Как векторизовать расчет площади под кривой
Моя цель: я вычисляю площадь под кривой одного из столбцов моего xts для каждых 5 строк.
Моя цель: мне было интересно, есть ли в R функция, которая могла бы сделать это быстрее (векторизовать ее) вместо создания вектора из столбцов myxts5 и затем циклически выполнять вычисления.
Спасибо за помощь.
Я включил мой код, вывод и набор данных:
#create an xts object
library(xts)
myxts5<-xts(dat5[,2:7],order.by=as.POSIXct(dat5[,1]))
colnames(myxts5)<-c("Open","High","Low","Close","Volume","RSI_10")
#make the data reproducible
dput(myxts5,file='so4.txt')
#my method to calculate the entire area under the RSI
library(MESS)
y1<-as.vector(myxts5[11:nrow(myxts5),"RSI_10"]) #remove the first 10 NAs
x1<-1:length(y1)
AUC_RSI10<-NA
for(i in 1:(length(y1)-4))
{
AUC_RSI10[i]<-auc(x1,y1,from=i,to=i+4,type="spline")
}
#output the result
dput(AUC_RSI10,file='so5.txt')
Вот мой вывод:
c(212.42031469304, 212.798819901101, 209.986805467201, 204.085562604063,
197.984367949833, 190.26277666882, 186.077746687353, 175.748595915665,
153.079882459862, 130.009179454897, 102.067828644029, 93.1546072252816,
106.253169598421, 126.695279601823, 156.84779427326, 171.19433284721,
177.724612560769, 176.407343545939, 180.185730377015, 185.540559407078,
181.492038514392, 189.691635230233, 184.490969841544, 188.753967108042,
207.705900307578, 214.048826298562, 218.30216750124, 212.29968278624,
199.551248663318, 188.776300102749, 182.52612752936, 181.256931078184,
186.756042540598, 192.301043062924, 192.527605116982, 194.728277897872,
189.022862111989, 184.468524998165, 185.39881870675, 196.154701535433,
206.890484681265, 207.327144844833, 212.703798768185, 198.013450923081,
181.641656558781, 176.54287628256, 164.743975467614, 162.034403175174,
162.412236153867, 162.309298857098, 166.286729859961, 176.547050171716,
192.181072883591, 205.515617818054, 218.07534078917, 218.140824515946,
205.641441980933, 201.576989476802, 196.867549251374, 190.783357752807,
197.903201932701, 202.879574501878, 206.106624821193, 220.374961483055,
227.474013530533, 223.343713145521, 229.246256446896, 243.286328522227,
262.117443779325, 263.840756142047, 240.806125975743, 215.212025274733,
187.537410808637, 181.697615578155, 189.007912680354, 184.797339348203,
181.36323163363, 180.650062530952, 179.317002557559, 185.586705150491,
186.662076288898, 188.57947064012, 203.125520580371, 203.930450146523,
203.495197679754, 202.028430483861, 194.680742214661, 193.31866654904,
191.777680494373, 191.023982678201, 188.354726404744, 188.21830097328,
195.985546556535, 203.55439816918, 208.861239277293, 213.888773137499,
214.806015837923, 214.330645702585, 213.514904083631, 226.469183651925,
236.327655260894, 237.566101775243, 252.190727914684, 243.354777400258,
231.51372836124, 229.798793976413, 221.107200373181, 217.996862355506,
