NormalCirculant: Multivariate normal with Circulant variance matrix.

In SuperGauss: Superfast Likelihood Inference for Stationary Gaussian Time Series

Multivariate normal with Circulant variance matrix.

Description

Provides methods for the Normal-Circulant (NCt) distribution, which for a random vector z of length N is defined as

z ~ NCt(uacf)   <=>   z ~ Normal(0, toeplitz(acf)),

where uacf are the Nu = floor(N/2)+1 unique elements of the autocorrelation vector acf, i.e.,

acf = (uacf, rev(uacf[2:(Nu-1)]),   N even,
    = (uacf, rev(uacf[2:Nu])),      N odd.

Methods

Public methods

• NormalCirculant$new()

• NormalCirculant$size()

• NormalCirculant$logdens()

• NormalCirculant$grad_full()

• NormalCirculant$clone()

---

Method new()

Class constructor.

Usage

NormalCirculant$new(N)

Arguments

N

Size of the NCt random vector.

Returns

A NormalCirculant object.

---

Method size()

Get the size of the NCt random vector.

Usage

NormalCirculant$size()

Returns

Size of the NCt random vector.

---

Method logdens()

Log-density function.

Usage

NormalCirculant$logdens(z, uacf)

Arguments

z

Density argument. A vector of length N or an ⁠N x n_obs⁠ matrix where each column is an N-dimensional observation.

uacf

A vector of length Nu = floor(N/2) containing the first half of the autocorrelation (i.e., first row/column) of the Circulant variance matrix.

Returns

A scalar or vector of length n_obs containing the log-density of the NCt evaluated at its arguments.

---

Method grad_full()

Full gradient of log-density function.

Usage

NormalCirculant$grad_full(z, uacf, calc_dldz = TRUE, calc_dldu = TRUE)

Arguments

z

Density argument. A vector of length N.

uacf

A vector of length Nu = floor(N/2) containing the first half of the autocorrelation (i.e., first row/column) of the Circulant variance matrix.

calc_dldz

Whether or not to calculate the gradient with respect to z.

calc_dldu

Whether or not to calculate the gradient with respect to uacf.

Returns

A list with elements:

ldens

The log-density evaluated at z and uacf.

dldz

The length-N gradient vector with respect to z, if calc_dldz = TRUE.

dldu

The length-Nu = floor(N/2)+1 gradient vector with respect to uacf, if calc_dldu = TRUE.

---

Method clone()

The objects of this class are cloneable with this method.

Usage

NormalCirculant$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

SuperGauss documentation built on Sept. 10, 2025, 10:32 a.m.