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@jburroni
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"
},
{
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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"
},
{
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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"
},
{
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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": {
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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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