Description Usage Arguments Details Value References See Also Examples
rExamples2D()
generates several example (locally) smooth target surfaces of HPD matrices corrupted by
noise in a manifold of HPD matrices for testing and simulation purposes. For more details, see also Chapter 2 and 5 in
\insertCiteC18pdSpecEst.
1 2 3  rExamples2D(n, d = 2, example = c("smiley", "tvar", "facets", "peak"),
replicates = 1, noise = "riemgaussian", noise.level = 1,
df.wishart = NULL)

n 
integer vector 
d 
row (resp. column)dimension of the generated matrices. Defaults to 
example 
the example target HPD matrix surface, one of 
replicates 
a positive integer specifying the number of replications of noisy HPD matrix surfaces to be generated based on the
target surface of HPD matrices. Defaults to 
noise 
noise distribution for the generated noisy surfaces of HPD matrices, one of 
noise.level 
parameter to tune the signaltonoise ratio for the generated noisy HPD matrix observations.
If 
df.wishart 
optional parameter to specify the degrees of freedom in the case of a Wishart noise distribution ( 
The examples include: (i) a (d,d)dimensional 'smiley'
HPD matrix surface consisting of constant surfaces of random HPD matrices in
the shape of a smiley face; (ii) a (d,d)dimensional 'tvar'
HPD matrix surface generated from a timevarying vectorauto
regressive process of order 1 with random timevarying coefficient matrix (Φ); (iii) a (d,d)dimensional 'facets'
HPD matrix
surface consisting of several facets generated from random geodesic surfaces; and (iv) a (d,d)dimensional 'peak'
HPD matrix surface
containing a pronounced peak in the center of its 2d (e.g., timefrequency) domain.
In addition to the (locally) smooth target surface of HPD matrices, the function also returns a noisy version of the target surface of HPD matrices, corrupted
by a userspecified noise distribution. By default, the noisy HPD matrix observations follow an intrinsic signal plus i.i.d. noise model with
respect to the affineinvariant Riemannian metric, with a matrix logGaussian noise distribution (noise = 'riemgaussian'
), such that the
Riemannian Karcher means of the observations coincide with the target surface of HPD matrices. Additional details can be found in Chapters 2, 3,
and 5 of \insertCiteC18pdSpecEst. Other available signalnoise models include: (ii) a LogEuclidean signal plus i.i.d. noise model, with
a matrix logGaussian noise distribution (noise = 'loggaussian'
); (iii) a Riemannian signal plus i.i.d. noise model, with a complex
Wishart noise distribution (noise = 'wishart'
); (iv) a LogEuclidean signal plus i.i.d. noise model, with a complex Wishart noise
distribution (noise = 'logwishart'
).
Returns a list with two components:

a ( 

a ( 
1  example < rExamples2D(n = c(32, 32), example = "smiley")

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