From cbcb120dda78dfe907a18e23bc04d108b2784621 Mon Sep 17 00:00:00 2001 From: Robert Lanzafame <R.C.Lanzafame@tudelft.nl> Date: Wed, 25 Sep 2024 08:34:00 +0200 Subject: [PATCH] add WS 1.5 --- content/week_1_5/WS_1_5_solution.ipynb | 905 +++++++++++++++++++++++++ content/week_1_5/linspace.jpg | Bin 0 -> 28322 bytes 2 files changed, 905 insertions(+) create mode 100644 content/week_1_5/WS_1_5_solution.ipynb create mode 100644 content/week_1_5/linspace.jpg diff --git a/content/week_1_5/WS_1_5_solution.ipynb b/content/week_1_5/WS_1_5_solution.ipynb new file mode 100644 index 00000000..f76d7219 --- /dev/null +++ b/content/week_1_5/WS_1_5_solution.ipynb @@ -0,0 +1,905 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "6cf87eaa-cae9-436c-86f5-b64181df5850", + "metadata": {}, + "source": [ + "# WS 1.5 Exploring Numerical Summing Schemes\n", + "\n", + "<h1 style=\"position: absolute; display: flex; flex-grow: 0; flex-shrink: 0; flex-direction: row-reverse; top: 90px;right: 30px; margin: 0; border: 0\">\n", + " <style>\n", + " .markdown {width:100%; position: relative}\n", + " article { position: relative }\n", + " </style>\n", + " <img src=\"https://gitlab.tudelft.nl/mude/public/-/raw/main/tu-logo/TU_P1_full-color.png\" style=\"width:100px\" />\n", + " <img src=\"https://gitlab.tudelft.nl/mude/public/-/raw/main/mude-logo/MUDE_Logo-small.png\" style=\"width:100px\" />\n", + "</h1>\n", + "<h2 style=\"height: 10px\">\n", + "</h2>\n", + "\n", + "*[CEGM1000 MUDE](http://mude.citg.tudelft.nl/): Week 1.5, Wednesday, Oct 4, 2023.*" + ] + }, + { + "cell_type": "markdown", + "id": "82cfc0b4", + "metadata": {}, + "source": [ + "## Problem definition: Numerical Integration\n", + "\n", + "Integration can be used to solve differential equations and to calculate relevant quantities in diverse engineering and scientific problems. When analyzing experiments or numerical models results, a desired physical quantity may be expressed as an integral of measured/model quantities. Sometimes the analytical integration is known, then this is the most accurate and fastest solution, certainly better than computing it numerically. However, it is common that the analytic solution is unknown, then numerical integration is the way to go. \n", + "\n", + "\n", + "You will use a function with a known integral to evaluate how precise numerical integration can be. " + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "caebff09-a533-40aa-9115-985c78e45693", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.interpolate import make_interp_spline\n", + "\n", + "\n", + "plt.rcParams['figure.figsize'] = (15, 5) # Set the width and height of plots in inches\n", + "plt.rcParams.update({'font.size': 13}) # Change this value to your desired font size\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "a6773319", + "metadata": {}, + "source": [] + }, + { + "cell_type": "markdown", + "id": "352f1493", + "metadata": {}, + "source": [ + "<div style=\"background-color:#AABAB2; color: black; width:95%; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px\">\n", + "<p>\n", + "<b>Task 1:</b> \n", + "\n", + "Calculate and evaluate the following integral by hand: \n", + "\n", + "$$I=\\int_a^{b} f\\left(x\\right)\\mathrm{d}x = \\int_0^{3\\pi} \\left(20 \\cos(x)+3x^2\\right)\\mathrm{d}x.