Generates spline basis matrices for fitting to time-course function

Usage

genspline(
  x,
  spline = "bs",
  knots = NULL,
  nknots = 1,
  degree = 1,
  max.time = max(x),
  boundaries = NULL
)

Arguments

x: A numeric vector indicating all time points available in the dataset
spline: Indicates the type of spline function. Can be either a piecewise linear spline ("ls"), natural cubic spline ("ns") or B-spline ("bs").
knots: A numeric vector indicating the location of spline internal knots (specified on the same scale as time in the dataset). Specifying knots overrides nknots.
nknots: The number of spline internal knots. If knots is not specified then these will by default be evenly spaced between 0 and the maximum follow-up time in the dataset (max.time).
degree: a positive integer giving the degree of the polynomial from which the spline function is composed (e.g. degree=3 represents a cubic spline).
max.time: A number indicating the maximum time between which to calculate the spline function.
boundaries: A positive numeric vector of length 2 that represents the time-points at which to anchor the B-spline or natural cubic spline basis matrix. This allows data to extend beyond the boundary knots, or for the basis parameters to not depend on x. The default (boundaries=NULL)is the range of x.

Value

A spline basis matrix with number of rows equal to length(x) and the number of columns equal to the number of coefficients in the spline.

Examples

x <- 0:100

genspline(x)
#>        1    2
#> 0   0.00 0.00
#> 1   0.02 0.00
#> 2   0.04 0.00
#> 3   0.06 0.00
#> 4   0.08 0.00
#> 5   0.10 0.00
#> 6   0.12 0.00
#> 7   0.14 0.00
#> 8   0.16 0.00
#> 9   0.18 0.00
#> 10  0.20 0.00
#> 11  0.22 0.00
#> 12  0.24 0.00
#> 13  0.26 0.00
#> 14  0.28 0.00
#> 15  0.30 0.00
#> 16  0.32 0.00
#> 17  0.34 0.00
#> 18  0.36 0.00
#> 19  0.38 0.00
#> 20  0.40 0.00
#> 21  0.42 0.00
#> 22  0.44 0.00
#> 23  0.46 0.00
#> 24  0.48 0.00
#> 25  0.50 0.00
#> 26  0.52 0.00
#> 27  0.54 0.00
#> 28  0.56 0.00
#> 29  0.58 0.00
#> 30  0.60 0.00
#> 31  0.62 0.00
#> 32  0.64 0.00
#> 33  0.66 0.00
#> 34  0.68 0.00
#> 35  0.70 0.00
#> 36  0.72 0.00
#> 37  0.74 0.00
#> 38  0.76 0.00
#> 39  0.78 0.00
#> 40  0.80 0.00
#> 41  0.82 0.00
#> 42  0.84 0.00
#> 43  0.86 0.00
#> 44  0.88 0.00
#> 45  0.90 0.00
#> 46  0.92 0.00
#> 47  0.94 0.00
#> 48  0.96 0.00
#> 49  0.98 0.00
#> 50  1.00 0.00
#> 51  0.98 0.02
#> 52  0.96 0.04
#> 53  0.94 0.06
#> 54  0.92 0.08
#> 55  0.90 0.10
#> 56  0.88 0.12
#> 57  0.86 0.14
#> 58  0.84 0.16
#> 59  0.82 0.18
#> 60  0.80 0.20
#> 61  0.78 0.22
#> 62  0.76 0.24
#> 63  0.74 0.26
#> 64  0.72 0.28
#> 65  0.70 0.30
#> 66  0.68 0.32
#> 67  0.66 0.34
#> 68  0.64 0.36
#> 69  0.62 0.38
#> 70  0.60 0.40
#> 71  0.58 0.42
#> 72  0.56 0.44
#> 73  0.54 0.46
#> 74  0.52 0.48
#> 75  0.50 0.50
#> 76  0.48 0.52
#> 77  0.46 0.54
#> 78  0.44 0.56
#> 79  0.42 0.58
#> 80  0.40 0.60
#> 81  0.38 0.62
#> 82  0.36 0.64
#> 83  0.34 0.66
#> 84  0.32 0.68
#> 85  0.30 0.70
#> 86  0.28 0.72
#> 87  0.26 0.74
#> 88  0.24 0.76
#> 89  0.22 0.78
#> 90  0.20 0.80
#> 91  0.18 0.82
#> 92  0.16 0.84
#> 93  0.14 0.86
#> 94  0.12 0.88
#> 95  0.10 0.90
#> 96  0.08 0.92
#> 97  0.06 0.94
#> 98  0.04 0.96
#> 99  0.02 0.98
#> 100 0.00 1.00

