{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Quadrature\n", "\n", "This notebook illustrates the quadrature routines available in \n", "quantecon. These routines are Python implementations of MATLAB \n", "routines originally written by Mario Miranda and Paul Fackler as part \n", "of their influential compecon toolkit ([http://www4.ncsu.edu/~pfackler/compecon/toolbox.html](http://www4.ncsu.edu/~pfackler/compecon/toolbox.html)). We are indebted \n", "to Mario and Paul for their pioneering work on numerical dynamic \n", "programming and their support for the development of Python \n", "implementations. For further information on the compecon toolkit see \n", "Miranda, Mario J, and Paul L Fackler. Applied Computational Economics and Finance, MIT Press, 2002. \n", "\n", "The Python versions of the routines are written by Chase Coleman and Spencer Lyon. \n", "\n", "The examples contained in this document were derived from the examples named demqua##.m that are provided with the CompEcon toolbox. Many of them come from the 2005 version of the toolbox, others come from the 2014 version. The year is indiciated next to each reference." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "from scipy.stats import multivariate_normal\n", "from quantecon.quad import *\n", "\n", "%matplotlib inline\n", "\n", "np.random.seed(42) # For reproducability" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot Equi-Distributed Sequences in 2-D\n", "\n", "### Based on demqua01.m (2005)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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GbpxJCF588WNw9OilLGI4j9NCpKceYhqidR6nhZtBnZSQtNeHXNGqHYeSIycO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\n2F1tQ+mD3TZXPaEFofbWwnpho2urzdg7atpOe4ta1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FKMUw49zmYROfnkCgObx5T5wzdu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kKz4CK5WRmIhkkS1lYNJmyDkcjcdpq7M3RqiE0WD93d3daVph7dHJ1JhKldYIvpKQ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\nkApfn0jgodpjBE7LXAhtYLHMwlIencc5dfoEvliEmEMutDmVslZDgp31YCQ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Q5pTk3ppy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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plotequi(ax, kind, n, a, b, **kwargs):\n", " \"\"\"\n", " This function is to simplify the plotting process. It takes\n", " the parameters to qnwequi and plots the output on the axis ax.\n", " \"\"\"\n", " kind_names = {\"N\":\"Neiderreiter\", \"W\":\"Weyl\", \"H\":\"Haber\", \"R\":\"Random\"}\n", " pts, wts = qnwequi(n, a, b, kind)\n", " \n", " pt_alph = wts/wts.max()\n", " \n", " if n > 1000:\n", " sze = 3\n", " else:\n", " sze = 10\n", " \n", " ax.set_title(\"2-D {} Type Sequence with n={}\".format(kind_names[kind], n))\n", " ax.set_xlabel(r\"$x_1$\")\n", " ax.set_ylabel(r\"$x_2$\")\n", " ax.set_xlim([0, 1])\n", " ax.set_ylim([0, 1])\n", " \n", " ax.scatter(pts[:, 0], pts[:, 1], s=sze, **kwargs)\n", "\n", " return None\n", "\n", "# Create a figure and subplots\n", "fig, axess = plt.subplots(2, 2, figsize=(14, 10))\n", "axess = axess.flatten()\n", "\n", "# Want to plot these kinds\n", "kinds = [\"N\", \"W\", \"H\", \"R\"]\n", "\n", "n = 4000\n", "a = np.array([0, 0])\n", "b = np.ones(2)\n", "\n", "for ind, kind in enumerate(kinds):\n", " plotequi(axess[ind], kind, n, a, b)\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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8llixNTiaXqd8k10tVREtVYKaksscYyxlvq4wWBp+U1dEhvrl8AmB9Ji23T4p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\nI24GnW+2v5MmFHvit8WR+js1Mdiukd1v5xXpNIa0HlWmLkr75DIiPdLf6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mOtorVDIhG3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\ncjN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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Create a figure and subplots\n", "fig, axess = plt.subplots(2, 2, figsize=(14, 10))\n", "axess = axess.flatten()\n", "\n", "# Want to plot these kinds\n", "kind = \"N\"\n", "num_n = [1000, 2000, 4000, 8000]\n", "\n", "a = np.array([0, 0])\n", "b = np.ones(2)\n", "\n", "for ind, n in enumerate(num_n):\n", " plotequi(axess[ind], kind, n, a, b)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Montecarlo Integration vs Integration by Quadrature\n", "\n", "### Based on demqua02.m (2014)\n" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The Montecarlo integration provides the result -0.98797\n", "The Quadrature integration provides the result -1.00000\n", "The difference between the two is: 0.01203\n" ] } ], "source": [ "#Set parameters for normal\n", "mu = np.zeros(2)\n", "sigma = np.array([[1., .5], [.5, 1.]])\n", "\n", "# Define a function\n", "f = lambda x: x[:, 0]**2 + 2*x[:, 0]*x[:, 1] - 3*x[:, 1]**2\n", "\n", "# Setparameters\n", "n = 50000\n", "\n", "# Montecarlo Int\n", "mvn = multivariate_normal(cov=sigma)\n", "randsamp = mvn.rvs(n)\n", "mc_int = f(randsamp).sum()/n\n", "\n", "# Quadrature Int\n", "n = np.array([3, 3])\n", "pts, wts = qnwnorm(n, mu, sigma)\n", "qnwnorm_int = np.dot(wts.T, f(pts))\n", "\n", "# Compute diff\n", "diff_int = mc_int - qnwnorm_int\n", "\n", "print(\"The Montecarlo integration provides the result %.5f\" %mc_int)\n", "print(\"The Quadrature integration provides the result %.5f\" %qnwnorm_int)\n", "print(\"The difference between the two is: %.5f\" %diff_int)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Compare Quadrature Methods\n", "\n", "### Based on demqua03.m and demqua04.m (2005)\n", "\n", "## 1d quadrature" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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KindlegechebtrapsimpNWHR
FunctionNumber of Nodes
f132.350342.354692.543082.362052.252552.252552.593481.99805
52.35042.350412.399172.351192.587072.587073.084212.11507
112.35042.35042.358232.350422.358512.358512.245792.24213
212.35042.35042.352362.35042.286012.286012.010921.96174
312.35042.35042.351272.35042.353212.353212.149882.47553
512.35042.35042.350722.35042.366762.366762.30512.33318
1012.35042.35042.350482.35042.343622.343622.225842.28676
4012.35042.35042.350412.35042.355172.355172.341412.33741
f230.9583331.156121.038461.358970.5280520.5280521.124020.752525
