toeplitz function

Toeplitz matrices operations.

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

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))