# Generate a quadratic B-spline with 1 equally spaced internal knot
genspline(x, spline="bs", nknots=1, degree=2)
#>          1      2      3
#> 0   0.0000 0.0000 0.0000
#> 1   0.0394 0.0002 0.0000
#> 2   0.0776 0.0008 0.0000
#> 3   0.1146 0.0018 0.0000
#> 4   0.1504 0.0032 0.0000
#> 5   0.1850 0.0050 0.0000
#> 6   0.2184 0.0072 0.0000
#> 7   0.2506 0.0098 0.0000
#> 8   0.2816 0.0128 0.0000
#> 9   0.3114 0.0162 0.0000
#> 10  0.3400 0.0200 0.0000
#> 11  0.3674 0.0242 0.0000
#> 12  0.3936 0.0288 0.0000
#> 13  0.4186 0.0338 0.0000
#> 14  0.4424 0.0392 0.0000
#> 15  0.4650 0.0450 0.0000
#> 16  0.4864 0.0512 0.0000
#> 17  0.5066 0.0578 0.0000
#> 18  0.5256 0.0648 0.0000
#> 19  0.5434 0.0722 0.0000
#> 20  0.5600 0.0800 0.0000
#> 21  0.5754 0.0882 0.0000
#> 22  0.5896 0.0968 0.0000
#> 23  0.6026 0.1058 0.0000
#> 24  0.6144 0.1152 0.0000
#> 25  0.6250 0.1250 0.0000
#> 26  0.6344 0.1352 0.0000
#> 27  0.6426 0.1458 0.0000
#> 28  0.6496 0.1568 0.0000
#> 29  0.6554 0.1682 0.0000
#> 30  0.6600 0.1800 0.0000
#> 31  0.6634 0.1922 0.0000
#> 32  0.6656 0.2048 0.0000
#> 33  0.6666 0.2178 0.0000
#> 34  0.6664 0.2312 0.0000
#> 35  0.6650 0.2450 0.0000
#> 36  0.6624 0.2592 0.0000
#> 37  0.6586 0.2738 0.0000
#> 38  0.6536 0.2888 0.0000
#> 39  0.6474 0.3042 0.0000
#> 40  0.6400 0.3200 0.0000
#> 41  0.6314 0.3362 0.0000
#> 42  0.6216 0.3528 0.0000
#> 43  0.6106 0.3698 0.0000
#> 44  0.5984 0.3872 0.0000
#> 45  0.5850 0.4050 0.0000
#> 46  0.5704 0.4232 0.0000
#> 47  0.5546 0.4418 0.0000
#> 48  0.5376 0.4608 0.0000
#> 49  0.5194 0.4802 0.0000
#> 50  0.5000 0.5000 0.0000
#> 51  0.4802 0.5194 0.0004
#> 52  0.4608 0.5376 0.0016
#> 53  0.4418 0.5546 0.0036
#> 54  0.4232 0.5704 0.0064
#> 55  0.4050 0.5850 0.0100
#> 56  0.3872 0.5984 0.0144
#> 57  0.3698 0.6106 0.0196
#> 58  0.3528 0.6216 0.0256
#> 59  0.3362 0.6314 0.0324
#> 60  0.3200 0.6400 0.0400
#> 61  0.3042 0.6474 0.0484
#> 62  0.2888 0.6536 0.0576
#> 63  0.2738 0.6586 0.0676
#> 64  0.2592 0.6624 0.0784
#> 65  0.2450 0.6650 0.0900
#> 66  0.2312 0.6664 0.1024
#> 67  0.2178 0.6666 0.1156
#> 68  0.2048 0.6656 0.1296
#> 69  0.1922 0.6634 0.1444
#> 70  0.1800 0.6600 0.1600
#> 71  0.1682 0.6554 0.1764
#> 72  0.1568 0.6496 0.1936
#> 73  0.1458 0.6426 0.2116
#> 74  0.1352 0.6344 0.2304
#> 75  0.1250 0.6250 0.2500
#> 76  0.1152 0.6144 0.2704
#> 77  0.1058 0.6026 0.2916
#> 78  0.0968 0.5896 0.3136
#> 79  0.0882 0.5754 0.3364
#> 80  0.0800 0.5600 0.3600
#> 81  0.0722 0.5434 0.3844
#> 82  0.0648 0.5256 0.4096
#> 83  0.0578 0.5066 0.4356
#> 84  0.0512 0.4864 0.4624
#> 85  0.0450 0.4650 0.4900
#> 86  0.0392 0.4424 0.5184
#> 87  0.0338 0.4186 0.5476
#> 88  0.0288 0.3936 0.5776
#> 89  0.0242 0.3674 0.6084
#> 90  0.0200 0.3400 0.6400
#> 91  0.0162 0.3114 0.6724
#> 92  0.0128 0.2816 0.7056
#> 93  0.0098 0.2506 0.7396
#> 94  0.0072 0.2184 0.7744
#> 95  0.0050 0.1850 0.8100
#> 96  0.0032 0.1504 0.8464
#> 97  0.0018 0.1146 0.8836
#> 98  0.0008 0.0776 0.9216
#> 99  0.0002 0.0394 0.9604
#> 100 0.0000 0.0000 1.0000

