{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 1\n", "\n", "Example solution provided by Tania Kozynets (AMAS-2021 TA), Feb. 10, 2021; see alternative solutions by [Jason](https://www.nbi.dk/~koskinen/Teaching/AdvancedMethodsInAppliedStatistics2021/Exercises/Lecture2_CircleArea.py) (course lecturer) and [Jean-Loup](https://www.nbi.dk/~koskinen/Teaching/AdvancedMethodsInAppliedStatistics2021/Exercises/Lecture2_CircleArea_Py3.ipynb) (AMAS-2019 TA).\n", "\n", "Here, we will set up the code needed to compute the area of a circle. We will use bits of this code later in Exercise 2 (also in this notebook)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib\n", "#import tqdm — see the note about the tqdm module later in the notebook! :)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### My pretty plotting routines\n", "\n", "Below are the functions that I use every time when plotting something in Python. These are my secret pathways to pretty plots. Feel free to use or discard completely! They have nothing to do with the circle area calculation." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def reset_plt(ticksize,fontsize):\n", " plt.style.use('seaborn-white')\n", " plt.rcParams['xtick.labelsize'] = ticksize\n", " plt.rcParams['ytick.labelsize'] = ticksize\n", " plt.rcParams['font.size'] = fontsize\n", " plt.rcParams['mathtext.fontset'] = 'stix'\n", " plt.rcParams['font.family'] = 'STIXGeneral'\n", " plt.rcParams['legend.facecolor'] = 'white'\n", " plt.rcParams['axes.formatter.limits'] = (-1,3)\n", " plt.rcParams['axes.linewidth'] = 2.25\n", " \n", "\n", "def put_ticks(this_fig,this_ax):\n", " this_ax.xaxis.set_tick_params(which = 'major', direction = 'in', width = 2.5, length = 12, zorder = 1, top = True)\n", " this_ax.yaxis.set_tick_params(which = 'major', direction = 'in', width = 2.5, length = 12, zorder = 1, right = True)\n", " this_ax.xaxis.set_tick_params(which = 'minor', direction = 'in', width = 1.5, length = 6, zorder = 1, top = True)\n", " this_ax.yaxis.set_tick_params(which = 'minor', direction = 'in', width = 1.5, length = 6, zorder = 1, right = True)\n", " dx = -3/72\n", " dy = -3/72\n", " y_offset = matplotlib.transforms.ScaledTranslation(0, dy, this_fig.dpi_scale_trans)\n", " x_offset = matplotlib.transforms.ScaledTranslation(dx, 0, this_fig.dpi_scale_trans)\n", "\n", " for label in this_ax.xaxis.get_majorticklabels():\n", " label.set_transform(label.get_transform() + y_offset)\n", "\n", " for label in this_ax.yaxis.get_majorticklabels():\n", " label.set_transform(label.get_transform() + x_offset)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Sampling the x,y coordinates\n", "\n", "Below, we will create a simple Monte Carlo set of x,y coordinates sampled from uniform distributions. Initially, we will aim to fit the entire square with $x_{\\mathrm{max}} = y_{\\mathrm{max}} = r$ (the radius). " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "#Chosen radius of the circle (can be any positive number)\n", "radius = 5.2\n", "#Number of the samples to fill the whole square with. This is equivalent to \"throws\".\n", "num_samples = 1000\n", "#Sampling x,y from the uniform distributions\n", "xy_samples = np.random.uniform(low=(0.0,0.0),high=(radius,radius),size=(num_samples,2))\n", "#Splitting the 2D array into the x,y components \n", "x_samples = xy_samples[:,0]\n", "y_samples = xy_samples[:,1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Finding the samples that fall within the quarter circle\n", "\n", "These will be our accepted samples for the accept-reject method." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "#np.where returns the indices of the samples in our x,y arrays such that they fall within the quarter-circle with the \n", "#specified radius\n", "accepted_sample_inds = np.where((x_samples**2 + y_samples**2) <= radius**2)[0]\n", "#There are many ways to find the indices of the rejected samples, including the following:\n", "rejected_sample_inds = np.array([i for i in range(num_samples) if i not in accepted_sample_inds])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plotting the accepted/rejected samples" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$y$')" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#custom function from my pretty plotting routines to set the font sizes, thicknesses of the ticks, etc\n", "reset_plt(24,24)\n", "\n", "#creating the canvas\n", "fig = plt.figure(figsize = (8,8))\n", "ax = fig.add_subplot(111)\n", "\n", "#plotting the accepted samples\n", "sc_accept = ax.scatter(x_samples[accepted_sample_inds],y_samples[accepted_sample_inds],\n", " label = 'accept')\n", "#plotting the rejected samples\n", "sc_reject = ax.scatter(x_samples[rejected_sample_inds],y_samples[rejected_sample_inds],\n", " label = 'reject')\n", "\n", "#evaluating the points that lie on the x**2 + y**2 = radius**2 curve\n", "x_linspace = np.linspace(0,radius,1000)\n", "y_linspace = np.sqrt(radius**2 - x_linspace**2)\n", "\n", "#plotting the boundary of the circle\n", "ax.plot(x_linspace,y_linspace,lw=3.5, color='black',ls='-')\n", "\n", "#displaying the legend\n", "ax.legend(loc = (1.02,0.83), frameon = True, framealpha = 0.85)\n", "\n", "#custom function from my pretty plotting routines to put the ticks\n", "put_ticks(fig,ax)\n", "\n", "ax.set_xlabel('$x$')\n", "ax.set_ylabel('$y$')\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### How to go about the area calculation?