrhoXuKqbGNq6svIiPfYDVl/ueftZEcvKZtUc1izJgx2LFjh0X/368UXEFc\nYBz8PAxH5xi0vKnP28Gkpxv0dzdgjeVttcukgf79gcxMQCi0fi0Akk8kiHwzEi4+JmZIWMhTgYHg\ncjh2bZVGCIFItBoCwRyblyUOeTkEyiIlKs/YtlXXvajVaqxatQpz5861+V483v9QULAbSiU7f79d\nuxq3OrOUHj16gBCCv//+2+y55yXn0ZPf0+g4o5Y39Xk7ECP+7gYSgxNRUVcBWbV5h1OZNTXIqq1F\nfzbKpDY0aWChu3x9UT0K9hSA/z/2wgP1wdwuF7tCJLKbdVpRcQoqVRlCQgbZfC/GhQF/Bh+i1fbr\nMv/DDz8gODgYvXv3tvleHh5RCAl5GVLpF1avVVqq7a89ZIj1cjEMgzFjxjQqQW0q5yTnTFLeiYna\npla6jmyoz9vRmKi8OQwHj/AfMdt1srOgACPCw+Gmr263uTT0t7RSCeZ9nofQIaFwjzDcv5EtBoeG\nokipxOmKCrvsp+0KPxMMY9unigYixkWg8lwlatJtn1JOCMHKlSsxd+5cuzU7EQhmQSr9DGq1gfYy\nJrB/v/YB0p+lqNRRo0Zh//79UCjMiwQ7Jz6HHnzjbRp9fIDAQECso/809Xk7GhPdJgDQk2+e60RD\nCHYWFGAMi/G36H77gMWCR8UG1DVqSL+QQjDTvGYE1uDCMJgjEGC5yPbWqVx+HVVV/yA8fIzN92rA\nxcsFvLd4duky/+eff0Iul5vVbMFavL3bwc+vBwoKzLdy70Vfn0pLiY2NRYcOHfDTTz+ZPKegugDl\ndeVoE2JanKI+14kbx426TRyGSqVtVpeQYNLwnvyeOCc2XXmfrqiAj4sLOvvozuCyCIbRvvutiHGV\nbZPB/zF/eLVhJxXeVMZEROBKdTX+s1GmaANi8RpERU2Fiwu7HVeMETU1CkUHi6DItzwfwBSWL1+O\n9957Dxy2nuZMJDp6NsTiNSDEsqSkrCztkU3//uzKNWbMGOzcudPk8ecl5/EI/5E7PSuNoe/QkrpN\nHElODhARAZjYVqk7rzsu5V8y+dt2x22rm/VH21GjtM+fFlQaJCoC8VoxBHPsZ3U34MHhYIZAgBU2\ntL7r6sQoLj4MHu8tm+2hD/dQd4SPDId0ve1S5v/++29kZmbiNWuCpC3Ez+8xuLmFoajoe4vm79ql\nrSBobdDV/bzyyitISUlBcbFp4ZrnJOfQg2fcZdKAPsubuk0ciYn+7gb8uf6IDYg1KVmnVq3G90VF\nGMmmy6SBuDjtO+qXX8yeWnigEB48D/j3ZDcV3lTejIzEH2VlyLRRswaJ5BNERIxjPRXeVASzBMj7\nKs9mXeYbmi24sa0BTYBhGERHz4FYvNLsg2dCtMqbTZdJA35+fhg4cCD27dtn0vhzknPoKTB+WNmA\nXsubhgo6ECM1TXRhasjgkZISdPP1RZSHh6XSGcYC1wkhBKIVIkTPi7aNTCbg6+qKqTweVuk6AbIS\npbIEMtl2CAQzWF/bVLixXAQ/F4y8TXmsr52WloZz585hwoQJrK9tKsHBg6BW16Ks7Hez5p07B7i6\nAg8/bBu5GmK+jaFUK/Fv3r94hPeIyWu3aWPA8qY+bwdhpKaJLkxN1tkhk2EMG7Hd+hg2DPjjD7PS\n5Ut/LgXDMAgaYHpXeFvwPx4Ph4qKIDEzQsAYUunnCAl5GR4etg9/NIRgjgCS9RKoa9ktWLVixQq8\n88478LK0Pg4LMAwH0dHvQSRabta8b74Bxo0zv4KgqfTr1w8SiQQ3DJUBBHCt8BpiAmLgzzX9yVMg\n0CZi31+givq8HYmZbhPANMtbVl+Pc5WVeCnENvVCAGhjrQYN0h7fmwAhBLnLchE9N9pu4WX6CHZz\nw/iICKxl0fpWq+WQSj9DdPRs1ta0FJ8OPvB92BcF37LXB1IoFOLnn3/GW2/Z35d/P2FhI1BXl21y\nwaqqKm0zqHHjbCeTq6srRo4cafTg8pzYtPjue+FwtDEN9xeooj5vR2JGmGADbUPaoqKuAuIK/Ypn\nT0EBXgoJgbepvZ0sZeJEYOtWk2K+K05VQFmoROirVtRXYZGZAgG+lclQyFJ7t/z8rfD37wUvL/P+\nnrYiel40RKtEICp2kpJWrFiByZMnw5+tAGkr4HDcIBDMMtn6/u474IkntLEBtqQh6sRQi7QTuSfw\nePTjZq+t69CS+rwdRXk5UFsLRJpX14PDcPBk3JP4K+cvnfcJIdh+u+mCzenVSxvueN64G0e0XATB\nHIHNClCZS5SHB0aEhbHSKk2jUUAsXo2YmHksSMYO/o/6gxvNRcFe661vsViMAwcOYPp09svaWkpE\nxARUVp6HXJ5mdOzXX2vtDFvToUMHhISE4K+/dH82NUSDv3L+Qr+4fmavrcvvTX3ejiIrC2jd2iIn\nXL+4fvhT+KfOe/9VV6NSrcYTAQHWSmgchrlrfRug6p8qyK/JETHGxqaPmbwXHY2v8vKsbpUmk22D\nt3dH+Pra6DTMQmIWxED0scjqcrErV67ExIkTEWJLN5yZuLh4gcd7B7m5ywyOS00FRCLg2WftI5eh\nFmmphakI5AZC4G9+mGxCAnDrVuNr1OftKIRCbcidBfSN64s/hH/oDJf69nZsN8defuUxY7QORX3t\nPgDkfJQDwXsCcDyc688bzeVicGgoPrXC+tZolBCJViAmZgGLkrFDQN8AuAa5ouig5TXY8/PzsWfP\nHsycabuytpbC401FWdlvqKnRU3YPWqt73DhtpIk9eO2113D06FFU6fg8/JH9B/rG9bVo3bi4pvXg\nqM/bUQiFQGysRVMTghJACEFWaVaj60qNBnsLCmwbZXI/ERHAk09qe0rpoOpyFaouViFyom3LvlrK\nvOhobMrLQ7nKMgumoGAnPD1bw9/fvEMoe8AwDGIWxCB3aS6IxjLre/Xq1RgzZgyrLc7YwtXVDzze\n23qtb4VCG9ttz8jG0NBQPPHEEzpbpP2Z86fFyjs2tqnypj5vR5GTY7HlzTAM+sU3dZ38UlqKRC8v\ntDYxY5M13nwT2LRJ58Fl7ke5iJ4TDRdP+xRoMpd4T088HxyM9RZY34SoIBItQ0zMhzaQjB2Cng0C\nh8uxqFlDQUEBtm/fjtmzHR9Bow8+/22Ulh5DbW1Wk3sHDgAPPQS0amVfmcaNG9ek0qBKo8Kp3FN4\nMvZJi9aMjAQqKrTHZA1Qn7ejsMJtAgB9Y7Wuk3vZzlbdbnPp31/bWf7MmUaXq69Wo/JcJSLfdE6r\nu4EPYmKwUSpFmZm+74KCvXB35yEgwPZlUS2FYRjEfBCD3CW5ZmclrlixAqNHjwbP2q4FNsTV1R88\n3rQm1jchwPr1AIsN7U1m4MCBSEtLg/AeU/mfvH8QExCDUG/Loq04HCA6WmvzNUB93o7CCrcJoPV7\n/5XzFzREG5ZUolTiz/JyvGpNqzNL4XCA//0P2LCh0eXcj3IhmCmAi5dzWt0NtPb0xEshIVhrhvWt\n0SiRm7sYcXGLbSgZOwQPCgYYoPgH061vqVSKHTt2YN4854mg0QeP9w6Ki480apV24YK2dvdzz9lf\nHnd3dwwfPrxRxuWfQstdJg3c7zqhPm9HQAiQm2uV8hb4CxDIDURqYSoAbWz3c0FB8LfXycz9jB2r\nzbi8nfhSdbkKFacrEDXFcG9OZ2FBTAw2SaUoNtH6Lij4FlxuLAIC+thWMBZgGAZxS+OQ82GOyZEn\ny5Ytw4QJExDhiCc5M3FzCwSPNw05OXe/SDdsAKZNA2yd6qCPBtdJQ8z3n8I/LQoRvJe4uPssb1oS\n1gHIZICfH+DtbdUyfeP63vF7fyOTYYKZMeOs4uenrXeyaRMAQPiBENHvR8PF27mt7gZiuFwMCwvD\nKhMqDmo0CuTkLEFs7Ed2kIwdggYEwcXPBYXfGW/EnJubi3379tm0sTDbCAQzUFr6C+TyNOTlaWum\njR/vOHm6dOkCHx8fnDhxAnWqOlyQXkDvGOvca/dHnLhx3KAizcxtcvz4cXTo0AFJSUlYuXJlk/ur\nV69GcnIy2rdvj969ezfyPTkFVrpMGugb1xe/Z/+Oy1VVKFOp0Ncesd2GmDYN2LoVFX8WQp4qR9Sb\nzcPqbmB+TAy+zs+HzEjWZX7+V/Dx6eiUESb6uGN9L8wxmnW5dOlSTJ48GaGOcMFZiKurPwSC2RAK\nP8Tmzdpe2Y78ODAMg9dffx3ffPMNzonPITk02WizYWPodJs0J8tboVBgypQpOH78OK5evYqDBw/i\n8uXLjcb06NEDly5dQmpqKl577TXMmOG4Km86sSLS5F6ein8Kp0SnsEUqxviICPvFduujdWuQbt0h\nnPIPYhfFOl1ctzF4Hh4YGxGBj+59Nr0PtboGubnLEBu7xH6CsURg30B4CDwg+1Z/H9T09HQcPnzY\nKeO6jcHjTUVR0X/YvFmJadMcLQ0wcuRIHD16FIeuHcKA1gOsXq+J26S5HVheuHABycnJ4PF4cHV1\nxbBhw3Ds2LFGY3r16gWP26VQH3vsMUiltitObxFWRpo0EOQZhIciu2NPgQzjnMQ3WdZ3NuqFFYgY\n4TzZeOYwPyYG+4uKkKGn3rdE8in8/R+Dr28XO0vGDnEfxyFnUY7eioPz5s3DnDlzEBTk2MqPluDi\n4oUzZ7YjOfkftGvnaGmAkJAQPP3M09h/dT9ebPui1evd7zZxtgNLo6dtEokEAsHd9FI+n4+UlBS9\n47ds2YIXX9T9P27RokV3fu7Tpw/69OljsqBWIRQC3bqxslRM65G4VStDDJfLynrWQNQE2bu9ERuf\nAuYwo21b0swIdnPDLIEA72dn41D79o3u1dcXQiJZhy5dzGsC7Uz49/SH3yN+kHwqQcy8mEb3zpw5\ng0uXLmHv3r0Oks466uuBr756HAsXDkFZ2RQEBj7laJHw1PCn8OOFH9EpvJPVa4WEaBOPKiu1R0z2\nStJJSUkxqGMbMKq8zSknunv3bly6dAknTpzQef9e5W1XhEJg6FBWlsr2aIuq9BVQa4bBhePYw8GC\nnQXgeHIQ+tGLwLy52tdo5z6HbPA2j4c2UinOVlTg0Xuq6OXkLEZY2Eh4erZ2oHTWE78iHpd6XELk\n65FwD3MHoC1oNnv2bCxduhRcJzAELGH3biAhgcELL7yGrKyZePjhS2AYx34mikOK4SZ0w7Vr19Cx\nY0er1mKYu37vTp3s5/O+37BdvFh3eKzRTzqfz4f4njrMYrG4kSXewO+//46PP/4YP/74o0NaNhmE\nJZ93Tl0d0hVq8JW5+FtqeTd3NlBXq5E9Pxut17UG89wAbYzWfe6s5oKniwuWxMVh9q1bdxJbamoy\nUFS0H7GxzlfDxFw8W3sifFQ4cpfk3rn2ww8/oKamBiNHjnSgZJajVgMrVgDvvw+EhAyGq6sfZLLt\njhYLP2X+hBfbvohvvvmGlfXu9Xs3O593t27dkJqaCqlUCqVSif3792PAgMaHAZcvX8bkyZNx9OhR\np6qEBkD7LpNItOlSVrI1Px8jw8LwcuJAHMk4woJwliNaLUJAnwD4PeKnNRHefx/4+GOTan07I6PD\nw1GtVmP/7U5B2dnvQSCYAzc3J3s/WUjMghgUfleImowa1NXVYc6cOVi1apXdO8KzxaFDQFCQtswO\nwzBo1WodhMIFUKn0F0yzNbJqGdKL0/HhmA+xa9cu1N6b224h9/q9nc3nbfSdw+VysWnTJvTv3x+d\nOnXC4MGD0aVLFyxcuBA//fQTAGDOnDmQy+UYMmQIOnfujJdeesnmgpuMRAKEhgJW9pZUajT4Oj8f\nk3RAiBoAACAASURBVKOiMKjNIIcqb4VEAelnUsQvj797cfBgbc3y//s/h8llDS4Mg40JCZh16xby\nin9DdfUV8Pn/c7RYrOEW7IboudHImp6FNWvWoEOHDnjmmWccLZZFaDTA0qVae6HBq+rn1w2Bgf0g\nFjcNJbYXRzOOon+r/mjTug26deuGAwcOWL3mveGCzlaYCsRO2HGrxqSkEPL441Yvc7CwkPS+dIkQ\nQohaoyaRayJJRnGG1etaQtqwNJI9P7vpjf37CenShRC12v5CscTotP/IT6fiSFHRj44WhXXU9Wpy\nJOEICfINIkKh0NHiWMzOnYT06EGIRtP4em2tiJw+HUxqajIdItfze54ne67uIYQQcvjwYfLoo49a\nveb33xMyaJD2533X9pFX979q9Zrmok93Ns9nNnNgKUxwc14eJkVpk2A4DAcvtHkBP2b8aPW65lL6\naykq/65E9Ps63EBDhmgPLFmwOBzFbI/DuK6OQpmXdanNzgjHjYNvor7BYM5gCELNbxDgDCgUwIIF\nwMqVTfuacLkCCATv4ebNqWYX5bIWeb0cJ3JOYECC1qU7cOBA5Obm4tq1a1ate6/bpNn5vJs9LGRX\nZtXW4kp1NV65JwNuSLsh2Jtq3xAvda0amVMzkfB5gu7iUwyjPUWaP18bx9XMqKvLQaVsIzwEK/FO\nVpbdFYCt+f3333FVdBVvPfsWcj/KNT7BCdm8GUhKAnrryTzn899FfX0+ior221Wuw+mH8Vj0Ywjg\natM8XV1dMXHiRGzZssWqdRvcJoQ0Q593s4eFSJMv8/IwNiICHvccLvWN64uC6oI7harsgWiZCD5d\nfBA8IFj/oH79tAWVjbRKczYIIcjMfBt8/nRMju0JsUKBvYXG64I0F+RyOSZNmoSNGzci+dNk5H+d\nD/l1uaPFMovKSmDZMmC5gT7EHI4bEhM3IytrBlSqCrvJtuPqDozpOKbRtYkTJ2LPnj2Qyy3//xwQ\noO0KVFrqfD7vlq+8rXSbKDQafCuT4c37ilC5cFwwquMo7LiyQ89MdpFflyNvcx5af2pCzPOKFcBH\nHxlsleZsFBbuRV1dNgSCWXDncLCtbVtMz8pCQTN8gtDF/Pnz8dhjj2HgwIFwj3BH3EdxSB+fzlq3\neXuwerW2lLyx8Gl//0cRHDwQ2dn2KW8rrZTiovQiXmrbOFCCz+ejV69eVidBNbhOml1tk2aPlW6T\nvYWFeMjHBwleXk3ujek0Bruu7rL5t7FGqUH6mHTELY2DR5QJUTOdO2s7wDoqKcpMFIp8ZGVNR9u2\n34LD0b6+h319MT4yEtMyMx0snfWcOXMG+/fvx6effnrnWuSkSLj6uUK02nhVRWfg1i1tAcuPPzZt\nfHz8SpSUHEVZ2e+2FQzA7mu7MbjdYHi6Ne1oNXXqVGzYsMEqF1yD68TNxY26TeyGSgUUFAB8vkXT\nCSFYL5Fguo6kJABICk0Cz4+HP7L/0HmfLUQfi+AW5mZeh5yVK4GdOwErD2xsDSEEN29OQlTUJPj6\ndm10b1FsLK7J5ThYZHlDX0dTW1uLCRMm4PPPP29Uv4RhGLTZ2gaSdRJUX