{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "

\n", " \n", "

\n", "\n", "### Prof. Dr. -Ing. Gerald Schuller
Jupyter Notebook: Renato Profeta\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "# Revision: Histogram, PDF, Numerical Integral" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "hide_input": true }, "outputs": [ { "data": { "text/html": [ "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%%html\n", "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Histogram and PDF Revision" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "### Signals" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "hide_input": true }, "outputs": [ { "data": { "text/html": [ "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%%html\n", "" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "# Imports\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import IPython.display as ipd\n", "import librosa" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "# Signal Processing Parameters\n", "Fs = 32000 # Sampling frequency\n", "T=1/Fs # Sampling Period\n", "t = np.arange(Fs)*T # Time vector" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "# Sine Wave\n", "A=1\n", "freq=500\n", "n_period=1\n", "period=np.round((1/freq)*n_period*Fs).astype(int)\n", "t = np.arange(Fs)*T # Time vector\n", "sinewave = A*np.sin(2*np.pi*freq*t)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "# Uniform Distribution Signal\n", "uniform_signal = np.random.uniform(-1,1,t.size)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "# Laplace Distribution Signal\n", "mu, b = 0, 1 # mean and scale\n", "laplace_signal = np.random.normal(mu, b, t.size)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "# Music Signal\n", "music_signal, sr = librosa.load('./audio/led-zeppelin-rock-and-roll.mp3', sr=32000, offset=10,duration=4)\n", "music_signal/=np.abs(music_signal).max() # Normalization" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Plot signals\n", "plt.figure(figsize=(16,10))\n", "plt.subplot(221)\n", "plt.plot(t[:period+1], sinewave[:period+1])\n", "plt.title('Sine Wave')\n", "plt.xlabel('Time [s]')\n", "plt.ylabel('Amplitude')\n", "plt.grid()\n", "plt.subplot(222)\n", "plt.plot(t[:period+1],uniform_signal[:period+1])\n", "plt.grid()\n", "plt.title('Uniform Distribution Signal')\n", "plt.xlabel('Time [s]')\n", "plt.ylabel('Amplitude')\n", "plt.subplot(223)\n", "plt.plot(t[:period+1],laplace_signal[:period+1])\n", "plt.grid()\n", "plt.title('Laplace Distribution Signal')\n", "plt.xlabel('Time [s]')\n", "plt.ylabel('Amplitude')\n", "plt.subplot(224)\n", "plt.plot(t[:period+1],music_signal[:period+1])\n", "plt.grid()\n", "plt.title('Music Signal')\n", "plt.xlabel('Time [s]')\n", "plt.ylabel('Amplitude');" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Sine Wave:\n" ] }, { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Uniform Distribution Signal\n" ] }, { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Laplace Distribution Signal\n" ] }, { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Music Signal\n" ] }, { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Listen to Signals\n", "print('Sine Wave:')\n", "display(ipd.Audio(sinewave,rate=Fs))\n", "print('Uniform Distribution Signal')\n", "display(ipd.Audio(uniform_signal,rate=Fs))\n", "print('Laplace Distribution Signal')\n", "display(ipd.Audio(laplace_signal,rate=Fs))\n", "print('Music Signal')\n", "display(ipd.Audio(music_signal,rate=Fs))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Histograms" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%%html\n", "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "**Definition of histogram**\n", "\n", ": a representation of a frequency distribution by means of rectangles whose widths represent class intervals and whose areas are proportional to the corresponding frequencies.\n", "\n", "\n", " From https://www.merriam-webster.com/dictionary/histogram\n", "" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "# Difine symbols and Functions\n", "from sympy import symbols, Function\n", "from sympy.stats import Uniform, Laplace\n", "x = symbols('x', real=True)\n", "p_x = Function('p')(x)\n", "U_x = Uniform('X',-1,1)\n", "L_x = Laplace('X',0,1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Observe:** A histogram becomes a **probability distribution** $P(x)$ (with x a signal value), if we divide it by the total number of samples in it, such that its sum becomes 1." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(16,10))\n", "plt.subplot(221)\n", "counts_sine, bins_sine, bin_edges_sine = plt.hist(sinewave[2:period], 20, density=True);\n", "plt.grid()\n", "plt.title('Sine Wave')\n", "plt.xlabel('Bins')\n", "plt.ylabel('Counts (Normalized)');\n", "plt.subplot(222)\n", "counts_uniform, bins_uniform, bin_edges_uniform=plt.hist(uniform_signal, 20, density=True);\n", "plt.grid()\n", "plt.title('Uniform Distribution Signal')\n", "plt.xlabel('Bins')\n", "plt.ylabel('Counts (Normalized)')\n", "plt.subplot(223)\n", "counts_laplace, bins_laplace, bin_edges_laplace = plt.hist(laplace_signal, 20, density=True);\n", "plt.grid()\n", "plt.title('Laplace Distribution Signal')\n", "plt.xlabel('Bins')\n", "plt.ylabel('Counts (Normalized)')\n", "plt.subplot(224)\n", "counts_music, bins_music, bin_edges_music=plt.hist(music_signal, 20, density=True);\n", "plt.grid()\n", "plt.title('Music Signal')\n", "plt.xlabel('Bins')\n", "plt.ylabel('Counts (Normalized)');" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Probability Density Functions (PDFs)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "**Definition of Probability Density Function**\n", "\n", "1: PROBABILITY FUNCTION
\n", "2: a function of a continuous random variable whose integral over an interval gives the probability that its value will fall within the interval.
