Compute Spacing Measuring Functions
space_measuring_functions.RdThis function is used to compute discretized functions, i.e. vectors, to explore functional spaces.
Arguments
- X
A dfts object or data which can be automatically converted to that format. See
dfts().- M
Integer for the number of functions to generate.
- space
String for the space of interest. Options are Brownian motion ('BM'), principal components ('PC'), and vectors in iid standard, random normals ('RN'). Additional options are forthcoming
Value
Data.frame with columns of discretized functions describing the space. Columns are independent functions.
Examples
space_measuring_functions(M = 10, space = "BM", X = electricity)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000
#> [2,] 0.078001258 -0.171349465 0.12742486 -0.196639685 0.05516466
#> [3,] 0.253053660 -0.202344557 -0.01633313 -0.149734673 -0.05002370
#> [4,] 0.092199836 -0.105931430 -0.11420821 -0.171400717 0.06726889
#> [5,] 0.063398747 0.136527817 -0.23801983 -0.205748501 -0.17258595
#> [6,] 0.188821972 -0.001141092 0.03060114 -0.150644905 -0.97253284
#> [7,] -0.162313110 0.231114112 0.06292841 -0.353230451 -0.87721631
#> [8,] -0.089546938 0.175141302 0.14370289 -0.079470461 -0.37887023
#> [9,] 0.261584854 0.110710609 0.04042730 -0.125683968 -0.47211747
#> [10,] -0.146686212 -0.075302614 -0.21859257 -0.358792137 -0.25725992
#> [11,] -0.083371764 -0.161113734 0.26509796 -0.432591858 -0.36740940
#> [12,] 0.157745114 -0.121278691 -0.01012542 -0.161162451 -0.43414008
#> [13,] -0.032988361 -0.243160027 -0.14245002 -0.291100096 -0.30137833
#> [14,] 0.259987047 -0.339774195 -0.24474682 -0.282577852 -0.29546694
#> [15,] -0.089765872 -0.158071627 -0.48475143 -0.093378767 -0.41976945
#> [16,] -0.246591800 -0.257519775 -0.41828340 0.020455691 -0.34892386
#> [17,] 0.008615776 -0.147166420 -0.60993303 0.006237936 -0.21744057
#> [18,] 0.047790860 -0.004543640 -0.30239849 0.137984804 0.11176375
#> [19,] -0.040011134 0.028451383 -0.29294721 0.225642528 0.04630933
#> [20,] -0.047250990 -0.101190703 -0.12444760 0.323067722 0.18831404
#> [21,] -0.039875365 -0.066313572 -0.35076761 0.276543166 0.39179475
#> [22,] -0.021683592 0.102087806 -0.29352052 0.464202942 0.44182851
#> [23,] -0.161991322 0.339324773 -0.17689579 0.806367766 0.33016185
#> [24,] -0.253144200 -0.037932890 0.11645772 0.503683351 0.24927709
#> [,6] [,7] [,8] [,9] [,10]
#> [1,] 0.00000000 0.000000000 0.00000000 0.000000000 0.000000000
#> [2,] 0.13842097 0.003430832 -0.15943614 -0.014860070 -0.058858336
#> [3,] 0.30238813 -0.292610329 -0.29296958 -0.335369213 -0.146564039
#> [4,] 0.20836161 0.088738971 -0.45133904 -0.333876299 -0.134823327
#> [5,] -0.02907600 0.077200869 -0.55538430 -0.414993593 -0.151280179
#> [6,] -0.18514063 0.016351716 -0.48238686 -0.157231200 -0.014713781
#> [7,] 0.02605086 0.012739571 -0.71945668 -0.047946965 0.225704497
#> [8,] 0.37405285 0.140528061 -0.96189948 -0.066990228 0.008375134
#> [9,] 0.25600140 0.087387995 -1.01781593 0.162130175 -0.272125951
#> [10,] 0.53351589 -0.222758043 -0.95543007 0.059727156 -0.376090354
#> [11,] 0.21162480 -0.246788989 -0.74028042 0.041213865 -0.220799537
#> [12,] 0.39496637 -0.040848938 -0.49444418 0.088763546 -0.089773938
#> [13,] 0.36724032 0.039932832 -0.56192026 0.123911408 -0.211390305
#> [14,] 0.39714337 0.290339771 -0.57345590 0.298551225 -0.312139998
#> [15,] 0.44345087 0.224001609 -0.49009371 -0.007347947 -0.543529982
#> [16,] 0.47412043 0.388355451 -0.46767348 0.016875160 -0.521768568
