{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# IA Paper 4 - Mathematics - Examples paper 2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Question 2: 3D plotting of planes\n", "\n", "Without solving the following simultaneous equations, determine the value of $s$ for which they have no solution when $t = 1$.\n", "\n", "\\begin{align}\n", "2x + y + 3z &= 5 \\\\\n", "6x - 2y - z &= 3 \\\\\n", "sx + z &= t\n", "\\end{align}\n", "\n", "For this value of $s$ determine the value of $t$ for which the equations have an infinite number of solutions. Use Python/Matplotlib to visualize the three planes for these and other values of $s$ and $t$. Make sure you understand how the planes' intersections relate to the values of $s$ and $t$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We first load the required modules:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# Import modules\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D\n", "\n", "# Special command for plotting inside a Jupyter notebook\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then, in order to plot the planes in `matplotlib`, we need to construct a grid of `x-` and `y-` values, so that we can evaluate `z` at each of these points." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# These commands construct a grid of x and y values on which we are\n", "# going to sample points to get the z values\n", "x = np.linspace(-5, 5, 100)\n", "y = np.linspace(-5, 5, 100)\n", "X, Y = np.meshgrid(x, y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can calculate the z-values for these plane. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# Change these values to see what effect they have on the planes\n", "s = 2.0\n", "t = 13.5/5.0\n", "\n", "# Now we calculate the z coordinates at all points on the grid, one\n", "# for each plane, using the three plane equations\n", "Z0 = (5 - 2*X - Y)/3\n", "Z1 = 6*X - 2*Y - 3\n", "Z2 = t - s*X" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And then plot these planes on a 3D plot. " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Create 3D figure\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111, projection='3d')\n", "\n", "# We now add colour on each plane\n", "ax.plot_surface(X, Y, Z0, color='r', alpha=0.4)\n", "ax.plot_surface(X, Y, Z1, color='g', alpha=0.4)\n", "ax.plot_surface(X, Y, Z2, color='b', alpha=0.4);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Question 6\n", "\n", "(i) Plot the function $f(x) = \\cosh(1 + x)$ and its power series expansions using 1, 2, 3, and 4 terms. Also plot the difference between the exact function $f(x)$ and the power series expansions. What are the x–ranges over which the power series expansions differ by less than 0.01 from the exact function?