Applies a fast transform created by fort() (x) to the columns of a conformable matrix (y).
Arguments
- x
An object of class
FastTransform, created usingfort().- y
A numeric (real) matrix/vector with an appropriate number of rows/elements.
Examples
Z <- fort(4, 1024)
Z %*% matrix(1:2, 4, 3) # output is a 1024 by 3 matrix
#> [,1] [,2] [,3]
#> [1,] -0.0290930869 -0.0290930869 -0.0290930869
#> [2,] 0.2006377720 0.2006377720 0.2006377720
#> [3,] -0.1783199325 -0.1783199325 -0.1783199325
#> [4,] -0.0087004561 -0.0087004561 -0.0087004561
#> [5,] -0.1415586079 -0.1415586079 -0.1415586079
#> [6,] 0.1372779301 0.1372779301 0.1372779301
#> [7,] -0.0229740812 -0.0229740812 -0.0229740812
#> [8,] 0.0060670667 0.0060670667 0.0060670667
#> [9,] -0.1750277214 -0.1750277214 -0.1750277214
#> [10,] -0.0054613761 -0.0054613761 -0.0054613761
#> [11,] 0.0638834352 0.0638834352 0.0638834352
#> [12,] 0.2025368476 0.2025368476 0.2025368476
#> [13,] -0.1052959156 -0.1052959156 -0.1052959156
#> [14,] -0.0732125796 -0.0732125796 -0.0732125796
#> [15,] -0.0419988195 -0.0419988195 -0.0419988195
#> [16,] 0.1478413587 0.1478413587 0.1478413587
#> [17,] -0.0125152099 -0.0125152099 -0.0125152099
#> [18,] -0.2029197257 -0.2029197257 -0.2029197257
#> [19,] -0.0769434597 -0.0769434597 -0.0769434597
#> [20,] -0.0816832407 -0.0816832407 -0.0816832407
#> [21,] 0.0757040945 0.0757040945 0.0757040945
#> [22,] -0.0047333583 -0.0047333583 -0.0047333583
#> [23,] 0.1387442675 0.1387442675 0.1387442675
#> [24,] 0.1631681035 0.1631681035 0.1631681035
#> [25,] 0.0005502185 0.0005502185 0.0005502185
#> [26,] 0.0002758088 0.0002758088 0.0002758088
#> [27,] -0.0744448165 -0.0744448165 -0.0744448165
#> [28,] 0.0521269525 0.0521269525 0.0521269525
#> [29,] 0.0209285207 0.0209285207 0.0209285207
#> [30,] -0.1157826878 -0.1157826878 -0.1157826878
#> [31,] 0.0609549884 0.0609549884 0.0609549884
#> [32,] 0.0051473679 0.0051473679 0.0051473679
#> [33,] -0.0389808210 -0.0389808210 -0.0389808210
#> [34,] -0.0002784496 -0.0002784496 -0.0002784496
#> [35,] -0.0775853872 -0.0775853872 -0.0775853872
#> [36,] -0.2088426205 -0.2088426205 -0.2088426205
#> [37,] -0.1110392319 -0.1110392319 -0.1110392319
#> [38,] 0.0723969547 0.0723969547 0.0723969547
#> [39,] -0.1488360372 -0.1488360372 -0.1488360372
#> [40,] -0.1880208907 -0.1880208907 -0.1880208907
#> [41,] -0.1834542813 -0.1834542813 -0.1834542813
#> [42,] 0.1033502783 0.1033502783 0.1033502783
#> [43,] -0.0092115097 -0.0092115097 -0.0092115097
#> [44,] 0.1777028210 0.1777028210 0.1777028210
#> [45,] -0.0008057704 -0.0008057704 -0.0008057704
#> [46,] -0.1387218153 -0.1387218153 -0.1387218153
#> [47,] -0.1566339394 -0.1566339394 -0.1566339394
#> [48,] -0.1282867735 -0.1282867735 -0.1282867735
#> [49,] -0.0843588583 -0.0843588583 -0.0843588583
#> [50,] 0.1612764772 0.1612764772 0.1612764772
#> [51,] 0.1363766338 0.1363766338 0.1363766338
#> [52,] 0.0525414732 0.0525414732 0.0525414732
#> [53,] 0.0965888205 0.0965888205 0.0965888205
#> [54,] 0.0485752020 0.0485752020 0.0485752020
#> [55,] -0.0474435455 -0.0474435455 -0.0474435455
#> [56,] -0.0416071963 -0.0416071963 -0.0416071963
#> [57,] 0.0869233255 0.0869233255 0.0869233255
#> [58,] 0.0683836341 0.0683836341 0.0683836341
#> [59,] -0.1152491518 -0.1152491518 -0.1152491518
#> [60,] -0.1972199412 -0.1972199412 -0.1972199412
#> [61,] -0.0416543391 -0.0416543391 -0.0416543391
#> [62,] 0.1337776292 0.1337776292 0.1337776292
#> [63,] -0.0150181015 -0.0150181015 -0.0150181015
#> [64,] 0.1266447212 0.1266447212 0.1266447212
#> [65,] -0.0395332047 -0.0395332047 -0.0395332047
#> [66,] 0.0183570430 0.0183570430 0.0183570430
#> [67,] -0.1013007718 -0.1013007718 -0.1013007718
#> [68,] -0.1685770583 -0.1685770583 -0.1685770583
#> [69,] -0.0624906990 -0.0624906990 -0.0624906990
#> [70,] -0.0757257201 -0.0757257201 -0.0757257201
#> [71,] -0.0668470172 -0.0668470172 -0.0668470172
#> [72,] 0.0350293687 0.0350293687 0.0350293687
#> [73,] -0.2879287939 -0.2879287939 -0.2879287939
#> [74,] 0.0323490317 0.0323490317 0.0323490317
#> [75,] -0.0035659277 -0.0035659277 -0.0035659277
#> [76,] -0.0294385284 -0.0294385284 -0.0294385284