\n", "\n", "\n", "From https://www.merriam-webster.com/dictionary/probability%20density%20function\n", "" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "hide_input": true }, "outputs": [ { "data": { "text/html": [ "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%%html\n", "" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "# Imports \n", "from sympy import Function, Eq, symbols, Integral, simplify, pi, sqrt, lambdify, sin\n", "from sympy.stats import Laplace, Uniform, density\n", "from sympy.plotting import plot\n", "\n", "# Configurations\n", "np.seterr(divide='ignore');" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "PDF: Sine wave:\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\frac{1}{\\pi \\sqrt{1 - x^{2}}}$" ], "text/plain": [ "1/(pi*sqrt(1 - x**2))" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Sine Wave\n", "S_x_pdf = 1 / (pi*sqrt(1-x**2))\n", "print('PDF: Sine wave:')\n", "display(S_x_pdf)\n", "pdf_sine=lambdify(x,S_x_pdf)\n", "plt.figure()\n", "plt.plot(np.arange(-1,1,0.1),pdf_sine(np.arange(-1,1,0.1)))\n", "plt.grid()\n", "plt.title('PDF: Sine Wave')\n", "plt.ylabel('Density')\n", "plt.xlabel('x');" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "PDF: Uniform Distribution (-1,1)\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\begin{cases} \\frac{1}{2} & \\text{for}\\: x \\geq -1 \\wedge x \\leq 1 \\\\0 & \\text{otherwise} \\end{cases}$" ], "text/plain": [ "Piecewise((1/2, (x >= -1) & (x <= 1)), (0, True))" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Uniform\n", "U_x_pdf = density(U_x)(x)\n", "print('PDF: Uniform Distribution (-1,1)')\n", "display(U_x_pdf)\n", "pdf_uniform = lambdify(x,U_x_pdf)\n", "plt.figure()\n", "plt.plot(np.arange(-1,1,0.1),pdf_uniform(np.arange(-1,1,0.1)))\n", "plt.grid()\n", "plt.title('PDF: Uniform Distribution')\n", "plt.ylabel('Density')\n", "plt.xlabel('x');" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "PDF: Laplace Distribution (mu=0,b=1)\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\frac{e^{- \\left|{x}\\right|}}{2}$" ], "text/plain": [ "exp(-Abs(x))/2" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Laplace\n", "L_x_pdf = density(L_x)(x)\n", "print('PDF: Laplace Distribution (mu=0,b=1)')\n", "display(L_x_pdf)\n", "pdf_laplace=lambdify(x,L_x_pdf)\n", "plt.figure()\n", "x_axis=np.arange(bins_laplace[0],bins_laplace[-1],bins_laplace[1]-bins_laplace[0])\n", "plt.plot(x_axis,pdf_laplace(x_axis))\n", "plt.grid()\n", "plt.title('PDF: Uniform Distribution')\n", "plt.ylabel('Density')\n", "plt.xlabel('x');" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "**Observe**: The PDF for the Music Signal has no closed form. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "**Example:** Let's calculate the probability that a value x is inside the intervals from -0.4 and -0.3 and from 0.8 to 0.9 in a Sine Wave." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\int\\limits_{-0.4}^{-0.3} \\frac{1}{\\pi \\sqrt{1 - x^{2}}}\\, dx$" ], "text/plain": [ "Integral(1/(pi*sqrt(1 - x**2)), (x, -0.4, -0.3))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "=\n" ] }, { "data": { "text/plain": [ "0.034" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\int\\limits_{0.8}^{0.9} \\frac{1}{\\pi \\sqrt{1 - x^{2}}}\\, dx$" ], "text/plain": [ "Integral(1/(pi*sqrt(1 - x**2)), (x, 0.8, 0.9))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "=\n" ] }, { "data": { "text/plain": [ "0.061" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Integrating the PDF of a Sine Wave\n", "p=Integral(S_x_pdf,(x,-0.4,-0.3))\n", "display(p)\n", "print('=')\n", "display(round(p.doit().evalf(),3))\n", "\n", "p=Integral(S_x_pdf,(x,0.8,0.9))\n", "display(p)\n", "print('=')\n", "display(round(p.doit().evalf(),3))" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Histogram