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To get the area from the above simulation, we need to: \n", "\n", "(1) find how many samples were accepted among the total number of samples (i.e. calculate the accepted fraction);\n", "\n", "(2) find the area of the square that was used as a boundary for our MC samples;\n", "\n", "(3) multiply the fraction from (1) by the area from (2) and get the area of the quarter circle;\n", "\n", "(4) multiply the area of the quarter circle by 4 to get the area of the whole circle. \n", "\n", "For example..." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.756" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fraction_accepted = len(accepted_sample_inds)/num_samples\n", "fraction_accepted" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "27.040000000000003" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "square_area = radius**2\n", "square_area" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "81.76896" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "quarter_circle_area = square_area*fraction_accepted\n", "full_circle_area = 4*quarter_circle_area\n", "full_circle_area" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 2\n", "\n", "Great! Above, we got some estimate for the circle area. As we were creating random Monte Carlo samples for the $x$ and $y$ coordinates, this estimate is subject to fluctuations. Let's estimate a bunch of areas, sampling 100 $(x,y)$ points 1000 times." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Running the 1000 tests to estimate the areas" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The function below attempts to estimate the full circle area by knowing the radius of the circle only and applying the accept-reject method." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "def calc_area(r,num_samples):\n", " #We will reuse bits of the previous code — no comments provided as we kind of know by now what it all means ;)\n", " xy_samples = np.random.uniform(low=(0.0,0.0),high=(r,r),size=(num_samples,2))\n", " \n", " x_samples = xy_samples[:,0]\n", " y_samples = xy_samples[:,1]\n", " \n", " accepted_sample_inds = np.where((x_samples**2 + y_samples**2) <= r**2)[0]\n", " rejected_sample_inds = np.where((x_samples**2 + y_samples**2) > r**2)[0]\n", " \n", " fraction_accepted = len(accepted_sample_inds)/num_samples\n", " full_circle_area = 4*fraction_accepted*r**2\n", " \n", " return full_circle_area" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "num_samples = 100 #I use \"samples\" and \"throws\" interchangeably\n", "num_tests = 1000 #similarly, \"tests\" = \"trials\" :)\n", "\n", "#placeholder for the areas (we will append the estimated values to this array as we go through the loop)\n", "area_estimates = []\n", "\n", "for i in range(num_tests):\n", " \n", " full_circle_area = calc_area(r=radius,num_samples=num_samples)\n", " area_estimates = np.append(area_estimates, full_circle_area)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plotting the histogram of area frequencies" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will now histogram our estimated areas and see where the gaps, if any, appear for the different bin sizes." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'circle area histogram\\n')" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize = (10,8))\n", "ax = fig.add_subplot(111)\n", "\n", "#these are the bin sizes that we want to use in our histograms\n", "bin_sizes = [3,1,0.1] #m^2\n", "colors = ['black','C3','C0']\n", "\n", "for ib,bin_size in enumerate(bin_sizes):\n", "\n", " ax.hist(area_estimates,bins=np.arange(np.min(area_estimates),np.max(area_estimates)+bin_size,bin_size),\n", " facecolor = 'none', histtype = 'step', lw = 3.0, color = colors[ib],\n", " label = 'bin width = $%s\\,\\mathrm{m}^2$'%bin_size)\n", " \n", "put_ticks(fig,ax)\n", "\n", "ax.legend(loc = 'upper left',frameon = True, fontsize = 22)\n", "ax.set_xlabel(r'estimated circle area [$m^2$]')\n", "ax.set_ylabel('frequency')\n", "ax.set_title('circle area histogram'+'\\n')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 3\n", "\n", "Now let's see if we can put the above area estimates to use and find the approximate value of $\\pi$. We all secretly know that the area of the circle should be $\\pi r^2$. So, to get the estimate of $\\pi$, we should divide our area estimates by $r^2$.