50.7069480.7366110.6571620.5300620.4530480.4530480.7467430.509264
110.5624580.5661560.5512220.5698340.6158040.6158040.6113330.62777
210.5496050.5496320.5492420.5485820.5504350.5504350.5885150.385857
310.5493650.5493680.5493060.5493940.5572390.5572390.6206540.569447
510.549360.549360.5493410.549360.5428210.5428210.5265720.488996
1010.549360.549360.5493550.549360.5516710.5516710.542470.616739
4010.549360.549360.549360.549360.548220.548220.5359570.617324
f330.9779020.82720410.6666671.294751.294750.8688171.15497
51.153521.13311.207111.276141.371371.371371.162641.02986
111.273951.269151.299481.273491.265661.265661.224521.21618
211.310111.309331.321021.32821.318911.318911.224291.20045
311.320241.31991.326551.321811.329471.329471.202561.36386
511.327071.326971.330141.327981.332741.332741.305841.26738
1011.331071.331051.332191.332871.331881.331881.32571.24815
4011.333051.333051.333191.333281.333631.333631.34891.3118
f432.055512.087461.880142.135932.266522.266522.835971.68155
52.051912.051522.010372.053782.174822.174822.772852.23331
112.051912.051912.045322.051962.155822.155822.231461.68229
212.051912.051912.050272.051922.067642.067642.107992.12581
312.051912.051912.051182.051912.058612.058612.226571.95981
512.051912.051912.051652.051912.067652.067652.133921.96271
1012.051912.051912.051852.051912.051722.051721.999742.06799
4012.051912.051912.051912.051912.05452.05452.027292.07971
\n", "
" ], "text/plain": [ "Kind lege cheb trap simp N \\\n", "Function Number of Nodes \n", "f1 3 2.35034 2.35469 2.54308 2.36205 2.25255 \n", " 5 2.3504 2.35041 2.39917 2.35119 2.58707 \n", " 11 2.3504 2.3504 2.35823 2.35042 2.35851 \n", " 21 2.3504 2.3504 2.35236 2.3504 2.28601 \n", " 31 2.3504 2.3504 2.35127 2.3504 2.35321 \n", " 51 2.3504 2.3504 2.35072 2.3504 2.36676 \n", " 101 2.3504 2.3504 2.35048 2.3504 2.34362 \n", " 401 2.3504 2.3504 2.35041 2.3504 2.35517 \n", "f2 3 0.958333 1.15612 1.03846 1.35897 0.528052 \n", " 5 0.706948 0.736611 0.657162 0.530062 0.453048 \n", " 11 0.562458 0.566156 0.551222 0.569834 0.615804 \n", " 21 0.549605 0.549632 0.549242 0.548582 0.550435 \n", " 31 0.549365 0.549368 0.549306 0.549394 0.557239 \n", " 51 0.54936 0.54936 0.549341 0.54936 0.542821 \n", " 101 0.54936 0.54936 0.549355 0.54936 0.551671 \n", " 401 0.54936 0.54936 0.54936 0.54936 0.54822 \n", "f3 3 0.977902 0.827204 1 0.666667 1.29475 \n", " 5 1.15352 1.1331 1.20711 1.27614 1.37137 \n", " 11 1.27395 1.26915 1.29948 1.27349 1.26566 \n", " 21 1.31011 1.30933 1.32102 1.3282 1.31891 \n", " 31 1.32024 1.3199 1.32655 1.32181 1.32947 \n", " 51 1.32707 1.32697 1.33014 1.32798 1.33274 \n", " 101 1.33107 1.33105 1.33219 1.33287 1.33188 \n", " 401 1.33305 1.33305 1.33319 1.33328 1.33363 \n", "f4 3 2.05551 2.08746 1.88014 2.13593 2.26652 \n", " 5 2.05191 2.05152 2.01037 2.05378 2.17482 \n", " 11 2.05191 2.05191 2.04532 2.05196 2.15582 \n", " 21 2.05191 2.05191 2.05027 2.05192 2.06764 \n", " 31 2.05191 2.05191 2.05118 2.05191 2.05861 \n", " 51 2.05191 2.05191 2.05165 2.05191 2.06765 \n", " 101 2.05191 2.05191 2.05185 2.05191 2.05172 \n", " 401 2.05191 2.05191 2.05191 2.05191 