ch08-figures.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Robert Johansson\n",
    "\n",
    "Source code listings for [Numerical Python - Scientific Computing and Data Science Applications with Numpy, SciPy and Matplotlib](https://link.springer.com/book/10.1007/979-8-8688-0413-7) (ISBN 979-8-8688-0412-0)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import matplotlib as mpl\n",
    "mpl.rcParams['mathtext.fontset'] = 'stix'\n",
    "mpl.rcParams['font.family'] = 'serif'\n",
    "mpl.rcParams['font.sans-serif'] = 'stix'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "import sympy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Integral"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "x, x0 = sympy.symbols(\"x, x_0\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "f = (x+0.5) ** 3 - 3.5 * (x+0.5) **2 + x  + 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x_{0} + \\left(x - x_{0}\\right) \\left(- 7.0 x_{0} + 3 \\left(x_{0} + 0.5\\right)^{2} - 2.5\\right) + \\left(x_{0} + 0.5\\right)^{3} - 3.5 \\left(x_{0} + 0.5\\right)^{2} + 3$"
      ],
      "text/plain": [
       "x_0 + (x - x_0)*(-7.0*x_0 + 3*(x_0 + 0.5)**2 - 2.5) + (x_0 + 0.5)**3 - 3.5*(x_0 + 0.5)**2 + 3"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.subs(x,x0) + f.diff(x).subs(x,x0) * (x - x0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "f_func = sympy.lambdify(x, f, 'numpy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "def arrowify(fig, ax):\n",
    "    xmin, xmax = ax.get_xlim()\n",
    "    ymin, ymax = ax.get_ylim()\n",
    "\n",
    "    # removing the default axis on all sides:\n",
    "    for side in ['bottom','right','top','left']:\n",
    "        ax.spines[side].set_visible(False)\n",
    "\n",
    "    # removing the axis labels and ticks\n",
    "    ax.set_xticks([])\n",
    "    ax.set_yticks([])\n",
    "    ax.xaxis.set_ticks_position('none')\n",
    "    ax.yaxis.set_ticks_position('none')\n",
    "\n",
    "    # wider figure for demonstration\n",
    "    #fig.set_size_inches(4,2.2)\n",
    "\n",
    "    # get width and height of axes object to compute\n",
    "    # matching arrowhead length and width\n",
    "    dps = fig.dpi_scale_trans.inverted()\n",
    "    bbox = ax.get_window_extent().transformed(dps)\n",
    "    width, height = bbox.width, bbox.height\n",
    "\n",
    "    # manual arrowhead width and length\n",
    "    hw = 1./25.*(ymax-ymin)\n",
    "    hl = 1./25.*(xmax-xmin)\n",
    "    lw = 0.5 # axis line width\n",
    "    ohg = 0.3 # arrow overhang\n",
    "\n",
    "    # compute matching arrowhead length and width\n",
    "    yhw = hw/(ymax-ymin)*(xmax-xmin)* height/width\n",
    "    yhl = hl/(xmax-xmin)*(ymax-ymin)* width/height\n",
    "\n",
    "    # draw x and y axis\n",
    "    ax.arrow(xmin, 0, xmax-xmin, 0., fc='k', ec='k', lw = lw,\n",
    "             head_width=hw, head_length=hl, overhang=ohg,\n",
    "             length_includes_head=True, clip_on=False)\n",
    "\n",
    "    ax.arrow(0, ymin, 0., ymax-ymin, fc='k', ec='k', lw = lw,\n",
    "             head_width=yhw, head_length=yhl, overhang=ohg,\n",
    "             length_includes_head=True, clip_on=False)\n",
    "\n",
    "    \n",
    "    ax.text(xmax*0.95, ymin*0.25, r'$x$', fontsize=22)\n",
    "    ax.text(xmin*0.35, ymax*0.9, r'$f(x)$', fontsize=22)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(8,4))\n",
    "\n",
    "xvec = np.linspace(-1.75, 3.0, 100)\n",
    "ax.plot(xvec, f_func(xvec), 'k', lw=2)\n",