211.122748333001, 210.582316625607, 208.01205675632, 209.26953269887,
225.397380909908, 230.483506508238, 227.694726952225, 224.967853799347,
218.724867445519, 216.905971862255, 221.52922790949, 225.631736902592,
230.891924036962, 241.177062846485, 249.246022464813, 254.246246799188,
256.317954002037, 247.643366520204, 238.622153789957, 227.473438159439,
214.560573157924, 212.790548936815, 208.420352726885, 208.640044465686,
214.931993510179, 212.72755394672, 219.410868549475, 233.687119760904,
246.692220779985, 264.374607939455, 269.70827693888, 268.536133748541,
272.85747899862, 274.53970011536, 283.600460826417, 295.875094542883,
302.745632060615, 309.701548644739, 319.260316467242, 326.643036235032,
332.342520658862, 338.413750490865, 343.136490698001, 348.603529563524,
352.398026008696, 357.650124476616, 358.743285419066, 344.637128752378,
324.347614348694, 296.899987957071, 260.178562036282, 235.165894610707,
218.512708871952, 201.615881861806, 204.662806854938, 214.207761875216,
221.261680991827, 236.578968494141, 248.278613344013, 258.043801399754,
274.96482029892, 286.236076785085, 285.602545656925, 285.686696242866,
283.210913624938, 287.152216650458, 295.150088828741, 299.214294408208,
304.574243471004, 307.788231278327, 313.280310293549, 319.207810872882,
318.414126071909, 305.570556389567, 290.312583077288, 286.828481019533,
284.595391529875, 289.607238027879, 298.301134488251, 292.448822019436,
286.489056604544, 279.206214787399)
Вот набор данных:
structure(c(3, 3, 3.24, 3.25, 3.35, 3.3, 3.19, 3.15, 3.2, 3.24,
3.24, 3.239, 3.24, 3.24, 3.24, 3.24, 3.24, 3.23, 3.19, 3.19,
3.18, 3.25, 3.05, 2.95, 2.95, 2.94, 2.96, 3, 3.05, 3, 3, 3.1,
3.15, 3.15, 2.99, 3.04, 3, 3.2, 3.18, 3.18, 3.15, 3.02, 3, 2.99,
2.99, 3, 3.1, 3.05, 2.99, 3, 3, 3, 3, 3.1, 3.2, 2.98, 2.85, 3,
2.9, 2.88, 2.85, 2.86, 2.86, 2.9, 2.9, 3, 3, 3, 3, 2.9, 2.91,
3, 3, 2.92, 3, 3, 3, 3.05, 3, 3, 3, 3.15, 3.3, 3.3, 2.9, 2.95,
2.99, 2.95, 2.91, 2.9, 2.9, 2.92, 2.99, 3, 2.95, 3.1, 3.25, 2.95,
2.92, 2.92, 2.95, 2.92, 2.9, 2.93, 2.93, 2.91, 3, 2.94, 2.99,
3.05, 2.99, 2.92, 3, 3, 3.2, 3.15, 3.21, 3.24, 3.05, 3.1, 3.1,
3.15, 3.01, 3.01, 3.15, 3.15, 3.25, 3.2, 3.23, 3.22, 3.19, 3.24,
3.24, 3.2, 3.24, 3.4, 3.35, 3.35, 3.35, 3.33, 3.3, 3.3, 3.26,
3.28, 3.27, 3.3, 3.3, 3.3, 3.39, 3.39, 3.5, 3.4, 3.45, 3.45,
3.54, 3.59, 3.55, 3.65, 3.68, 3.65, 3.72, 3.79, 3.84, 3.88, 3.9,
3.95, 3.95, 3.95, 4.05, 4.04, 3.97, 3.95, 3.89, 3.86, 3.8, 3.81,
3.95, 3.9, 3.95, 3.97, 4.05, 4.1, 4.13, 4.3, 4.2, 4.23, 4.29,
4.45, 4.48, 4.49, 4.57, 4.68, 4.7, 4.71, 4.77, 4.67, 4.65, 4.74,
5.16, 4.96, 5.26, 5.16, 5.27, 5.19, 3.2, 3.2, 3.25, 3.4, 3.35,
3.3, 3.19, 3.2, 3.2, 3.24, 3.24, 3.24, 3.24, 3.24, 3.24, 3.24,
3.24, 3.24, 3.19, 3.19, 3.18, 3.25, 3.05, 2.95, 2.95, 2.99, 2.96,
3.1, 3.05, 3, 3, 3.1, 3.15, 3.15, 2.99, 3.04, 3, 3.2, 3.18, 3.18,
