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> pkgname <- "splines"

> source(file.path(R.home("share"), "R", "examples-header.R"))

> options(warn = 1)

> library('splines')

> 

> base::assign(".oldSearch", base::search(), pos = 'CheckExEnv')

> base::assign(".old_wd", base::getwd(), pos = 'CheckExEnv')

> cleanEx()

> nameEx("asVector")

> ### * asVector

> 

> flush(stderr()); flush(stdout())

> 

> ### Name: asVector

> ### Title: Coerce an Object to a Vector

> ### Aliases: asVector

> ### Keywords: models

> 

> ### ** Examples

> 

> require(stats)

> ispl <- interpSpline( weight ~ height,  women )

> pred <- predict(ispl)

> class(pred)

[1] "xyVector"

> utils::str(pred)

List of 2

 $ x: num [1:51] 58 58.3 58.6 58.8 59.1 ...

 $ y: num [1:51] 115 115 116 117 117 ...

 - attr(*, "class")= chr "xyVector"

> asVector(pred)

 [1] 115.0000 115.4908 116.0170 116.6137 117.3153 118.1214 118.9894 119.8747

 [9] 120.7384 121.5787 122.4078 123.2380 124.0759 124.9181 125.7601 126.5980

[17] 127.4340 128.2735 129.1220 129.9792 130.8301 131.6572 132.4454 133.2228

[25] 134.0528 135.0000 136.1000 137.2727 138.4090 139.4026 140.2416 141.0276

[33] 141.8690 142.8564 143.9707 145.1507 146.3356 147.4868 148.6046 149.6935

[41] 150.7604 151.8353 152.9613 154.1817 155.5178 156.9329 158.3808 159.8173

[49] 161.2269 162.6180 164.0000

> 

> 

> 

> cleanEx()

> nameEx("backSpline")

> ### * backSpline

> 

> flush(stderr()); flush(stdout())

> 

> ### Name: backSpline

> ### Title: Monotone Inverse Spline

> ### Aliases: backSpline

> ### Keywords: models

> 

> ### ** Examples

> 

> require(graphics)

> ispl <- interpSpline( women$height, women$weight )

> bspl <- backSpline( ispl )

> plot( bspl )                   # plots over the range of the knots

> points( women$weight, women$height )

> 

> 

> 

> cleanEx()

> nameEx("bs")

> ### * bs

> 

> flush(stderr()); flush(stdout())

> 

> ### Name: bs

> ### Title: B-Spline Basis for Polynomial Splines

> ### Aliases: bs

> ### Keywords: smooth

> 

> ### ** Examples

> 

> require(stats); require(graphics)

> bs(women$height, df = 5)

                 1           2           3            4           5

 [1,] 0.000000e+00 0.000000000 0.000000000 0.000000e+00 0.000000000

 [2,] 4.534439e-01 0.059857872 0.001639942 0.000000e+00 0.000000000

 [3,] 5.969388e-01 0.203352770 0.013119534 0.000000e+00 0.000000000

 [4,] 5.338010e-01 0.376366618 0.044278426 0.000000e+00 0.000000000

 [5,] 3.673469e-01 0.524781341 0.104956268 0.000000e+00 0.000000000

 [6,] 2.001640e-01 0.595025510 0.204719388 9.110787e-05 0.000000000

 [7,] 9.110787e-02 0.566326531 0.336734694 5.830904e-03 0.000000000

 [8,] 3.125000e-02 0.468750000 0.468750000 3.125000e-02 0.000000000

 [9,] 5.830904e-03 0.336734694 0.566326531 9.110787e-02 0.000000000

[10,] 9.110787e-05 0.204719388 0.595025510 2.001640e-01 0.000000000

[11,] 0.000000e+00 0.104956268 0.524781341 3.673469e-01 0.002915452

[12,] 0.000000e+00 0.044278426 0.376366618 5.338010e-01 0.045553936

[13,] 0.000000e+00 0.013119534 0.203352770 5.969388e-01 0.186588921

[14,] 0.000000e+00 0.001639942 0.059857872 4.534439e-01 0.485058309

[15,] 0.000000e+00 0.000000000 0.000000000 0.000000e+00 1.000000000

attr(,"degree")

[1] 3

attr(,"knots")

[1] 62.66667 67.33333

attr(,"Boundary.knots")

[1] 58 72

attr(,"intercept")

[1] FALSE

attr(,"class")

[1] "bs"     "basis"  "matrix"

> summary(fm1 <- lm(weight ~ bs(height, df = 5), data = women))

