{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "### Shifted linear interpolation\n", "Examples based on the [paper](http://bigwww.epfl.ch/publications/blu0401.pdf): Blu T, Thévenaz P, Unser M (2004): Linear Interpolation Revitalized. IEEE Trans. Image Proc. 13(5), 710-9" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Shifted linear interpolation\n", "# \n", "# Interpolation of the Gaussian function\n", "# \n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "dx = 0.25;\n", "# vector of samples\n", "xk = np.arange(-5,5+dx/2,dx)\n", "fk = np.exp(-xk**2/2)\n", "plt.plot(xk,fk,'o-');\n", "plt.xlim([-5,5])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Calculation of the coefficient vector `c` and interpolation using the shifted basis points in `xks`." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# prefilter\n", "def prefilter(fk,shift):\n", " pole=shift/(shift-1)\n", " zero=1/(1-shift)\n", " c=np.zeros(len(fk))\n", " c[0]=fk[0]\n", " for i in range(1,len(c)):\n", " c[i]=pole*c[i-1]+zero*fk[i]\n", " return c\n", "\n", "# interpolation for arbitrary x\n", "def slintp(x,xks,c):\n", " dx=xks[1]-xks[0]\n", " if x<=xks[0]:\n", " return c[0]\n", " else:\n", " nk = (x-xks[0])/dx\n", " k = int(nk)\n", " deltax = dx*(nk-k)\n", " #print(deltax/dx)\n", " return (c[k]*(dx-deltax)+c[k+1]*deltax)/dx\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Residuals of the shifted linear interpolation" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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0IsZm4uWygfBuz7TLlwt/sxwImY+g1yTcxwYzCeOCInfY3dhx5pWucwDQl3biPglFk9B1nov6JBK2hWpEk6jWhS9ggi5t4fdXrLrmppxXH8pk/uk2jtcDxNTkqZUfSb7//rTTNGLNIvP3Rv0sCoY+ItOFiraUO9NduiIkiOhaItpDRPuI6HbNcSKiv/aOP0FEL281lojeSUS7iKhBRNu6MU/m5DgxX8Yffu0pvPcLD2uPqz/k1ppEQ+t4rdQa/k65menCFRL6BUX2d+hGC9BCOehfDQCZRDyHwdUkzNFNvk/CliYpQrUW1yQcRYgA8cZMhUodGa+xkbzfC6QmEdWgJOU2zE0WuZ+d7pqogt8UIaVqEqb3/aZPfA+vvuM/mrwTpht0LCSIyAZwJ4DrAGwFcBMRbY2cdh2ALd7/WwD8TRtjnwLwiwDM1eOYBUUujqbdmvpD1pmCZCKc3CnrWpiWvV25rr6Re9x9bCCdMOZJSE3CZP8+GaTW0OdpEulEvLWoqknoHNdysZfHHFvjk6g1Quao6HMAbge8bNJGzkvqkwJsoZENgaIalKRcrftaklZIeE55Xaa5O8a7phk3D0WnTaifuel9n5h3zYtcKXZh6YYmsR3APiHEfiFEBcCXAdwQOecGAH8nXB4CMEREo83GCiF2CyH2dGF+zCkid+imCJWwJmE2K8ikNJNpImlbSNlWU/t2c3NTcyfoyVBQWpMC8Mp4RzWJILrJd1w3KcuRsCgmIOX7BgK/hur8FkL45qZsj81Ncs01aoe1Bga9Bd50zZK2pa1ZpY4Z8L4XutcJmZtavO8T+c59UYyZbgiJtQAOKvcPeY+1c047Y5tCRLcQ0U4i2jk+Pn4yQ5kWyJ2kOZa9eXiq3NkPpJubk5rvOr3nyDgoVfUmK7l4VuqNtpyc9YbAvz1+ROvoznvjpU8ik7BRqmjMTX7kUrypUNQn4dhWzKRSa4jAZ+HEzU3lmutAzyiO6145cOVnbHq9UrXuL/Cma5Z03Las2hBZ5ZqankN97UKLcNjjsywkFpJuCAnSPBb9JZvOaWdsU4QQO4QQ24QQ21asWHEyQ5kWyB2cSZtXTUw6U5D88fuO6SamiZRhQVE1CfU5Q/NUzBGTbRTC+8IPn8dv/OOj+O9f3Kl5rrAmkU5YMXNIudZAykuAIyIkI1pQ1Cfh2IRq5EOsquYmz76jahJS6GaTvXdcSzlcNBXfqzV8U5FZkyDjNQ02D21qEi3MbLIQIrMwdENIHAKwXrm/DsCRNs9pZyyzSDQrzQCEBYPW3OQLCfMCL00TLXed8jk0r6MunlP51kLiq48cAgD87MA0Dkf8LYFPInBcq7taIYTrk7CDn05UC5JO6oRiTqpGNIlKXfgaREKTJyJNaJmEjWyPfRIy78Sc+1L3hYTRhOhYbmHDJln0za5psVr3tbVW5qZZFhILSjeExMMAthDRZiJKArgRwD2Rc+4B8B4vyumVAGaEEGNtjmUWiXyLRamluclbIJpqErUWC0rMyRk/R108W5XUnitVsefYHK7ZugoAsDOSgCcXZ+kHSHs+CWmCkb6FlJfbAMSFQLXegG2RHyXkWBaECCcfhnwSGnOTLySSNjKJ3kU3SV8I0CQbutbwTYjNrqmusCEQaKDS3KS7pqVqA8M5t59HqzpOrEksLB0LCSFEDcBtAO4DsBvAV4QQu4joViK61TvtXgD7AewD8FkA7282FgCI6BeI6BCAVwH4JhHd1+lcmZOjlXmjleM6am7SCwFlQWlqvzabJvKVmv8aky00iScPzUAI4Je2rUfCJuw5Gu7PHQgJaW6yIUQ8KTAZ0SSieRLS3wAE0UtRQZKIhMDqzU0ObIuQTljGHfWBiULXyli4fh/3tm5xrnoRawNNzH+qCVGnJUQ1CZO5SQoJnXBUv0umpD+mOzjdeBIhxL1wBYH62KeV2wLAB9od6z1+N4C7uzE/5tQwhUBK5I+3P+208Ek0sV97mcemXWfUJ6ETRoVKHeuWZbF7bLaluenxQzMAgG2blmHTSA57j8+HjsuFMSi+59VVqjRCvarl7l/ejtZuSihCRAqDWkSTiPokTOYmOQ/dgvzT5yfxS5/5MW7avh7/5xcvbfre20HdGOgc11HzX7PoJrMmERb8uvdVqtYxlE2AKPATheapaI+sSSwsnHF9FlOtN7B/fN54XDXjRG3qQLCIDOeS2jyJSkyT0C8oqSa7zrKXmCXzFrSaRLmGNYNpELld5Zqxf3weK/tTGMomsW5ZJpZNXq664a2Wt3DLCq1SCEZLbgCIOa5VU5J6rgyTFcItS5GImJvUz1gKK5lIl7T1eSQP7j4GALjnse648lTBoNMkShFTUVPt0BTWXI8EI2hep1h1S5JkErZWk1D9ZabMcKY7sJA4i/k/9z6DN/6/38Wx2ZL2uKpJ6H6o8rGhbNJgbgoS4QBDxVAlmU6rSXimi7ShUirgLij9aQcD6UTLXtAvTOSxaSQHAFg9mMHYdPi9l6p1pBUtQe7k5etGw1sBjbmpJkJCxJFCwkuoq0aS7XQZ13KxlkIqZSiWt+eYay7LV+qYmO88FFS9zs2ijprlSbh5JLaxLWuQTOf5JAyO63TCDf/VhcCqxQdNmsRTh2ew6fZvxkyKzMnBQuIs5kfPnQAAjM3ohUQ+JCTiu7VCtYakYyGX1Lff9Au9GXwSQggvnNQ27jrLXpRLWpam0GoSdWRTDkZyST8L18QLEwVsWp4FAIwOpjGRr8R8K2nFKS1vF2NCIqwpRPMkEk4gRBKeViKFgHwOaWbS+Szk8wU1ovTmphcnCn4k1v4T+abvvR1Uc1MzP1NfynHzQwzZ0mnHQtK2tWU3oiGw2kx77zpkk7be3KTM0+STeMDTsu5+