3.15, 3.05, 3, 3.03, 2.99, 3, 3.1, 3.05, 2.99, 3, 3, 3, 3, 3.2,
3.2, 3.05, 3.05, 3, 2.9, 2.88, 2.85, 2.86, 2.86, 2.9, 2.9, 3,
3, 3, 3, 2.92, 2.92, 3, 3, 2.92, 3, 3, 3, 3.05, 3, 3, 3.15, 3.29,
3.49, 3.3, 2.9, 2.99, 2.99, 2.95, 2.91, 2.9, 2.95, 2.92, 2.99,
3, 2.95, 3.1, 3.25, 2.95, 2.95, 2.95, 2.99, 2.95, 2.9, 2.93,
2.93, 2.95, 3, 2.99, 2.99, 3.05, 2.99, 2.99, 3, 3.2, 3.24, 3.2,
3.25, 3.24, 3.1, 3.1, 3.23, 3.15, 3.01, 3.3, 3.15, 3.25, 3.28,
3.25, 3.23, 3.22, 3.29, 3.24, 3.24, 3.24, 3.4, 3.4, 3.4, 3.35,
3.35, 3.33, 3.3, 3.3, 3.28, 3.31, 3.31, 3.3, 3.3, 3.3, 3.39,
3.54, 3.5, 3.47, 3.47, 3.54, 3.6, 3.59, 3.69, 3.75, 3.69, 3.75,
3.8, 3.84, 3.89, 3.93, 3.95, 3.95, 3.95, 4.1, 4.15, 4.1, 3.97,
3.95, 3.92, 3.86, 3.85, 3.81, 3.95, 4, 3.97, 3.99, 4.1, 4.19,
4.33, 4.33, 4.31, 4.3, 4.46, 4.49, 4.54, 4.65, 4.72, 4.72, 4.79,
4.79, 4.77, 4.7, 4.71, 5.17, 5.3, 5.39, 5.39, 5.39, 5.3, 5.19,
3, 3, 3.24, 3.25, 3.25, 3.1, 3.19, 3.15, 3.2, 3.24, 3.24, 3.239,
3.24, 3.24, 3.24, 3.24, 3.2, 3.2, 3.19, 3.18, 3.18, 3.05, 2.6,
2.95, 2.85, 2.94, 2.95, 3, 3, 3, 3, 3, 3.05, 2.82, 2.99, 3.04,
2.95, 3.2, 3.18, 3.15, 3.02, 3, 3, 2.99, 2.95, 3, 3.1, 2.99,
2.99, 3, 2.98, 3, 3, 3.1, 2.98, 2.8, 2.85, 2.85, 2.89, 2.76,
2.85, 2.86, 2.85, 2.88, 2.9, 3, 3, 3, 3, 2.9, 2.91, 3, 2.92,
2.92, 3, 3, 3, 3.05, 3, 2.85, 3, 3.15, 3.26, 2.8, 2.9, 2.95,
2.99, 2.95, 2.86, 2.9, 2.89, 2.92, 2.9, 3, 2.85, 3.1, 3.05, 2.9,
2.9, 2.9, 2.95, 2.85, 2.9, 2.93, 2.93, 2.91, 3, 2.92, 2.99, 2.99,
2.99, 2.92, 3, 3, 3.01, 3.15, 3.02, 3.05, 3.05, 3.1, 3.1, 3,
3.01, 3.01, 3.1, 3.15, 3.25, 3.18, 3.16, 3.19, 3.13, 3.24, 3.24,
3.2, 3.24, 3.4, 3.35, 3.35, 3.33, 3.3, 3.3, 3.22, 3.22, 3.28,
3.25, 3.3, 3.3, 3.3, 3.39, 3.35, 3.35, 3.38, 3.41, 3.43, 3.45,
3.45, 3.55, 3.6, 3.65, 3.65, 3.67, 3.78, 3.8, 3.86, 3.9, 3.9,
3.85, 3.93, 4.02, 3.97, 3.93, 3.82, 3.8, 3.8, 3.8, 3.8, 3.95,
3.85, 3.95, 3.97, 4.05, 4.06, 4.13, 4.16, 4.2, 4.22, 4.29, 4.35,
4.43, 4.49, 4.51, 4.65, 4.66, 4.71, 4.68, 4.6, 4.6, 4.74, 5,
4.91, 5.16, 5.14, 5.17, 5.19, 3.2, 3.2, 3.25, 3.4, 3.25, 3.1,
3.19, 3.2, 3.2, 3.24, 3.24, 3.24, 3.24, 3.24, 3.24, 3.24, 3.2,
3.2, 3.19, 3.19, 3.18, 3.05, 2.95, 2.95, 2.85, 2.99, 2.95, 3.1,
3, 3, 3, 3, 3.15, 2.85, 2.99, 3.04, 2.97, 3.2, 3.18, 3.15, 3.02,
3, 3, 2.99, 2.98, 3, 3.1, 2.99, 2.99, 3, 2.98, 3, 3, 3.2, 2.98,
3.05, 3.015, 2.85, 2.9, 2.86, 2.85, 2.86, 2.86, 2.88, 2.9, 3,
3, 3, 3, 2.92, 2.92, 3, 2.92, 2.92, 3, 3, 3, 3.05, 3, 3, 3.15,
3.29, 3.26, 2.8, 2.9, 2.99, 2.99, 2.95, 2.9, 2.9, 2.95, 2.92,
2.9, 3, 2.85, 3.1, 3.05, 2.92, 2.92, 2.95, 2.99, 2.9, 2.9, 2.93,
2.93, 2.95, 3, 2.99, 2.99, 2.99, 2.99, 2.99, 3, 3.2, 3.01, 3.2,
3.24, 3.05, 3.1, 3.1, 3.23, 3, 3.01, 3.2, 3.14, 3.25, 3.28, 3.2,
3.16, 3.19, 3.2, 3.24, 3.24, 3.24, 3.31, 3.4, 3.35, 3.35, 3.33,
3.3, 3.3, 3.22, 3.28, 3.31, 3.25, 3.3, 3.3, 3.3, 3.39, 3.42,
3.47, 3.47, 3.41, 3.54, 3.58, 3.59, 3.6, 3.69, 3.69, 3.74, 3.8,