bins: [-0.4 -0.3]\n", "Probability: 0.032\n", "Hisstogram bins: [0.8 0.9]\n", "Probability: 0.065\n" ] } ], "source": [ "# Looking at the Histogram (Normalized)\n", "print('Histogram bins:', bins_sine[6:8])\n", "print('Probability:', round((counts_sine[7]*np.diff(bins_sine[7:9]))[0],3))\n", "print('Hisstogram bins:', bins_sine[-3:-1])\n", "print('Probability:', round((counts_sine[-3]*np.diff(bins_sine[-3:-1]))[0],3))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Numerical Integration Revision" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "Numerical integration is the approximate computation of an integral using numerical techniques.\n", "\n", "\n", " From http://mathworld.wolfram.com/NumericalIntegration.html\n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%%html\n", "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "### Riemann Sum\n", "\n", "(From https://www.math.ubc.ca/~pwalls/math-python/integration/riemann-sums/)\n", "" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "f = lambda x : np.sin(x)\n", "a = -np.pi; b = +np.pi; N = 10\n", "n = 10 # Use n*N+1 points to plot the function smoothly\n", "\n", "x = np.linspace(a,b,N+1)\n", "y = f(x)\n", "\n", "X = np.linspace(a,b,n*N+1)\n", "Y = f(X)\n", "\n", "plt.figure(figsize=(15,5))\n", "\n", "plt.subplot(1,3,1)\n", "plt.plot(X,Y,'b')\n", "x_left = x[:-1] # Left endpoints\n", "y_left = y[:-1]\n", "plt.plot(x_left,y_left,'b.',markersize=10)\n", "plt.bar(x_left,y_left,width=(b-a)/N,alpha=0.2,align='edge',edgecolor='b')\n", "plt.title('Left Riemann Sum, N = {}'.format(N))\n", "\n", "plt.subplot(1,3,2)\n", "plt.plot(X,Y,'b')\n", "x_mid = (x[:-1] + x[1:])/2 # Midpoints\n", "y_mid = f(x_mid)\n", "plt.plot(x_mid,y_mid,'b.',markersize=10)\n", "plt.bar(x_mid,y_mid,width=(b-a)/N,alpha=0.2,edgecolor='b')\n", "plt.title('Midpoint Riemann Sum, N = {}'.format(N))\n", "\n", "plt.subplot(1,3,3)\n", "plt.plot(X,Y,'b')\n", "x_right = x[1:] # Left endpoints\n", "y_right = y[1:]\n", "plt.plot(x_right,y_right,'b.',markersize=10)\n", "plt.bar(x_right,y_right,width=-(b-a)/N,alpha=0.2,align='edge',edgecolor='b')\n", "plt.title('Right Riemann Sum, N = {}'.format(N));" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\int\\limits_{0}^{\\frac{\\pi}{2}} \\sin{\\left(t \\right)}\\, dt = 1.0$" ], "text/plain": [ "Eq(Integral(sin(t), (t, 0, pi/2)), 1.0)" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# The integral of a sinusoidal from 0 to pi/2\n", "t = symbols('t', real=True)\n", "Eq(Integral(sin(t), (t,0,pi/2)),Integral(sin(t), (t,0,pi/2)).doit().evalf())" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "# From https://www.math.ubc.ca/~pwalls/math-python/integration/riemann-sums/\n", "def riemann_sum(f,a,b,N,method='midpoint'):\n", " '''Compute the Riemann sum of f(x) over the interval [a,b].\n", "\n", " Parameters\n", " ----------\n", " f : function\n", " Vectorized function of one variable\n", " a , b : numbers\n", " Endpoints of the interval [a,b]\n", " N : integer\n", " Number of subintervals of equal length in the partition of [a,b]\n", " method : string\n", " Determines the kind of Riemann sum:\n", " right : Riemann sum using right endpoints\n", " left : Riemann sum using left endpoints\n", " midpoint (default) : Riemann sum using midpoints\n", "\n", " Returns\n", " -------\n", " float\n", " Approximation of the integral given by the Riemann sum.\n", " '''\n", " dx = (b - a)/N\n", " x = np.linspace(a,b,N+1)\n", "\n", " if method == 'left':\n", " x_left = x[:-1]\n", " return np.sum(f(x_left)*dx)\n", " elif method == 'right':\n", " x_right = x[1:]\n", " return np.sum(f(x_right)*dx)\n", " elif method == 'midpoint':\n", " x_mid = (x[:-1] + x[1:])/2\n", " return np.sum(f(x_mid)*dx)\n", " else:\n", " raise ValueError(\"Method must be 'left', 'right' or 'midpoint'.