    "\n",
    "xvec = np.linspace(-0.8, 0.85, 100)\n",
    "ax.fill_between(xvec, f_func(xvec), color='lightgreen', alpha=0.9)\n",
    "xvec = np.linspace(0.85, 2.31, 100)\n",
    "ax.fill_between(xvec, f_func(xvec), color='red', alpha=0.5)\n",
    "xvec = np.linspace(2.31, 2.6, 100)\n",
    "ax.fill_between(xvec, f_func(xvec), color='lightgreen', alpha=0.99)\n",
    "\n",
    "ax.text(0.6, 3.5, r\"$\\int_a^b\\!f(x){\\rm d}x$\", fontsize=22)\n",
    "ax.text(-0.88, -0.85, r\"$a$\", fontsize=18)\n",
    "ax.text(2.55, -0.85, r\"$b$\", fontsize=18)\n",
    "ax.axis('tight')\n",
    "\n",
    "arrowify(fig, ax)\n",
    "fig.savefig(\"ch8-illustration-integral.pdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quadrature rules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "from numpy import polynomial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "from scipy import integrate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "from scipy import interpolate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "a = 0\n",
    "b = 1.0\n",
    "\n",
    "def f(x):\n",
    "    return np.exp(-x**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "a = -1.0\n",
    "b = 1.0\n",
    "\n",
    "def f(x):\n",
    "    return 3 + x + x**2 + x**3 + x**4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "x = np.linspace(a, b, 100)\n",
    "xx = np.linspace(a-0.2, b+0.2, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(16, 4))\n",
    "\n",
    "npoints = 2\n",
    "npoints = 5\n",
    "\n",
    "X = np.linspace(a, b, npoints)\n",
    "\n",
    "ax1.plot(xx, f(xx), lw=1, color='k')\n",
    "ax1.fill_between(x, f(x), color='lightgreen', alpha=0.9)\n",
    "\n",
    "i = 0 # (b-a)*f_mid\n",
    "for n in range(len(X) - 1):\n",
    "    f_mid = f(X[n:n+2].mean())\n",
    "    ax1.plot([X[n], X[n]], [0, f_mid], 'b')\n",
    "    ax1.plot([X[n+1], X[n+1]], [0, f_mid], 'b')\n",
    "    ax1.plot(X[n:n+2], [f_mid] * 2, 'b')\n",
    "    ax1.plot(X[n:n+2].mean(), f_mid, 'xk')\n",
    "    \n",
    "    i += (X[n+1]-X[n])*f_mid\n",
    "\n",
    "#i = (b-a)*f_mid\n",
    "ax1.text(-1, 5.5, r'$\\int_{\\,a}^{\\,b} f(x)dx \\approx %f$' % i, fontsize=18)\n",
    "ax1.plot(X, f(X), 'ro')\n",
    "ax1.set_xlim(xx.min(), xx.max())\n",
    "ax1.set_title('Mid-point rule')\n",
    "ax1.set_xticks([-1, 0, 1])\n",
    "ax1.set_xlabel(r'$x$', fontsize=18)\n",
    "ax1.set_ylabel(r'$f(x)$', fontsize=18)\n",
    "\n",
    "names = [\"Trapezoid rule\", \"Simpson's rule\"]\n",
    "for idx, ax in enumerate([ax2, ax3]):\n",
    "    ax.plot(xx, f(xx), lw=1, color='k')\n",
    "    ax.fill_between(x, f(x), color='lightgreen', alpha=0.9)\n",
    "\n",
    "    i = 0\n",
    "    for n in range(len(X) - 1):\n",
    "        XX = np.linspace(X[n], X[n+1], idx+2)\n",
    "\n",
    "        f_interp = polynomial.Polynomial.fit(XX, f(XX), len(XX)-1)    \n",
    "        ax.plot([X[n], X[n]], [0, f(X[n])], 'b')\n",
    "        ax.plot([X[n+1], X[n+1]], [0, f(X[n+1])], 'b')\n",
    "        XXX = np.linspace(X[n], X[n+1], 50)\n",
    "        ax.plot(XXX, f_interp(XXX), 'b')\n",
    "        \n",
    "        F = f_interp.integ()\n",
    "        i += F(X[n+1]) - F(X[n])\n",
    "    ax.text(-1, 5.5, r'$\\int_a^{\\,b} f(x)dx \\approx %f$' % i, fontsize=18)\n",
    "    ax.plot(X, f(X), 'ro')\n",
    "    ax.set_xlabel(r'$x$', fontsize=18)\n",
    "    ax.set_ylabel(r'$f(x)$', fontsize=18)\n",
    "    ax.set_xlim(xx.min(), xx.max())\n",
    "    ax.set_title(names[idx])\n",