#> [17,] 0.37376405 0.371740130 -0.47992230 0.117218187 -0.578619069
#> [18,] 0.10787273 0.056320443 -0.17069044 -0.108333855 -0.664595980
#> [19,] -0.20065886 0.418236309 -0.04785981 0.365829683 -0.649893395
#> [20,] -0.15969953 0.548672014 -0.58772902 0.232289276 -0.593650837
#> [21,] -0.39602285 0.627075419 -1.01807661 0.245306270 -0.532503829
#> [22,] 0.26507032 0.604072546 -0.86008258 0.283946801 -0.312910458
#> [23,] 0.39362130 0.656326862 -0.91534660 0.324382200 -0.427845622
#> [24,] 0.57893608 0.526250093 -1.05487117 0.154622278 -0.533527105
space_measuring_functions(M = 10, space = "PC", X = electricity)
#> V1 V2 V3 V4 V5 V6
#> 1 146.68738 -8.147271 -857.04082 -58.46399 -99.75877 -356.5924
#> 2 361.84495 128.014796 706.64380 -1024.69043 1476.59352 -975.4319
#> 3 927.91943 -2054.157073 142.78603 477.83078 -1142.35369 -480.4093
#> 4 1320.11248 -164.493674 -1141.22770 -318.39312 689.62647 -1176.8475
#> 5 559.12121 -149.885713 -718.39386 72.14414 248.23730 -692.0707
#> 6 998.68341 -55.893519 -1501.58501 -115.19965 -1239.16444 -2341.4307
#> 7 158.04052 -365.914914 480.34949 1123.23523 -64.00014 159.6705
#> 8 -25.23838 -517.545103 763.39323 -1312.69805 -593.84958 905.9648
#> 9 138.50518 -1601.746852 140.45119 1981.38529 1230.03973 1143.0585
#> 10 -1102.89599 -4.355295 -47.37350 1071.42055 -13.09542 -1034.3718
#> 11 -1739.81857 372.539832 830.31611 -502.49262 -339.82662 -143.0574
#> 12 1773.31196 1638.208496 443.64036 560.26313 -170.52545 -1549.8707
#> 13 -1168.20483 1506.774640 16.08534 -166.85966 476.25809 613.4910
#> 14 245.61424 -282.140860 226.16997 -632.69545 -188.69584 1056.5878
#> 15 802.41649 1014.918868 864.78984 -606.97973 646.37779 -1792.0119
#> 16 -779.46109 -926.404413 700.07770 -1002.67672 1068.91701 -543.4961
#> 17 -175.50579 274.386056 -1363.19452 -1201.14368 1209.46229 458.7319
#> 18 -304.03318 -1028.257379 71.29990 1151.05035 -394.76878 -1057.0003
#> 19 130.66722 375.367930 -354.82867 -1184.69822 659.33384 -117.5622
#> 20 -1084.61348 -741.461674 -828.98513 -203.46038 -956.92022 328.5583
#> 21 1106.54395 1262.928876 -603.42127 390.60913 1760.99046 -1521.9477
#> 22 809.62453 403.644559 257.11091 716.00084 1077.61423 -794.5305
#> 23 -434.79316 -556.945400 1352.66753 -1118.20050 611.85995 -330.4368
#> 24 1021.71302 -712.559479 -306.78116 -132.13000 667.38079 334.2143
#> V7 V8 V9 V10
#> 1 1335.6109 315.0484 448.097605 840.2469
#> 2 325.9436 27.8203 -307.795939 435.8517
#> 3 -1063.1439 921.0491 433.119859 324.8692
#> 4 972.9142 -704.2226 -367.289297 -1380.0860
#> 5 -870.1990 1265.4994 -493.221185 -219.9842
#> 6 -1354.6273 838.0989 -7.507341 -183.7419
#> 7 170.1528 199.4609 -821.843013 -26.7916
#> 8 315.8206 539.1646 573.038312 -942.8285
#> 9 1355.1138 -358.1488 -300.714855 -688.4177
#> 10 107.7776 -600.3925 574.378396 1636.3607
#> 11 -163.4082 174.2887 -663.137789 -320.7157
#> 12 -752.2276 -571.6366 275.167355 -669.2234
#> 13 861.4064 -1154.1089 1782.872765 -610.1286
#> 14 2257.7097 -1386.9069 602.148774 -631.2297
#> 15 723.5664 1569.6106 741.423495 -2082.0083
#> 16 -71.4953 367.8151 1021.392478 313.3734
#> 17 -1009.8972 -728.1749 -108.119635 225.8127
#> 18 -1496.6838 -2918.8029 -170.542391 -112.5641
#> 19 -2594.1546 -800.1695 1435.613103 613.8603
#> 20 293.0887 -2020.4627 356.221249 563.5511
#> 21 -338.8389 573.7229 -570.108960 -357.2595
#> 22 -117.5313 125.4535 -1969.038525 -1788.7135
#> 23 -547.7483 -125.0167 -75.938427 418.5502
#> 24 729.5815 709.1740 398.505815 -655.5780