View Full Version : Woltring's quintic spline

Jesus Dapena
10-27-1996, 10:06 AM
Dear Biomch-L readers:

I am trying to use Herman Woltring's GCVSPL and SPLDER programs to
smooth data with quintic spline. I am using these programs in "Mode 1"
(where the smoothing factor is NOT decided by the program but by the person
running the program), and I am providing a value for VAL (the smoothing
factor). As I understand it, when in Mode 1, VAL is the upper limit of the
average squared deviation between the raw and smoothed location data.
Therefore, the sum of the squares of the differences between the raw and
smoothed location data (0th derivative) must be equal or smaller than N*VAL
(where N is the number of data points).

With the data points that Woltring provides in his GCVTST test
program (Kit Vaughan's golf ball drop data), I found that this holds true.
However, when I try other data, I find that the sum of squares is much
larger than N*VAL, which should not happen.

Has anyone in Biomch-L ever encountered this problem with Woltring's
programs? At this point, I tend to think that Woltring's programs work OK,
and that I am doing something wrong, but I can't figure out what it is!

In case there is someone curious enough to check this, here are the
data that I am having trouble with:

x( 1)= 9.660D0
y( 1)= 6.494D0
x( 2)= 9.680D0
y( 2)= 6.615D0
x( 3)= 9.700D0
y( 3)= 6.719D0
x( 4)= 9.720D0
y( 4)= 6.826D0
x( 5)= 9.740D0
y( 5)= 6.921D0
x( 6)= 9.760D0
y( 6)= 7.006D0
x( 7)= 9.780D0
y( 7)= 7.088D0
x( 8)= 9.800D0
y( 8)= 7.159D0
x( 9)= 9.820D0
y( 9)= 7.220D0
x(10)= 9.840D0
y(10)= 7.273D0
x(11)= 9.860D0
y(11)= 7.325D0
x(12)= 9.880D0
y(12)= 7.387D0
x(13)= 9.900D0
y(13)= 7.478D0
x(14)= 9.920D0
y(14)= 7.615D0
x(15)= 9.940D0
y(15)= 7.769D0
x(16)= 9.960D0
y(16)= 7.944D0
x(17)= 9.980D0
y(17)= 8.091D0
x(18)= 10.000D0
y(18)= 8.181D0
x(19)= 10.020D0
y(19)= 8.259D0
x(20)= 10.040D0
y(20)= 8.318D0
x(21)= 10.060D0
y(21)= 8.361D0
x(22)= 10.080D0
y(22)= 8.420D0
x(23)= 10.100D0
y(23)= 8.510D0
x(24)= 10.120D0
y(24)= 8.577D0
x(25)= 10.140D0
y(25)= 8.643D0
x(26)= 10.160D0
y(26)= 8.710D0
x(27)= 10.180D0
y(27)= 8.771D0
x(28)= 10.200D0
y(28)= 8.817D0
x(29)= 10.220D0
y(29)= 8.867D0
x(30)= 10.240D0
y(30)= 8.923D0
x(31)= 10.260D0
y(31)= 8.982D0
x(32)= 10.280D0
y(32)= 9.073D0
x(33)= 10.340D0
y(33)= 9.352D0
x(34)= 10.400D0
y(34)= 9.488D0
x(35)= 10.460D0
y(35)= 9.764D0
x(36)= 10.520D0
y(36)= 9.883D0
x(37)= 10.580D0
y(37)= 10.036D0
x(38)= 10.640D0
y(38)= 10.243D0
x(39)= 10.700D0
y(39)= 10.419D0
x(40)= 10.760D0
y(40)= 10.651D0
x(41)= 10.820D0
y(41)= 10.738D0
x(42)= 10.880D0
y(42)= 10.872D0

With these data and a smoothing factor VAL=0.000010, I get a sum of
squares ssq= 0.112067, when the maximum value that the sum of squares
should reach is (42*0.000010=) 0.000420.

If someone in Biomch-L who is a regular user of Woltring's package
runs these data ***in Mode 1, and with VAL=0.000010***, can you please tell
me if the sum of squares that you get is (a) 0.112067 (as I am getting) or
(b) the expected value (0.000420 or less).

Jesus Dapena
Jesus Dapena
Department of Kinesiology
Indiana University

Bloomington, IN 47405, USA