\n", "\n", "(ii) Repeat with the function $f(x) = (1 + x)/(1 − x^2)$. What are the ranges over which the power series expansions are acurate to $1\\%$ and $10\\%$ of the real fuction?\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, we load the modules." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# Import modules\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now look at the original function of $y = \\cosh(x+1)$. " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# The original function y = cosh(1 + x)\n", "num_points = 200\n", "x = np.linspace(-5.0, 3.0, num_points)\n", "y_ref = np.cosh(1 + x)\n", "\n", "# Plot the original function\n", "plt.plot(x, y_ref)\n", "\n", "# Add label for the plot\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"f(x)\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We need to write a factorial function that can be used later on. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "# Factorial function\n", "def factorial(n):\n", " temp = 1.0\n", " for i in np.arange(1, n + 1):\n", " temp *= i\n", " return temp" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Taylor series for the function $f(x) = \\cosh(x+1)$ is:\n", "\n", "$$\n", "\\cosh(x+1) = \\cosh(1) + x \\sinh(1) + \\dfrac{x^2}{2!} \\cosh(1) + \\dfrac{x^3}{3!} \\cosh(1) + \\mathcal{O}(x^4)\n", "$$\n", "\n", "We now plot the function obtained from a finite number of terms in the quoted Taylor." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Now the power series\n", "max_terms = 100\n", "\n", "# Initialise zero array\n", "y_power_series = np.zeros(num_points)\n", "\n", "# Initilise array to store the error\n", "error_conv = []\n", "\n", "# Split to two subplots\n", "fig1, ax1 = plt.subplots()\n", "fig2, ax2 = plt.subplots()\n", "# fig2, ax2 = plt.subplots(figsize=(8, 6))\n", "\n", "# Plot the reference function\n", "ax1.plot(x, y_ref, 'k', label=\"Reference\", lw=1.0, ls='--')\n", "\n", "# Step through the number of terms\n", "for i in range(0, max_terms):\n", " # Adding terms to power series\n", " if i % 2 == 0:\n", " y_power_series = y_power_series \\\n", " + np.power(x, i)/factorial(i)*np.cosh(1)\n", " else:\n", " y_power_series = y_power_series \\\n", " + np.power(x, i)/factorial(i)*np.sinh(1)\n", "\n", " if i <= 