2.0545 \n", "\n", "Kind W H R \n", "Function Number of Nodes \n", "f1 3 2.25255 2.59348 1.99805 \n", " 5 2.58707 3.08421 2.11507 \n", " 11 2.35851 2.24579 2.24213 \n", " 21 2.28601 2.01092 1.96174 \n", " 31 2.35321 2.14988 2.47553 \n", " 51 2.36676 2.3051 2.33318 \n", " 101 2.34362 2.22584 2.28676 \n", " 401 2.35517 2.34141 2.33741 \n", "f2 3 0.528052 1.12402 0.752525 \n", " 5 0.453048 0.746743 0.509264 \n", " 11 0.615804 0.611333 0.62777 \n", " 21 0.550435 0.588515 0.385857 \n", " 31 0.557239 0.620654 0.569447 \n", " 51 0.542821 0.526572 0.488996 \n", " 101 0.551671 0.54247 0.616739 \n", " 401 0.54822 0.535957 0.617324 \n", "f3 3 1.29475 0.868817 1.15497 \n", " 5 1.37137 1.16264 1.02986 \n", " 11 1.26566 1.22452 1.21618 \n", " 21 1.31891 1.22429 1.20045 \n", " 31 1.32947 1.20256 1.36386 \n", " 51 1.33274 1.30584 1.26738 \n", " 101 1.33188 1.3257 1.24815 \n", " 401 1.33363 1.3489 1.3118 \n", "f4 3 2.26652 2.83597 1.68155 \n", " 5 2.17482 2.77285 2.23331 \n", " 11 2.15582 2.23146 1.68229 \n", " 21 2.06764 2.10799 2.12581 \n", " 31 2.05861 2.22657 1.95981 \n", " 51 2.06765 2.13392 1.96271 \n", " 101 2.05172 1.99974 2.06799 \n", " 401 2.0545 2.02729 2.07971 " ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kinds = [\"lege\", \"cheb\", \"trap\", \"simp\", \"N\", \"W\", \"H\", \"R\"]\n", "\n", "# Define some functions\n", "f1 = lambda x: np.exp(-x)\n", "f2 = lambda x: 1 / (1 + 25 * x**2)\n", "f3 = lambda x: np.abs(x) ** 0.5\n", "f4 = lambda x: np.exp(-x*x / 2)\n", "func_names = [\"f1\", \"f2\", \"f3\", \"f4\"]\n", "\n", "# Integration parameters\n", "n = np.array([3, 5, 11, 21, 31, 51, 101, 401]) # number of nodes\n", "a, b = -1, 1 # endpoints\n", "a4, b4 = -1, 2\n", "\n", "# Set up pandas DataFrame to hold results\n", "ind = pd.MultiIndex.from_product([func_names, n])\n", "ind.names=[\"Function\", \"Number of Nodes\"]\n", "cols = pd.Index(kinds, name=\"Kind\")\n", "res_df = pd.DataFrame(index=ind, columns=cols)\n", "\n", "for ind, func in enumerate([f1, f2, f3]):\n", " func_name = func_names[ind]\n", " for kind in kinds:\n", " for num in n:\n", " res_df.ix[func_name, num][kind] = quadrect(func, num, a, b, kind)\n", "\n", "for kind in kinds:\n", " for num in n:\n", " res_df.ix[\"f4\", num][kind] = quadrect(f4, num, a4, b4, kind)\n", "\n", "res_df" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2d quadrature\n", "\n", "### Based on demqua04.m (2005)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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KindlegechebtrapsimpNWHR
FunctionNumber of Nodes
f1_2910.977910.999612.124611.03639.375511.468311.03715.344
2510.978210.978211.264310.982111.248911.386310.490711.4881
12110.978210.978211.023910.978311.047410.950811.076310.7374
44110.978210.978210.989610.978210.957710.971510.751211.3674
96110.978210.978210.983310.978210.977210.995411.027711.0893
260110.978210.978210.9810.978210.970210.981710.930311.4035
1020110.978210.978210.978710.978210.976910.978210.933811.0431
16080110.978210.978210.978210.978210.978410.978110.967610.9849
f2_294.572414.558114.692634.54925.398394.450854.457855.47389