#> [77,] -0.0441280230 -0.0441280230 -0.0441280230
#> [78,] 0.0420390724 0.0420390724 0.0420390724
#> [79,] -0.0142385435 -0.0142385435 -0.0142385435
#> [80,] -0.1089650041 -0.1089650041 -0.1089650041
#> [81,] -0.0774290318 -0.0774290318 -0.0774290318
#> [82,] -0.1197746186 -0.1197746186 -0.1197746186
#> [83,] -0.0658847437 -0.0658847437 -0.0658847437
#> [84,] -0.1175003882 -0.1175003882 -0.1175003882
#> [85,] 0.1555722901 0.1555722901 0.1555722901
#> [86,] 0.0207196435 0.0207196435 0.0207196435
#> [87,] 0.0517584978 0.0517584978 0.0517584978
#> [88,] -0.0019734331 -0.0019734331 -0.0019734331
#> [89,] 0.1024439634 0.1024439634 0.1024439634
#> [90,] -0.1394646228 -0.1394646228 -0.1394646228
#> [91,] -0.0595280521 -0.0595280521 -0.0595280521
#> [92,] 0.0285499724 0.0285499724 0.0285499724
#> [93,] 0.1454887418 0.1454887418 0.1454887418
#> [94,] 0.0406594114 0.0406594114 0.0406594114
#> [95,] -0.0658039538 -0.0658039538 -0.0658039538
#> [96,] -0.0628183017 -0.0628183017 -0.0628183017
#> [97,] 0.0359524536 0.0359524536 0.0359524536
#> [98,] -0.0500164758 -0.0500164758 -0.0500164758
#> [99,] 0.1205277766 0.1205277766 0.1205277766
#> [100,] -0.0217766278 -0.0217766278 -0.0217766278
#> [101,] -0.0890287329 -0.0890287329 -0.0890287329
#> [102,] 0.1060223556 0.1060223556 0.1060223556
#> [103,] -0.0190896605 -0.0190896605 -0.0190896605
#> [104,] -0.0384928939 -0.0384928939 -0.0384928939
#> [105,] -0.0094553585 -0.0094553585 -0.0094553585
#> [106,] -0.0819993154 -0.0819993154 -0.0819993154
#> [107,] 0.0372197449 0.0372197449 0.0372197449
#> [108,] 0.0559119406 0.0559119406 0.0559119406
#> [109,] -0.0196936222 -0.0196936222 -0.0196936222
#> [110,] 0.0721276160 0.0721276160 0.0721276160
#> [111,] -0.0175625762 -0.0175625762 -0.0175625762
#> [112,] -0.0430945636 -0.0430945636 -0.0430945636
#> [113,] -0.0163687099 -0.0163687099 -0.0163687099
#> [114,] 0.0242935718 0.0242935718 0.0242935718
#> [115,] 0.0101511203 0.0101511203 0.0101511203
#> [116,] -0.0006926440 -0.0006926440 -0.0006926440
#> [117,] 0.1148523767 0.1148523767 0.1148523767
#> [118,] 0.0136641025 0.0136641025 0.0136641025
#> [119,] -0.1642236042 -0.1642236042 -0.1642236042
#> [120,] -0.0964358016 -0.0964358016 -0.0964358016
#> [121,] -0.0441961400 -0.0441961400 -0.0441961400
#> [122,] -0.0681256488 -0.0681256488 -0.0681256488
#> [123,] 0.1172458065 0.1172458065 0.1172458065
#> [124,] 0.0355303528 0.0355303528 0.0355303528
#> [125,] -0.0439248704 -0.0439248704 -0.0439248704
#> [126,] 0.0188715661 0.0188715661 0.0188715661
#> [127,] -0.0899777022 -0.0899777022 -0.0899777022
#> [128,] 0.1527151385 0.1527151385 0.1527151385
#> [129,] 0.0911062807 0.0911062807 0.0911062807
#> [130,] 0.0657403710 0.0657403710 0.0657403710
#> [131,] 0.0277508889 0.0277508889 0.0277508889
#> [132,] 0.1100610263 0.1100610263 0.1100610263
#> [133,] 0.0210021045 0.0210021045 0.0210021045
#> [134,] -0.0596223327 -0.0596223327 -0.0596223327
#> [135,] 0.0449782540 0.0449782540 0.0449782540
#> [136,] -0.0309740374 -0.0309740374 -0.0309740374
#> [137,] -0.0552232724 -0.0552232724 -0.0552232724
#> [138,] -0.0632898941 -0.0632898941 -0.0632898941
#> [139,] -0.1443317201 -0.1443317201 -0.1443317201
#> [140,] 0.1440916498 0.1440916498 0.1440916498
#> [141,] -0.0579199337 -0.0579199337 -0.0579199337
#> [142,] -0.1696296320 -0.1696296320 -0.1696296320
#> [143,] 0.1778280478 0.1778280478 0.1778280478
#> [144,] -0.0043193041 -0.0043193041 -0.0043193041
#> [145,] -0.0400986259 -0.0400986259 -0.0400986259
#> [146,] -0.0668756707 -0.0668756707 -0.0668756707
#> [147,] -0.1806917658 -0.1806917658 -0.1806917658
#> [148,] 0.0031773208 0.0031773208 0.0031773208
#> [149,] 0.0032660198 0.0032660198 0.0032660198
#> [150,] -0.2442484065 -0.2442484065 -0.2442484065
#> [151,] -0.0638831196 -0.0638831196 -0.0638831196
#> [152,] 0.0069147546 0.0069147546 0.0069147546
#> [153,] 0.1235358551 0.1235358551 0.1235358551
#> [154,] 0.0918461308 0.0918461308 0.0918461308
#> [155,] 0.1340577445 0.1340577445 0.1340577445
#> [156,] -0.0989412559 -0.0989412559 -0.0989412559
#> [157,] -0.0564012763 -0.0564012763 -0.0564012763