9LD2ONMeLCTOYuQCeNygSai7Sl2kU6HsmgTSmqxkICi3YMpxkPfTCQspg829VG14jXfMCWWFSg25pI1VA2kca5JYNV+uYXyujE3LXU1idDANACFNSu0YJ+cm5wEEfoVEE8d11CfhRDSFqKDRlUr3fR+27F4XNzcJIXB4qohXbFoWex+nivx8k47V1NyUcmzPBKbXFNIJ288libdulRqo2c+kZpvrtFjZUrY/5Rg1CekL60Z14LMZFhJnMXKX2p65SaNJVOrIJmxtfSMAfqaySUjIxSLtmDWJaGmKqDO90RDuPJIOVg2kcNSgFQHAwckCAGDDsNQkMgDCmlSpWvcFA6A4rr25yjk6qrlJo0kkNY5raW6KNiXSmZuiDnJdiYuZYhWVegMXrxkE0J3MY6k9juSSTR3X6YQ5S1727/aFX/S6e/eHsknvfL0wSicsZJO2VljJ78GaoYwxT0KaHouGKrJMe7CQOIuRS9K0wdk7V6r6JhGdJlGs1pBJ2kg7enNTMbJjjAsJueC4u07Tc6QTtm9SiZoe5GvkUjZWDaZxfK5kbPMpBYgUDqs9TeJoSEg0NzdJTSIZ0hQokgMhQkIkGuLqFwD0zrEtgkXRLn3Bjh7wzE0RQXzc2yFvWdWHhE0Y74JPQr7Pkb5kU59EOmEbTWBSGwsEbPgcKXyWZfUhruG6VY5ek/CFRBozBsf1hBfpxppEZ7CQOIuRzr9pw05stlTzF1KjJpF03CJ4Ok2ihZMzWHAsbUlueU4maSObkqUpwufklYJ8qwfSqNaFMVfiqKcxyfck4/DV813HdSAkpOO6HPFJqELAsaxQAb9q1Nxk8ElETVK6Fqi+TyJhhUp0A8AJb/Fb2Z/G8r5UlzQJGbGW0u7gpaCSEWl6n4QrJDJJd+7R5ylV60g5FmyLvOilaHtYN1cj5WmQusz/vKpJGHwSk/PudT3aBTPc2QwLibMYqY430yRWD7gLanRxBmS/A9trU2nWJAYNJRykHyOdcEMdS5qeE3LRTtoWHItiC4oM082lbH+upkXh6EwJRMDK/pQ/LyKEIqJKSl0mOTd3HjIySee4ppBztlYXvmBQz5Vjdc+RtK1Qz4mouSlpxz9jaYsfyiawsj/VFU1Cfr7Lc3pNolxTNQm9n0Q6rqORYRLZlhWA1ucg7/elHPSl4z3GgWCDs2Yog0qtoZ2rFP7HZstG7ZJpDQuJM5j/eOaYH8EURYhgxz1T1O+8Z4uBJqHbzcn2mibHddHLOZA78+iuU92VZpJuJEy0pLZcUIjI21XqNYlMwsEqjflI5dhsCcv7Uv7ibFuEgXQCU4qQLFf1jusgukk6rtWMaiuUKFdvCL+7m3s8nExXqcWd3wmbQj0nKrUGiAItJJWwY5+f3EEPZBJY0Z8yBiCcDHKBXpZLGhzXgYlQlyUvzU8pxdyk0ySkAMlohETeL7Joez3G45uYfNkNVpAbEJ1fYsIrIV6pNYzO7ScPzeD4HGsazWAhcQbzq/93J9712Z9ojxWrdf8HrdMkqvUGitW6HwGkExIFrylO2rFRrYuQXR5wHdeZhA3LIiRsipmkwvZtvWmiWAkWlFzKiWkSfpRL2vEd0gc8B3WUsZmSr21IlmUToXpPpYiQSEUEXE2nSVgULrnRaOh9ErWwJpF0woJGfY6y5/wm8oSExkksk8gGPSHRKvy3HebLNaQTFvpSbmn2aEOfILrJ8npt6AW/1A4BxEqtF6uN4Jom49c0aCHroN9rHxvVBObLNeRSjp+1rRMCk/mKb1LUaZdCCPz8p36A13/8Pw2fBgOwkDhjUX/cus5dE/PBwqjzSUh1ftWA9EloNIVKHZmEo4SJaswKSlmJ6PGSEikjzQ+xcxRHcjZpx8xec4qQGMkl0Zdy8OKEXkgcmy3570cylE2GhKQ0lUii7UmDHIewpqBGJrmahCokZHST2SfhRneFzU1q6Q+daWe2VIVF8HbUScwW44vpyTJXqqI/nfCvhzls2UZGE2wQmKMsoyZRrASCWK9JSBOiKyQaIm7unCvX0Jd2MOw5v6ciG516Q2C6WMVFo/0AoA2NlmMKlTp3t2sCC4kzlONKRIfOVi0fGx1MazUJqeIvyyaRcixtsb9CNTA3AToh0fAXG51jWo25N9mv1ZDUXMqJRTfNld159qcTICJsHMnieUNS2dHZElYPpkKPLcsmMF1UfRJhTSIRaS0aZEtHzU1qCKyArQoRS4a4RkJgW5ibUiEhEY9umi1WMZBx3/dAxkGl3ui4O99syS2WmGliKgICIaAT6nK+8tprzU1JqR2azU25pO3nOkRNTrPFKgYzCYz0uUIimm0+VahACOCi1QMA9GHeL0wE3xOT9smwkDhjOTgVfOl1PaplWOB5K/swU6zEdqDSlDGQSXiLs95xnfUc10C8V7FquslosrJVc5NpUVK1kVaaBABsWp7DixNxIVGq1jFdqPrhr5Jl2SSm8tXQeWqehAx1LTfRJKLtSesNUxXYcLnxaNZ2NZJMp4bZ6kpczJZqftay/Ntpb4W5Us3VJJpcDyAQ7NFcipKiSQSCvxF7DvkZZxLxEFe1hay8rlHn9XShiiFFSJyIRLRJf9uFo56Q0PipDiga5zNHZ2PHGRcWEqcpjYbA3z/0orFS60FlZ6QruyGFxJaV/ajWRWwxkDu3/rTjLc7h16k33OY7mSaaRCm0GMSTogL7dVB2I9rgR42EySWdmG8kKiQ2j+RwcKoYm4t0ZuvNTRX/9aJ5ErLzXDTHIeGo5iYrFt1ka6KbpKYgfRNR53fI3FSPm5sq9bCPwNUk3PctbfOdls2eK1UxkHb86xHTDivh8FWjpuG057h2o5sifqZyEN1k0iRmPE1CmpuimoQ0p64ZTGM4l8QRzW9A1SSeMdR3mpgv45EXp7THzhZYSJym/GDfCXzka0/hj//tae1xVX02aRJEwDkr3BIVUZOTHzmTTrjOxYgmoXZwM/VgVp3O6YQda4ephsDKCCh1QanU3Xh53yeRiu86Z4tVv2kRAFy8ZgD1hogVdfNzJDSO63yljkqtEbK3q6hRPL6pyAprCmp70lrMJ9FOCGzY+V2uRoWEHXp9wF0oA03C8R7rLLt4zjM3Sb9M9JpK7REA0lrtUPFZSEETc1wHGqbO3ORrEinbF/6zMU2igqFsEo5tYVk2EfKxAfAjllb0p7B+OIsDk3Ht8sWJAtYOZbB5eQ7PjOmFxB/c/STe/jc/OquLBLKQOE15/OA0AODpMb2avO/4PNYPZ5BJ2DgyrdEk5ssYziaxvM+10ceFRLBDz6bimoQUEv1pJ+jBrMmG9kMdE3ZssQiZm6SjVO12Vwkv2jlNYpVrcgnaolyy1i1R8cThmdB50ia9aiDsk5CL0Hy5FgrJVVGFhD66KaxJ1BvCr9cEqD2svRBYTSXZRMSvEdUk5G3185ktKUKii5pEfyphDCSQCZRAvLWren46YQWCJipIKur3Iu5n8h3XSQf9qbi5qd4QmCvX/Pc80pfyw10l/vUeTGPjcFYbzPDiRB4bR7K4cHU/dhvMTY+8OA0A+NefHdIePxtgIbFEeXEij3973Nwj4GFPBT4wWdBGtOw7Po/zVvRhdCgd65kAuJrEiv6UXzJjOpIrIU0wy3JJrZlHhp72pRJBD2bdjjEZ+CSM5iYl8Uo9x++p4JsmnJh5TUbjSNYty2BZNuELUYm6aKj0eWPnS7WQZqOi1pWSC70T8Tk0RBBFVq03tJqENFXVNUUCE5pkupBPQgoJtSNbsRaYm7rqkzA7rmUpFiAwIarfP1Ubc2wLCZv0fiY1mS7yHPlyDRa5gkZnbporVSEEMCSFRC6JExFN4uhMGdmkjf6Ug40jWRyZLoZyOoQQeGGigI0jWVyydhAvThRimfpjM0U/rPgbT4xpf2dCCDzw9LEzujteV4QEEV1LRHuIaB8R3a45TkT0197xJ4jo5a3GEtEwEd1PRHu9v8u6MdfThf/2hYfxG//4KH52IG4PLVXr+OnzE0jYhJliFYemwkKg3hB4/kQe563sw5rBjNYee3y2FBISMxFNYjJfRdK2vAiT+OI870UV9Xk+CyDe7rSsxMNr7de1OhyL4NiKkNA0vZHlHQYyrrlJ3bXLRU1CRHj1ucvx3WfHQ/Z7ddFQkTWh5srVUIy/SsKhILqpoS8Vrh5zNYm441pqCjKpzo6YrKJVYKM+CSAckjpfrqEvJTUJvVnmZKjVGyhU6uhPJwJ/QhNzUyZpoyHCJjBVk3D/6k1SvuBPue1h1feVr9SQSzogIq3jWuZEyES65X3xHJFjs25ODBFhw3AWDQEcVsyu4/NlTOYrOH9VP7ZvHgYQ73f+vWfHAQC3vO4cHJ4u4mcHpmOf2TeeGMP7/m4nbtrxUCxP6EyhYyFBRDaAOwFcB2ArgJuIaGvktOsAbPH+3wLgb9