Call:

lm(formula = weight ~ bs(height, df = 5), data = women)

Residuals:

     Min       1Q   Median       3Q      Max 

-0.31764 -0.13441  0.03922  0.11096  0.35086 

Coefficients:

                    Estimate Std. Error t value Pr(>|t|)    

(Intercept)         114.8799     0.2167 530.146  < 2e-16 ***

bs(height, df = 5)1   3.4657     0.4595   7.543 3.53e-05 ***

bs(height, df = 5)2  13.0300     0.3965  32.860 1.10e-10 ***

bs(height, df = 5)3  27.6161     0.4571  60.415 4.70e-13 ***

bs(height, df = 5)4  40.8481     0.3866 105.669 3.09e-15 ***

bs(height, df = 5)5  49.1296     0.3090 158.979  < 2e-16 ***

---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2276 on 9 degrees of freedom

Multiple R-squared:  0.9999,	Adjusted R-squared:  0.9998 

F-statistic: 1.298e+04 on 5 and 9 DF,  p-value: < 2.2e-16

> 

> ## example of safe prediction

> plot(women, xlab = "Height (in)", ylab = "Weight (lb)")

> ht <- seq(57, 73, length.out = 200)

> lines(ht, predict(fm1, data.frame(height = ht)))

Warning in bs(height, degree = 3L, knots = c(62.6666666666667, 67.3333333333333 :

  some 'x' values beyond boundary knots may cause ill-conditioned bases

> ## Don't show: 

> ## Consistency:

> x <- c(1:3, 5:6)

> stopifnot(identical(bs(x), bs(x, df = 3)),

+           identical(bs(x, df = 4), bs(x, df = 4, knots = NULL)), # not true till 2.15.2

+           !is.null(kk <- attr(bs(x), "knots")), # not true till 1.5.1

+           length(kk) == 0)

> ## End(Don't show)

> 

> 

> 

> cleanEx()

> nameEx("interpSpline")

> ### * interpSpline

> 

> flush(stderr()); flush(stdout())

> 

> ### Name: interpSpline

> ### Title: Create an Interpolation Spline

> ### Aliases: interpSpline

> ### Keywords: models

> 

> ### ** Examples

> 

> require(graphics); require(stats)

> ispl <- interpSpline( women$height, women$weight )

> ispl2 <- interpSpline( weight ~ height,  women )

> # ispl and ispl2 should be the same

> plot( predict( ispl, seq( 55, 75, length.out = 51 ) ), type = "l" )

> points( women$height, women$weight )

> plot( ispl )    # plots over the range of the knots

> points( women$height, women$weight )

> splineKnots( ispl )

 [1] 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72

> 

> 

> 

> cleanEx()

> nameEx("ns")

> ### * ns

> 

> flush(stderr()); flush(stdout())

> 

> ### Name: ns

> ### Title: Generate a Basis Matrix for Natural Cubic Splines

> ### Aliases: ns

> ### Keywords: smooth

> 

> ### ** Examples

> 

> require(stats); require(graphics)

> ns(women$height, df = 5)

                 1            2           3          4             5

 [1,] 0.000000e+00 0.000000e+00  0.00000000 0.00000000  0.0000000000

 [2,] 7.592323e-03 0.000000e+00 -0.08670223 0.26010669 -0.1734044626

 [3,] 6.073858e-02 0.000000e+00 -0.15030440 0.45091320 -0.3006088020

 [4,] 2.047498e-01 6.073858e-05 -0.16778345 0.50335034 -0.3355668952

 [5,] 4.334305e-01 1.311953e-02 -0.13244035 0.39732106 -0.2648807067

 [6,] 6.256681e-01 8.084305e-02 -0.07399720 0.22199159 -0.1479943948

 [7,] 6.477162e-01 2.468416e-01 -0.02616007 0.07993794 -0.0532919575

 [8,] 4.791667e-01 4.791667e-01  0.01406302 0.02031093 -0.0135406187

 [9,] 2.468416e-01 6.477162e-01  0.09733619 0.02286023 -0.0152401533

[10,] 8.084305e-02 6.256681e-01  0.27076826 0.06324188 -0.0405213106

[11,] 1.311953e-02 4.334305e-01  0.48059836 0.12526031 -0.0524087186

[12,] 6.073858e-05 2.047498e-01  0.59541597 0.19899261  0.0007809246

[13,] 0.000000e+00 6.073858e-02  0.50097182 0.27551020  0.1627793975

[14,] 0.000000e+00 7.592323e-03  0.22461127 0.35204082  0.4157555879

[15,] 0.000000e+00 0.000000e+00 -0.14285714 0.42857143  0.7142857143

attr(,"degree")