#> [158,] -0.1063263325 -0.1063263325 -0.1063263325
#> [159,] -0.1433919564 -0.1433919564 -0.1433919564
#> [160,] 0.0078463001 0.0078463001 0.0078463001
#> [161,] 0.2121792286 0.2121792286 0.2121792286
#> [162,] -0.1115727206 -0.1115727206 -0.1115727206
#> [163,] -0.0754800785 -0.0754800785 -0.0754800785
#> [164,] -0.0286971189 -0.0286971189 -0.0286971189
#> [165,] 0.1165304885 0.1165304885 0.1165304885
#> [166,] -0.1052440486 -0.1052440486 -0.1052440486
#> [167,] -0.0411659884 -0.0411659884 -0.0411659884
#> [168,] -0.0534455765 -0.0534455765 -0.0534455765
#> [169,] 0.1411085615 0.1411085615 0.1411085615
#> [170,] -0.0042269723 -0.0042269723 -0.0042269723
#> [171,] 0.0124031476 0.0124031476 0.0124031476
#> [172,] 0.0802941807 0.0802941807 0.0802941807
#> [173,] -0.0093924465 -0.0093924465 -0.0093924465
#> [174,] 0.0184972493 0.0184972493 0.0184972493
#> [175,] 0.0969846881 0.0969846881 0.0969846881
#> [176,] 0.0407766569 0.0407766569 0.0407766569
#> [177,] -0.0364492876 -0.0364492876 -0.0364492876
#> [178,] -0.0221469125 -0.0221469125 -0.0221469125
#> [179,] -0.0404332244 -0.0404332244 -0.0404332244
#> [180,] -0.0007301280 -0.0007301280 -0.0007301280
#> [181,] 0.0080480855 0.0080480855 0.0080480855
#> [182,] 0.0506677749 0.0506677749 0.0506677749
#> [183,] -0.2032901581 -0.2032901581 -0.2032901581
#> [184,] 0.1261651326 0.1261651326 0.1261651326
#> [185,] 0.0228748157 0.0228748157 0.0228748157
#> [186,] -0.1295062690 -0.1295062690 -0.1295062690
#> [187,] -0.0464462480 -0.0464462480 -0.0464462480
#> [188,] 0.0371922050 0.0371922050 0.0371922050
#> [189,] 0.0128718056 0.0128718056 0.0128718056
#> [190,] 0.0083327785 0.0083327785 0.0083327785
#> [191,] -0.0693780746 -0.0693780746 -0.0693780746
#> [192,] 0.1189885444 0.1189885444 0.1189885444
#> [193,] -0.2021608414 -0.2021608414 -0.2021608414
#> [194,] 0.0102391555 0.0102391555 0.0102391555
#> [195,] -0.1380757377 -0.1380757377 -0.1380757377
#> [196,] -0.0267773503 -0.0267773503 -0.0267773503
#> [197,] 0.0498067859 0.0498067859 0.0498067859
#> [198,] -0.1136758818 -0.1136758818 -0.1136758818
#> [199,] 0.1552408153 0.1552408153 0.1552408153
#> [200,] -0.0890280841 -0.0890280841 -0.0890280841
#> [201,] -0.1547157862 -0.1547157862 -0.1547157862
#> [202,] -0.1064948463 -0.1064948463 -0.1064948463
#> [203,] 0.0548894578 0.0548894578 0.0548894578
#> [204,] 0.0698325852 0.0698325852 0.0698325852
#> [205,] 0.1923883678 0.1923883678 0.1923883678
#> [206,] -0.0590817337 -0.0590817337 -0.0590817337
#> [207,] -0.1462758689 -0.1462758689 -0.1462758689
#> [208,] 0.0983060517 0.0983060517 0.0983060517
#> [209,] 0.0109401119 0.0109401119 0.0109401119
#> [210,] -0.0404110622 -0.0404110622 -0.0404110622
#> [211,] -0.0277674554 -0.0277674554 -0.0277674554
#> [212,] -0.0719388085 -0.0719388085 -0.0719388085
#> [213,] -0.0205009109 -0.0205009109 -0.0205009109
#> [214,] 0.0523374733 0.0523374733 0.0523374733
#> [215,] -0.2624513544 -0.2624513544 -0.2624513544
#> [216,] 0.0912611875 0.0912611875 0.0912611875
#> [217,] 0.1010537625 0.1010537625 0.1010537625
#> [218,] -0.0808855548 -0.0808855548 -0.0808855548
#> [219,] 0.0710540079 0.0710540079 0.0710540079
#> [220,] 0.1196327908 0.1196327908 0.1196327908
#> [221,] 0.0099506233 0.0099506233 0.0099506233
#> [222,] 0.1161246841 0.1161246841 0.1161246841
#> [223,] -0.1967895887 -0.1967895887 -0.1967895887
#> [224,] -0.0540756853 -0.0540756853 -0.0540756853
#> [225,] 0.1808351285 0.1808351285 0.1808351285
#> [226,] -0.0207897002 -0.0207897002 -0.0207897002
#> [227,] -0.0192258521 -0.0192258521 -0.0192258521
#> [228,] -0.0240067601 -0.0240067601 -0.0240067601
#> [229,] -0.0581505231 -0.0581505231 -0.0581505231
#> [230,] 0.0167990220 0.0167990220 0.0167990220
#> [231,] -0.0700831993 -0.0700831993 -0.0700831993
#> [232,] 0.0777810285 0.0777810285 0.0777810285
#> [233,] -0.0142305934 -0.0142305934 -0.0142305934
#> [234,] -0.0488550031 -0.0488550031 -0.0488550031
#> [235,] -0.0184883100 -0.0184883100 -0.0184883100
#> [236,] -0.0444810756 -0.0444810756 -0.0444810756
#> [237,] -0.0464608203 -0.0464608203 -0.0464608203
#> [238,] -0.2047486240 -0.2047486240 -0.2047486240
