diff --git a/invisible_cities/demos/fit_functions_demo.ipynb b/invisible_cities/demos/fit_functions_demo.ipynb new file mode 100644 index 0000000..7f7766e --- /dev/null +++ b/invisible_cities/demos/fit_functions_demo.ipynb @@ -0,0 +1,580 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Demo of the fit_functions.py module" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Run last on Thu Mar 9 11:55:12 2017\n" + ] + } + ], + "source": [ + "import time\n", + "print(\"Run last on\", time.asctime())" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "plt.rcParams[\"figure.figsize\"] = 10, 8" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "import invisible_cities.core.fit_functions as fitf" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Data selection" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can select data in a range by applying the *in_range* function to it." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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SJGVmAJMkScrMACZJkpSZy1BIktRDuFxF5bACJkmSlJkBTJIkKTMDmCRJUmbO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\nSUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# create a dataset from a triangular distribution\n", + "x = np.random.rand(int(1e5)) - np.random.rand(int(1e5))\n", + "\n", + "# select those in the range [-.25, .25)\n", + "x_sub = x[fitf.in_range(x, -0.25, 0.25)]\n", + "\n", + "# let's plot an histogram of x in black\n", + "# and the same for x_sub in yellow\n", + "plt.hist(x , 200, (-1, 1), color='g', label=\"full set\")\n", + "plt.hist(x_sub, 200, (-1, 1), color='m', label=\"reduced set\")\n", + "plt.legend(prop={\"size\": 15});" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Predefined functions" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use the most common functions defined in the module. Let's draw them." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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bYRj1gDuwv/0liYiInLia7BqS/5BM0WdF9Jnch8g3InEPd7d1WdKLnHKYMk1z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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# generate a 1-dimensional grid\n", + "x = np.linspace(0, 1, 1000)\n", + "\n", + "# gauss with amplitude 1/√(2pi)/sigma, mean 0.5 and sigma 0.1 (black)\n", + "y_gauss = fitf.gauss(x, 1, 0.5, 0.1)\n", + "\n", + "# polynom 5 - x + 0.5 x^2 (blue)\n", + "y_poly2 = fitf.polynom(x, 5, -1, 0.5)\n", + "\n", + "# polynom 5 - 0.125 x + 1.75 x^2 - 4 x^3 (green)\n", + "y_poly3 = fitf.polynom(x, 5, -0.125, 1.75, -4)\n", + "\n", + "# exponential: 4 exp(-x/0.2) (red)\n", + "y_expo = fitf.expo(x, 4, -0.2)\n", + "\n", + "# power: 10 x^0.8 (purple)\n", + "y_power = fitf.power(x, 10, 0.8)\n", + "\n", + "plt.plot(x, y_gauss, \"k\", label=\"gauss\")\n", + "plt.plot(x, y_poly2, \"b\", label=\"poly2\")\n", + "plt.plot(x, y_poly3, \"g\", label=\"poly3\")\n", + "plt.plot(x, y_expo , \"r\", label=\"expo\")\n", + "plt.plot(x, y_power, \"m\", label=\"power\")\n", + "plt.legend(loc = \"upper left\", prop={\"size\": 15});" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Note how the degree of the polynom changes depending on the number of input parameters.**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Fitting data" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can fit any dataset to a 1-D function given the x,y coordinates of its points." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Note\n", + "\n", + "When creating an histogram with plt.hist (or np.histogram), it returns the *edges* of the bins. This means that the last element must be removed (it is the upper limit of the last bin) and the whole array shifted to get bin centers. This is done by the following function:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def get_centers(xbins):\n", + " # xbins should be shifted, as it contains the lower bounds\n", + " # and we want bin centers\n", + " return xbins[:-1] + np.diff(xbins) * 0.5" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Gauss (from histogram)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/Gonzalo/github/IC/invisible_cities/core/fit_functions.py:119: RuntimeWarning: divide by zero encountered in true_divide\n", + " chi2 = np.sum(np.ma.masked_invalid((fitx - y)**2/y))\n" + ] + }, + { + "data": { + "image/png": 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yMjJIT0/P0QPlzn6lsWbNGiZMmFDkdoX1igUFBbFu3ToefvhhRo0aRd26dZk6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\nJQUee8x3EpGoKXUBM7NGZvaBmS03sxwzuzuyfYSZbTazJZH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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# generate