[1] 3

attr(,"knots")

[1] 60.8 63.6 66.4 69.2

attr(,"Boundary.knots")

[1] 58 72

attr(,"intercept")

[1] FALSE

attr(,"class")

[1] "ns"     "basis"  "matrix"

> summary(fm1 <- lm(weight ~ ns(height, df = 5), data = women))

Call:

lm(formula = weight ~ ns(height, df = 5), data = women)

Residuals:

     Min       1Q   Median       3Q      Max 

-0.38333 -0.12585  0.07083  0.15401  0.30426 

Coefficients:

                    Estimate Std. Error t value Pr(>|t|)    

(Intercept)         114.7447     0.2338  490.88  < 2e-16 ***

ns(height, df = 5)1  15.9474     0.3699   43.12 9.69e-12 ***

ns(height, df = 5)2  25.1695     0.4323   58.23 6.55e-13 ***

ns(height, df = 5)3  33.2582     0.3541   93.93 8.91e-15 ***

ns(height, df = 5)4  50.7894     0.6062   83.78 2.49e-14 ***

ns(height, df = 5)5  45.0363     0.2784  161.75  < 2e-16 ***

---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2645 on 9 degrees of freedom

Multiple R-squared:  0.9998,	Adjusted R-squared:  0.9997 

F-statistic:  9609 on 5 and 9 DF,  p-value: < 2.2e-16

> 

> ## To see what knots were selected

> attr(terms(fm1), "predvars")

list(weight, ns(height, knots = c(60.8, 63.6, 66.4, 69.2), Boundary.knots = c(58, 

72), intercept = FALSE))

> 

> ## example of safe prediction

> plot(women, xlab = "Height (in)", ylab = "Weight (lb)")

> ht <- seq(57, 73, length.out = 200) ; nD <- data.frame(height = ht)

> lines(ht, p1 <- predict(fm1, nD))

> stopifnot(all.equal(p1, predict(update(fm1, . ~

+                             splines::ns(height, df=5)), nD)))

>           # not true in R < 3.5.0

> ## Don't show: 

> ## Consistency:

> x <- c(1:3, 5:6)

> stopifnot(identical(ns(x), ns(x, df = 1)),

+           identical(ns(x, df = 2),

+                     ns(x, df = 2, knots = NULL)), # not true till 2.15.2

+           !is.null(kk <- attr(ns(x), "knots")), # not true till 1.5.1

+           length(kk) == 0)

> ## End(Don't show)

> 

> 

> 

> cleanEx()

> nameEx("periodicSpline")

> ### * periodicSpline

> 

> flush(stderr()); flush(stdout())

> 

> ### Name: periodicSpline

> ### Title: Create a Periodic Interpolation Spline

> ### Aliases: periodicSpline

> ### Keywords: models

> 

> ### ** Examples

> 

> require(graphics); require(stats)

> xx <- seq( -pi, pi, length.out = 16 )[-1]

> yy <- sin( xx )

> frm <- data.frame( xx, yy )

> pispl <- periodicSpline( xx, yy, period = 2 * pi)

> pispl2 <- periodicSpline( yy ~ xx, frm, period = 2 * pi )

> stopifnot(all.equal(pispl, pispl2))  # pispl and pispl2 are the same

> 

> plot( pispl )          # displays over one period

> points( yy ~ xx, col = "brown")

> plot( predict( pispl, seq(-3*pi, 3*pi, length.out = 101) ), type = "l" )

> 

> 

> 

> cleanEx()

> nameEx("polySpline")

> ### * polySpline

> 

> flush(stderr()); flush(stdout())

> 

> ### Name: polySpline

> ### Title: Piecewise Polynomial Spline Representation

> ### Aliases: polySpline as.polySpline

> ### Keywords: models

> 

> ### ** Examples

> 

> require(graphics)

> ispl <- polySpline(interpSpline( weight ~ height,  women, bSpline = TRUE))