3.8, 3.85, 3.86, 3.95, 3.95, 3.95, 4.1, 4.05, 3.97, 3.96, 3.89,
3.8, 3.85, 3.81, 3.8, 3.95, 3.91, 3.97, 3.99, 4.1, 4.1, 4.33,
4.2, 4.25, 4.3, 4.45, 4.48, 4.43, 4.57, 4.68, 4.72, 4.7, 4.76,
4.7, 4.6, 4.71, 5.16, 5, 5.29, 5.16, 5.3, 5.19, 5.19, 8042, 7247,
1500, 2200, 1600, 1983, 1360, 400, 1500, 4800, 400, 1900, 450,
500, 1600, 25, 9190, 2685, 100, 2450, 2100, 14824, 12366, 400,
550, 7701, 4000, 2000, 2200, 1000, 400, 192, 1800, 9825, 776,
500, 5050, 2100, 1000, 526, 5262, 13470, 150, 5000, 825, 550,
1000, 1000, 835, 1000, 800, 1500, 2000, 6000, 23716, 2510, 5073,
4667, 5332, 6600, 11000, 1000, 4500, 5400, 500, 1000, 14260,
600, 230, 4500, 1500, 1200, 5372, 500, 6128, 1000, 3500, 500,
782, 1318, 2650, 9856, 15240, 9280, 100, 3500, 1000, 500, 9900,
2000, 1073, 3000, 1650, 3000, 5500, 1000, 7120, 3300, 8200, 3600,
630, 12800, 3800, 1500, 5000, 12000, 1433, 8450, 1500, 1420,
1000, 1088, 510, 3390, 15482, 850, 9900, 3240, 4860, 661, 4405,
21850, 675, 12475, 10030, 4747, 6449, 2771, 2400, 1900, 26130,
75, 1000, 20360, 18704, 1100, 6750, 910, 440, 4745, 1115, 12415,
1892, 1000, 4000, 100, 3200, 4000, 1000, 14715, 18365, 8100,
13375, 21693, 34433, 14629, 32341, 26850, 16369, 14310, 12150,
16731, 21046, 11623, 9380, 8760, 10850, 21129, 20312, 14727,
7393, 4879, 16760, 6538, 15113, 1200, 1500, 23771, 9575, 8150,
7774, 20177, 26701, 18467, 14485, 16184, 16318, 10731, 15647,
33617, 9598, 10061, 31855, 13082, 8919, 9716, 17170, 120717,
99373, 48754, 16061, 40634, 71196, 1550, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, 53.125, 53.125, 53.125, 53.125, 53.125, 53.125,
47.5346930503198, 47.5346930503198, 46.0394165349133, 46.0394165349133,
44.318305280762, 28.7784405800004, 22.1424718838612, 22.1424718838612,
17.2358309419688, 38.4516614314786, 35.5580201252693, 50.9409073335208,
43.2868577214891, 43.2868577214891, 43.2868577214891, 43.2868577214891,
57.7874913716085, 36.8498892395159, 46.8375224558739, 49.9770019079572,
45.7722513840718, 58.5146700229585, 57.2156823579705, 55.1742932408986,
47.0855992829417, 45.9344690510984, 45.9344690510985, 45.2515723462439,
44.5162256558408, 46.449998432825, 55.1367545352793, 46.0137841205261,
46.0137841205261, 46.9980428383782, 45.1680669242794, 47.441920921326,
47.441920921326, 65.2386620558215, 46.142307043277, 51.193099386028,
48.6580081770167, 38.6361289882013, 42.6156590089499, 40.2929460812456,
39.692011854992, 40.6750999191946, 40.6750999191946, 42.9705189551315,
45.3212400820865, 55.5094323592483, 55.5094323592483, 55.5094323592483,
55.5094323592483, 45.2327792238372, 45.2327792238372, 55.4216085337574,
45.9278679630622, 45.9278679630622, 55.3669503461937, 55.3669503461936,
55.3669503461936, 61.1772096913823, 53.4465567305418, 53.4465567305418,
68.2882384971981, 76.1676317292872, 71.9132908833502, 36.8483156083071,
