Eigen {fda}

Eigenanalysis preserving dimnames

Description

Compute eigenvalues and vectors, assigning names to the eigenvalues and dimnames to the eigenvectors.

Usage

Eigen(x, symmetric, only.values = FALSE, valuenames)

Arguments

x

a square matrix whose spectral decomposition is to be computed.

symmetric

logical: If TRUE, the matrix is assumed to be symmetric (or Hermitian if complex) and only its lower triangle (diagonal included) is used. If 'symmetric' is not specified, the matrix is inspected for symmetry.

only.values

if 'TRUE', only the eigenvalues are computed and returned, otherwise both eigenvalues and eigenvectors are returned.

valuenames

character vector of length nrow(x) or a character string that can be extended to that length by appending 1:nrow(x).

The default depends on symmetric and whether rownames == colnames: If rownames == colnames and symmetric = TRUE (either specified or determined by inspection), the default is "paste('ev', 1:nrow(x), sep=”)". Otherwise, the default is colnames(x) unless this is NULL.

Details

1. Check 'symmetric'

2. ev <- eigen(x, symmetric, only.values = FALSE, EISPACK = FALSE); see eigen for more details.

3. rNames = rownames(x); if this is NULL, rNames = if(symmetric) paste('x', 1:nrow(x), sep=”) else paste('xcol', 1:nrow(x)).

4. Parse 'valuenames', assign to names(ev[['values']]).

5. dimnames(ev[['vectors']]) <- list(rNames, valuenames)

NOTE: This naming convention is fairly obvious if 'x' is symmetric. Otherwise, dimensional analysis suggests problems with almost any naming convention. To see this, consider the following simple example:

X <- matrix(1:4, 2, dimnames=list(LETTERS[1:2], letters[3:4]))

	c	d
A	1	3
B	2	4

X.inv <- solve(X)

	A	B
c	-2	1.5
d	1	-0.5

One way of interpreting this is to assume that colnames are really reciprocals of the units. Thus, in this example, X[1,1] is in units of 'A/c' and X.inv[1,1] is in units of 'c/A'. This would make any matrix with the same row and column names potentially dimensionless. Since eigenvalues are essentially the diagonal of a diagonal matrix, this would mean that eigenvalues are dimensionless, and their names are merely placeholders.

Value

a list with components values and (if only.values = FALSE) vectors, as described in eigen.

Author(s)

Spencer Graves

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, svd qr chol

Examples

X <- matrix(1:4, 2, dimnames=list(LETTERS[1:2], letters[3:4]))
eigen(X)
Eigen(X)
Eigen(X, valuenames='eigval')

Y <- matrix(1:4, 2, dimnames=list(letters[5:6], letters[5:6]))
Eigen(Y)

Eigen(Y, symmetric=TRUE)
# only the lower triangle is used;
# the upper triangle is ignored.