> ## IGNORE_RDIFF_BEGIN

> print( ispl )   # print the piecewise polynomial representation

polynomial representation of spline for weight ~ height

   constant   linear   quadratic       cubic

58      115 1.731918  0.00000000  0.26808191

59      117 2.536164  0.80424574 -0.34040957

60      120 3.123427 -0.21698298  0.09355638

61      123 2.970130  0.06368616 -0.03381595

62      126 2.996054 -0.03776168  0.04170740

63      129 3.045653  0.08736054 -0.13301367

64      132 2.821333 -0.31168048  0.49034728

65      135 3.669014  1.15936136 -0.82837545

66      139 3.502610 -1.32576498  0.82315452

67      142 3.320544  1.14369857 -0.46424262

68      146 4.215213 -0.24902928  0.03381595

69      150 3.818603 -0.14758144  0.32897883

70      154 4.510376  0.83935505 -0.34973127

71      159 5.139893 -0.20983876  0.06994625

72      164 4.930054  0.00000000  0.00000000

> ## IGNORE_RDIFF_END

> plot( ispl )    # plots over the range of the knots

> points( women$height, women$weight )

> 

> 

> 

> cleanEx()

> nameEx("predict.bSpline")

> ### * predict.bSpline

> 

> flush(stderr()); flush(stdout())

> 

> ### Name: predict.bSpline

> ### Title: Evaluate a Spline at New Values of x

> ### Aliases: predict.bSpline predict.nbSpline predict.pbSpline

> ###   predict.npolySpline predict.ppolySpline

> ### Keywords: models

> 

> ### ** Examples

> 

> require(graphics); require(stats)

> ispl <- interpSpline( weight ~ height,  women )

> opar <- par(mfrow = c(2, 2), las = 1)

> plot(predict(ispl, nseg = 201),     # plots over the range of the knots

+      main = "Original data with interpolating spline", type = "l",

+      xlab = "height", ylab = "weight")

> points(women$height, women$weight, col = 4)

> plot(predict(ispl, nseg = 201, deriv = 1),

+      main = "First derivative of interpolating spline", type = "l",

+      xlab = "height", ylab = "weight")

> plot(predict(ispl, nseg = 201, deriv = 2),

+      main = "Second derivative of interpolating spline", type = "l",

+      xlab = "height", ylab = "weight")

> plot(predict(ispl, nseg = 401, deriv = 3),

+      main = "Third derivative of interpolating spline", type = "l",

+      xlab = "height", ylab = "weight")

> par(opar)

> 

> 

> 

> graphics::par(get("par.postscript", pos = 'CheckExEnv'))

> cleanEx()

> nameEx("predict.bs")

> ### * predict.bs

> 

> flush(stderr()); flush(stdout())

> 

> ### Name: predict.bs

> ### Title: Evaluate a Spline Basis

> ### Aliases: predict.bs predict.ns

> ### Keywords: smooth

> 

> ### ** Examples

> 

> require(stats)

> basis <- ns(women$height, df = 5)

> newX <- seq(58, 72, length.out = 51)

> # evaluate the basis at the new data

> predict(basis, newX)

