conditional_obasis: Conditional orthonormal basis

In coda.base: A Basic Set of Functions for Compositional Data Analysis

Conditional orthonormal basis

Description

Compute orthonormal ilr bases adapted to row-wise conditioning patterns.

Usage

conditional_obasis(X, scheme = c("zero", "zero_na"))

Arguments

X	A numeric matrix or data frame with one observation or conditioning pattern per row and one part per column.
scheme	Character string indicating the conditioning scheme. Possible values are '"zero"' and '"zero_na"'. Default is '"zero"'.

Details

Each row of 'X' defines one conditioning pattern on the parts of a composition. According to 'scheme', the parts are split into ordered blocks:

• '"zero"': parts equal to '0' and parts with strictly positive values,

• '"zero_na"': missing values ('NA'), zeros, and strictly positive values.

For each row, the function constructs an orthonormal basis of the clr-plane preserving the block structure induced by the selected scheme.

Under 'scheme = "zero"', if a row contains 'nz' zeros, then:

• the first 'nz - 1' coordinates describe the internal log-ratio structure of the zero block,

• the coordinate 'nz' describes the balance between the zero block and the positive block,

• the remaining coordinates describe the internal log-ratio structure of the positive block.

Under 'scheme = "zero_na"', the blocks are ordered as:

• missing values ('NA'),

• zeros,

• strictly positive values.

In this case:

• the first coordinates describe the internal structure of the 'NA' block,

• the next coordinate contrasts the 'NA' block with the positive block,

• the following coordinates describe the internal structure of the zero block,

• the next coordinate contrasts the zero block with the positive block,

• the remaining coordinates describe the internal structure of the positive block.

Value

A three-dimensional array of dimension '(D - 1, D, nrow(X))', where 'D' is the number of parts. Each slice contains one orthonormal ilr basis.

Examples

C <- rbind(
  c(0, 0, 1, 1, 0),
  c(0, 1, 0, 1, 0)
)

conditional_obasis(C)

X <- rbind(
  c(1, NA, 0, 2),
  c(NA, 3, 0, 4),
  c(1, 2, 3, 4)
)

conditional_obasis(X, scheme = "zero_na")

coda.base documentation built on May 8, 2026, 5:10 p.m.