# Generate a natural spline with 2 knots at times of 10 and 50
genspline(x, spline="ns", knots=c(10, 50))
#>                1          2           3
#> 0    0.000000000 0.00000000  0.00000000
#> 1   -0.014156667 0.03969467 -0.02551800
#> 2   -0.028112452 0.07916287 -0.05089041
#> 3   -0.041666470 0.11817812 -0.07597165
#> 4   -0.054617838 0.15651395 -0.10061611
#> 5   -0.066765674 0.19394389 -0.12467821
#> 6   -0.077909094 0.23024146 -0.14801237
#> 7   -0.087847215 0.26518020 -0.17047299
#> 8   -0.096379153 0.29853363 -0.19191448
#> 9   -0.103304027 0.33007527 -0.21219125
#> 10  -0.108420951 0.35957866 -0.23115771
#> 11  -0.111576347 0.38686644 -0.24869787
#> 12  -0.112805841 0.41195769 -0.26481407
#> 13  -0.112192366 0.43492063 -0.27953826
#> 14  -0.109818852 0.45582345 -0.29290238
#> 15  -0.105768230 0.47473438 -0.30493837
#> 16  -0.100123432 0.49172161 -0.31567818
#> 17  -0.092967387 0.50685335 -0.32515374
#> 18  -0.084383028 0.52019781 -0.33339701
#> 19  -0.074453285 0.53182320 -0.34043991
#> 20  -0.063261088 0.54179771 -0.34631440
#> 21  -0.050889370 0.55018957 -0.35105242
#> 22  -0.037421061 0.55706697 -0.35468591
#> 23  -0.022939091 0.56249812 -0.35724681
#> 24  -0.007526393 0.56655123 -0.35876706
#> 25   0.008734103 0.56929451 -0.35927861
#> 26   0.025759467 0.57079616 -0.35881340
#> 27   0.043466767 0.57112439 -0.35740338
#> 28   0.061773071 0.57034740 -0.35508047
#> 29   0.080595450 0.56853341 -0.35187663
#> 30   0.099850972 0.56575061 -0.34782381
#> 31   0.119456707 0.56206722 -0.34295393
#> 32   0.139329723 0.55755144 -0.33729894
#> 33   0.159387088 0.55227149 -0.33089080
#> 34   0.179545874 0.54629555 -0.32376143
#> 35   0.199723147 0.53969185 -0.31594278
#> 36   0.219835978 0.53252859 -0.30746679
#> 37   0.239801435 0.52487398 -0.29836542
#> 38   0.259536588 0.51679622 -0.28867059
#> 39   0.278958505 0.50836352 -0.27841425
#> 40   0.297984256 0.49964408 -0.26762834
#> 41   0.316530909 0.49070612 -0.25634481
#> 42   0.334515533 0.48161784 -0.24459560
#> 43   0.351855199 0.47244744 -0.23241264
#> 44   0.368466973 0.46326314 -0.21982789
#> 45   0.384267926 0.45413314 -0.20687329
#> 46   0.399175127 0.44512564 -0.19358077
#> 47   0.413105645 0.43630886 -0.17998228
#> 48   0.425976548 0.42775100 -0.16610977
#> 49   0.437704905 0.41952026 -0.15199517
#> 50   0.448207787 0.41168486 -0.13767043
#> 51   0.457420444 0.40430009 -0.12316276
#> 52   0.465350863 0.39736958 -0.10848045
#> 53   0.472025210 0.39088408 -0.09362707
#> 54   0.477469654 0.38483430 -0.07860618
#> 55   0.481710364 0.37921098 -0.06342134
#> 56   0.484773507 0.37400485 -0.04807613
#> 57   0.486685252 0.36920663 -0.03257410
#> 58   0.487471767 0.36480705 -0.01691882
#> 59   0.487159219 0.36079685 -0.00111385
#> 60   0.485773778 0.35716676  0.01483724
#> 61   0.483341610 0.35390749  0.03093090
#> 62   0.479888885 0.35100979  0.04716355
#> 63   0.475441771 0.34846438  0.06353163
#> 64   0.470026435 0.34626198  0.08003158
#> 65   0.463669046 0.34439334  0.09665984
#> 66   0.456395772 0.34284917  0.11341283
#> 67   0.448232780 0.34162021  0.13028700
#> 68   0.439206240 0.34069719  0.14727879
#> 69   0.429342320 0.34007084  0.16438462
#> 70   0.418667187 0.33973188  0.18160094
#> 71   0.407207009 0.33967104  0.19892417
#> 72   0.394987955 0.33987906  0.21635076
#> 73   0.382036194 0.34034666  0.23387715
#> 74   0.368377892 0.34106457  0.25149976
#> 75   0.354039218 0.34202352  0.26921504
#> 76   0.339046341 0.34321424  0.28701941
#> 77   0.323425429 0.34462747  0.30490933
#> 78   0.307202649 0.34625392  0.32288121
#> 79   0.290404170 0.34808433  0.34093151
#> 80   0.273056159 0.35010942  0.35905664
#> 81   0.255184786 0.35231993  0.37725306
#> 82   0.236816218 0.35470659  0.39551719
#> 83   0.217976624 0.35726012  0.41384548
#> 84   0.198692171 0.35997126  0.43223435
#> 85   0.178989027 0.36283072  0.45068025
#> 86   0.158893362 0.36582925  0.46917961
#> 87   0.138431342 0.36895757  0.48772886
#> 88   0.117629137 0.37220642  0.50632445
#> 89   0.096512914 0.37556651  0.52496280
#> 90   0.075108841 0.37902858  0.54364036
#> 91   0.053443087 0.38258336  0.56235356
#> 92   0.031541819 0.38622157  0.58109883
#> 93   0.009431207 0.38993395  0.59987262
#> 94  -0.012862583 0.39371123  0.61867135
#> 95  -0.035313382 0.39754414  0.63749147
#> 96  -0.057895021 0.40142339  0.65632941
#> 97  -0.080581333 0.40533973  0.67518160
#> 98  -0.103346149 0.40928388  0.69404449
#> 99  -0.126163302 0.41324658  0.71291450
#> 100 -0.149006623 0.41721854  0.73178808

