toeplitz: Toeplitz matrices operations.

In Rssa: A Collection of Methods for Singular Spectrum Analysis

Toeplitz matrices operations.

Description

A set of routines to operate on Toeplitz matrices stored in compact FFT-based form.

Usage

new.tmat(F, L = (N + 1) %/% 2, circular = FALSE, fft.plan = NULL)
is.tmat(t)
tcols(t)
trows(t)
tmatmul(tmat, v, transposed = FALSE)

Arguments

F	series to construct the Toeplitz version of L x L autocovariance matrix.
fft.plan	internal hint argument, should be NULL in most cases
L	the window length.
circular	logical vector of one element, describes series topology. 'TRUE' means series circularity
t, tmat	matrix to operate on.
transposed	logical, if 'TRUE' the multiplication is performed with the transposed matrix.
v	vector to multiply with.

Details

Fast Fourier Transform provides a very efficient matrix-vector multiplication routine for Toeplitz matrices. See the paper in 'References' for the details of the algorithm.

References

Korobeynikov, A. (2010) Computation- and space-efficient implementation of SSA. Statistics and Its Interface, Vol. 3, No. 3, Pp. 257-268

See Also

Rssa for an overview of the package, as well as, ssa,

Examples

# Construct the Toeplitz version of the autocovariance matrix for 'co2' series
h <- new.tmat(co2, L = 10)
# Print the number of columns and rows
print(trows(h)); print(tcols(h))

Rssa documentation built on Sept. 11, 2024, 7:20 p.m.