diff --git a/demos/binning/circular_average.ipynb b/demos/binning/circular_average.ipynb new file mode 100644 index 00000000..34d51011 --- /dev/null +++ b/demos/binning/circular_average.ipynb @@ -0,0 +1,251 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# RPhi and Circular Average\n", + "This example computes the radial and circular average using RadialBinnedStatistic and RPhiBinnedStatistic.\n", + "(Both derivates of `skbeam.core.accumulators.binned_statistic.BinnedStatisticDD`)\n", + "\n", + "See also the scikit-beam-example `construct_rphi_image`" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "%matplotlib inline\n", + "\n", + "from skbeam.core.accumulators.binned_statistic import RPhiBinnedStatistic,\\\n", + " BinnedStatisticDD, RadialBinnedStatistic\n", + "from skbeam.core.utils import radial_grid, angle_grid" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Generate some fake data" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/julienl/anaconda3/envs/py3/lib/python3.6/site-packages/ipykernel_launcher.py:6: RuntimeWarning: divide by zero encountered in true_divide\n", + " \n" + ] + }, + { + "data": { + "image/png": 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V6yOf/og49oqbw0bt//qVD3bat37n10S/694eNn5bVOn+4a//F9HvZ/7fMKYn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\nnQwpAlhSN5D3vUhhCt0wDGNEWCcKvVq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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "shape = np.array([100, 100])\n", + "center = (40, 80)\n", + "R = radial_grid(center, shape)\n", + "PHI = angle_grid(center, shape)\n", + "\n", + "img = 1/R**2*np.cos(PHI*10)**2\n", + "\n", + "plt.figure(2);plt.clf()\n", + "plt.imshow(img);plt.clim(0,.01)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Compute the RPhi Average and Circular Averages" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 49, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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ww7VlTTl4xw98EwBw4VtfL5bdf89nAACvufRJxbK/Wa5FlHtPSn/UI9naH/XQ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\nXZhyCpAsnGRdqAneZeZqgMq9JRoqBrO61yvVP+VigKrKU+1FdDy7798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lHC0sKjHMciwCvAyYkqIoL17furSGWgfKsmFa4ym2wT28xUQW4Xh6BRUePS5X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\nDIT/D0uKgLl17hOwAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# compute the bins\n", + "rphibinstat = RPhiBinnedStatistic(img.shape, origin=center, bins=(100,100))\n", + "rbinstat = RadialBinnedStatistic(img.shape, origin=center, bins=100)\n", + "\n", + "\n", + "binmap_rphi = rphibinstat.binmap.reshape((-1, *img.shape))\n", + "binmap_r = rbinstat.binmap.reshape((-1, *img.shape))\n", + "\n", + "plt.figure(3, figsize=(10,8));\n", + "plt.clf()\n", + "plt.subplot(2,2,1)\n", + "plt.title(\"Rs\")\n", + "plt.imshow(binmap[0])\n", + "plt.subplot(2,2,2)\n", + "plt.title(\"Phis\")\n", + "plt.imshow(binmap[1])\n", + "plt.subplot(2,2,3)\n", + "plt.title(\"flattened bins\")\n", + "plt.imshow(rs.xy.reshape(shape))\n", + "\n", + "plt.figure(4);plt.clf()\n", + "plt.title(\"binmap for radius\")\n", + "plt.imshow(binmap_r[0])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Compute the RPhi and Radial Averages" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 52, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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NPbQa1kcKaAmk9Wzw0Xbz0R57L1sf+FAyH+k97tjYnACN9m+aaptAuTWwomsM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\nhDj+P0i44cKMAnriAAAAAElFTkSuQmCC\n", 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# compute the r-phi average\n", + "res_rphi = rphibinstat(img)\n", + "plt.figure(4);plt.clf()\n", + "plt.imshow(res_rphi);plt.clim(0,.01)\n", + "plt.xlabel(\"$\\phi\\,$(degrees)\")\n", + "plt.ylabel(\"$r\\,$(pixels)\")\n", + "\n", + "# compute the r-phi average\n", + "res_r = rbinstat(img)\n", + "plt.figure(5);plt.clf()\n", + "plt.loglog(rbinstat.bin_centers, res_r)\n", + "plt.xlabel(\"radius (pixels)\")\n", + "plt.ylabel(\"intensity\")\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "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": "3.6.0" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}