#> [239,] -0.1961379571 -0.1961379571 -0.1961379571
#> [240,] 0.0426367392 0.0426367392 0.0426367392
#> [241,] -0.0302568742 -0.0302568742 -0.0302568742
#> [242,] 0.0635735617 0.0635735617 0.0635735617
#> [243,] 0.1055593325 0.1055593325 0.1055593325
#> [244,] 0.0191346448 0.0191346448 0.0191346448
#> [245,] 0.0944311461 0.0944311461 0.0944311461
#> [246,] 0.1265966175 0.1265966175 0.1265966175
#> [247,] -0.0702904526 -0.0702904526 -0.0702904526
#> [248,] 0.0103845801 0.0103845801 0.0103845801
#> [249,] 0.0242353481 0.0242353481 0.0242353481
#> [250,] -0.0944885441 -0.0944885441 -0.0944885441
#> [251,] -0.0648021721 -0.0648021721 -0.0648021721
#> [252,] 0.0861960053 0.0861960053 0.0861960053
#> [253,] 0.0422031070 0.0422031070 0.0422031070
#> [254,] -0.1071362381 -0.1071362381 -0.1071362381
#> [255,] 0.0347560320 0.0347560320 0.0347560320
#> [256,] 0.1066777085 0.1066777085 0.1066777085
#> [257,] -0.0378867953 -0.0378867953 -0.0378867953
#> [258,] -0.0896937432 -0.0896937432 -0.0896937432
#> [259,] -0.0275584772 -0.0275584772 -0.0275584772
#> [260,] -0.1011849142 -0.1011849142 -0.1011849142
#> [261,] -0.0593692905 -0.0593692905 -0.0593692905
#> [262,] 0.0693153610 0.0693153610 0.0693153610
#> [263,] 0.1332386540 0.1332386540 0.1332386540
#> [264,] -0.0202882546 -0.0202882546 -0.0202882546
#> [265,] 0.0551439755 0.0551439755 0.0551439755
#> [266,] -0.1224055730 -0.1224055730 -0.1224055730
#> [267,] -0.1241813745 -0.1241813745 -0.1241813745
#> [268,] 0.1025661485 0.1025661485 0.1025661485
#> [269,] 0.1418729282 0.1418729282 0.1418729282
#> [270,] -0.2050897278 -0.2050897278 -0.2050897278
#> [271,] 0.0832546153 0.0832546153 0.0832546153
#> [272,] 0.0001264807 0.0001264807 0.0001264807
#> [273,] 0.0221913547 0.0221913547 0.0221913547
#> [274,] -0.1075398220 -0.1075398220 -0.1075398220
#> [275,] -0.1771814429 -0.1771814429 -0.1771814429
#> [276,] 0.1088948386 0.1088948386 0.1088948386
#> [277,] 0.0414818507 0.0414818507 0.0414818507
#> [278,] -0.0965753264 -0.0965753264 -0.0965753264
#> [279,] 0.0054257542 0.0054257542 0.0054257542
#> [280,] -0.0383780936 -0.0383780936 -0.0383780936
#> [281,] 0.0793009271 0.0793009271 0.0793009271
#> [282,] 0.0713315443 0.0713315443 0.0713315443
#> [283,] 0.0455334023 0.0455334023 0.0455334023
#> [284,] -0.1914704232 -0.1914704232 -0.1914704232
#> [285,] -0.0316370724 -0.0316370724 -0.0316370724
#> [286,] 0.0048255244 0.0048255244 0.0048255244
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#> [665,] 0.0739578623 0.0739578623 0.0739578623
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#> [680,] -0.2537446447 -0.2537446447 -0.2537446447
#> [681,] 0.0542676821 0.0542676821 0.0542676821
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#> [687,] -0.0435711781 -0.0435711781 -0.0435711781
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#> [719,] -0.0115935132 -0.0115935132 -0.0115935132
#> [720,] -0.1174247903 -0.1174247903 -0.1174247903
#> [721,] 0.1279606600 0.1279606600 0.1279606600
#> [722,] -0.1906398269 -0.1906398269 -0.1906398269
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#> [762,] -0.1247343762 -0.1247343762 -0.1247343762
#> [763,] 0.1571338185 0.1571338185 0.1571338185
#> [764,] 0.1640747722 0.1640747722 0.1640747722
#> [765,] 0.0183443442 0.0183443442 0.0183443442
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#> [767,] -0.0176095074 -0.0176095074 -0.0176095074
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#> [784,] 0.0658448355 0.0658448355 0.0658448355
#> [785,] 0.0746552086 0.0746552086 0.0746552086
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#> [793,] 0.1228781805 0.1228781805 0.1228781805
#> [794,] 0.0643814851 0.0643814851 0.0643814851
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#> [796,] -0.0335453747 -0.0335453747 -0.0335453747
#> [797,] 0.0462249777 0.0462249777 0.0462249777
#> [798,] -0.1926948098 -0.1926948098 -0.1926948098
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#> [800,] -0.1472364055 -0.1472364055 -0.1472364055
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#> [802,] 0.0489966308 0.0489966308 0.0489966308
