Equicorrelation (constant-correlation) Gram matrix

\(R=(1-\rho)I+\rho\mathbf{1}\mathbf{1}^{\mathsf{T}}\). Positive semidefinite for \(\rho\in[-1/(J-1),1]\).

Usage

equicorrelation_gram(n_celltypes, target_cosine = 0)

Arguments

n_celltypes

Integer \(J\ge 2\).

target_cosine

Pairwise cosine \(\rho\).

Value

Symmetric \(J\times J\) matrix with unit diagonal.

Examples

equicorrelation_gram(3L, 0.4)
#>      [,1] [,2] [,3]
#> [1,]  1.0  0.4  0.4
#> [2,]  0.4  1.0  0.4
#> [3,]  0.4  0.4  1.0