Generate a simplex volume matrix

Simple helper function for generating a simplex volume matrix E (i.e. volume of simplex = det(E)/p-1!) of the following structure: | 1 1 ... 1 | | e_1 e_2 ... e_p | Where e_i is an i-th vertex point of the simplex.

.simplex_E(data, indices = 1:nrow(data), type = c("affine", "vector", "gram"))

.absdet(x)

Arguments

data

Matrix whose rows will be included in the simplex. This matrix should be reduced using using PCA or some other process so that it has p-1 columns before calling this function.

indices

Locations of the rows in the dataset to use as simplex vertecies

type

Type of simplex matrix to generate. Can be one of:

• "affine": Affine simplex matrix pxp, i.e. vertices matrix padded with 1s

• "vector": Vector simplex matrix (p-1)x(p-1), i.e. vertices matrix with the first row subtracted

• "gram": Gram-matrix simplex matrix (p-1)x(p-1), i.e. squared 'vector' simplex matrix

x

matrix

Value

A simplex volume matrix E, a p x p matrix whose first row contains only 1s

absolute value of determinant of x