
R Under development (unstable) (2022-03-19 r81942) -- "Unsuffered Consequences"
Copyright (C) 2022 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> options(digits=7)
> 
> ## powers
> outer(a <- -4:12,     -2:7, "^")
             [,1]        [,2] [,3] [,4] [,5] [,6]  [,7]   [,8]    [,9]    [,10]
 [1,] 0.062500000 -0.25000000    1   -4   16  -64   256  -1024    4096   -16384
 [2,] 0.111111111 -0.33333333    1   -3    9  -27    81   -243     729    -2187
 [3,] 0.250000000 -0.50000000    1   -2    4   -8    16    -32      64     -128
 [4,] 1.000000000 -1.00000000    1   -1    1   -1     1     -1       1       -1
 [5,]         Inf         Inf    1    0    0    0     0      0       0        0
 [6,] 1.000000000  1.00000000    1    1    1    1     1      1       1        1
 [7,] 0.250000000  0.50000000    1    2    4    8    16     32      64      128
 [8,] 0.111111111  0.33333333    1    3    9   27    81    243     729     2187
 [9,] 0.062500000  0.25000000    1    4   16   64   256   1024    4096    16384
[10,] 0.040000000  0.20000000    1    5   25  125   625   3125   15625    78125
[11,] 0.027777778  0.16666667    1    6   36  216  1296   7776   46656   279936
[12,] 0.020408163  0.14285714    1    7   49  343  2401  16807  117649   823543
[13,] 0.015625000  0.12500000    1    8   64  512  4096  32768  262144  2097152
[14,] 0.012345679  0.11111111    1    9   81  729  6561  59049  531441  4782969
[15,] 0.010000000  0.10000000    1   10  100 1000 10000 100000 1000000 10000000
[16,] 0.008264463  0.09090909    1   11  121 1331 14641 161051 1771561 19487171
[17,] 0.006944444  0.08333333    1   12  144 1728 20736 248832 2985984 35831808
> 
> for (n1 in 1:7)
+     print(zapsmall(polyroot(1:n1), digits = 10))
complex(0)
[1] -0.5+0i
[1] -0.3333333+0.4714045i -0.3333333-0.4714045i
[1] -0.0720852+0.6383267i -0.6058296+0.0000000i -0.0720852-0.6383267i
[1]  0.1378323+0.6781544i -0.5378323+0.3582847i -0.5378323-0.3582847i
[4]  0.1378323-0.6781544i
[1]  0.2941946+0.6683671i -0.3756952+0.5701752i -0.3756952-0.5701752i
[4]  0.2941946-0.6683671i -0.6703320+0.0000000i
[1]  0.4106842+0.6398894i -0.6341119+0.2876550i -0.2051437-0.6837970i
[4]  0.4106842-0.6398894i -0.2051437+0.6837970i -0.6341119-0.2876550i
> 
> ## lowess() {incl. sort, etc}:
> options(digits = 5)
> 
> lowess(c(3,2,6,3,8,4))$y # this used to differ on Linux
[1] 2.4259 3.4293 3.9896 5.2832 5.3386 4.9822
> 
> y1 <- c(3,1:2,5:2,4,1:3,3)
> lowess(y1)$y
 [1] 2.0723 2.4362 2.7508 3.0038 3.2036 3.2435 2.8485 2.4832 2.4197 2.5231
[11] 2.6286 2.7813
> lowess(y1, f = .4)$y
 [1] 2.7030 1.9593 2.4351 3.4933 4.0000 3.0000 2.4651 1.8579 1.7357 2.0000
[11] 2.7103 3.1184
> 
> lowess(c(y1,100), f = .4)$y
 [1] 2.2135 2.2468 2.5459 3.7984 4.0000 3.0000 2.8427 2.4999 2.1512 2.0000
[11] 2.7129 3.1195 3.4172
> 
> ## this is the test sample from Cleveland's original lowess.doc:
> x <- c(1:5, rep(6,10),8,10,12,14,50)
> y <- c(18,2,15,6,10,4,16,11,7,3,14,17,20,12,9,13,1,8,5,19)
> lowess(x,y, f = .25, iter = 0, delta = 0)$y
 [1] 13.6588 11.1446  8.7012  9.7220 10.0000 11.3000 11.3000 11.3000 11.3000
[10] 11.3000 11.3000 11.3000 11.3000 11.3000 11.3000 13.0000  6.4399  5.5959
[19]  5.4557 18.9982
> lowess(x,y, f = .25, iter = 0, delta = 3)$y
 [1] 13.6588 12.3466 11.0343  9.7220 10.5110 11.3000 11.3000 11.3000 11.3000
[10] 11.3000 11.3000 11.3000 11.3000 11.3000 11.3000 13.0000  6.4399  5.5959
[19]  5.4557 18.9982
> lowess(x,y, f = .25, iter = 2, delta = 0)$y
 [1] 14.8112 12.1154  8.9838  9.6757 10.0000 11.3460 11.3460 11.3460 11.3460
[10] 11.3460 11.3460 11.3460 11.3460 11.3460 11.3460 13.0000  6.7345  5.7437
[19]  5.4147 18.9981
> 
>