254.581154.582694.628634.588194.547994.531273.99394.22545
1214.5814.5814.589514.581284.579144.608954.501294.66052
4414.5814.5814.583164.581014.585674.583724.514484.31931
9614.5814.5814.581964.5814.581854.583964.657594.69355
26014.5814.5814.581344.5814.584444.582054.620294.54357
102014.5814.5814.581084.5814.583194.581074.596554.61698
1608014.5814.5814.5814.5814.581184.581014.58024.57298
\n", "
" ], "text/plain": [ "Kind lege cheb trap simp N \\\n", "Function Number of Nodes \n", "f1_2 9 10.9779 10.9996 12.1246 11.0363 9.3755 \n", " 25 10.9782 10.9782 11.2643 10.9821 11.2489 \n", " 121 10.9782 10.9782 11.0239 10.9783 11.0474 \n", " 441 10.9782 10.9782 10.9896 10.9782 10.9577 \n", " 961 10.9782 10.9782 10.9833 10.9782 10.9772 \n", " 2601 10.9782 10.9782 10.98 10.9782 10.9702 \n", " 10201 10.9782 10.9782 10.9787 10.9782 10.9769 \n", " 160801 10.9782 10.9782 10.9782 10.9782 10.9784 \n", "f2_2 9 4.57241 4.55811 4.69263 4.5492 5.39839 \n", " 25 4.58115 4.58269 4.62863 4.58819 4.54799 \n", " 121 4.581 4.581 4.58951 4.58128 4.57914 \n", " 441 4.581 4.581 4.58316 4.58101 4.58567 \n", " 961 4.581 4.581 4.58196 4.581 4.58185 \n", " 2601 4.581 4.581 4.58134 4.581 4.58444 \n", " 10201 4.581 4.581 4.58108 4.581 4.58319 \n", " 160801 4.581 4.581 4.581 4.581 4.58118 \n", "\n", "Kind W H R \n", "Function Number of Nodes \n", "f1_2 9 11.4683 11.037 15.344 \n", " 25 11.3863 10.4907 11.4881 \n", " 121 10.9508 11.0763 10.7374 \n", " 441 10.9715 10.7512 11.3674 \n", " 961 10.9954 11.0277 11.0893 \n", " 2601 10.9817 10.9303 11.4035 \n", " 10201 10.9782 10.9338 11.0431 \n", " 160801 10.9781 10.9676 10.9849 \n", "f2_2 9 4.45085 4.45785 5.47389 \n", " 25 4.53127 3.9939 4.22545 \n", " 121 4.60895 4.50129 4.66052 \n", " 441 4.58372 4.51448 4.31931 \n", " 961 4.58396 4.65759 4.69355 \n", " 2601 4.58205 4.62029 4.54357 \n", " 10201 4.58107 4.59655 4.61698 \n", " 160801 4.58101 4.5802 4.57298 " ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Define 2d functions\n", "f1_2 = lambda x: np.exp(x[:, 0] + x[:, 1])\n", "f2_2 = lambda x: np.exp(-x[:, 0] * np.cos(x[:, 1]**2))\n", "func_names_2 = [\"f1_2\", \"f2_2\"]\n", "\n", "# Set up pandas DataFrame to hold results\n", "a = ([0, 0], [-1, -1])\n", "b = ([1, 2], [1, 1])\n", "ind_2 = pd.MultiIndex.from_product([func_names_2, n**2])\n", "ind_2.names = [\"Function\", \"Number of Nodes\"]\n", "res_df_2 = pd.DataFrame(index=ind_2, columns=cols)\n", "\n", "for ind, func in enumerate([f1_2, f2_2]):\n", " func_name = func_names_2[ind]\n", " for num in n:\n", " for kind in kinds[:4]:\n", " res_df_2.ix[func_name, num**2][kind] = quadrect(func, [num, num], a[ind], b[ind], kind);\n", " for kind in kinds[4:]:\n", " res_df_2.ix[func_name, num**2][kind] = quadrect(func, num**2, a[ind], b[ind], kind);\n", " \n", "res_df_2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Compare Chebyshev and Legendre Quadrature Nodes and Weights\n", "\n", "### Based on demqua05.m (2005)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ENqAXSKfTSiaTSiaTSvO9lehGfLaAnsMtP4ASl06nVVFRodr4xqyJREJVVVUq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\n2TkA9CiOwaWLnjZ0q3Q6rYq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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Set