Created
June 15, 2015 19:49
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{ | |
"cells": [ | |
{ | |
"cell_type": "code", | |
"execution_count": 1, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"%matplotlib inline" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Fatima has done some previous analyses and has found that the stock price over any period of time can be modelled reasonably accurately with the following equation:\n", | |
"\n", | |
"Picture by Hans Hillewaert via Wikimedia Commons\n", | |
"\n", | |
"$price(k) = p * (\\sin(a * k + b) + \\cos(c * k + d) + 2)$\n", | |
"\n", | |
"where $p$, $a$, $b$, $c$ and $d$ are constants. Fatima would like you to write a program to determine the largest price decline over a given sequence of prices. Figure A.1 illustrates the price function for Sample Input 1. You have to consider the prices only for integer values of $k$.\n" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 16, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"import numpy as np\n", | |
"import pandas as pd\n", | |
"from matplotlib import pyplot as plt\n", | |
"import seaborn as sns" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 20, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"sns.set()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 8, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"price = lambda k: p*(np.sin(a*k+b)+np.cos(c*k+d)+2)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 4, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [], | |
"source": [ | |
"p, a, b, c,d, n = 42, 1, 23, 4, 8, 10" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 9, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"81.407575062486472" | |
] | |
}, | |
"execution_count": 9, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"price(1)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 10, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"indice = [i + 1 for i in range(n)]" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 11, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]" | |
] | |
}, | |
"execution_count": 11, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"indice" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 12, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"serie = pd.Series([price(k) for k in indice], index=indice)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 18, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"<matplotlib.legend.Legend at 0x10754c810>" | |
] | |
}, | |
"execution_count": 18, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
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], | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x1055126d0>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"serie.plot(label='precio')\n", | |
"plt.legend()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 21, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"<matplotlib.legend.Legend at 0x10765bbd0>" | |
] | |
}, | |
"execution_count": 21, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
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], | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x105509f90>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"serie.plot(label='precio')\n", | |
"serie.cummax().plot(label='cummax')\n", | |
"plt.legend()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 23, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"<matplotlib.axes._subplots.AxesSubplot at 0x10773e110>" | |
] | |
}, | |
"execution_count": 23, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": [ | |
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], | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x10766a190>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"(serie.cummax() - serie).plot()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 24, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"104.85511047739418" | |
] | |
}, | |
"execution_count": 24, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"(serie.cummax() - serie).max()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 26, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"1 81.407575\n", | |
"2 38.219528\n", | |
"3 133.166902\n", | |
"4 141.983307\n", | |
"5 54.948597\n", | |
"6 91.164758\n", | |
"7 37.128197\n", | |
"8 39.019020\n", | |
"9 149.153340\n", | |
"10 99.110236\n", | |
"dtype: float64" | |
] | |
}, | |
"execution_count": 26, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"serie" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 38, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"<matplotlib.legend.Legend at 0x107d578d0>" | |
] | |
}, | |
"execution_count": 38, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
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], | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x107762190>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"serie.plot(label='precio')\n", | |
"serie[::-1].cummin()[::-1].plot(label='cummin')\n", | |
"plt.legend()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 39, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"104.85511047739418" | |
] | |
}, | |
"execution_count": 39, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"(serie- serie[::-1].cummin()).max()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 41, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"104.85511047739418" | |
] | |
}, | |
"execution_count": 41, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"(serie.cummax() - serie[::-1].cummin()[::-1]).max()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 70, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"def optimo(p, a, b, c,d, n):\n", | |
" price = lambda k: p*(np.sin(a*k+b)+np.cos(c*k+d)+2)\n", | |
" indice = np.arange(n)+1\n", | |
" #indice = [k+1 for k in range(n)]\n", | |
" #serie = pd.Series(price(indice), index=indice)\n", | |
" serie = pd.Series(price(indice), index=indice)\n", | |
" return (serie.cummax() - serie[::-1].cummin()[::-1]).max()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 43, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"104.85511047739418" | |
] | |
}, | |
"execution_count": 43, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"optimo(42, 1, 23, 4, 8, 10)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 46, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"0.0" | |
] | |
}, | |
"execution_count": 46, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"optimo(100,7,615,998,801,3)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 71, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"CPU times: user 117 ms, sys: 20.8 ms, total: 138 ms\n", | |
"Wall time: 118 ms\n" | |
] | |
}, | |
{ | |
"data": { | |
"text/plain": [ | |
"160.67986754163996" | |
] | |
}, | |
"execution_count": 71, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"%time optimo(42, 1, 23, 4, 8, 10**6)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 53, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"array([ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10])" | |
] | |
}, | |
"execution_count": 53, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"np.arange(10)+1" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 73, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"<matplotlib.legend.Legend at 0x107f76190>" | |
] | |
}, | |
"execution_count": 73, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
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], | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x107ef9d90>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"serie.plot(label='precio')\n", | |
"serie[::-1].cummin()[::-1].plot(label='cummin')\n", | |
"plt.legend()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 72, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": [ | |
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], | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x107f56c90>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"serie.plot(label='precio')\n", | |
"serie[::-1].cummin()[::-1].plot(label='cummin')\n", | |
"plt.legend()\n", | |
"plt.xscale('log')\n", | |
"plt.yscale('log')" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [] | |
} | |
], | |
"metadata": { | |
"kernelspec": { | |
"display_name": "Python 2", | |
"language": "python", | |
"name": "python2" | |
}, | |
"language_info": { | |
"codemirror_mode": { | |
"name": "ipython", | |
"version": 2 | |
}, | |
"file_extension": ".py", | |
"mimetype": "text/x-python", | |
"name": "python", | |
"nbconvert_exporter": "python", | |
"pygments_lexer": "ipython2", | |
"version": "2.7.9" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 0 | |
} |
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