graphicalExtremes (version 0.3.4)

Gamma2Sigma: Conversion between Huesler-Reiss parameter matrices

Description

Converts between different matrices that parametrize the same Huesler-Reiss distribution: \(\Gamma\), \(\Sigma\), \(\Theta\), \(\Sigma^k\), \(\Theta^k\). The \((d-1) \times (d-1)\) matrices \(\Sigma^k\) and \(\Theta^k\) can also be given/returned as \(d \times d\) matrices with the kth row and column filled with zeros.

Usage

Gamma2Sigma(Gamma, k = NULL, full = FALSE, check = TRUE)
Gamma2Theta(Gamma, k = NULL, full = FALSE, check = TRUE)
Sigma2Gamma(Sigma, k = NULL, full = FALSE, check = TRUE)
Theta2Gamma(Theta, k = NULL, full = FALSE, check = TRUE)
Sigma2Theta(
  Sigma,
  k1 = NULL,
  k2 = NULL,
  full1 = FALSE,
  full2 = FALSE,
  check = TRUE
)
Theta2Sigma(
  Theta,
  k1 = NULL,
  k2 = NULL,
  full1 = FALSE,
  full2 = FALSE,
  check = TRUE
)
Theta2Theta(
  Theta,
  k1 = NULL,
  k2 = NULL,
  full1 = FALSE,
  full2 = FALSE,
  check = TRUE
)
Sigma2Sigma(
  Sigma,
  k1 = NULL,
  k2 = NULL,
  full1 = FALSE,
  full2 = FALSE,
  check = TRUE
)
Gamma2Gamma(Gamma, check = TRUE)
matrix2matrix(
  M,
  name1 = c("Gamma", "Sigma", "Theta")[1],
  name2 = c("Gamma", "Sigma", "Theta")[1],
  k1 = NULL,
  k2 = NULL,
  full1 = FALSE,
  full2 = FALSE,
  check = TRUE
)

Value

The desired parameter matrix corresponding to the specified inputs.

Arguments

Gamma

Numeric \(d \times d\) variogram matrix.

k

NULL if the input/output matrix is \(\Sigma\)/\(\Theta\). Else, an integer between 1 and d indicating the value of k in \(\Sigma^k\), \(\Theta^k\).

full

Logical. If TRUE and !is.null(k), the input/output matrix is a \(d \times d\) matrix with the kth row filled with zeros.

check

Whether to check the inputs and call ensure_matrix_symmetry_and_truncate_zeros on the outputs.

Sigma

Numeric \(d \times d\) or \((d-1) \times (d-1)\) covariance matrix.

Theta

Numeric \(d \times d\) or \((d-1) \times (d-1)\) precision matrix.

k1

NULL if the input matrix is \(\Sigma\)/\(\Theta\). Else, an integer between 1 and d indicating the value of k in \(\Sigma^k\), \(\Theta^k\).

k2

NULL if the output matrix is \(\Sigma\)/\(\Theta\). Else, an integer between 1 and d indicating the value of k in \(\Sigma^k\), \(\Theta^k\).

full1

Logical. If TRUE and !is.null(k1), the input is a \(d \times d\) matrix with the kth row filled with zeros.

full2

Logical. If TRUE and !is.null(k2), the output is a \(d \times d\) matrix with the kth row filled with zeros.

M

Numeric matrix, \(\Gamma\), \(\Sigma\), or \(\Theta\).

name1

Name of the input representation.

name2

Name of the output representation.

Details

If k, k1, or k2 is NULL, the corresponding full* argument is ignored.

Gamma2Gamma only checks and returns the input.

matrix2matrix is a wrapper function that calls the corresponding conversion function implied by name1, name2.

See Also

Other parameter matrix transformations: Gamma2graph(), chi2Gamma(), par2Matrix()