parameters\n", "n = 15\n", "a = -1\n", "b = 1\n", "\n", "pts_cheb, wts_cheb = qnwcheb(n, a, b)\n", "pts_lege, wts_lege = qnwlege(n, a, b)\n", "\n", "fig, ax1 = plt.subplots(1, 1, figsize=(10, 8))\n", "\n", "ax1.set_title(\"Quadrature Nodes and Weights\")\n", "ax1.set_xlabel(\"Points\")\n", "ax1.set_ylabel(\"Weights\")\n", "ax1.scatter(pts_cheb, wts_cheb, label=\"Chebyshev\", color=\"k\")\n", "ax1.scatter(pts_lege, wts_lege, label=\"Legendre\", color=\"r\")\n", "ax1.legend();\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Area under normal pdf using Simpson's rule\n", "\n", "### Based on demqua04.m (2014)\n", "\n", "This example provides a visual for how Simpson's rule calculates the cdf of the standard normal distribution up to the point $z=1$." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.stats import norm\n", "# Define parameters\n", "n = 11\n", "a = 0\n", "z = 1\n", "\n", "# Compute nodes/weights\n", "x, w = qnwsimp(n,a,z)\n", "\n", "# Define f as standard normal pdf\n", "f = norm(0, 1).pdf\n", "\n", "prob = 0.5 + w.dot(f(x))\n", "\n", "# Plot\n", "b = 4.0\n", "a = -b\n", "n = 500\n", "x = np.linspace(a, b, n)\n", "y = f(x)\n", "\n", "fig, ax = plt.subplots(figsize=(8, 5))\n", "\n", "ax.plot([a, b], [0.0, 0.0], \"k-\")\n", "ax.plot([z, z], [0, f(z)], \"k-\", lw=2)\n", "ax.plot(x, y, lw=2, color=\"#7F7FFF\")\n", "ax.fill_between(x, y, where=x\"))\n", "\n", "ax.set_xticks((z,))\n", "ax.set_yticks(())\n", "ax.set_xticklabels((r'$z$',), fontsize=18)\n", "ax.set_ylim(0, .42)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Willingness to pay, expected utility model\n", "\n", "### Based on demqua05.m (2014)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Expected utility: -0.1479\n", "Certain utility: 0.1353\n", "Willingness to pay: 0.0958\n" ] } ], "source": [ "n = 100\n", "mu = 0 \n", "var = 0.1\n", "alpha = 2 \n", "ystar = 1\n", "y, w = qnwlogn(n, mu, var)\n", "expectedutility = -w.dot(np.exp(-alpha*y))\n", "certainutility = np.exp(-alpha*ystar)\n", "\n", "ystar = -np.log(-expectedutility)/alpha\n", "wtp = w.dot(y)-ystar\n", "\n", "print(\"Expected utility: %.4f\" % expectedutility)\n", "print(\"Certain utility: %.4f\" % certainutility)\n", "print(\"Willingness to pay: %.4f\" % wtp)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Area under a curve\n", "\n", "### Based on demqua06.m (2014)\n", "\n", "This example provides a visual for the area that is computed when a function is computed on an interval" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Define function\n", "f = lambda x: 50 - np.cos(np.pi * x) * (2 * np.pi * x - np.pi + 0.5)**2\n", "\n", "xmin, xmax = 0, 1\n", "a, b = 0.25, 0.75\n", "n = 401\n", "x = np.linspace(xmin, xmax, n)\n", "y = f(x)\n", "\n", "# plot\n", "fig, ax = plt.subplots(figsize=(8, 5))\n", "ax.plot(x, y, lw=2, color=\"#7F7FFF\")\n", "where_inds = (a <= x) & (x <= b)\n", "ax.fill_between(x, y, 0.0, color=\"#8AC627\", \n", " where=where_inds, alpha=0.4)\n", "ax.set_ylim(25, 