gaussianly distributed data\n", + "x = np.random.normal(50., 10., size=int(1e5))\n", + "\n", + "# histogram data and get bins in x and heights\n", + "entries, xbins, _ = plt.hist(x, 200, (0, 100))\n", + "\n", + "# get bin centers\n", + "xbins = get_centers(xbins)\n", + "\n", + "# fit data to a gaussian with seed (1, 10, 10)\n", + "fitres = fitf.fit(fitf.gauss, xbins, entries, (1, 10, 10))\n", + "\n", + "# fitres contains four attributes:\n", + "# - fn : the function\n", + "# - values: the coefficients that minimize the chi2\n", + "# - errors: the errors associated with the coefficients\n", + "# - chi2 : the chi2 of the fit\n", + "# Lets draw the result\n", + "plt.plot(xbins, fitres.fn(xbins), \"r\")\n", + "text = \"\\n\".join([\"{} = {:.4g} $\\pm$ {:.4g}\".format(name, val, err)\n", + " for name, val, err in zip(\"A $\\mu$ $\\sigma$\".split(),\n", + " fitres.values,\n", + " fitres.errors)] + \n", + " [\"$\\chi^2$/ndof = {:.2f}\".format(fitres.chi2)])\n", + "plt.text(0, 1500, text, fontsize=15);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Polynom (from scattered data)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Fitting x,y data is simpler than fitting histograms, as we don't need to extract x, y points." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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Q3M/G5idKn7BUnTh7BU2TBERERKRGOHgsG4A/b4/jgO+VfHxtWJHy2kQJmoiIiNQIgX42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\nqRLONBhARETk0DWoBc05N7g++5nZv4H3fC+zgc6VNnfylWX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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# generate data according to a polynom + gaussian noise\n", + "N = 100\n", + "x = np.linspace(-10, 10, N)\n", + "y = 3.06 - x + np.pi * x**2 + 1.92 * x**3\n", + "y += np.random.normal(0, 5, size=N)\n", + "\n", + "plt.scatter(x, y)\n", + "# fit data to a gaussian with seed (1, 10, 10)\n", + "fitres = fitf.fit(fitf.polynom, x, y, (1, -2, 1, 1))\n", + "\n", + "# fitres contains four attributes:\n", + "# - fn : the function\n", + "# - values: the coefficients that minimize the chi2\n", + "# - errors: the errors associated with the coefficients\n", + "# - chi2 : the chi2 of the fit\n", + "# Lets draw the result\n", + "plt.plot(x, fitres.fn(x), \"r\")\n", + "text = \"\\n\".join([\"{} = {:.4g} $\\pm$ {:.4g}\".format(name, val, err)\n", + " for name, val, err in zip(\"c0 c1 c2 c3\".split(),\n", + " fitres.values,\n", + " fitres.errors)] +\n", + " [\"$\\chi^2$/ndof = {:.2f}\".format(fitres.chi2)])\n", + "plt.text(-5, 1000, text, fontsize=15);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Expo (from histogram)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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z5swZEiVKRO7cuRkzZgxeXl4hbRInTsyyZcsYPnw4Tk5OVKxYET8/v5A/+8e6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\nfx6+8Y1sfthVV0FVFfTs+bfXVZb2KYBFRH2y8DU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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# generate data exponentially distributed \n", + "x = np.random.exponential(50, size=int(1e5))\n", + "\n", + "# histogram data and get bins in x and heights\n", + "entries, xbins, _ = plt.hist(x, 200, (0, 100))\n", + "\n", + "# get bin centers\n", + "xbins = get_centers(xbins)\n", + "\n", + "# fit data to a exponential with seed (50, -10)\n", + "fitres = fitf.fit(fitf.expo, xbins, entries, (50, -10))\n", + "\n", + "# fitres contains four attributes:\n", + "# - fn : the function\n", + "# - values: the coefficients that minimize the chi2\n", + "# - errors: the errors associated with the coefficients\n", + "# - chi2 : the chi2 of the fit\n", + "# Lets draw the result\n", + "plt.plot(xbins, fitres.fn(xbins), \"r\")\n", + "text = \"\\n\".join([\"{} = {:.4g} $\\pm$ {:.4g}\".format(name, val, err)\n", + " for name, val, err in zip(\"A $\\lambda$\".split(),\n", + " fitres.values,\n", + " fitres.errors)] +\n", + " [\"$\\chi^2$/ndof = {:.2f}\".format(fitres.chi2)])\n", + "plt.text(70, 700, text, fontsize=15);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Custom function (from histogram)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the scenario of a complex (or simply different) distribution, we can still create our own function and pass it to the fitf.fit function." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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CALy9vTFp0iQUFhZiypQpJtczdYyJrIUJmBGVjs1rCLyYgBHdEHbt2oUrV65g2rRpuHKl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\nu24erFoF99zjYlWJ63p/RK/5FmotTzfpx8vfjSPrmeMEPdUdXn+db97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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# generate data distributed as a cosine signal mounted on\n", + "# a uniform background\n", + "x1 = np.arccos(2*np.random.uniform(size=int(1e5)) - 1)\n", + "x2 = np.random.exponential(0.15, size=int(2e4))\n", + "x = np.concatenate((x1, x2))\n", + "\n", + "# histogram data and get bins in x and heights\n", + "entries, xbins, _ = plt.hist(x, 200, (0, np.pi))\n", + "\n", + "# get bin centers\n", + "xbins = get_centers(xbins)\n", + "\n", + "# create custom function\n", + "def custom_f(x, amp, freq, offset, bkg_amp, bkg_decay):\n", + " # avoid problems of negative or zero frequencies\n", + " if freq <= 0:\n", + " return np.inf\n", + " return amp * np.cos((x-offset)/freq) + bkg_amp * np.exp(-x/bkg_decay)\n", + "\n", + "\n", + "# fit data to a our custom function with seed (50, 2, 1, 1, 0.01)\n", + "fitres = fitf.fit(custom_f, xbins, entries, (50, 2, 1, 1, 0.01))\n", + "\n", + "# fitres contains four attributes:\n", + "# - fn : the function\n", + "# - values: the coefficients that minimize the chi2\n", + "# - errors: the errors associated with the coefficients\n", + "# - chi2 : the chi2 of the fit\n", + "# Lets draw the result\n", + "plt.plot(xbins, fitres.fn(xbins), \"r\")\n", + "\n", + "text = \"\\n\".join([\"{} = {:.4g} $\\pm$ {:.4g}\".format(name, val, err)\n", + " for name, val, err in zip(\"A freq offset B decay\".split(),\n", + " fitres.values,\n", + " fitres.errors)] +\n", + " [\"$\\chi^2$/ndof = {:.2f}\".format(fitres.chi2)])\n", + "plt.text(1.5, 1000, text, fontsize=15);\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Beautiful!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Dataset profiles" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When making scatter plots we usually want to see the average trend of the data along some axis. Lets see how." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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5PeW1XrG/01AHhY/0sDWae56/L4wnN7cm5aHUZMtHQd3dCJ7Yg75PT2gb99nd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\nfCiovUPfJAeISrBGMs7And7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pbQzCchyDryyms+eXKd8F++zrEDj0NmQ08Z1pxRoO/abs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EAAAA\no0lEQVSDiciNAP5ZKXWriAwA74mpRGQq2jdBOAEcBvC/0P4QzftiEhH5BoBlaN+5XQngbwHkg/ck\nrUTkjwBuBDAQwCkAjwAoR5L7ICJfA3Af2u/bV5VSL6T1erM1+CIiIiIyQ7YuOxIRERGZgsEXERER\nURox+CIiIiJKIwZfRERERGnE4IuIiIgojRh8EREREaURgy8iIiKiNGLwRURERJRG/x8iiMfPiFQ3\nXwAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# create a custom dataset. x uniform between 0 and 100\n", + "# and y a function of x with some some gaussian distortion\n", + "N = int(1e5)\n", + "x = np.random.uniform(0, 100, size=N)\n", + "y = np.cos(x/10) + np.random.normal(0, 0.1, size=N)\n", + "\n", + "# draw data\n", + "plt.scatter(x, y)\n", + "\n", + "# get the average in x making 100 bins between dataset limits\n", + "xp, yp, ye = fitf.profileX(x, y, 100)\n", + "\n", + "# draw it on top of the scatter plot to see it bahaves properly\n", + "plt.plot(xp, yp, \"k\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Lets do the same with profileY" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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honKWsjiz0oJDIqtLG1OMgi8vRaj+BE48xWJGZGZWOPWApYyIbC1t7DTk33w/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\nJUbq8LMAAG2nDmpOQmQtuR4XC1k/sJS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feUbPrY8+8GNdQUuZoVM99O/bxsyfX0/bTffo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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# create a custom dataset: data on a circle\n", + "N = int(1e5)\n", + "x = np.random.normal(size=N)\n", + "y = np.random.normal(size=N)\n", + "r = (x**2 + y**2)**0.5 / np.random.uniform(0., 1.0, size=N)\n", + "x /= r\n", + "y /= r\n", + "\n", + "# draw data\n", + "plt.scatter(x, y)\n", + "\n", + "# get the average in y making 100 bins between dataset limits\n", + "xp, yp, ye = fitf.profileY(x, y, 100)\n", + "\n", + "# draw it on top of the scatter plot to see it bahaves properly\n", + "plt.plot(yp, xp, \"k\");" + ] + }, + { + "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": "3.5.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}