#> [803,] -0.0213628012 -0.0213628012 -0.0213628012
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#> [805,] 0.0362049677 0.0362049677 0.0362049677
#> [806,] 0.0383489105 0.0383489105 0.0383489105
#> [807,] 0.0381021018 0.0381021018 0.0381021018
#> [808,] 0.0702803094 0.0702803094 0.0702803094
#> [809,] -0.0808856483 -0.0808856483 -0.0808856483
#> [810,] 0.0182979169 0.0182979169 0.0182979169
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#> [812,] -0.0045301808 -0.0045301808 -0.0045301808
#> [813,] -0.0954097897 -0.0954097897 -0.0954097897
#> [814,] -0.0487697942 -0.0487697942 -0.0487697942
#> [815,] 0.1549398664 0.1549398664 0.1549398664
#> [816,] -0.0890674607 -0.0890674607 -0.0890674607
#> [817,] 0.0848067858 0.0848067858 0.0848067858
#> [818,] -0.0683082824 -0.0683082824 -0.0683082824
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#> [820,] -0.0637954096 -0.0637954096 -0.0637954096
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#> [829,] -0.0087365671 -0.0087365671 -0.0087365671
#> [830,] 0.0051860461 0.0051860461 0.0051860461
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#> [832,] -0.0124636164 -0.0124636164 -0.0124636164
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#> [834,] 0.2310946652 0.2310946652 0.2310946652
#> [835,] -0.1243010937 -0.1243010937 -0.1243010937
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#> [837,] 0.0004967239 0.0004967239 0.0004967239
#> [838,] 0.0478476167 0.0478476167 0.0478476167
#> [839,] 0.0708655313 0.0708655313 0.0708655313
#> [840,] 0.0094707220 0.0094707220 0.0094707220
#> [841,] 0.1598624188 0.1598624188 0.1598624188
#> [842,] 0.1784030856 0.1784030856 0.1784030856
#> [843,] 0.0827545604 0.0827545604 0.0827545604
#> [844,] -0.0515869554 -0.0515869554 -0.0515869554
#> [845,] -0.1387879324 -0.1387879324 -0.1387879324
#> [846,] 0.1005734148 0.1005734148 0.1005734148
#> [847,] 0.0216828541 0.0216828541 0.0216828541
#> [848,] 0.1226038160 0.1226038160 0.1226038160
#> [849,] -0.0581284018 -0.0581284018 -0.0581284018
#> [850,] 0.0372200171 0.0372200171 0.0372200171
#> [851,] -0.1179351957 -0.1179351957 -0.1179351957
#> [852,] -0.1183216598 -0.1183216598 -0.1183216598
#> [853,] 0.0270206811 0.0270206811 0.0270206811
#> [854,] -0.1107371350 -0.1107371350 -0.1107371350
#> [855,] -0.0818647768 -0.0818647768 -0.0818647768
#> [856,] -0.0807574418 -0.0807574418 -0.0807574418
#> [857,] -0.1419815399 -0.1419815399 -0.1419815399
#> [858,] 0.1906424021 0.1906424021 0.1906424021
#> [859,] -0.0693161848 -0.0693161848 -0.0693161848
#> [860,] -0.0901256394 -0.0901256394 -0.0901256394
#> [861,] 0.2438584816 0.2438584816 0.2438584816
#> [862,] -0.1198421481 -0.1198421481 -0.1198421481
#> [863,] -0.1235684566 -0.1235684566 -0.1235684566
#> [864,] -0.0267609496 -0.0267609496 -0.0267609496
#> [865,] 0.0006985794 0.0006985794 0.0006985794
#> [866,] -0.0594021005 -0.0594021005 -0.0594021005
#> [867,] 0.1431464031 0.1431464031 0.1431464031
#> [868,] 0.0816499840 0.0816499840 0.0816499840
#> [869,] -0.0421300992 -0.0421300992 -0.0421300992
#> [870,] -0.0524654758 -0.0524654758 -0.0524654758
#> [871,] -0.0126753985 -0.0126753985 -0.0126753985
#> [872,] 0.0047168521 0.0047168521 0.0047168521
#> [873,] -0.1384428301 -0.1384428301 -0.1384428301
#> [874,] -0.0182618508 -0.0182618508 -0.0182618508
#> [875,] -0.1904990976 -0.1904990976 -0.1904990976
#> [876,] -0.1520672249 -0.1520672249 -0.1520672249
#> [877,] 0.0663764962 0.0663764962 0.0663764962
#> [878,] -0.0388758137 -0.0388758137 -0.0388758137
#> [879,] -0.0139941206 -0.0139941206 -0.0139941206
#> [880,] -0.0521789634 -0.0521789634 -0.0521789634
#> [881,] -0.0801226723 -0.0801226723 -0.0801226723
#> [882,] 0.0465752100 0.0465752100 0.0465752100
#> [883,] 0.1076840608 0.1076840608 0.1076840608
#> [884,] 0.0623794721 0.0623794721 0.0623794721
#> [885,] 0.1604908759 0.1604908759 0.1604908759
#> [886,] 0.0434779809 0.0434779809 0.0434779809
#> [887,] -0.0081338896 -0.0081338896 -0.0081338896
#> [888,] -0.0497004603 -0.0497004603 -0.0497004603
#> [889,] 0.0422752429 0.0422752429 0.0422752429
#> [890,] -0.2084298654 -0.2084298654 -0.2084298654