    "    ax.set_xticks([-1, 0, 1])\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig('ch8-quadrature-rules-%d.pdf' % npoints)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x800 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ((ax1_2, ax2_2, ax3_2), (ax1_5, ax2_5, ax3_5)) = plt.subplots(2, 3, figsize=(16, 8), sharex=True)\n",
    "\n",
    "ax1, ax2, ax3 = ax1_2, ax2_2, ax3_2\n",
    "npoints = 2\n",
    "\n",
    "X = np.linspace(a, b, npoints)\n",
    "\n",
    "ax1.plot(xx, f(xx), lw=1, color='k')\n",
    "ax1.fill_between(x, f(x), color='lightgreen', alpha=0.9)\n",
    "\n",
    "i = 0 # (b-a)*f_mid\n",
    "for n in range(len(X) - 1):\n",
    "    f_mid = f(X[n:n+2].mean())\n",
    "    ax1.plot([X[n], X[n]], [0, f_mid], 'b')\n",
    "    ax1.plot([X[n+1], X[n+1]], [0, f_mid], 'b')\n",
    "    ax1.plot(X[n:n+2], [f_mid] * 2, 'b')\n",
    "    ax1.plot(X[n:n+2].mean(), f_mid, 'xk')\n",
    "    \n",
    "    i += (X[n+1]-X[n])*f_mid\n",
    "\n",
    "#i = (b-a)*f_mid\n",
    "ax1.text(-1, 5.5, r'$\\int_{\\,a}^{\\,b} f(x)dx \\approx %f$' % i, fontsize=18)\n",
    "ax1.plot(X, f(X), 'ro')\n",
    "ax1.set_xlim(xx.min(), xx.max())\n",
    "ax1.set_title('Mid-point rule')\n",
    "ax1.set_xticks([-1, 0, 1])\n",
    "ax1.set_xlabel(r'$x$', fontsize=18)\n",
    "ax1.set_ylabel(r'$f(x)$', fontsize=18)\n",
    "\n",
    "names = [\"Trapezoid rule\", \"Simpson's rule\"]\n",
    "for idx, ax in enumerate([ax2, ax3]):\n",
    "    ax.plot(xx, f(xx), lw=1, color='k')\n",
    "    ax.fill_between(x, f(x), color='lightgreen', alpha=0.9)\n",
    "\n",
    "    i = 0\n",
    "    for n in range(len(X) - 1):\n",
    "        XX = np.linspace(X[n], X[n+1], idx+2)\n",
    "\n",
    "        f_interp = polynomial.Polynomial.fit(XX, f(XX), len(XX)-1)    \n",
    "        ax.plot([X[n], X[n]], [0, f(X[n])], 'b')\n",
    "        ax.plot([X[n+1], X[n+1]], [0, f(X[n+1])], 'b')\n",
    "        XXX = np.linspace(X[n], X[n+1], 50)\n",
    "        ax.plot(XXX, f_interp(XXX), 'b')\n",
    "        \n",
    "        F = f_interp.integ()\n",
    "        i += F(X[n+1]) - F(X[n])\n",
    "    ax.text(-1, 5.5, r'$\\int_a^{\\,b} f(x)dx \\approx %f$' % i, fontsize=18)\n",
    "    ax.plot(X, f(X), 'ro')\n",
    "    ax.set_xlabel(r'$x$', fontsize=18)\n",
    "    ax.set_ylabel(r'$f(x)$', fontsize=18)\n",
    "    ax.set_xlim(xx.min(), xx.max())\n",
    "    ax.set_title(names[idx])\n",
    "    ax.set_xticks([-1, 0, 1])\n",
    "\n",
    "\n",
    "####\n",
    "ax1, ax2, ax3 = ax1_5, ax2_5, ax3_5\n",
    "npoints = 2\n",
    "npoints = 5\n",
    "\n",
    "\n",
    "X = np.linspace(a, b, npoints)\n",
    "\n",
    "ax1.plot(xx, f(xx), lw=1, color='k')\n",
    "ax1.fill_between(x, f(x), color='lightgreen', alpha=0.9)\n",
    "\n",
    "i = 0 # (b-a)*f_mid\n",
    "for n in range(len(X) - 1):\n",
    "    f_mid = f(X[n:n+2].mean())\n",
    "    ax1.plot([X[n], X[n]], [0, f_mid], 'b')\n",
    "    ax1.plot([X[n+1], X[n+1]], [0, f_mid], 'b')\n",
    "    ax1.plot(X[n:n+2], [f_mid] * 2, 'b')\n",
    "    ax1.plot(X[n:n+2].mean(), f_mid, 'xk')\n",
    "    \n",
    "    i += (X[n+1]-X[n])*f_mid\n",
    "\n",
    "#i = (b-a)*f_mid\n",
    "ax1.text(-1, 5.5, r'$\\int_{\\,a}^{\\,b} f(x)dx \\approx %f$' % i, fontsize=18)\n",
    "ax1.plot(X, f(X), 'ro')\n",
    "ax1.set_xlim(xx.min(), xx.max())\n",
    "#ax1.set_title('Mid-point rule')\n",
    "ax1.set_xticks([-1, 0, 1])\n",
    "ax1.set_xlabel(r'$x$', fontsize=18)\n",
    "ax1.set_ylabel(r'$f(x)$', fontsize=18)\n",