$$\n", + "\n", + "The result will be later used to explore how diverse numerical integration techniques work and their accuracy. \n", + "\n", + "</p>\n", + "</div>" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "80e263da", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The exact value of the integral is: 837.1694703680951\n" + ] + } + ], + "source": [ + "\n", + "# YOUR SOLUTION HERE\n", + "exact_integral_evaluated = 27*np.pi**3 #your integrated function here \n", + "\n", + "\n", + "\n", + "# Test your answer\n", + "assert abs(exact_integral_evaluated - 837.16947)< 1e-5, \"Oops it's incorrect. Please check your derivation the integral \"\n", + "print(\"The exact value of the integral is: \", exact_integral_evaluated)" + ] + }, + { + "cell_type": "markdown", + "id": "fea89e84", + "metadata": {}, + "source": [ + "**Function definition**\n", + "\n", + "Let's define the python function \n", + "\n", + "\n", + "$$f\\left(x\\right) = \\left(20 \\cos x+3x^2\\right)\\mathrm{d}x$$ " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "98e6e3b6", + "metadata": {}, + "outputs": [], + "source": [ + "# Define the function to be later integrated\n", + "def f(x):\n", + " return 20*np.cos(x)+3*x**2" + ] + }, + { + "cell_type": "markdown", + "id": "cd6b9447", + "metadata": {}, + "source": [ + "<div style=\"background-color:#AABAB2; color: black; width:95%; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px\">\n", + "<p>\n", + "<b>Task 2:</b> \n", + "\n", + "Call the function f written below to evaluate it at x=0. \n", + "</p>\n", + "</div>" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "de1759f8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "f evaluated at x=0 is: 20.0\n" + ] + } + ], + "source": [ + "## YOUR CODE HERE\n", + "f_at_x_equal_0 = f(0)\n", + "\n", + "print(\"f evaluated at x=0 is:\" , f_at_x_equal_0)" + ] + }, + { + "cell_type": "markdown", + "id": "f3bbdf8c", + "metadata": {}, + "source": [ + "<div style=\"background-color:#facb8e; color: black; width:95%; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px\">\n", + "<p>\n", + "<b>NOTE:</b> Calling f(x) is equivalent to evaluating it! \n", + "\n", + "</p>\n", + "</div>" + ] + }, + { + "cell_type": "markdown", + "id": "1c3d671e", + "metadata": {}, + "source": [ + "**Define an x vector to evaluate the function**\n", + "\n", + "The function `f(x)` exists in \"all space\". However, the integration is bounded to the limits `a to b`, $I=\\int_a^{b} f\\left(x\\right)\\mathrm{d}x = \\int_0^{3\\pi} \\left(10 \\cos(x)+4x\\right)\\mathrm{d}x$. \n", + "\n", + "<br><br>\n", + "Use those limits to create an x array using `linspace(a,b,n)`, where `a` is the limit to the left, `b` is the limit to the right and `n` is the number of points. Below you see the case with 5 points.\n", + "\n", + "<img src=\"linspace.jpg\" style=\"height:100px\" />\n" + ] + }, + { + "cell_type": "markdown", + "id": "add4309b", + "metadata": {}, + "source": [ + "<div style=\"background-color:#AABAB2; color: black; width:95%; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px\">\n", + "<p>\n", + "<b>Task 3:</b> \n", + "\n", + "Define the intervals `a,b` and the number of points needed to have a subinterval length $\\Delta x=\\pi$. \n", + "</p>\n", + "</div>" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "4b85d2a4", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x = [0. 3.14159265 6.28318531 9.42477796]\n" + ] + } + ], + "source": [ + "# YOUR CODE HERE\n", + "a = 0\n", + "b = 3*np.pi#\n", + "number_of_points = 4\n", + "\n", + "x_values = np.linspace(a, b, number_of_points)\n", + "dx = x_values[1]-x_values[0]\n", + "\n", + "print(\"x = \",x_values)\n", + "\n", + "\n", + "\n", + "# test dx value\n", + "assert abs(dx - np.pi)<1e-5, \"Oops! dx is not equal to pi. Please check your values for a, b and number of points.\"" + ] + }, + { + "cell_type": "markdown", + "id": "ec5511fb", + "metadata": {}, + "source": [ + "<div style=\"background-color:#AABAB2; color: black; width:95%; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px\">\n", + "<p>\n", + "<b>Task 4:</b> \n", + "\n", + "How do the number of points and number of subintervals relate? Write a brief answer below.