#> [891,] -0.0961312668 -0.0961312668 -0.0961312668
#> [892,] 0.0339049420 0.0339049420 0.0339049420
#> [893,] -0.0126459849 -0.0126459849 -0.0126459849
#> [894,] -0.0905183567 -0.0905183567 -0.0905183567
#> [895,] 0.0139753808 0.0139753808 0.0139753808
#> [896,] 0.0043335746 0.0043335746 0.0043335746
#> [897,] -0.0349121300 -0.0349121300 -0.0349121300
#> [898,] -0.0462410471 -0.0462410471 -0.0462410471
#> [899,] -0.0600126634 -0.0600126634 -0.0600126634
#> [900,] 0.0307373550 0.0307373550 0.0307373550
#> [901,] 0.0955190615 0.0955190615 0.0955190615
#> [902,] 0.0821264187 0.0821264187 0.0821264187
#> [903,] -0.0263196422 -0.0263196422 -0.0263196422
#> [904,] -0.0715039847 -0.0715039847 -0.0715039847
#> [905,] 0.1548443524 0.1548443524 0.1548443524
#> [906,] 0.1285849331 0.1285849331 0.1285849331
#> [907,] -0.1040763342 -0.1040763342 -0.1040763342
#> [908,] -0.0208595347 -0.0208595347 -0.0208595347
#> [909,] 0.0705040477 0.0705040477 0.0705040477
#> [910,] 0.0519555458 0.0519555458 0.0519555458
#> [911,] 0.0284457582 0.0284457582 0.0284457582
#> [912,] -0.0365184610 -0.0365184610 -0.0365184610
#> [913,] -0.0226336127 -0.0226336127 -0.0226336127
#> [914,] -0.1344050249 -0.1344050249 -0.1344050249
#> [915,] -0.0254093006 -0.0254093006 -0.0254093006
#> [916,] 0.1655253056 0.1655253056 0.1655253056
#> [917,] -0.1303240394 -0.1303240394 -0.1303240394
#> [918,] -0.0897472315 -0.0897472315 -0.0897472315
#> [919,] 0.0214208830 0.0214208830 0.0214208830
#> [920,] -0.0866092127 -0.0866092127 -0.0866092127
#> [921,] -0.0558654351 -0.0558654351 -0.0558654351
#> [922,] -0.1079081031 -0.1079081031 -0.1079081031
#> [923,] 0.0230867459 0.0230867459 0.0230867459
#> [924,] 0.0276533824 0.0276533824 0.0276533824
#> [925,] 0.0726589093 0.0726589093 0.0726589093
#> [926,] -0.1021939480 -0.1021939480 -0.1021939480
#> [927,] 0.0489438382 0.0489438382 0.0489438382
#> [928,] -0.0880305550 -0.0880305550 -0.0880305550
#> [929,] -0.0177965326 -0.0177965326 -0.0177965326
#> [930,] -0.1234337486 -0.1234337486 -0.1234337486
#> [931,] 0.0625443973 0.0625443973 0.0625443973
#> [932,] 0.0697990029 0.0697990029 0.0697990029
#> [933,] -0.2088152142 -0.2088152142 -0.2088152142
#> [934,] 0.0205728742 0.0205728742 0.0205728742
#> [935,] 0.0570224708 0.0570224708 0.0570224708
#> [936,] 0.0089458590 0.0089458590 0.0089458590
#> [937,] -0.0127134409 -0.0127134409 -0.0127134409
#> [938,] -0.0116448453 -0.0116448453 -0.0116448453
#> [939,] -0.0606501099 -0.0606501099 -0.0606501099
#> [940,] 0.0178898318 0.0178898318 0.0178898318
#> [941,] 0.1176389563 0.1176389563 0.1176389563
#> [942,] 0.0368415760 0.0368415760 0.0368415760
#> [943,] 0.0944428117 0.0944428117 0.0944428117
#> [944,] -0.0023227298 -0.0023227298 -0.0023227298
#> [945,] -0.0108405658 -0.0108405658 -0.0108405658
#> [946,] -0.0144770996 -0.0144770996 -0.0144770996
#> [947,] -0.0135967790 -0.0135967790 -0.0135967790
#> [948,] -0.1321284037 -0.1321284037 -0.1321284037
#> [949,] 0.1386089260 0.1386089260 0.1386089260
#> [950,] -0.0335070021 -0.0335070021 -0.0335070021
#> [951,] -0.2717395472 -0.2717395472 -0.2717395472
#> [952,] -0.0892284150 -0.0892284150 -0.0892284150
#> [953,] 0.0865028736 0.0865028736 0.0865028736
#> [954,] 0.0609045249 0.0609045249 0.0609045249
#> [955,] -0.0953447978 -0.0953447978 -0.0953447978
#> [956,] -0.0772889613 -0.0772889613 -0.0772889613
#> [957,] -0.1655211614 -0.1655211614 -0.1655211614
#> [958,] -0.1162030613 -0.1162030613 -0.1162030613
#> [959,] -0.2565364479 -0.2565364479 -0.2565364479
#> [960,] 0.0806884391 0.0806884391 0.0806884391
#> [961,] -0.0266378501 -0.0266378501 -0.0266378501
#> [962,] -0.0539377927 -0.0539377927 -0.0539377927
#> [963,] -0.0228132964 -0.0228132964 -0.0228132964
#> [964,] 0.0777617269 0.0777617269 0.0777617269
#> [965,] 0.0324030885 0.0324030885 0.0324030885
#> [966,] -0.0252790274 -0.0252790274 -0.0252790274
#> [967,] 0.1716286087 0.1716286087 0.1716286087
#> [968,] -0.0310960642 -0.0310960642 -0.0310960642
#> [969,] -0.1873891690 -0.1873891690 -0.1873891690
#> [970,] -0.2048118726 -0.2048118726 -0.2048118726
#> [971,] 0.0501029969 0.0501029969 0.0501029969