43.5024785084454, 48.8880404068233, 48.8880404068233, 46.4581004766477,
43.4580365276188, 43.4580365276188, 47.6329025895786, 45.3982034143251,
43.8735164139756, 52.6990228922181, 41.7559573740936, 57.9325988310753,
54.5648674809673, 46.7190334585342, 46.7190334585342, 48.8158219705131,
51.6355364603515, 45.3849436005241, 45.3849436005241, 47.9765292549334,
47.9765292549334, 49.9319385680271, 54.6652697441737, 53.5404685492423,
53.5404685492423, 53.5404685492423, 53.5404685492423, 53.5404685492423,
55.1048795718158, 74.3203906677712, 51.1923456182049, 63.7325679700046,
65.7886989290019, 50.6372228137231, 53.7516204585925, 53.7516204585925,
61.540372521279, 46.233933197312, 46.8722919081336, 57.5199212894259,
53.7407977117634, 59.2011388495268, 60.6100798191561, 54.9839832912961,
52.2875592667179, 54.1608587608694, 54.8178785295968, 57.5237409247848,
57.5237409247849, 57.5237409247849, 62.8627359282454, 68.5160644996568,
62.6307841423264, 62.6307841423264, 60.0822193137844, 56.2662526029152,
56.2662526029152, 46.5358654620614, 53.2702015941206, 56.3263815242224,
49.17892489837, 54.5222862433549, 54.5222862433549, 54.5222862433549,
63.8953027289306, 66.4558554034754, 70.3499117941237, 70.3499117941237,
60.026469332036, 70.4615938291669, 72.8818396542941, 73.4853107348059,
74.125093473292, 79.1548876794736, 79.1548876794736, 81.6071301038229,
84.1009697961463, 84.1009697961463, 86.0472783823051, 86.4167923755497,
89.2608680025719, 89.2608680025719, 89.2608680025719, 92.7374320331654,
82.8087109204784, 69.567643114619, 68.0562327567284, 58.2185653891826,
48.2539781801277, 53.1986881679786, 49.033768692775, 47.9901183825881,
61.6089181051025, 57.1731265162146, 61.7616734481797, 63.221137287655,
70.1771943992812, 70.1771943992812, 79.9607457795924, 66.3010390829917,
68.5938260901332, 70.8011706594854, 76.343417368729, 77.3008696102273,
71.911133672881, 76.9180575079281, 80.0263157494416, 81.0569834689864,
78.7980499036461, 80.600192632844, 73.6449272697599, 63.4978113677881,
68.7589068199776, 81.1248114717251, 70.1544736530449, 76.542694603108,
69.1685415119339, 72.3553875493797, 66.3666023398198, 66.3666023398197
), .Dim = c(204L, 6L), .Dimnames = list(NULL, c("Open", "High",
"Low", "Close", "Volume", "RSI_10")), index = structure(c(1391794931,
1391796453, 1391798428, 1391799253, 1391800289, 1391801398, 1391801991,
1391802911, 1391804252, 1391805482, 1391806437, 1391807621, 1391809180,
1391810164, 1391811085, 1391811953, 1391812974, 1391813874, 1391814356,
1391815389, 1391816676, 1392054295, 1392055042, 1392055641, 1392056480,
1392057860, 1392058660, 1392061125, 1392061818, 1392062871, 1392064406,
1392069454, 1392071161, 1392072828, 1392073926, 1392074435, 1392075588,
1392139818, 1392141787, 1392143229, 1392144209, 1392144981, 1392145281,
1392146999, 1392147895, 1392150775, 1392153349, 1392157752, 1392157949,
