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Type 'q()' to quit R. > 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") 33.33333% 66.66667% 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(`33.33333%` = 62.6666666666667, : 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") 20% 40% 60% 80% 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(`20%` = 60.8, `40%` = 63.6, `60%` = 66.4, `80%` = 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)) > 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 > 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") 20% 40% 60% 80% 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, deriv = 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" > > > > ### *