Circulant {SuperGauss}

Constructor and methods for Circulant matrix objects.

Description

Constructor and methods for Circulant matrix objects.

Methods

Public methods

• Circulant$new()

• Circulant$size()

• Circulant$set_acf()

• Circulant$get_acf()

• Circulant$set_psd()

• Circulant$get_psd()

• Circulant$has_acf()

• Circulant$prod()

• Circulant$solve()

• Circulant$log_det()

• Circulant$clone()

Method new()

Class constructor.

Usage

Circulant$new(N, uacf, upsd)

Arguments

N

Size of Circulant matrix.

uacf

Optional vector of Nu = floor(N/2)+1 unique elements of the autocorrelation.

upsd

Optional vector of Nu = floor(N/2)+1 unique elements of the PSD.

Returns

A Circulant object.

Method size()

Get the size of the Circulant matrix.

Usage

Circulant$size()

Returns

Size of the Circulant matrix.

Method set_acf()

Set the autocorrelation of the Circulant matrix.

Usage

Circulant$set_acf(uacf)

Arguments

uacf

Vector of Nu = floor(N/2)+1 unique elements of the autocorrelation.

Method get_acf()

Get the autocorrelation of the Circulant matrix.

Usage

Circulant$get_acf()

Returns

The complete autocorrelation vector of length N.

Method set_psd()

Set the PSD of the Circulant matrix.

The power spectral density (PSD) of a Circulant matrix Ct = Circulant(acf) is defined as psd = iFFT(acf).

Usage

Circulant$set_psd(upsd)

Arguments

upsd

Vector of Nu = floor(N/2)+1 unique elements of the psd.

Method get_psd()

Get the PSD of the Circulant matrix.

Usage

Circulant$get_psd()

Returns

The complete PSD vector of length N.

Method has_acf()

Check whether the autocorrelation of the Circulant matrix has been set.

Usage

Circulant$has_acf()

Returns

Logical; TRUE if Circulant$set_acf() has been called.

Method prod()

Circulant matrix-matrix product.

Usage

Circulant$prod(x)

Arguments

x

Vector or matrix with N rows.

Returns

The matrix product Ct %*% x.

Method solve()

Solve a Circulant system of equations.

Usage

Circulant$solve(x)

Arguments

x

Optional vector or matrix with N rows.

Returns

The solution in z to the system of equations Ct %*% z = x. If x is missing, returns the inverse of Ct.

Method log_det()

Calculate the log-determinant of the Circulant matrix.

Usage

Circulant$log_det()

Returns

The log-determinant log(det(Ct)).

Method clone()

The objects of this class are cloneable with this method.

Usage

Circulant$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.