6:\n", " ax1.plot(x, y_power_series, label='%d terms' % (i + 1), lw=2.0)\n", " ax2.plot(x, (y_ref - y_power_series), label='%d terms' % (i+1), lw=2.0)\n", "\n", " # Calculate the relative least-square difference\n", " error_conv.append(np.linalg.norm\n", " (y_power_series - y_ref) / np.linalg.norm(y_ref))\n", "\n", "# Insert legends\n", "ax1.legend(loc='center left', bbox_to_anchor=(1.0, 0.5))\n", "ax2.legend(loc='center left', bbox_to_anchor=(1.0, 0.5))\n", "\n", "# Set limit\n", "ax1.set_ylim((-10, 40))\n", "ax2.set_ylim((-1, 1))\n", "\n", "# Label axes\n", "ax1.set_xlabel('x')\n", "ax2.set_xlabel('x')\n", "ax1.set_ylabel('f(x)')\n", "ax2.set_ylabel('Error f(x)');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To offer a better understand, let's look at an interacting version of these plots. This can only be run locally, or at . You will need the package `ipywidgets` installed. " ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Let's try an interactive notebook\n", "from ipywidgets import *\n", "\n", "\n", "def plot_power_series(n):\n", " # Initialise zero array\n", " y_power_series = np.zeros(num_points)\n", " # Step through the number of terms\n", " for i in range(0, n+1):\n", " # Adding terms to power series\n", " if i % 2 == 0:\n", " y_power_series = y_power_series + \\\n", " np.power(x, i)/factorial(i)*np.cosh(1)\n", " else:\n", " y_power_series = y_power_series + \\\n", " np.power(x, i)/factorial(i)*np.sinh(1)\n", "\n", " # Plot the reference function\n", " plt.plot(x, y_ref, 'k', label=\"Reference\", lw=1.0, ls='--')\n", "\n", " # Update the plot\n", " plt.plot(x, y_power_series)\n", " plt.ylim([-10, 30])\n", "\n", " # Add axis label\n", " plt.xlabel('x')\n", " plt.ylabel('f(x)')\n", "\n", "interact(plot_power_series, n=(0, 20, 1));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can check the convergence rate of the Taylor series expansion by looking at the least-square error relative to the exact function. " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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UqFXkjMDMCqdrIIiIv0q//27/mtN/I/OMEdQrM5XFzankg3+0VqVRq3jWkJkVTi+DxaPAFcCPAaPZ+Yj41Rzb1TfdNqaBpI4g26BmtF5htF51HYGZFU4vBWWfBJ4KvAL4CrAeOJhno/opCwCNWvuic+msodbMGMFovcpoveqMwMwKp5dA8PSI+B3gcET8DfBq4EX5Nqt/sg/9eesIplrT+xQ36pWka8gZgZkVTC+BIFtb6HFJzwZOAk7Nr0n9Ne8SE9WZWUPjbRlBo171WkNmVji91BFcJ+kU4HdIlqNeCVyTa6v6aME6grbK4mX1KqP1iscIzKxwellr6CMRcSAivhIR50bEqRHxl708uaSLJd0naaekqxe47j9JCkmbF9P4pTDvYHFaRzDZbHF0copqRdSrSdeQMwIzK5qFCsreudAvHqugTFIVuBZ4GbAb2CZpa0Tc03HdKuDtwK29NnopLbRncbOVVBaPpo+N1qs8