{ "cells": [ { "attachments": { "Griffiths%20Pr%201.12.png": { "image/png": "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" } }, "cell_type": "markdown", "id": "50deb92b", "metadata": {}, "source": [ "![Griffiths%20Pr%201.12.png](attachment:Griffiths%20Pr%201.12.png)" ] }, { "cell_type": "code", "execution_count": 1, "id": "0c9dbd44", "metadata": {}, "outputs": [], "source": [ "import sympy as sp\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "sp.init_printing()" ] }, { "cell_type": "markdown", "id": "42340208", "metadata": {}, "source": [ "Consider the random variable θ between 0 and π and we want to compute the probability density function for cos(θ) then we can set up a monte carlo technique to see what that might look like." ] }, { "cell_type": "code", "execution_count": 92, "id": "6aab6dc8", "metadata": {}, "outputs": [], "source": [ "sample = np.random.random_sample(100000)*np.pi\n", "bins = np.histogram(sample, bins=40)\n", "bins_cos = np.histogram(np.cos(sample), bins=40)" ] }, { "cell_type": "code", "execution_count": 95, "id": "6dc0d093", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 95, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1,2, figsize=(10,5))\n", "ax1, ax2 = axes\n", "\n", "fig.suptitle(\"Relative Frequencies versus Bin\", fontsize=20, color=\"blue\")\n", "\n", "y, x = bins\n", "y = y/y.sum()\n", "ax1.grid()\n", "ax2.grid()\n", "ax1.bar(x[:len(y)], y, width=0.05)\n", "\n", "y, x = bins_cos\n", "y = y/y.sum()\n", "\n", "ax1.set_title(r\"Probability Density of $ \\theta $\")\n", "ax2.set_title(r\"Probability Density of cos $\\theta$\")\n", "ax2.bar(x[:len(y)], y, width=0.05)\n", "\n" ] }, { "cell_type": "code", "execution_count": 94, "id": "b4adee8f", "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAANIAAAAQCAYAAABjuSH9AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAABJ0AAASdAHeZh94AAAHEUlEQVR4nO2be4xfRRXHP1uRhwgFC7XxCW2othVcEUsrlkfUVq3FFosxpkRNoBog1pZW8JWvXxKi1VBdRQ0bifXRaLRAAwIVWonKQ0mkBEyrVAtIUZEWMUhpCrT+cebW2+nv7t57f3XdP/abbGZ3Zs7MOed778yZM3d79uzZwwhGMILucFBeYftVwOXAu4AxwN+ANYAl/bPuwLaXA6cAE4FjgGeBR9JYV0nanvWfD5wB9AJvBI4AVklaMMg8s4FFwOSSvr8DVki6u1u9kkwjn9juAc5PP1OAHmAT8B2gX9LuA2FLFzJvBy4GpgNHA9uBB4A+STdnfYcdL7Y/Anx3oPmB3ZJelM3RmJe69o/KhCYkYz8K3AN8FdiSHHK37TGDKF/GYuBw4DagD1gFPA98Abjf9quz/p8jyO0FHqszQXL+z4CTgbVpnnuB9wF32u5EdiO9Wvrkh0A/cBzwI4KolwDfBlYeKFtaynwZWEc8tDcAVwI3AccCZ3ZQbTjych/gip9fpD63dJijMS/UtD/fkb4FjAU+IekbRaXtFcnQK4CPVw2W4UhJO/NK21cAnwE+DVxYaloMbAX+RKwAtw80uO1xwFLgceAkSf8otZ1FOPRywnnd6NXIJ7bnAR8CHgKmStqW6g8GrgXOs71G0nXd2NJS5gJgGfA9YKGkXZkPXpz7hWHIi6T7iJep0/zFbtef1TfmJaGW/Xt3pLTyzgQeBr6Z9RPwTJrs8E4D5ejklISfpPKErP/tkjZLqntoey2h/2/LZBVjAU8Tq2xrvVr6ZF4qryzISvPuAj6f/rz4ANjSSMb2IcRL/xc6vERJ7rkOdcOOlyrYPhGYRuwcN2XNbXipbX85tDsrlbfmsaKkp4E7iW1w2sDmDIo5qby/y3E2A7uAqbaPKTfYPp2IZdd1qVcbn4xL5ZYOcxR1M9JKWKCNLU1l3kk8wNcBu23Ptn2p7UW2p3fQtS2GgpcqLEzlNZJeyNra8FIb5dDudal8sKLvZmJ1ngisrzuB7aXAS4HRRFz+NsIpX2qqbBmSnrR9KbAC2Gh7DXFongCcTcTaH+tSrzY+KVa74zv0H5/Kg9Lvf2hrSwuZt6RyJ7ABeEN5PNu/AuZLeqLC1loYIl46yR0GLABeIM4+ORrz0gTlHWl0Kv9V0beoP6rhHEuJMOiThFPWAjO7JQxA0teAcwgHXABcBpwLPAqszEOLFnq18UkRUiyx/bKiMp0/XOp3dLe2NJQZm8plwB5gBrE7nATcCpwO/LTCzkYYAl464QMED2slPdqhvRUvdTFq8C7dQdI4ST3E1noO8cZvsH1yt2Pb/hSwmsi4TCCyPm8mtupVKUM11Hr9GPh50mej7att9xGH4xnEGQVgn1CxjS0NZQqunwfOlnSHpH9LeoA4P2wFzjgQYd7/iZcirLu6or0VL3VRfpGK1XV0p46l+qfaTCTpcUnXE6HQGOD7bcYpYPtMYDlwg6QlkrZI2iHpXuLBeAy4xPb4AYYZTK/GPkmx+RxiFX4C+HD62Qy8lThsA5SzWY1taSFT6LhB0sOZD3YQDxnA1Apba2GIeMnnnEL4ditwc6c+bXhpgvKL9MdUTqzoW2RNqs4LtSDpEWAjMCU/jDbEe1O5XzoyPRj3EPa9qQu9WvlE0nOSlks6UdKhko6SNJfI/p0AbJP0UJe2NJUpbHmqwpbiYvmwiva6GApecgyUZCiP1ZSX2ii/SIXhM23nF7VHAKcBO4DftJkowytSWWl0DRySyv1SqVn9fmneAZDrdaB98kHgYOIysIw2tjSVWU+cjSbntiQUyYdWD1IXetVB5fNi+1DgvNR2TYMxy6jipTb2OlTSn4lD53HARVk/E3HuDyQ9s7fSnmD79flFnu2JtvcLh2yPShdsY4G71OCTow74dSoX2n5lNs+7iYd8J3BXW73a+CSNd2SHOXqBrxArf56BamxLU5m0st8IvIb4KqPcfyYwi9it1ua6N8T/nJcM5xIJglsqkgzl8ZryUhv5lw0XEgZ+3fE91ibgVOI+5UHgs1n/9cQF3PHE9ljgPcAXbd9BrHDbgZcTN8Pjgb8T2ZyyQXOBuenPIuc/3fbK9Ps2SUtLIquJ+4h3AJtsX5/GnUSEFz3AZdr327nGerXwCcBttp8Ffk/E3pOA2cT3Y3Mk/TXr38aWNjIXESHVCse3cBsI7uYSK/r5kvbJUA5jXgoUYV1/RXsZTXmpbf8+W3xagU8hsi2nApcQWY4+YJo6fNBZgXXENnsskXlZBrwfeJJYyadI2pjJ9PLfA+CsVDe+VDc/03U3QcBiIoael/SdRhw4Z0nq61avlj5ZTaSWFwBLiBRzPzBZ0i/zzm1saSmzlcieXUWcCRYR39fdCJwm6doOtvQyDHkBsD2JSJFXJhkyNOKlif09I/9GMYIRdI//AMPBw7owYoo2AAAAAElFTkSuQmCC\n", "text/latex": [ "$\\displaystyle 0.318309886183791$" ], "text/plain": [ "0.3183098861837907" ] }, "execution_count": 94, "metadata": {}, "output_type": "execute_result" } ], "source": [ "1/np.pi" ] }, { "cell_type": "markdown", "id": "2a71e0b5", "metadata": {}, "source": [ "The reasoning I am following here is that the random variable is coming from a uniform probability distribution on the domain [0, π]. Therefore after passing it through a function cos(x) then the domain is mapped to [-1, 1]. However if we divide the original uniform domain into N equal segments then all we have to do is track those individual segments and see where they end up after passing through cos(x). Note that the new range [-1,1] has a length of 2 so the new segments, on the x axis, should sum to that.\n", "\n", "$$ \\sum_{i=0}^{N} \\left [ \\left ( \\cos(\\frac{(i+1) \\pi}{N}) - \\cos (\\frac{i \\pi}{N}) \\right ) \\right ] = 2 $$\n", " \n", "$$ \\text{whereas } \\left ( \\cos(\\frac{(i+1) \\pi}{N}) - \\cos (\\frac{i \\pi}{N}) \\right ) \\textrm{pdf}(\\frac{(i+\\frac{1}{2}) \\pi}{N}) = \\frac{1}{N} $$\n", "\n", "dividing by 1/N and taking limits\n", "\n", "$$ \\lim_{ \\frac{1}{N} \\to 0} \\frac{\\left ( \\cos(\\frac{(i+1) \\pi}{N}) - \\cos (\\frac{i \\pi}{N}) \\right ) \\textrm{pdf}(x_i)}{\\frac{1}{N}} = \\sin(x_i) \\; \\textrm{pdf}(x_i) = 1 $$" ] }, { "cell_type": "code", "execution_count": 124, "id": "3c54f34b", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "N=40\n", "ii = np.arange(0.01, N+1)\n", "cs = np.cos(ii*np.pi/N)\n", "dcs = np.diff(cs)\n", "pdf = np.abs(1/(N*dcs))/pdf.sum()\n", "#print (pdf)\n", "\n", "plt.bar(ii[1:]/N*2.1-1/N-1.05, pdf, width=dcs*8)\n", "plt.grid()" ] }, { "cell_type": "code", "execution_count": 99, "id": "a22ed572", "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 99, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, np.pi,100)\n", "y = np.cos(x)\n", "plt.grid()\n", "plt.plot(x,y)" ] }, { "cell_type": "code", "execution_count": 162, "id": "f35b0e7f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 162, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = np.linspace(0.01, np.pi-0.01,100)\n", "y = 1/np.sin(x)\n", "A = 1/y.sum()\n", "plt.grid()\n", "plt.title(\"PDF of cos(X) = 1/sin(X)\")\n", "plt.plot(x,A*y)" ] }, { "cell_type": "markdown", "id": "2668f89c", "metadata": {}, "source": [ "compute \\, and σ" ] }, { "cell_type": "code", "execution_count": 126, "id": "015f1c42", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\int \\frac{x}{\\sin{\\left(x \\right)}}\\, dx$" ], "text/plain": [ "⌠ \n", "⎮ x \n", "⎮ ────── dx\n", "⎮ sin(x) \n", "⌡ " ] }, "execution_count": 126, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = sym.symbols(\"x\", real=True)\n", "sym.integrate(x/sym.sin(x))" ] }, { "attachments": { "recipsin.png": { "image/png": "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" } }, "cell_type": "markdown", "id": "66ee4131", "metadata": {}, "source": [ "The graph of x/sin(x) looks like the following and has no integral in terms of elementary functions.\n", "\n", "![recipsin.png](attachment:recipsin.png)" ] }, { "cell_type": "code", "execution_count": 148, "id": "927ecbf0", "metadata": {}, "outputs": [], "source": [ "from scipy.integrate import quad, quadrature" ] }, { "cell_type": "code", "execution_count": 153, "id": "92db396d", "metadata": {}, "outputs": [], "source": [ "def f(x):\n", " return x/np.sin(x)" ] }, { "cell_type": "code", "execution_count": 146, "id": "73d7e7a5", "metadata": {}, "outputs": [], "source": [ "res = quad(f, 0, np.pi-0.0000000001, full_output=1, limit=50 )" ] }, { "cell_type": "code", "execution_count": 158, "id": "30d67fdf", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/splat/venvs/jupyter-notebook/lib/python3.8/site-packages/scipy/integrate/_quadrature.py:276: AccuracyWarning: maxiter (1000) exceeded. Latest difference = 6.283111e-03\n", " warnings.warn(\n" ] } ], "source": [ "res = quadrature(f, 0, np.pi, maxiter=1000)" ] }, { "cell_type": "code", "execution_count": 159, "id": "d6eb2fbb", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\left( 45.6139114766399, \\ 0.00628311061097975\\right)$" ], "text/plain": [ "(45.61391147663986, 0.0062831106109797474)" ] }, "execution_count": 159, "metadata": {}, "output_type": "execute_result" } ], "source": [ "res" ] }, { "cell_type": "code", "execution_count": null, "id": "5d06697f", "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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }