corLevLowRank | R Documentation |
Compute the correlation matrix for a low-rank structure.
corLevLowRank(par, nlevels, rank, levels,
lowerSQRT = FALSE, compGrad = TRUE,
cov = 0, impl = c("C", "R"))
par |
A numeric vector with length |
nlevels |
Number of levels |
rank |
The rank, which must be |
levels |
Character representing the levels. |
lowerSQRT |
Logical. When |
compGrad |
Logical. Should the gradient be computed? This is only possible for the C implementation. |
cov |
Integer |
impl |
A character telling which of the C and R implementations should be chosen. The R implementation is only for checks and should not be used. |
The correlation matrix with size m
is the general symmetric
correlation matrix with rank \leq r
where r
is
given, as described by Rapisarda et al. It depends on (r - 1)
\times (m - r / 2) / 2
parameters
\theta_{ij}
where the indices i
and j
are such that 1 \leq j < i
for i \leq r
or such that 1 \leq j < r
for
r < i \leq n
. The parameters \theta_{ij}
are angles
and are to be taken to be in [0, 2\pi)
if j =
1
and in [0, \pi)
otherwise.
A correlation matrix (or its root) with the optional gradient
attribute.
This function is essentially for internal use and the corresponding
correlation or covariance kernels are created as covQual
objects by using the q1LowRank
creator.
Here the parameters \theta_{ij}
are used in
row order rather than in the column order. This order simplifies the
computation of the gradient.
Francesco Rapisarda, Damanio Brigo, Fabio Mercurio (2007). "Parameterizing Correlations a Geometric Interpretation". IMA Journal of Management Mathematics, 18(1): 55-73.
Igor Grubišić, Raoul Pietersz (2007). "Efficient Rank Reduction of Correlation Matrices". Linear Algebra and its Applications, 422: 629-653.
The q1LowRank
creator of a corresponding kernel object
with class "covQual"
, and the similar corLevSymm
function for the full-rank case.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.