oYezuAB4UQWwA86N0/bWgWrz5TrOJ9d+3Ex+97Rnvej5474Ydx/sNPDsSO/3j/BErVBn7rqi0AgCcOhU0rBycLKNcaOHdFH0YH0xjT+CQOTxexdiiDoYw+znwyX8aynBdemU7Eun/NlVSfhNfroayzPQeLRdw0ETiJ05o6P6oTFAgWBXXBcDWJ8MJ/zcWrMD5XxiOKgFUXDRXf3FSqoVIPF9WThDQJTba0rjZTKPopUg1Vnqeek4yYm8r1BpJKDamUrCGldLcrVGrIeTWtBgwOXh337TqqtbGrJkRT+Goh4mcCArMgEA5rBuKhzzIYQb6fbCJuqsyXa36trmzSLcmimkPlbbnBWTmQwrGZcGFHN9zZ1RrPWdEHAHhOaVUrfRAXrh7ApesGkXQs/OT5sJD47rPjGB1M4zfeeB76Uw7u+tELoeOVWgN/+cCzAIBdR2bx6e8+hyilah0f/fpT+M1/fFTrG1Q/l6VKN3pcbwewTwixHwCI6MsAbgCgelRvAPB3Xq/rh4hoiIhGAWxqMvYGAK/3xt8F4D8BfKjZRE7Ml/G57++H91zuX+W4Re7jRN7jRCD3DwjB4/I+yLUbO5YFi9xd+3SxghNzFeTLNWxZ1YdL1g5iRX8KjkWYyFew6/AMvvXUUfz0+Ulc/5JR/OZV5+G8lf3+HB4/OI3f+efHse/4PB7YfQyrB9J496s2+cfLtTr+5Bu7sWYwje2bh/HNJ8bwsbde7O94AeDfnzyKbNLGe169CX/14F48eXgGP3fpqH/8Sc8ef8naQRyZKWF8vhzamZaqdZyYr2DtUAbLcu4PbTJi053MV/0qnf1pJ6ZOh30S0twU8UmotudkPPGqFBEi8jF/vBQSyfBCOFOsYpmXSTtXqmFlf9iEdNVFqzCcS+LPvvUMfueaC/DNJ4/gm0+O4bINQ4giP9d5LzkLCFd4BYCkUu201nDbqYa1gLg5SZdMJzWIeiNeJPBkzU3lWgMNxakvy2SYWnkKIfDDfRP46iMH8bXHjmD7pmF85dZXhc6RY/vTTuhzUSlW6ljuhZ36Ia61Ogbh9YaIOP8zyfDmQH6OgSYRmCpHvHPylTpy3uNEhGW5RKh3+XREk1g7lEG+UsdssYZBT3AcnSnhCk9DuGC1+/vbPTaLN21dBSAIeb1wdT9Sjo1XnTOCB3Yfw0d+7iIQuTXCvrtnHG992Rr0pxN41xUb8Nnv78d/v/IcvzT7ju89h+fG8/jbm7fha48dwcfv2wMhBG698lw4toW9x+bwe//yBB71NJD7nz6Gd1y+DleevwKrBtKYK1Xx5OEZ/Puuo3jq8AwuXjOIS9cNYvPyHIayCdQb7m9gplDBZL6KQsX1wwxmEv7GDIBv6qwLt+oBEWCRW1nYimyKToVuCIm1AA4q9w8BuKKNc9a2GLtKCDEGAEKIMSJaqXtxIroFrnaC5Orz8Cff3H2Kb6N9cl7Y5z/tPKg9vn44gzdfvBoP7D6Gex4/gotGB7B2KIPD00XsHpvF8r4U/uF9V+BzP3geH71nFwDgv75yIyr1Bj701Sfw9NgsPvPuy7GiP4WvPXYEX/7pAbzvtecAcBfibz45hp97ySgG0glcuHogZpJ64tA0ko6FC1b3Y8/ROQgBHJoq+DsqqXavXZZByrExkHZi5ZSnCkFJg4FMAoVKPVTddF7VJDQVWhsNEXNcx0MhG6Edp/uYIiQqYZ+Ezjk7o4SBSvpSDn7/ugvxu199Ajd99iGkExbOWZ7Dmy9eHbtWfYrjWu70tY5rJRHOiQiRaL+IakPAjlSJBQKntxQWTjRCKlIqPKVzXHtzlJ+NulgMaIQ54AqI//FPj+Frjx3xNaeCpseCWgtKLtJRX5RbisUtf+JXeVWFQMTcFL3uBf+aeibEdPyazpdq/sYDcHNZJpXSKdJfJjUJmftyZKaIwWwCtXrD1Rw9TaLP80uozuknDs1gzWDa32xce8lq/P6/PoldR2ZxydpBfOvJo8hX6viFy9YBAN7/+vPw1UcO4Tf/8VF84b9txyMHJvHJB/bi514yiqsuWoXXblmBhhD4i28/i7/9wfNYlk1i/4k8BtIO7nzXy/GStYP4yweexT89fBBffOjF0Gd64ep+vHPbeuw7No9/eeSQtphmX8rV7maL1Y4TJk+WbggJnaiK6k6mc9oZ2xQhxA4AOwDgsssvF9/92DXwNTflmRpCQLjne38BAQHvn39f+Pfd227RuQbqQmAwk8BQJumr4sfnSnhmbA5ThQqqdYFl2QTOX9WPdcsyICJM5iv4ys6D+OG+Ezg0VcDyvhT+4PoL8a4rNqIv5eBlG4bwgS/9DH/49V3Y8f39KFYaODFfxu+++QJ/QXvtluW48zv78EuvWI+BdAJf/LGbG3Hj9g0AgFedO4Iv/PB578frXs7HD81g6+gAEraFzV6I6/Mn8oGQ8HwYa4fcH5db9yfstJvKV3DRGjcRaUCxC0vBoWoSugqtss2oXGxUJ6fU8lRzScJ7DnVBySthtgCUYm41ee0xXQi0CpV3bluPi9cM4sBkAa86d8QfG0WNnolWXpWkbMvPbajVRUzTCIRAoEkkrLg5SsoAeV5IG7EoVCQwlicRqf8kP19VSGST8UghAPjnnYfwtceO4DfeeB4+8Ibz8L++/hS+s2c8dp6sYTWcS/pmoPmoCbFSDzmuAUSumZyX+7lGQ5/9bOqUdLh7vhRFA5otVUPXaziXDGkSckMjI/NGh1xhMDZTxEWjAzgyXUKtIfxe5oC7EO864goJIQQefmES2zeP+Mevu2Q1/ujfnsbnf/A8/vwdl+L/+899OG9ln9/1bzCbwJ2/8nK89wsP43Uf/w4A4PKNy/Bn77gUgPud+dRNl+HtL1+Le588ikKlhndsW4df2rben+cnfvll+NNffAmePDyDqXwFuZSD81b2hXJ3Gl45kelCBY5lIZ2wMJBJhPxkpWodxUodUkkgECxL9iUh7z26a577H2ilUAz+mflYN4TEIQDrlfvrAETDckznJJuMPUZEo54WMQrgeKuJ2J79vFes7E/HTB0qw7kkbr3yXNx65bna49mkg8/d/Arc/ehhPPD0MSQdC+/ctg6v3bLCP+dD116It37qB/if//QYfvkVG/BXD+7F6y9Ygcs3ul/eV587gh3f24+fPD+JN1ywEvlyDY8emMJ7X7MZAHDO8kBISFRNAnB/bFFNYrJQ8ROVBpRKm1JISAepdDBGK7RGF4N0MnBQyi98XgmnBGRIZdiBqT5H4Jyt+uMr9YY/zyhb1wxgqyfoTIQ0ibpeSKitPKv1cPE+INyjWngqvyoALMs1ZdYjjutoPwnV8Rk1N0ntRUZXFWX1W+Xz02WkCyHw+R8+j0vWDuB/Xn0+iAhrh7IYnyujXKv7mhwQZCkvyyZhWaQNOZalWIDATxLWFGp+sh0gr2nwHPMRwa+LXpotVv3CkoAbYbf7SKAFnJivIGFTyNwEAIe9UG+ZJLdxJOuPecWmYdy36xiOTBdRqwscmy1j+6YgFmYom8S7X7URO763H89P5PHceB6fefflIR/WK88Zwbf/x+vwrafGsGogjetfMhq6hkSEN164Cm+8cBVMpBM2XrFp2HjcsgjDuaT/OzM9RzS4YiHphpB4GMAWItoM4DCAGwG8K3LOPQBu83wOVwCY8Rb/8SZj7wFwM4A7vL9f78Jclxy2RXjH5evwjsvXaY9fsnYQH3vrxfjoPbvwwO7jWDuUwZ+9/VL/+CvPGUFfysG3nhzDGy5YiR89N4FqXeD157uCZiibxLJsAvsVIbF/fB5Jx/LV9BX9KTyt/Ahr9UbI7m8yCfSlHFjeYpCNVPOMLgaqOSmInKmFdsKZSPbtvB8vH/dJAPB3l8sMQqIdMgkbFnmOaz8TOm5OmikGIbCqw1keB9zFPxAAEUGiaArS7BTVJGJlORRhlVAEERCYbbLKYtGnqZK7e2wOzxydwx+/7RJ/wVsjd97TJb/fN6B+nu7nnE3FQ58LGk1CzX8pKP4EwBXwalRRTJPIxKOXZku1kCYxkgubm07MlzGSS/nvxy3/Tr6GLMuyqO/N3Xjtxg/2nvC/x685b3novf3ONefj+RN5fH/vOH7n6vO15sn1w1nc8jr9pu9MpWMhIYSoEdFtAO4DYAP4vBBiFxHd6h3/NIB7AVwPYB+AAoD3NhvrPfUdAL5CRL8G4ACAd3Y619OV97xqE7ZvHsZzx/O48oIVISd2OmHjmotX4VtPHsVH3rIV//LIIQxlE7hc2SWdu6IP+44FkR17j8/j3BV9/iIV1SSmCm4c+kguqkmoC3g1NA834c6sSaimiSH/nDrWDAULfF8k1Db6HNHeAVNKLsepQkToSzkhn0TccW2FqsAmYwIg8DkEpqTwc9hW0OLU5JOIaRIhIeFFSEWFhGpuSjmxPAnZT+RNFwUuPalBHp4uhoVEoQqi4HOWn4ukVm+gUmsgm4hfU0k+Ivj7UmFtZD5yTfs1GxA1kxxwNwEzxSpqnj/oxHwZy/uDa25bhHOW92HfcTdi6cWJAtIJy28uBQDnr+rD2qEM/uGnB1Cq1vHSdYO++VWScmx89j3bwITphiYBIcS9cAWB+tinldsCwAfaHes9PgHgqm7M70zgwtUDuHC13nTyq6/ZjH/92WHc9g+P4vt7x/HrV54bMiNcvGYAX33kEBoNAcsi7D02j22KEFnRn8Jcuebv8oPsZHfHGTXzAOFoIMDrC6BdDIIoFyDs5FR9EkB8USqUayBSk+ls2Bb585DmkeFcZybG/nTC9UkYzU22f6zWzHFdF34YqyoA3PuWEt3kmqNUU4Z6HHCFQahshxMu7eE79ZUFOZe0cTSSOPnwC5NYP5wJFTYMzDPhc6cKFQxmEv77y0UW+KgfRBcmW1TyKNzncCLhrdJX5Z4TzYMoVd0SKQMRn4QQrvAY8XIipJ1fcv7qfjx20A3g2H10Fuet7At9vkSED7zhPPzB3U8CAD75yy8F0x6ccX0GcMnaQbzvv2zG954dx6aRHG553Tmx4/lKHftP5DFfruHwdBHnrwrCcqUwkEXwZEFAGR2iy+Z1d3tme3hBKdIGBCGRalZ2PrqgRDK758t1ZL2mRQC8nA0nMDcVOjc3yTnOl6vm6KZIxnXclBQU8JPaQNRvoWoS1UYjZGqSx6UZSgi3Q18yEiLrvn5Yk8hEHNfRzn0/OzCNV2wM28BHBzMgCgIYJJP5Ssi/k4s8X1QwZYzXNPheGLVD75yEl0gpv1tqhJVE2udlcMWJuQpWRITEBav6cHCyiLlSFU8cnMFL1w0hyo2vWI+P/vxW3PGLL8HbXrY2dpzR0xVNgll8PvKWrXj3qzZi1UA65tS61PvBPHZwGsunkt5jg/7xdRHzgyyGJ52Huu5fk/kq1g4FzsVcygm1gYw6naWwUBeUYmRB0dmvVfs24C4YUoOYzAc9LzpBNr5p5rhWS4VHfRZqKXC/bEdMkwj6RdQjPbDlc6iaBhDvNwEEyXxy9y5NP4AslhcsyFP5CsbnyrhwNNgQyPezsj+l1SRU011fyglVEI6auOS1KUS0v5B2mHRQrjX8zy3qqwJcbUJqElJYqBsQ6UM5MlPElpV9mMiXsbw/IiQ8LfsbT4xhrlzDS9cPIYplkR/QwbQPaxJnEBtHctqohy0r+7CyP4UHdx/DD/edQNK2sE3ZXUrzwyGvB8WxmRJsi3yVPudlvUZj1dXFOZdy/NwJIO64lguKLOchhPDKLzSxX1dqocUEgNfLuezPwaLwrvNUyEohYfBJpBwLlVoQ3RR3bAc+iUCTaO6T0AuRcL8J9TmSEZ9EEN1k1iT2jbt+qC0rw0ICcK95VJOYyld9pzXgmYrUQIJS9JrKMFlFSHjdCtXnAAINIupnAtzrJ5tHzSgtWYO5ulFKh6eKOD5XRrUu/O+sZPumYVgE/JFXFXnbxrOqis+CwkLiLMCyCFdvXYUHdh/DPz9yCNs2LQstLqODadgW+TWgxmZKWNGX8k0iRISRviQmlVyKyXx41zmg7AaB+GLQ5y8o7iJWqrplwDMRTSIf2ZVmU2Ght7I/7XfdOzZbwogyz1Ml62UFm/IkEnbQVKgWqcsEKGU5vJwaALE5OVbQ4rTWiPs1bMsNgRVCKPWhWpubshGfRMVzLgNukUfAbSwVZe2yLA5NhyujHp8L2/qj1yPoMeIu4CnH3TyouRQ6PxMQCJL5Sg1J2wp9xv1pxw+K0JmbZEWDw9NFP3JJ9jOXDGYTeOOFK1Gs1vGy9UMxpzRz6rCQOEt41xUbUK27yWc3v3pT6JhjW1g9kFaERNH3R0iGc0lMeGaeYqWOcq0R0iQGMgnMFKt+DRq5cMgQTVmITu5GA3OU2XGdL9dDmbeAu2CMz5UhhMDYTAlrBs15Ku2SSTooVs1CIpRxXWuEEuUANYehoZiKIj4HJXopWrYDCPpT1BtCqe2kCAnH4JNQNEdZ4kL6DvYdn0c6YcV23YCrSYxNl/w5VWpuIqd63ftSduh6zEYaPAFx53bMz+RrEu6cCuV66JoDrs9LmjIDc1MgJGyLMDqUxpHpot8nRc2BkPzpL7wE73/9ufjrGy+LHWNOHfZJnCVcvGYQd7//1ZguVvGGC+IVTtYty/hJSHuPz+PK81eEjqtCYrIQjqcH3B91zSvFkfUc0Llk4HSWC4NcUKIlNwBXSETt16MRIbCyP4VitY75cg1HIg74UyWbcG35lXoDRHF/QtK2UW8I/38qoY9uqinRTdEQWDV6qabxSdhqroVskarzSdQDn0Q6YfmfLxDkk+Qrbg2jw1NFrF+WDZ0jWbcsg1pD4PhcCaODGd+fpH7euZSDUrXhR3TNleILeC4i2KN+JjVZEdD7mZb3pbD3mBu+Kp3Tsj6UZM2gax47MFmAbRHWaATfyoE0fu/aC2OPM53BmsRZxGUblmkFBABcNDqAPUfnMDFfxvhcGeevCqvry/tSfotIP+lKNTfJMNmifjGQGsFcOapJmO3XrukirkkArmlkbKYU61l9KmQUn0TStmKVYqVmUak1UGsIrQAAXDOSn0yniV5SfRK2HdUkLP+Y70CPNDaScwAQKsMiCYrluZ/fkZmidjEFlFwJT3vUtXf181I8DUKaE9VaWar2Z/IzAYq5qVyLaYfL+91+EEIIjM+VQ9nUks3Lc9h/Io8XJgpYM5SO+YWYhYM/aQaAm0tRqNRx365jAIAtkR26GlUkSzWHzE2RpCi310GwGETLPAQ1fprYrzWmCVkGZe+xeRQqdT/ypRNkpdJyJIFNogoJralIzZPQ1GUCwtFNtUhtJ/X8uvIcqu/DsiiUlV2qNvzOb5I+X1tzP9sj02YhIW36L3gd22QUkyp0/YZUnuY4F3Fcy9vympr8TO6cFCERuaYr+lKo1BuYLdbcZlh9qZig3rpmAJP5Cu576ii2jjYvtcJ0FxYSDICg7ec/Pez2r7ggIiRG+pIoVNzCYjpzUzQberpQ9cs2S/rSQQSU38dYu6C4hQBni9VY5JIM131o/wQAdEWTyCZs1BrCrzsURa3yWovUZQKUUuGKJhF1bluk+iTieRJO6DXi5iZ3HpYvJNQaWBIZVZT3EiPdcvB6IbpxOIuETb5z+2gkNwYIrqn0F8yVqsgm7dC8VHNTQeNnklqDPGe6UMVQJGRZaofj82WMz5f9+yqyMVCl3mha+4jpPiwkGABumOxwLonHD81g8/JcbAe6POf+cE/Ml/2sXrUVaLSM91QkRBbwFpRK2HTRlwo7QQE3TFbmLUSfY92yDBI24du7jgIAzl2ZQ6fISK+ZYlVrxlAji2qR1qRAuIe13ysi5twOh7jGNQ33fLfqsN5kpUZZlav1mNbj96Wu1X3NwKRJOLYVKmVxYLKA/pQTyk8Y9BpSTftCohZr8KQmy+muaTQRc7pQ8TUUiYyoOuGZOldoimZesKofrzlvBCv6U3jbZZwI10tYSDAA3EXjfa91E41+XVO1VtqwD00VcXiqiP60E3JgRks+uzvGiCah5FLI3al6jtxhTheqfjb1UESTcGwL56/qx5GZEpK2hXO7EOootZnpQlVrblI7z7mtSU15EuZkOtUnUW+IeEKeL2gairkpHmWlahKpiCYhezgUKw2/r/nqAbM57rxVfdjraRJ7js3h/NX9ITNPVDucK4f7iQNuspw0JUXbigJuJJRtkX89pwrVmOCXQmJ8ruz3Xo9CRLjrvdvxww+9MVaSg1lYWEgwPr9+5bl4/KPX4JdesT52bP0y14Z9cLLgtz5ViWoS0WQ7IGy/1i0osqDgZL6itKiMZ1O/+ly3D8DlG5d1xYGZVTSJaCIdEK6bpE2EU3pYm5LpHLUsR11flgNwBYh0XEfDaFVzU6laj5nG1Eq7MkpIt+BKLlrdjwOTBUwXKnj22JzfwU0S+CRaaBIl8zW1LHKbBuWrbh+Eaj1kpgSCSKZjsyVM5stY0afPoHci+RVMb+AQWMaHKB5VIhkdchPuDk4VcHi6FBcSsox3wa2BlK/EF4NcysFk3nWUzhSrcCwKOa5ltNRUoaI4x+PzueV152K6UMWvvbY7JRZUc5Oujr80BVXr8V4RQBB55Jbl0CfT2Va47IZZ0AQhsLrMbt/cVGvEFuy0UpVVLtjNdt1XnDMCIYB/e2IM04VqzA8V9UlES3gDMiu7jkZDaIUE4BZgnGoi+IdzSWQSNh7aP4GGANYNx3MgmMWDxTLTFgnbwuhgGgcmCzg8VfDNT5KkY6E/5WAiX1HaS4YXAzezVpZfcLuPqeYNv/xHvtq0DPiK/hQ+/s6XGqviniwhTUJnblJ6OdQacZ+EDGetN8zJdI5lhctyGMuNBz0pdFFUFdXc5ETNTaomUYZtmYU+4NbvSicsfOLbe/z74dezkEva/uI+la/EzH+ys998pWYUErL9qKkgIxFh8/IcHtjt9hU7Z3nnfiame7CQYNpmw3AWjx6Yxmyp5pufVFYMpHB8roSpQtzfAADD2aR/TAoJFbXpvXSWRhelhUCtZqo1N/nRS254qi68FXDbk1YNIbCqJuE6v/VFAmuNhq+NaKObalJI1GNJfaq5aWK+gpFcUptIJ0k5Nq66cBWmClWsGUxrK6cOZoJs6BOayCNf+8tX/POiEWkyfHpKExUnUU1dulpTzOLB5iambS5ZO4gfPTfh346y0iu+Z9oxDvclUfT68+rCW+WYiXwF03m9NrIQqHWsWmsScadz4E9oaCu4AtIn4VWB1YXRaspy6Jof+Y7ragPpiCaRsAkWufkKup4LOj7ylouQcizcuH2DVqAsyyUxmS8jX66hUKnHnlP1I80Wq0g5Viw0V/aobuVnuvvRw1g/nImFTjOLCwsJpm1et2UFdnxvPwDgZZpSzCv703js4LRibgr/2OWCMpEvu+1RNYvFSF8SU4UKpgpV1/zUA0elmquhy5MIfBIN7QJvk9q+tIlPQikSGKvtpITRBpqEznEd+CSimgQRuT2lPXPTiMEBrDI6mMEnfvllxuOrB9I4MlPCCS/b3qRJTHqahM68NZxzr+mEn6kfP+dtl63FixMFXPeSeMtQZnHp6BdIRMNEdD8R7fX+auvzEtG1RLSHiPYR0e2txhPRCBF9h4jmiehTncyR6R6vOW8EH7zmfPzf974itPuWrOx3zU1+06KBaJFAd4FptqAsy7q7zuNzpVjPgIVCrR+lz7gO12aK+gosy93Bq1pAvAigUpZDY7KSmke9IVA1+DXCPol4dBPg+iVkdFO0Mc+psHowjaMzRV9IRGsqRSPSTNe0IYBnxmZhEbTzStgWPvjmC3DxmriGyiwunW7TbgfwoBBiC4AHvfshiMgGcCeA6wBsBXATEW1tMb4E4A8BfLDD+TFdhIhw2xu34PWG+k8rB1IoVRvYe3weSduKRQoN+5qEWUgs70vh2GzJq8vUecmNdlAXW51PopUmIc+peQUAASAiI/xS4ICpVLgURI2gwJ+li24yO64BV0gUq3Uvaa1zU93oYBpThapfIThqbhpuQ5OQCX07X5jCqoF07L0zS5tOr9YNAO7ybt8F4G2ac7YD2CeE2C+EqAD4sjfOOF4IkRdC/ACusGBOE2RxuJ+9OIXVg+lY/R256xyfLWO6oA83XT+cRb5Sx9NHZrGmCyU32iHdQpOIdp6LahJAkCwXRCbFfRJNQ2CVnhS62k2AK8Cq9QYaDYFKrWHQJCzMl2rIV+pNI5vaZbV3DZ46PAPA1RZVsp5JUDqmdYJJ1onac2zOmAHOLF06FRKrhBBjAOD91W0x1wI4qNw/5D3W7vimENEtRLSTiHaOj4+f7HCmi2wacUMXnzk6h3NWxMMYhz1TxR6vLPQqTTawXFCK1To29SgUMqRJ6MxN3s637HWni1aBdR9zfQ51YY5uCpLpzPWf1GS6qFbjRjcFx6M+CcB1wsumTIOZzl2OUpt77OA0bItigp2IMOJFLx2bLWH1YNyUtHEkC7lf6EZpd6a3tPwWEdEDAHTepA+3+Rq6GDzR5tiWCCF2ANgBANu2beva8zInzxalvHg0MQtwY+qTtoVdR9xd6aqB+IKydU2Q+xDNAF4oLIuQtN3GQroMbrmAl7y+0tEdPiCFQAP1Zp3plOimmM8iVJbDEALrRTeVq56Q0JmbHBtHvN7VnbZ1BQIh8fALUzhneU5rKhrOJXF01g19Xqmpu5RLOehPOZgt1fDSdexzON1oKSSEEG8yHSOiY0Q0KoQYI6JRAMc1px0CoNZ5WAfgiHe7nfHMaUI26WDr6ACeHpuNNS0C3F3n2mUZ/OT5SQCIdb8D3I5pI16Do1d55Td6QSrhColmtZtK1UbofvScuhDwLEV+xJOkVT8Jx0/IE8ZKsgmbUK41fI1GZ27KJG0c8zWJzoXExpGc3wP8XE0bVMD1OXx/r6vFm2pF/dWNl+HLDx/Az790TcdzYnpLp+amewDc7N2+GcDXNec8DGALEW0moiSAG71x7Y5nTiM+8+7L8Te/8nLjAr9hOAvPIoNzlusXnf/44Ovx3d99faiA4EIjd+WpJrWbpCahc1xLIdDwFviYEFCT6TQRUuE+2foIqYRlodZooOwl1EXzEeT7kMKoG0LCtshPsnvVOfprunE46wtQnZkRAN5w4Up85t3bYk2kmKVPp1fsDgBfIaJfA3AAwDsBgIjWAPicEOJ6IUSNiG4DcB8AG8DnhRC7mo33nuMFAAMAkkT0NgDXCCGe7nC+zAKzfjiL9U1q71w42o/vPjuO5X0pbRgt4C5u3VjgTgYpG5ppEkVpbjJoEmpJjbgmYaHuLf71uog5tm21u50hT0KG0bbSJCTdMDcBwEffuhVfe/QIbtweL/wIhP0M3ajKyywtOhISQogJAFdpHj8C4Hrl/r0A7m13vHdsUydzY5Ym1168Gp/57n78wmVLy+wgF3V9dJNXgltqEhptw/YW8IbQh8Cq/ST0tZuCXAw/mU6jbVTrwt+1a6OblMe6JWgvXD2A268z18l6zZblANzuhrpaW8zpDet+TE+5bMMy/OQProplYy82Mly3We2mUsUVEtFmQEA8TyKuKVAoT8LUma7mJdMlbIqFEDu2hVo9MDdF+0kAYU2iV9rY2qEM7vvt18Wq0jJnBnxVmZ6jC31dbOR6nNREDMkFXO7gm/kkpLYQPSXe41pflkOWCo8KGTmPWkOgXDWbm6SfIqmpobSQ9CoSjek9nPrIMFCFRJPoppo5BFYKgUZDwCLEtADbIjSEm1EtBGLF9KSTul5vuAl7xtcQKMs8iiZCYoB39UyXYCHBMAC8TX6oCZKEiJCwCcWKOZnOokCT0GkB0udRMfgbbMXcVGs0jOVB6l62NaA3jckWprocCoY5FVhIMAwA4TmcTRFXjmU1j27yTEENIWJOayAQAnKBjwqahB/dJFCt6TWJhG/2cueh0yRksUKdKYphTgX+JjEMAM+VEKoIq+LY5Gc6N6vdVDdoEnJMICTi4wFZBVbvk5CCpSAd6FpNIvBJMEw34G8SwwB+6KrO3AS4pp1ik7IcjiIkdM3g5AIvI5OsaOSSUpajrgmRBQJNIhAS8XNYk2C6DX+TGAaBJmESEo5NSsa1ocCfJyT0pcSb+yRkTwqZkGdK2AOAYqUGQO+TkMLBZDZjmJOFhQTDIPBJmMJGW/okPKdyXQijEAHgm6yMYbRCaDOygSCJT85DZ26aLbktQntVZp0582EhwTAIzE2mqKCkY7Ws3VRruAu8rqdOVJPQ9ZO2iNDwIqR0ryFzK3xzk8akJMu1v/kSbgPKdAcWEgwD4IaXuS1O+gwF6ByL/GQ6nS/AkaXChYjVbQICwSId18ZKsg2BeqOh93tITaKJT+KKc0bw8IffhDdfzEKC6Q6cccMwAP7wLVvx22/aYrTlJ2yrtU+i7laBjVaABQJntyzOF3VcA652UWuiSUQLDUarxEpW9Kg3OHN2wJoEw8Bd5Jv1hE4oBfpatS/VaRJSKFQNTYnk8zaE0LY3BQJBU6jU4VikNVkxTLdhIcEwbaB2ZGvqdBZCu3gH5iZ9e1P5WHNNIjA36ZzWDLMQ8DeNYdpA3dk38yc0DFpAtCyHTghIx3WrhLxCpab1RzDMQsBCgmHaQHUk6/o825bl5ziY/A0AUJUZ15pzHNVk1cLcxBnVTK/gbxrDtIG6s2+lSWhNSRGfhDYEVo1u0oXAKnkSbG5iekVH3zQiGiai+4lor/d3meG8a4loDxHtI6LbW40noquJ6BEietL7+8ZO5skwnaIu2lohYAf+BJNjGzBnXMtz6kKgVm/u12CfBNNLOv2m3Q7gQSHEFgAPevdDEJEN4E4A1wHYCuAmItraYvwJAD8vhHgJgJsBfLHDeTJMR9ht+SQaXhVYs7lJ5kmYhEBQJNBcu8kVEuyTYHpDp0LiBgB3ebfvAvA2zTnbAewTQuwXQlQAfNkbZxwvhHjU65MNALsApImIg7+ZRSPRRnSTX7tJl0znm5tE6H70nKC0hzm6qcDmJqaHdPpNWyWEGAMA7+9KzTlrARxU7h/yHmt3/NsBPCqEKOsmQES3ENFOIto5Pj5+im+DYZoT0iR0jmtq7nSWLo2gVPjJaxJqOXGu8sr0ipYZ10T0AABdjv+H23wNnV4s2hpIdDGAPwNwjekcIcQOADsAYNu2bW09L8OcLKHopiY+iUZDaCOPoo7rpn2y6/oigar2wJoE0ytaCgkhxJtMx4joGBGNCiHGiGgUwHHNaYcArFfurwMgTUnG8US0DsDdAN4jhHiujffCMAtGK8e1Y3k5DgZTkXyspZBoI+MaYCHB9I5