\n", + "</p>\n", + "</div>" + ] + }, + { + "cell_type": "markdown", + "id": "098d751a", + "metadata": {}, + "source": [] + }, + { + "cell_type": "markdown", + "id": "1049c443", + "metadata": {}, + "source": [ + "**Visualize a \"continuous\" function and list comprehension**\n", + "\n", + "For visualization purposes in the rest of the notebook, `f(x)` is here evaluated with high resolution. A \"list comprehension\" method is used for this purpose. **Understanding \"list comprehensions\" is esential to solve the rest of the notebook**.\n" + ] + }, + { + "cell_type": "markdown", + "id": "128a2522", + "metadata": {}, + "source": [ + "<div style=\"background-color:#AABAB2; color: black; width:95%; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px\">\n", + "<p>\n", + "<b>Task 5:</b> \n", + "\n", + "Reflect on list comprehension. \n", + " <br><br>\n", + " *Some explanation about using lists*\n", + " Two equivalent solutions to define f_high_resolution are shown below. The first one loops x_high_resolution and assigns its values to x, which is then used to evaluate f. \n", + " The second one creates an index list based on the number of points contained in x_high_resolution, then loops it to evaluate f at each element of x_high_resolution. Which method do you find easier to read/write? \n", + "</p>\n", + "</div>" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "65878405", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 1500x500 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# To plot a smooth graph of the function\n", + "x_high_resolution = np.linspace(a, b, 50)\n", + "\n", + "f_high_resolution = [ f(x) for x in x_high_resolution ] #first solution\n", + "\n", + "f_high_resolution = [ f(x_high_resolution[i]) for i in range(len(x_high_resolution))] #second solution\n", + "\n", + "\n", + "# Plotting\n", + "plt.plot(x_high_resolution, f_high_resolution, '+', markersize='12', color='black')\n", + "plt.plot(x_high_resolution, f_high_resolution, 'b')\n", + "plt.legend(['Points evaluated','continuous function representation'])\n", + "plt.title('Function for approximation')\n", + "plt.xlabel('x')\n", + "plt.ylabel('$f(x)$');" + ] + }, + { + "cell_type": "markdown", + "id": "a9ef5459-2ffb-4bde-830c-646264c3648a", + "metadata": {}, + "source": [ + "<b>The Left Riemann Sum</b>\n", + "\n", + "This method approximates an integral by summing the area of rectangles defined with left points of the function:\n", + "\n", + "$$I_{_{left}} \\approx \\sum_{i=0}^{n-1} f(x_i)\\Delta x$$\n", + "\n", + "From now on, you will use ten points to define the function.\n", + "<br><br>\n", + "\n", + "Let's look at the implementation of the Left Riemman sum following the same methods described in task 5. The differences are that (i) the index of the vector x ignores the last point, (2) the multiplication by $\\Delta x$ and (iii) the sum of the vector. Thus the result is not an array but a single number. \n", + "<br><br>\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "80eb6362", + "metadata": {}, + "source": [ + "<div style=\"background-color:#AABAB2; color: black; width:95%; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px\">\n", + "<p>\n", + "<b>Task 6:</b> \n", + "\n", + "Scrutinize the correct implementations below. Why is it necessary to ignore the last point in x_values? What would happen if you include it? \n", + "</p>\n", + "</div>" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "d3a75fe0-017b-4e8a-b729-68412a492854", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Left Riemann Sum: 710.303\n", + "Left Riemann Sum: 710.303\n" + ] + } + ], + "source": [ + "\n", + "x_values = np.linspace(a, b, 9) \n", + "dx = x_values[1]-x_values[0]\n", + "\n", + "# Left Riemann summation: 1st option\n", + "\n", + "I_left_riemann = sum( [f(x)*dx for x in