                 1            2            3          4            5

 [1,] 0.0000000000 0.0000000000  0.000000000 0.00000000  0.000000000

 [2,] 0.0001666667 0.0000000000 -0.025270112 0.07581034 -0.050540224

 [3,] 0.0013333333 0.0000000000 -0.050033132 0.15009940 -0.100066264

 [4,] 0.0045000000 0.0000000000 -0.073781966 0.22134590 -0.147563933

 [5,] 0.0106666667 0.0000000000 -0.096009523 0.28802857 -0.192019047

 [6,] 0.0208333333 0.0000000000 -0.116208710 0.34862613 -0.232417420

 [7,] 0.0360000000 0.0000000000 -0.133872434 0.40161730 -0.267744868

 [8,] 0.0571666667 0.0000000000 -0.148493603 0.44548081 -0.296987205

 [9,] 0.0853333333 0.0000000000 -0.159565123 0.47869537 -0.319130247

[10,] 0.1215000000 0.0000000000 -0.166579904 0.49973971 -0.333159807

[11,] 0.1666666667 0.0000000000 -0.169030851 0.50709255 -0.338061702

[12,] 0.2211666667 0.0001666667 -0.166622161 0.49986648 -0.333244323

[13,] 0.2826666667 0.0013333333 -0.159903185 0.47970955 -0.319806370

[14,] 0.3481666667 0.0045000000 -0.149634561 0.44890368 -0.299269122

[15,] 0.4146666667 0.0106666667 -0.136576928 0.40973078 -0.273153855

[16,] 0.4791666667 0.0208333333 -0.121490924 0.36447277 -0.242981848

[17,] 0.5386666667 0.0360000000 -0.105137189 0.31541157 -0.210274379

[18,] 0.5901666667 0.0571666667 -0.088276362 0.26482909 -0.176552724

[19,] 0.6306666667 0.0853333333 -0.071669081 0.21500724 -0.143338162

[20,] 0.6571666667 0.1215000000 -0.056075985 0.16822795 -0.112151970

[21,] 0.6666666667 0.1666666667 -0.042257713 0.12677314 -0.084515425

[22,] 0.6571666667 0.2211666667 -0.030651111 0.09245333 -0.061635555

[23,] 0.6306666667 0.2826666667 -0.020397854 0.06519356 -0.043462374

[24,] 0.5901666667 0.3481666667 -0.010315824 0.04444747 -0.029631648

[25,] 0.5386666667 0.4146666667  0.000777096 0.02966871 -0.019779141

[26,] 0.4791666667 0.4791666667  0.014063024 0.02031093 -0.013540619

[27,] 0.4146666667 0.5386666667  0.030724078 0.01582777 -0.010551844

[28,] 0.3481666667 0.5901666667  0.051942375 0.01567287 -0.010448583

[29,] 0.2826666667 0.6306666667  0.078900034 0.01929990 -0.012866600

[30,] 0.2211666667 0.6571666667  0.112779171 0.02616249 -0.017441658

[31,] 0.1666666667 0.6666666667  0.154761905 0.03571429 -0.023809524

[32,] 0.1215000000 0.6571666667  0.205345238 0.04746429 -0.031476190

[33,] 0.0853333333 0.6306666667  0.262285714 0.06114286 -0.039428571

[34,] 0.0571666667 0.5901666667  0.322654762 0.07653571 -0.046523810

[35,] 0.0360000000 0.5386666667  0.383523810 0.09342857 -0.051619048

[36,] 0.0208333333 0.4791666667  0.441964286 0.11160714 -0.053571429

[37,] 0.0106666667 0.4146666667  0.495047619 0.13085714 -0.051238095

[38,] 0.0045000000 0.3481666667  0.539845238 0.15096429 -0.043476190

[39,] 0.0013333333 0.2826666667  0.573428571 0.17171429 -0.029142857

[40,] 0.0001666667 0.2211666667  0.592869048 0.19289286 -0.007095238

[41,] 0.0000000000 0.1666666667  0.595238095 0.21428571  0.023809524

[42,] 0.0000000000 0.1215000000  0.578428571 0.23571429  0.064357143

[43,] 0.0000000000 0.0853333333  0.543619048 0.25714286  0.113904762

[44,] 0.0000000000 0.0571666667  0.492809524 0.27857143  0.171452381

[45,] 0.0000000000 0.0360000000  0.428000000 0.30000000  0.236000000

[46,] 0.0000000000 0.0208333333  0.351190476 0.32142857  0.306547619

[47,] 0.0000000000 0.0106666667  0.264380952 0.34285714  0.382095238

[48,] 0.0000000000 0.0045000000  0.169571429 0.36428571  0.461642857

[49,] 0.0000000000 0.0013333333  0.068761905 0.38571429  0.544190476

[50,] 0.0000000000 0.0001666667 -0.036047619 0.40714286  0.628738095

[51,] 0.0000000000 0.0000000000 -0.142857143 0.42857143  0.714285714

attr(,"degree")

[1] 3

attr(,"knots")

[1] 60.8 63.6 66.4 69.2

attr(,"Boundary.knots")

[1] 58 72

attr(,"intercept")

[1] FALSE

attr(,"class")

[1] "ns"     "basis"  "matrix"

> 

> 

> 

> cleanEx()

> nameEx("splineDesign")

> ### * splineDesign

> 

> flush(stderr()); flush(stdout())

> 

> ### Name: splineDesign

> ### Title: Design Matrix for B-splines

> ### Aliases: splineDesign spline.des

> ### Keywords: models

> 

> ### ** Examples

> 

> require(graphics)

> splineDesign(knots = 1:10, x = 4:7)

          [,1]      [,2]      [,3]      [,4]      [,5]      [,6]

[1,] 0.1666667 0.6666667 0.1666667 0.0000000 0.0000000 0.0000000

[2,] 0.0000000 0.1666667 0.6666667 0.1666667 0.0000000 0.0000000

[3,] 0.0000000 0.0000000 0.1666667 0.6666667 0.1666667 0.0000000

[4,] 0.0000000 0.0000000 0.0000000 0.1666667 0.6666667 0.1666667

> splineDesign(knots = 1:10, x = 4:7, derivs = 1)

     [,1] [,2] [,3] [,4] [,5] [,6]