Ov2n3wHUsw/v7dc05DwPYQkSbiSgJ4EZvnHE8EQ0B+CaA3xdC/LDDOTJMx9gtQmBty2raT8J3XNf1TYfc51BMVrqmQ8ocdBVgGWYh6PSbdgeAq4loL4CrvfsgojVEdC8ACCFqAG4DcB+A3QC+IoTY1Wy8d/55AP6QiB7z/uv8FQzTE9RooqZNhWqNpo7rZlVgfce1IU9CFRxJjm5iekRHVWCFEBMArtI8fgTA9cr9ewHcexLj/wTAn3QyN4bpJlIwOBaBmpUCrzdO2dxkWc2d3wmLzU1M7+FvGsO0gVyUdYs3EGgG5apeSFiREFidual1FVh2XDO9h79pDNMGqibR7Hil3mhRBba54zqoAmtugQqwkGB6B3/TGKYNpHBopUlUagZ/gtQ0mgiJcBVYc8Y1ACQd9kkwvYGFBMO0gcx2NjX6CYRAvWn70lZNh5pFSKlFBlmTYHoFf9MYpg10PadVpHmoUjOYm6LJdIZy4s3MUQ6bm5hFgL9pDNMGJjNTcNz92xB6v0WsLIeuD7ZFzZsSWQT5MAsJplfwN41h2sDksJaojuZmjut2NQnT60mTE+dJML2ChQTDtIFctIWhOpi6sW+aTCdDYDW/PJuam5sA+JXQWJNgegV/0ximDXSVX1XUvIemZTlqdff5DD2sW2kSwpNSXJaD6RX8TWOYNmhtbmrRua6NfhKWRUGIrEEoSU2GNQmmV/A3jWHaoKXjWln09Y7rsE/CaG5q0t4UABqelGCfBNMrWEgwTBu02rmrQqQtx3WLAn4moSRdIqxJML2Cv2kM0wa277jWe65D5qYmjutmGdettBH39d2/LCSYXsHfNIZpg0QL847VwichzUvNQmBb+TVUdN3vGGYh4G8aw7SBzIPQlQkHwot+W47rJiYpQB/9pMKaBNMr+JvGMG0gzT+mDX7L6CbvsXpDwCK9sDk5TYId10xv6EhIENEwEd1PRHu9v8sM511LRHuIaB8R3d5qPBFtVzrSPU5Ev9DJPBmmU2TtJl0fiOjjugWeiCBPMQmAsCbRXAiwJsH0ik6/abcDeFAIsQXAg979EERkA7gTwHUAtgK4iYi2thj/FIBtQoiXAbgWwGeIqKMuegzTCXIBN1WBVQsA6vwN6uMmQRMyWbXwgbCQYHpFp9+0GwDc5d2+C8DbNOdsB7BPCLFfCFEB8GVvnHG8EKLg9cYGgDSCyD+GWRT8UuGGtVtd+E2CRD5u0iSsFhFSKiwkmF7R6TdtlRBiDAC8vys156wFcFC5f8h7rOl4IrqCiHYBeBLArYrQYJie08rc1I6pSC78rRoXNXsOSSZhNz3OMN2ipQmHiB4AsFpz6MNtvobu295SMxBC/ATAxUR0EYC7iOhbQoiSZn63ALgFADZs2NDmlBjm5Agc161NRa0aE7Xjk2jluM6lWEgwvaGlkBBCvMl0jIiOEdGoEGKMiEYBHNecdgjAeuX+OgBHvNstxwshdhNRHsAlAHZqju8AsAMAtm3bxmYpZkEIOtPpj6uPm0xFct03H1c0iRY+iUyShQTTGzo1N90D4Gbv9s0Avq4552EAW4hoMxElAdzojTOO9851vNsbAVwA4IUO58owp0wrc5Oa12A0N7XZJ9s9p/lPM5fkOA6mN3QqJO4AcDUR7QVwtXcfRLSGiO4FAM+XcBuA+wDsBvAVIcSuZuMB/BcAjxPRYwDuBvB+IcSJDufKMKeM1SoySfklmc1Nlve3teOafRLMUqGj7YgQYgLAVZrHjwC4Xrl/L4B7T2L8FwF8sZO5MUw3kTWb2oluMgUeycfN2kj7PgmTIGKYbsNxdAzTBg3P29VOdJPJVNQquulkNAmG6RVs2GSYNpBr9kAmYTjeOsdBCoFWIbKAWZB86l2X4bED062myzBdg4UEw7TBeSv78LtvvgBvf/k67XGnjV4QLbO22yjw95ZL1+Atl65pa84M0w1YSDBMGxARPvCG84zH29ECfHNTC00DaF2Wg2F6BfskGKYLhPtJND/HrGkEt9knwSwVWEgwTBcIaxKn5rhWx7WKbmKYXsFCgmG6QDvF+awWPgm7Dec3w/QaFhIM0wXUnb8pWVqak8wZ2cpt9kkwSwQWEgzTBdqJTGrluLbbKO3BML2GhQTDdIF2Mq4Dc5P+eEiTYCHBLBFYSDBMFwiZm1qUE2/HcW3SRhim1/A3kWG6gLrumxb4IAS2uTkq+nwMs5iwkGCYLkDUhuPa90noj6vjiKObmCUCCwmG6TKtynKY+0nwz5FZevC3kmG6jCky6WQyrhlmqcBfS4bpMmbHtffXJETYxMQsQVhIMEyXaVkFto0WqAyzVOjoW0lEw0R0PxHt9f4uM5x3LRHtIaJ9RHR7u+OJaAMRzRPRBzuZJ8P0klaagrnp0IJNiWFOmU6/lrcDeFAIsQXAg979EERkA7gTwHUAtgK4iYi2tjn+kwC+1eEcGaanGDOu2XHNnIZ0+q28AcBd3u27ALxNc852APuEEPuFEBUAX/bGNR1PRG8DsB/Arg7nyDA9JWGIcfWFhLEsx4JNiWFOmU6/lquEEGMA4P1dqTlnLYCDyv1D3mPG8USUA/AhAP+7w/kxTM9xDKt9K02CHdfMUqRlZzoiegDAas2hD7f5Grpvvmgx5n8D+KQQYr5VUhER3QLgFgDYsGFDm1NimIUjaRISLXwSbG5iliIthYQQ4k2mY0R0jIhGhRBjRDQK4LjmtEMA1iv31wE44t02jb8CwDuI6M8BDAFoEFFJCPEpzfx2ANgBANu2bWslfBhmwTGZm1rlSbCMYJYinX4t7wFws3f7ZgBf15zzMIAtRLSZiJIAbvTGGccLIV4rhNgkhNgE4C8B/KlOQDDMUqRVj2tjHgUXbGKWIJ0KiTsAXE1EewFc7d0HEa0honsBQAhRA3AbgPsA7AbwFSHErmbjGeZ0xmQibZ1xzUKCWXq0NDc1QwgxAeAqzeNHAFyv3L8XwL3tjo+c87FO5sgwS4WWnenYcc0sQdgKyjA9wjc3sSbBnEawkGCYHmG1zJNgIcEsPVhIMEyPaN2ZjoUEs/RgIcEwPYaFBHM6wUKCYXpEw8vicUxlO9hxzSxBWEgwTI9oCFdKGDOyWZNgliAsJBimR9Q9VcIUAst9rZmlSEd5EgzDBCzvS2EyXzYel5pEM43h9usuxGu3LO/63BjmVGEhwTBd4ke3vxGiSe1KKSRMeRIAcOuV53Z9XgzTCSwkGKZLJJ3m1ltpbmIHNXM6wT4JhukRMrqJ+0YwpxMsJBimRzQarc1NDLPUYCHBMD2i7juuF3kiDHMS8NeVYXqE9EmwuYk5nWAhwTA9wlMkOB+COa1gIcEwPcLPk2AhwZxGsJBgmB7hh8Dyr445jejo60pEw0R0PxHt9f4uM5x3LRHtIaJ9RHR7q/FEtImIikT0mPf/053Mk2GWAg02NzGnIZ3uaW4H8KAQYguAB737IYjIBnAngOsAbAVwExFtbWP8c0KIl3n/b+1wngyz6KS8ZLtWSXcMs5To9Nt6A4C7vNt3AXib5pztAPYJIfYLISoAvuyNa3c8w5wR/NENF+P9rz8Xr9uyYrGnwjBt06mQWCWEGAMA7+9KzTlrARxU7h/yHms1fjMRPUpE3yWi13Y4T4ZZdEb6Uvi9ay/kkuDMaUXL2k1E9ACA1ZpDH27zNXS/CHMVNJcxABuEEBNEdDmArxHRxUKIWc38bgFwCwBs2LChzSkxDMMw7dBSSAgh3mQ6RkTHiGhUCDFGRKMAjmtOOwRgvXJ/HYAj3m3teCFEGUDZu/0IET0H4HwAOzXz2wFgBwBs27atlfBhGIZhToJOzU33ALjZu30zgK9rznkYwBYi2kxESQA3euOM44lohefwBhGdA2ALgP0dzpVhGIY5SToVEncAuJqI9gK42rsPIlpDRPcCgBCiBuA2APcB2A3gK0KIXc3GA3gdgCeI6HEAXwVwqxBissO5MgzDMCcJCXHmWGi2bdsmdu6MWaQYhmGYJhDRI0KIbbpjHLDNMAzDGGEhwTAMwxhhIcEwDMMYOaN8EkQ0DuDFxZ4HgOUATiz2JJYI/FkE8GcRwJ9FwFL4LDYKIbSlAM4oIbFUIKKdJifQ2QZ/FgH8WQTwZxGw1D8LNjcxDMMwRlhIMAzDMEZYSCwMOxZ7AksI/iwC+LMI4M8iYEl/FuyTYBiGYYywJsEwDMMYYSGxwBDRB4lIENHyxZ7LYkBEHyeiZ4joCSK6m4iGFntOvcbUvvdsg4jWE9F3iGg3Ee0iot9a7DktNkRke31zvrHYczHBQmIBIaL1cAsXHljsuSwi9wO4RAhxKYBnAfz+Is+np7Ro33u2UQPwO0KIiwC8EsAHzuLPQvJbcAufLllYSCwsnwTwe2jdZOmMRQjxba8SMAA8BLefyNlEs/a9ZxVCiDEhxM+823NwF8e1zUeduRDROgA/B+Bziz2XZrCQWCCI6K0ADgshHl/suSwhfhXAtxZ7Ej2mWfvesxYi2gTgMgA/WeSpLCZ/CXcT2VjkeTSlZWc6xkyL1q5/AOCa3s5ocWj2OQghZCOpD8M1N3ypl3NbApxK+94zGiLqA/AvAH5b15L4bICI3gLguNd58/WLPJ2msJDoAFNrVyJ6CYDNAB4nIsA1sfyMiLYLIY72cIo9oVmLWwAgopsBvAXAVeLsi7lu1r73rIOIEnAFxJeEEP+62PNZRF4D4K1EdD2ANIABIvp7IcR/XeR5xeA8iR5ARC8A2CaEWOwiXj2HiK4F8AkAVwohxhd7Pr2GiBy4DvurAByG2873XUp3xrMGcndMdwGYFEL89iJPZ8ngaRIfFEK8ZZGnooV9EsxC8ykA/QDuJ6LHiOjTiz2hXtKife/ZxmsAvBvAG73vwmPeTppZwrAmwTAMwxhhTYJhGIYxwkKCYRiGMcJCgmEYhjHCQoJhGIYxwkKCYRiGMcJCgmEYhjHCQoJhGIYxwkKCYRiGMfL/A6EMvHwJRIrKAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "std: 