x_values[:-1]] ) #method 1\n", + "print(f\"Left Riemann Sum: {I_left_riemann: 0.3f}\")\n", + "# Left Riemann summation: 2nd option\n", + "I_left_riemann = sum( [ f(x_values[i])*dx for i in range(len(x_values)-1) ] ) #method 2\n", + "print(f\"Left Riemann Sum: {I_left_riemann: 0.3f}\")" + ] + }, + { + "cell_type": "markdown", + "id": "409b0530", + "metadata": {}, + "source": [ + "<div style=\"background-color:#AABAB2; color: black; width:95%; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px\">\n", + "<p>\n", + "<b>Task 7:</b> \n", + "\n", + "Scrutinize the correct implementation below to visualize the bar plot (plt.bar) and location of the points (plt.plot with '*', in the line code below plt.bar) that define the height of each rectangle. \n", + "<br>\n", + "<br>\n", + "Tip: The bar plot requires one less element than the total number of points defining the function. \n", + "</p>\n", + "</div>" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "id": "0c09dc12", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 1500x500 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Visualization\n", + "# Plot the rectangles and left corners of the elements in the riemann sum\n", + "plt.bar(x_values[:-1],[f(x) for x in x_values[:-1]], width=dx, alpha=0.5, align='edge', edgecolor='black', linewidth=0.25)\n", + "plt.plot(x_values[:-1],[f(x) for x in x_values[:-1]], '*', markersize='16', color='red')\n", + "\n", + "#Plot \"continous\" function\n", + "plt.plot(x_high_resolution, f_high_resolution, 'b')\n", + "plt.title('Left Riemann Sum')\n", + "plt.xlabel('x')\n", + "plt.ylabel('$f(x)$');" + ] + }, + { + "cell_type": "markdown", + "id": "8906e8ab-9aa5-45db-a683-cd40a6729575", + "metadata": {}, + "source": [ + "**The Right Riemann Method**\n", + "\n", + "Similar to the left Riemann sum, this method is also algebraically simple to implement, and can be better suited to some situations, depending on the type of function you are trying to approximate. In this case, the subintervals are defined using the right-hand endpoints from the function and is represented by \n", + "\n", + "$$I_{_{right}} \\approx \\sum_{i=1}^n f(x_i)\\Delta x$$\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "0bbf4b11", + "metadata": {}, + "source": [ + "<div style=\"background-color:#AABAB2; color: black; width:95%; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px\">\n", + "<p>\n", + "<b>Task 8:</b> \n", + "\n", + "Complete the code cell below for the right Riemman method.. \n", + "\n", + "Tip: Consult the Left Riemann implementation above as a guide.\n", + "</p>\n", + "</div>" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "id": "3073db6e-430c-4f17-ad88-a4f2892a55f1", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Right Riemann Sum: 960.921\n" + ] + } + ], + "source": [ + "I_right_riemann = sum( [f(x)*dx for x in x_values[1:]] ) \n", + "\n", + "print(f\"Right Riemann Sum: {I_right_riemann: 0.3f}\")" + ] + }, + { + "cell_type": "markdown", + "id": "0cf7e125", + "metadata": {}, + "source": [ + "<div style=\"background-color:#AABAB2; color: black; width:95%; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px\">\n", + "<p>\n", + "<b>Task 9:</b> \n", + "\n", + "Complete the code cell below to visualize the right Riemman method.