geigen {fda}

Generalized eigenanalysis

Description

Find matrices L and M to maximize

tr(L'AM) / sqrt(tr(L'BL) tr(M'CM'))

where A = a p x q matrix, B = p x p symmetric, positive definite matrix, B = q x q symmetric positive definite matrix, L = p x s matrix, and M = q x s matrix, where s = the number of non-zero generalized eigenvalues of A.

Usage

geigen(Amat, Bmat, Cmat)

Arguments

Amat

a numeric matrix

Bmat

a symmetric, positive definite matrix with dimension = number of rows of A

Cmat

a symmetric, positive definite matrix with dimension = number of columns of A

Value

list(values, Lmat, Mmat)

References

Ramsay, James O., Hooker, Giles, and Graves, Spencer (2009), Functional data analysis with R and Matlab, Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2005), Functional Data Analysis, 2nd ed., Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2002), Applied Functional Data Analysis, Springer, New York.

See Also

eigen

Examples

A <- matrix(1:6, 2)
B <- matrix(c(2, 1, 1, 2), 2)
C <- diag(1:3)
ABC <- geigen(A, B, C)