#> [972,] 0.0660956454 0.0660956454 0.0660956454
#> [973,] -0.0285971911 -0.0285971911 -0.0285971911
#> [974,] -0.2298224093 -0.2298224093 -0.2298224093
#> [975,] 0.0209603310 0.0209603310 0.0209603310
#> [976,] 0.0524157250 0.0524157250 0.0524157250
#> [977,] 0.1095977827 0.1095977827 0.1095977827
#> [978,] -0.0749095053 -0.0749095053 -0.0749095053
#> [979,] 0.2403451604 0.2403451604 0.2403451604
#> [980,] -0.0615952089 -0.0615952089 -0.0615952089
#> [981,] 0.0922311854 0.0922311854 0.0922311854
#> [982,] 0.1096281928 0.1096281928 0.1096281928
#> [983,] 0.0587378142 0.0587378142 0.0587378142
#> [984,] 0.1370770517 0.1370770517 0.1370770517
#> [985,] -0.0214805304 -0.0214805304 -0.0214805304
#> [986,] 0.0395332083 0.0395332083 0.0395332083
#> [987,] -0.0020359466 -0.0020359466 -0.0020359466
#> [988,] 0.1632399862 0.1632399862 0.1632399862
#> [989,] 0.0041397207 0.0041397207 0.0041397207
#> [990,] 0.0450580574 0.0450580574 0.0450580574
#> [991,] -0.0185630714 -0.0185630714 -0.0185630714
#> [992,] 0.0824262153 0.0824262153 0.0824262153
#> [993,] 0.0284552988 0.0284552988 0.0284552988
#> [994,] 0.0779176846 0.0779176846 0.0779176846
#> [995,] 0.0888456493 0.0888456493 0.0888456493
#> [996,] 0.2409231009 0.2409231009 0.2409231009
#> [997,] 0.0596515510 0.0596515510 0.0596515510
#> [998,] 0.0405336691 0.0405336691 0.0405336691
#> [999,] 0.0556948819 0.0556948819 0.0556948819
#> [1000,] 0.0888777299 0.0888777299 0.0888777299
#> [1001,] -0.0753624828 -0.0753624828 -0.0753624828
#> [1002,] -0.0575553018 -0.0575553018 -0.0575553018
#> [1003,] -0.0609511928 -0.0609511928 -0.0609511928
#> [1004,] -0.0278070627 -0.0278070627 -0.0278070627
#> [1005,] 0.2121225452 0.2121225452 0.2121225452
#> [1006,] -0.1284395775 -0.1284395775 -0.1284395775
#> [1007,] -0.0567501579 -0.0567501579 -0.0567501579
#> [1008,] 0.1211979006 0.1211979006 0.1211979006
#> [1009,] -0.0025128511 -0.0025128511 -0.0025128511
#> [1010,] 0.0600197814 0.0600197814 0.0600197814
#> [1011,] 0.0367982644 0.0367982644 0.0367982644
#> [1012,] 0.0704874298 0.0704874298 0.0704874298
#> [1013,] 0.1764797164 0.1764797164 0.1764797164
#> [1014,] -0.0111603093 -0.0111603093 -0.0111603093
#> [1015,] 0.0515297806 0.0515297806 0.0515297806
#> [1016,] -0.0577966040 -0.0577966040 -0.0577966040
#> [1017,] 0.0296574337 0.0296574337 0.0296574337
#> [1018,] -0.1150115718 -0.1150115718 -0.1150115718
#> [1019,] 0.0901527674 0.0901527674 0.0901527674
#> [1020,] -0.0411556449 -0.0411556449 -0.0411556449
#> [1021,] -0.0177919339 -0.0177919339 -0.0177919339
#> [1022,] 0.0450993959 0.0450993959 0.0450993959
#> [1023,] 0.1282258166 0.1282258166 0.1282258166
#> [1024,] -0.0538863135 -0.0538863135 -0.0538863135
# the example below works: y is assumed to be a single column vector
Z %*% 1:4 # output is a 1024 by 1 matrix
#> [,1]
#> [1,] -0.1024273936
#> [2,] 0.2471246702
#> [3,] -0.2118561256
#> [4,] -0.0499997617
#> [5,] -0.2567716123
#> [6,] 0.1705893259
#> [7,] 0.0116800207
#> [8,] -0.0196879886
#> [9,] -0.2492445544
#> [10,] -0.1048042743
#> [11,] 0.1705051724
#> [12,] 0.2847100270
#> [13,] -0.1891102370
#> [14,] -0.0295827597
#> [15,] 0.0144298540
#> [16,] 0.1400549445
#> [17,] -0.0001919398
#> [18,] -0.2585098482
#> [19,] -0.1070890266
#> [20,] -0.0946372256
#> [21,] 0.1213174481
#> [22,] 0.1073357127
#> [23,] 0.2595999230
#> [24,] 0.1698895547
#> [25,] 0.1612732496
#> [26,] 0.0152937734
#> [27,] -0.1421922274
#> [28,] 0.2588465899
#> [29,] 0.1785088510
#> [30,] -0.0943683137
#> [31,] 0.1946004796
#> [32,] -0.0809650745
#> [33,] -0.0685680168
#> [34,] 0.0285322901
#> [35,] -0.1031159237
#> [36,] -0.3000170991
#> [37,] -0.2311382559
#> [38,] 0.0850982467
#> [39,] -0.2658562822
#> [40,] -0.2154115598
#> [41,] -0.2474502885
#> [42,] 0.2910721006
#> [43,] 0.0029668505
#> [44,] 0.2502507651
#> [45,] 0.0426902469
#> [46,] -0.1651044956
#> [47,] -0.2929992846
#> [48,] -0.1477097434
#> [49,] -0.0612741054
#> [50,] 0.2265445320
#> [51,] 0.2578055235
#> [52,] 0.1193086931
#> [53,] 0.1166742076
#> [54,] 0.0469391803
#> [55,] -0.1228550805
#> [56,] 0.0041374011
#> [57,] 0.0455094645
#> [58,] 0.1292887517
#> [59,] -0.1681831439