dnii/400M8vRQhnBqmN8HcsLgZ0R8UBETACfAS6d57rfAz4AjC2i3Uvm9JNGqVbEqasa0+dmrz46xWi6jWVSR+CuITMrloUKyp5sIdmZwK624910zDaS9HzgrIj4gqTf7PZEkrYAWwA2bFjarRBecPZT2P7eizhlxcj0uZmtKltJRpAGgqSOwF1DZlYsvexQdp6kmyXdnR4/R9JvP9kXllQBPkyyJ/KCIuK6iNgcEZvXrVv3ZF96jvYgAG1jBK1grDlFo552DdWqzgjMrHB6mT7618B7SKeRRsRdwGU9/N4e4Ky24/Xpucwq4NnAlyV9H7gA2DqIAeNOkqhVRHOqxfjkFMuyrqG6l5gws+LpJRAsj4hvdJxr9vB724BNks6RNEISPLZmD0bEExGxNiI2RsRG4OvAJRGxvce256pW1cxg8ayuIWcEZlYsvQSCfZKeBgSApNcBDx/rlyKiCbwNuAm4F7ghInZIer+kS55Em/uiXqkwOZVMHx2d7hpKMoKIGHDrzMyWTi8FZW8FrgOeKWkPyX7Fb+zlySPiRuDGjnPzFqNFxIW9PGe/1Kqa3o/g5HRTmkaaGYw3Z7IEM7Nhd8xAkG5NeZGkFSQZxBGSbp4Hc27bQNWqSUbQOX0UHAjMrFi6dg1JWi3pPZL+TNLLSALAW4CdwBv61cBBqVc0vVVlNmtoOiPwzCEzK5CFMoJPAgeAfweuBN4LCHhtRNzZh7YNVK1aodlKNq+fHixuywjMzIpioUBwbkT8OICkj5AMEG+IiIFUAPfbzBhBa3r6aBYQXEtgZkWy0KyhbPlpImIK2F2WIADJstQzYwSzt7N0LYGZFclCGcFzJf0o/VnAsvRYQETE6txbN0C1qhhrJltVjtZmZwSuJTCzIlloraFST4upVSocGkuSotE5XUPOCMysOHopKCulelUcGk8KqOd2DTkjMLPicCDoolapcHAsCQSNemfXkDMCMysOB4IualVxKA0EyzoKypwRmFmROBB0Ua9WODSRdQ05IzCz4nIg6KJWEdnactOLztWdEZhZ8TgQdJHtUga0rTWUzhry9FEzKxAHgi6yfYuB6TqC6UXnPH3UzArEgaCL2qyMIPm5UhEjtYozAjMrFAeCLmZlBG1LTjdqFWcEZlYoDgRd1Cpzxwiyn73EhJkViQNBF7VZGcHMP1Oj5g3szaxYHAi6mG/WUPazMwIzKxIHgi5qlSQjqFbUERScEZhZsTgQdJHNGsp2Jcs0alUXlJlZoTgQdFFPM4LOTepH6xUvMWFmheJA0MV0RtAZCJwRmFnBOBB0kdURtM8YAmjUKw4EZlYoDgRd1BfICNq7ht7xd3fyhbse7mvbzMyWkgNBF7Xq/GMEjbZZQ08cneQf7tjDLfc92vf2mZktFQeCLuqV2UtPZxq1mTqC7/zwIAD7D433t3FmZkvIgaCL6Yyg1jlrqDq91tD9PzwEwP7DE/1tnJnZEnIg6GJ61tBIR9dQrcLEVIupVnB/mhHsO+iMwMyGlwNBF9N1BPNkBAATzRb3PZIGgsMTRLadmZnZkMk1EEi6WNJ9knZKunqex98p6R5Jd0m6WdLZebZnMWbqCGb/E7VvV/mdRw8iJUHh0Hiz7200M1sKuQUCSVXgWuCVwPnA5ZLO77jsDmBzRDwH+Bzwwbzas1hdZw2lGcKex4+y79AE55++GoD9hzxOYGbDKc+M4IXAzoh4ICImgM8Al7ZfEBG3RMSR9PDrwPoc27Mo3WYNZcff2vMEAD/1tDUA7D/scQIzG055BoIzgV1tx7vTc91cAfzLfA9I2iJpu6Tte/fuXcImdlfvMmsoywju2p0FgrUA7HNGYGZD6oQYLJb0JmAz8KH5Ho+I6yJic0RsXrduXV/a1HWtoemM4HFOXl7nmaevAmCfawnMbEjlGQj2AGe1Ha9Pz80i6SLgvcAlEXHCfJpOZwQj888a+vbDBznv1FWsWdEAPEZgZsMrz0CwDdgk6RxJI8BlwNb2CyQ9D/grkiBwQq3TkO1ZPHc/guS42QrOe+pKRmoVVo/WXF1sZkMrt0AQEU3gbcBNwL3ADRGxQ9L7JV2SXvYhYCXwWUl3Stra5en67pQVdSqC01aPzjrf3lX0jNOSbqG1Kxvsc3WxmQ2pWp5PHhE3Ajd2nLum7eeL8nz9J+P0k5bx1d/6ec48edms8422DOG8tkDgjMDMhtUJMVh8olp/ynIkzTrXnhFkgWDNyhGPEZjZ0HIgWKRGOmto3aoGp6wYAZJA4FlDZjasHAgWKasjyMYHANasaHDgyCTNKe9lbGbDx4FgkbI6gk2nrZw+t3Zlkhk8dsTdQ2Y2fHIdLC6iRq3K/3jts/mZp6+dPrd25UwtwamrRrv9qpnZCcmB4Di88UWzF0lds9JFZWY2vNw1tATWpF1DHjA2s2HkQLAE1qbLTDgQmNkwciBYAquX1ahX5b2LzWwoORAsAUmsWeHqYjMbTg4ES8TVxWY2rBwIlsgaLzxnZkPKgWCJrF0xwr6D7hoys+HjQLBE1qwcYf/hcSJi0E0xM1sUB4