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

nv_eigh(x)

Arguments

x

(arrayish)
One input, a symmetric square matrix with exactly 2 axes. Can be any numeric data type: a float keeps its own, and an integer one is converted to the default float data type (see default_dtypes()). An R value materializes at its default data type and is converted in the same way.

Value

(named list of two arrayish)
Elements values (length n) and vectors (shape (n, n)). Both have the input's data type – or the default float data type (see default_dtypes()) where the input was an integer one.

See also

prim_eigh(), base::eigen()

Examples

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

# an integer matrix is decomposed at the default float data type
nv_eigh(nv_matrix(c(2L, 1L, 1L, 2L), nrow = 2))
#> $values
#> AnvlArray
#>  1
#>  3
#> [ CPUf32{2} ] 
#> 
#> $vectors
#> AnvlArray
#>  -0.7071  0.7071
#>   0.7071  0.7071
#> [ CPUf32{2,2} ] 
#>