\n", "\n", "We will need to do this for 100000 throws maximum, so let's do this in one go and then cut off the estimates at the smaller values when needed." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "num_throws_to_test = [10,100,1000,10000,100000]\n", "\n", "pi_estimates = []\n", "\n", "for num_throws in num_throws_to_test: \n", " \n", " full_circle_area = calc_area(r=radius,num_samples = num_throws)\n", " this_pi_estimate = full_circle_area/radius**2\n", " pi_estimates = np.append(pi_estimates, this_pi_estimate) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plotting the estimated pi values for several tested throw numbers" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$\\\\pi$ estimate')" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize = (10,8))\n", "ax = fig.add_subplot(111)\n", "\n", "#displaying the results for 10,100,1000,10000,100000 throws\n", "ax.plot(num_throws_to_test,pi_estimates,ls='none',marker = 'x', markersize = 15, color = 'black', mew = 2)\n", "#the true value of pi\n", "ax.axhline(y=np.pi, color = 'red', ls = '--')\n", "\n", "put_ticks(fig,ax)\n", "ax.set_xscale('log')\n", "\n", "ax.set_xlabel('number of throws')\n", "ax.set_ylabel(r'$\\pi$ estimate')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### More tests!\n", "\n", "Now, we will perform 200 more tests for num_throws varied between 1-10000." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "num_throws_to_test = np.random.choice(range(10000),200,replace = False)\n", "\n", "pi_estimates = []\n", "\n", "#A fun note: install tqdm module and run for num_throws in tqdm.tqdm(...) if you want to see the progress bar\n", "#for your for loop! Remember to import tqdm though.\n", "for num_throws in num_throws_to_test: \n", " \n", " full_circle_area = calc_area(r=radius,num_samples = num_throws)\n", " this_pi_estimate = full_circle_area/radius**2\n", " pi_estimates = np.append(pi_estimates, this_pi_estimate)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$\\\\pi$ estimate')" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize = (10,8))\n", "ax = fig.add_subplot(111)\n", "\n", "#displaying the results for 10,100,1000,10000,100000 throws\n", "ax.plot(num_throws_to_test,pi_estimates,ls='none',marker = 'x', markersize = 10, color = 'black', mew = 2)\n", "#the true value of pi\n", "ax.axhline(y=np.pi, color = 'red', ls = '--', lw = 3.5, label = 'true value of $\\pi$')\n", "\n", "put_ticks(fig,ax)\n", "ax.legend(loc = 'lower right',frameon = True)\n", "\n", "ax.set_xlabel('number of throws')\n", "ax.set_ylabel(r'$\\pi$ estimate')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Final notes: the Central Limit Theorem\n", "\n", "\n", "Now, we will attempt to estimate the value of $\\pi$ from 10,000 trials and using 1000 throws per trial, histogram the resulting distribution, and see how well that compares to a gaussian. We will just plot the histogram and overlay the gaussian on top, while the ambitious can perform the actual fit, evaluate the $\\chi^2$, etc. :) " ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "pi_for_clt = []\n", "num_tests = 10000\n", "num_samples = 1000\n", "\n", "#collecting the values of pi in just the same way as before! \n", "for i in range(num_tests): \n", " full_circle_area = calc_area(r=radius,num_samples = num_samples)\n", " this_pi_estimate = full_circle_area/radius**2\n", " pi_for_clt = np.append(pi_for_clt, this_pi_estimate)\n", " " ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize = (10,8))\n", "ax = fig.add_subplot(111)\n", "\n", "#histogramming the obtained pi values. notice the flag density = True; it means we're plotting the normalized PDF\n", "ax.hist(pi_for_clt,bins = np.linspace(np.min(pi_for_clt),np.max(pi_for_clt),15),density = True, alpha = 0.6,\n", " label = 'estimated $\\pi$ values')\n", "\n", "#creating the finely spaced domain for the evaluation of the gaussian\n", "pi_linspace = np.linspace(np.min(pi_for_clt)-0.1,np.max(pi_for_clt)+0.1,1000)\n", "\n", "#the gaussian distribution centered at true pi and normalized to 1\n", "sigma = np.pi/(2*np.sqrt(num_samples))\n", "normalized_gaussian = (1/np.sqrt(2*np.pi*sigma**2))*np.exp(-(pi_linspace-np.pi)**2/(2*sigma**2))\n", "\n", "ax.plot(pi_linspace,normalized_gaussian, lw = 3.0, color = 'red', label = 'Gaussian')\n", "\n", "put_ticks(fig,ax)\n", "ax.set_xlabel('$\\pi$ estimates')\n", "ax.set_ylabel('normalized PDF')\n", "\n", "ax.legend(loc = 'upper left',frameon=True,fontsize = 22)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "AMAS", "language": "python", "name": "amas" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }