as.dyadic: Extract a 'Dyadic' object from a numeric matrix

In DyadiCarma: Dyadic Matrices and their Algebra using 'Rcpp' and 'RcppArmadillo'

Extract a Dyadic object from a numeric matrix

Description

This function extract a Dyadic object of given height and breadth from a classic matrix. If the corresponding sub-matrix extracted is not dyadic, the returned result will be wrong.

Usage

as.dyadic(mat, type, height, breadth)

Arguments

mat	A dyadic matrix with the classic R matrix representation.
type	string, one of the following character strings: horiz, vert,symm, and asymm, which indicates the type of dyadic object to be extracted;
height	The height of the dyadic matrix.
breadth	The breadth of the dyadic matrix.

Details

This function converts a dyadic matrix of the classic matrix form into the corresponding Dyadic object. If the input matrix is not dyadic it extracts the entries for the dyadic structure of the given height and breadth that fits to the upper-left hand side corner. Entries outside the fitted dyadic structure are neglected even if they are not equal to zero.

Value

A Dyadic object of the input type, height, and breadth representing the input matrix.

See Also

Dyadic-class for a description of the class;

Examples

#-------------------------------------------------------------#
#------------Creating vertically dyadic matrices--------------#
#-------------------------------------------------------------#

N <- 4
k <- 3
d <- k * (2^N - 1)

mat1 <- matrix(0, nrow = d, ncol = d)
mat2 <- matrix(0, nrow = d, ncol = d)

for (i in 1:N) {
    st_col_id <- (2^(i - 1) - 1) * k + 1
    en_col_id <- (2^(i - 1) - 1) * k + k
    for (j in 1:2^(N - i)) {
        st_row_id <- st_col_id - (2^(i - 1) - 1) * k
        en_row_id <- en_col_id + (2^(i - 1) - 1) * k
        mat1[st_row_id:en_row_id, st_col_id:en_col_id] <-
            as.matrix(rnorm((2^i - 1) * k^2), ncol = k, nrow = (2^i - 1) * k)
        mat2[st_row_id:en_row_id, st_col_id:en_col_id] <-
            as.matrix(rnorm((2^i - 1) * k^2), ncol = k, nrow = (2^i - 1) * k)
        st_col_id <- st_col_id + 2^i * k
        en_col_id <- en_col_id + 2^i * k
    }
}

mat1
mat2

#-------------------------------------------------------------#
#----------Creating corresponding dyadic objects--------------#
#-------------------------------------------------------------#

V1 <- as.dyadic(mat1, "vert", N, k) # A "vert" dyadic object
V2 <- as.dyadic(mat2, "vert", N, k) # A "vert" dyadic object

mat1S <- t(mat1) %*% mat1 # A symmetrically dyadic matrix
mat1AS <- t(mat2) %*% mat1 # An asymmetrically dyadic matrix
S <- as.dyadic(mat1S, "symm", N, k) # A "symm" dyadic object
AS <- as.dyadic(mat1AS, "asymm", N, k) # A "asymm" dyadic object

all(as.matrix(S) == mat1S) # Should be TRUE.
all(as.matrix(AS) == mat1AS) # Should be TRUE.


#-------------------------------------------------------------#
#---------------Creating a non-dyadic matrices----------------#
#-------------------------------------------------------------#

mat3 <- diag(d + 5)
mat3[1:d, 1:d] <- mat1

V3 <- as.dyadic(mat3, "vert", N, k) # Extract the upper-left dxd dyadic sub-matrix
all(as.matrix(V3) == mat1) # Should be TRUE.

DyadiCarma documentation built on June 8, 2025, 12:45 p.m.