1392161101, 1392162668, 1392223583, 1392225001, 1392226078, 1392227071,
1392227853, 1392228856, 1392229625, 1392232022, 1392232952, 1392234128,
1392235169, 1392235962, 1392237413, 1392238825, 1392247565, 1392248355,
1392248933, 1392312896, 1392314399, 1392314919, 1392318896, 1392319091,
1392324415, 1392328718, 1392328923, 1392330638, 1392332327, 1392333020,
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2 ответа
Сначала мы генерируем сплайн для всего набора данных. Во-вторых, мы используем эту функцию для интерполяции средних точек, все сразу (таким образом, векторизовано). Используя их и начальные значения функций, мы формируем правило Симпсона для каждого интервала, получая точный интеграл сплайна. Наконец, мы используем функцию быстрого броска, чтобы добавить эти частичные суммы для всех комбинированных интервалов.
spl <- splinefun(x1, y1) # cubic spline
n <- length(x1)
xmid <- (x1[-1] + x1[-n]) / 2 # midpoints
# Simpson's rule
sums <- diff(x1)/6 * (y1[-1] + 4*spl(xmid) + y1[-n])
library(RcppRoll)
areas <- roll_sum(sums, 4)
# check accuracy
matplot(cbind(areas,AUC_RSI10), t="l")
# comparing with piecewise linear integration of @BondedDust
points(rollapply(y1, FUN=sum, width=4, by=1), pch="+", cex=0.5)
Сроки результаты:
microbenchmark(
+ loop = {
+ AUC_RSI10 <- vector("numeric", length(y1)-4)
+ for(i in 1:(length(y1)-4))
+ {
+ AUC_RSI10[i]<-auc(x1,y1,from=i,to=i+4,type="spline")
+
+ }
+ }, simpson = {
+ spl <- splinefun(x1, y1)
+ n <- length(x1)
+ xmid <- (x1[-1] + x1[-n]) / 2
+ sums <- diff(x1)/6 * (y1[-1] + 4*spl(xmid) + y1[-n] )
+ areas <- roll_sum(sums, 4)
+ }
+ )
Unit: microseconds
expr min lq median uq max neval
loop 56828.857 59390.3055 68435.338 75537.2380 217565.279 100
simpson 283.399 307.3585 325.642 340.8675 603.664 100
Если вы посмотрите на расположение значений NA, вы обнаружите, что все они находятся в начале, поэтому простое их суммирование должно дать AUC по крайней мере с предположением, что разрыв между значениями x составляет всего 1.
> rle(is.na(coredata(myxts5)[, "RSI_10"]))
Run Length Encoding
lengths: int [1:2] 10 194
values : logi [1:2] TRUE FALSE
> sum(coredata(myxts5)[, "RSI_10"], na.rm=TRUE)
[1] 10998.76
na.interp Функция в pkg:zoo (которая, я думаю, прикрепляется при загрузке 'xts'), могла бы использоваться, если бы NA были распределены больше. Чтобы получить его в группах по 5 человек rollapply из "зоопарка":
> rollapply(coredata(myxts5)[, "RSI_10"], FUN=sum, width=5,by=5, na.rm=TRUE)
[1] 0.0000 0.0000 265.6250 240.2732 134.6175 211.5243 228.0486 266.6539 228.7223 240.6124
[11] 251.4329 221.3958 209.3340 267.2705 247.8771 278.8042 296.7200 231.1503 231.3596 254.7514
[21] 238.3585 265.2186 287.6986 287.6617 265.9073 281.2436 290.2518 310.1261 261.5776 293.9180
[31] 344.0697 387.5273 429.9269 423.6355 276.7612 291.7550 355.2100 373.2746 394.1265 360.0787