6t2oITGIUTb+2POHEDP\nR6EJbm6BaNPmG6SnT4BKVW5D2Qi+vfItxnYaq/P+008/DZVKZVK6uT5iY7XtAFw5rtRtYjfy87Ux\n3hY2TDhZUYFajQbPBAbqHTO201h8e+VbvfetpfLvSkg3SdHm6zZmlSpAWBiweDEwdapTJ+4UFOxE\nXV0uYmI+aHKPy+FgW5s2mJaZCalC4QDprGfOnDno3LkzXn755Sb3uDFcxC+PR/q4dGiUGgdIZxqH\nD2uPjt5917x5QUFPIyRkEDIzbRevfyn/EmqVtXgs+jGd9xmGwbvvvtvoqcdceDxAKqXNGOyLVGqx\n1Q0A6yUSvMPjGSz9Orz9cPyc+TMqFZUW76MPtVyN9DHpSNiYAI9IC5KM3nwTqKnRtvR2QmpqbuLW\nrZlo124HOBx3nWN6+vtjGo+HUTduQO3EX0K6OHz4MH766Sds3rxZ75iI1yPgEekB4Xwnq4F/G7lc\nq7Q//xxw1/0nMkh8/EpUVl5AYaFtwld3XN2BMZ3GgMPoV2WjRo3C2bNncevWLYv24PNvK28aKmhH\nJBLt16YFZNfW4mRFBcYYKf0a4hWCvnF9sS91n0X76IMQgpuTb8Kvhx/ChoZZtoiLC/DFF9rnXSeL\n3FCra3H9+lDExX0EHx/DFeDm3S5tsCy3+YTXiUQiTJo0CXv37kWAgS4FDMOg7fa2KNxXiJKfSuwo\noWl8+CHw+OPaNHhLcHHxRrt2u5GZORU1NeyeX9Sp6rD32l6M7jja4DgvLy9MnDgRGzdutGgfHk+r\nSmiooD2RSCy2vD+TSjEhIgLeJjTlm9Z9Gj49/+m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LFqurn6Jen0SdLoQVFQ+wtTX//Nhq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\nQjJ5S5IkDUIyeUuSJA1C/w/XIY8zjuLnsgAAAABJRU5ErkJggg==\n",
"text": "<matplotlib.figure.Figure at 0x7fb0a6accd90>"
}
],
"prompt_number": 7
},
{
"cell_type": "code",
"collapsed": false,
"input": "# compare that to\n\nt = [0,0,0] + [0,2,4,6,8,10] + [10,10,10]\nc = zeros_like(t)\nc[1] = 1\nk=3\n\ny = scipy.interpolate.splev(x, [t, c, k])\nplot(x,y, 'k-')\naxis([-1,11,-.1,1.1]);\n",
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAW8AAAD5CAYAAADodLT+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text": "<matplotlib.figure.Figure at 0x2e37dd0>"
}
],
"prompt_number": 8
},
{
"cell_type": "markdown",
"metadata": {},
"source": "The same, if you know where to look"
},
{
"cell_type": "code",
"collapsed": false,
"input": "X[:,2]-y",
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 9,
"text": "array([ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n 0., 0., 0., 0., 0., 0., 0., 0., 0.])"
