PP3 (version 1.2)

PP3ix3dvsFromTU: Compute the projection index or its derivatives from the T and U statistics.

Description

Compute the projection index or its derivatives from the T and U statistics.

Usage

PP3ix3FromTU(the.init, avec, bvec, cvec, maxrow, k, maxcol, n, text)
PP3ix3dvsFromTU(the.init, avec, bvec, cvec, maxrow, k, maxcol, n, text, type = "value")

Arguments

the.init

Initialization information, such as from PP3init.

avec

First projection vector of length K

bvec

Second projection vector, of length K

cvec

Third projection vector, of length K

maxrow

Maximum number of variables

k

Actual number of variables (usually maxrow and k are the same.)

maxcol

Maximum number of observations

n

Actual number of observations. (usually maxcol and n are the same.)

text

Integer. If equal to one then information messages from the FORTRAN code are produced. If equal to zero, then they are not.

type

What type of information to return. If set to "deriv" then the derivative vector is returned. If set of "value" then the projection index is returned.

Value

If type is set to "value" then a single value of the projection index is returned. If type is set to "deriv" then a vector, of length 3xK, with the derivative with respect to avec, bvec and cvec is returned.

Details

The T and U third- and fourth-order moment related statistics are computed using PP3init. The projection index and its derivative are computed using these. This function can return either statistic. If you just want the index then you can supply the "value" argument, but it might be quicker to use PP3ix3FromTU which is called by the user-friendly PP3fastIX3.

References

Friedman, J.H. and Tukey, J.W. (1974) A projection pursuit algorithm for exploratory data analysis. IEEE Trans. Comput., 23, 881-890.

Jones, M.C. and Sibson, R. (1987) What is projection pursuit? (with discussion) J. R. Statist. Soc. A, 150, 1-36.

Nason, G. P. (1995) Three-dimensional projection pursuit. J. R. Statist. Soc. C, 44, 411-430.

Nason, G. P. (2001) Robust projection indices. J. R. Statist. Soc. B, 63, 551-567.

See Also

PP3init, PP3fastIX3, PP3slowDF3

Examples

# NOT RUN {
#
# Not for direct user use, but here is an example
#
#
# Load flea beetle data
#
data(beetle)
#
# Initialize T and U tensors
#
b.init <- PP3init(t(beetle))
#
# Get number of cases and dimensions
#
b.n <- nrow(beetle)
b.k <- ncol(beetle)
fortran.messages <- 0
#
# Select arbitrary projection vectors
#
b.pva <- c(1, rep(0, b.k-1))
b.pvb <- c(0, 1, rep(0, b.k-2))
b.pvc <- c(0, 0, 1, rep(0, b.k-3))
#
# Now compute the projection index for this data for this direction
#
answer <- PP3ix3FromTU(the.init=b.init, avec=b.pva, bvec=b.pvb,
	cvec=b.pvc, maxrow=b.k, k=b.k, maxcol=b.n, n=b.n,
	text=fortran.messages)
#
# Print out answer
#
answer
# [1] 13.49793
#
# Now compute the projection index derivatives for this data for this 
# direction
#
answer <- PP3ix3dvsFromTU(the.init=b.init, avec=b.pva, bvec=b.pvb,
	cvec=b.pvc, maxrow=b.k, k=b.k, maxcol=b.n, n=b.n,
	text=fortran.messages, type="deriv")
#
# Print out answer
#
answer
# [1]  0.000000e+00  0.000000e+00  0.000000e+00 -1.283695e-15  0.000000e+00
# [6]  0.000000e+00  0.000000e+00 -4.649059e-16  0.000000e+00  2.910680e+00
#[11] -4.941646e+00 -1.232917e+00  1.057721e-01 -4.608611e+00 -8.286708e-01
#[16] -1.602697e-01  1.724654e+00 -2.029220e+00
#
# The answer is a vector of length 3xb.k = 18. The first b.k=6 entries
# correspond to the derivative wrt b.pva, the next b.k=6 entries to
# b.pvb, and the last b.k=6 entries to b.pvc.
# }