\")" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Riemman left: 0.992125456605633\n", "Riemman midpoint: 1.0000102809119054\n", "Riemman right: 1.007833419873582\n" ] } ], "source": [ "print('Riemman left:',riemann_sum(np.sin,0,np.pi/2,100,'left'))\n", "print('Riemman midpoint:',riemann_sum(np.sin,0,np.pi/2,100,'midpoint'))\n", "print('Riemman right:',riemann_sum(np.sin,0,np.pi/2,100,'right'))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "### Trapezoidal Rule\n", "\n", "(From https://www.math.ubc.ca/~pwalls/math-python/integration/trapezoid-rule/)\n", "\n" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "f = lambda x : np.sin(x)\n", "a = -np.pi; b = +np.pi; N = 10\n", "n = 10 # Use n*N+1 points to plot the function smoothly\n", "\n", "x = np.linspace(a,b,N+1)\n", "y = f(x)\n", "\n", "X = np.linspace(a,b,n*N+1)\n", "Y = f(X)\n", "plt.figure(figsize=(10,8))\n", "plt.plot(X,Y)\n", "x_left = x[:-1] # Left endpoints\n", "y_left = y[:-1]\n", "plt.plot(x_left,y_left,'b.',markersize=10)\n", "for i in range(N):\n", " xs = [x[i],x[i],x[i+1],x[i+1]]\n", " ys = [0,f(x[i]),f(x[i+1]),0]\n", " plt.fill(xs,ys,'b',edgecolor='b',alpha=0.2)\n", "\n", "plt.title('Trapezoid Rule, N = {}'.format(N))\n", "plt.grid()" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "# From https://www.math.ubc.ca/~pwalls/math-python/integration/trapezoid-rule/\n", "def trapz(f,a,b,N=50):\n", " '''Approximate the integral of f(x) from a to b by the trapezoid rule.\n", "\n", " The trapezoid rule approximates the integral \\int_a^b f(x) dx by the sum:\n", " (dx/2) \\sum_{k=1}^N (f(x_k) + f(x_{k-1}))\n", " where x_k = a + k*dx and dx = (b - a)/N.\n", "\n", " Parameters\n", " ----------\n", " f : function\n", " Vectorized function of a single variable\n", " a , b : numbers\n", " Interval of integration [a,b]\n", " N : integer\n", " Number of subintervals of [a,b]\n", "\n", " Returns\n", " -------\n", " float\n", " Approximation of the integral of f(x) from a to b using the\n", " trapezoid rule with N subintervals of equal length.\n", "\n", " Examples\n", " --------\n", " >>> trapz(np.sin,a=0,b=np.pi/2,N=1000)\n", " 0.99999979438323316\n", " '''\n", " x = np.linspace(a,b,N+1)\n", " y = f(x)\n", " y_right = y[1:] # Right endpoints\n", " y_left = y[:-1] # Left endpoints\n", " dx = (b - a)/N\n", " T = (dx/2) * np.sum(y_right + y_left)\n", " return T" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Trapezoidal Rule: 0.9999794382396074\n" ] } ], "source": [ "print('Trapezoidal Rule:',trapz(np.sin,0,np.pi/2,100))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "#### MPMath and Scipy Numerical Integration" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/plain": [ "mpf('0.99999999999999989')" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# MPMath (Sympy)\n", "from mpmath import quad, sin\n", "\n", "f = lambda x : sin(x)\n", "quad(f, [0, np.pi/2])" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(0.9999999999999999, 1.1102230246251564e-14)\n" ] } ], "source": [ "# Scipy\n", "import scipy.integrate\n", "f = lambda x : np.sin(x)\n", "print(scipy.integrate.quad(f, 0, np.pi/2))" ] } ], "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": "3.7.4" }, "livereveal": { "rise": { "height": "90%", "width": "90%" }, "scroll": true, "theme": "sky", "transition": "zoom" }, "widgets": { "application/vnd.jupyter.widget-state+json": { "state": { "010411b23dde4ac9b0a3030e14cf116a": { "model_module": "@jupyter-widgets/controls", "model_module_version": "1.5.0", "model_name": "ButtonModel", "state": { "description": "Start", "layout": "IPY_MODEL_6a3bf4da31de478d94493fb7e7bf2612", "style": "IPY_MODEL_28c5906b489444688437bc5e2decf81a" } }, "02c9485b88554eb9992be45d9860b92e": { "model_module": "@jupyter-widgets/base", 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