Function calculates the W-norm for input objects or for objects stored in input ssa obect.
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## S3 method for class '1d.ssa' wnorm(x, ...) ## S3 method for class 'nd.ssa' wnorm(x, ...) ## S3 method for class 'toeplitz.ssa' wnorm(x, ...) ## S3 method for class 'mssa' wnorm(x, ...) ## Default S3 method: wnorm(x, L = (N + 1) %/% 2, ...) ## S3 method for class 'complex' wnorm(x, L = (N + 1) %/% 2, ...)
the input object. This might be ssa object for ssa method, or just a series.
arguments to be passed to methods.
L-weighted norm of series is Frobenius norm of its
L-trajectory matrix. So, if
x is vector (series), the
wnorm(x, L) is equal to
L)^2), but in fact is calculated much more efficiently. For 1d SSA and
wnorm(x) calculates weighted norm for stored
original input series and stored window length.
L-weighted norm of 2d array is Frobenius norm of its
* L-trajectory hankel-block-hankel matrix. For 2d SSA this method
calculates weighted norm for stored original input array and stored
Golyandina, N., Nekrutkin, V. and Zhigljavsky, A. (2001): Analysis of Time Series Structure: SSA and related techniques. Chapman and Hall/CRC. ISBN 1584881941
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wnorm(co2, 20) # Construct ssa-object for 'co2' with default parameters but don't decompose ss <- ssa(co2, force.decompose = FALSE) wnorm(ss) # Artificial image for 2D SSA mx <- outer(1:50, 1:50, function(i, j) sin(2*pi * i/17) * cos(2*pi * j/7) + exp(i/25 - j/20)) + rnorm(50^2, sd = 0.1) # Construct ssa-object for 'mx' with default parameters but don't decompose s <- ssa(mx, kind = "2d-ssa", force.decompose = FALSE) wnorm(s)
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