}
],
"prompt_number": 9
},
{
"cell_type": "markdown",
"metadata": {},
"source": "# Now compare bispline to ~ 0 + bs(x):bs(y)"
},
{
"cell_type": "code",
"collapsed": false,
"input": "x = linspace(0, 10, 100)\ny = linspace(0, 10, 100)",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 11
},
{
"cell_type": "code",
"collapsed": false,
"input": "data = {'x': [x_i for x_i in x for y_i in y],\n 'y': [y_i for x_i in x for y_i in y],}\n\nX = array(patsy.dmatrix(\"\"\"0 + bs(x,knots=[0,2,4,6,8,10],\n lower_bound=0,\n upper_bound=10,\n degree=3,include_intercept=True)\n :bs(y,knots=[0,2,4,6,8,10],\n lower_bound=0,\n upper_bound=10,\n degree=3,include_intercept=True)\"\"\", data))\nplot(data['x'], X, alpha=.5)\naxis([-1,11,-.1,1.1])\nprint X.shape",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "(10000, 100)\n"
},
{
"metadata": {},
"output_type": "display_data",
"png": 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2vV5HvW6S/7NsE5/dUFkk3GsBTtYDoJuUwaz7XmszRPOPf9zZotgo8u41bXAh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ShDQTl13rmfc+XzNRiiIifTBq01UZ6TxzHKWiLnKOKYqFpEdFzboXGxIcpzCq1BKSJryeMYXViM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\nTkSuQmCC\n",
"text": "<matplotlib.figure.Figure at 0x342ea90>"
}
],
"prompt_number": 13
},
{
"cell_type": "code",
"collapsed": false,
"input": "tx = [0,0,0] + [0,2,4,6,8,10] + [10,10,10]\nty = [0,0,0] + [0,2,4,6,8,10] + [10,10,10]\nc = zeros(len(tx)*len(ty))\nc[10] = 1\nkx,ky = 3,3\n\nz = scipy.interpolate.bisplev(x, y, [tx, ty, c, kx, ky])\nplot(x, z, 'k-')\naxis([-1,11,-.1,1.1]);",
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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BAzBnzhyMGDECALBq1SrMmzcPQUFB2L9/Pz799FOsXLkSNpsNd911F0pKSnDh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\nDm/GGHNCHN6MMeaEOLwZY8wJ/R8u30uTU1NDqQAAAABJRU5ErkJggg==\n",
"text": "<matplotlib.figure.Figure at 0x30afbd0>"
}
],
"prompt_number": 14
},
{
"cell_type": "code",
"collapsed": false,
"input": "min(abs((X.T-z.reshape(100*100)).mean(0)))",
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 15,
"text": "0.0"
}
],
"prompt_number": 15
},
{
"cell_type": "code",
"collapsed": false,
"input": "linalg.matrix_rank(X)",
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 16,
"text": "64"
}
],
"prompt_number": 16
},
{
"cell_type": "code",
"collapsed": false,
"input": "linalg.matrix_rank(column_stack((X,z.reshape(100*100))))",
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 17,
"text": "64"
}
],
"prompt_number": 17
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Check them all to be sure"
},
{
"cell_type": "code",
"collapsed": false,
"input": "XX = empty((100*100, 144))\n\nkx,ky = 3,3\ntx = [0,0,0] + [0,2,4,6,8,10] + [10,10,10]\nty = [0,0,0] + [0,2,4,6,8,10] + [10,10,10]\n\nfor i in range(144):\n c = zeros(144)\n c[i] = 1\n\n z = scipy.interpolate.bisplev(x, y, [tx, ty, c, kx, ky])\n\n XX[:, i] = z.reshape(100*100)",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 18
},
{
"cell_type": "code",
"collapsed": false,
"input": "plot(data['x'], XX, alpha=.5)\naxis([-1,11,-.1,1.1])",
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 19,
"text": "[-1, 11, -0.1, 1.1]"
},
{
"metadata": {},
"output_type": "display_data",
"png": 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H28/jz7I28m3a2Xh6vEwT4TegUrLOtZcHxwSKKr/4ZWIF7W0Thi288fM2+d9N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\nrkJggg==\n",
"text": "<matplotlib.figure.Figure at 0x34292d0>"
}
],
"prompt_number": 19
},
{
"cell_type": "code",
"collapsed": false,
"input": "# different, but maybe due to numerical imprecision?\nlinalg.matrix_rank(column_stack((X,XX)))",
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 20,
"text": "79"
}
],
"prompt_number": 20
},
{
"cell_type": "code",
"collapsed": false,
"input": "# direct comparison shows all columns of XX appear somewhere in X\nmax([min(((X.T-XX[:,i])**2).mean(0)) for i in range(144)])",
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 30,
"text": "0.0"
}
],
"prompt_number": 30
},
{
"cell_type": "code",
"collapsed": false,
"input": "",
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
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