{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "589bf8dd", "metadata": {}, "outputs": [], "source": [ "# importing the needed libraries\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "id": "1df7d37e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Most probable value: 7.9799999999999995\n", "Uncertainty: 2.0153852678279103\n" ] } ], "source": [ "# part I: finding the most probable and uncertainty values\n", "measures=np.array([9.0,4.3,8.2,9.5,6.4,10.4,8.1,7.3,10.6,6.0])\n", "mpv=measures.sum()/measures.size\n", "stdErr=np.sqrt(np.sum((measures-mpv)**2)/(measures.size-1))\n", "print('Most probable value:',mpv)\n", "print('Uncertainty:',stdErr)" ] }, { "cell_type": "code", "execution_count": 3, "id": "80de1e1c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'luminosity')" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# part II: best parameters and uncertainties\n", "# first I create the arrays of frequency, data, and uncertainties. \n", "# I use the results of part I for the missing data\n", "freq=np.array([1,1.5,2,2.5,3,3.5,4,4.5,5,5.5])\n", "meas=np.array([0.05,0.1,.0075,1.86,8.0,6.0,.41,.03,0.1,.05])\n", "errs=np.array([.1,.15,.12,.17,.64,.72,.3,.1,.13,.11])\n", "# plotting the result\n", "plt.errorbar(freq,meas,yerr=errs,marker='o',ls='None',label='Data')\n", "plt.xlabel('frequency')\n", "plt.ylabel('luminosity')" ] }, { "cell_type": "code", "execution_count": 4, "id": "e3432d35", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "These are the sizes of the guess arrays: (101, 151)\n" ] } ], "source": [ "# set up my guess parameter values and a matrix to store the chi^2 results\n", "nu0Guess=np.arange(2.5,3.50001,.01)\n", "deltaGuess=np.arange(.25,.400001,.001)\n", "chisq=np.zeros([nu0Guess.size,deltaGuess.size])\n", "print('These are the sizes of the guess arrays:',chisq.shape)" ] }, { "cell_type": "code", "execution_count": 5, "id": "cdb719cb", "metadata": {}, "outputs": [], "source": [ "# double loop over all the guess value pairs.\n", "chimin=1e100\n", "for inu in range(nu0Guess.size):\n", " for ide in range(deltaGuess.size):\n", " # first compute the model for the given parameter set\n", " model=10*np.exp(-(freq-nu0Guess[inu])**2/2/deltaGuess[ide]**2)\n", " # then compute the chi^2 value and store it\n", " thisChi=np.sum((model-meas)**2/errs**2)\n", " # check if this is the best chi^2 so far and, if true, save the parameter\n", " # values and the model for later use\n", " chisq[inu,ide]=thisChi\n", " if thisChi < chimin:\n", " chimin=thisChi\n", " nu0Best=nu0Guess[inu]\n", " deltaBest=deltaGuess[ide]\n", " bestModel=model " ] }, { "cell_type": "code", "execution_count": 6, "id": "b8fb8942", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "chimin compared to number of data 5.061721789417155 10\n", "The best value of the central frequency is: 3.149999999999986\n", "The best value of the width is: 0.3510000000000001\n", "\n", "SUCCESS!! You found a viable model\n", "\n" ] } ], "source": [ "# Cheching if the model and the data agree\n", "print('chimin compared to number of data',chimin,meas.size)\n", "print('The best value of the central frequency is:',nu0Best)\n", "print('The best value of the width is:',deltaBest)\n", "if chimin<(2*meas.size):\n", " print()\n", " print('SUCCESS!! You found a viable model')\n", " print()\n", "else:\n", " print('No luck!, change model')" ] }, { "cell_type": "code", "execution_count": 9, "id": "267e437a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$\\\\Delta_{\\\\nu}$')" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# plotting the uncertainty area for the parameters. \n", "# Best value shown as a red dot, 1-sigma uncertainty area\n", "# shown with a contour ellipse\n", "plt.contour(nu0Guess,deltaGuess,np.transpose(chisq),[chisq.min()+2.3])\n", "plt.plot(nu0Best,deltaBest,'ro')\n", "plt.xlabel(r'$\\nu_0$',fontsize=15)\n", "plt.ylabel(r'$\\Delta_{\\nu}$',fontsize=15)" ] }, { "cell_type": "code", "execution_count": 10, "id": "e9f79b47", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# plotting my best model on top of the data for visual satisfaction\n", "plt.errorbar(freq,meas,yerr=errs,marker='o',ls='None',label='Data')\n", "ff=np.arange(1,5.5,.001)\n", "mm=10*np.exp(-(ff-nu0Best)**2/2/deltaBest**2)\n", "plt.xlabel('frequency')\n", "plt.ylabel('luminosity')\n", "plt.plot(ff,mm,label='Best Model')\n", "plt.legend()" ] }, { "cell_type": "code", "execution_count": null, "id": "40e8f43d", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "c93b9c7a", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.9.12" } }, "nbformat": 4, "nbformat_minor": 5 }