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[S] bases of B-splines

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Subject: [S] bases of B-splines
From: TAKEZAWA Kunio <takezawa@affrc.go.jp>
Date: Fri, 23 Jul 1999 14:45:21 +0900
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Hi!
  I tried to draw the bases of B-splines.
The main part of the program is:

    xx <- seq(from = 1, by = 0.1, to = 3)
        knots <- c(1, 2, 3)
        bs1 <- bs(x = xx, knots = knots)
        print(bs1)

   The result is:

          1       2     3       4     5  6 
 [1,] 1.000 0.00000 0.000 0.00000 0.000  0
 [2,] 0.729 0.25675 0.014 0.00025 0.000  0
 [3,] 0.512 0.43400 0.052 0.00200 0.000  0
 [4,] 0.343 0.54225 0.108 0.00675 0.000  0
 [5,] 0.216 0.59200 0.176 0.01600 0.000  0
 [6,] 0.125 0.59375 0.250 0.03125 0.000  0
 [7,] 0.064 0.55800 0.324 0.05400 0.000  0
 [8,] 0.027 0.49525 0.392 0.08575 0.000  0
 [9,] 0.008 0.41600 0.448 0.12800 0.000  0
[10,] 0.001 0.33075 0.486 0.18225 0.000  0
[11,] 0.000 0.25000 0.500 0.25000 0.000  0
[12,] 0.000 0.18225 0.486 0.33075 0.001  0
[13,] 0.000 0.12800 0.448 0.41600 0.008  0
[14,] 0.000 0.08575 0.392 0.49525 0.027  0
[15,] 0.000 0.05400 0.324 0.55800 0.064  0
[16,] 0.000 0.03125 0.250 0.59375 0.125  0
[17,] 0.000 0.01600 0.176 0.59200 0.216  0
[18,] 0.000 0.00675 0.108 0.54225 0.343  0
[19,] 0.000 0.00200 0.052 0.43400 0.512  0
[20,] 0.000 0.00025 0.014 0.25675 0.729  0
[21,] 0.000 0.00000    NA      NA    NA NA
attr(, "knots"):
 [1] 1 1 1 1 1 2 3 3 3 3 3

   I do not understand why the number of the bases is six instead
of five, and why "NA"s appear on the last row.

   *****    Kunio Takezawa, Ph.D. (takezawa@affrc.go.jp)    *****
  *****            Research Information Section              *****
 **** Hokuriku National Agricultural Experiment Station, JAPAN ****
*****  <http://www.inada.affrc.go.jp/~takezawa/patent-e.html>  *****
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