\n", + "\n", + "</p>\n", + "</div>" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "id": "c510d26b", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "<Figure size 1500x500 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Right Riemann sum visualization\n", + "plt.bar(x_values[:-1],[f(x) for x in x_values[1:]], width=dx, alpha=0.5, align='edge', edgecolor='black', linewidth=0.25)\n", + "plt.plot(x_values[1:],[f(x) for x in x_values[1:]], '*', markersize='16', color='red')\n", + "#Plot \"continuous\" function\n", + "plt.plot(x_high_resolution, f_high_resolution, 'b')\n", + "plt.title('Right Riemann Sum')\n", + "plt.xlabel('x')\n", + "plt.ylabel('$f(x)$');" + ] + }, + { + "cell_type": "markdown", + "id": "24d26cbb-ab8f-435f-8238-0c22c0fce833", + "metadata": {}, + "source": [ + "**Midpoint Method Approximation**\n", + "\n", + "For a function defined with constant steps (uniform $\\Delta x$), the midpoint method approximates the integral taking the midpoint of the rectangle and splitting the width of the rectangle at this point. \n", + "\n", + "$$I_{_{mid}} \\approx \\sum_{i=0}^{n-1} f\\left(\\frac{x_i+x_{i+1}}{2}\\right)\\Delta x $$\n" + ] + }, + { + "cell_type": "markdown", + "id": "13d1d689", + "metadata": {}, + "source": [ + "<div style=\"background-color:#AABAB2; color: black; width:95%; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px\">\n", + "<p>\n", + "<b>Task 10:</b> \n", + "\n", + "Complete the code cell below to implemen the midpoint sum below.\n", + "</p>\n", + "</div>" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "id": "7ed26ad5-d2cb-450e-873d-5b21a596cedb", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Midpoint Sum: 8.346e+02\n", + "Midpoint Sum: 8.346e+02\n" + ] + } + ], + "source": [ + "I_midpoint = sum([f((x_values[i] + x_values[i+1]) / 2)*dx for i in range(len(x_values)-1)])\n", + "print(f\"Midpoint Sum: {I_midpoint: 0.3e}\")\n", + "\n", + "I_midpoint = sum([f(x_at_the_middle)*dx for x_at_the_middle in (x_values[:-1]+x_values[1:])/2 ])\n", + "print(f\"Midpoint Sum: {I_midpoint: 0.3e}\")" + ] + }, + { + "cell_type": "markdown", + "id": "e685d8c3", + "metadata": {}, + "source": [ + "<div style=\"background-color:#AABAB2; color: black; width:95%; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px\">\n", + "<p>\n", + "<b>Task 11:</b> \n", + "\n", + "Complete the code cell below to visualize the midpoint method.\n", + "\n", + "</p>\n", + "</div>" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "id": "370672eb", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "<Figure size 1500x500 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Midpoint sum visualization\n", + "plt.bar(x_values[:-1],[f(x_at_the_middle) for x_at_the_middle in (x_values[:-1]+x_values[1:])/2 ], width=dx, alpha=0.5, align='edge', edgecolor='black', linewidth=0.25)\n", + "plt.plot((x_values[:-1]+x_values[1:])/2,[f(x_at_the_middle) for x_at_the_middle in (x_values[:-1]+x_values[1:])/2 ],'*',markersize='16', color='red')\n", + "#Plot \"continous\" function\n", + "plt.plot(x_high_resolution, f_high_resolution, 'b')\n", + "plt.title('Midpoint Sum')\n", + "plt.xlabel('x')\n", + "plt.ylabel('$f(x)$');" + ] + }, + { + "cell_type": "markdown", + "id": "fcf6f8bc-5554-4309-81ce-0433fa947e34", + "metadata": {}, + "source": [ + "**Trapezoidal Rule**\n", + "\n", + "This method requires two evaluations of the function $f$ for each 'rectangle', at its left and right corners. In fact, it does not represent a 'rectangle anymore' but a trapezoid. For a 1D case, it is a rectangle with a triangle on top. \n", + "\n", + "$$I_{_{trapezoid}} \\approx \\sum_{i=0}^{n-1}\\frac{f(x_i)+f(x_{i+1})}{2}\\Delta x $$" + ] + }, + { + "cell_type": "markdown", + "id": "74bb23af", + "metadata": {}, + "source": [ + "<div style=\"background-color:#AABAB2; color: black; width:95%; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px\">\n", + "<p>\n", + "<b>Task 12:</b> \n", + "\n", + "Complete the following code to implement the trapezoidal rule for the sum. \n", + "\n", + "</p>\n", + "</div>" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "id": "b6e68930-f1d8-4d7e-8162-8cd59f985be0", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Trapezoidal Sum: 8.42337e+02\n" + ] + } + ], + "source": [ + "I_trapezoidal = sum([(f(x_values[i]) + f(x_values[i+1])) / 2 * dx for i in range(len(x_values)-1)]) \n", + "print(f\"Trapezoidal Sum: {I_trapezoidal: 0.5e}\")" + ] + }, + { + "cell_type": "markdown", + "id": "5a3a195c", + "metadata": {}, + "source": [ + "<div style=\"background-color:#AABAB2; color: black; width:95%; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px\">\n", + "<p>\n", + "<b>Task 13:</b> \n", + "\n", + "To visualize the trapezoidal method a plt.bar is not used rather plt_fill_between. Revise the code cell below.