Primitive Symmetric Eigendecomposition

Computes the eigendecomposition of a symmetric matrix x of shape (n, n): $$A = \mathrm{vectors} \, \mathrm{diag}(\mathrm{values}) \, \mathrm{vectors}^\top.$$ Only the lower triangle of x is read. The columns of vectors are the (orthonormal) eigenvectors and values is the length-n vector of (real) eigenvalues in ascending order. Output names and order match base::eigen().

Usage

prim_eigh(x)

Arguments

x

(arrayish)
One input, a symmetric square matrix with exactly 2 axes. Can be any float data type. An R value materializes at its default data type.

Value

(named list of two arrayish)
Elements values (length n) and vectors (shape (n, n)). Both have the input's data type.

Implemented Rules

• stablehlo

StableHLO

Lowers to hlo_custom_call() with target "eigh".

See also

nv_eigh()

Examples

# `values` and `vectors` both have the input's data type
x <- nv_array(c(2, 1, 1, 2), shape = c(2, 2), dtype = "f64")
prim_eigh(x)
#> $values
#> AnvlArray
#>  1
#>  3
#> [ CPUf64{2} ] 
#> 
#> $vectors
#> AnvlArray
#>  -0.7071  0.7071
#>   0.7071  0.7071
#> [ CPUf64{2,2} ] 
#>