IlsnZlg7HJFkcmpgbdFDOzRXEgWCKuLjazYeVAsESmq4sPe5zAzIaLA8ESWetN7M1sSDkQLBGvN2Rmw8qBYIlkgcDVxWY2bLwM9RJp1KqsGq1x044f8p1HD7H7wFEu/rGncuVLzh1008zMFuSMYAk96/TV3PPwj7jtwQPsOXCUP7tlJ5PevtLMTnDOCJbQp6+8gIigVq3wrzseYcsnb+NrO/dx4TNOHXTTzMy6ckawhKoVUasm/6QvOW8dKxs1bvzWwwNulZnZwhwIcjJar3LRs07lph0/dPeQmZ3QHAhy9KofP50njk7ytZ37Bt0UM7OuHAhy5O4hMxsGDgQ5cveQmQ0DB4Kcvfo5Z7h7yMxOaJ4+mrOf3bSWlY0af/7l7zI2OcVz1p/M6SeNImnQTTMzA3LOCCRdLOk+STslXT3P4w1Jf5c+fqukjXm2ZxBG61Wu+rlzueOhA1z1qdv5qT/4Ei//469y045HvImNmZ0QlNeHkaQqcD/wMmA3sA24PCLuabvmvwHPiYirJF0GvDYifmmh5928eXNs3749lzbnaWxyinsf/hF37nqcT339Qb679zCbzz6FK19yLutWNVg9WmP1aJ2Tltdp1KqDbq6ZFYyk2yJi87yP5RgIXgy8LyJekR6/ByAi/mfbNTel1/y7pBrwCLAuFmjUsAaCds2pFjds380f/9v97J1nn+PlI1VWj9apVoQEFYlK+p3kv2ndupjc8WRWPL/+C5t4zXPPOK7fXSgQ5DlGcCawq+14N/CibtdERFPSE8AaYNbIqqQtwBaADRs25NXevqlVK/zyizbw2uedyY4fPMHBsSYHx5s8cXSSJ45McODIJAfHJmkFtCJotYKA6eNpXcJldHvAzIbaScvquTzvUAwWR8R1wHWQZAQDbs6SWTZSZfPGpwy6GWZWcnkOFu8Bzmo7Xp+em/eatGvoJGB/jm0yM7MOeQaCbcAmSedIGgEuA7Z2XLMVeEv68+uALy00PmBmZksvt66htM//bcBNQBX4WETskPR+YHtEbAU+CnxS0k7gMZJgYWZmfZTrGEFE3Ajc2HHumrafx4DX59kGMzNbmJeYMDMrOQcCM7OScyAwMys5BwIzs5LLbYmJvEjaCzy4iF9ZS0elckmU8b7LeM9Qzvsu4z3Dk7vvsyNi3XwPDF0gWCxJ27utr1FkZbzvMt4zlPO+y3jPkN99u2vIzKzkHAjMzEquDIHgukE3YEDKeN9lvGco532X8Z4hp/su/BiBmZktrAwZgZmZLcCBwMys5AodCCRdLOk+STslXT3o9uRB0lmSbpF0j6Qdkt6enn+KpP8r6Tvp91MG3dalJqkq6Q5J/5wenyPp1vT9/rt0+fNCkXSypM9J+rakeyW9uCTv9TvS/7/vlvRpSaNFe78lfUzSo5Lubjs373urxJ+m936XpOc/mdcubCCQVAWuBV4JnA9cLun8wbYqF03gXRFxPnAB8Nb0Pq8Gbo6ITcDN6XHRvB24t+34A8AfR8TTgQPAFQNpVb7+F/DFiHgm8FyS+y/0ey3pTODXgc0R8WySZe0vo3jv9/XAxR3nur23rwQ2pV9bgL94Mi9c2EAAvBDYGREPRMQE8Bng0gG3aclFxMMRcXv680GSD4YzSe71b9LL/gb4xcG0MB+S1gOvBj6SHgt4KfC59JIi3vNJwEtI9vEgIiYi4nEK/l6nasCydCfD5cDDFOz9joivkuzL0q7be3sp8IlIfB04WdLpx/vaRQ4EZwK72o53p+cKS9JG4HnArcBpEfFw+tAjwGkDalZe/gT4LaCVHq8BHo+IZnpcxPf7HGAv8PG0S+wjklZQ8Pc6IvYAfwg8RBIAngBuo/jvN3R/b5f0863IgaBUJK0E/h74jYj4Uftj6fafhZknLOk/AI9GxG2Dbkuf1YDnA38REc8DDtPRDVS09xog7Re/lCQQngGsYG4XSuHl+d4WORDsAc5qO16fniscSXWSIPC3EfH59PQPs1Qx/f7ooNqXg58GLpH0fZIuv5eS9J2fnHYdQDHf793A7oi4NT3+HElgKPJ7DXAR8L2I2BsRk8DnSf4fKPr7Dd3f2yX9fCtyINgGbEpnFoyQDC5tHXCbllzaN/5R4N6I+HDbQ1uBt6Q/vwX4p363LS8R8Z6IWB8RG0ne1y9FxBuBW4DXpZcV6p4BIuIRYJekZ6SnfgG4hwK/16mHgAskLU//f8/uu9Dvd6rbe7sVeHM6e+gC4Im2LqTFi4jCfgGvAu4Hvgu8d9Dtyekef4YkXbwLuDP9ehVJn/nNwHeAfwOeMui25nT/FwL/nP58LvANYCfwWaAx6PblcL8/AWxP3+9/BE4pw3sN/C7wbeBu4JNAo2jvN/BpkjGQSZLs74pu7y0gklmR3wW+RTKj6rhf20tMmJmVXJG7hszMrAcOBGZmJedAYGZWcg4EZmYl50BgZlZyDgQ2FCSFpD9qO363pPct0XNfL+l1x77ySb/O69MVQ2/pOL9R0i/n/fpm3TgQ2LAYB/6jpLWDbki7tsrWXlwBXBkRP99xfiOwqECwyNc1W5ADgQ2LJsl+re/ofKDzL3pJh9LvF0r6iqR/kvSApD+Q9EZJ35D0LUlPa3uaiyRtl3R/upZRtt/BhyRtS9d8/y9tz/v/JG0lqXDtbM/l6fPfLekD6blrSIr/PirpQx2/8gfAz0q6M113v6fX7fX+0kzkbknflPTV4/z3twLzXxU2TK4F7pL0wUX8znOBZ5Es7/sA8JGIeKGSDXx+DfiN9LqNJEuXPw24RdLTgTeTlO7/pKQG8DVJ/5pe/3zg2RHxvfYXk3QGyTr5LyBZI/9fJf1iRLxf0kuBd0fE9o42Xp2ezwLQll5eV9KFPd7fNcArImKPpJMX8W9nJeGMwIZGJKuqfoJkk5JebYtkz4ZxknL87AP1WyQf/pkbIqIVEd8h+UB9JvBykvVc7iRZ2nsNyUYgAN/oDAKpnwS+HMkCaU3gb0n2EFiMxbxuL/f3NeB6SVeSbOpiNoszAhs2fwLcDny87VyT9I8aSRWgfcvC8bafW23HLWb//9+51kqQrOfyaxFxU/sD6V/ih4+v+T1ZzOse8/4i4ipJLyLZyMZfD0sAAAD0SURBVOc2SS+IiP15NNyGkzMCGyoR8RhwA7O3Jfw+SVcMwCVA/Tie+vWSKmm/+rnAfcBNwH9Nl/lG0nnpRjAL+Qbwc5LWKtku9XLgK8f4nYPAqrbj43ndriQ9LSJujYhrSDa2OetYv2Pl4ozAhtEfAW9rO/5r4J8kfRP4Isf31/pDJB/iq4GrImJM0kdIulduT5c/3ssxtkOMiIclXU2yRLKAL0TEsZZHvguYStt/PcneCot63WP4kKRNaXtuBr75JJ7LCsirj5qZlZy7hszMSs6BwMys5BwIzMxKzoHAzKzkHAjMzErOgcDMrOQcCMzMSu7/A9lEd8VHnEGXAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Let's plot the convergence, measured by least-square error\n", "# Plot the convergence against number of terms used\n", "plt.plot(range(1, max_terms+1), error_conv)\n", "plt.xlabel(\"Number of terms\")\n", "plt.ylabel(\"Relaive error\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(ii) The next function to look at is:\n", "\n", "$$\n", "f(x) = \\dfrac{1+x}{1-x^2}\n", "$$\n", "\n", "When plotting this graph, care is required to handle the case when $x = 1$ and $x = -1$. At these values of $x$, $f(x)$ will become `NaN` - Not A Number. We can replace these values of $f(x)$ with 0.5. " ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Hide the original numpy warning of division by 0\n", "np.seterr(divide='ignore', invalid='ignore')\n", "\n", "# Now the next function\n", "# y = (1+x) / (1 - x^2)\n", "num_points = 200\n", "x_ii = np.linspace(-1, 2, num_points)\n", "\n", "# There is going to be NaN values of y at x = -1\n", "# as the function becomes 0/0\n", "y_ii_ref = (1 + x_ii)/(1-np.power(x_ii, 2))\n", "\n", "# Check for NaN values\n", "nan_inds = np.where(np.isnan(y_ii_ref))\n", "\n", "# Replace NaN values\n", "y_ii_ref[nan_inds] = 0.5\n", "\n", "# Intilise figure size\n", "plt.figure(figsize=(8, 6))\n", "\n", "# Plot the reference\n", "plt.plot(x_ii, y_ii_ref);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, the Taylor series for $f(x)$ is:\n", "\n", "$$\n", "f(x) = \\dfrac{1+x}{1-x^2} = 1 + x + x^2 + \\mathcal{O}(x^3)\n", "$$\n", "\n", "We then plot the Taylor expansion using different number of terms, and again an interactive cell to illustrate the performance of the Taylor series." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Split to two subplots\n", "fig1, ax1 = plt.subplots()\n", "fig2, ax2 = plt.subplots()\n", "\n", "# Plot the reference function\n", "ax1.plot(x_ii, y_ii_ref, 'k', label=\"Reference\", lw=1.0, ls='--')\n", "\n", "# Define the maximum number of terms and initlise zero array\n", "max_terms = 100\n", "y_ii_power_series = np.zeros(num_points)\n", "\n", "# Initilise array to store the error\n", "error_conv = []\n", "\n", "# Step through the number of terms\n", "for i in range(0, max_terms):\n", " # Adding terms to power series\n", " y_ii_power_series = y_ii_power_series + np.power(x_ii, i)\n", "\n", " if i <= 6:\n", " ax1.plot(x_ii, y_ii_power_series,\n", " label='%d terms' % (i + 1), lw=2.0)\n", " ax2.plot(x_ii, (y_ii_ref - y_ii_power_series),\n", " label='%d terms' % (i + 1), lw=2.0)\n", "\n", " # Calculate the relative least-square difference\n", " error_conv.append(np.linalg.norm(\n", " y_ii_power_series - y_ii_ref)/np.linalg.norm(y_ii_ref))\n", "\n", "# Plot the relative functions\n", "ax1.legend(loc='center left', bbox_to_anchor=(1.0, 0.5))\n", "ax2.legend(loc='center left', bbox_to_anchor=(1.0, 0.5))\n", "\n", "# Set limit on y axis\n", "ax1.set_ylim([-5, 10])\n", "ax2.set_ylim([-1, 1])\n", "ax2.set_xlim([-1, 1])\n", "\n", "# Label axes\n", "ax1.set_xlabel('x')\n", "ax2.set_xlabel('x')\n", "ax1.set_ylabel('f(x)')\n", "ax2.set_ylabel('Error f(x)');" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Again, another interactive notebook\n", "def plot_power_series_ii(n):\n", " # Initialise zero array\n", " y_ii_power_series = np.zeros(num_points)\n", "\n", " # Step through the number of terms\n", " for i in range(0, n + 1):\n", " # Adding terms to power series\n", " y_ii_power_series = y_ii_power_series + np.power(x_ii, i)\n", "\n", " # Plot the reference function\n", " plt.plot(x_ii, y_ii_ref, 'k',\n", " label=\"Reference\", lw=1.0, ls='--')\n", "\n", " # Update the plot\n", " plt.plot(x_ii, y_ii_power_series)\n", "\n", " # Set limit on y axis\n", " plt.ylim([-10, 10])\n", "\n", " # Add axis label\n", " plt.xlabel('x')\n", " plt.ylabel('f(x)')\n", "\n", "interact(plot_power_series_ii, n=(0, 20, 1));" ] } ], "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": "3.7.6" }, "widgets": { "state": { "45c4d3412a7b4ca0a008c8cf38093a0c": { "views": [ { "cell_index": 29 } ] }, "d73af289fcea4196a196d3b400a19b32": { "views": [ { "cell_index": 22 } ] } }, "version": "1.2.0" } }, "nbformat": 4, "nbformat_minor": 4 }