[1,] -0.5  0.0  0.5  0.0  0.0  0.0

[2,]  0.0 -0.5  0.0  0.5  0.0  0.0

[3,]  0.0  0.0 -0.5  0.0  0.5  0.0

[4,]  0.0  0.0  0.0 -0.5  0.0  0.5

> ## visualize band structure

> 

> knots <- c(1,1.8,3:5,6.5,7,8.1,9.2,10)  # 10 => 10-4 = 6 Basis splines

> x <- seq(min(knots)-1, max(knots)+1, length.out = 501)

> bb <- splineDesign(knots, x = x, outer.ok = TRUE)

> 

> plot(range(x), c(0,1), type = "n", xlab = "x", ylab = "",

+      main =  "B-splines - sum to 1 inside inner knots")

> mtext(expression(B[j](x) *"  and "* sum(B[j](x), j == 1, 6)), adj = 0)

> abline(v = knots, lty = 3, col = "light gray")

> abline(v = knots[c(4,length(knots)-3)], lty = 3, col = "gray10")

> lines(x, rowSums(bb), col = "gray", lwd = 2)

> matlines(x, bb, ylim = c(0,1), lty = 1)

> 

> 

> 

> cleanEx()

> nameEx("splineKnots")

> ### * splineKnots

> 

> flush(stderr()); flush(stdout())

> 

> ### Name: splineKnots

> ### Title: Knot Vector from a Spline

> ### Aliases: splineKnots

> ### Keywords: models

> 

> ### ** Examples

> 

> ispl <- interpSpline( weight ~ height, women )

> splineKnots( ispl )

 [1] 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72

> 

> 

> 

> cleanEx()

> nameEx("splineOrder")

> ### * splineOrder

> 

> flush(stderr()); flush(stdout())

> 

> ### Name: splineOrder

> ### Title: Determine the Order of a Spline

> ### Aliases: splineOrder

> ### Keywords: models

> 

> ### ** Examples

> 

> splineOrder( interpSpline( weight ~ height, women ) )

[1] 4

> 

> 

> 

> cleanEx()

> nameEx("xyVector")

> ### * xyVector

> 

> flush(stderr()); flush(stdout())

> 

> ### Name: xyVector

> ### Title: Construct an 'xyVector' Object

> ### Aliases: xyVector

> ### Keywords: models

> 

> ### ** Examples

> 

> require(stats); require(graphics)

> ispl <- interpSpline( weight ~ height, women )

> weights <- predict( ispl, seq( 55, 75, length.out = 51 ))

> class( weights )

[1] "xyVector"

> plot( weights, type = "l", xlab = "height", ylab = "weight" )

> points( women$height, women$weight )

> weights

$x

 [1] 55.0 55.4 55.8 56.2 56.6 57.0 57.4 57.8 58.2 58.6 59.0 59.4 59.8 60.2 60.6

[16] 61.0 61.4 61.8 62.2 62.6 63.0 63.4 63.8 64.2 64.6 65.0 65.4 65.8 66.2 66.6

[31] 67.0 67.4 67.8 68.2 68.6 69.0 69.4 69.8 70.2 70.6 71.0 71.4 71.8 72.2 72.6

[46] 73.0 73.4 73.8 74.2 74.6 75.0

$y

 [1] 109.8042 110.4970 111.1898 111.8825 112.5753 113.2681 113.9608 114.6536

 [9] 115.3485 116.0971 117.0000 118.1214 119.3694 120.6168 121.8162 123.0000

[17] 124.1961 125.3995 126.5980 127.7930 129.0000 130.2237 131.4243 132.5557

[25] 133.6865 135.0000 136.6001 138.2531 139.6541 140.8021 142.0000 143.4815

[33] 145.1507 146.8334 148.4468 150.0000 151.5249 153.1289 154.9329 156.9329

[41] 159.0000 161.0269 163.0134 164.9860 166.9580 168.9301 170.9021 172.8741

[49] 174.8461 176.8181 178.7902

attr(,"class")

[1] "xyVector"

> 

> 

> 

> ### * <FOOTER>

> ###

> cleanEx()

> options(digits = 7L)

> base::cat("Time elapsed: ", proc.time() - base::get("ptime", pos = 'CheckExEnv'),"\n")

Time elapsed:  0.152 0.012 0.164 0 0 

> grDevices::dev.off()

null device 

          1 

> ###

> ### Local variables: ***

> ### mode: outline-minor ***

> ### outline-regexp: "\\(> \\)?### [*]+" ***

> ### End: ***

> quit('no')