\n", + "\n", + "</p>\n", + "</div>" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "id": "36cddace", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "<Figure size 1500x500 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Trapezoidal sum\n", + "for i in range(len(x_values)-1):\n", + " plt.fill_between([x_values[i], x_values[i+1]], \n", + " [f(x_values[i]), f(x_values[i+1])], \n", + " alpha=0.5)\n", + "\n", + "#Plot \"continous\" function\n", + "plt.plot(x_high_resolution, f_high_resolution, 'b')\n", + "plt.title('Trapezoidal Sum')\n", + "plt.xlabel('x')\n", + "plt.ylabel('$f(x)$');\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "14295e08-e9db-4735-927d-715989b62b81", + "metadata": {}, + "source": [ + "**Absolute errors in integral**" + ] + }, + { + "cell_type": "markdown", + "id": "d6b0720c", + "metadata": {}, + "source": [ + "<div style=\"background-color:#AABAB2; color: black; width:95%; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px\">\n", + "<p>\n", + "<b>Task 14:</b> \n", + "\n", + "Compute the absolute errors of each method. Are they similar to your expectatations? (i.e. corresponding to the orders of magnitude).\n", + "\n", + "</p>\n", + "</div>" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "id": "582e66ed-2016-4a84-a5f4-6d01d49671dc", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Left Riemann Error: 1.067e-04\n", + "Right Riemann Error: 1.238e+02\n", + "Midpoint Error: 2.584e+00\n", + "Trapezoidal Error: 5.168e+00\n" + ] + } + ], + "source": [ + "# Calculate absolute errors\n", + "left_riemann_error = abs(exact_integral_evaluated - I_left_riemann)\n", + "right_riemann_error = abs(exact_integral_evaluated - I_right_riemann)\n", + "midpoint_error = abs(exact_integral_evaluated - I_midpoint)\n", + "trapezoidal_error = abs(exact_integral_evaluated - I_trapezoidal)\n", + "\n", + "# Print the results\n", + "print(f\"Left Riemann Error: {left_riemann_error: 0.3e}\")\n", + "print(f\"Right Riemann Error: {right_riemann_error: 0.3e}\")\n", + "print(f\"Midpoint Error: {midpoint_error: 0.3e}\")\n", + "print(f\"Trapezoidal Error: {trapezoidal_error: 0.3e}\")\n" + ] + }, + { + "cell_type": "markdown", + "id": "ddc2f16f-7065-4829-aafc-91c95cc93aaf", + "metadata": {}, + "source": [ + "**Simpson's Rule**\n", + "\n", + "Simpson's rule is a method that uses a quadratic approximation over an interval that allows the top bound of the area 'rectangle' to be defined by a polynomial. In general, it can be a better approximation for curved, but mathematically smooth functions. It also has the requirement that subintervals must be an even number, so this is something to be aware of when using it in practise. As a sum, it is defined as \n", + "\n", + "$$\\int^{b}_{a}f(x)\\mathrm{d}x\\approx \\sum_{i=1}^{n/2}\\frac{1}{3}(f(x_{2i-2})+4f(x_{2i-1})+f(x_{2i}))\\Delta x$$\n", + "\n", + "where $n$ must be an *even integer*.