# Generate a piecewise linear spline with a knot at time=30
genspline(x, spline="ls", knots=30)
#>      1  2
#> 0    0  0
#> 1    1  0
#> 2    2  0
#> 3    3  0
#> 4    4  0
#> 5    5  0
#> 6    6  0
#> 7    7  0
#> 8    8  0
#> 9    9  0
#> 10  10  0
#> 11  11  0
#> 12  12  0
#> 13  13  0
#> 14  14  0
#> 15  15  0
#> 16  16  0
#> 17  17  0
#> 18  18  0
#> 19  19  0
#> 20  20  0
#> 21  21  0
#> 22  22  0
#> 23  23  0
#> 24  24  0
#> 25  25  0
#> 26  26  0
#> 27  27  0
#> 28  28  0
#> 29  29  0
#> 30  30  0
#> 31  30  1
#> 32  30  2
#> 33  30  3
#> 34  30  4
#> 35  30  5
#> 36  30  6
#> 37  30  7
#> 38  30  8
#> 39  30  9
#> 40  30 10
#> 41  30 11
#> 42  30 12
#> 43  30 13
#> 44  30 14
#> 45  30 15
#> 46  30 16
#> 47  30 17
#> 48  30 18
#> 49  30 19
#> 50  30 20
#> 51  30 21
#> 52  30 22
#> 53  30 23
#> 54  30 24
#> 55  30 25
#> 56  30 26
#> 57  30 27
#> 58  30 28
#> 59  30 29
#> 60  30 30
#> 61  30 31
#> 62  30 32
#> 63  30 33
#> 64  30 34
#> 65  30 35
#> 66  30 36
#> 67  30 37
#> 68  30 38
#> 69  30 39
#> 70  30 40
#> 71  30 41
#> 72  30 42
#> 73  30 43
#> 74  30 44
#> 75  30 45
#> 76  30 46
#> 77  30 47
#> 78  30 48
#> 79  30 49
#> 80  30 50
#> 81  30 51
#> 82  30 52
#> 83  30 53
#> 84  30 54
#> 85  30 55
#> 86  30 56
#> 87  30 57
#> 88  30 58
#> 89  30 59
#> 90  30 60
#> 91  30 61
#> 92  30 62
#> 93  30 63
#> 94  30 64
#> 95  30 65
#> 96  30 66
#> 97  30 67
#> 98  30 68
#> 99  30 69
#> 100 30 70