Primitive QR Decomposition

Computes the reduced QR decomposition of a matrix operand: $$A = Q R,$$ where \(Q\) has orthonormal columns (\(Q^\top Q = I\)) and \(R\) is upper triangular. For an \(m \times n\) input with \(k = \min(m, n)\), \(Q\) has shape \(m \times k\) and \(R\) has shape \(k \times n\).

Usage

prim_qr(operand)

Arguments

operand

(arrayish)
Matrix of data type floating-point with exactly 2 dimensions.

Value

Named list with elements Q (shape (m, k)) and R (shape (k, n)), where (m, n) = shape(operand) and k = min(m, n). Both have the same data type as operand.

Implemented Rules

• stablehlo

StableHLO

Lowers to a "geqrf" + "orgqr" stablehlo::hlo_custom_call() pair (backed by LAPACK on CPU and cuSOLVER on CUDA) + postprocessing.

See also

nv_qr()

Examples

x <- nv_array(1:6, shape = c(3, 2), dtype = "f32")
prim_qr(x)
#> $Q
#> AnvlArray
#>  -0.2673  0.8729
#>  -0.5345  0.2182
#>  -0.8018 -0.4364
#> [ CPUf32{3,2} ] 
#> 
#> $R
#> AnvlArray
#>  -3.7417 -8.5524
#>   0.0000  1.9640
#> [ CPUf32{2,2} ] 
#>