    "\n",
    "names = [\"Trapezoid rule\", \"Simpson's rule\"]\n",
    "for idx, ax in enumerate([ax2, ax3]):\n",
    "    ax.plot(xx, f(xx), lw=1, color='k')\n",
    "    ax.fill_between(x, f(x), color='lightgreen', alpha=0.9)\n",
    "\n",
    "    i = 0\n",
    "    for n in range(len(X) - 1):\n",
    "        XX = np.linspace(X[n], X[n+1], idx+2)\n",
    "\n",
    "        f_interp = polynomial.Polynomial.fit(XX, f(XX), len(XX)-1)    \n",
    "        ax.plot([X[n], X[n]], [0, f(X[n])], 'b')\n",
    "        ax.plot([X[n+1], X[n+1]], [0, f(X[n+1])], 'b')\n",
    "        XXX = np.linspace(X[n], X[n+1], 50)\n",
    "        ax.plot(XXX, f_interp(XXX), 'b')\n",
    "        \n",
    "        F = f_interp.integ()\n",
    "        i += F(X[n+1]) - F(X[n])\n",
    "    ax.text(-1, 5.5, r'$\\int_a^{\\,b} f(x)dx \\approx %f$' % i, fontsize=18)\n",
    "    ax.plot(X, f(X), 'ro')\n",
    "    ax.set_xlabel(r'$x$', fontsize=18)\n",
    "    ax.set_ylabel(r'$f(x)$', fontsize=18)\n",
    "    ax.set_xlim(xx.min(), xx.max())\n",
    "    #ax.set_title(names[idx])\n",
    "    ax.set_xticks([-1, 0, 1])\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig('ch8-quadrature-rules-%d.pdf' % npoints)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.0"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# mid-point rule\n",
    "(b-a) * f((b+a)/2.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.0"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# trapezoid rule\n",
    "(b-a)/2.0 * (f(a) + f(b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.333333333333333"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# simpsons rule\n",
    "(b-a)/6.0 * (f(a) + 4 * f((a+b)/2.0) + f(b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.066666666666667"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# exact result\n",
    "integrate.quad(f, a, b)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.3125"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrate.trapz(f(X), X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.083333333333332"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrate.simps(f(X), X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.066666666666666"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrate.quadrature(f, a, b)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.066666666666666"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrate.romberg(f, a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.33333333, 1.33333333, 0.33333333])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrate.newton_cotes(2)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.fill_between(x, f(x), alpha=0.25)\n",
    "ax.plot(X, f(X), 'ro')\n",
    "\n",
    "for n in range(len(X) - 1):\n",
    "    f_mid = f(X[n:n+2].mean())\n",
    "    ax.plot([X[n], X[n]], [0, f_mid], 'k')\n",
    "    ax.plot([X[n+1], X[n+1]], [0, f_mid], 'k')\n",
    "    ax.plot(X[n:n+2], [f_mid] * 2, 'k')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.fill_between(x, f(x), alpha=0.25)\n",
    "ax.plot(X, f(X), 'ro')\n",
    "\n",
    "for n in range(len(X) - 1):\n",
    "    f_mid = f(X[n:n+2].mean())\n",
    "    ax.plot([X[n], X[n]], [0, f(X[n])], 'k')\n",
    "    ax.plot([X[n+1], X[n+1]], [0, f(X[n+1])], 'k')\n",
    "    ax.plot(X[n:n+2], [f(X[n]), f(X[n+1])], 'k')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "npbook_py310",
   "language": "python",
   "name": "npbook_py310"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}