0.000876\n" ] } ], "source": [ "# optimum shift\n", "shift = 0.21\n", "# shifted node vector\n", "xks = xk+shift*dx\n", "# shifted linear interpolation\n", "xi = np.arange(-5,5.005,0.01)\n", "nxi = len(xi)\n", "fi = np.zeros(nxi)\n", "c = prefilter(fk,shift)\n", "#print(len(c)) # 41\n", "for i in range(0,nxi):\n", " fi[i] = slintp(xi[i],xks,c)\n", "dfis=np.exp(-xi**2/2)-fi\n", "\n", "plt.plot(xi,dfis)\n", "plt.xlim([-5,5])\n", "plt.show()\n", "\n", "# standard deviation of residuals\n", "L2s = np.std(dfis) # 0.000876\n", "print(\"std: {:.6f}\".format(L2s))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Traditional linear interpolation" ] }, { "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" }, { "name": "stdout", "output_type": "stream", "text": [ "std: 0.002072\n" ] } ], "source": [ "# not shifted linear interpolation\n", "shift = 0.0\n", "xks = xk+shift*dx\n", "c = prefilter(fk,shift)\n", "for i in range(0,nxi):\n", " fi[i] = slintp(xi[i],xks,c)\n", "dfil=np.exp(-xi**2/2)-fi\n", "\n", "plt.plot(xi,dfil)\n", "plt.xlim([-5,5])\n", "plt.show()\n", "\n", "L2l = np.std(dfil) # 0.002072\n", "print(\"std: {:.6f}\".format(L2l))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Gain of the shifted linear interpolation" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "gain: 7.476 dB\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# gain of shifted linear interpolation dB\n", "dBgain = 20*np.log10(L2l/L2s) # 7.476\n", "print(\"gain: {:.3f} dB\".format(dBgain))\n", "\n", "\n", "# interpolation gain in terms of shift\n", "def gain(shift):\n", " dx = 0.25;\n", " xk = np.arange(-5,5+dx/2,dx)\n", " fk = np.exp(-xk**2/2)\n", " xks = xk+shift*dx\n", " xi = np.arange(-5,5.005,0.01)\n", " nxi = len(xi)\n", " fi = np.zeros(nxi)\n", " c = prefilter(fk,shift)\n", " for i in range(0,nxi):\n", " fi[i] = slintp(xi[i],xks,c)\n", " dfis=np.exp(-xi**2/2)-fi\n", " L2s = np.std(dfis)\n", " L2l = 0.002072\n", " return 20*np.log10(L2l/L2s)\n", "\n", "s = np.arange(0,0.5+0.005,0.01)\n", "gs = np.zeros_like(s)\n", "ns = len(s)\n", "for i in range(ns):\n", " gs[i] = gain(s[i])\n", "\n", "plt.plot(s,gs)\n", "plt.xlim([0,0.5])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Prefilter coefficients" ] }, { "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": [ "# h(n) prefilter coefficients\n", "tau = 0.21\n", "kvec = np.arange(0,101)\n", "hn = (-1)**kvec/(1-tau)*(tau/(1-tau))**kvec\n", "\n", "plt.plot(kvec[:21],hn[:21])\n", "plt.xlim([0,20])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Synthesis function (interpolating)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def hat(x):\n", " if np.abs(x)>1:\n", " return 0\n", " else:\n", " return 1-np.abs(x)\n", "\n", "def fint(x,hn,tau):\n", " f = 0\n", " n = len(hn)\n", " for i in range(n):\n", " f = f + hn[i]*hat(x-i-tau)\n", " return f\n", "\n", "xf = np.arange(0,10+0.02,0.05)\n", "f = np.zeros_like(xf)\n", "for i in range(len(xf)):\n", " f[i] = fint(xf[i],hn,tau)\n", "\n", "# plot of the synthesis function\n", "plt.plot(xf,f)\n", "x0 = np.arange(0,11)\n", "z0 = np.zeros_like(x0); z0[0]=1\n", "plt.plot(x0,z0,'ro')\n", "plt.xlim([-0.08,10.08])\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Image interpolation" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.image as mpimg\n", "def rgb2gray(rgb):\n", " return np.dot(rgb[...,:3], [0.299, 0.587, 0.114])\n", "\n", "img = mpimg.imread('img/lena.png')\n", "l = rgb2gray(img)\n", "plt.imshow(l, cmap = plt.get_cmap('gray'))\n", "plt.axis('off')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**shift**\n", "\n", "conventional linear interpolation: 0\n", "\n", "shifted linear interpolation: $\\left( \\frac{1}{2} - \\frac{1}{\\sqrt{12}} \\right)$" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "shift = 