\n", + "\n", + " " + ] + }, + { + "cell_type": "markdown", + "id": "e0ed72e0-ced6-467c-8e01-a1b602a3613d", + "metadata": {}, + "source": [ + "<div style=\"background-color:#AABAB2; color: black; width:95%; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px\">\n", + "<p>\n", + "<b>Challenge</b>\n", + "\n", + "Take what you have seen in the other numerical implementation codes and implement Simpson's Rule for the same integral! A redefinition of x_values is done with 9 points instead of 10 as an uneven number of points is required to apply Simpson's Rule. \n", + "</p>\n", + "</div>" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "id": "ae169f8e-2d5a-4449-8c53-c8ca399af184", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Simpson's Rule Integral: 8.37169e+02\n", + "Simpson's Rule Absolute Error: 0.00000e+00\n" + ] + } + ], + "source": [ + "# Define Simpson's Rule here\n", + "x_values = np.linspace(a, b, 9)\n", + "dx = x_values[1]-x_values[0] \n", + " \n", + "simpson_integral = sum([(f(x_values[2*i-2]) + 4*f(x_values[2*i-1]) + f(x_values[2*i])) / 3 * dx for i in range(1,int(len(x_values)/2)+1)]) \n", + "\n", + "# Calculate the absolute error\n", + "simpson_error = abs(exact_integral_evaluated - simpson_integral)\n", + "\n", + "# Print the result and error\n", + "print(f\"Simpson's Rule Integral: {simpson_integral: 0.5e}\")\n", + "print(f\"Simpson's Rule Absolute Error: {simpson_error: 0.5e}\")\n" + ] + }, + { + "cell_type": "markdown", + "id": "8ffe7a1f", + "metadata": {}, + "source": [ + "<div style=\"background-color:#AABAB2; color: black; width:95%; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px\">\n", + "<p>\n", + "<b>Task 15:</b> \n", + " \n", + " \n", + "Refine the number of points using the integration by left riemmann until reaching a similar accuracy as for the trapezoidal rule. How much finer was your grid?\n", + "\n", + "</p>\n", + "</div>" + ] + }, + { + "cell_type": "markdown", + "id": "793cb6e5", + "metadata": {}, + "source": [] + }, + { + "cell_type": "markdown", + "id": "6aced257", + "metadata": {}, + "source": [ + "**End of notebook.**\n", + "<h2 style=\"height: 60px\">\n", + "</h2>\n", + "<h3 style=\"position: absolute; display: flex; flex-grow: 0; flex-shrink: 0; flex-direction: row-reverse; bottom: 60px; right: 50px; margin: 0; border: 0\">\n", + " <style>\n", + " .markdown {width:100%; position: relative}\n", + " article { position: relative }\n", + " </style>\n", + " <a rel=\"license\" href=\"http://creativecommons.org/licenses/by/4.0/\">\n", + " <img alt=\"Creative Commons License\" style=\"border-width:; width:88px; height:auto; padding-top:10px\" src=\"https://i.creativecommons.org/l/by/4.0/88x31.png\" />\n", + " </a>\n", + " <a rel=\"TU Delft\" href=\"https://www.tudelft.nl/en/ceg\">\n", + " <img alt=\"TU Delft\" style=\"border-width:0; width:100px; height:auto; padding-bottom:0px\" src=\"https://gitlab.tudelft.nl/mude/public/-/raw/main/tu-logo/TU_P1_full-color.png\" />\n", + " </a>\n", + " <a rel=\"MUDE\" href=\"http://mude.citg.tudelft.nl/\">\n", + " <img alt=\"MUDE\" style=\"border-width:0; width:100px; height:auto; padding-bottom:0px\" src=\"https://gitlab.tudelft.nl/mude/public/-/raw/main/mude-logo/MUDE_Logo-small.png\" />\n", + " </a>\n", + " \n", + "</h3>\n", + "<span style=\"font-size: 75%\">\n", + "© Copyright 2024 <a rel=\"MUDE\" href=\"http://mude.citg.tudelft.nl/\">MUDE</a> TU Delft. This work is licensed under a <a rel=\"license\" href=\"http://creativecommons.org/licenses/by/4.0/\">CC BY 4.0 License</a>." + ] + } + ], + "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": "3.12.4" + }, + "widgets": { + "application/vnd.jupyter.widget-state+json": { + "state": {}, + "version_major": 2, + "version_minor": 0 + } + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/content/week_1_5/linspace.jpg b/content/week_1_5/linspace.jpg new file mode 100644 index 0000000000000000000000000000000000000000..7a9d59198070ea9fdac3e1fe1e78799ed52266ee GIT binary patch literal 28322 zcmd?RdpuNM`!~Lwawa*2m_(_N5~;{2IVB<GSSI9@!;o`Lwg@>FMNuY|bdnq=hfL0u 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