#> [60,] -0.3172403382
#> [61,] 0.0034822174
#> [62,] 0.2159599325
#> [63,] -0.0349098732
#> [64,] 0.1615386168
#> [65,] -0.0640190367
#> [66,] -0.0088475068
#> [67,] -0.1433507705
#> [68,] -0.3452283289
#> [69,] -0.1845785787
#> [70,] -0.0545671266
#> [71,] -0.0621116527
#> [72,] 0.0347822476
#> [73,] -0.4863738592
#> [74,] -0.0187883242
#> [75,] -0.0462665843
#> [76,] -0.0951253023
#> [77,] -0.1490635910
#> [78,] -0.0130274843
#> [79,] -0.1416159543
#> [80,] -0.1519576616
#> [81,] -0.1821830747
#> [82,] -0.2640266783
#> [83,] -0.0618713032
#> [84,] -0.2544077052
#> [85,] 0.1947906716
#> [86,] 0.0777071046
#> [87,] -0.0116187197
#> [88,] 0.0171744764
#> [89,] 0.1888164623
#> [90,] -0.1903190145
#> [91,] -0.0342505652
#> [92,] 0.0581303138
#> [93,] 0.1853182300
#> [94,] 0.1416806570
#> [95,] -0.1435283821
#> [96,] -0.1671904126
#> [97,] 0.0527292121
#> [98,] -0.2682312707
#> [99,] 0.1926808042
#> [100,] -0.0211084762
#> [101,] -0.1255302879
#> [102,] 0.1744891348
#> [103,] -0.0484005494
#> [104,] -0.1181495755
#> [105,] -0.1926482656
#> [106,] -0.1807516028
#> [107,] -0.0041512518
#> [108,] 0.0126435277
#> [109,] -0.0550971288
#> [110,] 0.0926321552
#> [111,] -0.0803357562
#> [112,] -0.1457993686
#> [113,] -0.0315207127
#> [114,] 0.1049610346
#> [115,] 0.0243925057
#> [116,] 0.0104316672
#> [117,] 0.1419466992
#> [118,] -0.0435598043
#> [119,] -0.2810299924
#> [120,] -0.2447658308
#> [121,] -0.1077847395
#> [122,] -0.1991266244
#> [123,] 0.2192769979
#> [124,] 0.1127394292
#> [125,] -0.0019251512
#> [126,] 0.1290563667
#> [127,] -0.2583261106
#> [128,] 0.3332732978
#> [129,] 0.1674558919
#> [130,] 0.0272227213
#> [131,] -0.1315199974
#> [132,] 0.1826064795
#> [133,] 0.0876016465
#> [134,] -0.1011966422
#> [135,] 0.0124212657
#> [136,] 0.0492843371
#> [137,] -0.1072690589
#> [138,] -0.1425361341
#> [139,] -0.3177846995
#> [140,] 0.3262117333
#> [141,] -0.0446356972
#> [142,] -0.2067576040
#> [143,] 0.2297022732
#> [144,] -0.0061162116
#> [145,] -0.0358430715
#> [146,] -0.0735400777
#> [147,] -0.1892988374
#> [148,] 0.0483058133
#> [149,] -0.0766443139
#> [150,] -0.3428549032
#> [151,] 0.0857624114
#> [152,] 0.0334499269
#> [153,] 0.2580833968
#> [154,] 0.3163427489
#> [155,] 0.2818024452
#> [156,] -0.1441707545
#> [157,] -0.1500635327
#> [158,] -0.2102141455
#> [159,] -0.2402601331
#> [160,] 0.0074366242
#> [161,] 0.3146351837
#> [162,] -0.1670749880
#> [163,] -0.0805105320
#> [164,] -0.0369163323
#> [165,] 0.1576635641
#> [166,] -0.0644289969
#> [167,] 0.0166877801
#> [168,] -0.0157750989
#> [169,] 0.2635143705
#> [170,] 0.0294235049
#> [171,] 0.0521053307
#> [172,] 0.0649795978
#> [173,] -0.0430630973
#> [174,] 0.1040142205
#> [175,] 0.2144136142
#> [176,] 0.2090222497
#> [177,] -0.1816317237
#> [178,] -0.1006482627
#> [179,] -0.1248001077
#> [180,] -0.0368960149
#> [181,] 0.0800146209
#> [182,] 0.0733788766
#> [183,] -0.3172326830
#> [184,] 0.1702246463
#> [185,] 0.0222679722
#> [186,] -0.1819615046
#> [187,] -0.1175743967
#> [188,] 0.1294372449
#> [189,] -0.0247132557
#> [190,] -0.0584482297
#> [191,] -0.1001521003
#> [192,] 0.1822698902
#> [193,] -0.3378330485
#> [194,] 0.2124985480
#> [195,] -0.1841366691
#> [196,] -0.0358451167
#> [197,] 0.0506132327
#> [198,] -0.1604172305
#> [199,] 0.2211611408
#> [200,] -0.1565133308
#> [201,] -0.3669976754
#> [202,] -0.2569550667
#> [203,] -0.0136035271
#> [204,] 0.0643415842
#> [205,] 0.3802924647
#> [206,] -0.1411754401
#> [207,] -0.1617029072
#> [208,] 0.3088205392
#> [209,] -0.0277080982
#> [210,] -0.0475317631
#> [211,] -0.0118784458
#> [212,] -0.1129855989
#> [213,] 0.0329256327
#> [214,] 0.1095958389
#> [215,] -0.4527450385
#> [216,] 0.2213302897
#> [217,] 0.2214806729
#> [218,] -0.1250364152
#> [219,] 0.1695462185
#> [220,] 0.2008453563
#> [221,] -0.0120335309
#> [222,] 0.2674120607
#> [223,] -0.3081586413
#> [224,] 0.0297540120
#> [225,] 0.2692490173
#> [226,] 0.0205531779
#> [227,] 0.0245883821
#> [228,] 0.1007247022
#> [229,] -0.1639262650
#> [230,] 0.0175448383
#> [231,] -0.0409250004
#> [232,] 0.2021188216
#> [233,] 0.0527201856
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