0.0" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "# 2D prefilter of s in-place\n", "# convert the image samples into interpolation coefficients\n", "def samp2coeff(s,shift):\n", " (h,w) = s.shape\n", " for i in range(h):\n", " ci = prefilter(s[i,:],shift)\n", " s[i,:] = ci\n", " for j in range(w):\n", " cj = prefilter(s[:,j],shift)\n", " s[:,j] = cj\n", " #return s\n", "\n", "# interpolation of shifted-linear coefficients c for x, y\n", "def interpxy(c,w,h,x,y,shift):\n", " # perform the shift\n", " x -= shift\n", " y -= shift\n", " # compute the interpolation indexes\n", " i = int(np.floor(x))\n", " j = int(np.floor(y))\n", " xi = np.array([i,i+1])\n", " yi = np.array([j,j+1])\n", " # compute the interpolation weights\n", " ww = x - xi[0]\n", " xw = np.array([1.0 - ww, ww])\n", " ww = y - yi[0]\n", " yw = np.array([1.0 - ww, ww])\n", " # check the boundaries\n", " for k in range(2):\n", " if xi[k] < 0:\n", " xi[k] = 0\n", " if w <= xi[k]:\n", " xi[k] = w-1\n", " if yi[k] < 0:\n", " yi[k] = 0\n", " if h <= yi[k]:\n", " yi[k] = h-1\n", " # perform interpolation\n", " interpolated = 0.0\n", " for j in range(2):\n", " ww = 0.0\n", " for i in range(2):\n", " ww += xw[i] * c[yi[j], xi[i]]\n", " interpolated += yw[j] * ww\n", " return interpolated" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## image rotation test" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "rotation 1 of 6\n", "rotation 2 of 6\n", "rotation 3 of 6\n", "rotation 4 of 6\n", "rotation 5 of 6\n", "rotation 6 of 6\n" ] } ], "source": [ "# keep the original image\n", "ll = np.copy(l)\n", "(h,w) = l.shape\n", "\n", "# rotation angle step\n", "astep = 60\n", "nrot = int(360/astep)\n", "\n", "for n in range(nrot):\n", "\n", " print(\"rotation {:d} of {:d}\".format(n+1,nrot))\n", " # change of basis of ll\n", " samp2coeff(ll,shift)\n", "\n", " # prepare the geometry\n", " # rotation angle\n", " angle = astep\n", " # shift\n", " xs = 0\n", " ys = 0\n", " # rotation origin\n", " xo = w//2\n", " yo = h//2\n", " angle *= np.pi / 180.0\n", " a11 = np.cos(angle)\n", " a12 = -np.sin(angle)\n", " a21 = np.sin(angle)\n", " a22 = np.cos(angle)\n", " x0 = a11 * (xs + xo) + a12 * (ys + yo)\n", " y0 = a21 * (xs + xo) + a22 * (ys + yo)\n", " xs = xo - x0\n", " ys = yo - y0\n", "\n", " # visit all pixels of the output image and assign their value\n", " oi = np.zeros_like(l)\n", " p = oi.flatten('C')\n", " i = 0\n", " for y in range(h):\n", " x0 = a12 * y + xs\n", " y0 = a22 * y + ys\n", " for x in range(w):\n", " x1 = x0 + a11 * x\n", " y1 = y0 + a21 * x\n", " if (x1 <= -0.5) or ((w - 0.5) <= x1) or (y1 <= -0.5) or ((h - 0.5) <= y1):\n", " p[i] = 0.0\n", " i = i + 1\t\n", " else:\n", " p[i] = interpxy(ll, w, h, x1, y1, shift)\n", " i = i + 1\n", "\n", " p = p.reshape(l.shape)\n", " ll = p" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.imshow(p, cmap = 'gray')\n", "plt.axis('off')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "shift = (0.5 - np.sqrt(1.0 / 12.0))" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "rotation 1 of 6\n", "rotation 2 of 6\n", "rotation 3 of 6\n", "rotation 4 of 6\n", "rotation 5 of 6\n", "rotation 6 of 6\n" ] } ], "source": [ "ll = np.copy(l)\n", "\n", "for n in range(nrot):\n", "\n", " print(\"rotation {:d} of {:d}\".format(n+1,nrot))\n", " # change of basis of ll\n", " samp2coeff(ll,shift)\n", "\n", " # prepare the geometry\n", " # rotation angle\n", " angle = astep\n", " # shift\n", " xs = 0\n", " ys = 0\n", " # rotation origin\n", " xo = w//2\n", " yo = h//2\n", " angle *= np.pi / 180.0\n", " a11 = np.cos(angle)\n", " a12 = -np.sin(angle)\n", " a21 = np.sin(angle)\n", " a22 = np.cos(angle)\n", " x0 = a11 * (xs + xo) + a12 * (ys + yo)\n", " y0 = a21 * (xs + xo) + a22 * (ys + yo)\n", " xs = xo - x0\n", " ys = yo - y0\n", "\n", " # visit all pixels of the output image and assign their value\n", " oi = np.zeros_like(l)\n", " p = oi.flatten('C')\n", " i = 0\n", " for y in range(h):\n", " x0 = a12 * y + xs\n", " y0 = a22 * y + ys\n", " for x in range(w):\n", " x1 = x0 + a11 * x\n", " y1 = y0 + a21 * x\n", " if (x1 <= -0.5) or ((w - 0.5) <= x1) or (y1 <= -0.5) or ((h - 0.5) <= y1):\n", " p[i] = 0.0\n", " i = i + 1\t\n", " else:\n", " p[i] = interpxy(ll, w, h, x1, y1, shift)\n", " i = i + 1\n", "\n", " p = p.reshape(l.shape)\n", " ll = p" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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