65)\n", "ax.vlines([a, b], [0, 0], [f(a), f(b)], lw=2, linestyles =\"--\")\n", "\n", "# Annotate the plot\n", "ax.set_xticks((a,b))\n", "ax.set_yticks(())\n", "ax.set_xticklabels((r\"$a$\", r\"$b$\"), fontsize=18)\n", "\n", "ax.annotate(r\"$\\int_a^b f(x) dx$\", xy=(0.45, 35), fontsize=16)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Illustrating integration using Trapezoidal rule\n", "\n", "### Based on demqua07.m (2014)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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GetpY9elPjyt1lV06j/zyZioi9RAOjTuVScDwuSum/jOIiIjItFCQnSKFAvz+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\nbWdkwXo2hbrTZ0AVPfvtpkff3QyfUsUx760mp64C6zKEivOcXtOSQi4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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Define function\n", "c = np.array([2.00, -1.00, 0.50, 0.0])\n", "f = np.poly1d(c)\n", "\n", "# Basic Figure Setup\n", "xmin = -1.0\n", "xmax = 1.0\n", "xwid = xmax-xmin\n", "n = 401\n", "x = np.linspace(xmin, xmax, n)\n", "y = f(x)\n", "ymin = min(y)\n", "ymax = max(y)\n", "ywid = ymax - ymin\n", "ymin = ymin - 0.2*ywid\n", "ymax = ymax + 0.1*ywid\n", "fig, axs = plt.subplots(3, 1, figsize=(10, 6))\n", "fig.tight_layout()\n", "\n", "\n", "def trap_intervals(nint):\n", " \"Split the region defined above into nint intervals\"\n", " nnode = nint + 1\n", " xnode = np.linspace(xmin, xmax, nnode)\n", " ynode = f(xnode)\n", " \n", " # Calculate bins\n", " z = np.zeros(n)\n", " for i in range(1, nnode):\n", " k = np.where((x >= xnode[i-1]) & (x <= xnode[i]))[0]\n", " z[k] = ynode[i-1] + ((x[k]-xnode[i-1])*(ynode[i]-ynode[i-1]) \n", " /(xnode[i]-xnode[i-1]))\n", " \n", " return z, xnode, ynode\n", "\n", "\n", "def plot_regions(z, xnode, ynode, ax):\n", " \"\"\"\n", " Take \"interval\" data z and plot it with the actual function\n", " on the axes ax.\n", " \"\"\"\n", " nint = xnode.size - 1\n", " \n", " # plot\n", " ax.plot(x, y)\n", " ax.plot(x, z, \"r--\", lw=2)\n", " ax.fill_between(x, z, ymin+0.02, color=\"#8AC627\",\n", " alpha=0.4)\n", " \n", " # annotate\n", " # Set ticks\n", " ax.set_xticks(xnode)\n", " x_tick_labs = [r\"$x_0=a$\"]\n", " x_tick_labs += [r\"$x_%i$\" % i for i in range(1, nint)]\n", " x_tick_labs += [r\"$x_%i=b$\" % nint]\n", " ax.set_xticklabels(x_tick_labs, fontsize=14)\n", " ax.xaxis.set_ticks_position('bottom')\n", " ax.set_yticks(())\n", "\n", " # remove borders\n", " for d in [\"left\", \"right\", \"top\", \"bottom\"]:\n", " ax.spines[d].set_visible(False)\n", " \n", " # set plot limits\n", " ax.set_ylim(ymin, ymax)\n", " ax.set_xlim(xmin-0.05, xmax+0.05)\n", " \n", " # add lines to show bins\n", " ax.vlines(xnode, ymin, ynode, color=\"k\", linestyles=\"-\", lw=.25)\n", " \n", " return\n", "\n", "plot_regions(*trap_intervals(2), ax=axs[0])\n", "plot_regions(*trap_intervals(4), ax=axs[1])\n", "plot_regions(*trap_intervals(8), ax=axs[2])" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "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": "3.5.1" } }, "nbformat": 4, "nbformat_minor": 0 }